THE GRAND JUNCTION NUCLEAR TOOTHFAIRY TALE
By Ruth Marion Graf and Dr. Peter Calabria, PhD
©, Ruth Marion Graf, Nov. 7, 2015
Peter and the Wolf
You wouldn't expect it of a cop, not in this day and age of rampant cop murders of citizens and that punk faggot cop from Fox Lake who shot himself rather than go to jail because he knew what a horror and a torture it would be from inflicting it on others. But out came this federal cop from the Social Security office to spare severely pained and exhausted me from a near two mile walk to get to the nearest functioning bus stop.
He says, "You know, sir, the bus doesn't come way out to here unless you call them. I'll give 'em a call for you."
And then back he came outside again to tell me that when he called them they told him the bus doesn't come out after 1 PM, but that he told them that I was doing pretty rotten (I had mentioned to him inside the office that I'd been to the St. Mary's Hospital ER twice in the last few weeks) and that they had better come.
"Many thanks," I said, genuinely meaning it, "The pain's bad enough that I actually thought about taking a swim in the Colorado River."
"My son did that," he said, startling me though I showed it not at all partly because his remark had no emotion in it and partly because he was a cop and once you've been abused by cops you're as wary of them all as you are hateful. "Drove in, car and all," he continued in the same monotone.
"From pain?" I quickly said back, partly out of curiosity and partly because he was a cop and the situation called for some sort of response.
"Yeh, pain, he was 24." he continued in the same flat tone. Though who knows what kind of pain for I had a soninlaw whose father was a cop and who was treated badly enough in his childhood by his parents to hate them and eventually committed suicide by driving his car into a tree.
"I've got a lot of pain, too," the cop continued, "You just live with it; it's just a matter of attitude." I kind of sensed at this point he was saying that for my sake for I was so disoriented by my pain when I came into the SS office that he couldn't miss the look on my face.
"You can survive pain if you have the right attitude," he said twice more for stress, the conversation brought to an end with, "Hey, here comes your bus!"
First time I saw a cop as a human being, ever persisting negative thoughts about them as a group aside. And with that I was off to the Marillac Clinic in north Grand Junction with a nobenefits letter from Social Security in hand that I needed to get treatment for my pain that was bad enough to warrant a CScan for my head on my last visit to the ER.
Ruth and the Wolf
This is me at age 67 down in Lubbock next to my math
genius grandson and his mom the year our family wasted campaigning for the
Great False Hope.
Lubbock was also where Pete's TMJ problem (jaw, ear and head pain from dental misalignment) flared up a year before we got stuck in Grand Junction on our way West. Now, you would ask me from the political leanings suggested by Pete's cop story, what in God's unholy name were we doing hanging out in a place that's three times more conservative and church filled than very conservative Grand Junction. It goes way back. My father, the Rev. Arthur E. Graf, was a fundamentalist minister, who can say whether for good or evil without being accused of ideological bias. Objectively, though, and impossible to rationalize away is his nephew, my cousin, Ed Graf Jr., confessing in court below to murdering his two stepsons for insurance money by burning them to death.
Good family to run from, which I did. The fellow on the right is my older brother, Don, a senior partner in the largest law firm in West Texas who developed his aggressive style of legal maneuvering punching me, his 7 year old kid sister, on the arm and telling already frightened gullible me that a wolf was upstairs in my bedroom ready to get me when I went up to bed.
The family did not like it at all when I walked away, publicly shaming them. My mother left me and my three siblings $30,000 each when she died eight years back. Except my share was set in trust with my lawyer brother, Don, never meant to be disbursed to me except a hundred here and there as bait to keep me coming back for it. "You'll never see a penny of it unless you leave Pete," who it was I ran to when I ran from the family back then 42 years ago.
The whole inheritance thing was set up, very clever, to punish me by driving me crazy over it for the living's not easy for a 74 year old with all the typical health problems of old age. That punishment included Don's getting me locked up in Lubbock County Jail for a week for trespassing when I refused to leave his law office on a visit down from New York to get the money. Quite a well contrived revenge from the grave for my being a bad girl, pretty clever, mom.
Don't have photos of my weekly corporal punishment administering parents, burned them all. But they looked not different at all from Aunt Sue and Uncle Ed, the child killer's parents, ugly, selfrighteously cruel and perverse child abusers beneath the wolf in sheep's clothing platitudes Daddy spouted from the pulpit and Mom at the evening dinner table.
More on this story and more insulting truths on Don in a later section if you're curiosity's been aroused about this halfcentury family fight to the death and beyond. Hint as to the baddest bad feelings in recorded history: Pete backed Don down in a head to head in front of Don's trophy wife, Ruby, who a few months after that cuckolded him, right Donnie boy, and a year later divorced him.
The dentist assigned to Pete at the Lubbock Community Health Center was a Dr. K, a young lady who dressed during office hours, as I saw the one time I was her patient, in a fashion designed to show off the thighs, as they said in the old days, sufficient to get the attention and erection of as many of her male patients as she could. Though this is just one woman's opinion of another, whatever her state of mind and intentions in the clothes she wore beside the dentist chair.
This does not certify that K was a bad dentist. Pete's tooth that came to trigger his TMJ malady could have been unusually problematic, who knows, who can say, who can tell. But the pain began after she worked on it. And just got worse a few dentists later until the pain, which is sort of like having your little finger bent backwards, started driving him crazy especially in keeping him from getting any sleep for the two months before we see him at the ER and the Social Security office in Grand Junction, CO.
The Dental Clinic
The relatively young fellow who managed the Marillac Dental Clinic in Grand Junction by the name of Levi, as suggests an extreme religious upbringing, was unusual looking to be kind, top end obese and completely bald. Does such an extreme lack of attractiveness, especially in a young person, suggest an equally unattractive personality, somebody to be avoided for fear of no good coming from it? That would not be strange for attractiveness suggests somebody to be connected with that might have tangible value for you.
Functionally paranoid as such first impressions might be (consider the recent book title, Only the Paranoid Succeed), Levi turned out in the short term a lifesaver in facilitating the root canal and crown I needed to kill my near unbearable pain for a price I could actually pay, it was that inexpensive, $200 instead of $2000. Dismissing my first impression with no hesitation I told him from the heart, "Any appreciation I might express would have to be understatement." And that was not just because the price was right, but because he told me, and told Ruth separately, that they could start in a day or two. Whew! Suffering with a good attitude takes a back seat any day to getting rid of great pain. But atheist me made the mistake, seconded by Ruth, to mention to Levi that we were longtime peace activists, giving him one of our news articles from the 1980s Cold War period.
Knickerbocker News, Albany, NY,
May 1986
Given that we're all still here after 30 years, it's hard to refute the Chicken
Little label most people instantly tag the piece with, the divinely inspired
End of Timers irrelevant in the debate, their fears calmed with the hallelujah
resolution of life eternal in the afterlife.
That the end of it all does actually threaten us, maybe not in the last 30 years but sooner or later, has a strong historical, evolutionary and mathematical basis. If that sounds as trustworthy as Ben Carson's recitation of life events past, let me try to spell it out for you with as little of the math, a generally hated subject, as we can do with.
God, this is so hard to phrase without the math. Consider two distinct populations of organisms, from two different species or subspecies or lineages or, for man, cultures, living across generations in one niche or territory or environment. If the niche has lots of space and lots of resources, meaning that the two populations still have plenty of space and resources to increase their size in, there's a much less likely a chance of competition between the two relative to the case where the niche has reached its limit in terms of space and resources.
This case of where one population can grow only at the expense of the other in the niche is what, when the populations are human, prompts war between the two. To repeat, lots of room for expansion prompts peaceful coexistence and no room left prompts war.
That's what was great about America back then, lots of space and lots of resources. That's also what was great about the human race way, way back then. If early man had a problem with another group of early man, they just went their separate ways because there were a lot of separate ways available to go. And that's exactly how the planet got dispersed with our kind.
But all that changed once we filled the world up with our kind. No place to disperse to with the only alternative being your rival, your enemy, chewing you up if you don't want to fight back. And modern weapons made everything much worse. Fights between different Maori tribes in New Zealand were rough, it's true, even before the Brits got there, but horrible once the Maori picked up the white man's weapons to fight with for the best tool for mass murder is gunpowder.
When the weapons power is distributed in a sufficiently unbalanced way, one group wins out big and the rest are dead or on their knees. This is empire and it's the history of man whether one approves of it or not. It just is. Also irrefutably a part of history is that old empires fall and new one's are formed always, always by war. And no nation refrains from using a weapon in its arsenal because of fears of collateral damage, especially when they're playing from the down side of the game. Given time, the bigger competitions will arise, as we're already seeing now with nuclear biggies Russia and the US with China not exactly acting peaceably in the South China Sea.
Not stressed as much in the newspaper article was the other weapons issue, not of people being killed by them, but of being controlled by them, tyrannized, exploited, enslaved, made miserable and, as such, when the opportunity arises, more aggressive towards whomever they can release their unhappiness. And getting rid of weapons at this level gets rid of the problem. Ban all weapons use on pain of execution, just one law from the big guy, the people deciding all the rest.
It's very simple. And it's doable. Just have to get Putin together with a sane and sensible representative on our side, who seem to be in marked short supply at this time. So much so that I nominate Ruth for the job, maybe in tandem with ostensible jackass Trump, who at least has a realistic if immoderately selfish view of life. You must kill the weapons or we wind up like Hiroshima, the whole world.
This said, things turned out at the Dental Clinic not so good and that's possibly because we also called Levi's attention to the precursor of this website, which had been written in haste because of my head pain, a review of life and the world that was less polished and mannerly than what you just read:
a.) As Genghis Kahn once said: Every man wants to be the khan (the king, the top boss of it all, like he was) or be independent (no boss of any kind at all.)
b.) An interesting and quite correct observation on the part of Genghis considering that anybody within his reach (as a lot of people were back in the Mongolian empire of the 13^{th} Century) who attempted to be the Khan or to be independent and outside of his control was executed, usually by beheading.
c.) Now before we start making Genghis out to be some kind of unique devil figure in history, note that any honest history book on civilized man (and that excludes the history preached to the common folk within a nation by the rulers including to mind vulnerable children) will tell you that enslavement in one form or another has been with us since Ancient Egypt and Babylon and Sparta and Rome and in the serfdom of Medieval Christianity and British Colonialism and just last week in the 9 to 5 and beyond wage slavery all have to put up with in America.
d.) And should also tell you that top bosses (as with kings of old and _____ empowered by big money in modern times, the blank used because there are no politically correct, proper, words allowed for the billionaire wage slave controllers) would never say through the information outlets they control including religion, education and today’s quasireligion psychobabble, that people would rather be independent than be the happy wage slave suckers portrayed in the movies and media that only the millions of our billionaire rulers, may they all be given black eyes, are able to produce.
e.) And an honest telling would also make clear that life’s “personal” miseries as derive from failed and frustrated relationships (shhh, don’t tell your sisterinlaw or neighbor or coworker) are not the product of Satan or “mental illness” but of the 9 to 5 and beyond screwing people take in life as a matter of course from bosses and from authority controlled, yea owned, by money, as the police and courts certainly are (except on TV.)
f.) Really, can it be missed by any halfsensible person, the correlation between the unhappiness of the standard mass murderer and his suicidalhomicidal release from that unhappiness from his last few bloody moments? What do you mean, he was/is mentally ill and that’s why he did it? My, that’s so vague. It’s unhappiness in the heart that drives people mad, unhappiness that comes from the same place as for the rest of the suckers who can’t make the correlation between it and humiliatingly kissing the boss’s ass six ways six times a day as the years go by. Or, to push the logic of the connection one step further, let’s ask where “mental illness” comes from? Well, we just don’t know, say the welldressed shrinks on TV and their pundit and police chief sidekicks. We never have any idea what the mass murderer’s motive was, and that’s 300 such motiveunknown mass killings just in 2015. Hmmm.
g.) Though, c’mon, what’s the mass murder of a handful of people every day compared to the mass murder, legs and arms and heads blown off, of war? And does that come from the same place as domestic mass murder, from the tyranny of social control, whether from dictator setup police coercion or billionaire setup economic coercion? The boss or the authorities (in the schools now, too) too, kicks you in the ass, or threatens to day by day, but since you can’t kick the bastards back, you bullyingly and often sneakily pass your pain on to others who had nothing to do with causing your pain. And this extends to masses of people kicked in the ass passing on their hate to masses of other people, of different ethnicities, here and in other countries. Kill the bastards. That feels so good, to hate to cause others to suffer when you feel bad yourself. And it hits hard also on independent people who are often targets out of jealously.
h.) Way down in the cellar of causation, of course, it’s all Darwin’s fault, all this violent competition admixed with the worldwide economic competition that finances for the winners the best weapons, that plus the aforementioned blind hate and aggression that wells up from underlings dominated and beat up by the bosses passing their misery onto vulnerable others en masse.
i.) And there is no way to shut it down, as long as the social control font for it keeps flowing. No way to shut it down except to get rid of all the weapons in the world. And that would work because the simplest mathematics tells you that it’s absolutely impossible for a relative few people to control a whole lot of people without weapons. Which is the what the police are there for primarily, to prevent revolution, which is why it is necessary to take the weapons power away from the billionaire bosses, may their eyes be blackened, who own the police and effectively, better believe it, tell them what to do. Or is it too much to ask the question of why the billionaires NEVER go to jail.
j.) And as no small side effect of getting rid of all the weapons, you also get rid of war as we know it, up to and very importantly including mankind annihilating nuclear war, lots on exactly how to bell that cat in later sections where you’ll find that A.) It’s entirely necessary or we go up in smoke and B.) It’s quite possible to accomplish once people see clearly the 5000 years of misery up to the present that weapons have caused the human race, in war and peace.
k.) And we should also say something about the poor fellows and gal soldiers who do the billionaires’ bidding to grow and maintain the American Empire. To give your lives with arms and legs and brains blown away for the sake of maintaining the privileged lives of the decadent scum at the top? Nothing sadder than a veteran in a waiting room at a VA hospital. Really. Take a quick trip to the lunch room at the VA hospital up in the Hanover, NH, area. These poor bastards, masses of them impaired for life in irreparable ways. Even the most sensibly selfish of us can’t help feel the true horror of it. Let’s get rid of the weapons.
l.) And the rest of the a. through z. precepts of this new religion of happiness and sanity are scattered through the rest of this treatise prefaced by a bit more mathematics.
I'll get to the punch line of this not very funny joke now. After being appraised of the existence of our political awareness, not exactly what you'd say was right wing or fundamentalist, Levi tells me that they can't get to the pain problem driving me insane for a full month. Today's Nov. 6 as I'm writing this and the root canal isn't to be started until December 2, may God have mercy. So I'm just going to stick this on the front of whatever's on the website now for all those who aren't terrified of mathematics or of thinking and saying what the faggot authorities who own and run this show don't want them to know, including the low class academics in the Colorado University system including the dumb cowardly jerks at the local university here at Colorado Mesa University.
Look, when the leading candidate of the party of the rich and powerful says and worse believes that the pyramids were used to store grain as advised by the Biblical character Joseph instead of burying the pharaohs, you have to understand that the fucking sky is falling. Why, if you need a why. Because a significant fraction either believes that also or knows Uncle Potato Carson is lying and doesn't care because they believe that everybody, who's smart, lies to everybody, and that the country is a hostile place in that regard but also in the form of Orwell's take on modern life, the most perfect example of doublethink, that country is free but that we are lied to at every moment by our leaders. You don't think that the threat of nuclear war is real, assholes out there who masturbate on the toilet while watching the NFL game and drinking a beer with your free hand because you don't think much of yourself, or at least not much of yourself, and they really don't, Ruth. And that's why they are ever distracting themselves from the truth about themselves by entertaining their pained brains so as to not have to think about reality beyond the performances they have to give at work, physically and socially, their only pleasure watching the free die painfully in spirit and otherwise, the jealous faggots, all of them and including most certainly your sister, Don.
Ask yourself, who or what on earth could possibly murder by burning them to death two little kids? You don't think that's perverse. And you don’t think that somebody who would kill two babies in a pure torture way is perverse in his behavior. And if perverse in wanting to murder people for the pure pleasure of it and being quiet about that urge and those acts done is not also capable of being a smelly faggot and hiding the fact of it, Don with his observably socially dick sucking "yes" man, Kolander. They're all faggots and on the right the worst of them especially when they have power. At least I'll die with my balls still on, punks.
Those Jews with big cash at the top with tons of political power; they all look like Aunt Millie on steroids. Who’s that guy, and to his credit despised by Trump, Barry Diller. Jesus! John Paul Sarte, the world's last significant philosopher before they were collectively exterminated by the brilliantly executed near 24/7 mind cleanings of movies, media, education and the pulpit said that every person over the age of 40 is responsible for their own face.
The serfs of the medieval ages had it bad. But this modern version for it, so perfectly out of 1984 in his basics though hidden so much better that nobody even who read the book could fathom the tinseled worm infested tree they're perched in.
Every mammal past the time of maturity has sexual feelings put in them by Charles Darwin that drive them in as mammoth a way as hot pepperoni pizza being stuck under your nose makes it near impossible not to take a bite. And now the hint is that teen kids doing young adult sex in the way they are programmed for evolutionary fitness are being thought of as criminal felons liable at least according to the letter of the law, an easing of it for apparent generosity sake only done to make the law not seem as ridiculous as Uncle Ben's assertion about pyramids being used to bury grain in for God to eat to ease his constipation. How did the state get to be the complete arbiter by penal law of people's sexual behavior?
Oh, you say they're not, asshole? Well just because Uncle Ben's ding dong pulling lies are easy to see through does mean that there are people as in the media and the courts and who run businesses and social control institutions who do it a hell of a lot better than he does. And it's not that their bullshit can't be let out of the bag if they're framed scientifically, mathematically, but that all the STEM people are castrated psychologically no different than the monks who peopled the medieval universities.
The Colorado River almost seems good to think about but much more fun to think about beating the oligarchy that runs America who think their toilet paper scented with $5000 a bottle perfume is worth the pain suffered by the suckers on the bottom.
Now let’s get on to the mathematical analyses written up before we ever set foot in Grand Junction.
II: The β Diversity Index Demystification
of Entropy
By
Ruth Marion Graf, A. Thomas Rogovsky and Peter Calabria, PhD
Contact: ruthmariongraf@gmail.com
No technical article on Wikipedia is more primed with
“disputed” tags and the like than entropy (energy
dispersal). This is a strong hint that entropy, a confusing notion for
most, is also a bit of a mystery even for science despite Boltzmann’s famous entropy
equation considered almost sacrosanct from inscription on his tombstone.
Boltzmann’s 1906 Tombstone
Many years after the suicide by Boltzmann prompted by initial rejection of his entropy formulation, a British statistician and WWII code cracker, Edward Hugh Simpson, steps into the picture with three numerical measures of diversity for ecological and ethnic populations.
One of his diversity functions, the Simpson Reciprocal Diversity Index, is the precursor to a new diversity expression, the β Diversity Index, which reformulates entropy in as mathematically crisp a way as Boltzmann, but is much more common sense intelligible as energy diversity. But as Simpson developed his diversity indices back in 1948 as ad hoc quantifications of population diversity of interest mainly to biologists and sociologists, there was and has been little exposure of it to the physical scientists interested in entropy. And one can be fairly certain that any physicists who have come across it in the last 65 years did not give a second thought to considering it suitable for describing entropy.
All that changes though once diversity is derived, developed and generalized as a pure mathematics function. Then Simpson’s reciprocal diversity and a companion β diversity function are readily seen to have a greater than .9995 Pearson’s correlation to Boltzmann’s S entropy, which spells out as its having as good a fit to the empirical laboratory data as the S entropy and is preferable to the S entropy from both its simplicity and clarity. There are three pure mathematics perspectives on Simpson’s reciprocal diversity as the entry point to the β Diversity Index that solves the entropy problem. We will first take up the matrix arithmetic of natural sets derivation of it.
The term natural set refers to a set of objects we would see when we
open our eyes to the world around us. The Hiroshima photo, for example, presents
a set of objects that consists of 1 atom bombed out building, 15 window frames,
956 pieces of rubble and 1 semifortunate man in the foreground of the rubble.
A natural set distinguishes the objects in a set by kind and by the number of
each kind.
For mathematical simplicity and efficiency we work with regular natural sets. An example is of this set of colored objects, (■■■, ■■, ■), represented by the number set (3, 2, 1), that consists of unit objects (all the same size) as limits the set’s elemental numerical characteristics to the K number of objects in the set, for (■■■, ■■, ■), K=6; to the N number of subsets in the set, for (■■■, ■■, ■), N=3 color subsets; and to the number of objects in each subset, for (■■■, ■■, ■), x_{1}=3 red objects, x_{2}=2 green objects and x_{3}=1 purple object.
Obvious is the use of simple arithmetic to add up the objects in the N=3 subsets of (■■■, ■■, ■) to get the K=6 total number of objects in the set: K=x_{1}+x_{2}+x_{3}=3+2+1=6. What is less obvious is that the basic arithmetic operations of addition, subtraction, multiplication and division can be done not just with single numbers but with sets of numbers. When that is done systematically with a matrix, what is developed is a general diversity measure that underpins a unified mathematical explanation for everything.
Though forms of the β Diversity Index are salient in
the addition, division and product matrices we introduce it through the product
matrix because that develops it from the Simpson’s diversity index that
science is already well familiar with. The product matrix of the (3, 2, 1) set multiplies
every number in the set with every other number including itself.

3 
2 
1 
3 
(3)( 3) 
(3)( 2) 
(3)(1) 
2 
(2)( 3) 
(2)( 2) 
(2)(1) 
1 
(1)( 3) 
(1)( 2) 
(1)( 1) 
Figure 1. The Product Matrix of the (3, 2, 1) Set.
The sum of the products in this matrix of the K=6, (3, 2,
1), number set is K^{2}=36. Add them up to see. Keeping in mind that
the (3, 2, 1) natural number set represents a set of observable objects,
we readily show the origin of the K^{2}=36 parameter with a comparison
matrix of all the objects in the (■■■, ■■, ■), (3, 2, 1), set.

■ 
■ 
■ 
■ 
■ 
■ 
■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■■ 
Figure 2. The Comparison Matrix of (■■■, ■■, ■)
We count the total number of pairs in this matrix of the K=6 object, (■■■, ■■, ■), (3, 2, 1), set as K^{2}=36 as we also obtained from Figure 1 as the sum of all the products in the product matrix. Out of these K^{2}=36 comparison pairs, we count Y=22 different pairs like ■■ and Γ=14 alike pairs like ■■. (Γ is the Greek letter, gamma.) The Y=22 and Γ=14 matrix variables are also obtained from the product matrix in Figure 1 with Γ=14 the sum of the products in the diagonal of the matrix (highlighted in yellow) and Y=22 as the sum of all other products in the matrix. The Γ matrix function is of sufficient importance that we specify it below for any set of K objects distributed over N subsets as
3.)
From the above for the (3, 2, 1) set, Γ=x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=3^{2}+2^{2}+1^{2}=14. Important next is to see that the ratio of the K^{2}=36 pairs to the Γ=14 same color pairs is, D, the Simpson Reciprocal Diversity Index of the (■■■, ■■, ■), (3, 2, 1), set.
4.)
For the (■■■, ■■, ■), (3, 2, 1), set, this Simpson’s diversity is D=36/14=2.571. This D diversity is more familiar to ecologists and sociologists when expressed in terms of the p_{i} weight fractions of a number set, usually referred to by them as population densities.
5.)
For the (■■■, ■■, ■), (3, 2, 1), set that has x_{1}=3, x_{2}=2 and x_{3}=1, the weight fractions are: p_{1}=x_{1}/K=1/2; p_{2}=x_{2}/K=1/3; and p_{3}=x_{3}/K=1/6. Note that the weight fractions sum to unity.
6.)
Now from Eqs4&5, we express D in terms of p_{i} as
7.)
To develop the general form of the β Diversity Index we next substitute Eq6 in Eq7 to obtain
8.)
We can express this using a numerical index, β.
9.) ; β=1
And we form the β Diversity Index as a general diversity measure whose value depends on β, which has infinitely wide range as
10.)
There are diversity measures with different values for a set for β=1, the D Simpson’s reciprocal index, and for β=0, β= −1 and β=1/2. Interesting is that the three latter diversities derived from Eq10 for β=0, β= −1 and β=1/2 come about respectively from an addition matrix, a division matrix and a square root matrix and in all, as with D in Eq4, as the ratio of the sum of all terms in the matrix divided by the sum of terms in the diagonal of the matrix. Quite fascinating from a pure mathematics perspective, we do not wish to stop and considered the details of these other than for the square root matrix that generates the β=1/2 diversity in its having direct relevance to formulating the correct entropy (and temperature) measures of a thermodynamic system. And because of its importance in that regard we shall give D_{β}=D_{1/2} its own special symbol, h. Hence from Eq10, the h square root diversity index is
11.)
It is easiest to develop D_{1/2}=h using a new example set, the K=14, N=3, (■■■■■■■■■, ■■■■, ■), (9, 4, 1), set. Its p_{i} weight fractions of p_{1}=1/14, p_{2}=4/14 and p_{3}=9/14 obtain and D from Eq7 as D=2 and h from Eq11 as h=D_{1/2}=7/3=2.333. The square root matrix that develops D_{1/2}=h is a product matrix that specifies (9, 4, 1) on one axis of the matrix and the square root of the x_{i} of the set on the other axis as below.

9 
4 
1 
3 
(3)( 9) 
(3)(4) 
(3)(1) 
2 
(2)( 9) 
(2)( 4) 
(2)(1) 
1 
(1)(9) 
(1)(4) 
(1)( 1) 
Figure 12. The Square Root Matrix of the (9, 4, 1) Set.
The sum of all the products in the matrix is 84, the sum of the diagonal products, 36, and the ratio of these sums, 84/36=7/3=2.333=D_{1/2}. We need both D and h to reformulate entropy and temperature correctly but will put h on the back burner for a while to derive D next as a statistical function that is the direct entry to the derivation of entropy as energy diversity or dispersal. We start by noting that the central statistic in statistics is, but of course, the arithmetic average or mean of a number set, µ, (mu),
13.)
For the K=6, N=3, (■■■, ■■, ■), (3, 2, 1), set the mean or average number of objects in the N=3 color subsets is µ=K/N=6/3=2. We next use the µ mean as part of the definition of a primary error function in statistics, the σ^{2} variance_{, }
14.)
For the N=3, µ=2, (■■■, ■■, ■), (3, 2, 1), set the variance is σ^{2}=2/3. The square root of the σ^{2 }variance is the familiar standard deviation, σ, for the (3, 2, 1) set, σ=.816. Another commonly used statistic error is the relative error, r= σ/µ, the square of which, r^{2}, called the perfect error, is useful in this analysis.
15.)
For the N=3, σ^{2}=2/3, (■■■, ■■, ■), (3, 2, 1), set the perfect error is r^{2}=σ^{2}/µ^{2}=(2/3)/2^{2}=1/6. Algebraic manipulation of the end variance term in Eq13 with the D diversity expression of Eq4 obtains D as a statistical function.
16.)
This sees D as an important function of a natural number set in that it includes all three of the set’s basic parameters, the K total number of objects in the set, the N number of subsets in the set and the statistical error of the set as r^{2} that gives a measure of the spread of the (x_{i}) numbers in the set. Now for emphasis sake, we want to go back and repeat that D as originally conceived by Simpson as an ad hoc measure of the intuitively sensed diversity in an ecological or ethnic population was never thought of as a valuable function for physical systems by the physical science community who studied entropy. But we see in the above development of D as more of a pure mathematical structure is that D is a measure of any system in nature that can be represented as a natural set including specifically a thermodynamic system of K energy units randomly distributed over the system’s N molecules.
The development of D as a β diversity makes that all the more clear, for the β= −1 division matrix derived diversity, which we shall cover in detail at the end of this entropy presentation, shows the ratio of the µ mean to the β= −1 diversity, D_{1}, to perfectly calculate the inverse summing of series capacitance and parallel resistance and inductance of textbook circuit theory. And, hence, if that β= −1 diversity, D_{1}, shows itself to be a bona fide physical variable, so also must the β=1, D, and β=1/2, D_{1/2}=h diversities be considered in that vein able to be used to formulate and explain entropy properly.
With that encouragement for D as a valid specification of physical systems, we next turn to textbook multinomial theory to develop D as entropy where it is seen that for any distribution of K objects over N subsets,
17.)
The P_{i} term is the probability that any one of the K objects in a set will reside in the i^{th} of the N subsets of the set. Now a random distribution is an equiprobable distribution in the sense that all N subsets of a set have an equal P_{i} probability of containing one of the K objects. To clarify that, let’s look at the K=6, N=3, (■■, ■■, ■■), (2, 2, 2), set where we see that the P_{i} probability that any object chosen at random will be red, green or blue is P=1/3=1/N. Hence substituting P_{i}=1/N in Eq9, we see that the σ^{2 }variance of a random distribution of K objects over N containers is
18.)
Before we proceed too far, too fast, let us make it clear that this applies to a thermodynamic system in its being understood, as it is by all scientists without argument, as a random or equiprobable distribution of K discrete energy units over the N molecules of the system. And let us also make it clear just what the σ^{2} variance in Eq18 is referring to in a random distribution. We’ll do that by illustration with a minithermodynamic system or random distribution of K=4 energy units over N=3 molecules. The variance of this random K=4 over N=3 distribution from Eq18 is σ^{2}=(4/3)(2/3)=8/9. To understand where this σ^{2}=8/9 variance comes from consider next the “states” of this system that specify the various ways the K=4 energy units can be distributed over the N=3 molecules given in the table below along with the σ^{2} variance of each of the states as calculated from Eq14.
State 
σ^{2} Variance 
(4, 0, 0) 
32/9 
(3, 1, 0) 
14/9 
(2, 2, 0) 
8/9 
(2, 1, 1) 
2/9 
Table 19. The States of the K=4 over N=3 Random Distribution and their
Variances.
Now we will take the average of the state variances as weighted by the number of ways that each of the states can come about, aka, the permutations of each state. These are derived from textbook combinatorial statistics that specify the total number of permutations in the system as N^{K}=3^{4}=81 and the number of permutations per state as listed below.
State 
# of Permutations 
σ^{2} Variance 
(4, 0, 0) 
3 
32/9 
(3, 1, 0) 
24 
14/9 
(2, 2, 0) 
18 
8/9 
(2, 1, 1) 
36 
2/9 
Table 20. The States of the K=4 over N=3 Random Distribution and their Number
of Permutations
The various states and their permutations, whose relative values give an indication
of the relative time the system is in that particular state, come about by the
random molecular collisions and energy transfers that take place most easily
pictured as coming about for a system of gas molecules in a container of fixed
volume. Now the variances of the states are averaged by weighting them with the
fractional measure of the permutations of each state.
State 
# of Permutations 
Weight 
σ^{2} Variance 
Weighted Variances 
(4, 0, 0) 
3 
3/81=1/27 
32/9 
32/243 
(3, 1, 0) 
24 
24/81=8/27 
14/9 
112/243 
(2, 2, 0) 
18 
18/81=6/27 
8/9 
48/243 
(2, 1, 1) 
36 
36/81=12/27 
2/9 
24/243 




Sum =216/243=8/9= σ^{2}_{AV} 
Table 21. The States of the K=4 over N=3 Random Distribution and Pertinent
Measures to Determine Their Average Variance.
Hence the σ^{2} of Eq18 of the random K over N distribution is the
average variance of the distribution, σ^{2}_{AV}, and
should be specified as such.
22.)
Eq18 also obtains the average r^{2} perfect error for a random distribution from Eqs15 as
23.)
For the K=4 over N=3 random distribution, r^{2}_{AV}=1/2. The
above also obtains the D diversity for a random distribution of K objects over
N subsets from Eq16 as
24.)
For our K=4 over N=3 random distribution, D_{AV}=(4)(3)/6=2. Eq24 understands
D_{AV} as a weighted average of the D diversities of all the states of
a random distribution and, thence, as the diversity of a thermodynamic system
as a whole. Also the D_{AV} diversity provides a clear picture of the
thermodynamic system in the form of one of the states of the random
distribution, (2, 2, 0), that has the very same variance, σ^{2}=8/9,
the same perfect error, r^{2}= σ^{2}/µ^{2}=(8/9)/(4/3)^{2}=1/2,
and the same diversity, D=2, as the σ^{2}_{AV}=8/9, r^{2}_{AV}=1/2
and D_{AV}=2 of the system as a whole. This (2, 2, 0) state is called
the Representative State of the system.
Next let’s look at another random distribution, K=12 over N=6, to
reinforce this understanding of the Representative State. Its energy diversity
is from Eq24, D_{AV}=(12)(6)/(12+6−1)=4.235.
The state of the system that has this diversity as calculated from Eq4 is the
number set, (4, 3, 2, 2, 1, 0), which is the Representative State of the system
for that reason. If the Representative State truly represents the thermodynamic
system as a whole, it should have the characteristics of the system as a whole,
one of which should be the MaxwellBoltzmann energy distribution of a
thermodynamic system.
Figure 25. The MaxwellBoltzmann Energy Distribution
To see if it does we plot of the number of energy units on a molecule vs. the number of its molecules that have that energy for the (4, 3, 2, 2, 1, 0) set.
Figure 26. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=12 over N=6
Distribution
Calling
this a MaxwellBoltzmann distribution may seem a bit of a stretch, though the
plot could be (generously) characterized as a very simple, choppy form of a
MaxwellBoltzmann. What we need to make the point are larger K and N
distributions like the K=36 energy unit over N=10 molecules random distribution.
Its D_{AV} diversity is from Eq24, D_{AV}=8. The K=36, N=10 state
that has this diversity is (1, 2, 2, 3, 3, 3, 4, 5, 6, 7), and as such is the Representative
State of the system. A plot of the energy distribution of this set is
Figure 27. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=36 over N=10
Distribution
This curve was greeted without prompting as “It’s an obvious protoMaxwellBoltzmann,” by the author of a primary graduate text on the thermodynamics of surfaces, John Hudson, Prof. Emeritus of Materials Engineering, Rensselaer Polytechnic Institute. The larger the K and N of a random distribution, the better the fit to the MaxwellBoltzmann distribution of Figure 25 of a realistic thermodynamic systems that has extremely large K and N parameters. So next we’ll look at the K=40 energy unit over N=15 molecule distribution, whose diversity is from Eq24, D_{AV}=11.11. A Microsoft Excel search program finds four states that have this diversity including (0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6) whose number of permutations is the most of the four and is the most representative state from that perspective. Its plot of energy distribution is
Figure 28. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=40 over N=15
Distribution
This is a not very symmetric MaxwellBoltzmann, but we are getting there. Next we will look at the K=145 energy unit over N=30 molecule distribution whose D_{AV} diversity is from Eq24, D_{AV}=25. There are nine K=145, N=30 number sets with this diversity including (0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 10), which has the most permutations of the nine as the most representative state and whose plot of energy distribution is
Figure 29. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=145 over N=30
Distribution
At this point we are beginning to consider K and N values of random
distributions large enough to display a fairly good resemblance to the standard
MaxwellBoltzmann distribution of Figure 25. And as we progressively
increase the K and N values of distributions, the above plots would more and
more approach the shape of the realistic MaxwellBoltzmann distribution of
Figure 25. This suggests that this Representative State approach we have taken
is reasonable and that the D_{AV} diversity is a meaningful variable of
a thermodynamic system. In what way?
The entropy of a thermodynamic system is currently accepted to be Boltzmann’s equation inscribed on his tombstone, which is in modern terminology,
30.) S=k_{B}lnΩ
It easy to show that the D_{AV} diversity of a random distribution of Eq24 and Boltzmann’s S entropy of Eq30 are, for large K and N random distributions that mimic realistic thermodynamic systems, nearly directly proportional and, hence, can be substituted for each other mathematically. To demonstrate this we need not explore the meaning of the Ω (capital omega) variable in Boltzmann’s entropy formulation but only to render the Ω and lnΩ variables as functions of K and N (k_{B} is a constant) to show the extremely high correlation that exists between D_{AV} and lnΩ, hence, between energy diversity and entropy. This is easily done with a standard formula for Ω found in any advanced physics textbook.
31.)
And lnΩ is
32.)
For large K over N equiprobable distributions it is easiest to calculate lnΩ with Stirling’s Approximation, which approximates the natural logarithm (ln) of the factorial of any number, n, as
33.)
Stirling’s Approximation works exceedingly well for large n values as with ln(170!) =706.5731 being very closely approximated as 706.5726 by the Stirling’s. The Stirling’s Approximation form of the lnΩ expression of Eq20 is
34.)
We use this formula to compare the
lnΩ of a list of randomly chosen large K over N equiprobable distributions
to their D_{AV} diversity measure of Eq24.
K 
N 
lnΩ 
D_{AV} 
145 
30 
75.71 
25 
500 
90 
246.86 
76.4 
800 
180 
462.07 
147.09 
1200 
300 
745.12 
240.16 
1800 
500 
1151.2 
381.13 
2000 
800 
1673.9 
571.63 
3000 
900 
2100.88 
692.49 
Table 35. The lnΩ and D_{AV} of Large K over N Distributions
The Pierson’s correlation
coefficient for the D_{AV} and lnΩ of these distributions is .9995
as indicates a near perfect direct proportionality between the two as can be
appreciated visually from the near straight line of the scatter plot of these D_{AV}
versus lnΩ values.
Figure 36. A plot of the D_{AV} versus lnΩ data in Table 35.
This high .9995 correlation between lnΩ and D_{AV} becomes greater
the larger the K and N values of K>N distributions surveyed. For values of K
on the order of EXP20 as found in realistic thermodynamic systems, the
correlation for K>N distributions becomes.9999999 indicating a near perfect
direct proportionality between lnΩ and D_{AV}^{. }As the
Boltzmann S=k_{B}lnΩ entropy is judged to be correct ultimately by
its fit to empirical laboratory data, given the very high correlation of D_{AV}
to S, the diversity entropy formulation must also be judged correct from that
empirical perspective.
But that is not the end of the story because the D_{1/2}=h diversity of Eq11, of a random distribution, h_{AV}, also has an exceedingly high correlation with lnΩ and, as will be shown from its perfectly fitting the temperature measure of a thermodynamic system, is the correct β Diversity Index for entropy. Showing the correlation of h_{AV} to lnΩ is not as straightforward as it was for D_{AV}, however, because h_{AV} is not expressible as a simple function of K and N as was D_{AV }in Eq24 as D_{AV}=KN/(K+N−1). There is a remedy for that, though, because h_{AV} is the h diversity of the representative state of a thermodynamic system, a number of which we developed for the random distributions of Figures 2629. We obtain h_{AV} for the K over N distributions of Figures 2629 from the x_{i }and p_{i} values of the Representative States from Eq11. Below are listing their h_{AV} values along with the lnΩ values of those representative states from Eq32. And we also include their D_{AV} diversities from Eq24 for comparison sake.
Figure 
K 
N 
lnW 
D_{AV} 
h_{AV} 
26 
12 
6 
8.73 
4.24 
4.57 
27 
36 
10 
18.3 
8 
8.85 
28 
45 
15 
26.1 
11.11 
12.33 
29 
145 
30 
75.88 
25 
26.49 
Table 37. The lnΩ, D_{AV} and h_{AV} of the Representative
States of Figures 2225.
The Pearson’s correlation coefficient for the lnΩ and h_{AV} values in the above is .995. And for the lnΩ and D_{AV} values it is .997. Note that though this lnΩ and D_{AV} correlation of .997 is high, it is less than the .9995 correlation between lnΩ and D_{AV} from Table 35 for larger K and N distributions. This is attributed to the Pearson’s correlation coefficient between diversity and Boltzmann’s S entropy being a function of the magnitude of the K and N of the random distributions tested, those of the distributions in Figures 2629 used in Table 37 being significantly smaller than the K and N of the distributions in Table 35. Hence the Pearson’s correlation between lnΩ and h_{AV }of .995 for the K over N distributions in Table 37, being little different than the .997 correlation between lnΩ and D_{AV} for these distributions, implies that the lnΩ and h_{AV }correlation is, as was the .9995 between lnΩ and D_{AV }for larger K and N distributions, sufficiently great to have h_{AV} also accepted as a diversity candidate for entropy from its high correlation with the S=k_{B}lnΩ Boltzmann entropy.
To choose between the two turns out to be little problem as it is easily shown that h_{AV} derives the true microstate temperature of a thermodynamic system. This analysis will also make clear why the diversity function is so important for mathematics and mathematics based science. To that end consider the K=6, N=3, (■■, ■■, ■■), (2, 2, 2), set to be a balanced set given that all of its x_{i} have the same value of 2. Its D diversity is seen from Eq4 to be D=N=3. In general the D diversity and N number of subsets are one and the same for a balanced set.
Now recall that we devised the (■■■, ■■, ■), (3, 2, 1), set as a regular set made up of unit objects (all the same size) with the original rationale that it was mathematically easy to work with. But we could have said, as we will now, that the reason for using a regular set was that when things counted are the same size, the count of them is exact. But when things counted are not the same size, the count of them is inexact. This becomes intuitively clear if we vary the sizes of the objects in (■■■, ■■, ■) to be, say, (■■■, ■■, ■). Now while it is not forbidden to say there are K=6 objects in (■■■, ■■, ■), that count of them is inexact for we would never use this K=6 parameter to develop the mathematics of the set without taking into consideration the size variations of the objects in the set. The dictum of things counted needing to be the same size is why standard measures as for weight like the pound are all the same size. If they were not, one pound having a slightly different magnitude than another pound would make commercial transactions involving them be greatly open to question.
In the same way the N number of subsets in an unbalanced set, like N=3 for (■■■, ■■, ■), (3, 2, 1) is inexact because the N subsets are of different sizes, not all containing the same number of unit objects as was the case for the (■■, ■■, ■■), (2, 2, 2), set whose N=3 parameter is exact because the subsets are all the same size in having the same number of unit objects in each. Note that N being inexact for an unbalanced set like (■■■, ■■, ■), (3, 2, 1) strongly suggests that µ=K/N is also inexact or somehow in error for an unbalanced set. And that should not be surprising given that the µ=K/N mean is invariably accompanied by a measure of statistical error like the σ^{2} variance or the σ standard deviation or the r relative error or r^{2} perfect error, all of which are zero for balanced sets with that the absence of statistical error implying the absence of inexactness as a roundabout rationale for balanced sets (whose subsets are all the same size) being exact.
Now to make the point that the β Diversity Indices of a set are exact both for balanced and unbalanced sets. That is clear in a most intuitive way for D itself given its D=N/(1+r^{2}) specification from Eq16 in which the inexactness in N can be understood to be offset by the inclusion of the r^{2} statistical error within the D=N/(1+r^{2}) function for D. More generally, though, it is clear that all β diversity indices are exact because they are functions entirely of p_{i} as we see in Eq10. And p_{i}=x_{i}/K is exact because as we see for (■■■, ■■, ■), (3, 2, 1), the x_{i} of it as x_{1}=3, x_{2}=2 and x_{3}=1 are exact because the objects counted in each subset are all the same unit size and similarly for its K=6 parameter, exact because all objects in the set are unit objects.
The above makes it clear that D in particular and D_{β} in general are surrogates, exact surrogates, for inexact N. This is very important for the mathematical sciences, particularly thermodynamics, our mathematical science of immediate interest. For it question science’s acceptance of the N number of molecules in a thermodynamic system as exact. This discrepancy is profound, for however much we may use moderately inexact measures in practical situations (as in counting 12 oranges at the grocery store not all perfectly the same size as 12), nature does not operate on inexact counts and our use of inexact counts as being approximately correct should be understood as not obtaining the most exact and clear understanding of nature.
More to the immediate point, much as we can use D as an exact surrogate for the inexact N of an unbalanced set, we ask if we there is an exact average that is a surrogate or standin for inexact µ=K/N. One is obtained by replacing the inexact N in µ=K/N with exact D to form a biased average, φ, (phi),
38.)
The φ=K/D biased average is an exact average in being a function of K, which is exact, and of D, which is also exact as has been made clear earlier. The K=12, N=3, µ=K/N=4, D=2.323, (■■■■■■, ■■■■■, ■), (6, 5, 1), set has a biased average of φ=K/D=12/2.323=5.166. This is greater than this set’s arithmetic average of µ=K/N=4 from the φ biased average being weighted or biased towards the larger x_{i} values in (6, 5, 1). To intuitively appreciate the bias in the φ biased average towards the larger x_{i} values in an unbalanced set, we express φ from Eqs38,4&5 as
39.)
This shows the φ biased average to consist of the sum of “slices” of the x_{i}
of a set, slices that are p_{i} in thickness, as biases the φ
average towards the larger x_{i} subsets in weighting them with their
correspondingly larger p_{i} weight fraction measures. We can also
develop a square root biased average, ψ,
(psi), also exact, as the ratio of K to h, which from Eq11 obtains ψ as
40.)
The numerator in the rightmost term shows the ψ square root biased average to be the sum of “slices” of the x_{i} of a set of thickness p_{i}^{1/2}, which biases the average towards the larger x_{i} in the set in their having larger p_{i}^{1/2}. The ∑p_{i}^{1/2} term in the denominator of the rightmost term, it should be explained, is a normalizing function required to make the p_{i}^{1/2 }“slices” in the numerator sum to one, this summing to one of fractional “slices” being necessary for the construction of any kind of an average of a number set.
Having developed all this somewhat digressive, somewhat tedious material let’s show now how it formulates temperature correctly. The simplest form of the microstate temperature of a thermodynamic system is currently taken in the standard physics rubric to be the arithmetic average energy per molecule of the system, µ=K/N. But a flag is immediately raised that there might be something wrong with this specification of temperature because, as we have made clear, the µ=K/N arithmetic average of any unbalanced set is inexact and a thermodynamic system is decidedly an unbalanced set in its N molecules having different energies as is made unarguably clear from the MaxwellBoltzmann energy distribution of Figure 25, which has been empirically proven to be correct.
That says what the temperature isn’t. As to the function that properly represents temperature we must consider how it is actually measured, physically, with a thermometer. Each of the N molecules in the thermodynamic system collides with the thermometer to contribute to its temperature measure in direct proportion to its frequency of collision with the thermometer. And that is equal to the velocity of the molecule, which itself is directly proportional to the square root of the x_{i} number of energy units a molecule has. Because of this, the slower moving molecules with the smaller energies in the MaxwellBoltzmann energy distribution of Figure 25 collide with the thermometer less frequently and have their energies recorded or sensed by the thermometer in its cumulative compilation of the temperature measure less frequently, which records their energies with smaller p_{i}^{1/2} slices of the actual values of their energies. This is in contrast to the faster moving, higher energy molecules that collide with the thermometer more frequently and have their energies recorded as larger p_{i}^{1/2} slices of their actual energy. This biases the temperature measure towards the energy of the higher energy, faster moving, molecules as properly understands temperature as the square root biased average of molecular energy, ψ=K/h, rather than the simple, but inexact, µ=K/N arithmetic average of the molecular energy.
There is one more factor that must be added to this argument to make it precisely correct. As a thermodynamic system cycles through its many states over time with the average of the characteristics of those states being the characteristics of the representative state of the system and of the system as a whole, the temperature of the system is the ψ of the representative state or ψ_{AV}. And by logical extension from Eq40, the correct diversity measure for entropy is therefore
41.)
So, however much Boltzmann is revered, and rightly so, for his breakthrough efforts to understand entropy microscopically, its specification in terms of h_{AV} energy diversity, which is impossible to distinguish from Boltzmann’s S entropy quantitatively given the exceedingly high correlation between them, finally makes sense out of entropy as a physical quantity as energy diversity or energy dispersal.
Was Boltzmann, therefore, wrong? Unfortunately, especially given that he gave his life for science, literally, he was. Some who have reviewed this material came to the conclusion that though the analysis cannot be argued with, the diversity take on entropy provides a parallel understanding of entropy, not an overthrow of Boltzmann physics. But it is patently impossible for both Boltzmann and The β Diversity Index Demystification of Entropy to be correct because the two are mutually contradictory in their axioms. Boltzmann statistical mechanics starts off with the premise that the K energy units are indistinguishable and therefore subject to indistinguishable object combinatorial statistics while the β diversity prescription considers the K energy units to be distinguishable and subject to distinguishable object combinatorial statistics as the analysis of the K=4 energy units over N=3 molecules in Eq18 to Eq22 makes clear.
Hence they cannot both be right. Assuming Boltzmann wrong, let’s now consider just how this thoroughly canonized saint of science screwed up with the problem of distinction. There are two kinds of distinction in nature, categorical and fundamental. In the (■■■, ■■, ■), (3, 2, 1), set, it is obvious that a red object, ■, is categorically distinct, a different kind of object, than a green object, ■. That’s why they are put in different subsets in the set. But any two red objects, like the first and second red objects in (■■■, ■■, ■) are also distinct, or distinguishable from each other, in residing in different places. This is called fundamental distinction.
One can develop a quite extensive subscience of distinction and the lack of it. But to cut to the chase in regards to our focus on thermodynamic systems, not that even when all the molecules of a thermodynamic system are of the same kind and have no categorical distinction, as with all being Helium molecules, they are still distinct from each other, fundamentally distinct. And the easiest badge of that is that they are all in different places at any one moment in time. Indeed, Boltzmann statistical mechanics does not dispute this and accepts the idea that all N molecules in a thermodynamic system are distinguishable or distinct.
But the K energy units that reside in or on those molecules, which are in different places, are also in different places in being contained in or on molecules in different places. Thus at least as between energy units residing on different molecules, they are certainly distinguishable (however much Boltzmann’s unpolished intuitions about distinction may have told him different.) And one can also make the argument that during a collision between two molecules when there is a transfer of some of the energy units of a molecule to another molecule, certainly ne distinguishes between the energy units that left the parent molecule and the ones that remained.
Rather what happened is that Boltzmann’s sense of indistinguishable led to the use of indistinguishable combinatorial statistics, which produced an lnΩ based entropy, which never has made any intuitive sense to anybody over the last hundred years, which happened to have a happenstance very high numerical correlation to diversity, which Boltzmann didn’t have a prayer of using in his analyses, because it wasn’t invented until a full halfcentury after his death. We leave the details of a diversity centered thermodynamics to professionals in this area who are intelligent enough not to continue to favor Boltzmann and though he were an infallible true saint of some church of thermodynamics. And move now to the exposition of the full range of the β Diversity Index in the next part of this treatise.
III:
The β Diversity Index Demystification
of Nature,
Physical, Biological, Human and Perverse
By “perverse nature” we mean not only out of step with biology homosexual inclinations, but much more importantly the root cause of it beyond the left wing myth of genetics in the exploitive subjugation of people by the ruling classes up the top of nations including our own same sex relations heavy America. The problem with explaining social control and its unpleasant side effects which go way beyond the relatively trivial LGBT issue to the perverse aggression misdirected to innocent victims by unhappy midlevel wage slaves is that this fact is kept fairly well hidden by the black propaganda that shouts from ruling class misinformation outlets 24/7. For as Machiavelli philosophized back a half a millennium ago, the best way to keep the workplace serfs out of the rebellion their situation logically deserves is to never stop preaching the right wing the right wing myth that the peasants’ suffering on earth will be fully rewarded by an eternity, no less, of happiness, ecstatic no less, after they’ve gone to the grave.
Because the religious and ideological bunk is so ingrained in people’s heads from their preschool days to their death beds and because the harm done is so horrible up to and including man’s collective misery being the cause not just of our daily mass murders but also pointless vanitydriven wars like Bush’s slaughter in Iraq and potentially even soon to come nuclear war, the only way to can explain what’s going on in the world and with your life is to scientifically sketch out the truth in precise, logical, impossible to spin mathematical language .
Hiroshima, what this thesis proves the world is heading towards worldwide if we don’t get rid of the weapons.
So please bear up with the technical dryness of the exposition that immediately follows until we have enough ground to stand on quantitatively to spell the reality of life out in ordinary language in some of the later sections. Let’s start now.
We have already talked about the β=1 and β=1/2 diversities at length along with their associated matrices. The β=0 diversity sheds little light on nature – physical, biological, human or perverse – but tells a good deal about the cohesiveness of the mathematics that properly explains it. The β=0 diversity index is from Eq10
42.)
Notice how the β Diversity Index, D_{β}, “grows” for the N=3, (9, 4, 1), set from D=D_{1}=2 to D_{1/2}=2.333 to D_{0}=N=3 as we go from β=1 to β=1/2 to β=0, the spread of the numbers in the set being taken less and less into account in the specification of the diversity of the set as β gets smaller and smaller. This makes it clear that all of the β diversities are, indeed, measures of diversity given the intuitive origin of the notion of diversity. The derivation of the D_{0}=N diversity, which doesn’t take into account the spread of the numbers in a number set at all, from its associated matrix, the addition matrix, drawn out for the K=6, N=3, (3, 2, 1) set below, is also striking.

9 
4 
1 
9 
9+9 
9+4 
9+1 
4 
4+9 
4+4 
4+1 
1 
1+9 
1+4 
1+1 
Figure 43. The Addition Matrix of the (9, 4, 1) Set.
