Meaningful Information Theory (MIT):
A mathematically unified
understanding of things meaningful like money, food, health,
love, family, freedom, workplace slavery, outrageous income inequality,
capitalists as thieving cocksuckers, police state torture and murder,
God and His Holy Legion of faggot child rapists,
and the potential for this cruel, insane world
to take us to nuclear extirpation.
By Ruth Marion Graf
and Dr. Peter V. Calabria, PhD, Biophysics
© Ruth Marion Graf, 1/8/14
contact: ruthmariongraf@gmail.com
MIT (Meaningful Information Theory) is an extension and refinement of classical information theory that solves the problem of meaning in information 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.
MIT solves the problem of meaningful information to achieve two major breakthroughs in science: the development of mathematical functions for the human emotions; and a clarification of the centuries old mystery of entropy. The reasonableness of our claim to overthrowing 100 years of accepted physics by reformulating entropy in terms of meaningful information is suggested by a peer review from Bill Poirier, Distinguished Research Professor of Chemistry and Physics at Texas Tech University and author of the recently published Conceptual Guide to Thermodynamics, (Wiley, 2014):
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 telling us that the standard BoltzmannShannon take on entropy and our meaningful
information sense of it are both “mathematically correct.” But despite the
“limitations/issues” with the standard formulation Poirier cites that have
interminably confused students and professionals alike for the last 100 years, he
still favors the perplexing take on entropy come up with a century ago with limited
mathematical foundations because of a tunnel vision attitude that misses the firm
fact we will prove that physical systems cannot be correctly explained with
logarithmic information functions of the BoltzmannShannon type. His attitude
also derives from Poirier’s insistence in his book that entropy can be
explained from an information theory perspective despite the above article and
a number of others making it clear for a few decades now that classical information
theory cannot be applied fruitfully to physical systems.
The solution by MIT to the great question mark stuck in the middle of physics  “Just what is entropy?”  also points up the ability of MIT’s clarification of information to make precise mathematical sciences out of cognitive science and political science as are necessary to clarify and resolve the contentious sociopolitical issues of the day, the most meaningful of which is freedom.
1. Freedom
The right wing Christian stalwart, Rick Santorum, proclaimed during the 2008 Republican presidential primaries that “freedom is not doing what you want to do but what you ought to do”, this prime example of Orwellian doubletalk a rephrasing of federal prosecutor, Rudolph Giuliani’s, 1994 slogan, “Freedom is about authority.”
But is obedience freedom? Are we really free? It is the question of the ages.
No question about the slave empires of the early civilizations of Egypt, Assyria and Babylon. They made no effort to say that slavery was freedom. And ancient Rome also thrived on massive slave labor and was very proud of it. As did ancient Greece, the cradle of democracy, where slaves worked the fields and mines for the ruling class politicians and philosophers. Plato got his wealth from silver mines worked by slaves in chains. And the Christian serfs who did all the work in Europe during of the Dark Ages were nothing but slaves to their landlord masters who ruled them with medieval Christian trickery and the iron fist of police and the military.
Russia got rid of serfdom with the Communist Revolution of 1917, but the Russian people certainly had no freedom under Stalin or after that. And what of the Chinese? They certainly have little control over their own lives as the recent prodemocracy demonstrations in Hong Kong shut down by their police make clear. The workers there are all obvious slaves of their communist overlords though our government and media downplay that fact now because China supplies a quarter of our household goods.
We know that the field Negroes in preCivil War America were slaves in the most obvious sense of the word. No argument there. But what about us who live now in “free and fair” America? We’re not slaves, are we? Unless, maybe” you consider your boss to be a slavedriver. Well, no country on earth does democracy better than America, so let’s not go too far on the anticapitalist stuff, right? You don’t find any movies or TV shows about mean abusive bosses or about abusive landlords or abusive police or judges or teachers there. So we can pretty much assume from the TV story on it that there’s no wage slavery in America, right?
That conclusion is kind of tricky, though, for if a society did enslave its people, it would certainly downplay the fact of it in order to keep potential rebellion at a minimum. It’s a lot harder for people to revolt against a slave system that doesn’t seem to even exist. And for the same reason an economic slave system that also had control of the media would also make an effort to hide the source of the significant unhappiness that comes from obeying the boss, at times quite on your knees, humiliatingly, to keep the job or get a promotion or make sure you retain good references, so you don’t wind up out in the street homeless, as good as dead.
The Negro plantation slaves of old were told again and again, especially from the pulpit, that their enslavement was the best possible life for them. If television was around back then you can be sure that message would have been broadcast 24/7 to them, and likely in the most entertaining ways possible. People drugged with misinformation tend to stay in line, then and now.
But if you’re able to flush such propaganda out of your mind after a week or so free from watching television, (check out our 80s hit, Curse That TV Set),
it is clear that mankind is pretty much stuck with enslavement in one form or another whether as state capitalism as in China or Russia; or monarchy as in Saudi Arabia and the United Arab Emirates, where they still behead people; or the pseudodemocratic military dictatorship in Egypt we support where they killed thousands of the people who won the last fair election; or in our judicially corrupt, Wall St. run democracy that lock up of more of its people than any other nation on earth and in all of human history.
At the Ferguson murder grand jury hearing sixteen witnesses said Mike Brown, the teen murdered by the cop, had his hands up. Only two witnesses said he didn’t and one of them was shown very soon after to be an out and out liar coached by the prosecutor and the police. Nonetheless the cop escaped justice. As did the cop who strangled Eric Garner to death. Such things happens only in a police state as we’ll make clear in our mathematical analysis.
The talking heads in the Wall St. controlled mainstream media blabbed endlessly about what could be done to change things. But as anybody in the know knows, the police are paid primarily to be a protective barrier between the privileged ruling class and the exploited working class, black and white. The small town cop does the bidding of the small businessmen in town. Everybody knows that. And the big city cops do the bidding of the city’s major corporations and institutions. And the FBI, just a bunch of thugs with good PR, do the bidding of the national corporations and Wall St.
Cops just obey the money of the folks who pay their weekly salary to keep the suckers on the bottom in line. Of course the cops also keep the farm animals, the working class, from killing and stealing from each other, the stuff they broadcast ad nauseam in the news to justify police bullying and brutality. But that aspect of what cops do is secondary to their main function of holding the whip over the wage slaves in the lower levels of our social hierarchy. Today’s police are just like the slave drivers of old, with guns instead of whips and working for the capitalist pigs rather than the pharaoh and his cronies. A change in this situation of cops as the insurers of capitalist order with their fingers ready on the trigger and handcuffs ready to break your wrist with can’t possibly ever happen other than by kicking the moneyed class out who own the police out of their perch at the top, a relatively benevolent recipe for getting this job done a central part of the mathematical analysis in MIT.
And a footnote to the people who aren’t able to understand why some protestors to the police murders get angry towards them and to the business community that always supports what the cops do. The downside of police brutality isn’t just people being murdered by them. Anyone who has been arrested, even for the most nonviolent sort of crime, remembers the excessive force always used. Real pain is inflicted in these slam to the ground arrests. And anyone put through the next level of police abuse in being locked up in a jail cell never forgets the treatment received that so very often goes beyond sadistic humiliation to out and out sadistic torture. Common are prisoners in jail who have been beaten while completely in chains, who have been locked in a cell chilled below zero only in their underwear and who have been intentionally exposed by prison staff to rapist convicts in order to destroy the manhood of resisting prisoners. Torture is almost as common in ordinary U.S. jails and prisons as at Abu Ghraib and Gitmo. Note a headline in the New York Times on 12/17/14: “The Los Angeles County jail system, the nation's largest, agreed Tuesday to impose sweeping changes, a year after guards were charged with regularly beating prisoners…” Such cruelty and torture of prisoners, many locked up only for stupid pot violations is utterly common around the country.
And on that most meaning issue of homosexuality and its unhappy degradation of manhood, a mathematically firm genetic analysis with MIT will make it clear that the true source of homosexuality in America is the endemic humiliation of guys that is part and parcel of pseudodemocratic, workplace slavery, police state run capitalism. The worst people in America are the bosses and others in authority who have all the power with 90% of them sadistic faggots whatever their media painted respectability. If it’s wearing a suit and tie, it stinks. Many a guy has fallen down in his effort to get the most important thing in life, a girlfriend, because the boss’s foot is up his ass. And such fallen ever after make obedient workers too stupid to understand the dynamics of excessive dominance and how it kills your chances of success in what is most desired in life by a (once) healthy young man.
As we will also mathematically develop an important consequence of the unhappiness caused by abuse in its being passed on as the worst part of human nature to people who were not in any way the cause of the unhappiness. This dynamic of passing your unhappiness on to the next person won the line formally called redirected aggression occurs not just between individuals but also between groups all the way up to nations passing on their misery hatefully to others as a prime motivation for war. Hating people not you or in your group or your religion is a final dumping ground for the unhappiness caused by enslavement in one’s own circumstances in one’s own nation.