The sum of all the terms in the addition matrix is 2KN=84 and the sum of the diagonal terms, 2K=28. So as we saw with the β=1 and β=1/2 diversities, the β=0 diversity, D_{β}=D_{0}=N=3 is also the ratio of the total sum, 2KN, divided by the diagonal sum, 2K, as D_{0}=2KN/2K=N. Is there a contradiction here, though, given N as a β diversity measure, which we said were all exact, and N for an unbalanced set, which we said were all inexact? No, the D_{β}=D_{0}=N diversity measure is exact because the p_{i}^{0}=1 terms that directly generate N in Eq42 neutralize the spread or dispersion of the p_{i}=x_{i}/K weight fractions and the x_{i} they are functions of thus treating even an unbalanced like (9, 4, 1) as though it were balanced, showing internal consistency in the mathematics of The β Diversity Index Demystification.
We next consider the β= –1 diversity, which is important to our demystification of physical nature to be given its own symbol, M. For the K=14, (9, 4, 1), set, whose p_{i} are p_{1}=9/14, p_{2}=4/14 and p_{3}=1/14, D_{1}=M is
44.)
Note first how the diversity index continues to increase in
value for a given set as β decreases in value even into negative numbers. And
next note how M is derived from the division matrix shown below of (9, 4, 1) as
the ratio of the matrix sum of terms to the diagonal sum of terms as it did for
β=1, β=1/2 and β=0.

9 
4 
1 
9 
9/9 
9/4 
9/1 
4 
4/9 
4/4 
4/1 
1 
1/9 
1/4 
1/1 
Figure 45. The Division Matrix of the (9, 4, 1) Set.
The sum of all the terms in the division matrix is Я=343/18=19.0556. (Я is the Russian letter, ya.) And the sum of diagonal terms is N=3, with the ratio of these sums being Я/N=6.352, the β= –1 diversity. Hence, we generalize for the division matrix of all natural number sets,
46.)
Again we see that the N term in Я/N that M is a function of and might be thought to be inexact from our earlier arguments on N, thus making M inexact, is not exact as a count of the unit ratios in the diagonal, which shows the β diversity index, M=D_{1},_{ }to be exact as we generalized earlier for all β diversity indices. Again this shows the internal consistency of these mathematics.
More meaningful as regards science proper and the solving its “mysteries” is that the ratio of the µ mean of K=14, N=3, (9, 4, 1), which is µ=K/N=4.667, to the M=D_{1}=6.352 diversity is the inverse sum of the x_{i} of the set as we would find if the x_{i} were the values of capacitors in series or resistors or inductors in parallel.
47.)
For the K=14, N=3, M=6.352, (9, 4, 1) set, the inverse sum is K/NM=.7347. To understand more clearly what is being talked about here as regards capacitors in series, let’s look at a diagram for the RC circuit, an electronic resistancecapacitance circuit.
Figure 48. An RC Circuit
The capacitor on the right, with capacitance, C, is connected up with the battery on the left, with voltage, V_{S}, so as to fill the capacitor with electronic charges. If N=3 capacitors are used in the circuit together they can be arranged in two ways. One way is “in parallel” as shown below,
Figure 49. Capacitors in Parallel
In this parallel arrangement, the capacitance, C_{P}, of a set of N=3 capacitors, (9, 4, 1), as C_{1}=9, C_{2}=4 and C_{3}=1 is just their simple arithmetic sum.
49.) C_{S }= C_{1} + C_{2} + C_{3}
For our (9, 4, 1) set of capacitors, hence, the three behave as one capacitor of value C_{S }= C_{1} + C_{2} + C_{3}=14. This is intuitively very reasonable as the three capacitors act like three containers to be filled with charges whose amounts sum together little differently than the number of peaches you might fill up three wicker baskets of sizes (9, 4, 1) with. The other way the capacitors can be hooked up is “in series” as shown below,
Figure 50. Capacitors in Series
Now the three behave as one capacitor of value, C_{S},
51.)
For the (9, 4, 1) set of capacitors, C_{S}=.7347. Hence
52.)
There are a couple of important conclusions that can be drawn. The first is that this clarifies for the first time in science what the inverse sum of C_{S} means intuitively from C_{S}=K/NM. If we look at K divided by N by itself, it is obviously the µ=K/N mean or arithmetic average. And if we look at K divided by M by itself, it is, perhaps less obviously, a β diversity based biased average entirely akin to the φ=K/D biased average of Eq38 and the ψ=K/h square root biased average of Eq40. Hence we can understand this new representation of electronic circuit inverse summing as a double average that first averages the K=C_{1}+C_{2}+C_{3} simple sum of the capacitors over the N number of them and average that again over their M diversity, more to be said on this later.
The second is that inverse summing as derived from the pure mathematics of the β diversity index and the number set division matrix is a general mathematical structure, not one necessarily derived from or restricted to electronic circuits. That this is empirically the case is obvious when we take a look at the mammalian circulatory system to see the blood vessels fanning out, so much like parallel resistors in an electronic circuits, in order to optimally minimize the resistance to blood flow in mammals including man. And this suggests that inverse summing as fits circuit elements can also be used to explain some of the many mysteries of human relationships, for people tend to bond or connect with each other very often in obligate fashion, like capacitors in series, and also in optional fashion, like capacitors in parallel.
To explain relationships and indeed behavior in general in these very precise and clarifying mathematical ways, we must take the view that not only is inverse summing an elementary mathematical function that can be applied generally, but also that the elemental Kirchhoff’s Laws of electronic circuits (to be reviewed shortly) can be applied generally to nature. Before we begin that analysis, though, we want to mop up two “side show” aspects of the matrix and β diversity mathematics we have been dealing with, for they are both powerful instruments for science whether used in conjunction with each other or separately.
We have considered now the matrix
arithmetic of sets as it applies to addition, division and multiplication, the
latter also in square root form. Is there also a meaningful subtraction matrix
for a set? Our first attempt at forming one, as for the (3, 2, 1) set would
look like this.

3 
2 
1 
3 
(3−3) 
(3−2) 
(3−1) 
2 
(2−3) 
(2−2) 
(2−1) 
1 
(1−3) 
(1−2) 
(1−1) 
Figure 53. The Simplest Possible Subtraction Matrix of the (3, 2, 1) Set.
A quick glance at the diagonal terms
shows them all to be zero. And the sum of all the terms in the matrix is also zero,
which effectively renders the subtraction matrix in this form without little
ostensible value. We can rectify this problem, though, by squaring the
differences, which will give a measure of their magnitude without zeroing out
their sum.

3 
2 
1 
3 
(3−3)^{2} 
(3−2)^{2} 
(3−1)^{2} 
2 
(2−3)^{2} 
(2−2)^{2} 
(2−1)^{2} 
1 
(1−3)^{2} 
(1−2)^{2} 
(1−1)^{2} 
Figure 54. A Better Subtraction Matrix for the (3, 2, 1) Set.
Doing this doesn’t change the zero values of the diagonal differences but it does prevent the zeroing out of the sum of the matrix differences, which we see adding up to λ=12, (λ, the Greek letter, lambda.) The average of all N^{2}=9 squared differences in the matrix is λ/N^{2}=12/9=4/3. Note that this is exactly twice the σ^{2}=2/3 variance of the (3, 2, 1) set. And generally for any number set,
55.)
This λ/N^{2}^{ }function as the average of the λ sum of matrix terms per its N^{2} terms, though twice the σ^{2} variance, provides as good a measure of the spread of the numbers in a number set as does the σ^{2} variance, which should be understood as an inherently arbitrary specification of the spread, as indeed are all of the statistical error functions of the science of statistics. From this perspective the spread of numbers quantified in terms of the 1/N^{2} average of the λ matrix squared differences is as intuitively sensible, if not more so, than the 1/N average of the deviation of the x_{i} numbers in a set from the µ mean in the textbook definition of the σ^{2 }variance of Eq14. And from this perspective one could theoretically revamp the entirety of statistics using the λ/N^{2 }doubled measure of the σ^{2} variance from the subtraction matrix as the foundation statistical error of such a new statistics. It is much easier, of course, to retain statistics in the form it is presently in, of course, though recognizing that Eq55 as λ/2N^{2}=σ^{2}^{ }is valid alternative derivation of the σ^{2} variance that has some advantages.
One of these comes from averaging the λ sum of squared differences terms, not over an N^{2} number of terms that includes the zero value difference terms in the diagonal (which can be thought of, hence, as nonexistent) but over the N (N−1) nonzero differences in the matrix. Doing that derives not the σ^{2} population variance, but the S^{2} sample variance.
56.)
This provides a simple and direct explanation for the statistical science’s differentiation between the population standard deviation, σ, and the sample standard deviation, S, which if not as much of a mystery for science as entropy, has confused countless students and a goodly number of science professionals over the years.
And further validating the meaningfulness of this natural set matrix mathematics is comparison matrix of Figure 2 that derives from the product matrix, the quite illuminating as regards the foundation operation of the human mind of distinguishing or making a distinction shall take up in detail in a later section.
And before we get to an understanding of human behavior in terms of Kirchhoff’s Law circuits, we also want to make a few quick observations on the relationship between diversity and information, for however much Claude Shannon’s information theory (arrived 1947) has provided some interesting insights on information in the way we usually understand the word, it has failed, despite many attempts especially in its early days, to provide anything approaching a comprehensive understanding of information as the biological kingdom’s premier information processing machine, the human mind, uses it. As a brief preview of this we want to cite two logarithmic information functions that are closely associated with diversity.
One of these is the Renyi (information) entropy, simply just logD where D is our β=1 diversity of Eqs4,7&8, which does double duty in the science literature as both a central function for information in information theory and as the Renyi Diversity Index. And the other is the Shannon (information) entropy, which also does double duty as the central function for information in information theory in log_{2} form as the Shannon Diversity Index in natural logarithm form. While it does not have a perfect analog in the β diversity pantheon, it is very close in value for most sets and equal in value for some to logh, the h square root diversity of Eq11.
In a later section we will extend this synonymy of information and diversity to include an understanding, through the comparison matrix of Figure 2, of the (nonlogarithmic) β diversity functions and its derivatives as information, which provides a quite beautiful, mathematically precise specification of all of our human emotions including fear, excitement, relief, disappointment, hunger, sex and anger, the latter in conjunction with the mathematics of natural selection we also develop giving a perfectly clear understanding of violent behavior and why the only thing that can keep it from bringing about the greatest mass murder of all time as nuclear attack is for us to get rid of all the weapons in the world before the weapons get rid of all of us.
Now doubling back to the RC circuit of Figure 48, we will first explain its dynamic behavior in terms of Kirchhoff’s Law and then use that to explain goal directed human behavior.
Figure 48. An RC Circuit
The capacitor on the left, C, connected up the battery on the right, V_{S}, fills the capacitor with charges. What is relevant to human behavior is that activity directed to achieving a goal, a task, can be configured conceptually as filling up a container with some kind of valuable, needed, objects as with filling a bushel basket with apples at harvest time or, indeed, filling up one’s stomach or other storage places like the liver and fatty tissue with food. While that is a simple ordinary language intro to this analysis, it’s nuances and ramifications cannot be understood with recourse to the RC form Kirchhoff’s law spelled out in the language of differential calculus as
57.)
We see that the rate of filling up of the capacitor with q charges, dq/dt, from a batter with voltage, V_{S}, is inversely proportional to the resistance, R, and the capacitance, C. The greater the R resistance, the longer it takes to fill it; the greater the C capacity of the capacitor, the longer it takes to fill it. Applied to human behavior as the task of filling a container, the bigger it is, the larger its capacity, analogous to C, the longer it takes to fill it; and the greater the environmental resistance, how difficult the task is, analogous to the R resistance, the longer it takes to fill it. Capacitance in series represents tasks that require more than one person to do them. And …
[Painful Illnesses from the natural breakdown of the body as occurs once you get substantially into your 70s regardless of what the smiling sucker ads on TV for the purgatory of retirement say has put a halt to our writing. Before we quit, though, we’ll write up the a. to z. precepts as in a scientific bible for what life actually is about along with what’s best to do about it. And following that is a ton more mathematics that underpins these precepts done in years past. For that reason, there are breaks here and there in in the topics covered and in the equation numbers, though the material is yet well ordered and well written enough to be read quite easily, the newness of some of the mathematics aside. And there are also a few extended sections written in ordinary language mixed in with tit that help to fill in the blanks in the a. to z. precepts that follow.]
a.) As Genghis Kahn once said: Every man wants to be the khan (the king, the top boss of it all, like he was) or be independent (no boss of any kind at all.)
b.) An interesting and quite correct observation on the part of Genghis considering that anybody within his reach (as a lot of people were back in the Mongolian empire of the 13^{th} Century) who attempted to be the Khan or to be independent and outside of his control was executed, usually by beheading.
c.) Now before we start making Genghis out to be some kind of unique devil figure in history, note that any honest history book on civilized man (and that excludes the history preached to the common folk within a nation by the rulers including to mind vulnerable children) will tell you that enslavement in one form or another has been with us since Ancient Egypt and Babylon and Sparta and Rome and in the serfdom of Medieval Christianity and British Colonialism and just last week in the 9 to 5 and beyond wage slavery all have to put up with in America.
d.) And should also tell you that top bosses (as with kings of old and _____ empowered by big money in modern times, the blank used because there are no politically correct, proper, words allowed for the billionaire wage slave controllers) would never say through the information outlets they control including religion, education and today’s quasireligion psychobabble, that people would rather be independent than be the happy wage slave suckers portrayed in the movies and media that only the millions of our billionaire rulers, may they all be given black eyes, are able to produce.
e.) And an honest telling would also make clear that life’s “personal” miseries as derive from failed and frustrated relationships (shhh, don’t tell your sisterinlaw or neighbor or coworker) are not the product of Satan or “mental illness” but of the 9 to 5 and beyond screwing people take in life as a matter of course from bosses and from authority controlled, yea owned, by money, as the police and courts certainly are (except on TV.)
f.) Really, can it be missed by any halfsensible person, the correlation between the unhappiness of the standard mass murderer and his suicidalhomicidal release from that unhappiness from his last few bloody moments? What do you mean, he was/is mentally ill and that’s why he did it? My, that’s so vague. It’s unhappiness in the heart that drives people mad, unhappiness that comes from the same place as for the rest of the suckers who can’t make the correlation between it and humiliatingly kissing the boss’s ass six ways six times a day as the years go by. Or, to push the logic of the connection one step further, let’s ask where “mental illness” comes from? Well, we just don’t know, say the welldressed shrinks on TV and their pundit and police chief sidekicks. We never have any idea what the mass murderer’s motive was, and that’s 300 such motiveunknown mass killings just in 2015. Hmmm.
g.) Though, c’mon, what’s the mass murder of a handful of people every day compared to the mass murder, legs and arms and heads blown off, of war? And does that come from the same place as domestic mass murder, from the tyranny of social control, whether from dictator setup police coercion or billionaire setup economic coercion? The boss or the authorities (in the schools now, too) too, kicks you in the ass, or threatens to day by day, but since you can’t kick the bastards back, you bullyingly and often sneakily pass your pain on to others who had nothing to do with causing your pain. And this extends to masses of people kicked in the ass passing on their hate to masses of other people, of different ethnicities, here and in other countries. Kill the bastards. That feels so good, to hate to cause others to suffer when you feel bad yourself. And it hits hard also on independent people who are often targets out of jealously.
h.) Way down in the cellar of causation, of course, it’s all Darwin’s fault, all this violent competition admixed with the worldwide economic competition that finances for the winners the best weapons, that plus the aforementioned blind hate and aggression that wells up from underlings dominated and beat up by the bosses passing their misery onto vulnerable others en masse.
i.) And there is no way to shut it down, as long as the social control font for it keeps flowing. No way to shut it down except to get rid of all the weapons in the world. And that would work because the simplest mathematics tells you that it’s absolutely impossible for a relative few people to control a whole lot of people without weapons. Which is the what the police are there for primarily, to prevent revolution, which is why it is necessary to take the weapons power away from the billionaire bosses, may their eyes be blackened, who own the police and effectively, better believe it, tell them what to do. Or is it too much to ask the question of why the billionaires NEVER go to jail.
j.) And as no small side effect of getting rid of all the weapons, you also get rid of war as we know it, up to and very importantly including mankind annihilating nuclear war, lots on exactly how to bell that cat in later sections where you’ll find that A.) It’s entirely necessary or we go up in smoke and B.) It’s quite possible to accomplish once people see clearly the 5000 years of misery up to the present that weapons have caused the human race, in war and peace.
k.) And we should also say something about the poor fellows and gal soldiers who do the billionaires’ bidding to grow and maintain the American Empire. To give your lives with arms and legs and brains blown away for the sake of maintaining the privileged lives of the decadent scum at the top? Nothing sadder than a veteran in a waiting room at a VA hospital. Really. Take a quick trip to the lunch room at the VA hospital up in the Hanover, NH, area. These poor bastards, masses of them impaired for life in irreparable ways. Even the most sensibly selfish of us can’t help feel the true horror of it. Let’s get rid of the weapons.
l.) And the rest of the a. through z. precepts of this new religion of happiness and sanity are scattered through the rest of this treatise prefaced by a bit more mathematics.
All processes in nature can be unified in our understanding of them in terms of their common property of moving towards some quantifiable end point. An example of this unifying generalization is found in the thermostatic heating of a room initially at θ=32^{o}F to the θ_{S}=72^{o}F temperature set on the room’s thermostat. The Ԑ (epsilon) error function in this classic negative feedback control system is the difference between the actual room temperature, θ, and the end point temperature the process is moving towards, θ_{S}.
901.) Ԑ = θ_{S }− θ
When an Ԑ error is sensed by the system, Ԑ=θ_{S}−θ=40^{o}F, a furnace automatically turns on to heat the room to the θ=θ_{S} set point to eliminate the error, Ԑ=(θ_{S}−θ)=0, at which point the furnace turns off. From a purely mathematical perspective Ԑ can alternatively be specified as a negative quantity
902.) Ԑ = θ_{ }– θ_{S }
It is clear that the negatively signed error, Ԑ = θ_{ }– θ_{S }= −40^{o}F in this example, is also eliminated when the room temperature reaches the set point temperature on the thermostat, θ= θ_{S}, to zero out the error, Ԑ=θ_{ }– θ_{S}=0. While textbook feedback control theory specifies the sign of the Ԑ error as positive, its negative specification has intuitive advantage in couching an error as a deficit. All processes in nature are unified in behaving in some way as a cybernetic or negative feedback control system that proceeds to some end point by eliminating some form of Ԑ= θ−θ_{S} error. This unification clarifies a spectrum of otherwise confusing phenomena that range from thermodynamic entropy to human emotion and behavior.
The Cybernetic Age was born from mathematical theories of negative feedback control developed at MIT in the 1940s. This research soon led to the building of the forerunner machines of modern day computers. The cybernetic science developed though these efforts also led to a clear understanding of homeostasis or negative feedback control in biological systems. One such homeostatic system warms a person up when cold by the negative feedback control process of shivering that comes about from the brain sensing a θ skin temperature that deviates from a genetically inborn θ_{S} temperature set point for the body, the difference as an Ԑ=θ− θ_{S} error being eliminated by the muscle movement of shivering that generates an increase in body temperature. This is textbook physiological negative feedback control.
A third way to get warm when one feels cold is by warming behavior like walking into a warmer room or putting on more clothes or building a fire in a fireplace. Warming behavior starts with feeling the unpleasant sensation of cold as an emotional measure of Ԑ=θ−θ_{S} error that is zeroed out or eliminated by such behaviors. To explain all of the human emotions in a precise mathematical way as elements in a negative feedback control of behavior we start with behavior directed not to achieving the pleasurable end point goal of attaining warmth but to the broader pleasurable goal of obtaining money. This mathematical formulation of the human emotions develops a math based cognitive science that explains precisely how the mind works while avoiding the psychobabble vagueness of ideologically corrupt, pseudoscience standard psychology.
In doing so A Theory of Epsilon will enable us to address the troublesome and contentious problems of the day with the same assurance one has in solving technical problems using the mathematical sciences of Newtonian mechanics and electronic circuit theory. While many, disliking mathematical analysis, would prefer to discuss contentious issues in the same entertaining and easy to follow format television employs there are great advantages in using logical mathematical analysis because the unambiguous meaning of mathematical symbols makes impossible the spin enabled by the ambiguities of ordinary language that tolerates lies as patent as “You are Now Entering the No Spin Zone” that should provoke ridicule at the level of outing Bill O’Reilly as an even worse predatory closet faggot than fellow Republican spin masters Ted Haggard, Dennis Hastert and Karl Rove. That should clarify which side of the issues we are not on.
I should also make clear that the primary problem we have been concerned with over the last forty years of developing A Theory of Epsilon is the threat of nuclear annihilation.
To that end A Theory of Epsilon directs itself to explaining human nature, especially our violent emotions, well enough to encourage readers to actively participate in a worldwide political movement to change our planet into A World with No Weapons. This not only gets rid of the misery and horror of war but also the near equally miserable unhappiness that results from exploitive control ultimately sustained by the ruling class in such societies including capitalism through their military and police armed with weapons.
To explain such treasonous attitudes with unarguable mathematical precision consider next a specific behavior that has as its end point goal getting money through a behavior that provides a V dollar payoff gotten with probability, Z. This approach to understanding human emotion and behavior cybernetically that is examined in great detail in Sections 913 starting with Eq84 is sketched out here in a simpler way with a game of chance that uses one die.
If you roll a 3 on the die, which has a probability of Z=1/6, you win V=$60. The mathematical expectation, E, which is your average payoff if you play the game repeatedly, is
903.) E = ZV
Specifically the expectation for this game is E=ZV=(1/6)($60)=$10. If you play six times, for example, on average you win the V=$60 prize one time in six for an average payoff of E=$10 per play. In this game the negative expression of Ԑ error of Eq902 takes the form of
904.) Ԑ = θ – θ_{S }= ZV –V
Here we see the V dollar prize as the end point goal of the process in parallel to θ_{S} for the heating system and the ZV expectation as where you are prior to rolling the die to achieve the V prize in parallel to the θ temperature as where the heating system is at prior to achieving the θ_{S} set point temperature from the furnace heating the room. The Ԑ= ZV –V error can also be expressed in terms of U=1–Z, where U is the probability of failing to win the prize when you toss the die or the improbability or uncertainty in winning, as
905.) Ԑ = ZV –V = –UV
This Ԑ= –UV error is sensed as a neural signal from the brain as displeasure, specifically of the anxiety felt in the uncertainty about getting the V dollars. The greater the U uncertainty and the greater the V dollars one is uncertain about getting, the greater the displeasure in the Ԑ= –UV anxiety. In synchrony with a person instinctively wanting to eliminate unpleasant feelings, they thusly act to eliminate the error that is associated with the displeasure of anxiety. That is why displeasure evolved, to motivate behavior directed to eliminating the Ԑ error in the feedback loop associated with attaining a goal, here obtaining money. The full set of emotions associated with this behavior is brought out by next spelling out the E=ZV expectation of Eq903 from Eq905.
906.) E = ZV = V –UV
Much as –UV specifies an unpleasant anticipatory emotion via its negative sign, so does V in the above specify from its implicit positive sign a pleasant anticipatory emotion, that of anticipating the pleasure of obtaining V dollars or pleasure in one’s contemplation or wish or desire for money. The words one uses for the pleasant anticipation of obtaining V dollars is secondary to its primary symbol representation as V. And similarly with the word we gave to the –UV symbol, anxiety, which can also be called in ordinary language anxiousness or worry or concern or fear. Indeed there is so much latitude in which word or words in ordinary language we might call –UV that we will give it the technical name of meaningful uncertainty meaning U uncertainty associated with the meaningful item of money or V dollars.
This makes it clear that the E=ZV is a measure of the pleasure of one’s hopes of getting V dollars tempered or reduced by one’s unpleasant feelings of anxiousness or doubt about actually getting the money as would be universally felt by anyone playing this game, the marginal effect of the player’s wealth on the pleasure experienced in anticipating V=$60 notwithstanding.
The ZV, V and –UV emotions of hope, desire and anxiety are all anticipatory feelings experienced prior to doing the behavior of tossing the die. There is also a fascinating set of mathematically welldefined emotions that arise after one tosses the die. These depend, of course, on whether or not the toss is successful. If it is one feels pleasure as joy in getting or realizing the money we will label as R=V, the R symbol specifying a pleasure that comes from an actual realization rather than expectation. The amount of pleasure in getting V dollars, of course, depends on how big the V prize is. The bigger V is, the greater the pleasure, taken for simplicity to be a linear relationship and further a measure that ignores the wealth of the player, which without question has a marginalizing effect on the intensity of the pleasure experienced.
There is also an additional pleasure from winning, the excitement of winning that depends on the intensity of the –UV anxiousness from its negation from winning which we’ll represent with the letter, T.
907.) T = – (–UV) = UV
The greater the uncertainty, U, and the amount money one is uncertain about getting, V, the greater the UV excitement in winning it. If one plays a variation of this dice game with the V=$60 win coming about if one rolls a 1, 2, 3, 4 or 5 with probability Z=5/6 and with uncertainty U=1–Z=1/6, as one pretty much expects to win, though there is R=V joy in winning the V=$60 in either case, as there is much less meaningful uncertainty or anxiousness beforehand, there is less of a T=UV thrill or excitement than in the Z=1/6 game won only with the roll of a 3. Specifically the easier game to win at elicits a thrill of T=UV=$10 measurable as the pleasure of getting an extra $10; and the harder game, more of a thrill as T=UV=$50.
The T symbol stands for transition emotion, which categorizes excitement as a transition emotion in contrast to an E expectation and an R realized emotion, the other two broad categories of emotion humans experience in their goal directed behaviors. We can also define the T emotion in a more general way as
908.) T = R – E
We will refer to this function as The Law of Emotion. For a winning toss of the die with E=ZV expectation, the realized emotion is R=V and, hence, as derives UV thrill or excitement in a way different than Eq907,
909.) T = R – E = V – ZV = (1 – Z)V = UV
The Law of Emotion of Eq908 also generates a T transition emotion for when one does not throw a winning number. In that case, as no money is realized, a realized emotion is lacking, R=0, and the T transition emotion produced is from Eq908
910.) T = R – E = 0 – ZV = –ZV
This T= –ZV emotion is the disappointment felt when one fails to win the V dollar prize, an unpleasant feeling as denoted by its prefatory minus sign and one greater in intensity the greater the E=ZV expectation of winning felt beforehand. To wit as is universal among humans, a low expectation of winning carries with it little disappointment when you lose.
People don’t just behave to get good things like money; they also act to avoid losing good things they already have like money. This is illustrated with the same one die game of chance where you have to roll, say, the 3 to avoid losing v=$60 (lower case v.) The probability of failing to roll a 3 is U=5/6 so the expectation of incurring the v=$60 penalty is
911.) E= –Uv
The endpoint goal of throwing the die is to lose 0 dollars, which allows us to specify the Ԑ error that exists prior to the throw as
912.) Ԑ = E= 0 – Uv
The Ԑ error is eliminated or reduced to zero, Ԑ = 0, when the 3 is thrown and no money is lost, R=0, as the U uncertainty of avoiding the loss goes to U=0. The Ԑ error of Ԑ=E=0– Uv to be eliminated is associated with a feeling of displeasure, the fear of losing v dollars. As one acts to eliminate the displeasure by this or that behavior, here to toss the die to roll a 3, one also is behaving to eliminate the error in keeping with the generalization that all dynamic systems direct themselves to some quantifiable end point aiming to eliminating the Ԑ error in the system.
Two other expectation emotions besides E= –Uv fearful expectation that are familiarly associated with avoiding a loss become salient once Eq911 is expanded via U=1–Z to
913.) Ԑ = E= –Uv = –(1–Z)v = –v + Zv
In the above the –v term is the anticipation of incurring the penalty, dread of it we might say, a distinctly unpleasant feeling as its minus sign implies. And +Zv is the hope one has of avoiding this penalty, the emotional measure of the security one feels in this situation, a pleasant feeling as implied by its prefatory positive sign. This makes it clear that the E= –Uv emotion of fear of incurring the v penalty is a tempered sense of what we are calling one’s –v dread of the penalty tempered by one’s sense of +Zv security or hope that the penalty will be avoided by rolling the 3. The many nuances of these three emotions of fear, dread and security are detailed in Section 9 starting at Eq120. 3The T=R–E Law of Emotion of Eq908 also applies to behaviors directed to the goal of avoiding a loss. When one is successful in that effort by rolling the 3, no money is taken and R=0. With that and E= –Uv the T transition emotion for a successful throw of the die is
914.) T = R – E = 0 –(–Uv)= Uv
The positively signed T=Uv transition emotion is the pleasant emotion of relief felt when one avoids losing something of value as in incurring the v dollar penalty in this game. The intensity of the pleasure of T=Uv relief is greater the greater the v penalty that might be incurred and the greater the U probability of incurring it. The emotion realized when the penalty is incurred is R= –v, the grief or sadness felt when you lose something of value like money. Again with E= –Uv as one’s fearful expectation,
915.) T = R – E = –v –(–Uv)= –v +Uv = –v(1–U) = –Zv
The T= –Zv emotion is the dismay felt in losing v dollars whose displeasure is greater the greater one’s zV hopes of avoiding the loss. This T= –Zv dismay felt from Zv hopes of avoiding the penalty being dashed is above and beyond the –v grief felt in losing the money. We can lump the positive pleasant T transition emotions of UV excitement and Uv relief together as elation and the negative unpleasant ones of –ZV disappointment and –Zv dismay as depression. The function or purpose of the T transition emotions in man’s emotional machinery along with some of their other important nuances and ramifications are developed in detail in Sections 912 starting at Eq84 in a fashion spectacular enough to derive the Economics 101 Law of Supply and Demand from the T=R–E Law of Emotion of Eq907. Then in Section 13 starting at Eq235 we substitute the penalty of losing one’s v*=1 life for losing v dollars to derive the feeling of cold we have that threatens one’s life as the emotion couched error whose displeasure motivates us to warming activity to save our life or survive.
Having in the above given the necessary directions for tying that ribbon of getting money and getting warmth together, we want to double back now to the thermostatic heater to develop systems engineering’s basic expression for 1^{st} order negative feedback that will further show the generality of cybernetic control in nature’s processes and then lead to a clearer understanding of our emotions (as with emotional energy and how it is gained and lost) and of the evolutionary processes that created them over time. To do that we will use mathematics a bit more advanced than the simple algebra we have tried hard to stick with to make the entry to this introductory section as easy to follow as possible.
A special kind of thermostatic heater is a proportional heater, called that because its rate of θ temperature increase from the furnace, dθ/dt in calculus terms, equal to the rate at which the Ԑ=θ_{S}−θ error is eliminated, is directly proportional to the Ԑ error as
916.) −dԐ/dt = −d(θ_{S}−θ)/dt = d(θ−θ_{S})/dt = dθ/dt = k(θ_{S}−θ)
In the above k is a constant of proportionality. The proportional heating system raises the θ room temperature to the θ_{S} temperature set on the thermostat to eliminate the Ԑ=θ_{S}−θ error according to the solution to Eq916 presented in chart form below.
Figure 917. θ Temp (in green) & Ԑ=θ_{S}−θ Error (in blue) over Time for Proportional Heating
The horizontal axis is time. And the
numbers on the vertical axis represent the θ room temperature as it
increases over time on the green curve, keeping the numbers simple, from
θ=0^{0}C to a θ=θ_{S}=5^{o}C
thermostatic set point. And the descending blue curve in the graph represents
the elimination of the Ԑ=θ_{S}−θ
error, which as it approaches closely 0^{0}C is eliminated as
automatically shuts off the furnace that’s has been heating the room up. Eq216
is the textbook function for 1^{st} order negative feedback control.
It is very general in nature as we will see next.
The RC circuit diagrammed below operates in basically the same way as the thermostatic heater.
Figure 918. An RC (resistancecapacitance) Electronic Circuit
Electric charge in coulombs,
q, flows from the battery on the left with a voltage of V_{S}=2.5 volts
to the capacitor on the right with a capacitance of C=2 farads. The maximum number
of charges the capacitor can hold, the RC circuit’s end point, is q_{max}=CV_{S}=5
coulombs. With its textbook Kirchhoff’s Law representation in which R
and C are constants we see that the current or rate of charging up, dq/dt, is
directly proportional to an effective Ԑ error for the circuit, (q_{max}−q).
919.)
−dԐ/dt = −d(q_{max}−q)/dt = dq/dt = k(q_{max}−q)= (1/RC)(q_{max}−q)
This is in perfect parallel to the error eliminating 1^{st} order negative feedback control function of Eq916. Indeed the temperature graph of Figure 917 perfectly fits the behavior of the RC circuit with the number 5 on the vertical axis representing the maximum number of coulombs of charge on the capacitor, q_{max}=5. This identifies the RC circuit as negative feedback control, albeit “passive” feedback control as the systems engineering textbooks categorize it. This distinction between active and passive feedback control in terms of the source of the end points, θ_{S} for the thermostatic heater deriving from a person’s wishes and the q_{max} end point being a fixed part of the RC circuit, is a minor difference relative to the cybernetic properties that the RC circuit and the proportional heater have in common.
Without getting into the technical details, a discharging RC circuit is also an instance of passive 1^{st} order feedback control as is an LR (inductanceresistance) circuit both for the growth and decay of current. And the function for another basic electronic circuit, an LC (inductancecapacitance) circuit, perfectly fits albeit passively textbook 2^{nd} order feedback control in which the quantifiable end point of a process is not a single value but an average of a repeated set of harmonically oscillating values.
Now without expanding this list of electronic circuits in detail we can say that every circuit is an instance of passive feedback control in its being directed towards some quantifiable end point in a way that eliminates some Ԑ error. This makes it clear that there is another broad category of cybernetic processes beyond manmade automatic machines and biological and behavioral homeostasis seen in electronic circuits. This cybernetic interpretation of electronic circuits, as we shall see later in this introductory section, allows emotion to be most fully described by circuit functions and most basically by the Maxwell’s Equations for electromagnetism that underpin circuits.
Ultimately we will show that all processes are essentially cybernetic, minimally in terms of their attempting to move towards some quantifiable end point by eliminating some form of Ԑ error. Seeing nature in this unified cybernetic way is extremely helpful in explaining how the more complex processes in nature operate. In that regard we note a variation of 2^{nd} order feedback control that has as its end point the average of a statistical distribution of values. A clear example of this is the average of the number of Heads that appear as the end point of the repeated flipping of N=6 coins, namely 3 Heads and 3 Tails. Such stochastic 2^{nd} order feedback control is also manifest in thermodynamic processes, which have as their end point an average of the energy diversity of the system as its entropy, a variation of a Simpson’s Diversity Index developed in Section 5 starting at Eq31 as an intuitively sensible entropy replacement for Boltzmann’s century old intuitively incomprehensible entropy formulation. As such thermodynamic processes provide yet another class of processes that can be understood as essentially cybernetic in nature.
We can also add to this list of processes governed by negative feedback control, Newtonian mechanics. All applications of Newton’s laws of motion can be derived from circuit theory itself understood as cybernetic as made clear above. While this interpretation of Newton called “kinetic theory” is less in fashion today than it was fifty years ago when it was first developed, the mathematical parallels of mechanical to electronic circuit processes are eminently clear. For example, the transfer of the kinetic energy of a body moving over a surface with friction is governed by a differential equation identical in form to that for the RC circuit in Eq919. Newtonian kinematics interpreted cybernetically also can provide a mathematical understanding of “behavioral driving forces” and “emotional energy.”
There are limits to any explanation of human emotion and behavior in cybernetic terms without first understanding their origin in evolution, the topic we will take up next. Doing so will also introduce us to the above mentioned Simpson’s Diversity Index that is also necessary for a proper microstate understanding of thermodynamics. And explaining evolution as a cybernetic process will also clarify why money is meaningful and where the possession of it gets its pleasure from.
The two main components of biological evolution are the natural selection of populations by competition and the coming on the scene of new populations from variation to join in the competition. An equation for natural selection useful for pointing out its cybernetic properties was first worked out by the classical population biologists of the 1920s, R.A. Fisher, J.B.S. Haldane and Sewell Wright. This equation is also derived by us in a more direct way in Section 14 at Eq269, the critical term in it for determining which of two rival populations wins out in evolutionary competition being
920.) F_{1 }= g_{1}−g_{2}= (b_{1}−d_{1}) − (b_{2}−d_{2}) =b_{1}−d_{1}−b_{2}+d_{2}
F_{1} is the competitive fitness of
population #1 of two populations that occupy the same niche and compete for the
resources and space in it needed for a population to persist from generation to
generation and avoid dying out or going extinct in the niche. The b and d terms
in F_{1} are birth and death rates, b_{1} and d_{1}
of population #1 and b_{2} and d_{2} of population #2. And the
g=b−d terms in it are the growth rates of the two competing
populations. When the g_{1}=b_{1}−d_{1} growth
rate of population #1 is greater than the g_{2}=b_{2}−d_{2}
growth rate of population #2, hence F_{1}>0, population #1 in blue
below flourishes to eventually occupy the entirely of the niche while
population #2 in red below goes extinct in the niche.
Figure 921. Competitive Population Growth or Natural Selection
Essential to this process is the limit to the number of organisms of either population the niche can hold called the carrying capacity, K. In the example competition in Figure 921, K=100 organisms, the maximum the niche can hold. There is no arguing with this dynamic for it is purely mathematical in form and valid for any two distinguishable populations of objects located in the same niche or container of limited capacity, even if the objects are not living organisms as with the red and green populations of M&M’s seen in the basket below.
Figure 922. Natural Selection of Competing M&M Populations
I will load more M&M’s into the basket right up to the very tippity top,
but many more red than green, which specifies the “birth rate” of red M&M’s
in the basket to be greater than the “birth rate” of the greenies. Then after
stirring all the M&Ms in the basket around to mix them up well I’ll scoop
out all the M&M’s at the top until I get the basket back to the same level
started with as seen above. This random removal of M&M’s produces an equal
“death rate” for the two kinds and given the superior “birth rate” of the reds,
a superior “growth rate” for the red M&M’s. If I do this repeatedly as
mimics biological reproduction generation after generation in time all that’s
left is the basket are the red M&Ms. Try it yourself to see! Even the
legion of double talking assholes on Fox News doing this experiment will see
that the red M&M’s have been naturally selected and the green one’s “gone
extinct” because of their different growth rates. Note that there is no
intelligent design of this outcome of which color of M&M’s survives in the
basket, just relentless application of the differential growth rate dynamic of
natural selection.
The general validity of the natural selection dynamic made clear, let’s return now to the fitness function of Eq920 as F_{1 }= b_{1}−d_{1}−b_{2}+d_{2} applied to living populations to make clear the nuts and bolts of how the population with the greater growth rate succeeds in persisting over evolutionary time. Unarguably the population that has the greatest g growth rate and, hence, positive F fitness, say population #1 with F_{1}>0, wins out. But how do the members of population #1 behave so as to make F_{1}>0? To maximize the likelihood of F>0 for any population, its members should behave in a way that maximizes F. And for the members of population #1 this means behaving so as to optimize the variables in F_{1 }= b_{1}−d_{1}−b_{2}+d_{2} by maximizing b_{1} and d_{2} and minimizing d_{1} and b_{2}.
An organism behaves to minimize its population’s d_{1} death rate by trying to stay alive as long as it can. That’s why being in the cold, feeling cold, is an error for the organism felt as something unpleasant to get rid of and avoid. The value of staying warm then, from the F fitness function, is that it keeps one alive. This makes it clear that one source of the pleasure in and value of money is in its enabling survival behaviors including its enabling one to purchase food and shelter as directly affects the life span of the organism and by extension the minimization of its population. Note that “errors” in survival, like lacking food as causes hunger, are generally unpleasant as prompts activity directed to eliminate the error and its genetically associated displeasure.
The F_{1 }= b_{1}−d_{1}−b_{2}+d_{2} fitness function is also maximized when the b_{1} birth rate of population #1 and d_{2} death rate of rival population #2 are maximized by behaviors of the members of population #1.These evolutionary drives driven by our emotions of sex and violence are difficult to discuss because sexual and violent behavior is very much affected beyond the instinctive emotions that influence it by significant cultural restrictions on sexual and aggressive behavior. It is obvious from the simple algebra of the F fitness function and from the M&M experiment that having a high birth rate helps make for a successful population. The intense pleasure of sex that drives this is the origin of male lasciviousness, the curbing of which via the sexual mores of a culture, though, also contributes to the survival of a population without our getting into the details of the mechanics of it. And the pleasure of murdering a rival for resources, space and mates derives from the same source of optimizing evolutionary fitness whatever the cultural sculpting of it that glorifies violence under some circumstances and condemns and punishes it most severely under others. The main body of the text in Section 14 gets into these matters in greater detail. The point is that the F fitness function directs us by pleasure and pain to survive, to reproduce and to compete, sometimes mortally.
The naturalness of violence especially in men, in a way the main topic in this thesis, is further clarified by explaining natural selection in evolution as a feedback control process that moves inexorably towards a quantifiable end point while eliminating a welldefined Ԑ error. Understanding evolution in that way will make super clear how the cybernetic characteristics of natural selection get so easily confused with the cybernetic characteristics of cognitive selection so as to attribute evolution to the intelligent design of a super powerful person, be it our God the Father or the equally delusional Allah of the Muslim humanoids. This is very important to make clear for the retaining of an unseen god in one’s thoughts as an agent that makes real things happen magically is totally destructive of the sensible thinking (based on your senses) needed to solve the terrible problems that confront mankind individually and collectively as include the unhappiness of wage enslavement and the possibility of nuclear annihilation.
Natural selection is passive feedback control that aims at an end point of ecological uniformity or zero diversity for taxa competing for the resources of a common niche. To see this requires the introduction of a mathematical function for diversity called the Simpson’s Reciprocal Diversity Index.
923.)
Consider a niche occupied by with N=3 competing populations that has a K=1000 carrying capacity. Its population #1 has x_{1}=200 members, population #2, x_{2}=300 members and population #3, x_{3}=500 members. Each population can also be specified quantitatively in terms of its population density,
924.) p _{i}= x_{i}/K
Population #1 has a population density of p_{1}=200/1000=.2; population #2 of p_{2}=300/1000=.3; and population #3 of p_{3}=500/1000=.5. The diversity of this niche is thus from Eq923
925.)
The densities of N balanced populations, all with the same x_{i} size, are p_{i}=1/N. And their diversity with 1/N substituted for p_{i} in Eq923 is
926.) D = N; balanced
Hence the Simpson’s Diversity Index is just the N number of populations reduced by the imbalance in their sizes as it is for our example set of N=3 population that has a diversity index of D=2.63. When these N=3 populations have different growth rates of, say, g_{1}=1.6, g_{2}=1.4 and g_{3}=1.2, they inherently compete over time until population #1 with the largest g growth rate wins out in the niche according to a function derivable from Eqs262&263 in Section 14 of
927.)
With x_{i0} as the initial sizes of the N=3 populations given above, the competition proceeds as below with population #1 in blue, population #2 in green and #3 in green.
Figure 928. Natural Selection in an N=3 Population Competition
The abscissa of the graph is time in years and the ordinate, the x_{i}
size of the populations. What we see is that population #1 comes to occupy the
entire niche and that the other two populations die out in time. The N=1
population that triumphs in the competition has from Eq926 a diversity index of
D=1, no diversity at all. One can also develop the D diversity in the niche
from Eqs923,924&927 as a function of time as graphed below, which also
shows the end point diversity to be D=1.
Figure 929. Diversity vs. Time for the Natural Selection in Figure 928
The D=1 diversity is the end point or set point diversity of this natural selection process, best written with the S subscript as D_{S}=1. This D_{S}=1 is the end point of every natural selection process that occurs with the Ԑ error eliminated passively in this passive feedback control process of natural selection being
930.) Ԑ = D_{S }–D =1 − D
Ԑ is eliminated, made to be Ԑ=(1−D)=0, by generation after generation repetitive processes of competitive survival, reproduction and combat won by the population with the greatest g growth rate. This was also made clear earlier for the N=2 case in Figure 921 where again only N=1 population with diversity D=N=1 occupies the niche in the end. This tells us that natural selection can be added to our growing list of processes that operate via movement towards a quantifiable end point and the elimination of some form of Ԑ error as we progressively show that every process in nature can be understood as cybernetic and unified from that common feature.
We can further unify processes by identifying all change other than purely mechanical or kinematic not just as cybernetic but also evolutionary. The logic of it is very direct. Everything that exists had to come into existence at some rate, its effective birth; and, except for an eternally stable item, go out of existence at some effective death rate. Religions do this and nations do it and biological species do it and cultures do it and molecular species do it and businesses do it. Do what? Compete actively or passively with parallel forms to continue to exist at the expense of their rivals.
If this notion of general evolution seems excessive outside of biological and cultural evolution consider the evolution of competing molecular populations in the in vitro transformation of amorphous calcium phosphate (ACP) to crystalline calcium phosphate or hydroxyapatite (HA) as mimics bone and tooth maturation in animals including man. This is described in detail in Section 18 where it is shown that both the ACP and the HA have a precipitation constant, b, that specifies the rate they come into solid phase existence and a dissolution constant, d, for the rate they go out of existence as solids. In this transformation the HA molecular species, which has the larger growth rate constant, precipitation minus dissolution, increases its number of crystalline molecules autocatalytically to eventually become the only calcium phosphate moiety in the mix while the ACP with the lower growth rate constant goes completely out of existence.
This section is worth reading because it shows evolution to
be a very general process spelled out with the simplest mathematics and that
efforts to deny its reality by the right wing is stupidity at a level even
beyond denying global warming in the face of endless floods, fires and
tornados. It is also worth reading for its clarity on the recommendation of a
leading American mathematician, Dennis Sullivan,
the National Medal of Science winner in 2004.
Mon, 27 Feb 2006 23:50: why not publish the part that explains Posner's data in terms of the logistical equation first... then do some of the rest next... etc... then as your acceptance takes hold do the more radical parts...as it is you may be preempting any real success by indulging your own deeply felt philosophy... by the way your explanations in the first parts were very clear....you may want to read how Einstein in similar and simple layman's terms dispelled the notion of absolute time in the 1905 paper....and how he did it without being untoward...
good luck
dennis Sullivan
If not entirely in response to Sullivan’s admonitions we tried over the last
decade to become less “untoward” towards some of the bonehead academics we’ve
come across while trying to educate them with math as correct and clear
as 2+3=5. But it’s not that easy to be nice to dumb jackasses posing as
scientists. Most recently I tried to explain to
the science faculty of Colorado State University at Pueblo (CSUP), that all of
nature  physical, biological and human  can be understood in a mathematically
unified way in terms of the Ԑ error
function of feedback control systems. But this CSUP crew led by Frank Zizza,
Chairman of the Math/Physics Dept. there, is a perfect example of the worst
that university teachers have become in America, most of them memorizers
incapable of understanding anything other than what they can regurgitate from
the textbooks they ground their way through in school to get their degrees and
positions.
Worse than that as regards the welfare of the students at CSUP as I make clear at the end of Section 17 one of these I got into an email exchange with is a strong bet to be your typical position empowered dominant closet fag predator. This crew epitomizes an American academia that truly stinks in caring more about paychecks, position and power over students than scientific truth. It’s bad enough that our American media has evolved into hard science deniers, Fox News leading the way. But that the science profession as a whole just sits there with its mouth shut so passive at this critical time for America looking for all practical purposes like the bunch of laughable beanie babies in The Big Bang Theory is utterly unforgivable.
Professionals ignoring innovative science that clarifies the cause of the violent troubles plaguing America today puts them at the level of the monks in medieval universities who rejected Copernican science that contradicted the dogma and ideology of that day to please the ruling class of the day. For this modern era is no freer than any of the serf and slave based societies seen in human history including our professional class equivalent of the castrated obedient scribes that served the emperors of China and the pharaohs of Egypt for thousands of years. It’s right out of the South Korean masterpiece, Snowpiercer.
Well that’s enough of a smoke break from the math writing. It really does helps the rebel in you. That’s why for the last 50 years since the late 60s rebellion (which was much more against the warmongering capitalist system than for same sex marriage) they locked up people who smoked weed, locked them up in a cage where as you know if you’ve ever done time, even if just for stupid stuff, they torture you until the rebel in you is killed and you become a “normal” wage slave who lives off delusions like a gloriously happy life after death as compensation for the pain they put you through in life before you die. Gives you that occasional boost you need to temper the downside of the obligate paranoia needed to keep you aware enough of actual reality to keep on plotting against the regime and to keep on avoiding their agents. Who are many, anybody with police power, including in many venues as the experienced rebel knows, managers of the nostar motels we flit around in, like the managers of the Santa Fe Inn in Pueblo, CO, whose gross obesity and ugly faces betray their ugly predatory inclinations. Like they say in the Matrix movie, when you see such effective police agents don’t hang around too long.
Fuck the Orwellian ruse of ISIS as every American’s worst enemy. Our hearts and spirits are murdered everyday by smiling sadists right here at home like the boss who never has to tell you he has Trump’s “You’re Fired” hanging over your head to kick your ass in daily with the threat. Speaking of whom, somebody should tell Boss Trump that he won’t win in the third party bid he’ll have to create without picking up more than a few progressive votes. And that the best way to do that is to use his quick if avaricious mind to understand that we have to get to A World with No Weapons or we all lose big. It’s a long shot tricky maneuver given that Trump’s not exactly Mother Theresa. But with nuclear annihilation as the worst thing that can happen to us and not at all that unlikely, if the light clicks on in this smart moneymaker’s head, the NoWeapons Party ticket for 2016 of Graf and Trump might could make it to the White House. Who better to make a deal with Putin to set aside nuclear weapons once and for all? I used to think Elizabeth Warren might do the trick as you’ll read in material I penned earlier. But looks like the next woman president might best be me if the science community and Trump wake up on time.
Well, enough bullshit. I’m going to end this intermission
from mathematical analysis with the Orwellian bit I started the blog with first
but didn’t put on because I thought the truth of it too threatening to the
butchers up at the top who might find grounds to put 74 year old grandmother me
into the torture pit. As Orwell’s protagonist resurrected below might say,
kids, be willing to die to defend your happiness. It’s all you have in your
brief existence on the planet that’s worth anything. And do read on past my
Orwell blurb attempt at creative writing and the first bunch of math sections
to see how the nonviolent revolution I am proposing can actually be pulled
off.
A Geometry of Time: 2084
By Pete Peterson, PhD
Love was in the air or, I should say, on the air. Love was in the fast foods and JELLO commercials that beckoned you to eat them. Love was in the cars they beckoned you to be deliriously happy in. Love was in the pretend smiles of the women in the ads and talk shows and in the interminable giggling of the fauxhappy journalists who spun the morning news. Love was even in the laxative they said, with inappropriate musical accompaniment, was better than the other laxatives and in the toilet paper they promised would make you swoon with joy when you used it.
But beyond the applauded samesex and other substitute relationships of the 3^{rd} Millennium, love was not to be found, not on a springtime walk or in any place real except the minds of a few young men in 2084 America who had managed to escape the systematic psychological castration used to tamp down rebellion against this Disneyland Hell whose control of information was so complete that the adult humanoids who watched TV endlessly in their off hours to forget the pain of their enslavement actually believed the silly lies broadcast 24/7 that the miserable lives they led as wage slaves were happy, free and fair.
How to draw a true picture from this black hole of misinformation was in Dr. Peterson’s thoughts every moment as he struggled to avoid losing his own manhood and happiness. For though it was possible to run from the shackles of the regime for a short time, without any real intent or tangible plan to destroy the clockwork predation, it was impossible to avert succumbing to the unavoidable stream of institutionally applied slaps that eventually killed everyman’s vigor. Especially with the lock up in a cage reserved for the most resistant young men where pressure could be applied through torture disguised as needed correction for a criminal attitude that threatened, as blared 24/7 on TV, the security and happiness of all of society. From his training as a scientist who had been groomed for the junk food pampered enslavement of working in the technological sector, Dr. Peterson worked instead in hiding on an information weapon to kill the regime, a treatise that exposed the horror he called A Geometry of Time.
Extending technical work started 70 years earlier in A Theory of Epsilon Dr. Peterson came to mathematically explain the ways in which people in this America of 2084 were so tightly controlled cognitively as to turn them into humanoids with thinking completely rewired and stripped down from human instinct to what was efficient for a workplace machine part. Peterson was also sure it would explain the daily cluster of mass murders that young men caught up in the suicidehomicide provoking hell of the regime’s castration program were the perpetrators of. His approach was based on the passive feedback control of an RC circuit that he was well familiar with. Peterson thought hard about the Kirchoff’s Law expression for it we first brought up in Eq919,
919.) dq/dt = (1/RC)(q_{max}−q)
He saw that if you divide both sides of the equation by q_{max} you got
930.) dp/dt = (1/RC)(1 – p)
In the above p is the fractional or percent measure of the extent to which the capacitor in the RC circuit has been filled with charge, p = q/q_{max}. It can also be a similar percent measure of completion for any goal directed behavior a person may engage in as such making 1−p what’s left to do to achieve the goal, in essence a very general form of the Ԑ error of negative feedback control. In this representation, the C capacitance is understandable as a measure of “the size” of the task or goal aimed at: the bigger is C, the longer it takes to finish the task. And R is understood as the “resistance” to getting the task finished as derives from all the other factors that slow down finishing the task and getting p to p=1=100% and the error to Ԑ=1−p=0.
So eliminating the Ԑ=1−p error or what you have left to do is a simple and inarguable way of describing how one attains a goal. This generalizes all goal directed behavior as cybernetic in the sense that doing them eliminates or reduces the Ԑ=1−p error. The shape of the time course of an activity that expressly follows Eq930 is that of the green curve of Figure 917. Making the dp/dt rate of getting a job done a perfect function of the Ԑ=1−p error or what’s left to be done is, of course, a mathematical simplification or idealization in deriving it from the RC circuit equation. But the broader point to be made is that every goal directed behavior we do is directed to eliminating a Ԑ=1−p error from the person continuously working to complete the Ԑ=1−p remainder of what’s left to be done. And as we shall show later this is the case for every conceivable human behavior, goal directed or not.