And this aspect of internationally redirected aggression is especially dangerous in this era of nuclear weapons. It’s astonishing how much Putin sitting over there in Russia with 7000 nukes at the ready is painted in our media as a worthy object of derision and hate. The same with ridiculing Muhammad in Western Christian countries and so on. MIT will make it clear mathematically that a large part of hate between nations starts at home with each nation’s abusive control of its own citizens though, of course, those at the top in every nation must deny this source of unhappiness and hate and have enough control over their mouthpiece media to do it cleverly. This problem of mass redirected aggression, though, is very real and our blindness to it and failure to try to find a remedy for it really is a harbinger for nuclear extinction of the human race for as any guy who is tough enough at the street fighter level knows, when you’re about to be beaten, you let out all the bombs at your disposal, with little to no regard for the consequences. Very bad when the last weapon in the about to be a loser’s arsenal is nuclear.
As this dynamic of domestic and international hate caused by police enforced workplace enslavement will continue to be denied with the usual doubletalk, the only way to show its harsh truth and where it is leading us is to clarify the problem with mathematical exactness. This quantitative spelling out of the reality of modern workplace enslavement will also make clear the part that religion plays in the mess, innocently and otherwise. MIT will mathematically disprove a God creator as clearly and unarguably as one proves that 2+3=5.
We will do that by showing that what people call free, the way our mind makes choices, has the exact same form mathematically as Darwinian natural selection, you know the evolution stuff that 2/3 of Americans, the dunce slaves, have been led not to believe in. Well, God isn’t going to save anybody from enslavement and its pains. Actually God encourages obedience to authority, even its worst forms. And God isn’t going to save us from nuclear war even if most Christians think that if the unthinkable happens, it’s God’s will and that He’s going to compensate all the pig brained with an eternity of happiness in Heaven. As long as the suckers continue to believe in that bullshit, there’s no way people will come together in sufficient numbers for the worldwide movement needed to get rid of the weapons that enslave and threaten us all.
Now as for our making this argument with mathematical precision, there are some who say that God can make 2+3 be something other than 5 if He wishes. But for those of you whose brains aren’t yet reduced to the level of a pig, make an effort to read the math. And for those of you who get it gist of what we are talking about, but aren’t that keen on mathematics, we also provide the true life story of how MIT came to be written. It’s down at the end of the mathematics and gives a sense of the ideas in easy to read form. And it also provides a truer sense of real life contrary to the endless smiley faced crap you see on TV. And it sketches out how we can realistically bring about the maximum balance of power between individuals by taking away everybody’s weapons to achieve real freedom and an end to war and all its bloodletting to boot. Understanding the need for this and how it can be done whether from your own intuition sense of things and/or from MIT is the start of a worldwide political movement towards A World with No Weapons. It’s a doable social improvement, not just a false utopia, as you’ll see when you read further and it’s absolutely necessary to have it as the only way to obtain freedom and to end war and the possible termination of the human race.
If upon reading down further you find yourself woken up to the realities of police state enforced workplace enslavement and to the worst effects of it from violence and war and you would like to encourage me to run for elected office to do something tangible about it, scroll back to this point once the light goes on in your head and click here. In these days of endless skullduggery and violence we need a woman in the White House. But, please, not Hillary. She’s just one of them, just another villain in sheep’s clothing. And now on to the math that gives proof to what I am saying.
2. Information
We begin with the Shannon information entropy of standard information theory. Put your thinking cap on.
01.)
_{ }
Misinterpreted by many as a general function for information, H is well defined as the amount of binary digit or bit information in a message sent from a source to some destination. This is the kind of “bits and bytes” synthetic information your computer runs on. The p_{i} variable in H of Eq01 is the probability of a message being sent from a set of N possible messages.
If you’re new to this, it may sound more than a bit confusing. To explain it in the most simple way, consider a set of K=8 buttons in a bag in N=4 colors, (■■, ■■, ■■, ■■). I’m going to pick one of the buttons without looking and then send a message of the color I picked to some destination. Because the number of buttons of each color are equal, 2 buttons of each, the probability, p_{i}, of my picking any one of the N=4 colors is equally for all,
02.) p_{i }= 1/N = 1/4
There’s a 1 chance in 4 of my picking red, a 1 chance in 4 of picking green, and so on. This p_{i}=1/N=1/4 probability is also the probability of my sending out a message about the particular color I picked. So there is a p_{1}=1/4 probability of the message I send saying: “I picked red,” a p_{2}=1/4 probability of the message saying, “I picked green,” and so on. Plugging these p_{i}=1/4 probabilities into Eq01 obtains the amount of information in whatever color message I send as
03.)