This understanding of human behavior as cybernetic implies that our behavior functions automatically or in a machine like way much as does, by definition, every piece of feedback control machinery developed like the RADAR guided antiaircraft guns developed for use against the Luftwaffe in WWII that fired automatically. How is our behavior controlled by our nervous system automatically? Our central nervous system or CNS, which includes the brain and the network of peripheral nerves that flow into and out of it, operates generally in a negative feedback control way. But rather than give a minitreatise on all aspects of biological homeostasis, we just want here to stress how the CNS works automatically in machinelike fashion.
What you see, hear, smell, taste and feel, your basic senses, all derive from measurable physical properties as with visible electromagnetic waves of variable frequency and intensity for sight and waves of air molecules of variable frequency and intensity for sound. One property of your nervous system that affects the information you get about the objects and events in your environment is the intensity of the incoming (afferent) sensory signals. Very low intensity inputs, we humans just don’t sense. Nerve impulses for them just don’t make it all the way to the brain. Understanding this properly will make it clear that we do not decide what to do on the basis of “free will” but rather act automatically like a machine.
At night time visual energy from objects has a much lower
intensity and very low intensity objects are just not seen. The threshold of
energy needed to register sensory data in an organism’s brain is different for
different species, an owl, for example, seeing objects at night that a human
doesn’t see. Shortly we’ll mathematically explain how the CNS disregards insignificant
energy input for the right wing taffy pullers out there skilled enough in
rhetoric to successfully argue that a fish’s ass is twice as morally powerful
as the hypotenuse of an oblique triangle. But let me begin with a textbook
illustration of a nerve impulse. Bear up with the neurophysiology lecture for a
moment that will be easy to follow because I’ll be talking only about one small
part of a nerve impulse.
Figure 932. Diagram of a Nerve Impulse
The “threshold of excitation” tag tells us that only nerve impulses with energy
above a certain level discharge sufficient to get the neural signal all the way
to the brain. You don’t sense the insignificant sensory inputs because they
never make it to your brain. This evolutionary design of the CNS makes a great
deal of sense pragmatically because little objects that reflect few light rays
from the sun to your eyes generally speaking can’t do you much good or much
harm, so why even see them or notice them?
What does get to the brain then goes on a roller coaster ride of information processing (details given later) that often causes the brain eventually to send neural signals in the opposite (efferent) direction, out to your muscles, which gets you to move about and speak. Not all of the efferent nerve impulses make it to the muscles. The insignificant one’s below threshold die out and cause nothing to happen.
This sense of neural significance versus insignificance
is important to understanding how and why we do what we do. It shows up at
higher, conscious levels in a way that can be spelled out mathematically. Information as processed by the human mind has measure
in the D diversity index of Eq923 interpreted more broadly than ecological
diversity as the number of significant subsets in a set. This is
covered in great detail in Section 3 towards Eq17. That the human mind
routinely operates on significance factors is made clear with the three sets of
colored objects shown below, each of which has K=21 objects in N=3 colors.
Sets of K=21 Objects 
Number Set Values 
D, Eqs923&924 
Rounded to 
(■■■■■■■, ■■■■■■■, ■■■■■■■) 
x_{1}=7, x_{2}=7, x_{3}=7 
D=3 
D=3 
(■■■■■■, ■■■■■■, ■■■■■■■■■) 
x_{1}=6, x_{2}=6, x_{3} =9 
D= 2.88 
D=3 
(■■■■■■■■■■, ■■■■■■■■■■, ■) 
x_{1}=10, x_{2}=10, x_{3}=1 
D=2.19 
D=2 
Table 934. Sets of K=21 Objects in N=3 Colors and Their D Diversity Indices
The N=3 color set, (■■■■■■■■■■,
■■■■■■■■■■,
■),
(10, 10, 1), has a diversity index of D=2.19, which rounded off to D=2 implies
D=2 significant subsets. And that further implies that the one
object purple subset is insignificant in its being the smallest subset
that contributes only token diversity to the set. In contrast the D=3, (■■■■■■■,
■■■■■■■,
■■■■■■■),
(7, 7, 7), set has 3 significant subsets, red, green and purple as does the (■■■■■■,
■■■■■■,
■■■■■■■■■),
(6, 6, 9), set when the D=2.88 diversity of the set is rounded off to D=3. A
more intuitive sense of the mind’s automatic evaluation of significance and
insignificance is had by manifesting the K=21, N=3, colored object sets in
Table 25 as K=21 threads in N=3 colors in a swath of plaid cloth.
(10, 10, 1), D≈2 
(7, 7, 7), D=3 
(6, 6, 9), D≈3 

A woman who owns a plaid skirt with the (10, 10, 1), D≈2, pattern on the left, as I do, would spontaneously describe it as her red and green plaid skirt, omitting reference to the low density insignificant threads of purple in the plaid. She would make this description automatically without conscious consideration because the human mind just does automatically disregard the insignificant. And it does this, indeed, not just in its peripheral if any visual sense of the insignificant but also in our automatically not verbalizing the insignificant. This verbalization of only the significant colors in the plaid should not be surprising given that the word “significant” has as its root, “sign” meaning “word”, which suggests that what is sensed by the mind as significant is signified or verbalized, while what is insignificant in not being sensed or noticed isn’t assigned a word in discourse or in thought. Another example would be of minorities with few people in them like “South Sea Islanders” being omitted as separate groups on a census.
Insignificance is not only disregarded by the CNS when afferent or sensory but also when it is efferent. Only when neural signals sent by the brain to the muscles are over threshold do they reach our muscles to cause behavior. The neural impulses, which can be complex in origin, must be over threshold to get us to act. Playing the dice game in A Theory of Epsilon for a penny rather than V=$60, for example, though there is some prize, it is so insignificant that it is not acted on whatever the specifics of the neural mechanism that causes that inaction. It is enough to understand the CNS controlled behavioral system being as automatic as the propagation of nerve impulses as automatic, propagating those over threshold but dying out for those that are subthreshold or insignificant.
In the debate over “free will” this makes it clear that while “decision” is important, it is not determining. While a million Americans decide to go on a diet every day, more than half over the age of 25 are obese and that is because once the neural impulses go over threshold, the displeasure of not eating and anticipated pleasure of shoving that ice cream or pepperoni pizza in your mouth, you do it as cybernetic machine like as nerve impulse propagation generally, as 100 million pathologically obese Americans will attest to. The psychobabblers, even the fat ones, will argue that you can “decide” otherwise. But motivation for successful dieting comes in the form of having strong competing goals to binge eating, like very much wanting to look good at the beach, stress on “very much.”
One concludes from the above that people are basically automatic machines (made of biological cells rather than metal parts) designed by evolution to optimize the F fitness function as their set point in order to succeed in persisting over time from generation to generation. This is not to say that humans have no “control” over what they do. But that is only by understanding the causes of the overthreshold neural impulses that bring about behavior.
And that is exactly what Dr. Peterson said in his A Geometry of Time to the young people of 2084 and the handful of adults yet salvageable. He first explained how the human machine works instinctively and then how the ruling class takes advantage of the natural mechanisms to control the subjugated population’s behavior much to their detriment and sorrow as you can read about in detail in all that follows starting with the problems of this present time in history, 2015, that must be solved.
UNKILLING THE MESSENGER: THE BALTIMORE RIOTS AND BEYOND
The obvious message in the Baltimore riot photo is that these people are angry
about the police murder of Freddie Gray. It’s not just the fellow smashing the
window whose anger is released in this act of destruction. It’s the people
behind him, too, along with the thousand others who helped tear Baltimore
apart. And not just because of the killing of this one man but because they
all, as with millions of others across America, black and white, have been the
target of police abuse in one form or another. That’s the message the media
incessantly kill, that the police are predators on nonprofessional people
effectively making America with its highest lockup rate in the world and in all
of human history a police state.
Oh, no its not, say the journalist, politician and clergy mouthpieces of the ruling class who control the media message. The people who trashed Baltimore are thugs, bad people who used Freddy Gray’s death in police custody as an excuse to steal and destroy property for no sensibly justifiable reason. These are two very different messages. It matters a lot which of them is understood to correctly represent reality. It matters a lot which one people believe is true.
This is Hiroshima, 1945, right after the bomb fell. The utter destruction of
that city many years before the Baltimore riots came from the same emotion, the
violence from man’s evolutionary heritage intensified by the unhappiness caused
by civilization’s inbuilt restrictions and exploitation. Hiroshima’s can happen
again and on a scale that terminates the human experiment. For that reason it
is important to get the message right. What is the true nature of man,
especially as it concerns his [propensity towards violence? What is his
predictable fate? Only in getting the message straight can we find the way to
prevent more Baltimore’s, more Sandy Hook mass murders, more police murders, by
and of them, and more Hiroshima’s.
We are going to show which message is correct using science. We’re going to prove it with a mathematical argument that is logical and trustworthy and starts off in a somewhat different place than cybernetics. Now there are some out there who think God is above mathematics in being able to make 2+3 be equal to something other than 5 if He wishes. Such people believe whatever anyone in authority tells them, be it God, the media or the police. The violence in the world that threatens to end it will not be quelled with the help of such stupid people who are beyond sensible arguments that even an elevenyearold can understand. Indeed, let me introduce you to this mathematical take on violence and what to do about it with the help of one such elevenyearold.
One day in 2008 down in Acapulco, Mexico, while in retreat there from the Bush regime of 20002008, my grandson, a dropout in attitude but with a high speed curious mind, asked me: How did they measure distance before rulers and such were invented, Gram? They measured distance in feet with their actual feet instead of with one foot rulers, I answered. If you wanted to know how long a road was in ancient times you walked the distance off, one foot pressed in front of the other, while counting the number of feet you walked off.
Champ, the nickname we gave the boy at birth in hopes that fate would be kinder to him than most, quickly replied: But that’s not very exact because unless you had one guy measuring the distance of all the roads in an ancient kingdom with just his feet, the difference in the length of the feet of the different people who might be doing this measuring would lead to inaccuracy in the distances measured.
Smart kid, a bit lazy like I said, but with a very quick mind. For that is very true and, as we shall see, the basis of an elementary correction in mathematics that configures science differently. That includes not only revising thermodynamics to clarify the centuries old mystery of entropy but also the human sciences to mathematically clarify the emotion of anger and how to tamp down violence and the horror it causes domestically and in war. To see the unarguable connection between extreme violence and tyranny and the inexactness in the count of things unequal in size you have to do the homework needed to follow the mathematical argument.
A count of things unequal in size, of people’s feet with different lengths or of molecules with different speeds, is inaccurate or inexact. Early humans took care of the inexact distance problem when they replaced people’s anatomical feet as measures of distance with foot long rulers, all of whose feet, unlike people’s feet, are the same size and whose count is, hence, exact. The problem of inexactness in counting things unequal in size goes beyond the distance measure problem, though, and is troublesome even today for a proper understanding of physical nature and of human nature.
Count the number of objects in (■■■■). There are 4, of course. Now count the number of objects in (■■■■). There are also 4, you answer quickly. But is that count of 4 for (■■■■) an exact count? No more than a count of the number of feet an ancient road is long is exact when the feet walked off are of different sizes. This problem of inexactness is why the concept of entropy has remained so difficult to understand for so long. And it’s also why the psuedoscience of psychology is as vague in explaining human nature with its elusive psychobabble as Christian dogma is in explaining the birth of God Jesus with the Virgin Mary’s magical, biologically impossible, nosex pregnancy.
Perhaps it was God, the Father of Jesus, who slipped it in with Mary so fast asleep she didn’t notice? Or perhaps the Devil did the dirty work with Mary not as asleep as she pretended to be?
Excuse the blasphemy. The point I’m trying to make with this joke on the Pope and His followers is that supervague notions like God’s ability to shit without needing to wipe His Ass, Satan’s evil and the ever mysteriously caused disease of “mental illness” don’t give rational cause and effect explanations for the mass dysfunctional behavior, unhappiness and violence we see in modern times. True believers in psychology should question its validity as an authoritative science right from the getgo in psychology giving a pass to all the nutty superstitions of religion as acceptable thinking for welladjusted people. Psychology’s failure to label praying (talking to a personality nobody can see and asking a favor of it) as delusional, even if emotionally comforting, is quite contrary to how all the other sciences, the ones that make our computers and fly us to the moon, operate. Can people be so blind as to not see that psychology acts consistently like religion, as a moral code whose central preachment is that disobedience to and revolution against the authority of the ruling class is wrong?
Holding the misleading notions of religion and clinical psychology in one’s mind as firm truth makes impossible a causal explanation of the bad things that happen in life, like today’s epidemic unhappiness from failure in love, and, thus, impossible to correct. Resolving the error in counting inexactness gets science spruced up enough to properly explain not only complex physical phenomena like entropy but also today’s epidemic unhappiness and the violence it brings about and what can be done to eliminate the worst of both the unhappiness and the violence. If this sounds like bullshit at least as doubtful as Mike Huckabee’s promise that an electric bass playing fundamentalist minister in the White House would bring God’s favor upon America, you have the read the God damned mathematics. Before Newton’s mathematical theory of gravitation was accepted, everybody in medieval Europe, rich and poor, educated and peasant, believed as firmly as the sun rising in the East each morning that angels commanded by God pushed the planets around in their observable orbits.
The problem with resolving today’s contentious issues with mathematics, though, is that the scientists who do understand mathematics fluently are effectively paid off in pay and status to avoid speaking out on matters that cast doubt on the benevolence of the ruling class and that the little people who take the greatest hit from their lowly position on the totem pole see mathematical language as readable as Transylvanian Bulgarian. All use basic math and trust it without question when it comes to adding up the groceries at the checkout counter and computing the dent the grocery bill makes in one’s weekly paycheck. But the article about whether Kim or Taylor’s cute ass is the cuter is invariably read with more interest than a mathematical explanation of life’s pains, even if the latter can clearly explain their cause and what can be done about them. To get around such math phobia I’ll start off in this new area of mathematics minus the equations that give the math haters indigestion. That should give the math compromised the gist of the argument if not the proof while also encouraging the more educated readers to go on to the Section 1 where we begin the mathematical analysis needed to nail the truth down in an unarguable way.
Ancient peoples had to develop standard measure devices like twelve inch foot rulers or they would not have been able to make the impressive things they came to construct in centuries past like the pyramids.
If the building blocks of a pyramid aren’t made exact in size with standard measure, they won’t fit together well enough to make a pyramid. Another thing needed was a lot of people, all guys back then, to do the backbreaking work to make the pyramids the pharaoh used to glorify himself. Was it slaves who made the pyramids? Whatever the spin put on working class life in ancient Egypt, one thing for sure was that there was a lot of slavery around back then, in Egypt and Babylon and Persia and then Rome and Greece and then in the medieval Christian Europe that fueled itself on the labor of its jillions of serfs and slaves and then in the precivilwar Southern states of America.
Not only are people made miserable being under the thumb of a slavemaster mentality ruling class, but also, hard truth be told, women, of which I am one, are not impressed by men who are slaves and have the welladjusted slave mentality. I’m not saying women lack admiration for slaves who have the balls to resist their enslavement by rebellion or flight. Three large cheers for any Django Unchained type who retaliates on his masters with guns blazing. But run of the mill male slaves that suck off their master to avoid a whipping or get a meal, women do not turn on to or fall in love with. With sincere apologies to the sensibilities of my suffering black brethren, Thomas Jefferson’s black slave mistress, Sally Hemings, much preferred screwing President Jefferson by whom she had six kids than the niggers that Jefferson owned as slaves who picked his cotton and cleaned his toilets.
Excuse the word nigger that I use, as has Pres. Obama, to hammer home an important point, namely that slavery, in any and all of its forms, be it plantation or modern wage slavery, makes a nigger out of a guy, black or white, as makes a mess out of love. It doesn’t matter if you’re only the boss’s slave for just 40 hours a week. Women just aren’t attracted to men made jerks out of in this way. Not that a woman doesn’t give such men a try, for the female mind says instinctively in the absence of an emotionally healthy fellow, maybe this one will do. But in the end, after a couple of years and a couple of kids, the smell that lingers from hubby’s cleaning the boss’s toilet during the work hours, despite the gewgaws his salary might provide, eventually overwhelms the perfume of love. The initial glow of love she felt turns to contempt and eventually that overpowering urge to reject him unless the prospect of living alone in relative poverty comes to tolerate his noxious smell as the lesser of evils.
Now not only does slavery, in whatever Christmas paper the slave culture wraps it in, destroy love, but breaking up makes the male slave feel much like a dumb dog out in a pounding rain just happy just to have a bone thrown to him and not very prone to rebel against the subservient state that caused the breakup to begin with. Conversely, few things make a man feel more vigorous and strong than the love of a woman and prone as such to resist the slave state of existence.
The frustration and loss of love, then, is an effective emotional crippling of men that kills the rebel in them. The providence of this for the ruling class, so happy to have slaves who lack the rebel element in them, has made true love taboo. Sexually successful men are much more likely to rebel against control, which slants the culture morally sharply against their kind. On the one hand sexually dominant men are displayed to the girls in the media and in other ruling class controlled information outlets as devils with cruel and abusive horns. The word is out: stay away from this kind of men; they’re going to do nothing but hurt you, rape you, use you, abandon you, make you miserable. And girls who disregard these warnings are made to feel like inferior, stupid fools. What you want, they are told 24/7, is a nice soft squishy slave type guy who will commit to bringing home the bacon and to not fussing too much when you agree to have sex with him only once every two weeks with him on the bottom and your toy up his ass. It’s hard for the girl to avoid rejecting healthy men and choosing a jerk when every movie, sitcom and news article tells the girls to beware the aggressive male who might have any vigor in him to make things click.
And in recent times the “men are bad” campaign that Christianity has fostered for the last millennia has been ramped up by laws across America that make a lingering glance by a man attracted to a pretty girl liable to be taken as “sexual harassment” of some kid that could destroy his life as a “sex offender”, a fate not much worse than being crucified slowly. This broad antilove strategy imposed by the ruling class through its religious, psychology and politician mouthpieces also turns out to be hell for women in the end. Yes, you get to be a Queen in your teen years and early twenties, the slim girl with a practiced smile who tells the guys to get down on their knees for a sniff of the backside of her jeans. But in the later years it all comes back to haunt the women when they wind up with lives devoid of any intimacy and anybody to love them. Except for the company of other women, which, whatever its glorification these days, has great limits as you can see from the vast ocean of unhappy unattractive women over the age of 30, professional actress bitches on TV and in the movies, who are full of crap in everything they say and do and fake smile about, notwithstanding.
To sum up, wage slavery, along with its associated social controls and restrictions, is the reason for the pained epidemic of frustrated and broken love relationships. Failed lovers make better slaves. And, not incidentally my dears, women wage slaves make better whores for the bosses at work who bleed the last juice from the women in the labor force who lack strong loving men to protect them from asshole bosses emotionally and otherwise.
And, wait a minute, that’s not the end of it. For what comes ultimately from the unhappiness of slavery and the failed love it causes in modern civilization is the channeling of that unhappiness into aggression towards others. For passing on one’s unhappiness to others, so often individuals who had nothing to do with causing the unhappiness, is a main way of mitigating your unhappiness, indeed, often the only way in highly controlled societies that don’t let you punch the abusive boss who caused the unhappiness in the face.
Such aggression towards innocent victims to tamp down unhappiness caused by an institutionally protected tyrant is termed redirected aggression. It is so common in life that we take it for granted. And beyond the petty meanness it causes in day to day existence it is the real reason for the mass murders endlessly seen in the news that are persistently touted as having no discernable motive. We just have no idea, say the TV journalists, why the guy killed his wife and his neighbors or the kids at the elementary school or his boss and coworkers. The possibility that the fellow was unhappy enough to crazily kill for the aforesaid reasons of the pain of being a jackass wage slave is never considered though his unhappiness is utterly obvious if one even lightly scratches below the surface of the story. God forbid that his unhappiness and violence might come from the life he’s forced to live in today’s hyper1984 societies. The fellow who mass murdered the 150 people by driving the airplane into the Alps? The scary looking Adam Lanza who murdered all those second graders at Sandy Hook Elementary? These and the rest of their kind are just the extreme tip of the iceberg of unhappy individuals sideeffect manufactured by our highly ordered society. Killing others makes them feel better than doing nothing at all. It reduces the unhappiness in them that comes from the humiliations and restraints of wage slavery and its effect on the possibility of them finding and keeping love.
Redirected aggression emanates not just from an unhappy individual but also from an unhappy group of people. Hate and violence fostered by the unhappiness of civilized life spills across national borders as a significant cause of war. Nothing better than having a foreign enemy with different values and beliefs to hate and kill to distract people from the unhappiness caused them by the rule they live under in their own countries. And these dysfunctional emotions of redirected aggression that make nations prone to war can cause the very worst for mankind when nuclear weapons are in the arsenals of aggressor nations. Doesn’t it make sense that a person as enthralled with mass murder as Adolph Hitler was had to be an unhappy man to begin with, a nut in that sense? And if Hitler had nukes to use, need we question whether or not he would have used them? Can’t we see the dangers in the endless bloodletting in the Middle East and in the Ukraine as to where these might escalate once real weapons of mass destruction come into play? Are people so pacified in their thinking not to see the ease with which a nuclear player backed up against the wall and facing impending defeat by a hated enemy might use his nuclear weapons?
There is only one sensible solution. The people have to get rid of the weapons before the weapons get rid of the people. Two profoundly good things come out of this. For one, it’s very hard for one person or one group of people to control others significantly without weapons. The ruling class in America ultimately controls the subservient population with police who enforce laws written by legislatures owned through campaign contributions by the wealthy ruling class. The police ultimately keep the people in line with weapons. Get rid of the weapons and you get rid of the tyranny. And, of course, getting rid of the weapons also gets rid of the horrors of war.
Now you have the gist of the main idea minus the mathematical proof of it. You say you don’t like this picture as too strong a condemnation of the free and fair America you love so much? Or you don’t like the solution of eliminating the weapons as too idealistic or against citizens’ constitutional right to own weapons and use them against bad people who deserve to be shot dead? Or you think this attack on the religious ideas that blur the reality is sinful or on psychology crazy? Well, that’s what the mathematics is for. It makes perfect sense out of these controversial issues to anybody who believes that 2+3=5 provides truth that can’t be denied.
As to actually achieving A World with No Weapons to solve the problem of violence, it’s just a matter of convincing Russia, the world’s other dominant nuclear power, that any war between us two big guys on the block is the end of the game for both of us and for all of us. This is not impossible, for the Russians have produced some of modern history’s top mathematicians and trust in science, whatever our endless vilification of Putin, at least as much as evolution denying America does. Then working with Russia, our two nations can convince the rest of the world, which we two dominate weapons wise, to give up their weapons, or be destroyed by our two nation coalition if they should refuse to give up their weapons. Other nuances of this utterly indispensible Utopia, achievable with great effort and a small miracle or two, are spelled out at the end of the nonmathematical Section 15. And the mathematics that shows how indispensible A World with o Weapons is for mankind’s avoidance of extinction is also indispensible, for people are not about to drop whatever they have felt is so important in their lives to dedicate themselves to a movement for a mass weapons ban without some form of tangible proof that it absolutely must be done to avoid the mass death of themselves and their kids and grandkids.
We begin such mathematical proof with a discipline called information theory. It will take us back in a formal way to our original the problem of inexactness in the counting of things unequal in size and help to develop a solution to that technical problem. Information theory is the science of the digital, synthetic, information that computers run on as distinct from the meaningful information that the mind runs on. This inability of information theory to develop mathematical specifications of meaningful information is a major shortcoming of it as is made clear in a June, 1995, Scientific American article, From Complexity to Perplexity:
Created by Claude Shannon in 1948, information theory provided a way to quantify the information content in a message. The hypothesis still serves as the theoretical foundation for information coding, compression, encryption and other aspects of information processing. Efforts to apply information theory to other fields ranging from physics and biology to psychology and even the arts have generally failed – in large part because the theory cannot address the issue of meaning.
It is most important to solve this problem because the greatest impediment to mankind avoiding an annihilating nuclear war is our failure to correctly understand the mind’s information processing operations which include man’s propensity for violence that is so dangerous in this era of nuclear weapons. The solution to this problem shown by the mathematics to be A World with No Weapons must begin in the United States and must have political muscle to succeed. To that end we strongly urge support for Elizabeth Warren in 2016 as the only candidate who is honest and caring enough about people to lean in this direction.
She stands in contrast to Hillary Clinton who merely as an astonishingly good actress pretends to care about people. Further it is important to understand that beyond her genius as a politician during campaign time, Hillary is as stupid a thinker as she is disingenuous. Certainly hubby Bill Clinton gets the Blue Ribbon as the smoothest liar American politics has ever seen. Do you think that this smooth talker’s wife can possibly have a different mindset after four decades of mutual plotting and scheming to hold the public stage?
And it is so important to have an intelligent person in the White House, for the repeated warnings of Vladimir Putin to use nuclear weapons if push comes to shove must be taken seriously in the absence of rapprochement with America. Hillary Clinton calling recently for more military assistance for Ukraine, (4/17/15), makes clear what a stupid she is in this most important issue of our time.
A sensible peace with Russia
and movement towards A World with No Weapons will not come about under Hillary.
That is for sure. Or under any of the Republican war hawks who might be
elected. That pointedly includes current Republican frontrunner, Jeb Bush,
whose blood relationship to the pair of assholes in the Bush monarchical
dynasty who contrived the War in Iraq strongly suggests a continuation of
maximum bloodshed in the Middle East with all that portends for eventual world
destruction, anybody who believes Jeb’s campaign denials of it understood to be
even stupider than Jeb looks. Once you understand the stakes, given Putin’s
determination to never back down to the US, Elizabeth Warren is the only sane
choice for president.
Those who wish to help start up a movement towards A World with No Weapons with
a donation of $20 can do so by clicking here. In asking for it we’re either Bernie Madoff in some very
mathematically elaborate sheep’s clothing or we’re the real thing. Read the
mathematical analysis that follows before you decide which. It provides a most
beautiful mathematical explanation of the human emotions and how man’s violent
ones can be tamed only by getting rid of weapons that make aggression so
horribly bloody. And for the resolute nonmath readers, to highlight the
underlying social causes of violence, there’s my personal story in Section 15,
“Revolution in the Garden of Eden”, that tells of child murders by my
cousin, Ed Graf, and my brother, Don Graf, both of them members of the
fundamentalist LCMS Christian sect I managed to escape from many years ago.
That’s cousin, Ed Graf, on the left pleading guilty in court to burning his
stepson’s to death to get insurance money, and lawyer brother, Don Graf, on the
right. And Section 16, “Waiting for the Bomb”, also provides some
nonmathematical material for the reader who wants to pass on the technical
analysis that begins below.
1. Some Basics of Information Theory
The central structure in information theory is the information channel or message channel diagrammed below.
The set of messages that can be sent through a particular message channel have mathematical representation in terms of their relative probabilities of being sent. Consider a message set consisting of N=4 color messages, red, green, purple or black, that derive from a person blindly picking one object from a set of K=12 objects, (■■■■■, ■■■, ■■■, ■), which consists of x_{1}=5 red, x_{2}=3 green, x_{3}=3 purple and x_{4}=1 black object. The probability of the color picked being red and of a message about it being sent to some receiver is p_{1}=x_{1}/K=5/12; that of green, p_{2}=x_{2}/K=3/12=1/4; of purple, p_{3}=x_{3}/K=1/4; and of black, p_{4}=x_{4}/K=1/12. The message set of N=4 color is specified in terms of these probabilities as [p_{i}] = [p_{1}, p_{2}, p_{3}, p_{4}] = [5/12, 3/12, 3/12, 1/12].
The
amount of information in a message is a function of the probabilities of the N messages,
p_{i}, i=1,2,…N. There are two main functions used for information in
information theory. The one used most often is the Shannon (information)
entropy.
1.)
The other important information expression in information theory, which is closely related functionally to the Shannon entropy, is the Renyi entropy, in logarithm to the base 2 form,
2.)
The key to understanding information as we ordinarily understand that word as information that has meaning for us entails understanding the Renyi entropy rather than the Shannon entropy as the primary function for information as follows. We note from the blurb on it in Wikipedia that the Renyi entropy is important in ecology and statistics as an index or measure of diversity. That is not surprising given that the nonlogarithmic part of the Renyi entropy is another longtime used measure of diversity in ecology and sociology, the Simpson’s Reciprocal Diversity Index,
3.)
This allows us to specify the Renyi entropy, R, in terms of the Simpson’s diversity index, D, as
4.) R=log_{2}D
An equiprobable message set for color would derive from a random pick of an object from a balanced set of objects like (■■■, ■■■, ■■■, ■■■), whose N=4 colors have equal probabilities of being picked and sent a message out about of p_{1}= p_{2}= p_{3}= p_{4}=1/N=1/4. Substitution of p_{i}=1/N in Eq3 obtains a simplified D diversity index expression for the balanced case of
5.) D = N, balanced
This is intuitively sensible as indicating that the diversity of a set of objects is measured by the N number of different kinds of objects, in (■■■, ■■■, ■■■, ■■■) as D=N=4 differently colored kinds of objects. Note how this also simplifies the Renyi (information) entropy as
6.) R=log_{2}N
Clearly R is a function of the number of color messages derived from random picking from the (3, 3, 3, 3) set of objects, (■■■, ■■■, ■■■, ■■■), namely, R=2 bits. In contrast the D diversity index of the (5, 3, 3, 1) unbalanced set of objects, (■■■■■, ■■■, ■■■, ■), and the message set derived from it is from Eq3 and its [p_{i}] = [5/12, 3/12, 3/12, 1/12], D=3.273, with a Renyi entropy from Eq4 of R=log_{2}(2.323)=1.71. Now we are not at the moment interested in the meaning of R, but rather that R is for all sets a function of the D diversity of the message set. This includes R=log_{2}N for the equiprobable or balanced case in which N is equal to D from Eq5 and can be considered a diversity measure for the balanced case also. Hence the R Renyi entropy as information is a function of the D diversity of the message set. This gives diversity a central role in information. Why is this? It has to do with the problem of exactness in counting things.
2. Counting
The simplest items in mathematics are the counting numbers: 1, 2, 3, 4, and so on. But counting isn’t as simple as it seems. Count the number of objects in (■■■■). You count 4 objects here, of course. Now count the number of objects in (■■■■). It is also 4 one says at a glance. But is that count of 4 an exact count?
There is something not quite right with counting the unequal sized objects in (■■■■) as 4. Counting 4 objects in (■■■■) should be understood to be inexact as follows. You remember the grade school caveat against adding things together that are different in kind like adding 2 galaxies and 2 kittens together. This caveat also holds for adding things or counting things that are different in size. Consider (■■■■) as pumpkins of sizes (5, 3, 3, 1) in pounds. Is the count of them of 4 pumpkins exact? A grocer selling the pumpkins would think not, which is why pumpkins are sold not by the pumpkin, but by the pound, all of which pounds being exactly the same in size. Four pounds is an exact enumeration of pounds because all pounds are the same size in weight while four pumpkins is an inexact count of pumpkins when the pumpkins counted are not the same size. This requirement of sameness in size for a count of things to be exact applies to all standard measure whether pounds, fluid ounces or inches. That is why standard measure underpins all commercial transactions unless things bought and sold are the same size, like large eggs, which are sold by a straightforward count of them, as by the dozen.
We make this point of inexactness in a count of things not the same size in a more rigorous way by next considering our set of K=12 unit objects, all the same size, (■■■■■, ■■■, ■■■, ■), divided into N=4 color subsets that are not the same size in having different numbers of unit objects in some of them. The K=12 count of all the objects is exact because the objects are “unit objects” all the same size. But the N=4 count of the subsets, on the other hand, is inexact because the subsets are not the same size in having a different number of unit objects in some of them. To make it analytically clear that there is some sort of error in counting the number of subsets in (■■■■■, ■■■, ■■■, ■) as N=4, we first formally specify the set as consisting of x_{1}=5 red, x_{2}=3 green, x_{3}=3 purple and x_{4}=1 black object or in shorthand the (5, 3, 3, 1) natural number set. The sum of the objects in each of the N=4 subsets is the K=12 total number of objects in the set, or generally for any natural number set,
7.)
For the (■■■■■, ■■■, ■■■, ■) set, the total number of objects is K = x_{1}+ x_{2}+ x_{3}+ x_{4 }= 5+3+3+1 =12. Now it is a simple matter to show that the N=4 count of the unequal sized subsets in (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), is inexact or in error with statistical analysis. The basic statistic of a set of numbers like (5, 3, 3, 1), here representing (■■■■■, ■■■, ■■■, ■), is the mean or arithmetic average, µ, (mu).
8.)
For the K=12, N=4, set, (5, 3, 3, 1), the arithmetic average is µ=K/N=12/4=3. That the µ arithmetic average is inexact is well made in 47 chapters of myriad examples in the modern classic, The Flaw of Averages by Sam Savage of Stanford. A more immediate register of the inexactness or error in the µ arithmetic average comes from noting that it is always associated with a statistical error measure, explicitly or implicitly, the most common of which is the standard deviation, σ, (sigma),
9.)
For the N=4, µ=3, (5, 3, 3, 1) set, the standard deviation is
10.)
Another commonly used statistical error is the relative error or percent error, r,
11.)
For the µ=3, σ=1.414, (5, 3, 3, 1), set, the relative error is r=σ/µ=1.414/3=.471=47.1%. The statistical error in the µ=K/N=3 arithmetic average of (5, 3, 3, 1), whether expressed as σ=1.414 or r=47.1%, implies a counting error in the N number of subsets parameter in µ=K/N. The K=12 count of the unit objects in (■■■■■, ■■■, ■■■, ■) in µ=K/N is exact because its K=12 unit objects are the same size. Hence the statistical error or inexactness in µ=K/N must arise from the inexactness in the N=4 count of the unequal sized subsets in (■■■■■, ■■■, ■■■, ■).
To further make the point of the straight N count of unequal sized subsets being inexact via the statistical error associated with it, we look at the µ, σ and r of the K=4 object, N=4 subset, “balanced” set of objects, (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), all of whose subsets are the same size, x_{1}=x_{2}=x_{3}=x_{4}=3. This set also has a µ=K/N=12/4=3 arithmetic average, but from Eq9, it has no statistical error, σ=r=0, which logically implies from what we just said above that there is no error or inaccuracy in µ=K/N for it and, hence, no error or inaccuracy in the K or in the N variables of µ=K/N. And this fits perfectly with our understanding of an exact count coming about when things counted, including the N=4 subsets in (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), are all the same size.
Now while the N=4 count of the number of subsets in (■■■■■, ■■■, ■■■, ■) is inexact, its diversity index of D=3.273 is an exact quantification of the subsets in the set. And this holds generally for any set, balanced or unbalanced. To see this, let’s formally define the p_{i} of a set in terms of the K and x_{i} of a set as
12.)
The two variables that p_{i} is a function of are exact, both the K count of the total number of same size objects in a set and the x_{i} number of (same sized) unit objects in each subset. From this perspective, D in being entirely a function of the p_{i} of a set in Eq3 is exact. Another way of appreciating the exactness in the D diversity index comes from understanding D as a statistical function. To do that we first express the σ standard deviation of Eq3 as its square, σ^{2}, called the the variance statistical error.
13.)
And then we solve this for the summation term to obtain
14.)
Now from Eq12, we express the D diversity index as
15.)
And lastly inserting the summation term in Eq14 into D of Eq15 obtains D also via Eqs8&11 as
16.)
This derives an exact D quantification of the subset constituents of a set as a function of their inexact N count effectively made exact by the inclusion of the r relative error measure of the inexactness in N in the function. This understands D as an exact correlate or substitute for inexact N that can be used in place of N as an exact quantification of the constituent subsets of an unbalanced set. And it further understands diversity, in its sense as an exact quantification of balanced or unbalanced subset constituents of a set, as what information is in the most general sense of the word. Let us back up a bit to make what we mean clear here. Earlier we made note that the R Renyi entropy is used in the scientific literature as a measure of diversity, a logarithmic measure of diversity. Now let’s also note that the Shannon information entropy has also been used in the scientific literature of the last 60 years as a measure of ecological and sociological diversity as called the Shannon Diversity Index, it’s configuring as a natural logarithm rather than a base 2 logarithm being irrelevant to the synonymy of information and diversity in the Shannon entropy as well as the Renyi entropy. Furthermore both the logarithmic diversities, Shannon and Renyi, and the linear diversity, D, are exact functions as defined above.
This strongly suggests that the D diversity index is information also. Later we shall prove this rigorously with a bit signal encoding recipe interpretation of D and with a Gödel based rebuttal of the Khinchin argument in its derivation of the Shannon entropy as the only correct form for information (along with the Renyi entropy generalization of the Shannon entropy). These tedious technical proofs, though, are delayed for the moment as too much of a digression from showing rather and first how the D diversity index is readily understandable intuitively as meaningful information.
3. Diversity as a Measure of Meaningful Information
Information as processed by the human mind has measure in the D diversity index
interpreted as the number of significant subsets in a set. The
exercise that follows will explain how the mind intuitively distinguishes what
is significant in its sense and memory of things from what is insignificant. We
illustrate with an item in the recent news about the makeup of the K=53 man
Ferguson Police Dept. at the time of the protest over the death of Mike Brown,
namely x_{1}=50 White officers and x_{2}=3 Black officers. Few
have a problem intuitively understanding the Black contingent of the Ferguson
P.D. to be insignificant (quantitatively) even without any mathematical
analysis. But D diversity index interpreted as the number of significant
subsets in a set makes the understanding of insignificance mathematically
precise.
The Ferguson P.D. as the number set, (50, 3), has from Eq15 a diversity of D=1.12, which rounded off to the nearest integer as D=1 implies that there is only 1 significant subset or subgroup in the department. Were the force made up in a more diverse way of, say, x_{1}=28 Caucasians and x_{2}=25 Blacks, the diversity of its (28, 25) representative number set of D=1.994 rounded off to D=2 would indicate that both subgroups were (quantitatively) significant. Returning to the actual (50, 3) makeup calculated to have a rounded diversity measure of D=1 significant subset, the x_{1}=50 preponderance of the White contingent suggests that it is the significant subgroup and, hence, that the x_{2}=3 Black officer subgroup is insignificant as can also be interpreted as its contributing only token diversity to the police force.
Before we continue this analysis, given the contentiousness of this issue, it should be made clear that considering the police as the enemy of a hoped for genuinely free and fair society is a mistake. Police are strictly the hired hands of the ruling class business and political leaders of communities that range in size from the small city of Ferguson to the entire USA. Police do not make policy. They simply execute it and do so on threat, like the rest of Americans who work jobs, of being fired and having their lives ruined if they fail to comply with the directives of the upper echelon in the American social hierarchy. There is no good cop, bad cop dichotomy, therefore, only a good leader versus bad leader differentiation. And this current crop of leaders in America are as disgustingly predatory, uncaring of the little people and deceitful as any ruling oligarchy you’ll read about in history. If you want change, that’s where you have to look for change, in the people at the top, not the cops who are the ruling class’s well controlled ultimate instrument of coercive control of the people.
That important political digression aside, let’s now continue the mathematical analysis of significance versus insignificance by showing how to assign a significance index to each one of the constituent subsets of a set. We will use the K=12, N=3, (■■■■■■, ■■■■■, ■), (6, 5, 1), x_{1}=6, x_{2}=5, x_{3}=1, set to introduce significance indices. We calculate from Eq15 a D=2.323 diversity index for this set, which rounded off to D=2 suggests 2 significant subsets, the red and the green, with the purple subset that is represented by only x_{3}=1 object in it understood as insignificant. To specify these attributions of significance and insignificance to each subset in a more direct way, we define next the root mean square average, aka the rms average, of a number set, ξ, (xi) as
17.)
The rms average squared, ξ^{2}, is
18.)
The ξ rms average of the K=12, N=3, µ=K/N=4, (■■■■■■, ■■■■■, ■), (6, 5, 1), unbalanced set is ξ =4.546 with ξ^{2}=62/3=20.667. And the rms average of the K=12, N=3, µ=K/N=4 balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), which we will use for comparison sake, is from the above ξ=µ=4 with ξ^{2} =µ^{2} =16. Next note from Eqs13,8&18 that the D diversity index can be expressed as
19.)
We define the significance index of the i^{th} subset of a set as s_{i}, i=1, 2,…N,
20.)
This obtains the D diversity as the sum of its s_{i} significance indices as
21.)
For sets, balanced and unbalanced, that have N=3 subsets containing a number of objects in each of x_{1}, x_{2} and x_{3},
22.) D = s_{1} + s_{2} + s_{3}
For the N=3, (■■■■, ■■■■, ■■■■), (4, 4, 4), set, x_{1}=4, x_{2}=4 and x_{3}=4, the D=N=3 diversity index of this balanced set from Eq5 alternatively computed from the above is
23.) D = s_{1} + s_{2} +s_{3 }= 1 + 1 + 1 = 3 = N
What D=3=1+1+1 tells us is that all N=3 subsets in having significance indices of s_{1}=s_{2}=s_{3 }= 1 are significant. Now consider the unbalanced (■■■■■■, ■■■■■, ■) set, whose subset values of x_{1}=6, x_{2}=5 and x_{3}=1 develop its significance indices from Eqs22&23 as
24.) D = s_{1} + s_{2} +s_{3 }= 1.161 + .968 + .194 = 2.323
What D= 1.161 + .968 + .194 indicates is that the x_{1}=6 red objects subset in having a significance index of s_{1}=1.161 rounding off to s_{1}=1 is significant; that the x_{5}=5 green objects subset in having a significance index of s_{2}=.968 rounding off to s_{2}=1 is significant; and that the x_{3}=1 purple object subset in having a significance index of s_{3}=.194 rounded to s_{3}=0 is insignificant. This analysis applied to the Ferguson P.D. situation has us interpret from the s_{1}=1.056 index evaluated from the above for the x_{1}=50 White cops and rounded to unity that they are (quantitatively) significant and from the s_{2}=.056 rounded off to s_{2}=0 for the x_{2}=3 Black cops specifies them as (quantitatively) insignificant.
That the human mind genuinely
operates with these significance functions, or some neurobiological facsimile
of them, is made clear in the next illustration of significance and
insignificance of the three sets of colored objects shown below, each of which
has K=21 objects in it in N=3 colors.
Sets of K=21 Objects 
Number Set Values 
D, Eq15 
Rounded to 
Significance Indices, Eq21 
(■■■■■■■, ■■■■■■■, ■■■■■■■) 
x_{1}=7, x_{2}=7, x_{3}=7 
D=3 
D=3 
s_{1}=1, s_{2}=1, s_{3}=1 
(■■■■■■, ■■■■■■, ■■■■■■■■■) 
x_{1}=6, x_{2}=6, x_{3} =9 
D= 2.88 
D=3 
s_{1}=.824, s_{2}=.824, s_{3}=1.24 
(■■■■■■■■■■, ■■■■■■■■■■, ■) 
x_{1}=10, x_{2}=10, x_{3}=1 
D=2.19 
D=2 
s_{1}=1.04, s_{2}=1.04, s_{3}=.104 
Table 25. Sets of K=21 Objects in N=3 Colors and Their D Diversity and s Significance Indices
The N=3 set, (■■■■■■■■■■, ■■■■■■■■■■, ■), (10, 10, 1), has a diversity index of D=2.19, which rounded off to D=2 implies D=2 significant subsets, the red and the green from their s_{1}=s_{2}=1.04 significance indices. And that also implies that the one object, purple subset is insignificant as reinforced by its s_{3}=.104 significance index as might also be interpreted as the purple set contributing only token diversity to the set. In contrast, the D=3, (■■■■■■■, ■■■■■■■, ■■■■■■■), (7, 7, 7), set has 3 significant subsets, red, green and purple, s_{1}=1, s_{2}=1, s_{3}=1; as does the (■■■■■■, ■■■■■■, ■■■■■■■■■), (6, 6, 9), set whose D=2.88 diversity rounds off to D=3 with s_{1}=.824, s_{2}=.824, s_{3}=1.24.
One gets the most intuitive sense of the mind’s automatic or subconscious evaluation of significance and insignificance by manifesting the K=21, N=3, colored object sets in Table 25 as K=21 threads in N=3 colors in a swath of plaid cloth.
(10, 10, 1), D≈2 
(7, 7, 7), D=3 
(6, 6, 9), D≈3 

A woman who owns a plaid skirt with the (10, 10, 1), D≈2, pattern on the left, as I do, would spontaneously describe it as her red and green plaid skirt, omitting reference to the low density and, hence, relatively insignificant threads of purple in the plaid. She would make this description automatically without any conscious calculation because the human mind just does automatically disregard the insignificant and, indeed, not just in its visual sense of it but also in its not verbalizing things sensed as insignificant. This verbalization of only the significant colors in the plaid swath of red and green should not be surprising given that the word “significant” has as its root, “sign” meaning “word”, which suggests that what is sensed by the mind as significant is signified or verbalized while what is sensed as insignificant and little or not at all sensed or noticed, isn’t signified or assigned a word in discourse or in one’s thoughts.
Our sensory perceptions are generally quite automatically affected by the magnitude of the sensory input, small inputs being insignificant and disregarded in our sense of them as with our lack of sensing or tasting salt added to a stew when it is just the slightest pinch of salt. This sense of the possibility of insignificant ingredients in a recipe when added in the smallest yet nonzero amounts is what gave me the conceptual germ of A Theory of Epsilon.
Quantitative significance is not just a characteristic of the size or quantity of things but also of the frequency of our observation of things and events. Consider a game where you guess the color of an object picked blindly from a bag of objects, (■■■■■■■■■■, ■■■■■■■■■■, ■). Assume that you don’t at all know the makeup of the objects in the bag ahead of time as you go about guessing and observing which colors get picked and in with what frequency. Then your sense of what colors are significant or insignificant comes only from the frequency the colors are picked from the bag (picked with replacement). And over time, as you see purple picked so infrequently that the purple color will come to seem insignificant in your mind as a possible pick and to also be disregarded as a color you might think likely to be picked. The human mind’s operating automatically to disregard the insignificant is an important factor for behavior because we generally think, talk about, pay attention to and act on what we consider significant while automatically disregarding the insignificant in our thoughts, conversations and behaviors.
From a sociopolitical perspective the development of one’s sense of the significance of some things and insignificance of others via media exposure a central aspect of propaganda and mind control because issues and opinions frequently disseminated through mass media and other ruling class information outlets are subconsciously taken to be significant to some degree and tend, as such, to take up much of one’s thoughts, conversations and behavioral considerations in contrast to issues, observations and opinions infrequently brought up or not at all broadcast, which become regarded, as such, as insignificant and effectively paid little regard if any at all.
In this way personally immaterial sporting events and entertainments along with political opinions with minimal factual bases come to be subconsciously thought of as significant, crowding out issues and interpretations of news events that are genuinely meaningful for people’s individual welfare, but in being shown infrequently or not at all, such as the daily abuse in workday life people take from all powerful bosses, become insignificant in discourse and in thought for people and in their intentions for future action. This does not come about by chance for people drugged with such an endless stream of misinformation tend to stay in line. To hear a warning to avoid such brain washing set to music, take a few minutes break from the mathematical analysis to listen to Curse That TV Set.
An obvious example of propaganda via frequent repeat of a message is seen in Republican talking point strategy. This political party instrument of the ruling class repeats things as nonsensical as the sky is green and the trees are blue through media controlled by ruling class TV station and newspaper ownership and through advertising with such frequency that the drugged population out there in the audience come to think that such opinions have significance. Hey, maybe there is something to the idea of a green sky and of no evolution and of no climate change and of working people not always living fearfully on the edge of homelessness while the privileged amuse themselves with expensive trivialities purchased at the expense of the misery of the working class.
A classic illustration of political disingenuousness via a distortion of significance is found in the Republicans getting the public to support the war in Iraq in 2003 by describing our invading force as a “coalition.” It consisted approximately of K=163,700 soldiers from N=32 nations distributed set wise as (145,000, 5000, 2000, 2000, 1000, 1000, 1000, 1000, 500, 500, 500, 500, 500, 500, 500, 200, 200, 200, 200, 100, 100, 100, 100, 100, 50, 50, 50, 50, 50, 50, 50, 50). The invading force set’s number of significant members calculates from Eq15 as D=1.26, which rounded off to D≈1 specifies 1 significant nation in the socalled coalition, the United States, distinctly at odds with the general sense of a coalition as a plural entity rather than a collection of subordinates dominated by on nation, here the modern American empire.
The cleverness of calling it a coalition along with the endlessly repeated WMD talking point as rationalizations for entering this costly and unnecessary bloody war were clear enough to be recognized by the astute back then as raw political hokum without need for the D diversity index to clarify N−1=31 nations in the “coalition” as insignificant, though using D as a measure of the number of significant nations allows us to call out the deceitfulness of the politicians and the media that supported them with mathematical precision.
Manipulation of the intuitive D diversity based operation of the mind to assess significance is a cornerstone foundation of propaganda. It works by repetition of mistruth as evident both in patently totalitarian societies, organized religions and in capitalist pseudodemocracies where almost all politicians are controlled by the big money of corporations and Wall St., an obvious and highly meaningful fact that is made to be insignificant in the minds of people in its seldom being publically voiced. And those who do bring such facts to light, whether about the harsh realities of war or the institutional corruptions and misery of a highly ordered peace, are made to seem significantly bad.
A case in point is the documentary film maker, Michael Moore, whose primary sin is feeling disgust in both areas and making it known. His calling out Bush’s vanity driven Iraq War that, for no good national purpose and supported by endlessly repeated lies, unnecessarily took the lives of 5000 young American soldiers, crippled 30,000 more and destroyed well a million Iraqi lives, not to speak of the instability it caused that brought cutthroat ISIS to power in the Middle East, all these hard facts made to seem insignificant. Indeed, Moore’s insightful and prophetic castigation of the war at the Oscar nominations in 2003 and later in his documentary, Fahrenheit 9/11, brought about an active encouragement by right wing snake, Glenn Beck, held up in the media as a paragon of virtue, to go out and literally murder Michael Moore.
Those reading this and in despair about finding anything that can be done about it can be given one word of good advice that fits well with their desperation: run. To retain some modicum of selfrespect and the possibility of squeezing any real happiness out of life: run. That’s the best you can do in the short term to avoid the powerful if well hidden agencies of control in modern America. One thing that you can, and must, avoid is the TV set. This is one very important route to maintaining a sane view of life. It is admittedly a limited cure for the bigger problem. To solve that you have to fight back, not just run. And you do that by supporting and placing your hopes in the only true solution to this mess of human existence, helping to bring about A World with No Weapons, not just for bypassing nuclear Armageddon but also in a weapons ban restoring a true balance of power to life, the details to be talked more about in later sections.
To get to A World with No Weapons requires political power, it must be pointed out. Anarchy, everybody doing their own thing, is great if you can get it. But you can’t get it in the real world where the rules forbid it and punish those who break the rules. You have to first get to A World with No Weapons, which has to start with somebody in the White House here in America who actively carries that destiny on their shoulders. As I’m the only suitable candidate for that in 2016, encourage me by dropping a line to ruthmariongraf@gmail.com and sending a $20 donation to join the movement for A World with No Weapons and for the democratic revolution needed to make it happen by clicking here.
4. A Biased Average
The sense of a Utopia where there is no war or tyranny still must seem to most farfetched. We need more precise mathematical argument to make clear that it’s the only direction we can go in to get out of the hell of debilitating control in our lives and to avoid nuclear annihilation. To that end we next want to consider an adjunct function to the exact specification of the inexact N subsets in an unbalanced set, namely an exact average of the number of objects in each subset. As we made clear earlier, the µ=K/N arithmetic average number of objects per subset in an unbalanced set of K objects distributed over N subsets is inexact. Much as we form the arithmetic average as the ratio of the K objects in a set to the N inexact number of subsets in the set as µ=K/N, we can form an exact average as the ratio of the K objects to the D exact quantification of the subsets as K/D, an exact if biased average, to which we give the symbol, φ, (phi).
27.)
The φ=K/D biased average is an exact average in being a function of K, which is exact, and of D, which is also exact as was made clear earlier. The K=12, N=4, µ=K/N=4, D=2.323, (■■■■■■, ■■■■■, ■), (6, 5, 1) set has a biased average of φ=K/D=12/2.323=5.166. This is greater than this set’s arithmetic average of µ=K/N=4 from the φ biased average being weighted or biased towards the larger x_{i} values in (6, 5, 1). To see the details of the bias in the φ biased average of an unbalanced set towards the larger x_{i} values in the set, let’s develop the µ=K/N arithmetic average in an unusual way from Eqs7&8 as
28.)
This understands the µ mean or arithmetic average as the sum of “slices” of the x_{i} of a set of thickness 1/N. We can develop a function for the φ biased average with a parallel form from Eqs27,13,8&12 as
29.)