We’ll explain what the H= 2 bits of information means in one second. But first to tell you that because the message set is equiprobable, with all of the color messages have the same p_{i}=1/N=1/4 probability of being sent, we can simplify the scary looking Shannon entropy equation of Eq01, by substituting 1/N for p_{i }in it, to _{ }
04.) H= log_{2}N
This shorter equation for equiprobable message sets is an easier way to get the same result of H=2 bits of information in Eq03.
05.) H= log_{2}N= log_{2}4= 2 bits
This H= 2 bits amount of information in a color message gotten from (■■, ■■, ■■, ■■) is interpreted most basically as the minimal number of bits or binary digits, (1s or 0s), needed to encode the colors as bit signals. The bit signal encoding for the N=4 colors in (■■, ■■, ■■, ■■) is [00, 01, 10, 00]. Red might be encoded as 00, so when the receiver gets 00 as the message, he decodes it back to red. The number of bits in the bit signal of a color message is the H amount of information in the message, here H=2 bits of information. This information coded in bits is the synthetic or digital information that computers run on.
Now let’s do the same for another set of buttons, K=16 of them in N=8 colors, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■). Because this set is balanced, the probability of picking any particular color and sending a message about it is the same for all N=8 colors, p_{i}=1/N=1/8. The amount of information in a color message picked from this equiprobable set can also be calculated from the simple, equiprobable, form of the Shannon entropy in Eq04 to obtain
06.) H= log_{2}N= log_{2}8= 3 bits
This encodes the N=8 colors in (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) with N=8 bit signals, [000, 010, 100, 001, 110, 101, 011, 111], with each bit signal consisting of H=3 bits, that understood as the amount of information in a color message sent. Note that as the N=8 colors in (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) are all distinguishable from each other intuitively, so are the N=8 bit signals for them in [000, 001, 010, 100, 110, 101, 011, 111] also distinguishable from each other. This parallel distinguishability of messages and their bit signal encoding is necessary for all N=8 possible color messages to be properly represented in their bit signal encoding. Note also the parallel distinguishability of the N=4 distinguishable colors in (■■, ■■, ■■, ■■) encoded with the N=4 distinguishable bit signals in [00, 01, 10, 11].
Another interpretation of H here is how much uncertainty a color message resolves for the receiver when he gets the message. Presumed is that the receiver of the message does not know the color picked from the bag before getting the message and so has uncertainty about the color. The amount of uncertainty felt beforehand is said to be the amount of information gotten when the message is received. This sense of the information in a message deriving from the resolution of the uncertainty felt before the message is received is intuitively quite reasonable. A message I send you that Osama bin Laden was the mastermind of 9/11, for example, something you certainly knew beforehand, would not provide information for you because you had no uncertainty about that fact.
The amount of uncertainty is specified in information theory by the H Shannon entropy interpreted as the number of yesno binary questions one would need to ask about the colors in (■■, ■■, ■■, ■■) to determine which color had been picked. By a yesno binary question is meant one that is answered with a “yes” or a “no” and that cuts the number of colors in half. One might ask of (■■, ■■, ■■, ■■) inquiring of half the colors, “Is the color picked red or green?” Whatever the answer, a “yes” or a “no”, the number of possible colors that might have been picked is cut in half.
If the answer to the above question were “yes”, the next question asked might be, “Is the color green?” If the answer to that next question is “no”, by process of elimination, the color picked has to be red. It took H=2 questions to find that out. So the amount of uncertainty about which color was picked and which color message was sent to some receiver is H=2 now as the number of binary questions needed to be asked to determine the color. And the amount of information gotten from receiving the color message, H=2 bits, is understood as the amount of uncertainty measured as H=2 binary questions, that was resolved by getting the message,
For (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) the H=3 bits measure it has can be interpreted as the amount of uncertainty about which color was picked from it because it takes H=3 binary questions to determine the color picked and message sent. The first question for (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) might be, “Is the color red, green, blue or orange?” as when “no” is the answer cuts the field in half to (■■, ■■, ■■, ■■). And two more binary questions will then reveal the color picked. With the amount of uncertainty about the color picked from (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) being H=3 bits as 3 binary questions, the amount of information in the color message is H=3 bits as the resolution of the H=3 bits of initial uncertainty the receiver of the message would feel before getting the message.
The H entropies that derive from these sets of colored objects can also be understood as a measure of the diversity in them. The N=8 color set, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), is obviously more diverse in color than the N=4 color set, (■■, ■■, ■■, ■■), as is confluent with the H=3 Shannon entropy of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) and lesser H=2 entropy of (■■, ■■, ■■, ■■) when H is interpreted as a measure of diversity. And this is the case in hard fact for H as a measure of diversity, ecological and ethnic, is found in the biological and sociological literature of the last sixty years when specified with the natural logarithm rather than the log to the base 2, in which case it is called the Shannon Diversity Index rather than the Shannon information entropy.
07.) H=
This using of log_{2} form of H as a measure of information in Eq01 and of the ln form of H as a measure of diversity in the above strongly suggests an identification of information as diversity. This synonymy of information and diversity is further suggested in the Renyi entropy, R, an information function that generalizes the H Shannon entropy, being simply the logarithm of the Simpson’s Reciprocal Diversity Index, D, itself a frequently used measure of ecological and ethnic diversity.
08.) R = logD
Let us introduce the D diversity index as a function of the basic properties of
a set of objects like (■■■■, ■■■■, ■■■■). This set has K=12
objects in it in N=3 colors, x_{1}=4 red objects, x_{2}=4 green
objects and x_{3}=4 purple objects. The K=12 number of objects in the
set are the sum of the x_{i} number of objects in each of its N=3
subsets, i=1,2,…N, a relationship we generalized for any set of unit objects, (same
sized objects), as
09.)
This formally states the obvious that the 4 objects in each of the N=3 subsets of (■■■■, ■■■■, ■■■■) sum to the K=12 total objects in the set. And the D diversity of a set of objects as a function of the K total number of objects and x_{i} number in each of the N subsets of a set is
010.)
For (■■■■, ■■■■, ■■■■), which can be represented in shorthand by the natural number set, (4, 4, 4), the D diversity index is
011.)
For a balanced set like (■■■■, ■■■■, ■■■■), we see that the D diversity index is just the N number of subsets in the set, D=3=N. From Eq010 we find the diversity of the N=8 balanced set, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), (2, 2, 2, 2, 2, 2, 2, 2), to be D=N=8. And for the N=4 balanced set, (■■, ■■, ■■, ■■), (2, 2, 2, 2), we calculate the D diversity from Eq10 to be D=N=4. In general, for any balanced set of N subsets,
012.) D = N (balanced)
From Eq010 we can also calculate the D diversity index of an unbalanced set like (■■■■■■, ■■■■■, ■), (6, 5, 1) with x_{1}=6, x_{2}=5 and x_{3}=1 to be
013.)
For this (6, 5, 1) set and for all unbalanced sets the D diversity index is less than the N number of subsets. One might explain that for the (6,, 5, 1) set by saying that the x_{3}=1 purple set contribute little or just token diversity to the set’s diversity. In general, for all unbalanced sets,
014.) D < N (unbalanced)
The D diversity index is an excellent measure of the diversity in a set in terms of the N distinguishable subsets in a set, the more N subsets there are, the greater the diversity as fits with our intuitive sense of diversity as does in D from N for unbalanced sets some of whose subsets contribute only token diversity. It can be pointed out, though, that the D diversity has one salient lack of fit with our intuitive sense of diversity in its specifying the diversity of a uniform set like all red, (■■■■■■■■■■■■), via Eqs010&012 as D=N=1 even though intuitively there is no diversity, zero diversity, in this or any other uniform set. This problem is readily resolved, though, with a simple variation of D we will call the Exact Diversity Index, L,
015.) L = D – 1
The L diversity index has an immediate advantage over D in its evaluation of the diversity of uniform sets like (■■■■■■■■■■■■) as L=D–1=0 as fits the lack of diversity or zero diversity of a uniform set. And L has a couple of other special properties that argue strongly for its being understood as an elemental function for information. First of all consider its value for our balanced sets: L=D–1=2 for the N=3, (■■■■, ■■■■, ■■■■), set; L =D–1=3 for the N=4, (■■, ■■, ■■, ■■), set; and L= D–1 = 7 for the N=8, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), set. In general, for any balanced set, from Eqs014&015
016.) L = N – 1
The measure of L for the example balanced sets will show us next that L is not only a measure of diversity but also of distinction. In the N=4, L=3 set, (■■, ■■, ■■, ■■), we intuitively distinguish any one of its subsets from the L=N–1=3 other subsets in the set. And similarly for the other balanced sets, their L diversity index is a measure of the number of subsets that any one set is distinguishable or distinct from. We will show this for unbalanced sets shortly.