This shows φ to be the sum of “slices” of the x_{i} of a set that are p_{i} in thickness to bias the φ average towards the larger x_{i} subsets weighting them with their correspondingly larger p_{i} weight fraction measures. Much as the human mind’s sense of significance is affected in a biased way by the diversity of what it senses, so also is its sense of the average of the constituent subsets of set affected in a biased way towards the greater x_{i} of a set as representing the size of the objects in a set and/or the frequency with which they are sensed. A familiar example is our sense that a dinosaur is generally speaking very, very big. This comes about as a biased average of dinosaur sizes both in terms of the larger ones biasing our sense of the average towards the large sized dinosaurs and also from the fact that people see images of dinosaurs that are very large much more frequently than they see medium sized dinosaurs or small ones. Note also that the diversity index, D, can be understood as a function of the φ average when Eq27 is solved for D as
30.)
This expression for D tells us that the K total number of something in a set divided by its φ biased average is its D diversity. This relationship allows us to corroborate this analysis of significance and insignificance for the mind by showing it for physical systems where the concepts of significance and insignificance have measurable, empirical, reality. Specifically we will do it for a thermodynamic system of K energy units distributed over N molecules with a highlight on the concept of entropy, the tight argument presented reinforcing the D diversity based understanding of the highly contentious issue of brain washing propaganda.
5. Entropy
Entropy is a somewhat mysterious concept. Feeling cold in wintertime and hot in summertime comes about from the 2^{nd} Law of Thermodynamics said to be caused by an increase in entropy. But what it is exactly that’s increasing in these processes has been a confusion for science for the last two centuries since the French engineer, Sadi Carnot, first became aware of processes described in terms of entropy. The equation for entropy in terms of measurable quantities is the Clausius macroscopic formulation of entropy
31.)
Even though this differential equation tells us that entropy, S, is dimensionally, energy, Q, divided by temperature, T, it still leaves us with a confused mysterious sense of entropy because we lack an intuitive sense of what energy divided by temperature might be. Some light is thrown on the problem by next noting that (absolute) temperature is explained in the standard rubric of physical chemistry as being directly proportional to the µ=K/N arithmetic average of the K energy of a thermodynamic system per its N molecules. But this immediately raises a red flag because we made it very clear earlier that the µ arithmetic average is inexact for an unbalanced set and because the N molecules of a thermodynamic system are an unbalanced set of constituents of a thermodynamic system from the energy units of the system being distributed over them in a skewed or unbalanced way from the empirical MaxwellBoltzmann energy distribution.
Figure 32. The MaxwellBoltzmann Energy Distribution
The inexactness in the µ=K/N average energy function that derives from the
inexactness in the N number of molecules parameter suggests that it is an error
in physical science assuming that systems in nature necessarily operate in an
exact way. Or alternatively we might say that this arithmetic average
specification of temperature is a poor one in being inexact and is perhaps the
reason why the S entropy is so poorly understood and mysterious as a physical
quantity.
Following this line of reasoning tell us that temperature might be better understood as a biased average of energy per molecule. That supposition provides us with a very clear and physically sensible interpretation of entropy for as we see from Eqs30&31, K total energy divided by φ as a biased average energy would be the D diversity of the system of molecules which in perfectly fitting dimensionally Q energy divided by T temperature as S entropy pegs S entropy as the energy diversity of the system. As this quite fits the intuitive or qualitative sense of entropy as energy dispersal, just another word for energy diversity, (see entropy as energy dispersal in Wikipedia), it is worth tracking it down further and provide hard core evidence to show if this is truly the case. Doing so will also increase our confidence of the D diversity as a measure of significance and insignificance in cognitive systems and underpinning of a mathematical specification of the human emotions. And it will also provide us with a mathematical template for the generalizations of ideas and thoughts that the human mind also operates on. The evidence we will provide shows a mathematically perfect fit of energy diversity to the Boltzmann formulation of entropy, understood in science to be the most basic expression for entropy as honored by its inscription of Boltzmann’s tombstone in the terminology of 100 years ago as
33.) S = klogW
Ludwig Boltzmann’s 1906 Tombstone
Diversity is a property not only of a set of K objects divided into N color categories, but also of K candies divided between N children and K discrete or whole numbered energy units divided between N molecules. The distribution of K=4 candies to N=2 children takes the form of three natural number sets: (2, 2) for both children getting 2 of the K=4 candies with a diversity from Eqs5&8 of D=2; (4, 0) for one child getting all 4 of the K=4 candies and the other child none with a diversity from Eq5 of D=1; and (3, 1) for one child getting 3 of the K=4 candies and the other child, 1, with a diversity from Eq5 of D=1.6. The (2, 2), (3, 1) and (4, 0) manifestations of the random distribution are also referred to as the configurations of the distribution. The distribution of K=4 energy units over N=2 molecules has the same diversity values as the distribution of K=4 candies over N=2 children: for (2, 2), both molecules having 2 of the K=4 energy units, a diversity of D=2; for (4, 0), one molecule having all 4 of the K=4 energy units and the other molecule none, a diversity of D=1; and for (3, 1), one molecule having 3 of the K=4 energy units and the other molecule, 1, a diversity of D=1.6.
The candies over kids distribution is easiest to picture and follow, so we begin with it. The random or equiprobable distribution of candies to children as might come from grandma tossing K=4 candies of different color, (■■■■), blindly over her shoulder to her N=2 grandkids, Jack and Jill, has a number of ways of occurring, ω,
34.) ω = N^{K}
ω (small case omega) is referred to as a combinatorial statistic. Specifically for K=4 candies distributed randomly to N=2 children, the ω number of ways that can occur is
35.) ω = N^{K} =2^{4}= 16
These ω =16 ways are, with Jack’s candies set to the right of the comma and Jill’s candies to the left,
36.)
(■■■■, 0); (■■■, ■); (■■■,
■);
(■■■,
■);
(■■■, ■); (■■, ■■); (■■, ■■); (■■, ■■)
(■■, ■■); (■■, ■■);
(■■,
■■); (■■■, ■);
(■■■, ■); (■■■, ■); (■■■, ■);
(0, ■■■■)
The probability of each of these permutations or ways or microstates of the random distribution is the same,
37.) 1/ω=1/16
If grandma did the tossing of the K=4 candies to the N=2 kids 16 times, on average, Line16 would come about though not necessarily in the sequence depicted. It is possible to compute the average diversity of this random distribution. Here we see that the probability of a (4, 0) permutation is 2/16=1/8; of a (3, 1) configuration, 8/16=1/2; and of a (2. 2) permutation, 6/16=3/8. It is a simple matter to compute the σ^{2 }variances of these permutations from Eq11: for (4, 0), σ^{2}=4; for (3, 1), σ^{2}=1; and for (2, 2), σ^{2}=0. Note that (4, 0), (3, 1) and (2, 2) are also referred to as the configurations of the distribution. The average variance of the ω = 16 permutations, also understandable as the probability weighted average variance of the configurations, is
38.)
The average variance, σ^{2}_{AV}, enables us to calculate the average diversity of the random distribution, D_{AV}, from Eq16 with σ^{2}_{AV} replacing σ^{2} and D_{AV} replacing D.
39.)
Understanding the arithmetic average of the number of energy units per molecule for the K=4 energy unit over N=2 molecule distribution to be µ=K/N=4/2=2, the parameters of σ^{2}_{AV}=1 and N=2 have us calculate the average diversity of the random distribution, D_{AV}, as
40.)
This dynamic plays out as above  it must be emphasized  even if the candies are all of the same kind, say K=4 red candies, (■■■■). This comes about because the candies, even though all of the same kind, are fundamentally different candies. Let’s back up a minute to explore this in greater depth. The (■■■■) candies are said to be categorically distinct or distinct in kind. But we don’t just distinguish things as being different kinds, as between a red candy, ■, and a green candy, ■. We also distinguish between two of the same kind of thing, as between two red candies, ■■, which though they are categorically indistinguishable or the same kind of thing, are yet distinguishable fundamentally. If you are holding one of these red candies in your hand and the other is on the kitchen table, you definitely distinguish between the two.
This is called fundamental distinction. It is different than categorical distinction, but yet a distinction between things people make as intuitively as they distinguish between different kinds of things. To show the fundamental distinction between K=4 red candies, (■■■■), we can represent them each with a different letter as (abcd). With the fundamental distinction so marked, the number of ways or different permutations of K=4 red candies, (abcd), that come about from their random distribution to N=2 kids is also calculated as ω= N^{K} =2^{4}= 16 of Eq35, those permutations being
41.)
(abcd, 0); (abc, d); (abd, c); (adc, b); (bcd, a}; (ab, cd); (ac, bd); (ad, bc)
(bd, ac); (bc, ad); (cd, ab); (a, bcd); (b, acd}; (c, abd}; (d, abc};
(0, abcd)
Note that everything we said for the random distribution of (■■■■) in Eq37 to Eq40 applies also to the random distribution of (■■■■) as is readily understood once we delineate the fundamental distinctions in (■■■■) as (abcd). Now determining the average diversity, D_{AV}, for random distributions gets a bit tedious as the K and N of random distribution get large, indeed, practically impossible for very large K and N values. Fortunately we can develop a shortcut formula for the D_{AV} average diversity of any K energy unit over N molecule random distribution from a shortcut formula for σ^{2}_{AV} that already exists in standard multinomial distribution theory. In general for any multinomial distribution of K objects over N containers,
42.)
For an equiprobable multinomial distribution, the P_{i} term is P_{i}= 1/N, a relationship that tells us that each of the N containers in a K over N distribution has an equal, 1/N, probability of getting any one of the K objects distributed to it. This P_{i}=1/N probability for an equiprobable distribution is the P=1/N=1/2 probability of each of grandma’s N=2 kids having an equal, 50%, chance of getting any one candy blindly tossed by grandma. The P_{i} =1/N probability for a random distribution greatly simplifies the multinomial variance expression of Eq24 for the equiprobable case to
43.)
As things turn out this variance of an equiprobable multinomial distribution is the average variance of an equiprobable distribution, σ^{2}_{AV}, of Eq38 we developed for the K=4 over N=2 random distribution. Hence we can write Eq43 as
44.)
That the variance of an equiprobable multinomial distribution is, indeed, the average variance, σ^{2}_{AV}, is demonstrated by calculating the σ^{2}_{AV}=1 average variance of the K=4 over N=2 distribution in Eq41 from the above as
45.)
Eq44 can now be used to generate a shortcut formula for the average diversity, D_{AV}, by substituting its σ^{2}_{AV} into Eq39 to obtain
46.)
And we can further demonstrate the validity of the above shortcut formula for D_{AV} by calculating the D_{AV}=1.6 average diversity of the K=4 over N=2 distribution obtained in Eq43 with it.
47.)
These conclusions also hold for a system of K=4 energy units distributed equiprobably over N=2 gas molecules flying about in a container of fixed volume. The equiprobable or random distribution results from collisions between the N=2 molecules that result in random energy transfers of the energy units between molecules. In that case, Line41 represents the microstate permutations that arise on average from the collisions, though not necessarily in that sequence. The average variance, σ^{2}_{AV}, of the microstate permutations and their average diversity, D_{AV}, is the same as for the random distribution of K=4 candies between N=2 children.
With this picture of a thermodynamic system as our template, we can now confirm the dimensional analysis that suggested from the Clausius macroscopic formulation of entropy that entropy is basically energy diversity or energy dispersal. This is done specifically by showing that the average diversity, D_{AV}, has near perfect direct proportionality to the expression for microstate entropy Boltzmann developed that is expressed in modern terminology as
48.) S=k_{B}lnΩ
To demonstrate this we need not explain the meaning of the Ω (capital omega) variable in Boltzmann’s S entropy, held off until later, nor the k_{B} term in the function, a constant, but only show the exceedingly high correlation coefficient between D_{AV} and lnΩ. That is easy to demonstrate because both D_{AV} and Ω are functions solely of the K number of energy units and N molecules in a thermodynamic system, D_{AV} as seen in Eq46 and Ω from a standard formula in mathematical physics.
49.)
And the lnΩ as a function of K and N is
50.)
For large K over N equiprobable distributions it is easiest to calculate lnΩ using Stirling’s Approximation, which approximates the natural logarithm (ln) of the factorial of any number, n, as
51.)
Stirling’s approximation works very well for large n values. For example, ln(170!) =706.5731 is very closely approximated as 706.5726. The Stirling’s approximation form of the lnΩ expression of Eq50 is
52.)
We can use this formula to compare the lnΩ of randomly chosen large K over N equiprobable distributions to their D_{AV} average diversity of Eq46.
K 
N 
lnΩ, Eq52 
D_{AV}, Eq46 
145 
30 
75.71 
25 
500 
90 
246.86 
76.4 
800 
180 
462.07 
147.09 
1200 
300 
745.12 
240.16 
1800 
500 
1151.2 
381.13 
2000 
800 
1673.9 
571.63 
3000 
900 
2100.88 
692.49 
Table 53. The lnΩ and D_{AV} of Large K over N Distributions
The Pierson’s correlation coefficient for the D_{AV} and lnΩ of these distributions is .9995, which indicates a very close direct proportionality between the two as can be appreciated visually from the near straight line of the scatter plot of these D_{AV} versus lnΩ values.
Figure 54. A plot of the D_{AV} versus lnΩ data in Table 33
This high .9995 correlation between lnΩ and D_{AV} becomes greater yet the larger the K and N values of K>N distributions surveyed. For values of K on the order of EXP20 the correlation for K>N distributions is .9999999 indicating effectively a perfect direct proportionality between lnΩ and D_{AV} as fits very large, thermodynamically realistic, K over N equiprobable distributions. As the Boltzmann S=k_{B}lnΩ entropy is judged to be correct ultimately by its fit to laboratory data, given the near perfect correlation of the D_{AV} to it, this diversity entropy formulation must also be correct from that purely empirical perspective. This correlation of diversity entropy to the Boltzmann microstate formulation of entropy powerfully reinforces the dimensional analysis of entropy as energy diversity done from the Clausius macroscopic formulation of entropy.
It must be emphasized, though, that the two microstate formulations of entropy, diversity and Boltzmann, cannot both be correct even though both mathematically fit the data because the assumptions that underpin the two formulations are absolutely mutually contradictory. This requires some explaining. The ω = N^{K} number of ways combinatorial statistic of Eq34 implies from the 16 microstate permutations of Line21 for the K=4 over N=2 distribution that the energy units are all fundamentally distinguishable from each other. Understanding the random distribution in this way is what made possible the foregoing derivation of the average variance, σ^{2}_{AV}, and the average diversity, D_{AV}.
A quite different combinatorial statistic exists for enumerating the number of observably different ways that K categorically indistinguishable objects can be arranged in N containers. It is the Ω variable that we have already seen from Eq49 that sits in Boltzmann’s S=k_{B}lnΩ entropy.
49.)
Irrespective of Boltzmann’s use of it in his entropy equation, Ω can specify the number of ways that K=4 red candies, (■■■■), which are categorically indistinguishable even if as we made clear they are fundamentally distinguishable, can be arranged over N=2 containers or N=2 children. From Eq49 that is 5 ways
55.)
These Ω=5 ways are as we see below with Jack’s candies to the right of the comma and Jill’s to the left.
55a.) (■■■■, 0); (■■■, ■); (■■, ■■); (■, ■■■); (0, ■■■■)
However the Ω=5 value this has absolutely no meaning as regards the random distribution of K energy units over N molecules because such a distribution is necessarily governed from elementary probability theory by the ω = N^{K} combinatorial statistic of Eq14 that implicitly assumes that the energy units, though they are categorically indistinguishable, are fundamentally distinguishable. This perspective is bolstered by the energy units residing in distinguishable molecules, which themselves reside in different places in space. This suggests that Boltzmann researched a number of mathematical functions associated with the distribution of energy units over molecules until he came to one, lnΩ, which fit the data. In theoretical physics such a fit of a mathematical hypothesis to empirical data is generally taken as strong proof that the hypothesis is correct. In this case, though, it turns out that lnΩ is little more than a fluke fit to another function, D_{AV}, which not only also fits the data, but also makes physical sense out of entropy as energy diversity or energy dispersal One adds that neither Ω nor lnΩ make any sense out of entropy as a physical quantity, the reason for entropy’s mysteriousness over the last century.
One readily absolves Boltzmann for this error given that mathematical formulations for diversity did not come into existence until near half a century after his death and we emphasize that without Boltzmann’s breakthrough efforts my clarification of entropy as diversity would have been impossible. The complete acceptance of Boltzmann’s notions for the last hundred years from their perfect fit to data makes his ideas very difficult to overthrow for Boltzmann is as much a revered “saint” of physical science as Newton or Maxwell or Einstein. The task of rectifying our understanding of entropy as energy diversity would be much easier, for that reason, if both interpretations in their both fitting the data empirically, could be accepted. However the two assumptions of energy unit distinguishability and energy unit indistinguishability are totally incompatible and only one can be accepted. Hence Boltzmann is overthrown rather than just refined, difficult to accept for physical scientists who have embraced him as correct in the most foundational way over the last century.
This impediment to a correction of Boltzmann’s error, thus, asks for as much supporting evidence for the diversity entropy proposition as can be mustered. This is doubly important for not only does diversity explain entropy correctly and clearly for the first time in science, but also understanding diversity as a measure of entropy also very much makes clear the underpinning of meaningful information with diversity. That includes not only showing the concept of significance as a marker for what is meaningful in a very firm way in physical systems, but also uncovers a welldefined mathematical structure for the generalizations that the human mind operates on verbally called compressed representation.
A very strong supporting argument for diversity based entropy shows that my diversity based statistical mechanics much better explains the MaxwellBoltzmann energy distribution than Boltzmann statistical mechanics does.
Figure 32.
To show it we next introduce a new structure in mathematics called the Average
Configuration of a random distribution. The configurations of the K=4 over
N=2 distribution are listed below with their variances and diversity indices.
Configuration 
Microstates 
Variance, σ^{2} 
Diversity, D 
(4, 0) 
[4, 0], [0,4] 
4 
1 
(3, 1) 
[3, 1], [1, 3] 
1 
1.6 
(2, 2) 
[2, 2] 
0 
2 
Table 56. The Variance, σ^{2}, and Diversity, D, of the Configurations of the K=4 over N=2 Distribution
Recall now the average variance of σ^{2}_{AV}=1 of the K=4 over N=2 distribution from Eq38&45 and its average diversity of D_{AV}=1.6 from Eqs40&47. We see in the above table that the same values of a σ^{2}=1 variance and a D=1.6 diversity are seen for the (3, 1) configuration. On that basis the (3, 1) configuration is understood to be a compressed representation of all of the distribution’s configurations of (4, 0), (3, 1) and (2, 2) and as such is called the Average Configuration of the distribution. The Average Configuration is one configuration that represents all the configurations of a random distribution in compressed form much like the µ arithmetic average is one number that represents all the numbers in a number set in compressed form as, for example, the μ=K/N=4 arithmetic average does for all the numbers in the K=24, N=6, (6, 4, 2, 1, 5, 6), number set.
A configuration includes all of the permutations describable with the same number set, much as the (4, 0) configuration of the K=4 over N=2 distribution includes the permutations, (abcd, 0) and (0, abcd). Hence the Average Configuration should be understood as a compressed representation not only of all of a distributions configurations but also of all ω=N^{K }of its permutations as develop physically over time as the system’s microstates, each of which exists at any one moment in time. This exceedingly clear microstate picture of a thermodynamic system is worth taking a moment or two to sketch out. Recall the ω=16 permutations or microstates in Line21 for the K=4, N=2 distribution.
41.)
(abcd, 0); (abc, d); (abd, c); (adc, b); (bcd, a}; (ab, cd); (ac, bd); (ad, bc)
(bd, ac); (bc, ad); (cd, ab); (a, bcd); (b, acd}; (c, abd}; (d, abc};
(0, abcd)
These should be understood as appearing in this proportion on average though not necessarily in this sequence over 16 moments of time as coming about from the random molecular collisions and transfers of energy in a thermodynamic system. As such, the (3, 1) Average Configuration represents the state of the system as measured over an extended period of time. Now if this microstate picture of a thermodynamic system is correct, the MaxwellBoltzmann energy distribution should be the average energy distribution of all the microstate configurations as manifest in the energy distribution of the Average Configuration.
The K=4 energy units over N=2 molecules distribution has too few K energy units and N molecules for its Average Configuration of (3, 1) to show any resemblance to the MaxwellBoltzmann energy distribution of Figure 32. Rather, we need random distributions with higher K and N values. And we will look at some starting with the K=12 energy units over N=6 molecule distribution. To find its Average Configuration we first calculate from Eq44 the σ^{2}_{AV} average variance of this distribution to be
57.)
The Average Configuration of the K=12 over N=6 distribution is a configuration that has this variance of σ^{2}_{AV} =1.667. The easiest way to find the Average Configuration is with a Microsoft Excel program that generates all the configurations of this distribution and then locates the one/s that has the same variance of σ^{2}=σ^{2}_{AV}=1.667. It turns out to be the (4, 3, 2, 2, 1, 0) configuration, taken to be the Average Configuration on the basis of its having as its variance, σ^{2}_{AV}=1.667. A plot of the number of energy units on a molecule vs. the number of its molecules that have that energy for this Average Configuration of (4, 3, 2, 2, 1, 0) is shown below.
Figure 58. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=12 over N=6
Distribution
Seeing this distribution as the MaxwellBoltzmann energy distribution of Figure 32 is a bit of a stretch, though it might be characterized generously as an extremely simple choppy form of a MaxwellBoltzmann. Next let’s consider a larger K over N distribution, one of K=36 energy unit over N=10 molecules. Its σ^{2}_{AV} is from Eq44, σ^{2}_{AV}=3.24. The Microsoft Excel program runs through the configurations of this distribution to find one whose σ^{2} variance has the same value as σ^{2}_{AV} =3.24, namely, (1, 2, 2, 3, 3, 3, 4, 5, 6, 7). A plot of the energy distribution of this Average Configuration is
Figure 59. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=36 over N=10
Distribution
This curve was greeted without prompting by Dr. John Hudson, Professor Emeritus of Materials Engineering at Rensselaer Polytechnic Institute and author of the graduate text, Thermodynamics of Surfaces, with, “It’s an obvious protoMaxwellBoltzmann.” Next we look at the K=40 energy unit over N=15 molecule distribution, whose σ^{2}_{AV} average variance is from Eq44, σ^{2}_{AV} =2.489. The Microsoft Excel program finds four configurations that have this diversity including (0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6), which is an Average Configuration of the distribution on the basis of its σ^{2}=2.489 variance. A plot of its energy distribution is
Figure 60. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=40 over N=15
Distribution
And next we look at the K=145 energy unit over N=30 molecule distribution whose average diversity is from Eq44, σ^{2}_{AV} =4.672. There are nine configurations with a σ^{2 }=4,672 including this natural number set of (0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 10), which is an Average Configuration of the distribution on that basis. A plot of its energy distribution is
Figure 61. Number of Energy Units
per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=145 over N=30
Distribution
At this level we are considering K and N values large enough to display a
moderately good resemblance to the classical MaxwellBoltzmann distribution of
Figure 32.
Figure 32.
As we progressively increase the K and N values of distributions, the plot of the energy per molecule versus the number of molecules that have that energy more and more approaches and eventually perfectly fits the shape of the above realistic MaxwellBoltzmann distribution. Now it should be clear that this unorthodox development of the MaxwellBoltzmann distribution as a property of the Average Configuration comes directly from the mathematics of a random distribution of distinguishable energy units and does not require any additional assumptions, which the Boltzmann derivation of the MaxwellBoltzmann decidedly does. As only one theory, mine or Boltzmann’s, can be correct because of the mutually contradicting assumptions for the two theories of distinguishable versus indistinguishable energy units, there is a strong argument in favor of mine from the Occam’s razor principle that is used generally in science to decide between two competing explanations on the basis of which has the fewest assumptions, in this case the diversity based explanation.
The other reinforcing argument for diversity based entropy comes about from the use of a diversity index slightly different than the D diversity index, one whose biased average perfectly fits microstate temperature and so makes the dimensional argument with the Clausius formulation of entropy air tight. We began our consideration of diversity based entropy with the D diversity index because of the mathematical regularities it has that made it easy to work with, but now that we have developed the basic concepts of diversity based entropy from D, we will switch our focus to Square Root Diversity Index, h.
62.)
This h diversity index not only provides a precise dimensional argument for diversity based entropy with the Clausius macroscopic entropy formulation, but also has, like D, a very high Pearson’s correlation to the Boltzmann microscopic entropy. As such it is the proper diversity underpinning of entropy. The p_{i }in h are the weight fraction measures of the x_{i} number of objects in each subset. The K=12 object, N=4 color, (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), set, x_{1}=5, x_{2}=3, x_{3}=3 and x_{4}=1 has p_{i}=x_{i}/K weight fractions of p_{1}=x_{1}/K=5/12, p_{2}=x_{2}/K=3/12=1/4; p_{3}=1/4 and p_{4 }=1/12. This makes for an h square root diversity index of the set of
63.)
Note that the h diversity index is exact in being solely a function of p_{i}, which we made clear earlier is exact. Note also that the h=3.464 of the (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), set compares well to its D=3.273 index in being, as is D, a reduction from the N=4 of this unbalanced set, though not quite as much as D=3.273 is. The two diversity indices, D and h, have comparable measures for the sets below with h=N=D for balanced sets and h < N for unbalanced sets as is D<N.
Set of Unit Objects 
Subset Values 
D, Eq3 
h, Eq62 
(■■■, ■■■, ■■■, ■■■) 
x_{1}=x_{2}=_{ }x_{3}=x_{4}=3 
4 
4 
(■■■■■, ■■■, ■■■, ■) 
x_{1}=5, x_{2}=_{ }x_{3}=3, x_{4}=1 
3.273 
3.468 
(■■■■■■, ■■■■■■) 
x_{1}=x_{2}=6 
2 
2 
(■■■■, ■■■■, ■■■■) 
x_{1}=x_{2}=_{ }x_{3}=4 
3 
3 
(■■■■■■, ■■■■■■, ■■■■■■■■■) 
x_{1}=x_{2}=6, _{ }x_{3}=9 
2.882 
2.941 
(■■■■■■, ■■■■■, ■) 
x_{1}=6, x_{2}=5,_{ }x_{3}=1 
2.323 
2.538 
(■■■■■■■■■■, ■■■■■■■■■■, ■) 
x_{1}=x_{2}=10,_{ }x_{3}=1 
2.194 
2.394 
Table 64. Various Sets and Their D and h Diversity Indices
Earlier back in Eqs2729 we developed an exact biased average for the D diversity of φ=K/D. We can also develop an exact biased average for the h square root diversity of Eq42 that we’ll call the Square Root Biased Average. In parallel to K/N=µ and K/D=φ, we define the square root biased average as K/h and give it the symbol, ψ, (psi).
65.)
The ψ=K/h biased average is an exact average in being a function of K, which is exact, and of h, which is also exact. The K=12, N=3, µ=K/N=4, h=2.538, (■■■■■■, ■■■■■, ■), (6, 5, 1), set has a square root biased average of ψ=K/h=12/2.538=4.72, greater than the arithmetic average of this set, µ=4, in being biased towards the larger x_{i} values in the (6, 5, 1) set. We detail the basis of this bias in the ψ average towards the larger x_{i} in a set by expressing ψ from Eqs3,8&62 as
66.)
The numerator in the rightmost term shows the ψ square root biased average to be the sum of “slices” of the x_{i} of a set of thickness p_{i}^{1/2}, which biases the average towards the larger x_{i} in the set in their having larger p_{i}^{1/2}. The ∑p_{i}^{1/2} term in the denominator of the end fraction is a normalizing function used to make all the p_{i}^{1/2 }“slices” in the numerator sum to one, this summing to one of the fractional “slices” being necessary for the construction of any kind of an average of a number set. We next invert Eq60 to express the h square root diversity index as a function of the φ square root biased average as
67.)
Now let’s understand ψ of Eqs65&66 as the microstate temperature of a thermodynamic system of K energy units distributed over N gas molecules. As we said earlier back after Eq31, the microstate temperature is currently understood in the standard physics rubric to be the arithmetic average energy per molecule, µ=K/N. And we made clear that what is wrong with that is that the K energy units of the system being distributed over the N molecules in an unbalanced way as seen in the MaxwellBoltzmann energy distribution of Figure 32 tells us that the this µ=K/N arithmetic energy average is an inexact specification because the N number of molecules parameter in µ=K/N is inexact. Earlier we suggested a replacement of inexact µ=K/N with the exact biased average, φ=K/D and we saw how doing that quickly developed a dimensional argument from (normalized, absolute) temperature being the φ=K/D exact biased energy average and S entropy being dimensionally from the dS=dQ/T Clausius entropy expression of S entropy deriving from the division of energy by temperature.
We can make the same dimensional argument for the square root biased average, ψ, as temperature and it is a substantially better one based on how temperature is actually measured physically with a thermometer. Each of the N molecules in the thermodynamic system collides with the thermometer to contribute to its temperature measure in direct proportion to its frequency of collision with the thermometer, which is equal to the velocity of the molecule, which itself is directly proportional to the square root of the x_{i} number of energy units a molecule has. Because of this, the slower moving molecules with the smaller energies in the MaxwellBoltzmann energy distribution of Figure 32 collide with the thermometer less frequently and have their energies recorded or sensed by the thermometer in its compilation of the temperature measure less frequently to record or sense smaller p_{i}^{1/2} slices of their energies. And conversely, the faster moving, higher energy molecules, which collide with the thermometer more frequently have their energies recorded or sensed as larger p_{i}^{1/2} slices of their energy thus biasing the temperature measure towards the energy of the higher energy molecules in an unarguable way. This determines the molecular energy average to be the square root biased average energy per molecule, ψ=K/h.
This first order model is incomplete, however, because it does not take into account the fact that the h energy diversity of a thermodynamic system along with its ψ=K/h biased energy average is changing at every moment in time from one microstate permutation to another as the system’s molecules collide with and transfer energy between themselves, thus continuously altering the distribution of the K energy units over the system’s N molecules. Hence the ψ and h parameters that form the basis respectively of the system’s temperature and entropy must be their average measures, h_{AV} and ψ_{AV}, which are properties also of the system’s Average Configuration that represents the system as a whole. This makes it clear by extension from Eq66 that the K total number of energy units divided by the ψ_{AV} square root biased energy average as temperature is the h_{AV} square root diversity of the system
68.)
Now it is only one quick stop at the Clausius macroscopic entropy formulation, dS=dQ/T, to see from a dimensional argument that h_{AV} diversity is the measure of the entropy of the system. As S entropy is dimensionally Q energy divided by T temperature and K energy divided by ψ_{AV} temperature is h_{AV} diversity, h_{AV} diversity must be dimensionally entropy.
To conclude that h_{AV} is the proper function for entropy based on its dimensional fit to the Clausius macroscopic entropy, we must also show that h_{AV} has a high correlation to Boltzmann’s S=k_{B}lnΩ entropy (or more simply, to lnΩ.) To demonstrate this, though, is not as straightforward as it was for D_{AV} because h_{AV} is not a simple function of the K energy units and N molecules of a thermodynamic system as D_{AV }was back in Eq46 as D_{AV}=KN/(K+N−1). There is a remedy for this problem, though. Because h_{AV} is the h diversity the Average Configuration much as D_{AV} was the D diversity index of the Average Configuration, we can obtain h_{AV} for the K over N distributions for which we have a specific Average Configuration and its x_{i }and p_{i} values. Those are the K over N distributions of Figures 5861. Below we list their h_{AV} values as calculated from Eq62 alongside the lnΩ values of those Average Configurations as calculated from Eq50. And we also include their D_{AV} diversity indices from Eq46 for comparison sake.
Figure 
K 
N 
lnW 
D_{AV} 
h_{AV} 
36 
12 
6 
8.73 
4.24 
4.57 
37 
36 
10 
18.3 
8 
8.85 
38 
45 
15 
26.1 
11.11 
12.33 
39 
145 
30 
75.88 
25 
26.49 
Table 69 The lnΩ, D_{AV} and h_{AV} of the Distributions in Figures 7376
The Pearson’s correlation coefficient between the lnΩ and h_{AV} values of the above is .995. And between lnΩ and D_{AV} it is .997. Note that though this lnΩ and D_{AV} Pearson’s correlation of .997 is high, it is less than the .9995 correlation between lnΩ and D_{AV} seen in Table 53 for larger K and N distributions. This is attributed to the Pearson’s correlation coefficient being a function of the magnitude of the K and N parameters of the random distributions, those of the distributions in Figures 5861 used in Table 69 being substantially smaller than the K and N of the distributions in Table 53. Hence the Pearson’s correlation between lnΩ and h_{AV }of .995 for the K over N distributions in Table 69 being little different than the .997 correlation between lnΩ and D_{AV} implies that the lnΩ and h_{AV }correlation is also, as was the .9995 between lnΩ and D_{AV }for larger K and N distributions, understood to be sufficiently great to have h_{AV} accepted as a candidate for entropy from its high correlation with the S=k_{B}lnΩ Boltzmann microstate entropy.
Now we will show how the h_{AV} diversity index replaces S in the 2^{nd} Law of Thermodynamics. The standard form of the 2^{nd} Law is
70.) ΔS > 0
This says that entropy, S, always increases in an irreversible or spontaneous process. One such process the 2^{nd} Law applies to is thermal equilibration. In it two bodies at different temperatures both go to some intermediate temperature upon thermal contact. While the mathematics of this is unarguable when entropy is expressed in dS=dQ/T form, any sense of the increase in entropy microscopically or molecularly that can be gleaned from representing entropy with the Boltzmann S entropy is unintuitive and conceptually mysterious. And that, we posit, is not because entropy is inherently difficult to understand or mysterious, but because S=k_{B}lnΩ is incorrect and must be replaced with h_{AV} diversity to make any sense out of the process intuitively.
To show this we will demonstrate the h_{AV} diversity based entropy increasing in a thermal equilibration between two “minithermodynamic” subsystems. Subsystem A has K_{A}=12 energy units distributed randomly over N_{A}=3 molecules. And subsystem B has K_{B}=84 energy units distributed randomly over N_{B} =3 molecules. These two subsystems are initially isolated out of thermal contact with each other. From Eq44 the average variance of the K_{A}=12 energy units over N_{A}=3 molecules subsystem is σ^{2}_{AV }=2.667, which calculates an Average Configuration for the subsystem, which has that variance, of (6, 4, 2) along with a normalized microstate temperature of the subsystem from Eq66 of ψ_{AV}(A)=4.353. And the K_{A}=84 energy units over N_{B}=3 molecules subsystem B has from its Eq44 average variance of σ^{2}_{AV}=18.667 an Average Configuration of (34, 26, 24) with a normalized microstate temperature from Eq66 of ψ_{AV}(B)_{ }=28.328.
Upon thermal contact the system, now comprised of the two subsystems as one whole system, consists of N=N_{A}+N_{B}=6 molecules over which are distributed K=K_{A}+K_{B}=96 energy units. At the first moment of contact, we represent the whole system as a composite of their separate Average Configurations, to wit as (6, 4, 2, 34, 26, 24). At this first moment there is no ψ_{AV} temperature of the composite system because it is not in thermal equilibrium. But it can be understood to have a square root diversity index of h_{AV}=4.394 from Eq62. This specifying of the composite system not in equilibrium as h_{AV}, as an average diversity, is awkward in (6, 4, 2, 34, 26, 24) being made up of the average h diversities of the two subsystems. But the meaning of h_{AV} is clear here despite the (6, 4, 2, 34, 26, 24) set being made up of the h_{AV} of the subsystems.
After molecular collisions sufficient to bring about a random distribution of the K=96 energy units over the N=6 molecules, the Average Configuration as obtained from the σ^{2}_{AV }=13.333 average variance of Eq44 is (11, 14, 15, 16, 17, 23). It has a square root diversity index from Eq62 of h_{AV}=5.85 and a normalized microstate temperature from Eq66 of ψ_{AV}=16.409.
Note that the usual computation of temperature of the whole system from the 1^{st} Law of Thermodynamics, an energy conservation law, suggests a temperature that is the simple average of the temperature of the two subsystem’s, which would be of the ψ_{AV }normalized microstate temperatures, (4.353 + 28.328)/2 =16.341. The discrepancy between this value of 16.341and ψ_{AV}=16.409 calculated from Eqs62&66 is not a violation of energy conservation because temperature from our unorthodox diversity based perspective is understood as an average molecular energy biased toward the higher energy molecules.
What is important to demonstrate here is that the h_{AV} energy diversity or energy dispersal understood as entropy increases upon thermal contact from an initial value of h_{AV}=4.39 for (6, 4, 2, 34, 26, 24) to a final value of h_{AV}=5.85 for (11, 14, 15, 16, 17, 23). The change in h_{AV} energy diversity is, hence,
71.) Δh_{AV}=5.85 – 4.39 = +1.46
This fits the increase in entropy for thermal equilibration demanded by the 2^{nd} Law of Thermodynamics with entropy now expressed as h_{AV} energy diversity.
72.) Δh_{AV} > 0
There are two things that are different about this unorthodox manifestation of the 2^{nd} Law entropy increase for thermal equilibration. The first is that the entropy increase expressed in terms of Δh_{AV }=1.46 is measured as a change in the whole system of N=6 molecules. And the second is that what is happening physically in the thermal equilibration process is very clear intuitively when the entropy increase is understood as an increase in energy diversity or dispersal. Indeed, nothing could be clearer intuitively especially by comparison to the standard take on entropy increase as an increase in the Ω microstates of the system, which makes zero sense out of entropy as a physical quantity. This diversity based entropy change quantitatively fits the sense of entropy as energy dispersal, (See Wikipedia), which though taken by most scientists to be the qualitatively sensible interpretation of entropy, has never been given a firm quantitative basis until now.
There are other major improvements in thermodynamics that come about from this diversity based statistical mechanics as in a clearer understanding of free energy and of a real gas law in terms of diversity. We will not detail these and other improvements in thermodynamic theory that a diversity based entropy brings about, leaving that to specialists in the field who have sense enough to expand on our seminal work in the detail it warrants.
6. Entropy and Information
Two concepts that derive from the development of diversity based entropy have relevance to the information processing operations of the mind. The first is that the h diversity index of Eq62, like the D diversity index of Eq3, is understandable as a measure of the number of significant subsets in a set. In the (■■■■■■■■■■, ■■■■■■■■■■, ■), (10, 10, 1), set of Table 25 and Figure 26 it was seen that the D=2.19 diversity index of the set could be interpreted, when rounded off, as the set having D=2 significant subsets, the x_{1}=x_{2}=10 red and the green subsets, with the x_{3}=1 purple subset understood as insignificant. This interpretation of the D=2.19 measure was reinforced with significance indices for it from Eq21 of s_{1}=1.04≈1 for the red subset, s_{2}=1.04≈1 for the green subset and s_{3}=.104≈0 for the purple subset. The h diversity index of this set, h=2.394 from Eq62, rounded off to h=2, can also be understood as specifying 2 significant subsets in the set.
This has us interpret h_{AV} diversity based entropy as the number of energetically significant molecules in a thermodynamic system, that is, in its Average Configuration or equivalently as the average number of them in the system. For example, consider the K=36 energy units over N=10 molecules random distribution of Figure 59 as its (1, 2, 2, 3, 3, 3, 4, 5, 6, 7) Average Configuration and its h_{AV} from Eq62 of h=8.853≈9. This is readily interpreted as the system having 9 energetically significant molecules, the molecule with just 1 energy unit being insignificant energetically. This sense of the energetic significance versus insignificance of molecules goes a long way to understanding temperature specified as ψ_{AV}=K/h_{AV} as coming about from molecular collision with the thermometer that is biased towards the faster moving, more energetically significant molecules. That, in turn, makes clear that the “reality” of a thermodynamic system as manifest in its most basic property of temperature as ψ_{AV}=K/h_{AV} depends not just on the molecular energies of the system but also on how the molecular energies are tallied in the temperature measure in a biased way.
This also makes clear by parallel the human mind’s appreciation of significance in its sensory operations as measured by the D diversity index. Ultimately this parallel derives from the commonality between thermodynamic and sensory systems in the measures of both being affected by the magnitude of their subset constituents, be it of the energy of molecules measured in a biased way by a thermometer or of the size of color subsets sensed by the CNS, the central nervous system.
And this helps make clear that our perceptions and the thoughts we developed from them as used to guide our behaviors and communication with others depend not just on what it is that objectively exists out there but also on how they are sensed or measured with our CNS sensing apparatus. Hence understanding entropy as diversity in physical systems as diversity strongly validates the reasonableness of the concept of significance in our sensory apparatus, which tells us that reality for people is what is sensed or measured rather than some totally objective phenomena that lies outside our senses. From a purely epistemological perspective, then, this greatly calls into question transcendental notions like gods and angels and devils that have absolutely no basis in anybody’s sense of them as these items claimed to exist somehow have never been sensed. This is very important to developing a clear picture of what is meaningful in life for plaguing our sense of life with nonsensed imaginations muddies the picture critically.
Significance is one major determinant of what makes information meaningful. Later we will make it clear that the other determinant of the meaningfulness of things is the association of emotion with them major, something diversity will also present a beautiful picture of by enabling a representation of our basic emotions of fear, hope, excitement, relief, sex, love, warmth, anger and the like with great mathematical precision in a later section.
The other concept basic to the mind’s information processing introduced through diversity based entropy is compressed representation. The µ mean is the most familiar and commonly used compressed representation. Specifying the number of objects in a subset of the K=12, N=4 set of (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), as its µ=K/N=12/4=3 arithmetic average compresses the number of numbers needed to describe the set from N=4 of them, (5, 3,3, 1) to the one number of µ=3. While that constitutes efficiency in description in using less information to describe the set, note that the loss of some information in this compression generates error as seen in the statistical error associated with the arithmetic average of an unbalanced set. This compressed representation of the arithmetic average is also inexact as we made clear earlier.
Another compressed representation of the (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1) is its D=3.273 diversity index. Again, like the arithmetic average, this is a 1 number representation of an N=4 number, number set and an efficient compression in that regard. It also leaves out information about the set but less so than the set’s µ=3 arithmetic average because D includes a measure of the distribution of the K objects over the N=4 subsets as is clear from D=N/(1+r^{2}) of Eq16 inclusion of r^{2} as a measure of set distribution. And D=3.273 is also an exact compression of the set as is the h=3.468 square root diversity index of the set.
The h_{AV} average diversity or entropy of a thermodynamic system is a higher level compressed representation in representing the h diversity compressed reductions of all of the microstate permutation of the system as their average. And the ψ_{AV}=K/h_{AV} average square root biased average is another higher level compressed representation as the average over time of the square root biased average energy per molecule that changes over time from continuous collisions between molecules.
We can appreciate these mathematically formulated compressed representations as one category of the generalizations we make about the world around us, quantitative generalizations. The usefulness of these compressed representations or quantitative generalizations is obvious enough that we need not enumerate them.
These quantitative compressed representations also shed great light on the nonmathematical generalizations we humans use as compressed representations that range from the common nouns and verbs we use to represent objects and actions with to our generalized knowledge of complex processes of all sorts. In the simpler case of common nouns as compressed representations, note that the word “dog” conjures up a picture in the mind of a person who hears the word that is an average or morph of all the dogs a person has come across including in picture books and movies seen. The mind compresses everything it comes into sensory contact with in its memory of those things. Such compressed information from the past is used in the interplay of emotions and of thought manifest as generalization, which very much affects both the things we decide to do and our communications with others.
This section has been a relatively qualitative discussion of two important information concepts gleaned from our development of diversity based entropy: significance and compressed representation. In the next section we will use the diversity concept to more formally revise information theory.
7. Revising Information Theory
To do that, let’s start back with the central function for information in information theory, the Shannon (information) entropy of Eq1.
1.)
Information theory was developed in 1948 by Claude Shannon to characterize messages sent from a source to a destination. Consider (■■■, ■■■, ■■■, ■■■) as a set of K=12 colored buttons in a bag in N=4 colors. I’m going to pick one of the buttons blindly and then send a message of the color picked to some destination. The probability of any color of the N=4 colors being picked is the p_{i} weight fraction of the color, for all the colors in this case,
73.) p_{i }= 1/N = 1/4.
So there’s a p_{1}=1/4 probability of my sending a message saying “I picked red.” And a p_{2}=1/4 probability of my message saying, “I picked green,” and so on. Plugging these p_{i}=1/4 probabilities into messy Eq71 obtains the amount of information in the color message sent as
74.)
This tells us that there’s H=2 bits of information in a message sent. What does that mean? The most basic interpretation of the H=2 bits is as the number of binary digits, 0s or 1s, minimally needed to encode the color messages gotten from (■■■, ■■■, ■■■, ■■■) in bit signal form, namely as [00, 01, 10, 11]. Red might be encoded as 00, green as 01, and so on. Then when the receiver of the message gets 00 sent, he decodes it back to red. The H=2 bits measure is considered to be the amount of information in a message as the number of bit symbols in each bit signal. This bit signal information is the synthetic or digital information that computers run on. There is a simpler form of the Shannon information of Eq1 used for balanced or equiprobable sets like (■■■, ■■■, ■■■, ■■■). Because the p_{i} probabilities are all the same for a balanced set as p_{i}=1/N, substituting 1/N for p_{i} in Eq1 derives the simpler form for H of
75.) H= log_{2}N
This equation gets us the same H=2 bits result for messages sourced from (■■■, ■■■, ■■■, ■■■) as did Eq74, but in a simpler way as H= log_{2}N = log_{2}4 = 2 bits. Now let’s also use Eq75 to calculate the amount of information in a message that derives from a random pick of one of K=16 buttons in N=8 colors, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■). Because this set is balanced, the probability of picking a particular color and sending a message about it is the same for all N=8 colors, p_{i}=1/N=1/8. And the amount of information in a color message from this set can be calculated from the simple, equiprobable, form of the Shannon entropy of Eq75 as H= log_{2}N= log_{2}8= 3 bits. This has us encode messages from N=8 color (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) with the N=8 bit signals, [000, 010, 100, 001, 110, 101, 011, 111]. Each bit signal has H=log_{2}8=3 bits in it understood as the amount of information in a color message derived from this set.
Now we want to make the case that information and diversity are synonymous with each being a measure of the other. We already tried to make that case before by suggesting that the D diversity interpreted as the number of significant subsets in a set was an instance of meaningful information. The synonymy of diversity and information can also be demonstrated in a more technical way. First of all it is well known that the H Shannon information entropy expressed in natural log terms is the Shannon Diversity Index used over the last 60 years in the scientific literature as a measure of ecological and sociological diversity. Paralleling Eq1 for the Shannon information entropy is the Shannon Diversity Index of
76.)
And for a balanced set, paralleling Eq75, the Shannon Diversity index is H = lnN. The difference between the Shannon entropy as information and the Shannon entropy as diversity is merely the difference in logarithm base, the direct proportionality between the two telling us from measure theory in mathematics that what one function is the measure of, the other must also be a measure of, here both of information and diversity. Another conceptual equivalence between diversity and information that derives from classical information theory comes from Renyi entropy, R, which is taken in information theory to be information in being a parent function or generalization of the Shannon information entropy. Its connection to diversity lies in its being the logarithm of the D Simpson’s Reciprocal Diversity Index as we saw earlier in Eqs24.
4.) R = logD
This also strongly suggests a synonymy between diversity and information. The above two diversityinformation associations suggest two kinds of diversity indices that further imply two kinds of information functions. The two kinds of diversity indices are the logarithmic kind, as with H and R; and the linear kind, as with D. To better understand the two kinds of information that the two kinds of diversity indices, logarithmic and linear, imply we next develop the D (linear) diversity index as a bit encoding recipe that parallels H as the bit encoding recipe we introduced it as. The sociopolitical implications of this somewhat tedious exercise are profound and make the following technical considerations worth our time and effort.
Recall the H=2 bits for (■■■, ■■■, ■■■, ■■■) that specify for its N=4 color messages an encoding of N=4 bit signals, [00, 01, 10, 11], each consisting of H=2 bits or binary digits. We can also use the D=4 diversity index as a bit encoding recipe. The D=4 diversity index of this set translated as the number of bits in a bit signal obtains N=4 bit signals for the N=4 colors of the set of [0001, 0011, 0111, 1111], each of which consists of D=4 bits. And for the N=8 color set of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) whose H=3 bits measure encoded it as [000, 001, 010, 100, 110, 101, 011, 111], the D=8 diversity index used as a coding recipe encodes it as [00000001, 00000011, 00000111, 00001111, 00011111, 00111111, 01111111, 11111111], with each bit signal consisting of D=8 bits. Note in both D encodings that only one permutation of a given combination of 1s and 0s can be used. This restricts us writing the 20s and 61s combination of bits in only one permutation of it, as for example as 01111011 or as 00111111, but not both. And also note that the all 0s bit signal is disallowed in this D encoding recipe.
Anyone familiar with information theory will immediately note that the D bit recipe is inefficient as a practical coding scheme in its requiring significantly more bit symbols for a message than the H Shannon entropy coding recipe. This is not surprising since Claude Shannon devised his H entropy initially strictly as an efficient coding recipe for generating the minimum number of bit symbols needed to encode a message in bit signal form. The D diversity index as a coding recipe fails miserably at that task of bit symbol minimization. But we have developed it not trying to engineer a practical coding system but rather to show how D can be understood in parallel to H as an information function in being understandable as a bit coding recipe, its efficiency for message transmission being quite beside the point.
We show D to be an information function for a very familiar kind of information, quantitative information, by next looking carefully at the details of the difference between the H and D bit encodings. Recall the (■■■, ■■■, ■■■, ■■■) set, whose N=4 colors are encoded in H encoding with [00, 01, 10, 11] and in D encoding with [0001, 0011, 0111, 1111]. Now look closely to see that these are two very different ways of encoding the N=4 distinguishable color messages derived from (■■■, ■■■, ■■■, ■■■) with N=4 distinguishable bit signals. What is special about the D bit encoding of (■■■, ■■■, ■■■, ■■■) with [0001, 0011, 0111, 1111] is that all of these N=4 bit signals are quantitatively distinguishable from each other with each bit signal having a different number of 0s and 1s in it than the others.
This is not the case for the H encoding of (■■■, ■■■, ■■■, ■■■) with [00, 01, 10, 11]. For with them it is seen that the 01 and 10 signals have the same number of 0s and 1s in them and, hence, are not quantitatively distinct from each other. Rather the distinction between 01 and 10 is positional distinction from the 0 and 1 bit signals being in different positions in 01 and 10. So 01 and 10, we could say, are qualitatively distinct rather than quantitatively distinct.
This quantitative versus qualitative distinction for D and H encoding is even more clear for the N=8 set, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), and its D=8 bit encoding of it as [00000001, 00000011, 00000111, 00001111, 00011111, 00111111, 01111111, 11111111]. For there we see that every one of the N=8 bit signals is quantitatively distinguished from every other bit signal in each having a different number of 0s and 1s in them. This quantitatively distinguishable bit encoding with D contrasts to the H=3 bit encoding of that color message set as [000, 001, 010, 100, 110, 101, 011, 111] in which we see that the 001, 010 and 100 signals are not quantitatively distinguished, each of them having 20s and 11, but rather distinguished entirely by the positions of the 1 and 0 bits in them. And that positional or qualitative distinction is also seen between the 011, 101 and 110 signals of its H bit encoding, all of which are quantitatively the same rather than quantitatively distinct.
The qualitative versus quantitative H versus D encodings corresponds to our everyday sense of information as being either of two broad kinds, qualitative or quantitative. When I tell you General George Washington worked his Virginia planation with slaves rather than hired help, that’s qualitative information for you. But when I tell you that Washington owned 123 slaves at the time of his death, that’s quantitative information. With our example set of (■■■, ■■■, ■■■, ■■■) we see that the color subsets are all qualitatively distinct from each other as is well represented with their [00, 01, 10, 11] H bit encoding. It is also clear, though, that there are N=D=4 color subsets, which is well denoted with [0001, 0011, 0111, 1111], which distinguishes them as the 1^{st} color, the 2^{nd} color, the 3^{rd} color and the 4^{th} color, which effectively counts the number of colors.
This qualitative versus quantitative differentiation explains why the H, the qualitative coding recipe is logarithmic and why the D quantitative coding recipe is linear. H is logarithmic because it is a coding recipe for information communicated from one person to another. The human mind distinguishes intuitively between the positions of things as between 20s and 11 arranged as 001 or 010 in different positions. This property of mind allows us to represent distinguishable messages sent from one person to another, like ■ and ■, encoded with signals distinguished via positional or qualitative distinction like 001 and 010. Because the N number of distinguishable messages that can be constructed from H variously permuted, variously positioned, bit symbols is determined by N=2^{H}, a power function, the information in one of those messages specified as the H number of bits in each bit signal is inherently logarithmic via the inversion of N=2^{H} as H=log_{2}N.
Compare this to D=4 encoding of the N=4 colors in (■■■, ■■■, ■■■, ■■■) as [0001, 0011, 0111, 1111]. This D encoding recipe encodes the colors via the number of 1s in the bit signals or effectively with ordinal numbers that encode the colors as the 1^{st} color, the 2^{nd} color, the 3^{rd} color and the 4^{th} color, which is most basically just a count of the number of distinguishable colors, clearly quantitative information about them. D is linear because counting is inherently linear as with 1, 2, 3, 4 and so on. While much information transmitted or communicated from one person to another is qualitative in form as suits practical efficiency, information sourced directly from nature is quantitative in form when it is a precise description of nature as every practitioner of physical sciences understands. As such an encoding of such quantitative information from nature should be most basically linear in form rather than logarithmic as is the h diversity encoding of the number of energetically significant molecules in a thermodynamic system.
The above development of quantitative versus qualitative information provides the broadest understanding of information as diversity. That includes logarithmic diversity for information communicated from person to person as the H Shannon information entropy also understandable as the Shannon Diversity Index provides; and linear diversity, linear in form as D or h. Take careful note that quantitative descriptions of items can also be represented and communicated via positional distinctions as seen in the Arabic numerals that write thirteen as 13 rather than 1111111111111 for efficiency sake, with 13 distinct position wise from thirtyone as 31. But that should not take away from the reality of the elemental linear nature of counting and, hence, of science’s distinguishing things quantitatively in the linear rather than logarithmic form the D and h diversity indices have.
This argument that information can be logarithmic or linear in form runs sharply counter to the notion by many information theorists that that the only proper form of information is from the Khinchin derivation of it, the Shannon information entropy, which is logarithmic. That this rigid perspective, which makes impossible an understanding of meaningful information, is nonsense is easy to show in the Khinchin derivation of information as the Shannon entropy defines information to begin with, in a narrow way that obviates our familiar sense of what information is, and then proceeds to derive information as it specified information must be in its axiom set. This approach is a prime example of the value of Gödel’s incompleteness theorem, which considers all axiomatic schemata invalid for that very reason of any conclusions one wishes to attain being achievable via a biased selection of the axiomatic underpinning of the argument to fit the conclusions.
Recognizing this and allowing the D diversity index to be understood as a measure of quantitative information allows us to understand one cornerstone of meaningful information to be information that is judged significant by the human mind rather than insignificant. In a nutshell: significant information is meaningful information. And D diversity also allows is to develop the other cornerstone of meaningful information and that is information associated with emotion, the central topic of the section following this next one, which deals with significance as it affects people.
8. The Significance of Individuals
Much of what people do and think is affected by their sense of themselves as being significant or insignificant individuals. This is important for our understanding corruption in social institutions as deriving from an individual’s selfinterest being greater than his or her commitment to the institution. That is, we can attribute corruption to the great need of an individual to feel significant rather than insignificant, which is generally very difficult to achieve in a hierarchically ordered, exploitive, society. This drive is a determinant not only in the Wall St. corruption that jiggled the mortgage market and caused the 2008 recession that near destroyed many American families, but also in the unspoken judicial, political and medical corruption that abounds in today’s America. And such corruption extends to an academic community whose selfinterest in status and position tends to trump considerations of truth. This condemnation of academia is so harsh and so difficult to make stick that we approach this problem of people’s motives to cheat with mathematical analysis.
Social dominance, malevolent and benevolent, is a universal reality however much the concept is unspoken because it abrades on the hope and promise of freedom and fairness. In general the dominant individual is thought to be significant by himself and others and the subordinate person, insignificant. Dominance in a two person relationship, the simplest to analyze, depends ultimately on the relative probabilities of success in competition between the two whether the competition be explicit as in contact sports or implicit as in the track and field, “I can do this better than you can” type. The characteristics of explicit competition are clearer and, hence, is easiest to consider first.
Consider the random selection of an object from the K=10, N=2 color set, (■■■■■, ■■■■■), x_{i}=5 and x_{2}=5, p_{1}=1/2 and p_{2}=1/2, where the p_{1} and p_{2 }weight fractions of the set are the probabilities respectively of red and green being picked. If red is picked, the player assigned red gets $100 from the player assigned green, and vice versa. And in contrast to this balanced game, consider it played with the (■■■■■■, ■■■■) set, x_{i}=6 and x_{2}=4, p_{1}=6/10 and p_{2}=4/10, in which the red player has an edge over the green player of
77.) Δp = p_{1}−p_{2 }=6/10 – 4/10 = 2/10 = 20% =.2
This Δp=.2 measure is also understandable as the vulnerability of the green player. Assume now that this “unfair game must be played by the green player unless he or she opts out of playing by paying the red player $25. Of course, it makes little sense financially for the green player to pay $25 to avoid the game because the average loss is less than that as Δp=.2($100)=$20 per game. Now let’s change the game further to one where the color is picked randomly from (■■■■■■■■■, ■), x_{i}=9 and x_{2}=1, p_{1}=9/10 and p_{2}=1/10. The edge for the red player has increased now to
78.) Δp = p_{1}−p_{2 }=9/10 – 1/10 = 8/10 = 80% =.8
In this game it makes great sense for the green player to pay $25 to avoid the game because the average loss is greater than $25 at Δp=.8($100)=$80 per game. This doesn’t completely obviate the possibility that the green player might get lucky if he plays and win, thereby getting $100 instead of losing the $25 by forfeit without any attempt to win. But generally speaking in any kind of competition that has this form of two players having very different probabilities of winning, past some critical Δp value the additional cost for losing after playing the game and trying to win gets the inferior player to capitulate to the superior player and accept the lesser penalty without a fight.
If a game with lopsided probabilities were played frequently as part of the ongoing relationship between the two players, this level of control and exploitation would instinctively make the inferior player feel insignificant. This emotional outcome of the lopsided relationship has firm mathematical expression in the D diversity index as expressed as D=N/(1+r^{2}) in Eq16 when its r^{2} relative error term is given in terms of the weight fraction probabilities as
79.)
This expression for r^{2}
is easily derived from previous functions we’ve considered but is just simply
demonstrated here with an example for expediency sake. Consider the K=9, N=3
natural number set, (4, 4, 1), which from Eqs2,3&4 has a relative error of
r=.471 and r^{2}=.222=2/9. With p_{i} = (4/9, 4/9, 1/9), the r^{2}
statistical error of (4, 4, 1) is calculated from Eq79 as
80.)
This demonstrates the validity of Eq79 for r^{2}. For an N=2 set of relative probabilities of success of two persons in a competition of p_{1} and p_{2}, the r^{2} term is obtained from Eq79 as
81.)
This develops the number of significant people in the N=2 person relationship from D=N/(1+r^{2}) as
82.)
When there is perfect balance in the competition and, hence, in the relationship, p_{1}=p_{2}1/2 and r^{2}= (Δp)^{2}=0, as brings about D=2, which indicates that there are 2 significant people in the relationship. In such both persons tend to think of themselves and of the other person as significant, a positive or pleasant feeling both in terms of what you think of yourself and what the other person thinks of you. In competitions between N=2 persons where the probabilities of winning are p_{1}=.9 and p_{2}=.1, the D diversity is
83.)
Rounding off D=1.22 to D=1 indicates that there is but 1 significant person in the relationship, the person with the large p_{1}=.9 probability of winning, the other person, the one with the slight p_{2}=.1 chance of winning, being insignificant in the relationship. That is, the mathematically insignificant person feels insignificant and is also thought to be such by the dominant person. There are other factors in a relationship that mitigate the displeasure of being the insignificant partner in a relationship, it must be stressed. A child inherently thinks of its adult parent as the “big person”, the significant one, and is yet quite happy with a parent who gives love as makes up for this lesser and unequal role in the relationship. But this changes necessarily as the child matures and seeks to develop its own sense of significance. Indeed this mathematical specification of personal significance is a manifestation of a person’s “ego” or sense of self as propounded by Sigmund Freud. The mathematics of the factors of caring for another less able individual, as a child is relative to an adult parent objectively, must wait until we develop functions for the emotions in later sections, some of which provide balance for the generally unpleasant feelings of being insignificant or inferior.
Until then we will understand insignificance as a generally unpleasant enough feeling that it causes people to prefer to be significant as an equal or as dominant rather than to be insignificant. Let us repeat for emphasis that there are other factors involved than just competition in relationships and we will get to those in due time. In the meantime we will generalize that people prefer having power than not having power. Nobody who plays an explicit competitive game prefers anything other than winning for this reason.
Tom Brady of football fame from his success in the game feels significant and is thought of as significant, while the fellow on the losing end in games and in scrimmages who soon gets cut from the roster feels insignificant and is thought of as such by others in and out of his profession, (indeed, as insignificant, usually not thought of at all.) We need not dwell at length on the obvious rewards of being and feeling significant. Hence, the question to be asked is whether Tom Brady would cheat to win and be significant and enjoy the rewards of being significant? Would Tom deflate the footballs to be significant? This is not asking the question of whether or not he actually did. We know Tom Brady personally and can vouch for the fact that he’s not that kind of a guy. But maybe somebody other than Tom Brady would deflate the footballs to achieve Brady’s significance. That’s the point. Would somebody do that or something like that if he or she could get away with it?
The payoff for winning, for having a high p probability of winning, for having the edge in competition and being significant, is so high and the cost of having a low p probability of winning, of being vulnerable to loss and being insignificant, is so great emotionally, that in many situations, people who can get away with corruption, with cheating on the rules, just do it. Moreover it is also the case that such corrupt behavior is never openly confessed to or in any way revealed because doing so kills the “getting away with it” factor in making a deal with the devil.
For that reason, there’s lots of corruption and not much open talking about it. Really does any even halfintelligent person think that no Wall Streeter going to jail, not even for a day, after six years of investigation of this multibillion dollar scam by the Justice Dept. is anything but a manifestation of consummate business, judicial and political corruption? Even though nobody with a public voice ever says, in contradiction to the Orwellian doublespeak reasons why there was no prosecution of this grand theft by Wall Street banks on tens of millions of Americans, that our social system is thoroughly corrupt, is it not apparent on its face?
Indeed capitalism is corrupt. All civilized social systems are inherently corrupt. The drive to be on top, to be significant, to avoid insignificance, is a powerful incentive to break any code of fairness held up as the moral norm in a society. Even heads of state in a military dictatorship never tell their underling citizens that the game is corrupt and unfair. Be sure that Hosni Mubarak of Egypt, 30 years the military dictator of that vassal state of the USA, a fellow who scuttled billions for himself and his family through systematic corruption, never went on Egyptian TV before the Arab Spring to tell the Egyptian peasants that he was robbing and fucking them blind.
All power systems work this way including our capitalism, which never buys two hours of airtime on TV to proclaim to the American people that it is robbing them blind. The only difference between military dictatorship and capitalism is how the edge is obtained, not whether it exists and is used for the benefit and privilege of those who have the edge. Buying and selling is inherently corrupt and deceitful. The game is to buy cheap and sell dear. The seller is always out to tell the buyer anything he has to in order to extract the maximum amount of money out of the buyer. In the small, as hagglers over price in a New Delhi marketplace know, it is part of the game of the seller to lie in order to get the maximum cash out of the buyer. Institutional corruption comes in when the political system and the judicial system joins in the game against the rules in order to tolerate the inherent corruption and deceit of the marketplace.
But these instances of corruption get way ahead of the game and require much more analysis for their picture to be drawn our fully. What we want to talk about in this section in detail, rather, is the corruption in the marketplace of analytical ideas, that makes it impossible in the end to honestly talk about and uncover the corruption in the broader society that will soon be taking us all to nuclear hell because of the stupidity and lack of foresight from leaders who attained their power through cleverness in becoming socially significant by maximum capability at corruption and deceit rather than really being smart. Beyond the exceptions like Bill Gates, who is too much of a coward and a pussy to enter the tussle of the political and economic arenas where real people suffer daily, the entrepreneur is nothing but a clever thief.
In academics, as in all other professions, there is a hierarchy of power and as in all other hierarchies, it is corrupt as long as it can get away with being corrupt as requires centrally hiding the corruption. As in all areas of corruption, people maintain their p probability of being successful by helping to enable other people’s p probability of being successful. That is, in colloquial language, you scratch my back and I scratch yours. The temptation to do this in obviation of the rules is very strong because the penalty for not doing it is frequently that one winds up with little p probability of winning in competition and of being insignificant, while the prize for “playing the game” is attaining some significance, which feels much better than being insignificant.
In academics, just as in every profession, some people do the hiring and firing, the awarding of cash grants to do research and the editing of journals where research papers are published as enable position and grant support. Most often the people on the top of this game are “experts” in the field. Or better said they are recognized as experts by others in the field, which gets you right back to the “you scratch my back, and I’ll scratch yours” game. Of course, playing that game with the devil is lost if one advertises the fact that one is an academic entrepreneur. One most amusing instance of it in recent times was the Complexity Theory bullshit engineered by Stuart Kauffman whose debunking was the primary focus of the Scientific American article by John Horgan, From Complexity to Perplexity, I brought up at the beginning of A Theory of Epsilon.
Unlike my quip about Tom Brady, we actually do very much know Stuart Kauffman personally. And it is interesting that long before we read Horgan’s article ridiculing complexity theory, we had a sense after an hour’s long lunch with Kauffman from the obvious lack of clarity in his doubletalk mathematics that he was as slick a charlatan as Bernie Madoff. For what Kaufmann did was to spin a mathematical argument so complex about complexity that it was near impossible to take apart, for a while anyway. Before it was taken apart publically and Kaufmann chased off to Canada to talk his nonsense to the more naïve Canuck academics he enjoyed great significance in association with the Santa Fe Institute and even wound up a McArthur grant winner.
The corruption in academics is not as obvious in most cases as Kaufmann’s carny game. In our case at hand it has consisted of “experts” in the field of thermodynamics being unwilling to admit that the material they claim to be experts at is incorrect. Though we have run into a good number of them over the years in various universities, the attitude of Bill Poirier stands out. Note his comments to us about our revision of microstate entropy.
In short, though the Gibbs and Boltzmann Shannonlike formulations of entropy have their limitations/issues, there is nothing really mathematically "wrong" about themthey are what they claim to be, within wellknown caveats. Conversely, this is not to say that your approach is "wrong" or otherwise without value; as I said in an earlier email, there may well be more than one useful quantity associated with the same general concept. But I would be wary of making claims that classical entropy is "fundamentally incorrect", and that your approach "provides the only correct understanding of microstate entropy."
Poirier is alluding to both the BoltzmannShannon take on entropy and our meaningful information derivation of it being mathematically equivalent and both correct in that regard. Yet despite the “limitations/issues” with the standard formulation that Poirier cites, which have interminably confused students and professionals alike for the last 100 years, he still favors the standard, perplexing take on entropy unable to shake the inferior explanation he has grown to accept over the years despite its obvious shortcomings. Proof that Poirier is dead wrong lies in his insistence in Chapter 10 his recent book that entropy can be explained from information theory despite the general understanding in the scientific community conveyed in the above Scientific American quote that information theory, as it presently stands, cannot be applied to explaining physical systems. Our extension and elaboration of information theory to include meaningful or significant information as it is found both in physical and in human nature makes the intimate association between entropy and information clear enough that even a high school chemistry student can understand entropy now.
We also mention lightly the pettiness and stupidity of today’s scientists in clinging to orthodoxy for the sake of retaining the crown of “expert” and the position, status and pay that go along with it. A perfect example of this is of our front page poster boy, Bill Poirier of Texas Tech in Lubbock. Perusal of Chapter 10 in his recent book, A Conceptual Guide to Thermodynamics shows a frivolous notion of an information theory interpretation of thermodynamic entropy. It can be judged on its merit by anybody who takes the time to pick up the book and read that chapter in it. His frivolous interpretation of entropy as “the amount of information you don’t know about the thermodynamic system” should be damned because it totally misunderstands the mathematical similarities between information and entropy that scientists have been aware of for the last 65 years. The reason for the similar form of the two is that both are inexact measures of sets of things that are generally unbalanced and whose exactness mathematically and as a clear correct understanding of them is provided by the same functional replacement for the N number of constituents in a set, namely diversity be it D or h. He personally should also be damned for not being willing to budge an inch for fear of making a fool of himself in his hypothesis being shown to be wrong, this after a many email exchange with him that laid out the foregoing in a series of first drafts of this material.
He is hardly the only one out there who thinks this way, science having fallen into the same state as all other endeavors in modern day mathematics where people learn to feather their own nests at the expense of the broader needs of society. If such is the case in the natural sciences, that much more is it prevalent in the human sciences, which are thoroughly adulterated by ideology to ascribe people’s unhappiness to the bugaboo of mental illness which is almost as vague, spirit like and intangible as Satan as the cause of evil and unhappiness. Clinical psychology never prescribes rebellion against unfair authority and its humiliations as a remedy for the unhappiness caused by it, but rather “adjustment” to the pain of it and that by any means which includes developing a chronic dependency on psychotropic drugs and delusional belief in religious superstition. God, Heaven, after life and the devil are quite alright with the pseudoscience of clinical psychology.
From a purely logical perspective, one should have great doubt about a supposed science that purports to understand abnormal emotion without giving any clear sense of the normal human emotions, as we will do starting in the next section as the foundation of a new set of mathematics based human sciences.
9. The Mathematics of Human Emotion
We do not wish to throw the baby out with the bathwater in our revision and expansion of information theory in Section 6. It is in no way a denial of all of its basic principles, a primary one of which we form the foundation of our specification of all of the human emotions in mathematical form. That principle I am talking about is information theory’s alternative interpretation of the H Shannon entropy of Eq71 as the amount of uncertainty that getting a message resolves upon being received. Uncertainty and information are closely related in information coming about as the resolution of uncertainty. If you have no idea of the way Company XYZ you hold stock in is going and I tell you from what my cousin, the president of the company, told me that they are contemplating bankruptcy in two weeks, that message is information for you because you had uncertainty about the company’s situation to begin with. But if I tell you that Osama bin Laden was the mastermind of 9/11, something you certainly knew beforehand, that message would not be information for you because you had no uncertainty about that.
In a more mathematically treatable way, if you are playing a game where you must guess which of N=4 colors I’ll pick from the set of K=8 colored buttons, (■■, ■■, ■■, ■■), inherently you have uncertainty about what the color is. Keep in mind from our earlier considerations the H=2 bits amount of information associated with this set. That value of H=2 is a measure of the amount of uncertainty you have as the number of yesno binary questions one needs to ask about the colors in (■■, ■■, ■■, ■■) to determine which color I picked. By a yesno binary question is meant one that is answered with a “yes” or a “no” and, as binary, cuts the number of possible color answers in half.
One might ask of (■■, ■■, ■■, ■■), “Is the color picked a dark color?” meaning either purple or black? Whatever the answer, a “yes” or a “no”, the number of possible colors picked is cut in half. Assume the answer to the question was “no”, then the next question asked might be, “Is the color green?” If the answer to that next question is also “no”, by process of elimination the color I picked was red. It took H=2 such questions to find that out. So the amount of uncertainty about which color I picked is understood to be H=2. And the amount of information gotten from receiving a message about the color picked is H=2 bits understood as the amount of uncertainty felt beforehand.
Let’s play that game with (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) now whose H=3 bits Shannon entropy is the amount of uncertainty you feel about which color I picked from that set of buttons because it takes H=3 yesno binary questions to determine the color. The first question for (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) might be, “Is the color a light color?” meaning red, green, aqua or orange. When “no” is the answer, it halves the field of colors picked to (■■, ■■, ■■, ■■). And two more yesno binary questions will then reveal the color picked. The amount of uncertainty for the color picked from (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) is then its H Shannon entropy of H=3 bits interpreted as 3 binary questions. And the amount of information you would get if I sent you a message about which color was picked would be H=3 bits of information as the resolution of the H=3 bits of uncertainty felt beforehand.
That information is affected by emotion is obvious from the sense of information underpinned by uncertainty, something people generally feel as an unpleasant emotion. Moreover when uncertainty is resolved, by whatever means, a person tends to feel something akin to relief or elation, a generally pleasant emotion. Now while it is true that the H Shannon entropy provides some measure of uncertainty as discussed above, the human mind really doesn’t work on logarithmic measures for the most part. We tend rather to evaluate uncertainty probabilistically. Let’s go back to guessing the color picked from the N=4 color set, (■■, ■■, ■■, ■■).
The probability of guessing correctly, which we’ll give the symbol, Z, to, is
84.)
And the probability of failing to make the correct guess, understood as the uncertainty in guessing, is
85.)
Now let’s recall the D diversity of a balanced set from Eq4 to be D=N. This allows us to understand the U uncertainty as
86.)
Now let’s make a table of sets of buttons that have more and more D diversity and list the U uncertainty in guessing the color picked from them.
Sets of Colored Buttons 
D=N 
U=(D–1)/D 
(■■, ■■) 
2 
1/2=.5 
(■■, ■■, ■■) 
3 
2/3=.667 
(■■, ■■, ■■, ■■) 
4 
3/4=.75 
(■■, ■■, ■■, ■■, ■■) 
5 
4/5=.8 
(■■, ■■, ■■, ■■, ■■, ■■) 
6 
5/6=.833 
(■■, ■■, ■■, ■■, ■■, ■■, ■■) 
7 
6/7=.857 
(■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) 
8 
7/8=.875 
Figure 87. Various Sets and Their D and U Values
Very obviously the U uncertainty is an increasing function of D diversity. That
is, as D increases, U increases. More formally U is an effectively continuous
monotonically increasing function of D. This, from measure theory in mathematics,
tells us that whatever D is a measure of, U is a measure of. Earlier we made it
clear that D diversity was a measure of information. And that would also make
the U uncertainty measure understandable as information, which fits with the
classical information theory take on information as the resolution of
uncertainty.
This gives us two ways to specify the resolution of uncertainty being information, one as H in a logarithmic way, the other as U in a linear probabilistic way. The breakthrough in psychology that finally makes sense out of human nature is to understand emotion as meaningful information. And to do that we need to specify the uncertainty that precedes information in terms of probability, U, not only because the human mind is geared to sensing uncertainty as probability rather than in bits and bytes, but also because doing so, using U, allows us to connect it up with something meaningful, and that meaningful something is money.
Specifically, configuring uncertainty and information in terms of U probability connects uncertainty up with that meaningful item of money through a game of chance designed to have a cash penalty imposed on you if you fail to win at it. It is a color guessing game that uses the N=3 color set of colored buttons of (■■, ■■, ■■). If you fail to guess the color I pick, you pay a penalty of v=$120. The probability of guessing correctly is
88.)
And the probability of failing to guess correctly is
89.)
Now the product of the penalty, v, and the uncertainty, U, which is the probability of paying the penalty, is called the expected value of the game
90.) E= –Uv
Putting in the values, U=2/3 and v=$120, we calculate the E expected value or expectation to be
91.) E= –Uv= –(2/3)($120)= –$80
The negative sign specifies E= −$80 as a loss of money, the average loss incurred if you are forced to play this game repeatedly. If you play the game three times, for example, on average you will roll a lucky number and escape the v=$120 penalty one time out of three; and you will fail to roll a lucky number and pay the v=$120 penalty two times out of three as adds up to a $240 loss that averaging out over three games is an E= −$240/3= −$80 loss per game.
The E= –Uv term that is the product of the U uncertainty and the v penalty of money, a meaningful item, can also be understood as meaningful uncertainty. A more familiar expression for this E= –Uv meaningful uncertainty is the fear you have of losing money when you are made to play this game. That E= –Uv is a fitting equation for such fear is clear from three perspectives. The first is that your fear of losing money is a function of the U uncertainty or your probability of failing to guess the color. If we change the game to my randomly picking a colored button from the N=8 color set of buttons of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), then the probability of a successful guess goes down to
92.) Z = 1/N =1/8 = .125
And the probability of failing to guess correctly and of your having to pay the v=$120 penalty goes up to
93.) U=1–Z=7/8=.875
And the expected value translated as the amount of fear you have in having to play this game is
94.) E= –Uv= –(7/8)($120)= –$105
That fear feels unpleasant is manifest in the negative sign of the E= –Uv expectation. And you see that this function also fits the natural sense of fear that would be felt including as a measure of the displeasure in it if we change the v penalty. If we increase it to v=$360, the displeasure of fear felt for this game played with (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) goes up to
95.) E= –Uv= –(7/8)($360)= –$315
We have introduced emotion now in a very straightforward way in terms of understanding meaningful uncertainty as fear. Next now consider what happens if there is a third person involved in this game who sees which color I picked and tells it to you on the quiet. Then you can use it as your guess and avoid paying the penalty. To go along with the basic algorithm that information is the resolution of uncertainty in information theory, we’ll understand the amount of information you got in the color told you, meaningful information from its resolving your meaningful uncertainty, to have the same measure as the meaningful uncertainty, –Uv, except we’ll get rid of the – minus sign understanding the removal of the meaningful uncertainty to be specified as
96.) T= –(–Uv) = Uv
We’ll explain where the T symbol comes from later on, understanding it now to represent the amount of meaningful information you got from the message told you about color. Now intuitively, you are going to feel an emotion of relief in getting this meaningful information. And the T=Uv function is a very good measure of the amount of relief, how pleasant it is in intensity. For the greater the v penalty, the greater the relief you feel in avoiding it. And the greater the U uncertainty, the greater the relief also. And the implicit (+) positive sign of T=Uv= +Uv, is a reasonable marker for the positive feeling or pleasure you get in relief, that as opposed to the E= –Uv fear, which is unpleasant as it (–) minus sign denotes.
Of course, the amount of fear you feel in expectation of paying the v penalty and the amount of relief you feel in avoiding the penalty are both dependent not only on the U probability of paying the penalty and the v amount of the penalty, but also on how much money, how much wealth, you already have. A millionaire doesn’t really care about losing $80 or get that much pleasure of relief in avoiding the loss as compared to a person who had but $5 in their purse or bank account. This marginality aspect that affects the emotions involved, we’ll obviate by making everybody who plays this game and in every game played have the same amount of wealth.
With that we have the basics down: getting rid of E= –Uv meaningful uncertainty by some activity, here guessing a color randomly chosen, generates T=Uv meaningful information. And this also introduces two primary emotions people feel, fear as E= –Uv and relief as T=Uv. The color guessing game was fine for an introduction to emotion, but next we want to develop the basic emotions, and there are a few more of them, in a more general way. Specifically we want to do it for all goal directed behaviors.
And to do that we are going to switch the game to a dice game called Lucky Numbers. It will develop mathematical functions for a fuller spectrum of our most basic emotions like hope, anxiety, excitement, disappointment, fear, relief, dismay, relief, joy and depression, which we’ll refer to as our operational emotions. And then later we’ll modify the game played to develop functions for our visceral emotions like sex, anger, hunger and the taste pleasures of eating.
We’ll start off playing this Lucky Numbers dice game for a prize, one of V=$120. The lucky numbers in the game are the 2, 3, 4, 10, 11 and 12. If you roll any one of them you win a prize of V=$120. The individual probabilities of rolling the numbers 2 through 12 on a pair of dice are:
97.) p2=1/36; p3=2/36; p4=3/36; p5=4/36; p6=5/36; p7=6/36; p8=5/36; p9=4/36; p10=3/36; p11=2/36; p12=1/36
And the probability, Z, of rolling one of these lucky numbers, 2, 3, 4, 10, 11 and 12, is just the sum of their individual probabilities.
98.) Z = 1/36 + 2/36 + 3/36 + 3/36 + 2/36 + 1/36 =12/36 =1/3
This obtains the probability of rolling a number other than one of these lucky numbers of
105.) U=1− Z=2/3
(Note: equation numbers 99104 are not used.) This U=2/3 is the improbability or uncertainty in success of rolling a 2, 3, 4, 10, 11 or 12 lucky number. The amount of money one can expect to win on average in this V=$120 prize game is
106.) E = ZV = (1/3)($120) = $40
E is the expected value of the game, the average amount won per game played. If you played this dice game three times you could expect to win V=$120, on average, one play in three for an average payoff of E=$40 per game played. Eq105 enables us to write the expected value of E=ZV in Eq106 as
107.) E = ZV = (1−U)V= V −UV
The E expected value has three component terms in the above, E=ZV, V and – UV. To understand E=ZV and V in Eq107 in terms of the pleasure associated with them we need to fast forward for the moment to the successful outcome of playing this game of winning the V=$120 prize. We label the prize money gotten or realized with the letter R, hence, R=V=$120. This distinguishes it from the V=$120 in E=V−UV of Eq107, which is most broadly an expectation or anticipation of getting money that is quite different than actually getting or realizing money.
And assumed is that getting money is pleasurable with the intensity of the pleasure greater the more money gotten. Consider a spectrum of prizes offered that can be won by a player. Then R=V=$120 is understood to be more pleasant than R=V=$12 and both less pleasant than R=V=$1200. This assumption is reasonable in being universal in people old enough and sane enough to appreciate money. The pleasure of the R=V emotion of winning is referred to variously as joy, delight or elation.
For simplicity sake we will take R=V=$120 to provide ten times more pleasure than R=V=$12 and R=V=$1200 to provide ten times more pleasure than R=V=$120. So we will understand the pleasure experienced in getting R=V dollars to be a simple linear function of V. This simplifies the relationships derived for the mathematics of human emotion. One could also assume that the pleasure involved in getting money is marginal, that the more money one gets, the less pleasure felt per unit of money gotten. We could also develop a mathematics of human emotion with functions that model this assumption of marginality, but in the end, the cornerstone relationships of the emotion mathematics derived would be essentially the same as with the linear model, but the computations involved significantly more difficult to develop and to follow.
It is also accepted that the pleasure in getting a certain amount of money is a function of how much money the receiver of some R+V amount already has in her purse or in the bank. Clearly getting R=V=$12 means a lot more and provides more pleasure to a homeless woman with $2 in her purse and no money in the bank than it does to someone like Bill Gates. This is just another manifestation of marginality that we can also omit from consideration by assuming that all recipients of R=V dollars have the same amount of money already in their possession.
The V term in E= V− UV of Eq107 differs from an R=V realization of money in its being the anticipated goal of playing this prize awarding Lucky Numbers game. The V dollar prize in E=V− UV is what the player wants. It is his desire, his wish, his goal in the game, to obtain the V=$120 prize. There is a pleasure in the V wish or desire for obtaining the V dollar prize. Again we will understand the intensity of that pleasure to be directly proportional to or a linear function of V.
We will also understand the pleasure in anticipating V dollars to be equal to the pleasure in realizing R=V dollars. At first this seems incorrect. Surely, one would think, people enjoy greater pleasure in getting R=V dollars than in expecting to get V dollars. That confusion, though, is cleared up by understanding the –UV term in E=V−UV of Eq107 as a measure of the anxiousness or anxiety felt about getting the V dollar prize. The greater the U uncertainty in success, the greater the anxiety in expecting it as also inflated by the V size of the prize expected. That is, the greater the V size of the dollar prize desired or wished for, the greater the −UV anxiousness about getting it. The negative sign in –UV is understood as indicating that the emotion of anxiousness is unpleasant, which is in experience universal for people.
Note then that the –UV anxiousness reduces the V pleasure of anticipating the prize in E=V−UV of Eq107. This understands the E expected value as a measure of the realistic hope or hopes a person has in getting the as a reduction of the wish for the V prize via the –UV anxiousness the player has about succeeding. That is our realistic hopes take into account both the desire or wish for the V prize and the U probability of not getting it. Indeed, when that U improbability or uncertainty of success is not taken into account, we call it wishful thinking.
Very often, and especially in a game of chance like the prize awarding Lucky Numbers game, there is always some U uncertainty in expectation of the prize. Hence anticipation of the prize in terms of the E=V−UV measure of realistic hope for it is very often less intense pleasure wise than the R=V pleasure of actually realizing the prize. But that is not always the case as is clear when a person anticipates a paycheck at the end of the week with absolute surety, Z=1, and no uncertainty, U=1−Z=0. In that case E=V−UV=V, and experientially there is no significant difference between surely expecting to get the R=V money on the day before pay day and actually getting it on pay day, E=V=R=V.
Backing up a bit we see that our hopes are a function of what we hope for, V dollars in this case, and our sense of the likelihood or probability of getting it, Z in this case. The greater the V prize desired and the Z probability supposed of getting it, the “higher” our hopes and greater the pleasure in the E=ZV expectation. Note that we use the word “supposed” in association with Z and the pleasure incumbent in our E=ZV hopes. In this Lucky Numbers game, it is taken that the supposed probability is the true probability of success in rolling a winning lucky number. But generally speaking people may have false hopes, excessive hopes, which actually do feel more pleasant in anticipation of success than if a lesser, more realistic, probability were supposed. Indeed much of the pleasure in believing in religion and the reward of a happy after life derives from a delusional high hope of its actually happening, the reality of the outcome irrelevant to the true believer’s pleasure in anticipating it.
Backing up again we also should understand that the –UV anxiousness felt also goes in ordinary language by other names like anxiety or fear or concern or worry about getting money wished for. For that reason we also give –UV a technical name, that of meaningful uncertainty as uncertainty, U, made meaningful by its association with V dollars in –UV, money generally being a meaningful or valuable item for people.
Next we want to state a general function for all the emotions involved in this prize awarding Lucky Numbers game, The Law of Emotion. To do that we have to add one more elemental function to the mix. It is what is realized when a lucky number is not rolled. Nothing is gotten or realized as expressed by R=0. The elemental emotions we have considered up to this point now allow us to write the Law of Emotion as
108.) T = R − E
We are already familiar with two of the three functions in The Law of Emotion. E is the expectation of winning a V dollar prize and R the realization or outcome of the attempt to win by throwing the dice, R=V for a successful attempt and R=0 for an unsuccessful one. The T term is now introduced as a transition emotion that comes about as a combination of what was expected, E, and what was actually realized, R. In a failed attempt where R=0, the transition emotion develops from T=R−E, The Law of Emotion, as
109.) T = R −E = 0 −ZV = −ZV
This T= − ZV transition emotion is the disappointment felt when one’s hopes of winning the V prize, E=ZV, are dashed or negated by failure to throw a lucky number. Disappointment is specified as unpleasant from the minus sign in T= − ZV and its displeasure is seen to be greater, the greater is the V size of the prize hoped for but not won and the greater the Z probability the player felt he had to win. In the game for a V=$120 prize that can be won with probability of Z=1/3, the intensity of the disappointment is
110.) T = −ZV = −(1/3)($120) = −$40
The T= −$40 cash value of the emotion of disappointment indicates that the intensity of the displeasure in it is equal in magnitude, if not in all its nuances, to losing $40. The T= − ZV disappointment over failing to win a larger, V=$1200, prize hoped for, is greater as
111.) T= − ZV= − (1/3)($1200)= − $400
Note that though the realized emotion, R=0, produces no feeling, pleasant or unpleasant in itself, from failure to achieve the goal of obtaining the V dollar prize in the game, failure does produce displeasure in the form of the T= − ZV transition emotion. This transition emotion and the three more basic transition emotions we will consider have a specific function in the emotional machinery of the mind that we will consider in depth once we have generated those three T emotions from The Law of Emotion.
We call attention to the universal emotional experience of T= − ZV disappointment being greater the more V dollars one hoped to get but didn’t. The T= − ZV disappointment is also great when the Z probability of winning is great. Consider this Lucky Numbers dice game where every number except snake eyes, the 3 through12, is a lucky number that wins the V=$120 prize. These lucky numbers have a high probability of Z=35/36 of being tossed, so the hopes of winning are great as
112.) E = ZV = (35/36)($120)= $116.67
And we see that the disappointment from failure when the ZV hopes are dashed or negated to –ZV by rolling the losing 2 is also great as
113.) T= −ZV = − (35/36)($120)= − $116.67
Compare to T= − ZV = −$40 in Eq10 played for the same V=$120 prize, but when the probability of success was only Z=1/3. This fits the universal emotional experience of people feeling great disappointment when they have a high expectation of success and then fail. And at the other end of the spectrum, as also predicted by T= −ZV, people feel much less disappointment when they have a very low Z expectation of success to begin with. As an example, consider the T=−ZV disappointment in this dice game when to win you must roll the low Z=1/36, probability snake eyes, the 2, as the only lucky number to win with. Then the disappointment is much less as
114.) T= ZV= − (1/36)($120)= −$3.33
Now let’s consider the T transition emotion that arises when one does win the V dollar prize with a successful toss of the dice. With hopeful expectation as E=ZV and realized emotion as R=V, the T transition emotion is from the Law of Emotion of Eq108, T=R−E, via the U=1−Z relationship in Eq105,
115.) T = R−E = V −ZV = (1− Z)V = UV
The T= UV transition emotion is the thrill or excitement of winning a V dollar prize under uncertainty. It is a pleasant feeling as denoted by the implied positive sign of UV with the pleasure in the thrill greater the greater is the V size of the prize and the greater is the U uncertainty of winning it felt beforehand. When one is absolutely sure of getting V dollars with no uncertainty, U=0, as in getting a weekly paycheck, while there is still the R=V pleasure of delight in getting the money, the thrill of winning money under uncertainty is lacking. That is, with uncertainty present, U>0, there is an additional thrill or excitement in winning money as in winning the lottery or winning a jackpot in Las Vegas or winning a V=$120 prize in the Lucky Number dice game. In the latter case, with an uncertainty of U=2/3 from Eq105, the intensity of the excitement in winning the V=$120 prize is from Eq115
116.) T=UV=(2/3)($120)=$80
That this additional pleasure of T=UV excitement in obtaining V dollars over and above the R=V delight in getting money depends on feeling U uncertainty prior to rolling the dice is made clearer if we look at an attempt to win V=$120 by rolling the dice in a game where only tossing snake eyes, the 2 on the dice, with probability Z=1/36 and uncertainty U=35/36, wins the prize. In that case, if you do win, as with winning in any game of chance where the odds are very much against you, the uncertainty very great, there’s that much more of a thrill or feeling of excitement in the win.
117.) T= UV= (35/36)($120)= $116.67
By comparison consider a game that awards the V=$120 prize for rolling any number 3 through 12 with Z=35/36 probability of winning and low uncertainty of U=1−Z=1/36 as makes the player near sure he is going to win the money. While there is still the R=V=$120 delight in getting the money upon rolling one of these many lucky numbers, there is much less thrill because like getting a paycheck, the player was almost completely sure of getting the money in this Z=35/36 dice game to begin with.
118.) T=UV=(1/36)($120)=$3.33
This relationship between the uncertainty one has about getting something of value and the excitement felt when one does get it is clear in the thrill children feel in unwrapping their presents on Christmas morning. The children’s uncertainty about what they’re going to get in the wrapped presents is what makes them feel that thrill in opening them up. This excitement is an additional pleasure for them on top of the pleasure realized from the gift itself. That special thrill in opening the presents under the Christmas tree is not being felt when the youngsters know ahead of time what’s in the Christmas presents and feel no uncertainty about it.
As is predicted by T=UV, it is seen to be universal for people that winning a V=$1200 prize in a game of chance is more thrilling than winning a V=$120 prize when the U uncertainty (or probability of not winning) is the same in both cases. And we get a fuller picture yet of the T=UV thrill of winning under uncertainty from the T=R−E Law of Emotion of Eq108 when the E expectation term in it is expressed from Eq107 as E=V− UV.
119.) T = R− E =V−(V−UV) = − (−UV)=UV
This derivation of T=UV as the negation –UV anxiousness, T= − (− UV) =UV, derived for the Lucky Numbers dice game is the basis of excitement coming about generally by the negation or elimination of anxiousness via a successful outcome. Adventure movies generate their excitement or thrills for the audience in just that way by being loaded with anxiousness or dramatic tension at the beginning of a drama from the hero’s meaningfully uncertain situation, which the audience feels vicariously. When the hero’s uncertain situation is resolved by success towards the end of the movie, it vicariously brings about thrills and pleasurable excitement for the audience that empathizes with the hero by negating or eliminating the anxiousness they felt about his or her situation to begin with. Though the emotions felt by the audience are vicarious, the essence of the dynamic is essentially the same as spelled out in Eq119.
We have in the above explained excitement as resulting from an outcome of goal directed behavior of success. People are also generally aware of excitement as a feeling that prefaces success. That is also very easy to explain mathematically, as we will in Section 8, but only after a proper workup that makes its understanding instantly simple and clear.
THE OTHER broad category of goal directed behavior that people engage in is to try to avoid losing something of value, like money. This category is well illustrated with the v= S120 dollar penalty game we introduced earlier in the color guessing game. The player is forced to play this game and the penalty can be avoided with the Z=1/3 probability roll of a 2, 3, 4, 10, 11 or 12 lucky number. The probability of not rolling one of these lucky numbers as results in paying the v=$120 penalty is U= 1− Z =2/3. And the expected value as Uv=$80 is given below in more proper form with a negative sign as
120.) E= U(−v)= −Uv= −(2/3)($120)= −$80
The negative sign on –v makes clear that the v dollar value represents a loss of dollars for the player. The E= −Uv= −$80 expected value of this game is the average penalty paid if one were forced to play this game repeatedly. It tells us that if you played three of these penalty games, on average, you will fail to roll a 2, 3, 4, 10, 11 or 12 lucky number two times out of three to pay the v= −$120 penalty for a total of $240 as averages out over the three games to a penalty per game of E= − $80.
E= –Uv is a measure of the fearful expectation or fear of incurring the penalty. The negative sign prefix of E= −Uv indicates that this fear is an unpleasant emotion with the intensity of the E= −Uv displeasure of the fear greater the greater the U probability of incurring the v penalty and the greater the size of the v penalty, as fits universal emotional experience.
The −Uv fear goes by a number of other names in ordinary language including worry, distress, apprehension and concern. This plethora of names for E= –Uv fear has us give it the technical name also of meaningful uncertainty as puts –Uv fear, as an anticipation of the possibility of losing dollars, in the same general category as −UV anxiety, as an anticipation of the possibility of failing to win V dollars that are hoped for. That both –Uv fear and –UV anxiety are classified together as forms of meaningful uncertainty should not be surprising given that they are very often referred to with the same names of fear, anxiety, concern, worry, distress, apprehension, trepidation, nervousness and so on. Note that we refer in this treatise to –Uv as fear and –UV as anxiety to distinguish between the two however the words are often used interchangeably in ordinary language. We will have more to say about the naming of emotions shortly after we develop a more complete list of them.
Next we consider the realized emotions of the penalty game. The first is the realized emotion that comes about when the v penalty is realized from the player failing to roll one of the 2, 3, 4, 10, 11 or 12 lucky numbers, R= −v. This unpleasant emotion is one of the grief or sadness or depression felt from losing money. Again there are many names for it in ordinary language. And when the outcome is of a successful toss of a lucky number the realized emotion is given as R=0 because as no money changes hands when the player is spared the penalty, there is no emotion that comes from the outcome, per se.
That is not to say that there is no emotion felt from avoiding the penalty, but it is a T transition emotion derived from the T= R−E Law of emotion of Eq8 rather than as a form of R realized emotion. When the lucky number is rolled the fearful expectation of E= −Uv is not realized, R=0, and the T transition emotion is from the T=R−E Law of Emotion of Eq108,
121.) T = R−E = 0 − (−Uv) = Uv
This T=Uv measures the intensity of the relief felt from escaping the v dollar penalty when you roll one of the lucky numbers. The positive sign of T=Uv specifies relief as a pleasant emotion with its pleasure greater, the greater is the v loss avoided and the greater is the U improbability of avoiding the loss. The T=Uv relief felt when a 2, 3, 4, 10, 11 or 12 lucky number is tossed in the v=$120 penalty game with uncertainty U=2/3
122.) T= Uv= (2/3)($120) =$80
To make clear how dependent the intensity of Uv relief is dependent on the U uncertainty, note that if one plays a v=$120 penalty game where rolling only the 2 avoids the penalty, with uncertainty U=35/36, there is greater relief in successful avoidance of the penalty by rolling the lucky number because you felt prior to the throw that most likely you would lose.
123.) T=Uv=(35/36)($120)=$116.67
This increase in relief with avoidance of a penalty under greater uncertainty is universal. But if you play a v=$120 penalty game that avoids the penalty with any number 3 through 12, with uncertainty of only U=1/36, there is much less sense of relief because you felt pretty sure you were going to avoid the penalty, with high probability of Z=35/36, to begin with.
124.) T=Uv=(1/36)($120)=$3.33
Note also that the larger the v penalty at risk, the more intense the relief felt in avoiding it as with a v=$1200 penalty in the game where only rolling the 2 lucky number game with uncertainty, U=35/36, escaped the penalty.
125.) T=Uv=(35/36)($1200)=$1166.67
Compare to the relief of T=$116.67 in Eq123 when the penalty was only v=$120. The universal fit of mathematically derived Uv relief to the actual emotional experience of feeling relief is remarkable. We also use the Law of Emotion of Eq108 of T=R−E to obtain the T transition emotion felt when the player does incur the v penalty by failing to roll a lucky number. In that case, with expectation of E=−Uv and a realized emotion of R= − v, the T transition emotion is via Z=1− U
126.) T = R − E = −v − (−Uv) = −v+ Uv= −v(1−U)= −Zv
This T= − Zv transition emotion is the dismay or shock felt when a lucky number is not rolled and the v penalty is incurred. The T= −Zv emotion of dismay is an unpleasant feeling as implied by its negative sign and one greater in displeasure, the greater the Z probability of escape one supposed before rolling. Its value for the 2, 3, 4, 10, 11 or 12 lucky number v=$120 penalty game with Z=1/3 is
127.) T= − Zv = − (1/3)($120)= − $40
But if you have a very small Z probability of avoiding a v=$120 dollar loss as in the dice game where only rolling the 2 as the lucky number provides escape from the v penalty to probability, Z=1/36, there is little − Zv dismay when you fail to roll that lucky number and must pay the penalty because you had such a high sense of E= −Uv with U=35/36=.9667 surety that you’d have to pay the penalty to begin with.
128.) T= − Zv = − (1/36)($120)= − $3.33
One develops a more intuitive feeling for dismay by expressing the E= −Uv fearful expectation via U=1− Z as
129.) E= −Uv = −(1–Z)v = −v + Zv
The − v term in Eq129 is the anticipation of incurring the entire v penalty, which we will call one’s dread of the penalty for want of a better word. The displeasure in the dread of paying the v penalty is marked by the negative sign of − v with the intensity of its displeasure greater, the greater the v dollar penalty that is dreaded. Were the penalty raised to −v= − $1200, the dread and its displeasure would be proportionately greater than the –v= −$120 penalty. This −v dread in E= − v + Zv of Eq129 is partially offset by the +Zv term in it as the (pleasant) hope one has that one will escape the penalty by rolling a lucky number.
This Zv term is understandable emotionally as the sense of security one has that one will avoid the penalty, the greater the Z probability of escaping the penalty in +Zv and the greater the v penalty one is protected from by Z, the greater the sense of security one has when one is forced to play the penalty game that one will be able escape the penalty. The combination of unpleasant –v dread and pleasurable +Zv security produces the realistic fear or fearful expectation of incurring the penalty, E= −v + Zv = −Uv, of Eq129.
Expressing the E expectation as in Eq129 adds an important nuance to the derivation of dismay from the T=R−E Law of Emotion of Eq108.
130.) T = R –E = −v −(−v + Zv)= −(Zv)= −Zv
This understands T= –Zv dismay as coming about from the dashing or negation of one’s Zv hopes or expectation of avoiding the v penalty by failure to roll a lucky number. The low dismay that results from failure preceded by low Zv expectation is why some people subconsciously develop a strategy of low expectations in life to avoid the unpleasant feeling of dismay if they do fail. This contrasts to the considerable T= − Zv dismay or shock felt in the v=$120 penalty where the lucky numbers on the dice that are needed to avoid the penalty are the 3 through 12 whose probability of being rolled is Z=35/36.
131.) T= − Zv = − (35/36)($120)= − $166.67
In short the dismay in this case is high because of the high Zv expectation of not paying the penalty to begin with. Great dismay from failure preceded by a high Z=35/36 probability of escaping failure is also felt and referred to as shock, familiarly as a person’s surprise at failure when what was expected from the preceding high probability was success. Unpleasant unexpected surprise specified here as great −Zv dismay is also the fundamental basis of horror.
The above development of the E fearful expectation as E=− Uv = − v + Zv gives us functions for three more elementary emotions: the − v dread of incurring a penalty; the Zv sense of security one feels in the possibility of escaping the penalty; and the probability tempered E= −Uv fear of incurring a penalty. These add as expectations to the V desire of getting a V prize, the –UV anxiousness about getting it and the E=ZV probability tempered hopes of getting a prize considered earlier to give a complete set of our basic anticipatory emotions.
The −Uv, ZV, V, −v, Zv and –UV symbols are the best representations of our anticipatory emotions rather than the more familiar names for them in ordinary language respectively of fear, hope, desire, dread, security and anxiety. Ludwig Wittgenstein, regarded by many as the greatest philosopher of the 20^{th} Century, made the point well in his masterwork, Philosophical Investigations, of the inadequacy of ordinary language to describe our mental states. Words for externally observable things like a “wallet” are clear in meaning when spoken from one person to another because if any confusion arises in discourse, one can always point to a wallet that both the speaker and the listener can see. “Oh, that’s what you mean by a wallet.” But with emotions, however, as nobody feels the emotions of another person, the words we use for an emotion have no common sensory referent one can point to in order to clarify its meaning.
The mathematical symbolwords of −Uv, ZV, V, −v, Zv and –UV, on the other hand, are at least clear in meaning because they have countable referents of money as V and v and numerical probabilities of Z and U as components. And the fit of these therefore mathematically welldefined wordsymbols to emotional experience, pleasant and unpleasant, is universal. That is, all people feel these −Uv, ZV, V, −v, Zv and –UV anticipatory feelings in the same way when playing the V prize and v penalty Lucky Number games assuming all have the same quantitative sense of dollars and of probability. Hence quibbling over the “correct” names to call −Uv, ZV, V, −v, Zv and –UV or any of the other mathematical symbols we will develop for the emotions is not a valid criticism of this analysis.
Our expectations determine our behavioral selections, what we choose or decide to try to do. The basic rules are simple.
Rule #1. If we have a choice between entertaining a hopeful expectation as with E=ZV of the V prize awarding Lucky Numbers game and a fearful expectation as with E= −Uv of the v penalty assessing Lucky numbers game; we act on the behavior that generates hope rather than fear. This is so intuitively obvious that it is almost not worth stating at all other than for the sake of completeness. We can understand Rule #1 as sensible from the standpoint of a V dollar gain being preferred to a –v dollar loss; or, hedonistically, from the pleasure felt in ZV hopes triumphing cognitively over the displeasure of –Uv fear.
Rule #2. If we have a choice between two hopeful expectations, E_{1}=Z_{1}V_{1} and E_{2}=Z_{2}V_{2} with E_{1}>E_{2}, we choose E_{1} whether E_{1}>E_{2} comes about via Z_{1}>Z_{2} or V_{1}>V_{2} or both. As an example, one would choose to play the standard Z=1/3, V=$120 prize game with E=$40, than a V=$120 game with just 2, 3 and 4 as the lucky numbers, Z=1/6 and E=$20. We may attribute the underlying cause of greater hopeful expectation triumphing cognitively over less hopeful expectation to the anticipated average gain in E_{1} being better than in E_{2}; or, hedonistically, to their being greater pleasure in entertaining E_{1}=Z_{1}V_{1 }than in E_{2}=Z_{2}V_{2}. _{. }
Rule #3. If we have a choice between two v penalty games, one with fearful expectation, E_{1}= –U_{1}v_{1}, and the other with E_{2}= –U_{2}v_{2}, one of which games we must play, we choose the game with the smaller expectation (in absolute terms.) Or more exactly, if E_{1}>E_{2 }numerically, we choose to play the E_{1} game. To clear up any confusion, as between the games in Eqs4&5, we choose to play the E_{1}=–80 game, E_{1}>E_{2}, rather than the E= –$240 game if we have to play one of them. This comes under the colloquial heading of “choosing the lesser of two evils”, also known as a Hobson’s choice.
The nuances and extensions of these three rules are many. The main point is that they show the primary function of our expectations, hopeful and fearful, to be to determine the choices we make. The next section explains the function of the transitional emotions of excitement, relief, disappointment and dismay in our emotional machinery. And then we go on to show how the Law of Emotion derives the Law of Supply and Demand in the most elementary way, something that even the most ardent capitalist hater of our revolutionary ideas cannot deny.
10. The Function of the Transition Emotions
We continue with our systematic explanation of our emotional machinery by explaining the purpose and function of the transition emotions of T= −ZV disappointment of Eq109, T=UV excitement of Eq115, T=Uv relief of Eq121 and T= −Zv dismay of Eq125. Recall that they all come about from the T=R−E Law of Emotion of Eq108. In it the E expected value depends in a very direct way on the Z and U probabilities: of the E=ZV=V−UV hopeful expectation in the V prize game; and of the E= −Uv= −v+ Zv fearful expectation in the v penalty game.
In our analysis up to this
point, the player’s sense of the values of the Z and U probabilities were taken
directly and correctly from the mathematics of throwing dice. But that need not
be the case. A player may suppose any probabilities of success or
failure, which affects the player’s E expectations, and in turn, affects from
the T=R−E Law of Emotion, the intensities of the T transition emotions
from T=R−E the player experiences upon success or failure.
As an example of a player supposing incorrect values of Z and U, consider in
the V=$120 prize game where rolling a lucky number of 2, 3, 4, 10, 11
or 12 has an actual probability of Z=1/3 that a naïve player supposes it is
Z’=1/2 for whatever reason. This distorts the hopeful expectation from the
player thinking she will win half the time instead of just 1 time in 3 from the
correct expected value of E=ZV=(1/3)($120)=$40 of Eq107 to
191.) E’=Z’V=(1/2)($120)=$60
(Note: Equation numbers 132190 are not used.) The player has higher hopes of winning than she should and though that cannot affect the actual (average) R outcomes or realizations it does from the T=R−E Law of Emotion of Eq108 affect the T transition emotions that arise. To show this let’s assume the game is played three times as results in the average winloss record of winning 1 time in 3 with R realizations of (0, 0, $120). And we’ll also assume that the player sticks to her incorrect probability suppositions for all three games played. The transition emotion felt after the first failed attempt of a realization of R=0, labelled T’, is
192.) T’=R−E’=0−Z’V= −Z’V= −$60
This T’= −Z’V= −$60 emotion is of disappointment in greater intensity than the disappointment of T= −$40 of Eq10 felt when the correct Z=1/3 probability is supposed. This is because the naïve player thought she had a greater possibility of winning. The 2^{nd} game played is also an R=0 failure and again a T’= −$60 disappointment is felt. On the 3^{rd} play, though, as fits the average % of games won a lucky number is rolled for R=V=$120 and the thrill of winning with E’=Z’V=$60 is from the law of emotion as T’=R−E’
193.) T’=R−E’=V−Z’V=$120−$60=$60.
This a smaller excitement than the E=ZV=$80 of Eq16 that would have been felt had the player supposed the correct probability of winning of Z=1/3. The player, hence, feels greater disappointment and less excitement over the three games, the sum of the T’ emotions experienced being
194.) ∑T’_{ }= −$60 −$60 +$60 = −$60
And the average of these T’ transition emotions per game is
195.) ∑T’/3 = T’_{AV}= −$60/3= −$20
Now, though the player retained her incorrect suppositions of probability for the three games, failure to meet her expectations over the three games manifest as an overall unpleasant set of transition emotions of ∑T’_{ }= −$60 and T’_{AV}= −$20 per game lowers her hopeful expectation in the next game she plays and, as we will show below, to the correct E=$40 per game.
Her emotional machinery does this with a T=R−E Law of Emotion inversion that understands T for a game as the T’_{AV} average of prior games, E as E’, the incorrectly supposed expectation and R as what is realized cognitively from T’_{AV} and E’, which is a revised or new expectation, E_{NEW}. Hence, not T=R−E, but
196.) T_{AV} =E– E’
Or solving for E_{NEW}, we arrive at the Law of Emotion Inversion,
197.) E_{NEW} = E’ + T_{AV}
For the example case developed above, this obtains an E_{NEW} expectation of
198.) E_{NEW }= $60 −$20 = $40
Now this revised E_{NEW}=$40 is just the E=ZV=$40 of Eq110 that arises from the correct Z=1/3 probability. So we see that the function of the transition emotions is to correct errors in expectation, and to do it using the E_{NEW} = E’ + T_{AV} variation of the general T=R−E Law of Emotion of our emotional machinery. If this seems too beautifully precise and simple a way for out emotional machinery to act, let’s try another example.
This will be of a fellow who has no confidence at all that he can win at any game, Mr. Unlucky. His sense of probability is hence, Z’=0 and of expectation, E’=Z’V=0. Again we will consider a three game play that realizes R outcomes of the actual average of (0, 0, $120). From the Law of emotion as T’=R−E’, we see that his first two games result in –Z’V disappointments of
199.) T’=R−E’=0−Z’V= −Z’V=0
He has no disappointment in the losses because he had absolutely no hopes of a win to begin with. The excitement of winning on the 3^{rd} game, though, is, from R=V=$120, great, as
200.) T’=R−E’=$120−0=$120
Note that this is an excitement greater than the T=$80 of Eq116 he would have felt had he supposed correctly a probability of winning of Z=1/3 and an expectation of E=ZV=$40. Now we see that the sum of his T’ transition emotions felt are
201.) ∑T’_{ }= 0 + 0 + $120 = $120
And the average of these T’ transition emotions per game is
202.) ∑T’/3 = T’_{AV}= $120/3 = $60
And from the Law of Emotion Inversion of Eq197 we obtain the correct expectation felt in the next play of the game of
203.) E_{NEW} = E’ + T_{AV}= 0 + $60 = $60
From the two above examples we see, as fits universal emotional experience, that preponderant disappointment in a goal directed behavior reduces subsequent hopeful expectation or confidence in that behavior and that preponderant excitement from winning increases subsequent confidence. The fit of function to experience is unarguable, quite remarkable, and makes clear that the function of the transition emotions is to keep one’s expectations in line with one’s reality of outcomes. This is reinforced all the more if one repeats the above exercise starting with the correct supposition of E=$40. In this case over the play of three games that realizes outcomes (0, 0, $120), the (correct) transition emotions felt of disappointment and excitement are (−$40, −$40, $80), which sum to 0 as produces no change in expectation from the Law of Emotion Inversion of E_{NEW} = E’ + T_{AV}.
This Law also works in a numerically exact way for the v penalty Lucky Numbers game to show that preponderant relief in repeated play of a penalty game results in subsequent decreased E= −Uv fear of losing; and that preponderant dismay results in a subsequent increase in E= −Uv fearful expectation; as universally fits emotional experience.
While this analysis cannot without neurobiochemical assay say absolutely that the mind uses this exact functional algorithm to keep our expectations in line with the reality of actual experience, the fit of the equations to experience in the broad ways cited above and the exactness of the corrective dynamic they bring about, especially as based on a variation of the Law of Emotion as seen in Eq197 makes clear that the mind’s neurobiochemistry and neurophysiology must operate as controlled by these functions in some way.
The universality of the fit of the equations for the emotions and of the Laws of Emotion of Eqs108&197 that control the relationships between these basic emotions is very important, for it counters any facile rebuttal of this understanding on the basis of the human emotions not being susceptible to empirical verification. Rather this mathematical explication of the emotions is effectively empirical in being universal.
Our specification of disappointment as the −ZV negation or dashing of ZV hopes, for example, is universal in that all human beings feel disappointment when they fail to achieve a desired goal. Indeed, all of the emotional specifications and dynamic relationships we have considered are universal. Such universal agreement is the fundamental factor in all empirical validation. When ten researchers all read the same data off a laboratory instrument, that data is taken to be empirically valid because all ten agree on what they see. This criterion for empirical validity of universal agreement extends to the emotions of the dice game laid out as what all people would feel if they played it. To deny the validity of the above interlocking, experience reflecting, quantitatively precise emotion specifications and relationships on the basis of an abstract principle of absence of empirical verification is to fail to understand the underlying basis of empirical validity in universality.
11. Emotions of Partial Success
To further provide observable, empirical proof of the emotion mathematics, we will next consider the emotions that arise from partial success. To that end we alter the Lucky Number V prize awarding game to one where you must roll a lucky number of 2, 3, 4, 10, 11 or12 not once but three times to win the prize, one of V=$2700. The excitement gotten from the partial success of rolling the 1^{st} lucky number of the three needed to win the V prize has observable reinforcement in parallel games of chance seen on television. The three rolls of the dice taken to roll three lucky numbers and win the V=$2700 prize may be with three pair of dice rolled simultaneously or with one pair of dice rolled three times in succession. The probability of rolling a 2, 3, 4, 10, 11 or12 lucky number on any one roll of dice is from Eq2, Z=1/3. Hence for the 1^{st} roll or with the 1^{st} pair of dice, Z_{1}=Z=1/3; for the 2^{nd} roll or pair of dice, Z_{2}=Z=1/3; and for the 3^{rd} roll or pair of dice, Z_{3}=Z=1/3.
204.) Z_{1}=Z_{2}=Z_{3}=Z=1/3
And the U uncertainties for each toss are
205.) U_{1}=(1− Z_{1})=_{ }U_{2}=(1− Z_{2})_{ }=U_{3}=(1− Z_{3})=(1−Z)=2/3
The probability of rolling a lucky number of 2, 3, 4, 10, 11 or12 on all three rolls is the product of the Z_{1}, Z_{2} and Z_{3} probabilities, which is given the symbol, z, (lower case z).
206.) z = Z_{1}Z_{2}Z_{3 }= Z^{3 }= (1/3)^{3 }= 1/27
And the improbability or uncertainty of making a successful triplet roll
successfully is
207.) u=1–z = 26/27
The expected value of this triplet roll game to win the V=$2700 is in parallel to Eq6,
208.) E = zV =V−uv=Z_{1}Z_{2}Z_{3}V_{ }= (1/27)($2700) = $100
This is also a measure of the intensity of the player’s pleasant hopes of winning the game. The displeasure of disappointment from failure to make a successful triplet roll is from the T=R−E Law of Emotion of Eq108 with R=0 in parallel to Eq109,
209.) T=R−E = 0−zV= −zV= −(1/27)($2700)= −$100
And the pleasure of the excitement or thrill in making the triplet roll, R=V=$2700, is, in parallel to Eq115
210.) T=R−E = V−zV=(1−z)V= uV= −(−uV)=(26/27)($2700)=$2600
Next we derive the emotion felt from rolling a lucky number on the 1^{st} throw of three sequential throws on one pair of dice. After a 1^{st} toss that does roll a lucky number, the probability of winning the V=$2700 prize by tossing lucky numbers on the next two rolls increases to
211.) Z_{2}Z_{3 }=(1/3)(1/3) = 1/9
And the hopeful expectation of making the triplet roll after a lucky number is rolled on the 1^{st} toss is, increases from the original E=Z_{1}Z_{2}Z_{3}=$100 to
212.) E_{1 }= Z_{2}Z_{3}V = (1/9)($2700) = $300
Next we want to ask what is realized when the 1^{st} toss is successful. It is not R=V=$2700, for the V prize is not awarded for just getting the 1^{st} lucky number. And it is not R=0, what is realized when the player fails to make the triplet roll and win the V=$2700 prize, for rolling the 1^{st} lucky number successfully quite keeps him on track to roll the next two numbers successfully and win the V=$2700 prize. Rather what is realized when the 1^{st} roll is of a lucky number is the E_{1}=$300 increased expectation in Eq212. This understanding of the increased E_{1}=$300 expectation as what is realized has us specify E_{1} as a realization with the R symbol as
213.) E_{1}=R_{1}=Z_{2}Z_{3}V = $300
Now we use the Law of Emotion of T= R−E, of Eq108 to obtain the T transition emotion that arises from a successful 1^{st} toss. This specifies the T term in T=R−E as T_{1}; the R term in it as R_{1}=Z_{2}Z_{3}V from Eq213; and the E term in T= R−E as the expectation had prior to the 1^{st} toss being made, E=zV=Z_{1}Z_{2}Z_{3}V of Eq208. And with U_{1}=(1−Z_{1}) from Eq205 we obtain T_{1} as
214.) T_{1 }= R_{1}–E = E_{1}– E= Z_{2}Z_{3}V –Z_{1}Z_{2}Z_{3}V = (1−Z_{1})Z_{2}Z_{3}V =U_{1}Z_{2}Z_{3}V =(2/3)(1/3)(1/3)($2700) =$200
Now we can ask what kind of emotion this T_{1}=U_{1}Z_{2}Z_{3}V transition emotion is. We answer that by noting that the T=uV excitement of Eq210 from making the triplet toss and winning the V=$2700 prize can be written, given R=V for success, as
215.) T=uV=uR
And we also see that we can substitute Z_{2}Z_{3}V=R_{1}=E_{1} from Eq113 into the T_{1}=U_{1}Z_{2}Z_{3}V term in Eq219 to obtain T_{1} as
216.) T_{1 }=E_{1}−E=U_{1}Z_{2}Z_{3}V =U_{1}E_{1}=U_{1}R_{1}
The parallel of this T_{1}=U_{1}R_{1} to the T=uR excitement of Eq215 identifies T_{1}=U_{1}R_{1} as the excitement experienced from rolling the 1^{st} lucky number, excitement that is felt even though no money is awarded for rolling just the 1^{st} lucky number. Note that the intensity of this partial success excitement of T_{1}=$200 of Eq214 is much less than the T=$2600 excitement of Eq210 that comes about from making the triplet roll and actually getting the V=$2700 prize.
This development of partial success excitement from the T=R−E Law of Emotion is borne out from observation of situations that go beyond the Lucky Numbers dice game. Excitement from partial success is routinely observed on TV game shows like The Price is Right where a contestant is observed to get visibly excited about entry into the Showcase Showdown at the end of the show, which offers a large prize, by first getting the highest number on the spinoff wheel, which offers no prize in itself. This and other observed examples of the partial success excitement on TV games shows and the like derived as above from the Law of Emotion is a form of empirical validation of the law, even if not a perfectly quantitative validation.
We can further validate the Law of Emotion with this partial success analysis as follows. We understood that what is realized from getting the 1^{st} lucky number is an increase in expectation from the original E=zV=$100 of Eq108 to E_{1}=Z_{2}Z_{3}V=$300 in Eq212. Now we ask what is realized in rolling the 2^{nd} lucky number after the 1^{st} lucky number is gotten. It is a greater expectation yet of making the full triplet roll and winning the V=$2700 prize,
217.) R_{2}= E_{2 }=Z_{3}V=(1/3)($2700)=$900
The transition emotion that comes from rolling a 2^{nd} lucky number after having gotten the 1^{st} lucky number is specified as T_{2 }and from the Law of Emotion, T=R−E, with T as T_{2}, R as R_{2}=Z_{3}V from the above and E as the expectation felt after the 1^{st} lucky number was gotten as E_{1}=Z_{2}Z_{3}V in Eq213, is
218.)
T_{2} = R_{2}−E_{1 }= E_{2}−E_{1}=Z_{3}V−
Z_{2}Z_{3}V =(1−Z_{2})Z_{3}V = U_{2}Z_{3}V
= (2/3)(1/3)($2700) = $600
Expressing T_{2 }= U_{2}Z_{3}V via Z_{3}V=R_{2}
of Eq217 as T_{2}=U_{2}R_{2} makes it clear from its
parallel form to the excitement of T=uR of Eq215 that T_{2}=U_{2}R_{2}
is the excitement felt when the 2^{nd} lucky number is guessed after
the 1^{st} lucky number has been rolled.
And
we can also use the Law of Emotion, T=R−E, of Eq108 to derive the
excitement felt in getting the 3^{rd} lucky number after getting the
first two, which wins the V=$2700 prize. What is realized in that case is
the R=V=$2700 prize. Given the expectation that precedes getting the 3^{rd}
lucky number of E_{2}=Z_{3}V from Eq217, the Law of Emotion,
T=R−E, obtains a T_{3 }transition emotion of
219.) T_{3 }= R−E_{2 }= V –Z_{3}V
= (1−Z_{3})V = U_{3}V = (2/3)($2700) = $1800
Now expressing T_{3 }=U_{3}V from R=V as T_{3}=U_{3}R and noting its parallel form to T=uR excitement of Eq215 identifies T_{3 }= U_{3}R as the excitement of rolling the 3^{nd} lucky number after the first two have already been rolled as obtains the V=$2700 prize. Note that the intensity of the T_{3}=$1800 excitement from rolling the 3^{rd} lucky number and getting the V=$2700 prize is significantly more pleasurable than the T_{1}=$200 and T_{2}=$600 excitements for the antecedent partial successes.
Such significantly greater excitement in actually winning the prize than from achieving prefatory partial successes is what is observed in game shows like “The Price is Right” where actually winning the Showcase Showdown has the winner jumping up and down and running around screaming and showing more excitement than the excitement felt and shown from the prefatory partial success of getting into the Showcase Showdown by getting the highest number on the spinning wheel. Again this fit of observed excitement in the approximate relative amounts suggested in the above analysis with the Law of Emotion constitutes an empirical, if not perfectly quantitative, validation of the Law of Emotion.
Also note that the Law of Emotion, T=R−E, of Eq108 is further validated from the three partial excitements, T_{1}, T_{2} and T_{3} of Eqs214,218&219 summing to the T=uV=$2600 excitement of Eq210 that arises from making the triplet roll in one fell swoop as you might from throwing three pair of dice simultaneously.
220.) T_{1 }+ T_{2 }+ T_{3 }= $200 + $600 + $1800 = $2600 = T = uV
The internal consistency in this equivalence is another validation of the T=R–E Law of emotion. It is also revealing and further validating of the Law of Emotion to calculate what happens when you roll the first two lucky numbers successfully but then miss on the 3^{rd} roll and fail to get the V=$2700 prize, R=0. To evaluate the T_{3} transition emotion that arises from that we simply use the T_{3}=R−E_{2} form of the Law of Emotion in Eq119 that applies after the first two lucky numbers are gotten, but with the R realized emotion as R=0 from failure to obtain the V=$2700 prize.
221.) T_{3 }= R−E_{2 }= 0 – Z_{3}V = – Z_{3}V = −(1/3)($2700)= −$900
This T_{3 }= −Z_{3}V= −$900 is the measure of disappointment felt in failing to make the triplet roll after getting the first two lucky numbers and after experiencing the prefatory partial success excitements in getting them. Note that this T_{3}= −Z_{3}V= −$900 disappointment is significantly greater than the T= −zV= −$100 disappointment of Eq209 that arises from failure to roll the lucky numbers in one fell swoop. And note that the −$800 increase relative to the T= −$100 disappointment in the T_{3}= −$900 disappointment felt after partial success is exactly equal to T_{1}+T_{2}=$200+$600=$800 sum of the two partial success excitements of Eqs114&119. This understands the additional −$800 displeasure of disappointment from failure in the 3^{rd} roll to rescind or negate the prefatory $800 pleasure of excitement that was followed by ultimate failure. This fits the universal emotional experience of an increased let down or disappointment when initial partial success is not followed up by ultimate success in achieving a goal as the letdown felt when one counts their chickens before they hatch and they then do not hatch.
The sequential scenarios that end in success in Eq220 and in ultimate failure in Eq221 universally fit emotional experience and as such are a convincing validation of the Law of Emotion, T=R−E, of Eq108. The linear sums and differences of the transition emotions in these two instances also importantly show that understanding our emotions to reinforce each other positively and negatively in a linear fashion via simple addition and subtraction of the emotion intensity values provides an excellent modeling of our emotional processes regardless of the factor of marginality that affects the linear aspects of emotional intensity.
In a slight digression, everybody knows that we don’t just feel excitement from winning in a game as T=UV but also in anticipation of a win. The above analysis can be used to derive this sense of prefatory excitement felt by people in anticipation of success. To do that consider the emotional state of a person to whom the opportunity to play this triplet V=$2700 prize game is denied or not offered. For that person the expectation of winning is zero, specified as E_{0}=0. It is only when the game is offered and available to play that there is any expectation of winning, namely or E=zV=$100 of Eq208. Much as we saw that sequential increases in expectation produced a T transition emotion of excitement in Eqs214,218&219, so should we also see that this increase in expectation from E_{0}=0 to E=zV=$100 from being offered the game produces from the T=R−E Law of emotion as it did for other increases in expectation a feeling of excitement. Specifically, with T as T_{0} and E as E_{0}=0, the original expectation prior to the game being offered, and R=E=R_{0} as the expectation realized once the game is offered, the T=R−E Law of emotion generates the excitement felt as
222.) T_{0}=E−E_{0}=zV−0=zV
As E=R_{0}=zV and as the probability of success prior to game availability is Z=0 and of failure, U=1, then E=R_{0}=zV can also be understood as
223.) T_{0}= E=R_{0}=zV=UzV=UR_{0}
Again by parallel to T=uR excitement of Eq215, T_{0}=UR_{0} is excitement, the excitement of getting to play the game to begin with. Note that its value is equal to the expectation or the player’s hopes of winning. Next we see in a successful game that expectation increases as each lucky number in the triplet is tossed. As they are, excitement is also felt as we saw in Eqs214,218&219. The difference between the increasing expectations and the excitement that accompanies their experience is that the excitement is cumulative, it adds to prior excitement or builds with progressive success. This very much fits excitement building in a sequential composite effort to achieve a goal. And it explains the origin of the prefatory excitement that, again, is a universal in emotional experience. All of the transitional emotions, whether excitement, disappointment, relief or dismay, can be shown to have this sense of existence prefatory to the final R outcome of success or failure and in the same entirely exact mathematical way.
We next consider the transition emotions of partial success in the v penalty Lucky Numbers game. Consider a game one is forced to play that exacts a penalty of v=$2700 unless the player rolls three of the lucky numbers of 2, 3, 4, 10, 11 or12. In parallel to the E= −Uv expectation of Eq120 and with u=26/27 from Eq207 as the improbability of rolling three lucky numbers, the fearful expectation of incurring the v=$2700 penalty is
224.) E= −uv= −(1−Z_{1}Z_{2}Z_{3})v= −(26/27)($2700)= −$2600
The Law of Emotion, T=R−E, of Eq108 generates a uv emotion of relief from avoiding the v penalty, R=0, when one successfully rolls a lucky number on three pair of dice simultaneously as
225.) T=R−E=0−(−uv)=uv=$2600
With the game played with three sequential rolls on one pair of dice, the increased expectation of avoiding the v=$2700 penalty after rolling a lucky number on the 1^{st} toss of the dice, E_{1}, understood as what is realized from the toss, R_{1}, is, with the improbability of escaping the penalty then as 1−Z_{2}Z_{3}
226.) E_{1}=R_{1}= −(1−Z_{2}Z_{3})v= −(1−(1/9))$2700= −(8/9)($2700)= −$2400
Hence the transition emotion, T_{1}, is, via the T=R−E Law of Emotion expressed as T_{1}=R_{1}−E, and with R_{1}=E_{1} from the above
227.) T_{1}=R_{1}−E= E_{1}−E=−(1−Z_{2}Z_{3})v−[−(1−Z_{1}Z_{2}Z_{3})]=(1−Z_{1})Z_{2}Z_{3}v=U_{1}Z_{2}Z_{3}v=$200
Now recall the parallel forms of the T=UV excitement of Eq115 and the T=Uv relief of Eq121. This understands T_{1}=U_{1}Z_{2}Z_{3}v, in parallel to the partial excitement of U_{1}Z_{2}Z_{3}V of Eq214 for the V prize game, to be the partial relief felt upon rolling the 1^{st} lucky number in the v penalty game. The rest of the analysis for the triplet v penalty game then perfectly parallels that for the triplet V prize game except that the partial emotions felt in sequentially rolling the 1^{st}, 2^{nd} and 3^{rd} lucky numbers are those of relief in escaping a v=$2700 loss of money rather than excitement gotten from a V=$2700 gain of money. The universal fit of this v penalty game analysis to universal emotional experience with sequential behaviors whose goal is escape from a penalty validates the law. And further validating the Law of Emotion and its underlying mathematics is its next deriving the Law of Supply and Demand.
12. The Law of Supply and Demand
The Law of Supply and Demand of Economics 101 states that the price of a commodity is an increasing function of the demand for it and a decreasing function of the supply of it. An alternative expression of the Law of Supply and Demand determines the price as an increasing function of the demand for the commodity and of its scarcity as the inverse of its supply or availability.
Now let’s return to the triplet lucky number V=$2700 prize game with the 1^{st} lucky number in the triplet sequence understood as a commodity that can be purchased. This assumes the existence of an agent who runs the dice game and pays off the V prize money and who will give this commodity of the 1^{st} lucky number to the player for a price. Question: what would be the fair price of the 1^{st} lucky number?
As having the 1^{st} lucky number changes the probability of winning the V=$2700 from z=Z_{1}Z_{2}Z_{3}=1/27 in Eq106 to Z_{2}Z_{3}=1/9 in Eq211, it is certainly a valuable commodity for the player. But exactly what is its value, what is the fair price of it? It is the difference between the E_{1}=$300 average payoff of Eq213 expected when the 1^{st} lucky number has been gotten and the E=$100 average payoff of Eq108 expected prior to any of the three lucky numbers being attained. Or given the symbol, W_{1}, the fair price for the 1^{st} lucky number is
228.) W_{1 }= E_{1}−E
This W_{1} fair price is a function of a number of variables associated with the E_{1}−E term in Eqs214&216.
229.) W_{1 }= E_{1}−E = Z_{2}Z_{3}V – zV = U_{1}Z_{2}Z_{3}V = T_{1} = U_{1}E_{1 }=$200
This W_{1}=$200 is the fair price for the 1^{st} lucky number in the latter increasing the average payoff from E=$100 to E_{1}=$300. From the perspective of economic optimization the player as buyer would want to pay as little as possible for the 1^{st} lucky number and the agent as seller would want to charge as much as possible for it. But W_{1}=$200 is the fair price of the 1^{st} lucky number from that price paid by the player effectively maintaining the initial average payoff of E=$100 for the player.
The fair price expressed in Eq229 as W_{1}=U_{1}E_{1 }is a primitive form of the Law of Supply and Demand given in terms of the emotions that people feel that control the price they’ll pay for a commodity. W_{1}=U_{1}E_{1} is an increasing function of the scarcity of the 1^{st} lucky number as the uncertainty in rolling it on the dice, U_{1}=2/3, and is an increasing function of the demand for the 1^{st} lucky number as the E_{1}=Z_{2}Z_{3}V=$300 average payoff it provides with its value as such understood as the underlying determinant of the demand for it. This derivation from the emotion mathematics of the Law of Supply and Demand, a firm empirical law of economics universally accepted as correct, is a powerful validation of it.
There are a number of important nuances in this formulation of the Law of Supply and Demand. Note the equivalence in Eq229 of the W_{1}=$200 fair price for the 1^{st} lucky number and the T_{1}=W_{1}=$200 pleasurable excitement gotten from rolling the 1^{st} lucky number on the dice. This equivalence of T_{1} excitement and W_{1} price suggests that the price paid for a commodity is a measure of the pleasurable excitement the commodity generates for the buyer. This fits economic reality quite well as seen from TV commercials for automobiles and vacations and foods that hawk these products by depicting them as exciting.
And, further, the value of the 1^{st} lucky number can be calculated not just in terms of the W_{1} amount of money one would spend for it but also in terms of the time spent in acquiring the money needed to purchase the 1^{st} lucky number. Given that the time taken to obtain money, risk based investment aside, is directly proportional to the money earned as in a dollars per hour wage, W_{1} is understandable as a measure of the amount of time spent to get the 1^{st} lucky number. This has the W_{1}=U_{1}E_{1}=T_{1} Law of Supply and Demand showing that people spend their time to obtain commodities that pleasurably excite them, whether as the time spent working to get the money to spend on the commodity or as time spent directly to obtain pleasurable excitement like watching the Super Bowl for some.
We can also derive a parallel primitive Law of Supply and Demand from the v penalty game that requires the toss of three lucky numbers to avoid the penalty. The W_{1} fair price of the 1^{st} lucky number is again W_{1}=E_{1}−E, but with E_{1}−E from Eq227 in the v penalty as
230.) W_{1 }= E_{1}−E = U_{1}Z_{2}Z_{3}v = T_{1} = $200
This form of the primitive Law of Supply and demand tells us that people also spend their money for commodities that provide T_{1}=U_{1}Z_{2}Z_{3}v=W_{1} relief. This is in addition to commodities that provide T_{1}=U_{1}Z_{2}Z_{3}V=W_{1} excitement as seen in Eq229. The two forms of the Law of Supply and Demand of Eqs229&230 provide a strong empirical validation of the Law of Emotion of Eq108 that underpin them from the observed fact that people do spend their money and their time to obtain commodities, goods and services, that provide relief and excitement. This is readily seen in the complete spectrum of TV ads, all of whose products are pitched in ads as providing relief, as with insurance and antacids and other medicines, or excitement, as with exciting cars, foods and vacations.
Next we want to express the primitive Law of Supply and Demand in as simple a form as possible. We do this as preface to our deriving in the next section simple functions for our visceral emotions like the pleasures of feeling warm and of eating food. In Eq229 we saw the equivalence of the W_{1} fair price with T_{1} partial success excitement, W_{1}=T_{1}. This implies that the simplest form of T excitement we have seen in Eq115 as T=UV for the one number Lucky Number game should also be a measure of the fair price, W, one would pay for this one lucky number.
231.) W=T=UV
Now in recalling Eq116 we see the value of the T excitement in getting the V=$120 prize to be T=$80, which allows us to express the fair price of being given the lucky number that gets the V=$120 prize as
232.) W=T=UV= $80
At first this may seem odd. One may ask what sense there is in paying $80 to win the V=$120 prize. The point is rather that W=$80 is the fair price that you would pay. Consider what happens if you do this for three games, with the total price paid being 3($80)=$240. This wins the player $120 in each game for a total of 3($120)=$360 for the three games. The net winnings for the three games are, thus, $360−$240=$120. And this is what is won on average in three games played strictly from the throw of the dice with no lucky number purchased. That is V=$120 is won one time out of three. Hence W=T=$80 is, indeed, the fair price of the lucky number. And W=T=UV is a most simple form of the Law of Supply and Demand with U as the uncertainty in rolling the lucky number as a measure of its scarcity and V as the cash value of the prize as a measure of the demand for it.
Next we want to write this most simple form of the Law of Supply and Demand with a slight algebraic manipulation as
233.) W= UV= −(−UV)
This tells us that people spend W dollars or spend equivalent time both to obtain UV excitement and to negate or eliminate –UV anxiety as very much fits universal emotional experience. And without our going through the details of its derivation or explanation we can write an equivalent simple Law of Supply and Demand pricing law based on T=uV relief of Eq121 with W=T assumed from earlier considerations as
234.) W= Uv= −(−Uv)
This tells us that people also spend W dollars or spend equivalent time both to obtain Uv relief and to negate or eliminate their –Uv fears, again as very much fits universal emotional experience. To sum up for emphasis, this mathematics derives people spending their money and time, being motivated to do that, both in the pursuit of the pleasures of excitement and relief and in the avoidance of the displeasures of anxiousness or anxiety and fear. Understanding behavior to be motivated by the pursuit of pleasure and the avoidance of displeasure is the essence of hedonism. It should be made clear that this sense of hedonism is not an encouragement for people to seek pleasure and avoid displeasure, but rather a conclusion drawn from the foregoing mathematical analysis that people just do behave so as to achieve pleasure and avoid displeasure as the essence of human nature. To generalize hedonism you need, of course, to also take into consideration the visceral emotions that motivate our behavior at the most basic levels like hunger and feeling cold and the pleasures of eating and warmth along with the pleasures and displeasures of social and sexual behavior, which we will begin explaining mathematically in the next section.
13. Survival Emotions
Many of our most basic emotions are associated with surviving or staying alive. We derive the pleasant and unpleasant emotions that drive survival behavior from the primitive Law of Supply and Demand in the form of Eq234 of W=Uv= −(−Uv). We do that by applying it not to avoiding the loss of v dollars but to avoiding the loss of one’s v*=1 life. That is, the penalty for failing at a survival behavior like getting food to eat or air to breathe is the loss of one’s own v*=1 life rather than the loss of v dollars. The other terms in W=Uv= −(−Uv) are also asterisked in using it to explain survival behavior to show that they are all associated with avoiding the loss of one’s V*=1 life rather than the loss of v dollars.
235.) W*=T*= U*v*= −(−U*v*)
It is best to introduce this function with specific survival behaviors and save the generalizations of what these variables mean until after we do that. Let’s start with the survival behavior of breathing air whose emotional properties are cut and dried. Consider Eq235 for a situation where air to breathe is lacking whether from a person being underwater and drowning or having a critical asthmatic attack or having a pillow placed forcibly over his face or being water boarded. From Eq235 understood as the Law of Supply and Demand, U* is a measure of the scarcity of air as the uncertainty or improbability of getting air. We can assign a very high value to it in this case of suffocation of, say, U*=.999, also interpretable as the high probability of losing one’s v*=1 life under these circumstances.
The T*=U*v* transition emotion in Eq235 experienced when a behavior is done to obtain air under this U*=.999 circumstance is, in parallel to T=Uv relief of Eq21, the very pleasurable relief felt in getting air to breathe when one is suffocating. While not all have had the experience of suffocation followed by escape those who have will attest to the great intensity of the pleasurable relief felt. One measure of this great relief is from Eq235 evaluated for the v*=1 life saved and its prior U*=.999 scarcity of air or uncertainty in getting it as
236.) T*=U*v*=(.999)(1) =.999
This .999 fractional measure of relief very close to unity, 1 or 100%, is a good way of indicating an intensely pleasurable level of relief. We can also specify the relief in dollar terms as we did in the Lucky Number games by putting a cash value or price on one’s v*=1 life, the one that one doesn’t want to lose. One measure might be if one was alone in the world, all the money one had, let’s say v*=$100,000. That calculates a cash value for the T*=U*v* relief of
237.) T*=W*= –(–U*v*)=U*v*=(.999)$100,000=$99,900
This effectively says that one would pay a price of W*=$99,900 or pretty much all of one’s money to escape terminal suffocation, which is true of all with the above assumption of nobody else to worry except the pathological. The –U*v* term in Eqs235&237 that is negated or resolved by the behavior of escaping suffocation to T*= –(–U*v*)=U*v* relief is a measure of the fear instinctively felt upon suffocation, parallel to the E= −Uv fear in Eq120 of losing money in the Lucky Numbers v penalty game.
The W*=T* equivalence of Eq235 also makes clear that the W*=T*=U*v function that governs the emotional dynamic operates as the Law of Supply and Demand with the demand for some commodity, be it goods or service, object or behavior, that provides escape from suffocation and preservation of one’s v*=1 life measured by the instinctively great value a person places on his or her life; and with the supply of what is needed to preserve that life measured inversely by the scarcity of air to breathe or uncertainty in getting it as U*.
The fact that we can so simply derive the emotions of breathing under suffocation, the panic fear it causes and the great relief experienced in escape from the suffocation, is a remarkable validation of Eq235, W*=T*_{}=U*v*= −(− U*v*), and of its derivation from the cash based Lucky Numbers game. It gives confidence that this mathematical understanding of man’s emotional machinery can impact the central problem for mankind of unhappiness from enslavement and the violence that emanates from it that stimulates war and can put the world’s nations into terminal nuclear conflict. And it should give confidence also in the remedy to these problems this mathematical analysis provides of our moving collectively towards A World with No Weapons.
The W*_{ }= T*_{}=U*v*= −(− U*v*) Law of Supply and Demand of Eq235 also holds in the normal situation for people where there is no scarcity of air, no uncertainty in the body’s cells getting oxygen, no probability of losing one’s v*=1 life from lack of oxygen, U*=0. This is made clear by inserting U*=0 into Eq235 to obtain
238.) W*=T*=U*v*= −(−U*v*)=0
This expression of Eq235 quite perfectly fits normal breathing when there is plenty of air to breath in indicating no unpleasant fearful feeling, −U*v*=0, no noticeable relief in breathing, T*=U*v*=0, and no money a person is willing to pay for air, price W*=$0. The mathematically derived conclusions for U*=.999 suffocation and U*=0 normal breathing universally fit observable human experience.
And so does the intermediate situation with air in short supply but not critically scarce, as say, U*=.2, as might apply to COPD (Chronic Obstructive Pulmonary Disease.) In this U*=.2 case, the –U*v* displeasure is felt as pulmonary distress but less horribly unpleasant than the panic fear of U*=.999 suffocation. Also significant is the T*= −(−U*v*)=U*v* relief felt when bottled oxygen is supplied to a COPD sufferer. And we also see in this not uncommon ailment for older people that they are willing to pay a W*=U*v* price for relief, a lot if necessary though not every last penny a person has as a person would pay if their life was critically threatened as it is at the U*=.999 level of suffocation.
Temperature regulation as avoidance of the extremes of cold and heat is, like breathing, centrally important for avoiding the loss of one’s v*=1 life. Temperature below 68^{o} puts the heat needed by the body to function well in short supply, makes it scarce with the uncertainty of the body getting the heat needed specifiable as U*_{ }>0 in Eq235 whatever the specific value of it we may choose to indicate that scarcity. Generally speaking the colder the skin temperature is, the greater is the U* scarcity of heat and from W*=T*=U*v*= −(−U*v*) of Eq235, the greater is the –U*v* unpleasant feeling of cold.
The –U*v* unpleasant sensation of cold is not quite the feeling of fear as was the –Uv term in Eq120 felt as fear of losing money, but it has the same effect as fear in making one want to do something to avoid the cold as though you did fear it. The range of the displeasure of cold extends to truly freezing cold we would represent as a U*=.999 scarcity of heat, which for those who have felt it approaches the feeling of pain.
Negating the –U*v* displeasure of cold by warming up provides via Eq235 the T*= −(–U*v*)=U*v* relief of warmth and its pleasure that is universally for all people greater in intensity as U*v* the greater is the displeasure of the −U*v* antecedent cold. As further validates this mathematical understanding of temperature regulation, note that a person is quite willing to pay a W*=T*=U*v*= −(−U*v*) price from Eq235 to alleviate the −U*v* displeasure of cold and obtain the U*v* pleasure of warmth, the amount of money willing to be paid being proportional to the U* scarcity of heat in the –U*v* felt as antecedent cold.
And by understanding the W* money spent to get warm when one is cold to be directly proportional to the time spent to make that money, Eq235 also tells us as fits universal experience that a person is willing to spend time to get warm directly as by cutting wood to burn in a fireplace and/or by making clothes to put on to stay warm.
It is also universal experience that when a person is continuously above the optimal 68^{o }temperature of feeling cold to begin with where there is U*=0 no scarcity of heat, the pleasant feeling of warmth is not felt as is mathematically specified by –U*v*=0 (no unpleasant feeling of cold) generating T*= U*v*=0, (no pleasant feeling of warmth.)
We will also show shortly in other familiar survival behaviors, unpleasant feelings of excessive heat, of hunger from lack of food and of pain from trauma and disease, all of whose pathologies can cause the loss of one’s v*=1 life, how the −U*v* term of Eq235 determines the displeasures of these survival threats and the U*v*term the pleasures of their resolution by appropriate behavior. But before we do that we want to show how the breathing air and obtaining warmth dynamics considered in detail above are negative feedback control or homeostatic systems. This will take a paragraph or two to do, but it is well worth spending the time on it because it will show how firmly our analysis fits in with existing accepted science.
A typical mechanical negative feedback control system is found in most homes in states that feel the cold of winter, a thermostatic controlled heating system. The idea is quite simple. The thermometer part of the thermostat measures the room temperature, θ, (theta). You set the temperature you want on the thermostat to a set point, θ_{S}. The difference between the two is the error, Ԑ, (capital epsilon),
239.) Ԑ = (θ_{S }−θ)
The existence of an error turns on the furnace, which heats the room up until the room temperature, θ, is equal to the set point, θ_{S}, the temperature you set on the thermostat, at which point the ERROR=0, and the furnace shuts off. That is the essence of negative feedback control, the elimination of set point error by appropriate automatic mechanisms.
That’s how the air and heat emotion regulated systems operate. The set point, where the system is set to go, is to have a U*=0 possibility of losing the v*=1 life. And where the system is when the situation is threatening is at a −U*v* value where there is a U*>0 probability of your losing your v*=1 life from lack of air or lack of heat. The error function in either case is
240.) Ԑ = (0_{ }–(−U*v*) )
The system is turned on whenever the Ԑ error is not zero. It turns on in our survival situations when the amount of air or heat available is less than adequate and does it by neurologically effecting the feeling of −U*v* suffocation fear or of cold. This motivates the person to act so as to alleviate the situation of suffocation or cold, which brings on the respective pleasure of relief from suffocation or warmth, which shuts off the system when there is no U* probability of the loss of one’s v*=1 life, which takes the error to zero.
Hence the system which operates on the Law of Supply and Demand of Eq238, W*=T*= U*v*= −(−U*v*), which derives ultimately from the T=R−E Law of Emotion as a special form of it, is also a simple negative feedback control system. And as one that operates on the general notion of homeostasis in biological systems as part of the rubric of accepted biological science, both the Law of Emotion and of the primitive Law of Supply and Demand it derives are seen to be also within the rubric of accepted biological science in their confluence with the workings of negative feedback control in biological systems. The three survival behavior systems we’ll consider next also in operating on the Eq235 Law of Supply and Demand are also negative feedback control or homeostatic systems.
Temperature regulation also demands that body surface temperature be less than about 82^{o}F. Above that we may talk about a “scarcity of coolness” the body needs to operate optimally, hence, U*>0, with the −U*v*>0 displeasure in Eq135 manifest as feeling hot and with the pleasurable alleviation or negation of it by appropriate cooling felt as pleasant relief from the heat, T*= −(−U*v*)=U*v*>0. And it is also clear from Eq235 as fits universal experience that a person is willing to pay for air conditioning to stay cool, W*=T*=U*v*>0. The lack of a pleasant feeling of relief from the heat when one is continuously below 82^{o}F to begin with is also specified by Eq235 to fit universal experience.
Obtaining food to keep an individual from losing his or her v*=1 life from lack of it also follows Eq235, but not in as simple and direct manner as with breathing and temperature regulation because of the complicating factor of the intermediate storage of the food in various organs of the body, short term in the stomach and long term in fat and the liver. We dodge that problem by minimizing the effect of its storage on the emotions involved for we are only interested in understanding it in the broadest way that it generates the displeasure of lacking food as hunger and the pleasures of eating primarily as the delicious taste of food.
That said, we consider that when one hasn’t eaten for some time, the glucose or blood sugar in the blood vessels of the body becomes in short supply or scarce for the body’s cells, U*>0. Then the emotion of feeling hungry arises as −U*v*>0 of Eq235 or when U*>0 is small as the disquiet of appetite. This −U*v* feeling of being hungry, quite unpleasant as hunger in high intensity, is negated or relieved to the T*= −(−U*v*)=U*v* pleasure of eating that includes both the deliciousness of food taste and the pleasant relief felt from the filling of the stomach.
The T*= −(−U*v*)= U*v* equivalence in Eq235 tells us that the intensity of the pleasure of eating, T*=U*v*, is greater, the greater the antecedent −U*v* hunger. This is readily validated by those who have had genuine hunger and experienced marked pleasure in eating to relieve the hunger even with eating just a piece of stale bread or cracker, which tastes very delicious under that circumstance. Almost all of us have experienced the fact that feeling hungry before eating makes the food taste better or be more pleasant as fits Eq235. And Eq235 also tells us that people are willing to spend W* dollars to obtain food and also to spend time for that end whether time to earn the money needed to purchase food or, as our primitive huntergatherer ancestors did by gathering plants and hunting animals, time spent directly to get food.
When blood sugar levels are high and the stomach full, U*=0, that is, there is no scarcity of food chemicals for the body’s cells and under normal circumstances, hence, no feeling to eat, −U*v*=0. Under these circumstances, eating food pretty much lacks the T*=U*v*>0 pleasure produced when one does have a −U*v*>0 appetite. In such a state, absent the abnormal, constantly present hunger that is pathologically responsible for modern man’s epidemic obesity, there is neither a pleasure nor displeasure motivation to eat.
Lastly as a survival behavior we want to consider physical trauma like a fracture that causes pain. Pain is signified as –U*v* with U*>0 the uncertainty or scarcity or lack of a healthy mechanical condition that threatens losing one’s v*=1 life. In this way pain is in obvious parallel to the scarcity of air, warmth or food, all unhealthy circumstances that threaten the loss of one’s v*=1 life,. Behavior that eliminates or negates the −U*v* pain as with not putting mechanical pressure on the fracture as −(−U*v*)=U*v*>0 produces U*v*>0 relief from the pain, which is felt as pleasant in proportion to the antecedent pain that pampering the fracture relieves.
Now let us make it clear that the unpleasant emotions of suffocation, hunger, cold, excessive heat and physical trauma and the pleasant emotions of their alleviation, all of which derive from W*=T*= U*v*= −(−U*v*) of Eq235, are different from the emotions of behaviors utilized to get the commodities that satisfy these survival needs when they are not immediately available.
When one is hungry, for example, eating may proceed in a very direct and immediate fashion when food is readily available, as when a roast beef sandwich is there in the refrigerator to satisfy the −U*v* hunger of a starving person who just woke up after being passed out for two days from a drinking binge. But one must have food first before one can eat it. Explaining the relationship between the emotions for getting food to those for eating it is best done with an example of food procurement that is mathematically welldefined like playing a Lucky Number dice game where food is the prize for the rolling of a lucky number by a hungry player.
Eating this food prize alleviates a hunger of –U*v* to produce the eating pleasure of T*= −(−U*v*)=U*v*. This behavior to get food has in the standard game a Z=1/3 probability of success and an improbability of U=(1−Z)=2/3. One’s expectations in this game are not via E=ZV the prize of V dollars but rather of getting the W*=T*=U*v* pleasure of eating the food. Because this T* pleasant emotion gotten has an explicit dollar value from W*=T*=W*v* of Eq235 we can substitute W* for the V dollar term in E=ZV to obtain our hopes of pleasure as
241.) E=ZW*=ZT*=ZU*v*=(1−U)U*v*=U*v*−UU*v*
This E=ZU*v*=U*v*−UU*v*expectation or hopes of obtaining T*=U*v* food pleasure nominally worth W*=T* dollars to probability Z stands in comparison to E=ZV=V−UV of Eq107 as the hopes of getting V dollars. In the latter, the pleasurable desire is for V dollars while in the former of Eq241 the desire is for U*v* food pleasure. Then much as the pleasant desire for V dollars is reduced by the –UV meaningful uncertainty about winning the money to one’s uncertainty tempered hopes of E=ZV, so is the U*v* pleasant thought of eating the food reduced by −UU*v* meaningful uncertainty in getting the food to the uncertainty tempered expectation of ZU*v*. This latter term is the intensity of pleasure felt in one’s hopes of satisfying one’s hunger by a particular behavior of getting food, here by playing the dice game to get food to eat. And this is exactly how the mind works in seeking pleasure by a particular behavior characterized by some Z probability of success in achieving that pleasure.
We can also develop a T transition emotion felt when one rolls a lucky number and gets the food. From the Eq8, Law of Emotion, T=R−E, what is realized following a successful throw of the dice is the R=U*v* pleasure of eating the food gotten as the prize. But also because there is U uncertainty in getting the food, there is an additional pleasure in the thrill or excitement in getting the food to eat,
242.) T=R−E= U*v*− (U*v*−UU*v*) =UU*v*
When there is no uncertainty in getting the food as in reaching into the refrigerator to pull out a ham sandwich, there is no excitement involved in the act of getting the food to eat. Contrast this to a hunt for food for people who have no immediate food store or to a search to gather berries to eat under the same circumstances of otherwise having nothing to eat. Then upon making the kill for meat or the finding of berry bush, there is great excitement.
In that sense UU* in UU*v in the above is a compound improbability, the U* improbability of your body’s cells getting what they need in food chemicals because your blood stream is low on blood sugar and the U uncertainty or improbability of your getting the food to eat in order to replenish your blood stream with the blood sugar it needs to provide the body’s cellular needs.
The T=UU*v* excitement in getting the food, hence, is a function of the U=2/3 uncertainty in getting the food and of the T*=U*v* pleasure in eating the food, itself a function of the –U*v* antecedent hunger via T*=U*v*= −(−U*v*) of Eq235. One gets both the R=U*V* pleasure of eating the food and the T=UU*v* thrill of obtaining it under uncertainty, which is what our hunter gatherer ancestors surely felt when searching for vegetative food or hunting for animal food with uncertainty, U. One can picture such a group having an exciting feast following a successful hunt or search. In contrast if there is no U uncertainty in getting food, from T=UU*v*=0, there is no excitement or thrill in getting the food despite the R=U*v* pleasure in eating it, much as when one needs but to open the door of one’s refrigerator to grab a ham sandwich or an apple to eat if one is hungry.
Note also in the food prize dice game the disappointment that is felt, assuming the game can be played only one time, when the lucky number is not rolled and food is not obtained under a condition of –U*v* hunger. In that case with E*=ZU*v* and R=0 for no prize realized, from the Law of Emotion, T=R−E,
243.) T=R−E*= 0−ZU*v*= −ZU*v*
This tells us that beyond the factor of one’s Z confidence in getting the food, the more –U*v* hungry you are and the more U*v* pleasure you anticipated in getting the food, the greater is the T= –ZU*v* disappointment in failing to get the food.
Now we have developed a good mathematical understanding of the emotions associated with our basic survival behaviors. The nuances and ramifications of this analysis are manifold and we will consider many of them in subsequent sections. We also want to develop the emotions for two other centrally important classes of human activity, violent behavior and sexual behavior. A mathematically clear explanation of the emotions of violence and sex based on Eq235 and similar Law of Supply and Demand functions can be very controversial, though, because sex and violence are heavily laden with morality injunction, which itself provides a group of emotions that must also be independently explained. Hence, we need to be very careful in approaching those topics and will begin prior to applying the Law of Supply and Demand to them by first considering natural selection in evolution and how it affects our understanding of violence and sex.
14. Natural Selection
We take great pains to
explain natural selection mathematically because of the controversial issue
that evolution has become in America. The mathematics moves up to a slightly
higher level, but we’ll do our best to keep it as simple as possible. We will
start with a formula from the banking industry for interest in a savings
account that nobody sane disagrees with. It is found in all junior high math
texts.
244.)
The x_{0} term is the initial deposit in the savings account; x is the amount of money in the account after t years assuming no more money was deposited; and g is the annual interest or growth rate of the money. If in a savings account that has an annual interest rate of g=5%=.05 you start with x_{0}=$100 and keep that money in the bank for t=2 years, the initial x_{0}=$100 will grow according to
245.)
You could also get a savings account with a quarterly or daily compounding of the interest. This modifies the interest formula in Eq245 a touch to
246.)
The m term is the number of times a year the interest is compounded or paid. So with the same initial deposit of x_{0}=$100 and same interest rate of g=5%=.05, if the savings account had quarterly interest paid, which is m=4 times a year, the money in the account would grow in t=2 years to
247.)
And if a savings account had interest compounded daily, or m=365 times a year, the $100 you originally started the account with would grow over t=2 years to
248.)
An alternative formula for the daily compounding case is
249.)
The letter, e, is Euler’s number, e=2.7183. So with x_{0}=$100, g=5%=.05 and t=2 years we calculate from it the x=$110.52 for daily compounding we saw in Eq248 but as
250.)
Eq249 is the formula for exponential growth, which means the growth of something at a rate that depends on how many of that something there already are. This fits the growth of money in a daily compounded savings account, which depends on how much money you already have in the account. Often, indeed usually, the formula for exponential growth is written in a different form than Eq249, in differential form as
251.)
The dx/dt symbol is the rate of growth of the money and this differential equation tells us that it depends on the x amount of money in the account and the g annual interest or growth rate. Eqs249&250 apply not only to the exponential growth of money in a daily compounded savings account but also to the exponential growth of a population of x organisms that also depend on the number of organisms that already exist and which generate additional organisms by reproducing themselves. For biological exponential growth, the annual growth rate, g, assumed like the annual interest rate for money to be constant as a reasonable simplifying assumption, depends not just on the birth rate of new organisms, b, but also on the death rate of existing organisms, d.
252.) g = b − d
Also this formula only applies when, like dollars in a daily compounded savings account that have just come into existence immediately “giving birth” to more new dollars on the same day, biological organisms just produced are themselves able to reproduce more newborn organisms the same day they come into existence. This happens with bacteria and other single celled organisms, but not with multicellular organisms such as man unless the “birth” of an organism is taken to be the coming into existence of a sexually mature organism, puberty or adolescence for humans, which itself, like a bacterium, is immediately able to biologically reproduce, whatever the cultural taboos against it. That important consideration fits the exponential growth formula of Eqs249&251, to be kept in mind for the later discussion of the emotions experienced by the parents of human offspring.
For now we want to get back to the basics of population growth in order to understand the nuts and bolts of natural selection. Pure exponential growth has a population grow without limit. In Eq149, as t, time, increases generation after generation, the x population size just grows and grows and never stops growing. In a population that starts with x_{0}=10 organisms, the population grows by g=1.1 organisms per existing organism per year, Eq249 tells us that after t=10 years, there will be x=598,785 organisms in the population and in another 10 years, upwards of 358 billion.
In reality, though, there is a limit to how many organisms a particular environment or niche can sustain called the carrying capacity of the niche, K. Back in the 19^{th} Century a Belgian mathematician, named Pierre Verhulst, came out with a modification of exponential growth in Eq251 that takes the reality of limited growth into account. It is, with K as the carrying capacity,
253.)
This Verhulst equation or logistic equation spells out growth over time in differential form is expressed as a time equation as
254.)
Eq253 and Eq254 translate into each other much as do Eq249 and Eq251, the details of the operation omitted. Now let’s consider the growth of the same population of x_{0}=10 organisms with a g=1.1 organisms per existing organism growth rate, but with the limit of growth or the carrying capacity, K=1000 organisms.
Figure 255.
Limited Growth of a Population of x_{0}=10
Organisms with a g=1.1 Growth Rate over t=10 years
A second impediment to the unlimited growth of a population is the presence of a competing population. To see how competition affects growth, consider two populations of organisms, #1 and #2, which both grow exponentially in unlimited circumstances according to Eq249 as
256.)
256a.) g_{1} = b_{1} – d_{1}
257.)
257a.) g_{2} = b_{2} – d_{2}
The x_{10} and x_{20} terms are the initial sizes respectively of the #1 and #2 populations; g_{1} and g_{2} are their annual growth rates; and x_{1} and x_{2} are their sizes at any time over time, t, in years. The sum of the x_{1} and x_{2} sizes of these populations, x_{1}+x_{2}, at any time t is calculated from the above to be
258.)
We calculated this x_{1}+x_{2} sum because it allows us to
track the fractional size of each population over time, t, that is, the
x_{1} and x_{2} sizes of each population relative to the x_{1}+
x_{2} sum of the populations.
Now consider these two populations existing and growing together in the same niche that has a carrying capacity, K, limit to the total number of organisms that the niche can support. When that limit is reached, the sum of the two population sizes must equal the K carrying capacity.
261.)
If the g growth rates of the two populations are unequal, g_{1} ≠
g_{2}, the population sizes of the two populations will still continue
to change even at the K carrying capacity of their mutual niche.
262.)
263.)
This x_{1}+x_{2}=K condition of the niche we assumed will also be understood as applying to the initial population sizes of x_{10} and x_{20}.
264.)
This expresses Eq252 via x_{20}=K−x_{10} as
265.)
This
expression for x_{1} is further simplified by dividing the numerator
and denominator of the right hand term by to get
266.)
We can simplify Eq256 further by expressing the difference in growth rates, g_{1}−g_{2}, as F_{1}, the competitive fitness, or more simply, the fitness of the #1 population
267.) F_{1} = g_{1} – g_{2}
268.)
Noting the sameness in form of the above to the Verhulst time equation of Eq254 tells us that we can write it in a differential form that has the same form as the Verhulst differential function of Eq253.
269.)
Next we define the fitness of the #2 population, F_{2} to be
270.) F_{2 }= g_{2} – g_{1 }= –F_{1}
This allows us in parallel to Eqs268&269 for x_{1} to write for the x_{2} size of population #2,
271.)
272.)
A graph of Eqs268&271
makes clear the fate of these two competing populations. Consider the niche
they live in together to have a carrying capacity of K=100 organisms with an
initial size of x_{10}=1 for the #1 population (asexual reproduction
assumed for simplicity) and x_{20}=99 for the #2 population and with
growth rates of g_{1}=2 and g_{2}=1 as shows x_{1} in
blue and x_{2} in red over time.
Figure 273. Competitive Population Growth or Natural Selection
The #1 population in blue, which has the higher growth rate of g_{1} =2, is seen to flourish over time while the #2 population in red, which has the smaller growth rate of g_{2} =1, dies out or goes extinct in the niche. For these and for any two competing populations, the one with the greater g growth rate or positive F fitness, here population #1 with F_{1}=g_{1}−g_{2}=1_{ }>0, eventually takes over the entire niche, x_{1}=K=100, and the one with the lesser g growth rate or negative F fitness, here population #2 with F_{2}=g_{2 }− g_{1 }= −1_{ }<0 decreases in size and eventually dies out or goes extinct in the niche, x_{2}=0. We get a better sense of this natural selection dynamic by expressing the F fitness functions of the two populations with Eqs267&270 expanded with Eqs256a&257a.
274.) F_{1 }= g_{1 }− g_{2 }= (b_{1}−d_{1}) − (b_{2}−d_{2})
275.) F_{2 }= g_{2 − }g_{1} = (b_{2}−d_{2}) − (b_{1}−d_{1})
This mathematical description of natural selection perfectly fits its description in nonmathematical language as given by the Harvard grandmaster evolutionist, Ernst Mayr,
“.....it must be pointed out that two kinds of qualities are at a premium in selection. What Darwin called natural selection refers to any attribute that favors survival, such as better use of resources, a better adaptation to weather and climate, superior resistance to diseases, and a greater ability to escape enemies. However, an individual may make a higher genetic contribution to the next generation not by having superior survival attributes but merely by being more successful in reproduction.” (Mayr, Ernst; One Long Argument: Charles Darwin and Modern Evolutionary Thought; Harvard Univ. Press, 1991, p.88).
(We also point out that
the defining functions for the natural selection dynamic of Eqs268272 are not
new and can also be derived from the preWW1 work of the classical population
biologists, R.A. Fisher and J.B.S. Haldane, though done here in a much simpler
way.)
The advantage of having a mathematical formulation for natural selection is not only in showing the underlying mechanism of the dynamic but also in providing a clear understanding via the F fitness function of where the primary behaviors of humans of survival, reproduction and combat come from as seen in the expansion of the F_{1} fitness of Eq253 to
276.) F_{1}=b_{1}−d_{1}−b_{2}+d_{2}
Population #1’s chances of its F_{1} fitness being positive, F_{1 }>0, and of its surviving from generation to generation and flourishing are greatest when its members behave in such a way as to maximize its F_{1} fitness. This optimization of F_{1} mathematically entails in part minimizing the d_{1} death rate in F_{1}=b_{1}−d_{1}−b_{2}+d_{2 }through survival behaviors like eating and staying warm that keep the organisms of population #1 alive and maximize their life span, for when the life spans of member organisms are great, the d_{1} death rate of their population is small. This minimization of the d_{1} term in F_{1}=b_{1}−d_{1}−b_{2}+d_{2} comes about as we saw by the homeostatic survival behaviors that operate on the emotional machinery described earlier that derive from Eq235. The negative feedback control systems that regulate behavior and motivate it through our emotions have as their implicit goal the evolutionary success of a population over time from generation to generation. This is clear from the simplest logic of surviving populations necessarily having competent, emotion driven survival behaviors. Those that don’t do not survive in evolutionary time and go extinct.
It is also clear from F_{1}=b_{1}−d_{1}−b_{2}+d_{2} that F_{1} fitness and the possibility of evolutionary success is optimized by maximizing the b_{1} birth rate and the d_{2} death rate of a rival population in the niche. On the face of it, this suggests in the maximization of b_{1} that biological organisms including humans should have been programmed emotionally by evolution to maximize the number of offspring they produce. It also suggests from the nature of the foundation function of exponential growth for natural selection laid out in Eqs249,251&252 that humans should be programmed emotionally to raise their children to adolescence. And in regard to maximizing d_{2}, the death rate of rivals, in order to optimize F_{1} that there be emotional programming to kill off rivals in the niche or drive them out of the niche as produces the same outcome prescribed by the mathematics of lowering the population size of rivals in the niche.
Another alternative conclusion to combat is one group conquering another and taking them as slaves. As slave labor by definition results in greater wealth for the conquerors, it necessarily improves the life span of individuals and lowers the death rate, −d_{1}, of the dominant population of slave masters. Keeping people in chains physically or economically also effectively removes them from the competing competition, kills them as competing individuals and in doing so increases d_{2}. As both a decrease in −d_{1} and an increase in d_{2} helps to maximize the evolutionary fitness of a group, the behavior of slave taking and the economic control of others generally is favored in evolution. This is hardly to say that the positive emotions involved in being a slave master are actively advertised because doing so would run contrary to having a maximally efficient control. The lion does not advertise the fact as he stalks the wildebeest that he is about to kill and eat it. And, indeed, this behavioral deception that is general in just about all predators is matched by varieties of passive signal deception such as the lion’s coat being the color of savannah grass so as to hide its approach to its prey. In short if we all did live in a slave society, the last thing it would do is advertise the fact of it.
And in conjunction with this comes the hiding of the consequences of being controlled in an exploitive way, religion blaming the devil or the person himself or herself for their pains and clinical psychology the equally vague evil spirit of mental illness and/or the person, himself or herself. Most unhappiness comes from one’s loss of true freedom along with much of violence we see in the news, domestically and internationally. To clarify these issues takes further mathematical analysis based on the foundation ideas we have developed up to this point.
But talking about the emotions related to sex, love (parental and romantic) and violence, however, and what the mathematically prescribed behavioral outcomes of these emotions are or are not is fraught with problems because sex, love and violence are very much tied up with values and morality. And these considerations get all the more confused and contentious, on the one hand, when moral restrictions are used to control people and their behaviors in a servile society, one that depends on the enslavement of its people for its strength and survival; and on the other hand, when the morality of behaviors are broadcast with fiction that utterly distorts the reality of life and with supposed nonfiction news programming that is at heart as nonrepresentational of real life as the fictional programming in television series and in movies.
For the above reasons, before we dive into these problems with considering violence and sex, epistemologically and morally, we are required to first present a template for reality in the form of true life stories that are more representative of not just what happens to people but in the emotions that people feel generally. For that reason, despite the fact that I would prefer to keep my failures and humiliations to myself, as people generally do which keeps the harsher truths of life all the more hidden, I tell my story in the following section. Then we will continue with the mathematical analysis in the sections after that.
15. Revolution in the Garden in Eden
Ed Graf Pleading Guilty to Murdering His Two Stepson’s for Insurance Money and Ed’s cousin, my brother, Don Graf
The prosecution said at his first trial in Waco in 1988 that Ed Graf left work early on Aug. 26, 1986 and picked up his two sons from daycare. He told his wife to stay at work late. He and the kids got home about 4:40 in the afternoon. Ed Graf then rendered the boys unconscious, dragged them from the house to this small wood shed in the backyard, poured gasoline around near the door, closed the door, locked it and went back to the house. By 4:55 p.m., flames engulfed the shed and burned it to almost nothing in minutes. One of the most damning pieces of evidence in the case that found him guilty and had him serve 25 years in prison before he was granted a retrial in 2014 was the fact that Ed had taken out insurance policies on the eight and nine year old boys about a month before the fire.
Bail was set for his retrial at a million dollars. But Ed’s brother, Craig, was only able to raise $100,000 so Ed remained in jail during the retrial. It was nearing its end when I first came across the story of how my cousin had burned his kids alive. I was in shock because though I’m Ed’s cousin too and was close enough to the family in my younger days to be brother, Craig’s, baptismal sponsor, the first I heard of the murders was when I came across the story entirely by chance while browsing the Internet during the retrial. I was in the dark about the killings for the last thirty years because I was the one lucky Graf who escaped from this fundamentalist clan as a young woman, never to be told by anybody in my estranged family about this hideous skeleton in the closet that makes an evidenced case of why I ran away from them all those years ago.
Toward the end of Ed’s retrial, with the jury polled to be leaning in favor of conviction, 102, which would have locked him up for life with no chance of parole, he suddenly pleaded guilty to the murders as part of a most unusual last minute plea bargain that released him on parole a few days later. A letter to the editor that appeared on the front page of the Waco Tribune shortly after makes clear the outrage caused by his being freed. It read in part: “I would venture to say in the opinion of 99.9 percent of the public who have followed the Edward Graf murder retrial, the handling of this case, including its outcome, is a travesty of the judicial system. It is an enormous injustice to those two boys’ lives that he took and to the family of those two boys who have had to relive their nightmare not once but twice. And now this man, if you want to call him that, is going to be able to walk the streets of society again.”
I’ll speak to these twin evils of Ed’s child murders and the judicial corruption that released him from my own experience as a former member of the Graf extended family. I was the one who rebelled against its control and abuse and threw the pain of my suffering back in the face of those who caused it while Ed absorbed the worst of it without resistance and passed his lunatic unhappiness from it onto the two youngsters he burned alive. This release of unhappiness as violence on innocent victims who weren’t its cause is utterly common from the petty meanness people daily endure from those who have some power over them to the mass murders so familiar in the news to the butchery of war, the grand release of one nation’s unhappiness from the control imposed on its people on another. And that will reach its maximum horror in the megadeath of nuclear conflict. This true view of adult life as highly controlled ultimately by those at the top of the social hierarchy for their benefit runs counter to the American Dream picture presented to young people in ruling class controlled media.
To expose the reality of life, one calls on the one picture of it that one is sure of, the reality of one’s own life. Nothing, though, is as difficult as revealing the truth about, especially the bad things that happened to you. For whatever feels bad inside when you think about it brings greater humiliation yet in the public confessing of it. But the cost of keeping private matters hidden from others is also great if making life clear is important to you, for only the raw truth spat out is able to show that the society we live in has problems, significant institutional problems that must be spelled out clearly if there is to be any chance of doing anything about them. And after I finish my story I’ll talk about the important issues in precise mathematical language.
I was born four months before
America entered WWII as part of the last wave of women whom fundamentalist
tradition was set up to control them as tightly and painfully as the foot bound
women of imperial China. My father was a minister in rural parishes in Cullman,
Alabama, where I was born, and later in Serbin, Texas, north of Austin, where
his superior ability to extort tithes from parishioners elevated him to a
position at Lutheran seminary where he taught Stewardship, a fancy name for
extracting cash from the congregation.
My mother was a shrewd bulldog faced woman right out of Stephen King's, Carrie,
crazy enough to think and tell us kids that Jesus talked to her every day and
that the fossils in Dinosaur National Monument were plaster fakes secretly
buried in the ground by people who hated God. This gave her cover for raising
her children with the switch, including this little girl, me, with near weekly
humiliating and painful britches pulled down whippings. If she didn't get off
sexually with this game, for she had a way of twisting truth in all matters, I
wouldn't believe it. Mildred Graf was 50 Shades of Grey with a halo.
Fear ruled my life, fear of punishment for taking a cookie without permission,
fear of my mother whenever I approached my house coming home from school, fear
of the dark, fear of dogs and a fear of the moon at night that stretched into
my early thirties, at which time I was miraculously able to escape from this
idiotic pointless terror of disobeying and everything else conditioned in me by
childhood brutality disguised and blessed by my minister father as a proper
Christian upbringing.
Some of the worst of my early years was my role as ego fodder for my brother, Don, older than me by two years. He was the recipient of the same sort of corporal punishment I got until he firmed into the role of my mother's toad and henchman over me. My hearing her spank Don used to bring on tears in me for him, but a waste of emotional energy in that my mother's iron rule could never be softened with tears and in Don's passing on a good amount of the pain he got from her to his younger sister, me. If my recall of his punching me in the shoulder at least once a day is an exaggerated memory, it is not by much. And once you are scared of somebody physically, even suggestions to stupid things potentially frightening become effective like being told there was a wolf upstairs in my bedroom that brought on a kind of terror I showed outwardly that he delighted in.
I was lucky, though. I was not so destroyed as to be unable to hate my mother, for she and my minister father left enough in dumbbell me by pampering on the margins to make me a pretty if frightfully awkward girl child, for the minister's daughter is a public figure and if thought pretty by the congregation, a valuable status symbol helpful for stewardship and for the minister’s promotion in the pastoral ranks.
Alone in a piously brutal
regime, all that mattered to me growing up was the thought and hope of love and
rescue. The most daring books in our home library in those days were the Zane
Grey novels. My imagination translated the cowboy heroes in them into would be
lovers scooping me up on their horses and taking me far away from my family while
squirting me in my preteen private parts with some warm liquid of unknown
composition.
Beyond this seeping in of instinctive sexual feeling under the repression my
attitude towards men was also shaped my father, a classic ever smiling father
knows best type minister who is both an extreme asshole and an extreme bastard
underneath the smile. And also by my brother, Don, who sustained his imperious
position over me with constant disdain and disapproval even as I grew beyond
the punch in the arm years. I was the model he practiced on in learning to
control and humiliate people successfully as a lawyer in later life.
My early romances once I reached adolescence were the typical failures of young
Christian girls. The boy I came to love most, the one who loved me the most, my
parents hated and never stopped talking him down. Unfortunately the poor
fellow, only seventeen like me, lacked the vigor and toughness of a Zane Grey
hero even if his fondling was enough to kindle a strong flame of desire and
affection in me for him. It takes more weapons and courage to be the knight in
shining armor that rescues a damsel as much in distress as I was than any
seventeen year old boy could possibly have mustered. My tears from the
inevitable breakup were doubly painful with my mother reveling in soothing me
over what I took emotionally to be a personal failure and shortcoming on top of
the loss of love.
I remember the humiliation of being seventeen and dragged along by my parents on Sunday family trips devoid of any male attention or admiration. It was on one of these family jaunts to Wichita Falls in Texas that I first have a memory of Edward E. Graf Jr. This photo of his parents suggest a childhood for Ed Jr. little different than mine if the ugliness of parents is any indication of the way they treat their offspring as it was with my also strikingly ugly mother and father.
Uncle Ed and Aunt Sue, the Killer’s Parents
That Sunday visit, Ed Jr. was sixyearsold, eleven years my junior. My memory
of him back then was that he was puny, though glossed with a reputation for
being smart, perhaps what you might expected for a first born boy raised in a
corporal punishment believing family. I don’t want to make too strong a
comparison to my brother, Don, as a way of cutely suggesting that Don would
have burned children to death for insurance money, but in fact he was also puny
as a young man, my corporal punishing mother constantly haranguing him to “walk
with your shoulders back” and glossing him as a very smart boy. They were both
standard middle class momma’s boys. As were Ed and Sue and my parents, in
personality and looks, your standard fundamentalist ugly looking piously mean
parents.
A few years later, shortly after I got married, I ran into Ed Jr. again after we went back to Wichita Falls for a visit with Aunt Sue and Uncle Ed right after Don’s wedding down in Galveston. I remember Ed Jr. more critically then when he was about ten as being awkward to the point of what southern girls called back then, punky, and his mother, Sue, as your typically unattractive Christian mother who talked to Ed Jr. like some school teachers do to their students, in a continuously controlling tone. He definitely did not strike me as a “killer” at that time, but you learn as you age in these circles that whatever sinfulness resides in a fundamentalist person, hint of killer? In this case, they don’t show their feelings. Indeed one piece of advice my fundamentalist mother gave me, likely a commonplace tip in Missouri Synod Lutheran families, was “never say what you think.”
But killer aside, what you do see here is the makings of an injured soul of a little boy who is overdominated by his less than empathetic mother. Two decades later I ran into him again a few years just before he killed his stepsons and then the results of his less than perfect childhood began to show an adult level pathology. But that is getting way ahead in my story.
The fellow my wounded heart connected with in marriage, or better, was connected to me by my parents, was a seminary student in my father's class at Concordia Theological Seminary in Springfield, Illinois. What I soon found out about him, that he was a toady type who filtered all his thoughts before he spoke them, I had absolutely no way of appreciating when I met him, for my father, like ministers generally, behaved this way as an integral part of being a minister, a job that is 95% acting. After two years of college at age twenty I married this Len Schoppa, a classic Texas phony. The error in it was inadvertently forewarned by my brother Don’s not bothering to attend my wedding whether he really did need to study for an important law school exam or from the utter disdain he had for me on this supposed most important day in a woman’s life. It was a fairy tale omen of worse things to come with Len and, indeed, with brother Don, too,
To speak of myself as
gullible as Len and I headed off two years later to Japan as Lutheran
missionaries is as much an understatement as calling a blind person gullible. I
came equipped for my role as wife only with a thoroughly ingrained sense of
duties to be performed, cook and wash the dishes and prepare the Sunday
communion wafers and such, along with a few primitive feelings that escaped my
mother's guillotine like my continued strong longing for love including sex not
satisfied in this very emotionally empty Christian marriage. Further, the
usually subtle misery of this loveless, effectively arranged marriage
manifested itself in the less than subtle daily migraine headaches I'd had
since early grade school that worsened as the anniversaries piled up.
Can I make a light joke of the preposterousness of the goal of converting the
Japanese to Christianity? For my minister husband it was all dominance games
aimed mostly at the young Japanese guys who came to our mission church in
search of escape from the empty life that awaited that generation of losers to
America in World War II. For me it was being unwittingly being used as the
pretty young wife of the missionary pastor, my vacant, submissive personality a
fine fit to docility expected of Japanese women. I was a very efficient window
dressing for his game. Many young men fell in love with me in this part I
blindly played like Elizabeth Taylor in Suddenly Last Summer with Len beating
the boys into subordination to him as the guy who had the woman they were all
falling in love with. And down they went to him, all these poor bastards, one
of them committing suicide as a result of this love triangle game Len played
that I was completely unaware of. This story you won’t find in the Bible or
preached about on televangelist TV.
I hesitate to say anything about my relationship to the three kids I bore for
this haloed predator, they being the only love this inadequate mother ever had
in her life. If they got anything good it was because they were everything in
my life, but my failure was so clearly revealed in the end by the lack of any
sparkle in their eyes as they approached adolescence. That makes you wish you
were dead if you’re unable to rationalize such things, as I was not. For as bad
as what is done to you in life and what you become as a result of it, worse is
what you pass on to others, intended or not, especially to the innocents. On
the other hand, my leaving Len in a dramatic way (as I’ll get into in a moment)
smack in the middle of the kids’ preadolescence turned out to be an intended
amelioration of the worst of me that I have always been grateful for in
retrospect. They all turned out to be rather good looking creatures in their
adult lives.
As a pastor's wife in mildly idiot type rather like Sandy Dennis in Whose
Afraid of Virginia Wolf I would have been totally devoured by the older
women in any American congregation. But in Japan I was protected from the
lady’s groups by my semiworship by a vast gaggle of Japanese men that extended
out beyond our mission church boys to the classes of college age guys I taught
English to at Hokkaido University. This support that nature gives free of
charge to girls who manage, by care or luck, to keep their waist slim was
raised to a better level when fate, most miraculously, handed me a side role in
life as a commercial model on Japanese TV. One of our social contacts through
the mission church was a television producer who signed me on to pitch canned
bean soup on Japanese television, the equivalent of Campbell’s soups. For six
years I was known all over Japan in this guise, stopped by strangers on the
street and at restaurants when I dined out and asked, "Aren't you the
Koiten Soup Girl?!!"
A sort of Zane Grey hero soon came into my life in the form of a Japanese
college boy, a ski bum sort of fellow who took the missionary's wife bait that
the Reverend Schoppa dangled in front of all the young men, too her off to bed.
This happened on church sponsored ski trips up on the slopes of Hokkaido that
Len didn't come to because he didn't ski. It was real love as close as I'd ever
been to it. He liked me a lot and I loved him for him for loving me that much
and loved him too. The affair, whenever I could get it, was a great relief from
the empty life I’d had with my mom and dad appointed missionary husband.
Physical love that works for a woman in her twenties is fairly close to Heaven
when you’re in the middle of it as much as not having it is quite hell.
Perhaps affairs like this are easy to hide for the smart women on the Real
Housewives of New Jersey TV shows, but in a crowd of 30 fellow LCMS
missionary couples we were but one of, some of whom also went on these
Christian Fellowship ski trips, once the slightest suspicion arose about Mrs.
Schoppa and her ski partner, the gossip fell like rain from the sky on the
doorstep of the Rev. Schoppa. The climax of the confrontation between him and I
was funny in its surprising twists and turns only in distant recollection of
it.
I didn't hesitate to confess once he accused. I was much too dumb to tell a
good lie and, to tell the truth, I had no good reason for wanting to hide it
from him for by this time, I hated him for plaguing my life with his presence
and instinctive female intuition must have primed me to unload with the truth
with both barrels once he popped the question. What surprised me was his
falling smack on the floor when I told him, yes, yes, I did it, and then
writhing on the rug like a big piece of bacon frying in a pan turned up high;
and while twisting all about like that confessing in a series of blurts to
having had sex with farm animals, sheep, pigs and even the large dog his
parents named, "Lassie." Even at this, though, I was sure later that
he was lying, for he was the quintessential toady type who had to lie about
everything in his toady life. What his preferring to fuck geese better than me
had to do with my having had an affair the last six months with one of our
converts did not, could not, register in my head at the moment of his deep
confession and only in retrospect a few days later did I realize that the rumor
that he had had sex with his retarded cousin, Larry, that a few of the good old
boys in Harrold, Texas, had lightly joked about must have been true.
Once you have a sense of that, parallax with pastor personalities generally so
similar to his and my father’s makes it clear that they're all closet fags of
one kind or another. Sense would tell you that the Protestant Christian clerics
couldn’t be that much different than the Catholic Christian clerics, however
seldom you see one get his trousers pulled down in public like Ted Haggard and
Jim Bakker. It quite fit my own father, who though he likely sinned only in his
heart in this regard I would guess, had to be perverse sexually in marrying
anyone as bearishly ugly as my mother. Indeed, the truest truth ever spoken on
TV had to be about queer conservatives as the norm by Joel McHale at the 2014
White House Correspondent’s Dinner. I mean, the brief titter and then drop dead
silence tells it all. I mean, who looks prissier and weirder and queerer than
pretty boys Ted Cruz and Marco Rubio and slippery ugly boys Rush Limbaugh and
Karl Rove.
And back closer to home, it would
take a very kind woman not to see my brother, Don, quintessentially
conservative in his outward religious and political behavior, as faggy. That’s
not to say he never married, did twice. But on the other hand both divorced
him. And a wealthy lawyer has to be a pretty something off the norm to be left
behind when he’s got that much status and that much money in the bank, and by
two women no less. That’s just an educated guess, mind you, though the extent
of his hating women, which I know a lot about as you’ll see, (I am not
labelling him as a murderer for nothing), is a bit of a tip off on what he does
on his frequent weekend trips out of town.
Anyway, angry gossip aside and back to the main story, the headline of
Missionary’s Wife Has Affair with College Boy Convert in Japan quickly spread
beyond our Lutheran missionary circle in Japan to all the Christian
missionaries in Japan and shortly, in less than a year, all but one of our 30
LCMS (Lutheran Church Missouri Synod) missionary couples were recalled back to
America. Sounds like a very funny movie, but that actually did happen, I’m
proud to say. The scandal hit home stateside, too, for my father was way up
there in the LCMS church hierarchy and seeking just at this inopportune time to
be elected Bishop of the Texas District of our church. Indeed, he lost not long
after Len and I crawled home. You also have to understand that the Graf clan’s
primary occupations were in the church as ministers or teachers in LCMS
parochial schools. So I was not exactly welcomed back with smiles and flowers.
So, I mean that as, as a result of this, the word was put out by my immediate
family who were all, including my brother Don, directly affected by the
scandal, that I was mentally ill. For why else would a girl from such a good
Christian family do something so horribly sinful and to such a wonderful fellow
minister (and soninlaw) as Len, as seeking another man’s carnal
companionship.
Mentally ill, though, was not
how I began feeling shortly after the plane touched down in Dallas. Scared
rather to see my family siding with the now villainous poisonous snake of a
husband I had that I was longing to make my exsnake. They all became snakes at
this point, and snakes with a mind to bite down hard on me as punishment for my
sin and to get me back with Len, the thought of whom at this point,
animalfucker and so on, made me feel like vomiting any time I came into visual
contact with him. Ted Haggard's wife remained “loyal” to her homosexual
fundamentalist minister husband after his Tuesday night affairs with the
muscular ass fucking prostitute was made public by the latter, but she knew
what she and he was getting into to begin with and hung around wither fake
brave smile as a heavily invested business partner. That kind is her own kind
of Christian perversity that God fortunately did not curse me with
too.
Ah, the silver lining to the story I will now backtrack to. It came in the form
of a Japanese baby girl Len and I adopted at Len’s insistence to make us look
like the spitting image of Holy Family to the Japanese around us. Bachan, the
nickname I gave her shortly after I fell in love with this most darling baby
child, was the product of a young, very pretty prostitute from Yokohama, whom I
met before she gave the baby up, and of her Norwegian seaman few weeks lover,
so she said. Bachan was strikingly adorable with her unusual mix of Asiatic
and Nordic features.
Bachan was special also in my being able to love her as other than a cooffspring of the snake. My ski fellow lover was also in love with her, always brought her on the ski trips, so she also provided bonding in that way. And Bachan also provided a splendid excuse for my avoiding Len at night for the last three years of the marriage by needing to sleep on the couch near Bachan to keep her from crying. This avoided his touch, a special dispensation for me under the circumstances and one packed with plausible deniability for my loathing of him, a face saver for him. I loved her in a special way that had no poison in it.
Anyway, whatever hell was there for me back in the States if I didn't go back with Len to please my father and the hundred minsters pressuring me to do so, it was impossible to do that, on par with my being forced to amputate one of my fingers with a kitchen knife. So I ran away in my mind even if not in physical reality. But a lot of good that did as they all ran after me, calling me on the phone incessantly with preachments and ringing the doorbell to talk Jesus and God’s love to me. Actually I was going mad because I couldn't leave the kids behind, I knew that, and the whole deal just frightened the hell out of me. The most I could do was spend a few hours a day curled up in a ball fantasizing impossible Zane Gray level solutions to this impossible problem. Even thought some about my boyfriend back in Japan at times, who wrote to beg me to come back to Japan. But he was no Zane Grey hero because he was just a college kid who lacked the high caliber punch this quite dangerous situation I was in required. Len pushed and pushed for reconciliation to save his reputation and as he did it got brutal, emotionally and at times, physically, for there was none of this rape or violence on a wife stuff for a husband back in those days.
Oddly, as luck would have it
or I wouldn’t be writing this, my fantasies did come true. This was in the
guise of a fellow appearing on the scene just in the nick of time. I had
insisted to Len upon our being booted out of Japan that we go to Berkeley where
I'd read in an issue of International Time Magazine that things were happening,
new things that gave hope in a general way, just what I needed in my personal
life at that time of despair. I insisted we go to Berkeley.
Len enrolled at this school, a Presbyterian seminary just north of San
Francisco, to get a Master’s Degree in something called pastoral counseling so
he could become a marriage counselor or drug counselor, his sense of being a
minister having taken a good beating. We got set up in an apartment in student
housing at this seminary in San Anselmo in Marin County barely speaking to each
other.
It was like being locked up
in a cage. I avoided the other minister's wives, all sweetly phony kinds I
couldn’t stand beyond my situation with Len that was not the norm on campus.
This was not at all what I had come to the Bay Area hoping for. So a great
relief it was to go 40 miles away to a youth hostel at Point Reyes National
Seashore for a weekend of environmental education with my oldest boy's seventh
grade class. It was an especially great relief because I was due on that Monday
following the weekend to go with Len to see two psychiatrists who were teachers
of his as some sort of marriage therapy he said he had set up to patch us back
together again. Like a doll with a broken arm stuffed with sawdust in the head
I agreed to this, perhaps as evidence of just how stupid I was. For Len had
already dragged me to one marriage counselor back in Japan and the eighth grade
suggestions made by this toad who was almost as low as Len could have only
worked if the wife wanted to stay with a husband for material reasons despite
despising him.
The collection of people who were out at this youth hostel included not only
all the other kids in my son, Lenny's, classroom and some of their parents but
also what you’d have to call genuine users of a youth hostel just north of San
Francisco in the early 70s, many of them guys with long hair and girls with
torn jeans and actual flowers in their hair, the kind that favored organically
produced cheese. They were mostly a sweet kind of looking people, not that
strong, but all trying to be, all except for one who wasn't particularly sweet
looking.
Pete was coming from New York, a dropout from graduate school at Rensselaer
Polytechnic, one credit shy of a PhD in biophysics. And he was different than
the others in being very tough looking, more what you’d think a Hell’s Angel
would look like than scientist. It was easy to see that he was not afraid of
anybody or possibly anything. Later he would tell me that a dream he had while
sleeping in a campground in Spain across from the coast of Africa got him to
prefer death, actually, to losing his freedom. Of the many creatures who
inhabited the interesting world of the late sixties in America, a lot of them
following the style of the day, he was very, very real, a real give me liberty
or give me death character.
Later he would also tell me that on first seeing me that he thought I looked
like a model in a Woman’s Day magazine, which wasn't far from the truth as I
had been a TV model in Japan. We talked for six hours that evening I first met
him, his eyes that rather glowed never leaving mine. He said the selfhelp
psychology book I had brought with me was nonsense, that they all were all
nonsense, and that the true cause of unhappiness was abuse and the cure for it,
rebellion against abusive people and situations, period. He couldn’t have found
a more receptive audience for his politics, for without knowing my situation,
he spelled it out for me perfectly. When I told him about my husband as the
night went on and my being about to go to a therapy session with Len's two
psychiatrist professors, he said not to go. “I wouldn’t trust the bastard. It's
possibly a trap. Two psychiatrists can commit a person involuntarily. Don’t
go.” He was smart, tough and careful.
The next morning at breakfast in the communal kitchen of the youth hostel, he
got to talking with two Australian fellows in my presence who were arguing that
you had to compromise in life to survive and that anybody who didn’t was a
fool. Pete, not liking the implication and likely especially not in front of
me, retorted that he thought it cowardly if you compromised with
people who were abusive or insulting towards you, which could have included the
two of them at this moment. Both of these Australians were big guys. But when
it became clear that their differences were irreconcilable and the remarks
going back and forth picked up steam, Pete just raised his eyebrows and lowered
his tone and stopped smiling and they both more or less ran out of the kitchen.
He was not somebody who made you afraid of him, never me, but it was also clear
that he would not back down in a fight, not even against two, not unlike my
heroes in the Zane Grey novels.
We separated during a group tour of the seashore later that afternoon and when
we met again I opened up to him. When he asked why I seemed so sad, I said,
"Look at my son, look at his eyes." To me, anyone could tell that
Lenny Jr. hadn't turned out as well as he might have. And that killed me, for I
did love the boy. Pete talked to reassure me, saying that Lenny didn't look
that bad, “looks better than a lot of other kids his age.” He meant it, too,
you could tell, and that made me feel better. Our conversations went on and on
that night too, Saturday night, touching a lot on politics for Pete was heavily
into the idea of actual revolution for he said that the hierarchy you had to
submit to in order to survive was deadly to selfrespect and with that lost, you
might as well be dead.
We parents and our kids were all due to leave the next morning on Sunday. At
some point during our last exchange before I left, he touched my upper arm in a
firm way as I was about to go, something I could feel down to my knees. As my
son and I were about to get into our blue Toyota, I suddenly turned and asked
him on impulse, stupidly in retrospect, if he wanted to come over to the house
and have dinner with the family. Given my situation with Len, I don't know why
those words came out of my mouth. I suppose I wanted to see him again, but
didn't know how to say it in a socially acceptable way.
He smiled and shook his head and said, "Three doesn't work." And we
parted. That night after Lenny and I got back home I told Len I wasn't going to
the therapy session he'd set up. And the next morning after Len went off to
class for the day I called the youth hostel and told Pete I wanted to make the
40 mile drive back to see him and talk some more.
He was very forward when I got there, aggressive at the level of putting his
hands down my jeans without saying a word a minute after I arrived and we were
alone. The thought came into my head that he was some sort of a sex maniac you
hear about and that women are told, of course, to avoid. As it turned out I
suppose he was sort of a sex maniac, but what he was doing was something so
instantly pleasurable that you can't help but want him to keep doing it. It was
a little more aggressive and forceful than you might think a honeymoon
encounter should be. But like a new great flavor of pizza you’d never heard of
before shoved down your throat to begin with, once you've tried one slice, it's
hard to not want more. And he quite felt the same way about me, maybe even
doubly judging from the second and third slices he wanted right away.
I stayed overnight and by the time morning came and I knew I had to get back to
the kids, Pete was telling me that he had never seen a girl as beautiful as I
looked that morning, not in a movie, not in a magazine, not in real life, not
ever. As I've been with him 41 years now, I know he meant it at that moment,
though some credit to him because all that physical attention does make a girl
feel and look really good. He also said that first intimate day, "I'd die
for you. I'd kill for you." As such, given my circumstances, he was
"just what I needed" as things would turn out.
Whatever the nonsense in pop psych books about guys “needing to make a
commitment”, Darwin says it all much better than Freud or the Pope. When the sex
clicks, you just are committed. And when it doesn't, there's no future in the
relationship. Either the guy's got the testosterone and heart capable of love
required or he doesn't. There's little love in America today, it’s all breakups
and divorce and loneliness, even in marriages that hold together for money
sake, because all the guys but the bravest ones who resist critical compromise,
have been gelded, castrated, made cute little boys out of at best and those
worth little in the long run.
What was truly amazing and unarguable as to the power of love was that starting after that morning up at the youth hostel, my migraine headaches went away. I don’t mean that they were less painful, but that they just completely went away, never to come back again for the rest of my life. That’s physical proof of the power of love. It also tells you something about where migraines come from. And it tells you one way to get rid of them, though it’s obviously not something you can buy over the counter or get a prescription for.
Len knew what was up the minute I got back home late that morning. "I can tell by your eyes," he said, but better he could tell by the fact that I had been out all night. Pete said to tell him the minute I got back home to get out of the house. I did. He refused at first until I told him angrily that I'd run screaming out onto the seminary campus if he didn't. It helps to be furious at critical moments. He left.
The pious fraud I'd had the misfortune to live with for the previous ten years came back the next day, though, and tried to rape me. I ran from the apartment with bruises on my shoulders and arms. Len went out the door and took the car keys with him. Pete was furious when he heard about what he’d done when I hitchhiked out to the youth hostel the following day. "I'll kill the bastard," he made clear.
He didn't have to wait long to have the opportunity. Len drove out to the youth hostel to ask questions and confront him a couple of days later. Pete's best war story was how he backed down a gang of ten Puerto Ricans on East 11th St. in Manhattan where he lived by beating the leader of the gang in front of them. This was just before he came to California and met me. By the time he left New York City he had picked up a couple of knife scars and four bullet holes and had never backed down in a fight even when confronted with the gun.
He’s told me the story of the fight with Len that day often over the years and without going into all the words said between them and the punches thrown, Pete in the end got Len down in a position where he could have ripped Len's eyes out and felt angry enough to do it but didn't because he knew that would go over the line and surely get him locked up. He didn't have to do anything that hash, though, because whatever the details of their fight, Len got the point and was scared enough of Pete after that to never come over and bother me again.
But that was hardly the end of the pain Len could cause. Immediately after my filing for divorce a few days later, Len got visitation rights and it was impossible not to see how he loved coming over to take a bite out of me with the courts backing him up, something 50 million women in America in the same situation have to have experienced. It was so obvious in my case because Len never cared anything about the kids any more than he did about me  until I filed for divorce. Before that we were little more than window dressing for the creep. Now he was their loving father doing more with them in the next couple of months than he’d done in the previous ten years. I should make it clear that through all this, Len wanted me back, both to please my parents and to not look like the biggest loser in the world to everybody else as the minister whose wife ran off and left him. So endless intrusions in every way he was licensed by the law to make them through the kids. Even Pete had to swallow his urge to crack Len’s skull when he came round, which caused him noticeable if not unbearable discomfort when Len came for the kids every other weekend.
All of these maneuvers by Len during the divorce were calculated to get me back, not to produce a livable divorce. Len made no bones about it. Neither did my parents or my brother, Don, who called from Texas and talked to me endlessly like I was a disobedient eight year old. As this phase dragged on it became clear that much of Len's legal strategizing was engineered by Don. Pete and I felt sure of this because Len's actual lawyer in California was a cheapo prematurely balding grease head who mostly wanted me to like him when we had contact and who seemed half in the dark about the maneuvers Len was making on his own.
Like I said a good part of the endless harassment to get me to leave the evil Pete and go back to worthy Len was near daily phone calls and house calls from a dozen or so Lutheran ministers in the area. I felt a jolt every time I heard the front door bell ring. One ring, though, produced not a dark robed minister but my mother in an unannounced fly up from Texas. She brought along a large roast beef. Fortunately Pete happened to be right there in the living room two feet from the front door when the bell rang.
The interaction between the three of us was relatively brief and to the point. My mother, whom Pete once described as looking remarkably like the "basilisk", a mythical lizardlike monster, threatened us both with punishment from God and told Pete more than a few times the hour she was there what she had told me when I was young, that Jesus spoke to her directly on a daily basis. What Pete suggested God could do, shouted back in her face, is exactly what you might imagine a politically radical, physically confident lover fed up with the crap that had been rained down on me since the day I filed the divorce would say, namely that God and she could both go fuck themselves and for her to get the hell out of the house. When she hesitated, Pete more or less pushed her out the front door and to make his point even more emphatically, he tossed her roast beef in the garbage can sitting on the porch next to the front door.
"Seemed to me more like
a squabble with a dyke over their mutual girlfriend,” he said the minute she
cleared the driveway with her luggage in her hand. “Your mother really is
weird. No wonder you hated her so much when you were young." My memory of
some of her more invasive, hygienic sort of, punishments my mother abused me
with made that picture of her a fairly accurate one. She was disgusting on top
of being cruel and overbearing.
I'm positive, though I don't know how I'd go about proving it, that maternal
rape of children has to be common and the most hidden crime. I'm sure even
though I don’t know how to prove it that Adam Lanza’s mother screwed his ass
into the painful hell his life became because of her that drove him to take all
those kids there to hell with him as some twisted revenge on his pious fraud
mother. Forget the happy kids’ faces on the cereal commercials on TV. Go take a
look at real kids in real daycare facilities and in real schools in America and
be shocked at the obvious unhappiness and fear that sits on their obedient
faces.
One thing for sure is that Columbine and the Virginia Tech and Newtown mass murders were all perpetrated by unhappy kids. And it’s hard to dismiss the fact that a lot of the unhappiness in unhappy kids has to come from the mothers, whether from their predation or neglect. I am sure fathers too, but whatever the psychobabble nonsense of parental equality drummed up by the propaganda chorus to insure that capitalism has a willing female labor force, bad mothering in an especially big way is the problem because we women are what we are as mothers in a very basic instinctively way whatever the myth. Pity the children.
When my mother saw how forceful Pete was during that brief time and got a quick but telling picture of how much my kids liked and respected him, she and Len and Don changed strategy with respect to custody of the kids. First Len said that, of course, I'd get the kids, the strategy in that being that he'd get to keep his feet in the game with every visitation and that eventually the kids would influence me to go back to being Mrs. Ruth Schoppa. But after my mother's visit, the legal papers changed abruptly to Len asking for custody of our three biological kids, this to take the kids away from me and break my heart, which it did, as a means to get me back with Len so I could be back with them. With both sets of their grandparents on Len’s side, the kids’ tone quickly became, “We're going with daddy; and you should come back with him, too.” Nothing more to be said.
This thing of losing custody of your children is portrayed if at all in the media as something as casual as going for an annual checkup at the doctor, no big deal. But it's damn not like that at all. It killed me. Almost. At that point nearly turning me into the crazy person they said I was because of the kids deciding under the influence of all the “good” adults in the game to leave me. Still I refused to go back to him and reunite with this bunch of bastards. That wasn't going to work, fuck you all and your horrible games, I thought.
In the end in tough times your heart weighs all the options and tells you what to do. As pained as I was about the kids, I never once had the slightest impulse to go back to the Graf clan. Soon after the kids went off with Len and out of the house, Pete and I bought an $800 trailer to live in with threeyearold Bachan whom I still had custody of. They left her behind, not fighting for custody, to keep up Len's connection to me, for the theme was relentlessly, come back, Ruth, come back.
Len still had legal visitation rights with little Ba every other weekend. After the other kids left, his comings and goings to get her were very difficult. Almost too sad to talk about was the third or fourth one of these weekend visitations. When he brought Bachan back this time, she wouldn't speak. She was completely unresponsive. Wouldn't talk, wouldn't smile, wouldn't do anything but crawl around on the floor after a while making sounds like a kitty cat. Whatever had been my baby Ba seemed dead, just not there anymore and replaced with something truly out of a horror story, but one you’re a part of instead of one you’re reading.
After a half an hour of this nightmare scene in the living room of the trailer, I called Len on the phone and screamed out, "What did you do to her!?" Only to hear him immediately reply in a clearly faked, contrived manner, "What did you do to her?" This doubled the scariness of what had happened by making it clear that something had been done by them that they were aware of, for his tone was not at all terrified for what might have happened to her, but accusatory towards me. Whatever they had done to produce this horror, they wanted to use it on me, on us, to destroy me and us by destroying the baby while blaming it on us, which made it clear that they had intentionally done something to destroy this poor little three year old.
What did we do? We ran the next day, terrified. Pete remarked that he was usually prepared for anything, but not this. That while he despised Len, he found it impossible to believe that anybody could do something this horrible. We just picked up stakes and hitched the trailer to the pickup truck and drove away, up the highway not sure where we were going, but to someplace unknown to them, just out of there where Len knew our location. Screw the legality of it, rather be locked up for violating court ordered visitation than ever let him get his hands on her again, we quickly agreed without debate.
Soon we crossed from
California into Oregon. Leaving the state upping the potential charges for
violating visitation to the felony level. We didn't care. Threatening letters
from Len and his lawyer and the authorities came to the Post Office Box we kept
on the California side of the border. We didn't care. We worried constantly
that they'd track us down, every sight of a car in Oregon with California or
Texas plates producing a feeling of sharp fear and violent anger. Pete said if
he ever came across Len after what had happened, he'd literally kill him. And
he would have. I was so sad and crazy after that, I don't know how we made it
through the days. Pete never quit. All the love available between the three of
us went to Bachan after that. We spoiled her with anything and everything she
wanted just to get her to keep her smile. And that worked. We became like her
slaves, tiring and often humiliating for she developed a bit of a mean streak
like you might think a frightened individual might do if it had power over you.
But this kind of treatment kept her looking beautiful, no matter the cost in
time and energy and however much it made her one very selfinterested child.
Pete never quit. I was half crazy over the loss of the three kids and what
they’d done to Bachan and she was a load to handle every minute she was awake.
He was a real fighter, to the death against the viciousness of life under the
control of those who had the power. I should talk about that to make it clear
why he had this extremely dedicated disposition that is so rare in this post
9/11 era. When Pete was in graduate school, his thesis advisor, a fellow high
up in science by the name of Dr. Posner, stole his research, publishing what
Pete had done on his own without Pete's name on it. Pete said at first he
couldn't believe it. Then Posner told Pete that he wouldn't sign his thesis to
get him his PhD degree unless Pete kissed his ass, figuratively, of course, but
in such a blatant way that it was almost a literal demand. In a way this was
just part of who Posner was, for he had a reputation, Pete found out after the
fact, of being the worst kind of bastard, an academic manipulator supreme. But
also his megaextreme treatment of Pete was in no small way because Pete was
and very much looked like a 60s rebel, antiVietnam war radical, long hair,
antiauthoritarian attitude and the rest.
Posner’s game was pure power play, teaching Pete who was the boss, a kind of
rape of a young man that’s not that uncommon in the academic community if you
read the last chapters of the book by Desmond Morris, The Human Zoo. So
what did Pete do in response to all this? He told Posner along with the rest of
his thesis committee, some in on the gang rape, others too cowardly to
challenge big science Posner, to go fuck themselves. All five of them were sent
telegrams in high style telling them this.
And from that experience of resisting abusive authority, he said he experienced a genuine miracle, an unexpected major uptick in his life, reborn with a new level of confidence in his heart. He joked that his sex life, which wasn't the worst even before this, (he lived with a lingerie model his junior and senior year in college) took off to new heights where women started near fighting to see who could sit on his lap in the watering holes on 1^{st} Avenue in Manhattan. And on his way from New York to California shortly before we met, he'd had sex with three different girls on the Greyhound bus ride cross country. He said it was a new life impossible to turn back from even though he gave up his PhD as the price paid to get it. And he got that back, too, ten years later when his biophysical research on bone growth was validated by a research team in Czechoslovakia who gave him credit for the discovery.
Anyway, he was a fighter in all things he believed in and that led to his fighting every day to bring Bachan back to life, always propping me up and telling me to never lose hope. This was a hard task because Bachan hardly ever spoke a word over the next three years. But what she did do was draw all the time. She was a precociously gifted artist almost as a compensation for her not communicating by talking. And when she was about six years old, she started drawing cartoon frames like I was doing at the time, hers about strange looking creatures with large threatening eyes that Pete guessed might have a connection to whoever had hurt her on that visitation. He got this idea because many of these cartoon frames had a background of rain storms in them and of a child sad n being stuck in endless rain.
Right about at this time Pete took a special course in the Montessori Method of teaching reading to deaf children and he used it to teach Bachan how to read and all the talk back and forth from the reading lessons loosened Bachan’s tongue until it gradually got her talking again. Not only did her talking seem a miracle in itself but it also got to make sense out of what had been done to her.
As a critical part of this story I must introduce the fact now that Bachan never used a pillow when she went to bed. She just didn't like a pillow. Unusual we thought, but no big deal. Eventually, though, Bachan told us that they had beaten her up with the excuse that she wouldn't be quiet in church on that weekend when they took her on visitation. They took her home after church and beat her up. And then, horror of horrors revealed, they put a pillow over her face, so she said, and partially suffocated her and then told her if she ever told anybody, they'd smother her. And that put that level of fear in her that made her act that way that day Len brought her back to us. I'm not exaggerating.
She also talked about things done to her that seemed sexual, but Pete never took that part too seriously because once you start thinking and talking in that way about somebody that you hate, especially from the recall memory of a six year old talking about when she was three, nobody would believe you. It was horrible enough that they beat her dumb without accusing them of anything more than that. Though I thought it odd that this young child was putting things in her vagina like pieces of foam rubber from her mattress. Was this possibly evidence that some of the bizarre tales she started telling about what they made her do sexually were actually true?
What was amazing was that after two weeks of intense focus and her talking about what had happened to her, her lightening up was marked and, lo and behold, on one of these remarkable days she started playfully throwing a pillow on our bed up in the air again and again. And however much it may seem too much made up to fit the story as one might like to tell it, she started using a pillow to sleep with ever after that.
The cartoons June drew she got the basics of from a comic book I was doing at that time about my life. I can’t overstate how much the combination of losing three of my kids and Bachan being turned into an incubus by the beating shattered me. Frequent sex, believe it or not, and constant comforting reassurance from Pete helped. But he said again and again, “You’ve got to fight back.” And suggested I write up the story of my life as a way of sorting things out in my head. This was back near 40 years ago and try as I may I couldn’t put sentences together in any readable way. I was no writer.
He asked then, “Can you draw?” Underground comics, as they were called back in the 60s, were big in those days. “Can you draw?” Well I couldn’t. And neither could Pete. But like I said, he was stubborn about everything and said, “It can’t be that hard, you just follow the lines you see and put them down on paper as you see them.” He tried that doing a drawing of Bachan’s pretty face, and it came out startlingly well. And he said: “If I can draw and I always hated drawing, you can draw. Just follow the lines and tell the story of your life in drawings, your childhood and your marriage exactly as they happened.”
And I did. I entitled it Minister’s Daughter, Missionary’s Wife. Parts were very raw and real. I talked in comics frames openly about the abuse I’d gotten from my parents, some of it from my mother interpretable as sexual abuse. He said what mattered was to be completely honest, so I talked in a few frames about an incident I had with one of my own children. I might as well repeat it here. It’s the truth and it does shed some light on the emotional grip I was in all my life. When my first born came along, he’s now the head of a Dept. of Political Science in a university whose name I won’t mention, I was utterly devoted to him, at least as well as someone like me could be. He was really the focus of everything minute I had available in my life beyond the household and minor mission chores I was responsible for.
When the second child came along, a girl, I don’t know, maybe it was harder to give attention to her because I was so bound like a Siamese twin to the first born. Whatever the reason, she had a hard time going to bed at night and she’d cry. And her crying would drive me crazy because some nights I couldn’t soothe it. One night it drove me so crazy, I started hitting her, “Shut up! Shut up!” I can’t remember if that got her to shut up. What I do remember, and this feels twice as difficult to tell now as it was to put it in a cartoon frame, which was still very difficult to do back then, it turned me on sexually, hitting her did.
This was in about the third year of my marriage to Len. It was horrifying. You don’t try to analyze something like that. You just feel revulsion for yourself, full of selfloathing, so much you don’t ever want to think about it. It happened twice and then never again because I never came a mile near to hitting any of my kids for anything after that. But years alter and now that I’m talking about to again here, obviously there was something wrong with me. And since something like that can’t possibly be genetic, the connection had to be with my upbringing, the regular whippings and invasiveness my mother laid on me, which is the really the whole point of my telling this story, how horrible all that stuff done in the name of raising a child to be obedient is. For if something like that was possible for me, forget that I totally resisted it once it came out like that and eventually ran away from this nutty bunch of people, what wasn’t possible with others who were all raised the same way, with beatings and minutely rigid rules about everything, rules that hid the sadism and freakishly dominating nature of the people doing this to children. And, of course, I think of Ed Graf Jr. burning those children to death, not all that strange in the context of the way he was also raised as a Graf. And what about a lot of the violence out there that hits the headlines. You are telling me that all these young people’s unprovoked mass murders don’t have some origin in their own childhoods, that their parents aren’t to blame or that the control placed on the parents in our authoritarian society, even if well disguised as such, isn’t the ultimate cause of crazy violence like this?
The truth is hard to tell, which is why nobody really tells it, or even sees it in their own lives, prefers to accept the fluff show on TV and in the movies as the reality out there, and the reality of their own lives. My book turned out very well in two respects. Years after I sent out copies of it around to 1000 people connected with my family and Len, including neighbors and lots of Lutheran ministers, I sent a copy to a fellow named Robert Crumb. He was the premier commix artist of the 60s, hands down in just about everybody’s opinion back then. He wrote back that he loved it, “a masterpiece of sorts” he said in a postcard he wrote me. But he didn’t like the ending, the very last page of the 20 page comic book that showed me poisoning my mother to death with black widow spiders. He didn’t like that because he was a pacifist, against violence generally. But in reality, that was more or less what I did do sending around the comic book like that, poison her reputation and Len’s too.
Because the story was believable from my telling the truth about my own “sins”, the book caused my jerk of a minister father to be near instantly retired from the ministry, fired pretty much as the pastor of a Lutheran congregation in Waco, TX. He became a real estate salesman after that, interestingly, which should tell you what the profession of minister is really all about, both being most basically inflated sell jobs on people. And the book also caused Len to come down with throat cancer six weeks after I sent the book around to anybody he ever knew. Maybe my cause and effect supposition between emotional travail and cancer is less than provable, but it made me very happy to hear he had cancer even if by odd coincidence after I sent the book out with the intent of hurting him.
The last frame on the very last page of the comic book said it all: “Revenge gives a person a second life.” That’s an Old Italian saying, you know. And it works. At least it did for me. For I felt a thousand times better after writing the book up and sending it out and hearing from this or that channel the harm it did to these people who had done so much over so many years to make my life miserable. Fighting back, getting revenge, does matter. You don’t complain. You don’t take your pain out on other people who did nothing to hurt you. You give it back to the bastards who caused it. That’s what revolution is, fighting back.
Things changed course in our life shortly after this, which will soon take us back to child murderer, Ed Graf. As we entered the year, 1979, almost ten years after Pete had dropped out of graduate school, he found out that certain research work he had done on bone growth but kept out of the plagiarizer’s hands had been validated by the then newly invented SCM or scanning electron microscope and that he had been credit for the initial discovery in the scientific journal, Calcified Tissue Research.
This had Pete head back to Rensselaer Polytechnic in Troy, New York, (RPI), with me and a New Bachan in tow. There the news that Pete’s theoretical work had been validated observationally with the SCM got Posner removed from his PhD committee and Pete, now regarded as sort of a prodigal son genius, not only his PhD but also a position on faculty in the Dept. of Biomedical Engineering at RPI. This sudden leap in status for the family from cliff dwellers up in an abandoned gold mine in Northern California where we had hid from Len after running off with Bachan to Professor Calabria and his beautiful wife and daughter enabled us to travel down to Texas to see my three kids after six long years away from them. Pete with his once long and scraggly 60s hair now cut and trim looked as socially acceptable as Robert McNamara for the occasion.
Neatened up on the
way to the inlaws.
Our first stop was Vernon, TX, where Len and my two oldest were living. Then we were off to Waco where the youngest, Nathan, was at some religious indoctrination get together for young people at Baylor and where my parents were still living. Uncle Ed and Aunt Sue looking a touch younger but no less ugly than in that photo of them were also living in Waco as were their kids, now grown Ed Jr. and Craig. Because I was doing my best to make nice on this Texas trip for the sake of my three kids, we went along with my mother’s suggestion for us, now respectable what with Pete’s doctorate and faculty position in hand, to visit Uncle Ed and Aunt Sue. And we even brought a wedding present to then recently married Craig Graf, my godson, and his wife.
Ed Graf Jr., the future murderer, stood out sharply on this occasion for a couple of reasons. For one thing he was still living with his parents in his thirties. And this was with no recession at hand in the country to rationalize this not usual living situation. Another was that he was, immediately upon introduction to us, afraid and apprehensive about me and Pete, really you’d have to say in a general state of fear and apprehension, because despite Pete’s moderately imposing presence, Pete was charismatic enough that almost everybody liked him on first sight, not feared him. Most odd was that right in the middle of a make nice, hi, how’re you doing, exchange, Ed Jr. suddenly did an about face and ran out the back door into Sue and Ed’s lushly gardened back yard. Also odd is that neither Uncle Ed or Aunt Sue breathed a word, made a sound, stirred the slightest, about this odd action from Ed Jr. that was totally misfit to the occasion of our long belated family visit to the family.
I doubt Ed was seeing a psychiatrist or getting any professional help because LCMS Lutherans just don’t do that. It wasn’t just that they just resolved such things by prayer and similar, but also that our kind of people in the Graf clan, who were so professionally connected with the church, avoided scandal like a model avoids chocolate cake. This attitude no doubt was instrumental in the suicide of Pastor Rick Warren’s son. All the fundamentalist Christians must be ostensibly at all times and in all ways as close to perfect as God wants them and blesses them to be, until they turn out on the front page to be homosexuals like the Rev. Ted Haggard or suicides or child murderers.
Anyway, it was clear that Ed Jr. had problems back then, eight years before the murders, significant enough to call our attention to them. We thought little about it afterward because without my going through the full menagerie of my Graf relatives, most of them ostensibly had observable quirks if not problems like patent ugliness or obesity on a grand scale as showed in Uncle Ed and Aunt Sue possibly as a marker for their more perverse undercoat that produced their first born offspring, Ed, the Child Murderer. I knew the reality of the deviations from emotionally healthy for my own parents, but could only guess at those for the parents that created Ed, the Child Murderer.
The last person on the menu for this trip to Texas trip was my brother, Don Graf. He was over in Lubbock. It was something we weren’t keen on doing but did so on repeated cajoling from my parents, whom, like I said, I was inclined to placate in minor ways because of the influence they had on my kids whom I still had great affection for and wanted to maintain contact with. As things would turn out, though, the trip to Lubbock wasn’t a minor item. The visit with my parents for a few days had an undercurrent of intense if fairly well concealed hate that stemmed at this point in time not just from my leaving Len and the church back then, but also from the devastating effect the comic book had had on them. One might have expected worse to come through their forced politeness and formal hospitality. And it did come, over in Lubbock.
We bought a box of chocolate doughnuts to bring over to Don’s house for breakfast, a little nosh to share with him and his then wife, Ruby. Good thing we brought a full dozen because, lo and behold, also invited to this family reunion sort of breakfast was, surprise, surprise, Ruby’s father, a large sized Texas pig farmer, and Ruby’s sister and her husband, an enormous Texas speedway owner with the classic back of the neck fat roll and the hard beady eyes of a movie cast Southern bully boy.
What a coincidence! Don’s inlaws showed up just at the same time that sister, Ruth, is coming home to see the family for the first time in seven years! The few conversational bites that came from the supersized fatherinlaw and brotherinlaw made it clear that they would intimidate Pete if they could. But it was equally clear that Pete was not pressed in that direction in the slightest for his winning record in street violence, one with a touch of blood spattered on it, made Pete think, correctly or not, sane or crazy, that if he stepped into the ring with Muhammad Ali, he’d beat his ass in. So he gamely engaged in light conversation with the “boys” just like they were all a bunch of good old boys.
Attorney Don Graf’s trophy wife, Ruby, was all smiles and asking friendly flirty Southern gal questions of Pete at the breakfast table as though everything was “jus’ fine.” Her gab was friendly enough to make me wonder how much of it was tinsel and how much personal stimulation by Pete. Brother Don, despite being a senior partner in the oldest and largest law firm in West Texas did not strike Pete or me as impressive in appearance or demeanor as noted to each other after we left Lubbock. Though it’s hard to tell if that was an objectively fair impression by me given how much I disliked this pansy ass creep who wore cowboy boots to Sunday breakfast to keep up his pretense of mother blessed manhood.
The participants on their team seemed eager to hurry through breakfast and I saw why when Pete and I were suddenly invited at the second cup of coffee to check out Don’s newly purchased winery out on the outskirts of Lubbock. Participants on this tour will include Ruth and Peter and Don and his two large sized male inlaws, but not Ruby or her mousy sister. Despite a sharp chill brought back no doubt from earlier times of punches in the shoulder, with Pete leading the way as recklessly brave as a teenage matador and I still as naïve as a newborn rabbit, we all jumped into our respective vehicles and off we went.
That picture worth a thousand words would do better at this point, but we have to settle for the verbal snapshot of my brother, Don, standing on one side of the table at the winery where corks are put in the wine bottles with a cork hammer. He is banging one such hammer on the table surface as his insulting voice starts to throw emotional punches at me, then again and again. This, as planned by him, but of course, is making me progressively more and more uncomfortable and starting to feel shaky as in my victimized days of old. Don knows me well, which buttons to push. And next to me on my side of the table, getting progressively more irritated while naively trying to disguise his bubbling up fury for the sake of maintaining some semblance of family civility, is Pete. To complete the picture worth a thousand words, the two henchmen inlaws are standing about fifteen feet away, waiting for the real action to begin that will call them on stage too.
As the tempo of Don’s bangs with the hammer and bangs with his voice at me increases in tandem with Pete’s less and less well disguised look of violence about to come out of him, I suddenly got a sense of full security. Pete’s supremely excessive physical confidence from ghetto living on the Lower East Side after he dropped out of school blocked out any feelings of fear as his faced welled up in a twist of violent hatred towards Don for what he was trying to do to me. He looked as though he were about to leap on Don and strangle him to death, which kept me sane and intact. And at this point in the upward spiraling drama, Don dropped the hammer, his face fell and he slunk away from the table and from the two of us.
The tour of the winery was then as suddenly declared over as the invitation to it at Don’s house at breakfast was suddenly tendered. Out in our car on a dirt road that circled this winery muddied from rain the night before, I took a good look at Pete’s face and told him to look in the rear view mirror to see what he looked like. ”Christ,” he said, “I look like some kind of killer you might see in the movies.” He said he hoped he hadn’t made a bad impression. I wondered for ten seconds if he really meant that. Another ten seconds after that, though, Pete said, as I realized also before he spoke us, “Punk faggot piece of shit couldn’t pull the trigger,” meaning that Don was supposed to provoke Pete into a fight that the other two would join in on to either beat Pete up, three on one, and/or to call the sheriff in on it to have Pete locked up for assault or such and be destroyed in that way. No wonder my mother pushed so hard and so smoothly to get us to come to Lubbock.
Don and his inlaws at this point are in a car in front of us on this puddle drenched road. And as we slowly meander down its muddy path, their car comes to an abrupt stop. And, of course, as we are right behind them, so does ours. We wait tensed. It is a long minute and a half until Donald Lee Graf jumps out of their car and runs over to Pete’s driver’s side window, sputtering nervously, “We got stuck in the mud, honestly!” He seemed like he was afraid that Pete really was about to kill him, whatever the specific motive for his saying that. I wasn’t thinking that at the time, though, but rather blurted out to Don from my passenger side spontaneously, surely this aggressive only because I sensed such fear in his face, “Were you in California with Len the summer of 1974?” At that the fear on his face turned to a look of terror and half bobbing his head up and down twice in affirmation, he ran back to his car, jumped in and drove away.
At that I knew he was the bastard who did it, the one who killed my baby Bachan’s soul or gave the order or suggestion to do it or was seriously in on it somehow, likely carrying out a plan that had originated in my mother’s dark heart. And beyond that and being a conservative closet gay, a pedophile too?
Less than a year later back up in New York we received a letter out of the blue from Don’s wife, Ruby, telling us that she had just divorced Don. It was filled with bitter spiteful words obviously designed to hurt Don as much as she could by telling us about his humiliation of being left by her. Understand that this was to two prime enemies he had at this point in his life. We guessed that Ruby’s male relatives seeing what a coward punk her meal ticket lawyer husband was must have taken her beyond the critical point of putting up with the bad small of a subpar husband, well off lawyer or no. I recently read a piece from a 40s issue of The New Yorker about the Nuremberg Trial that talked about Goebbels escape from execution by taking cyanide indicating that Goebbels was the exception to the rule that all bullies are cowards. Whether Goebbels was or not, Don wasn’t such an exception.
Pete’s stay at the university in the early 80s didn’t last long. He was a favorite of his students, being the only professor I have ever heard of who received a standing ovation at a final exam, this from three classes he taught engineering thermodynamics to. And he had the highest student evaluations in the School of Engineering at RPI for the ten years they were conducted. But he found his position in the hierarchy and the degree of control over him not that much improved from his days as a graduate student. Ten years of pretty much complete freedom made him a poor candidate for the upper middle class role of a university professor.
So after gleaning considerable pleasure in paying back the four professors who had fucked with him in his graduate school days in various ways, revenge actually improving one’s life and mood considerably as one finds out when one takes it, we went back to a life of anarchy, no rule over you, with all that implies for survival being a true, and somewhat dangerous, adventure.
After two years at the university we devoted all of our attention, outside of survival and the kids who came along, to solving the problem of hierarchical control and the unhappiness it generated, and the problem of violence enhanced by weapons, especially nuclear weapons. From his personal experiences as a street fighter in his younger days, he understood that once a fight starts with punches thrown, the fellow leaning towards the losing side will do ANYTHING to keep from losing, no care as to the consequences since losing is near the equivalent of death.
The translation of this scenario to the world stage is simple and straightforward. If Russia was losing in a war with the United States, would it use nuclear weapons? It has already said it would a dozen times in a dozen ways over the last few years. And if we were on the losing end, truly losing, would we use nuclear weapons to keep that from happening? Whatever a moralist lacking in actual fighting experience might conclude, those who have felt the emotions involved know better. And as to the start of such a fight, where do you think this proxy conflict in the Ukraine between America and Russia is heading? Certainly not to a settlement at the peace table as ongoing events make eminently clear.
The culmination of this conclusion unavoidable for anybody who understands violent aggression from a personal sense of it is that only getting rid of the weapons that cause the horrendous deaths and crippling of war can solve the problem. You can’t get rid of violence without castrating all the male members of the human race. We’re already getting close to doing that in America psychology and with not very palatable results other than for the erectile dysfunction medication manufacturers. You have to get rid of weapons to get rid of the mayhem of major violence.
And in its bringing about a much more equable balance of power between individuals, the total elimination of all weapons in a society most definitely ameliorates the problem of the loss of freedom from excessive social control because, while one man with a gun can control ten others without one, when all are denied the use of weapons, the level of control possible in a society greatly decreases to produce a concomitant increase in personal freedom, which is the most important enabler of success in the pursuit of happiness in life. No freedom, no happiness, as is obvious in this joyous world mankind currently inhabits. To these ends we worked hard to write up and then publish the following newspaper article that directs all men and women to achieving A World with No Weapons.
Knickerbocker News, Albany, NY,
May 1986
What would a world with no weapons be like? The blueprint we have in mind is a rough sketch, for details in building a realistic Utopia have to be open to progressive refinement. But this is our first take on it. A world with No Weapons would have to be divided into two sectors, the biggest sector consisting of a large number of city states of about a quarter to a half million people, none of whom would have any weapons at all. This banning of all weapons is not just for the individuals living in it, but for the city state as a whole, including the police, who must in A World with No Weapons enforce any rules a city state wishes to impose on its citizens without the use of weapons. This proviso gives maximum freedom for the citizens of the city state, for as we see again and again in the world today, the wishes of the people in popular uprisings against tyranny are inevitably brought down and the people defeated by police power that relies first and foremost on the weapons that police have and that the people don’t have. This is not to say that rules decided by each city state can’t exist along with punishment of some sort for breaking the rules. But such enforcement and punishment must occur without weapons. There are no guns and no jails in the city states of A World with No Weapons as makes for the true balance in power needed to keep individual freedom at a maximum.
This is freedom in the real sense even if obtained at a loss of order and efficiency. The next broad question is how the ban on weapons would be enforced. It would be done by the second sector in A World with No Weapons, the Guardians of Freedom. Anyone holding a weapon whose sole use is for resolving conflict is put to death. This rule also extends for anybody who uses a tool like a knife in fighting with another person. The maximum weapons allowed in a conflict that can only be settled by force is one’s fists. Any use of a weapon results in a sentence of death executed by the Guardians of Freedom.
Mercy would be shown. And that would be especially to the young. This mercy would be in the form of a reprieve is possible by the rolling of a lucky number in a dice game to be considered in the mathematics section of this work. In it the lucky numbers assigned and the probability of escaping the death penalty that accrues from rolling one of them would be a function of the circumstances involved in breaking of the no weapons law. Invasion of another city state is also punishable by death. Those are the two principle rules enforced by the Guardians of Freedom. The city states decide on all other rules they wish to impose on their citizens, few, it should be obvious, given that the only way to enforce them would be through the muscle power of police who have no weapons themselves.
There is obviously a lot of uncertainly in an existence without rules enforceable by weapons, lots of excitement in it for each person or family or clan or wider group must protect themselves for the most part. But there is also lots of freedom and from our own experience in living the life of rebels, the intoxicating pleasure of freedom greatly outweighs the lack of protection by armed police, too much of whose actions nowadays are unjust and excessive in force as part of their daily routines.
Another great question is: How do you get to this World with No Weapons? For most who hold the advantage of power will necessarily be reluctant to give it up. It is only the consequence of continuing down the deadly path we are currently on that can convince a critical mass of people currently in power to join in this quest. Mankind is heading inevitably for nuclear war, the math that follows this essay and story section will show in an unarguable way. That is why we will be spelling out that fate for man with mathematical precision. If the inevitability of the nations of the world going to that most undesirable place of megadeath without a banning of weapons is not understood, no effort will be made in that direction. Read the math that follows.
This effort must be led by the United States because only it has the moral authority and the military power to make it happen. We have the carrot to offer sensible nations to get them to lay down their weapons with the reward of getting us all to A World with No Weapons and peace that will ensure that mankind continues to live on. And we have the stick to hit reluctant nations with in terms of our military might. Accomplishing this task of saving the world from nuclear annihilation effectively requires a coalition of the leaders of sensible nations who will be the future Guardian of Freedom to come together to effectively conquer the world against all of those unwilling to join in this effort. Winning such a war for worldwide peace absolutely requires the carrot of peace that our mathematics say will come from nations laying down their weapons. If that diplomatic weapon didn’t exist, pure military might could never work to conquer the world for the sake of peace and freedom.
But, it must also be stressed that military might matters because some nations will not want to give up their weapons and will only do it when there is a gun to their heads or when the trigger is pulled to eliminate them from obstruction of the goal entirely. If this effort must kill a billion to save the other 6 billion, that’s much better than all of us going down in Nuclear Armageddon. My guess is that Russia will join with us once Putin sees that this path is the only alternative to the end of the world; and possibly China, too, though, less certain than Russia. Personally I have absolutely nothing against the Chinese. It’s just that there’s less cultural cohesion between them and us than between us and quasiwestern Russia. And frightening were Chinese plans revealed on May 26 in The Global Times  a newspaper regarded as the mouthpiece of the Chinese government. It said: “If the United States’ bottom line is that China has to halt its activities, then a USChina war is inevitable in the South China Sea.” The article added that Beijing does not want a conflict with the US  “but if it were to come, we have to accept it”. This sounds more like a harbinger for war with this nuclear armed country than peace and if anything a further strong piece of evidence for why A World with No Weapons is necessary.
In that regard the question comes up as to the Guardians of Freedom in the weapons free Utopia having all he weapons and the city states having none. That is unavoidable. History shows a repeated control of territory within grasp by one empire particular empire. There are two dangers that an existing empire must concern itself with. The first is being overthrown by outside nations or empires. And the other problem that concerns the rulers of an empire is revolution from within. In a world that is entirely dominated by one empire or ruling group, the concern about invasion from the outside that is the primary worry of the ruling states of today, like the USA and Russia, does not exist in A World with No Weapons.
This makes a major difference in two ways. It very much lessens the need to enslave the people in the city states under it, very much unlike today where internation stability requires that nations or empires control their people to a significant degree in order to maintain the military and associated economic power needed to protect themselves from conquest by competing nations or empires. The only problem is for the Guardians of Freedom, who are admittedly the rulers of this new social matrix, to retain control over the city states. And that is quite easy given that the Guardians of Freedom have all the weapons and the city states absolutely none. As to those who see this as a scam given that there will still be rulers and the ruled, the circumstances of this social set up make for a singularly novel world situation, whose factors for continued survival are so significantly changed as to make for significant changes in the lives of people.
To those who want Heaven on earth, it no more exists than Heaven after death. A common sense understanding that we will reinforce with precise mathematical analysis makes clear that the above solution to man’s problems of war and tyranny is the best social matrix that can be devised. Once that is realized, if people are not already so stupidly inculcated with ideology that fails to appreciate the realistic fearful expectations we should all have and understand the limits of hopeful expectation in terms of delusions about the future that distort realistic foresight, they will join together to do their best, all of us, to make this one long shot for the survival of the human race become a reality.
In the above regard it must be stressed that a major impediment to the clear thinking needed to pull this off is religious delusions about our future. On the one hand, God isn’t going to save the world from nuclear annihilation because there isn’t any God except in people’s infantile hopes that there’s something “up there” who loves us like some allpowerful parent that loves a desperate child. That thought is a near total impediment to we the people doing something real to stop nuclear annihilation. The thought of just wishing it will happen and praying to something that’s not there is not going to save us.
And the second religious delusion as impediment to saving the world is that even if the world does go to hell, all the “good” people are going to Heaven, so who cares if God destroys the world in a nuclear war for whatever Divine Reason He might have. This is banana brained idiocy that lies beyond further comment. If there is nuclear salvation, we the people are going to have to make it happen. For these reasons we make it a point in the mathematical sections that follow to make it clear that the thought of God and the emotional feelings people have about him arise only as an odd fuck up in human nature taken advantage of by the exploiting class over the centuries to maintain their privilege and abuse of the people under them by promising some impossible recompense for it “after death”. This is so stupid that religion should be ridiculed in every guise it manifests itself in. Besides the horror that hides wearing the halo of religion, saving the world unavoidably requires clear rather than childish superstitious thinking
It is impossible to condemn religion too much. No matter the nonsense by some that bloodthirsty cruel ISIS is not religious extremism, none of those murdering bastards would have done what they did, whether ending 3000 lives and destroying the happiness of 3000 families with the 9/11 attack or beheading young Americans if they were not surged up to do it with the notion that some superior being up there in the sky would make them exquisitely happy after they gave their lives in martyrdom. That this includes the notion of the Allah God giving his butchers each 20 virgins to jump into the hay with does not minimize the monstrous idiocy of Christian belief and the respect it is given despite 10,000 priests and ministers screwing 10,000 nineyearold boys in the ass and getting away with it. If any other group committed crimes that heinous and that broad a level, the group would be rightly decried as a group of disgusting monsters, and not allowed to continue to exist. The reason that they are allowed to get away with it is because these slimy assholes preach obedience to authority as the centerpiece of the Ten Commandments, aka, the ruling class whose lives are filled with sex parties and other privileges that are equally as disgusting when viewed through the prism of the suffering of families and their children whose poverty in the face of the wealth of our ruling class is a true horror. Religion for all its moralizing turns a blind eye to the true miseries of life and offers the beaten in spirit a recompense of an existence after death that only a madman or a three year old could possibly accept as practically tenable. Short of suggesting that all clerics are deserving of corporal punishment and elimination from the human race, whether Muslim or Christian, all religion should be forcibly flushed down the toilet once and for all.
I should end this now with a word or two about how things ended up with our Bachan. The picture of me with her with the youngest of her three kids up the top says it all. Love, perseverance and knowing who the enemy is make all the difference.



Now let’s fast forward to the present down in Las Vegas where much of this last edition of this website was written up. This lunatic city is valuable as a microcosm of America in a number of ways. First of all are the casinos. Nobody wins in them, yet everybody plays thinking they’re going to win. Is the inability of anybody to win my idea? No. One owner of a very flashy and successful casino on The Strip said it all on CBS Sixty Minutes. To paraphrase Steve Wynn, never saw anybody come out a winner. Eventually everybody loses.
The reason for this is, first of all, raw mathematics. The odds in every form of casino gambling are in the house’s favor. And the law of large numbers, not argued about in mathematics, says that over time, the casino has to win and you have to lose. That’s not to say you can’t win in the short run. And some people do. But human nature specified in terms of the mathematics of human emotion on this website tell it clearly. If you win with something, the instructions to that brain of yours, quite inadequate to cope with the statistical nature of gambling, tells you to go back and play again. And the law of large numbers takes over. And you lose. You just do, and even more what you first one because your stupid brain has to be taught the lesson of a significant loss before it gets the picture.
Assisting in this clockwork fleecing is a generalized form of propaganda that we’ll get into later mathematically that is the other leg of brain washing. The first was how insignificant things could be made to be significant by outsizing and repetition, like the possibility of winning in a casino as paraded with the big wins that happens every once and a blue moon. The other has to do with associating positive emotion with casino play in a general way. That emotion is excitement. Normally, if you win at something difficult or uncertain, it is exciting and as made clear in Section to on the function of the transition emotions, excitement leads to confidence in winning in future efforts of the same kind.
But excitement can also come about in an indirect way via communication with others. Nature set you up this way because if someone close to you wins at something and shows excitement, by smiling, by dancing about as TV contestants do instinctively on game shows, by singing, you get excited too. And alcohol gets you artificially excited, which is why they give it away for free in casinos. And music gets you excited. And girls with their skirts hiked up close to their privates get the males who make up the bulk of gamblers excited. All of this artificial excitement tells your stupid brain, which then conveys the message to your stupid mind, that good things are about to happen.
Made insignificant and in sharp contradiction to all the smiles and laughter and such seen in every form of publicity for casinos are the frowns of the losers, and the incessant run of suicides by jumping off the roof of the Golden Nugget Casino’s parking lot, and the like. Information in, behavior out. Bad information in, bullshit propaganda, bad behavior out.
And you have to see the people who play to understand why they play. These are not James Bond and Ms. Pussywhistle playing at the slot machines. These are unattractive people, who play and hope to win as part of their general spectrum of delusional expectations in life. If they don’t have the delusions, they feel as bad as they look. And you don’t have the delusion of winning at casino gambling unless you do it. It’s a con game, pure and simple. And the biggest losers in a con game are those who are desperate for some kind of success in their loser’s life. Religious delusions of happiness after you’re in the casket are very similar in kind to gambler’s delusions. And their promulgated in the same way, by making meaningless things appear to be meaningful with the usual bag of propaganda techniques, the ones we’ve just gone over. The choir in the church balcony is singing to you the message that all here is happy and bright, have confidence in the promise of God. It’s really no different than the function and consequences of the upbeat never ending music in casinos. Hey this is a happy place. Put your money down and win the equivalent of happiness for eternity, enough money by fortuitous gambling to never have to worry about it again.
And this is exactly what life in capitalism is about. Great promise, and no discovery of the promise as a false promise until you’re too damn old to do anything about it. Which is why all the casino players, the youngest crop of adults who play from natural youthful enthusiasm tricked excluded, look so damn ugly. And why adult Americans past the glow of youth look so damn ugly in reality. The entirety of TV programming is a con game. The endless excitement; the endless old “song and dance” to make you think, hey you really are in the Garden of Eden. Just be a good boy or girl and you’ll wind up with a smile as bright as the plaster smiles placed on the professional actors and actresses who make up the news corps and the characters in all those dramas that have little to nothing to do with the dramas that murder people’s spirits clockwork in workaday reality life. And make them look very ugly by the time the beginning of middle age sets in.
Anyway it’s all clear in Las Vegas, not just how you’re robbed of your life and its potential for happiness with tricks and games, but also the end consequences of the false promises and the delusional behavior it drives. That’s easy to see if you ride the city bus in Lubbock, the one that the working people, not the tourists ride on. All you see, accent on the word, “all”, are miserable people. They’re miserable in the way they look. And they’re miserable in the way they feel. Oh, and yes, this shows so much in the way much of this misery is expiated through redirected aggression, meaning that the misery flows rapidly wherever and whenever it can from one miserable person to whomever is vulnerable to its reception.
Black on white is clear as a bell down in the lower echelons. Black people, real black people, basically hate white people because it’s white people who basically are the ones that fuck them over in the broader institutional power structures in America. The association of “my source of pain” for a black person with a white face is simple Pavlov conditioning. Now you think that I’m a bleeding heart in all I’ve said so far against the conservative assholes. But reality is what’s important, the pain and the hate out there. And I’ll make that clear in two very real, very personal stories that happened to us when we were in Las Vegas. The first was an episode of what happened on the bus, the Las Vegas RTC, to Pete. I’ll let the note he emailed to the RTC, which was never answered, speak for itself. It’s a bit tongue in cheek here and there as any letter to an uncaring institution has to be, but the crux of it is 100% true.
Dear RTC: I flew down to Las Vegas from New York on business and have reason to frequent UNLV up on Maryland Parkway. After minor shock at the daily taxi fare to UNLV from and back to Fremont St. where I’m staying, I had the pleasure of making acquaintance with your transit system, as things turned out not very pleasant at all. The inconvenience of the crowds is one thing, something a New Yorker is used to, but to have the potentially dangerous experience I had this morning on one of your busses, another thing entirely. I’m going to spell it out in the detail it deserves. Please bear with any seeming intermediate trivialities.
I found out I qualified for reduced fare as a senior citizen and always show my ID by holding it very visibly with my thumb above the RTC card when I swipe it. Drivers can’t and haven’t ever missed it, until this morning. When I got on the BHX bus (# 845) today at 6:55AM at Fremont a couple of miles from the Casino section, the driver, a black fellow, that fact not incidental to the what happened, was in the middle of a chat with a passenger, another black fellow, and took no notice of my reduced fare ID, which as I said was unmistakably obvious had he been looking at me swipe my card instead of talking to the passenger. So he stopped me as I walked past him by shouting out for me to show him my reduced fare card. I turned back and said as I held up the RTC card and the ID together, “It was on my thumb.” Couldn’t be missed. “I didn’t see it,” he replied. No problem here. People make mistakes, this one totally minor.
But the black fellow he was talking to me touched my shoulder as I walked back to my seat on the bus and said something to the effect that I better be cool. My reply as I went back to get a seat was, “Don’t touch me.” I’m old enough to know that sticks and stones can break my bones but words alone can never hurt me. But touching is in the category of sticks and stones, and potentially dangerous, a forewarning of worse possibly coming, which is why battery or touching is a crime. This fellows’ response to my resistance to his touching was to race back towards the rear of the bus where I was seated and standing over me six inches away shouting, “My daddy just died two days ago, and I’ll kill you, motherfucker, if you give me any trouble.”
Now it is important to make clear that I am generally cognizant of and sympathetic with blacks in their underdog position in society. Had your RTC contact format allowed for it, I would have included newspaper articles that make it clear that I have been a civil rights and peace activist all of my life. Indeed I was a primary speaker at a rally for Trayvon Martin in Las Vegas a few years back, videoed on YouTube. And one of the OP pieces that shows my liberal bent is on our mathematical sociopolitical website.
So I was able to reckon that this fellow, whatever his level of violence, considerable, was quite nuts at the moment, and maybe with understandable reason. And I gave out a sentence or two of sympathy to cool things down, though adding as I took out my cell phone, “If you touch me again, I’ll call 911 and have you locked up.” That was enough to get him to back off and return to the front of the bus next to the driver. But amazing is what he did next, turning his fury deflected from me to this old man white passenger sitting in the seat closest to the front of the bus and the bus driver, all of which was impossible for the driver to miss. The black fellow’s words to the old man were unmistakably racist, hateful and violent. But, as I said, who cares about words, especially in nut town Las Vegas (at least my estimate of your fair city that circumstances have forced me to be in again.) What was horrible to watch, though, was that this black guy started grabbing the old white man by his nose and his ear as he cursed him repeatedly.
Now my complaint to you isn’t about this unfortunate black fellow, whatever misery in life, present and past, drove him to his dangerous behavior – also dangerous for him given his shouting out in the middle of his ranting that he was on probation and didn’t “give a fuck” about what anybody might do to him in that regard. My complaint is rather about the driver, a coward it certainly seemed, or even something worse for not respecting the plight of the poor white bastard or the four or five onlooker passengers who were shouting to him at this point to get the guy off the bus. No effort was made to that end. All the driver had to do was stop the bus and tell the guy, “I’m not going anywhere until you get off the bus and if not, I’ll call in security. Nothing was done anywhere close to that. Let me emphasize that that the level of curses, threats and mayhem was such that the situation would have been apprised by any objective observe of this real life movie scene as potentially very dangerous.
Recognizing this, I jumped off at the next bus stop in the Casino area instead of proceeding directly to the UNLV Law Library via the Bonneville Transit Center and the #109 bus. By chance walking through the intersection of Fremont and Las Vegas Blvd. I encountered an RTC cop I quickly told the story to. He pulled out his phone and said he’d call the Transit Center to notify them of what happened and possibly do something about it if he made contact on time. I then cooled my heels with a cup of coffee in one of the casinos for an hour or so and got back on the bus to get to my originally intended destination. While back on the bus, I ran into another RTC cop who was also sympathetic and who directed me to a supervisor at the Transit Center to file a complaint.
I was hoping to hear and thought reasonable that the driver would have immediately told one of the handful of RTC cops you usually see at the Transit Center about the incident, which was clearly criminal, and minimally had the perpetrator, who was quite off his head and possibly on drugs, to cool it down. That was not the case. And the supervisor I spoke to, also black if that matters, bordered on curt in his reaction in telling me that he had heard about the incident and already reprimanded the driver, not interested in what happened to me including the death threat, as though there was really nothing to it and what was I making such a fuss about.
The rest of the note and the lack of any reply by the RTC transit system is irrelevant. What is relevant is the degree of hate between people that sits on the end of a hair trigger. Well, you say, big deal, who cares what could have happened. All that id happen was some nonfatal slapping of one guy in the face by another on the bus and a black driver doing nothing to prevent it or punish it. And maybe that’s cool, the real point being the enormous amount of random violence going about that is impossible to even guess at it from the endlessly smiling faces on TV who endlessly make out that life is nothing but a bowl of cherries, past, present and future. Ok, let’s try the next story, which was not incidental and at a distance from us. Well, again, it wound up in a letter written by Pete about it, this time sent to the Las Vegas PD, that I’ll let speak for itself.
Dear Las Vegas Metro Police,
My wife and I are on our way out of Las Vegas as I drop this note in a mail box, happy to be leaving. If my interpretation of the events I’ll relate is emotionally excessive, please excuse. But it is better to err on the side of caution. These are strange and dangerous times.
We have been down here for the last five weeks, not for gambling but interacting with academic types including Dr. Kathy Robins up at UNLV. We wound up staying at the Siegel’s Suites on Fremont and 15^{th}, not because I’m poor or like “slumming it” but because I’m severely asthmatic, doubly dangerous at age 71, and this Siegel’s place has tile floors rather than the rugs that every other hotel in Las Vegas has that I can be super sensitive to asthmatically.
The very nice woman who manages the place, Sharon, will corroborate any of the odd parts of what I’m saying concerning my asthma if you ask her. She went out of her way to set us up when we first got here with a room easy to breathe in. We ran into her and this place by chance a year or so back during an asthmatic episode on me that came out of the blue when I was staying at one of the casino hotels.
Off to the side of my having a PhD in Biophysics, I am also a lifelong political activist. If you check out these two OpEd pieces I wrote in years past, it will be clear that I am antiviolence and also pro civil rights and against police brutality against minorities. As to why I am giving you this background, the studio apt. at Siegel’s next to ours, Room 216, had a class of people in it I was not familiar with and that nobody would want to be. Lots of noise, swearing, loud music late at night and so on. If they weren’t using drugs regularly (though to be honest I never caught any smell of marijuana) they must have had a special instinct for whoops and hollers come the late hours.
I tolerated it because asthma at its worst feels little different than suffocating from waterboarding and this room was healthwise pain and stress free. Staying there I did not use my asthma medicine at all the entire five weeks we were in Las Vegas. As Sharon will tell you if you ask, the window in Room 217, our place, was missing, not the screen, just the glass window. The only room available in the place the day we got into town was this one, no window in it. But we took it because the fresh air flowing in constantly is positive for my condition. The point of my bringing it up is that the missing window had me hearing just about everything from next door when their door was open, which was often, and when they were outside, which was very often.
I should mention that the principal person in this room, possibly the leader of a gang (?), is a very large black guy always dressed almost in a uniform consisting of a totally white pullover and a distinctive kind of cap he wore even when the weather got warmish.
Anyway it was the night after the news broke out about the two police officers shot in Ferguson. These guys (some of them we heard often might just have been frequent visitors to the room rather than residents) went nuts over the shootings. There was no doubt about this from what they were shouting out to each other about feeling great over what happened. But this was also likely with a million other black guys of this type around the country, so nothing special about it. What got to me sharply, though, was a phrase that popped out unmistakably no less than three times during the evening  “gonna get one of these motherfuckers myself.”
Now I want to make it clear at this point that I heard nothing of any plans to do anything tangible. So there was a good chance that those words came out only to impress each other. I should make clear that I have as little prejudice towards blacks as any white in the country. I just don’t. I spoke at a Trayvon Martin rally right here in Las Vegas a few years back. In fact it was hosted on the business property of a black woman Metro Police detective, also a hairdresser, who said she was the daughterinlaw of the first big city black mayor in America, Carl Stokes of Cleveland. I think her name was Dorothy, Dorothy Stokes, but it was a while back and I’m not entirely sure of the first name. I’m sure she must remember me and how much I was on the side of oppressed blacks. I talked with her head to head for more than a few minutes and then spoke publically to all the blacks there about the need for a political process to get justice for Trayvon Martin.
That is to say that there is no way I’d exaggerate what I’m saying, and perhaps when you check things out with the black guy in Room 216, you might find out that he was, in fact, just a loud mouth punk with no real intentions. But to hear people talking about murder, whatever the level of real intention, sent real chills up my spine. Actually did. This is just a few days back. Talking it over with my wife I didn’t think I could live with myself if I saw on the evening news in a week or two that cops were murdered in Las Vegas in an ambush or something, and possibly because I said nothing. Whatever happens next, at least, with this note, my conscience is clear.
Sincerely,
What precipitated this letter in all honestly just wasn’t the hard facts of what we heard. Pete actually did think that it was all bluff and bravado mainly because he sensed the main guy in the story as a genuine punk, a faker, a faggot of the predatory kind, a bully and too much of a loser in life to ever try anything like killing a cop other than shout out words about it to his buddies. When we first moved into the place, the thug was right on the scene parading in front of our window and shouting out motherfucker this and motherfucker that to this friend up on our second floor tier or down to the street below. Was he doing it on purpose to get to us well groomed white people whom he thought he could screw over? Or was this just life in the ghetto that everyplace in Las Vegas not part of the tourist casino scene more or less is? Well, having more important things to do like try to save the world from nuclear annihilation and with hairy mathematics no less and also trying to convince small minded scientists up at UNLV of the correctness of our science, we opted for an intermediate disposition that while the jerk could have been trying to intentionally get on our nerves, it was better to pay him no attention and just stay at a nonresponding distance from him.
Then as fate would have it, avoiding came to an end by chance when Pete came back from UNLV walking through a narrow corridor at the same time this Porky Pig fellow was coming in the opposite direction. Pete gave a polite “pardon me” and moved to the side as they closed in while Porky addressing Pete as “sir” made little effort to do the same. Cute. This was a cute bastard. And that was followed up by Porky walking past our window not two minutes later, with a string of loud screeching motherfucker this and that. And at that point he began to get on Pete’s nerves, be worrisome, in his life, in our lives. The evening hours certified the problem as real as the music post 11PM was too loud to get to sleep by and Porky’s walking back and forth in front of our window repeatedly with the music blaring was as unsubtle a subtle threat as could be constructed by a cute bastard.
Now despite Pete being 71 and Porky somewhere around 31 and at least 100 pounds bigger and five or six inches taller, Pete put on his pants and opened the door intercepting Porky in his walk back from our place to his. While he didn’t say it with excessive politeness, for the situation didn’t call for a Miss Manners approach, Pete’s request/demand that Porky turn the music down wasn’t all that impolite. Porky thought otherwise.
Porky: “You disrespecting me, talking to me like that!”
Pete: “You’re disrespecting me and my wife playing the music like that.”
Porky: “I’ll fix your ass soon enough.”
Pete: “You make the next two plays and I’ll make the final play.”
And with that Pete shut the door. The next two hours were rough, at least from a noise and threat perspective. Whether they came from his room or from the neighborhood, every quickly there were four or five thuggish voices and the insults and threats were anything but subtle. I wasn’t sure what Pete’s “final play” would be and neither was Pete. The words just came out of his mouth that way, in a spontaneous way, for he was a spontaneous person, with a kind of like a talking animal personality. But you could never tell with Pete. Many years before that, we had a problem with a landlord who eventually brought a new tenant into the building who was extremely aggressive. Dickie Yadoo started parking his porch chair right out in front of our bathroom window, getting right into our life not unlike what Porky was doing. Dickie was muscular and looked very thuggish, so Pete just twisted in the wind for a couple of days all tightened up like a ball of string with a tangle of knots in it. Then Dickie brought in some relative and his 11 year old kid who went into the backyard and made our two year old still in diapers start crying. Pete went bananas and picked up a red magic marker and went up to Dickie’s 2^{nd} floor porch and wrote FAGGOT on the vinyl covering on the chair in big letters.
Sure enough Dickie Yadoo came down and they met on the porch, Pete rushing him and almost throwing him over the railing. By the time the fight ended, Dickie conceding, Pete had pretty much ripped his eyes out, for Dickie had two streams of blood rolling out of his eyes, something I never saw or heard of before. When the cops came, they reassured us that we didn’t have a problem with them. They told us that they just wanted to know who had whipped Dickie Yadoo, a known thug for hire in town, so bad that he’d even think of calling them.
So you never know what Pete might do. And neither did he. The next day was bad for him, he told me when he got home, because Porky was on his mind all day. Then just before he got on the bus to return home, he said he started worrying about me. And that got him to go a bit mad with anger. He said he started clenching his fists and biting down hard on his teeth and shaking uncontrollably on the bus like when he was a kid and angry. And the thought came through his mind that he could take Porky despite their age, weight and health differences, that he got determined to kill him if it came to it. By the time he came inside he looked not unlike that time with my brother, Don, out at the winery, like a murderer set on murdering somebody. But instead of doing the next step physically, he went for Porky’s throat by writing out that letter to the Las Vegas police. And that calmed him way down.
Now the point of this story, at least one that’s meaningful in the context of the larger problem the world has in terms of its near universal unhappiness and violence, is that when men are pushed far enough in the wrong direction, they don’t care about consequences. Pete would have thrown the punch, whatever the consequences, if that’s all that remained that could be done. He didn’t care about consequences. And you see that a lot in the world today if you care to look closely enough not to dress it away with psychobabble. Past some point angry people just don’t care about consequences, including those with nuclear weapons in their hands. Man has to rid the world of weapons before the weapons rid the world of man. Lousy fag bastard, hope the cops break every bone in your body.
16. Waiting for the Bomb
It’s near impossible to interest people in the coming of the end of the world, let alone trying to do something about it. For us the frustrations are also personal. In our seventies now, this has been the focus of our life’s efforts. The hypothesis is simple and quite precise even when expressed in nonmathematical terms. Human aggression, particularly in males, is an ineradicable instinct dictated by the evolutionary demand to optimize survival from generation to generation. This propensity to aggression is obvious in history’s never ending warring, in the daily domestic violence and murders seen in the news and even in the endless attention given to sports aggression. And whatever aggression comes about naturally from evolutionary factors, it’s made all the worse from the unhappiness of man that arises from social control expiated by violence on innocent vulnerable others as redirected aggression. And that is made worse yet by mankind’s development of superlethal weapons up to an including nuclear weapons.
But our shout for the last thirty years as peace activists that our worst fearful expectation of nuclear war is eventually going to be realized unless weapons are expunged from the planet has been ignored. This is also part of human nature for people pretty much instinctively ignore impending disasters they don’t think they can do anything at all about. And this blind man’s attitude toward coming nuclear catastrophe is made all the worse by its being made to seem insignificant from its near absence from main stream media considerations.
We recognized this back 30 years ago when we stated in our Weapons Ban newspaper article that nothing would be done until the first world leader with access to a nuke went emotionally over the brink to use it. Of course we hoped for better, hoped that somehow the message of the need for a weapons ban might be received so well wrapped in a firm mathematical analysis that some initial nuclear detonation would not be needed to wake people up to the need to rid the world of weapons before the weapons come to rid the world of all its people. So while our work developing the mathematics that explains man’s emotional nature at the heart of the problem has been very satisfying as pure science, reaching people with it to make clear the more meaningful problem of potential nuclear annihilation has been nothing but decades’ long frustration as we enter our seventies now. Quite exhausted from the lack of response to our efforts, hence, we are just sitting back and waiting for the bomb. We’ll spend the rest of our writing time dotting a few i’s and crossing a few t’s we might have missed.
The media does well hiding the visceral horror of our endless domestic mass murders and of the world’s endless wars by hiding images of the blood and body parts of victims including our own soldiers, their torn apart bodies never being shown to the public. But a nuke dropped and a million killed in a flash will not be able to be hidden by the media. And then people will understand that if A World with No Weapons is no achieved there will be no world left for any people to live in.
This thought was paramount as we fled Las Vegas and landed in a relative paradise far from Hate City where we are just nursing the normal wounds of aging and passing time waiting for the bomb. It is an odd strategy, effectively betting what’s left of our lives on our hope of a nuclear detonation that will happen before Election Day, 2016. The lead players in this statistical prediction are Israel dropping a nuke on Iran or Putin one in an open field in the Ukraine to let the West know that Russia will not put up with encroachment this close to its borders. And let’s not forget bit player North Korea as the pit bull on a leash of ever increasingly militaristic China. And one never knows what nuclear armed Pakistan and India will do in their endless strife that without fail comes to murder a few dozen citizens on each side every year.
Something should also be said about our newfound fear and dislike for black people. Our bad experiences in Las Vegas just grabbed hold of us emotionally. It is a distinctly uncomfortable state for people who have been mega pro civilrights all our lives, impossible for us to not empathize with the ugly oppression and travail of blacks in America. Indeed, we actually were primary speakers at a Las Vegas Trayvon Martin rally, the only whites that day. But effectively threatened with destruction in an obviously hateful way intuitively makes you very wary of blacks who harbor a generalized hatred of whites from the generations of oppression put on them up to and including the current cluster of unwarranted police killings of them.
People have to come together to understand what their common oppressor is, the current power structure up at the top. And they have to understand the ultimate common problem we all have, the possibility of nuclear annihilation if we don’t get together and act together. It’s so important that we all tamp down our instinctively driven petty hatreds of each other. Whites, other than the wealthy powerful ones who gain from everybody else’s pain, are not the enemies of blacks, nor are blacks the enemies of white working people, though both realizations can be emotionally difficult especially for people on either side of the game who have felt the sharp bite of the other. We hope this impediment to collective action is overcome once both races realize the common problems and enemies they have. Our Las Vegas story and the feelings we experienced in it are laid out exactly as we experienced them to make clear just how powerful these racial antagonisms can be from bad personal experiences. We hope that as time passes, a few months, the worst of our bad feelings will pass and that we’ll be able to take our own advice, for any possibility for common salvation lies in the many victims of mass aggression shaking the antagonisms the ruling class sets up between us and loves to see keeping us separate and at odds with each other.
I’d also like to make clear my attitude towards homosexuals. Certainly there is no way that depriving them of their basic civil rights should be excused or tolerated. But it is equally absurd to fail to see homosexuality as what it is most basically, a consequence of reproductive failure that comes about primarily not by genetic aberration but developmentally from the excess social control I’ve been talking about from the start. This, of course, will be argued against by critics of A Theory of Epsilon as being unscientific, but the socalled data used to argue homosexuality as inescapably genetic is as mythical and misleading as the data that shows lower black IQ to irremediably arise as a cause of inherent black stupidity from the genetic makeup of blacks.
To argue this I’ll report and explain some very firm mathematical data about homosexuality whose conclusions are impossible to avoid. Younger brothers in a family have on average, as measured from a statistically significant sample population, a one third greater frequency of homosexuality. This is an unarguable fact. A second born brother has a onethird greater chance of becoming homosexual than the eldest brother; a third born brother has a onethird greater chance than a second born brother; and so on down the line. These numbers cannot be spun or dismissed as irrelevant.
Any male who has brothers, be he an older or a younger brother, understands the obvious that older brother/s are generally dominant to the younger one/s. And conversely younger males in a family strongly tend to be subordinate to the older ones. The Boston Bombing case, which has nothing to do with gay men, illustrates this characteristic of older brother dominance in a clear way. Nobody who thinks objectively can fail to see that of Tamar and Dzhokhar Tsarnaev, the older brother was dominant to the younger. And that is utterly obvious even if one chooses to excuse in any way the behavior of the younger brother. That is but one of a million examples of older brothers being dominant to younger ones quite independent of the issue of sexual orientation.
Dominance and sexual behavior, however, are, generally speaking, not independent of each other. This is clear between men and women. In the arena of heterosexual sex, personal experience overrides silly exhortations of the ideological notion of perfect equality between the sexes as it relates to women in the labor force. A woman not at least somewhat impressed or dominated by the élan and vigor of a guy suitor does not turn on to him sexually. The evolutionary argument for this is obvious and observed in all mammals where the males are larger and stronger. There is always some form of at least ritual struggle between the female and the male; and the male who loses in it is shooed away by the female. And this fact of male dominance as a propitiator of sexual arousal should also be obvious in the absolutely bestselling erotic book of all time, “Fifty Shades of Grey” making it clear that women being dominated to a significant degree is an instinctive prompt for sexual acquiescence.
Taking this clutch of ideas together, the dominance of older brothers, the undeniably higher incidence of homosexually in the dominated younger ones and the notion of sexual arousal from social dominance as a significant factor leads to the conclusion not, it must be stressed, that older males make homosexuals out of their younger brothers, but that male dominance generally is a significant factor in the making of a male homosexual. That is, that sexual seduction of a male by another male goes hand in hand with dominating behavior by the former, this as opposed to same sex relationships somehow coming about strictly from some mutant thread of DNA.
And add to that another undeniable fact of the generally excessive subordination of males in our Goebbels society that develops American men now more and more with subordinate female personalities and you are quick to catch the primary cause of male homosexuality in such femaletype men both being unable to woo females successfully and in their being susceptible to sexual dominance by other men.
In agreement with this perspective is the firm fact that every professional biologist knows about, namely that expression of a gene is generally very much dependent on the environment of the developing organism. A most telling illustration of this lies in the formation of feathers on the legs of baby chicks as grow in a chicken egg. People with enough brains to accept evolution as scientific fact understand that all birds including chickens descended from dinosaurs, their lizardlike evolutionary ancestors.
The egg the chick develops in has a certain concentration of calcium ions. With the normal concentration of calcium, the growing chick develops feathers on its legs normally. But if you increase the egg’s concentration of calcium ions with an injection of calcium chloride, the chick develops lizardlike scales on its legs from its dinosaur ancestry instead of chicken feathers. This is only one of a million illustrations of genetic expression being dependent on the environment of the gene that can be cited. And, generally speaking, the more complex the anatomical, biochemical, physiological and/or neurobiological characteristics of the organism that come about from a gene, the greater the weight of the environmental effect on the expression of the gene.
The conclusion of a purely genetic causation for a trait as socially complex as homosexuality is poppycock, such a perspective being useful only for hiding the true origin of homosexuality as a substitute for reproductive sex by those males in a population inclined to fail at such because of the position of males as wage slaves and/or by their parents, obedient wage slaves themselves, raising the boys in an overobedient emotionally unhealthy way.
This is not to say that homosexuality is a “choice” that a gay man can make either way as the religious goofballs insist on. But rather that it is, once firmly developed in a male, an emotionally unavoidable behavioral propensity that is as difficult to choose not to do as the pleasurable gross overeating of the millions of obese people who die fat whatever might be their inclination or “choice” to do otherwise.
The worst in all of this are homosexuals who have power over weaker males and can effectively seduce or emotionally rape them. There’s neither sense nor fairness in denying homosexuals basic civil rights. But incaution on the part of young men from this current American culture denying the cause of the lesser sociosexual achievement of homosexual union as the result of exploitive subordination is equally without sense and fairness to young men who, from an evolutionary perspective should be willing to fight, indeed to the death if necessary, to preserve their honor and reproductive competency. Be wary, my boys, whom you submit to and for what reasons as you approach adult life. The oft used phrase, “protect your ass,” should be taken literally.
Now let’s start to work our way through a number of mathematical explanations of various aspect of human nature to fill in the big picture as completely as possible. To show that our emotions are information for us in the sense of their being described mathematically by diversity functions we made clear earlier were measures of information, we next want to develop the probability component of the emotions as with the Z of E=ZV of Eq106 and the U of E= –Uv of Eq90 as a function of diversity indices. We do that by developing a matrix basis for the D diversity index. This exercise also provides a superclear explanation of the most basic foundation of how the mind works by making distinctions between some things and sensing others as being the same.
The D Simpson’s diversity index of Eqs3&16 is an excellent measure of the diversity in a set in terms of the N distinguishable subsets counted in the set as the prime variables for diversity, the N more of subsets there are in the set, the greater the diversity of the set. It is seen, though, that the D diversity index has one shortcoming in this regard and that is in its specifying the diversity of a uniform set, like the all red, N=1 subset, uniform set, (■■■■■■■■■■■■), as having from Eqs3,13&5 a Simpson’s diversity of D=N=1, which does not fit our intuitive sense of there being no diversity or zero diversity in this (■■■■■■■■■■■■) uniform set or in any other uniform set. This problem is readily resolved, though, with a simple variation of D that we will call the Exact Diversity Index, L,
277.) L = D – 1
The L Exact Diversity Index, also called Number Information, has an immediate advantage over D in its specification of the diversity of uniform sets like (■■■■■■■■■■■■) as L=D–1=0 as fits the zero diversity of a uniform set. And L has a couple of other very fundamental properties that make it special as we’ll see. Consider L for balanced sets like the N=3, (■■■■, ■■■■, ■■■■), set whose L value is from Eqs277&5, L=D–1=N–1=2; and the (■■, ■■, ■■, ■■), N=4 balanced set with L=D–1=N–1=3; and the N=8, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), balanced set with L=D–1=N–1=7. In general, for any balanced set, from Eqs277&5,
278.) L = N – 1
Now we will see that L for balanced sets is not only a measure of their diversity but also of distinction. In the N=4, L=3 set, (■■, ■■, ■■, ■■), we intuitively distinguish any one of its N=4 subsets from the L=N–1=3 other subsets in the set. Hence L=3 for the (■■, ■■, ■■, ■■) set is the number of distinctions that any one subset has in the set from all the other subsets. And we see the same for the other balanced sets, (■■■■, ■■■■, ■■■■) and (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), in their L diversity index being a measure of the number of subsets that any one subset in the set is distinguishable from.
Next we’ll make the point that L diversity, aka L number information, is truly a measure of information from the perspective that it is a measure of the distinctions between subsets in a set, which are commonly understood as information for us. Consider 4 apples on a table, which when seen at a distance are sensed to be all the same variety of apple, but as they are approached more closely they come to be seen and distinguished as 2 Macintosh apples and 2 Delicious apples. This distinction in kind or variety of apple that comes from closer inspection of the apples is readily understood intuitively as information for the observer about the apples. In that way we understand L diversity to be as a measure of distinction a measure of information. This perspective also bolsters the synonymy between diversity and information we developed in a number of sections in the foregoing.
The sense of L as distinction and, hence, as information is further bolstered by showing L to be a measure not only of the distinctions between the N subsets of a set but also of the distinction between objects in a set such as between the different colored objects in the K=6 object, N=3 color set, (■■, ■■, ■■), (2, 2, 2). As this set, (■■, ■■, ■■), is a balanced set, L=N–1=2. We can show its L=2 to be a measure of distinctions between the different colored objects in the set by comparing all K=6 objects in the set to each other in a systematic way with a comparison matrix as shown below.

■ 
■ 
■ 
■ 
■ 
■ 
■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■■ 
■ 
■■ 
■■ 
■■< 