For the moment we want to show that L is a measure of distinction not just between subsets of different color but also between objects of different colors. Consider the K=6, N=3 color, (■■, ■■, ■■), (2, 2, 2), set. As it is a balanced set, it has L=N–1=2. To understand L as a measure of distinctions between objects of different color in (■■, ■■, ■■) as with our distinguishing the first red object in (■■, ■■, ■■) from the last purple object as ■■, we compare all objects in the set to each other in a systematic way in a comparison matrix.

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Figure 017. The Comparison Matrix of (■■, ■■, ■■)
Out of K^{2}=36 comparison pairs in the matrix, we count Y=24 distinctions, pairs of objects with different color like ■■; and ε=12 samenesses, pairs of objects with the same color like ■■. (ε is the Greek letter epsilon.) Note first that for the matrix of this set and all sets, a comparison pair must be either the same or different, hence,
018.) Y + ε = K^{2}
Next note that the ratio of Y distinctions to ε samenesses, Y/ ε, yields the set’s L exact diversity index
019.)
This relationship is valid for all sets, balanced or imbalanced and is formally written and elaborated from Eq018 as
020.)
We will show this for the unbalanced case also with the K=6, N=3, (3, 2, 1) set, (■■, ■■, ■■), that has x_{1}=3, x_{2}=2 and x_{3}=1. From Eq010, its D diversity index is D=18/7=2.571 and from Eq015, L=D–1=11/7=1.571. The set’s comparison matrix is

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Figure 020. The Comparison Matrix of (■■, ■■, ■■)
Out of K^{2}=36 comparison pairs, we count Y=22 distinctions and ε=14 samenesses as obtains L=Y/ ε=22/14=11/7=1.571. It is clear from the two matrix analyses and Eq020 that, for constant K, the L diversity is an increasing measure of the Y distinctions between objects. Thus from measure theory, as an (effectively) monotonically increasing function of Y, the L diversity is also a measure of what Y is a measure of, namely object distinction. Hence L is a measure of distinction, both subset distinction and object distinction.
This sense of L as distinction further implies that L is a measure of information to the extent that distinction and information can be taken to be synonymous as the following example strongly implies. Consider 4 apples on a table, which when seen at a distance are thought and sensed to be all the same variety. But as they are approached more closely they come to be distinguished as 2 Macintosh apples and 2 Delicious apples. This distinction in kind or in the variety of apple that comes about upon closer approach is readily understood as information for the observer about the apples.
Despite the above intuitively reasonable argument for L diversity as a measure of distinction and, hence, of information, many diehard information theorists will insist that only the Shannon entropy can be the correct general function for information. Much of this derives from the work of Alexandr Khinchin, The Mathematical Foundations of Information Theory. Claude Shannon developed the Shannon entropy as a coding recipe for bit encoding in 1948 and Khinchin then developed it in the early 1950s as a general function for information.
The problem with it is that as an axiom based schema, it suffers from, indeed is a powerful example of, Gödel’s utterly unarguable complaint against all axiomatic mathematical structures in Khinchin presumed sense of information as an axiom preordaining the perfect fit of the Shannon entropy he derives to what he considers information to be, indeed, what it must be. In raw fact, though, from empirical observation that is acceptable to Gödel’s criteria, the ShannonKhinchin entropy of Eq01 can be shown to only give a reasonable understanding of qualitative information, walking entirely past quantitative information. These two distinct kinds of information, qualitative and quantitative will explained and the latter developed now as we proceed.
A powerful argument for L and D as measures of information, specifically of the kind we are calling quantitative, which is centrally important for a clarification of both the physical and cognitive sciences, is understanding L as an alternative bit coding recipe to the Shannon entropy. We saw earlier that N=4 color (■■, ■■, ■■, ■■) was encoded with bit signals of H=log_{2}N=2 bits as [00, 01, 10, 11]. But this set using L as a bit coding recipe can also be encoded as [000, 001, 011, 111] with each bit signal consisting of L=N–1=3 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], its L=N–1=7 exact diversity index as a coding recipe encodes it as [0000000, 0000001, 0000011, 0000111, 0001111, 0011111, 0111111, 1111111] with each bit signal consisting of L=7 bits.
Note in both of the L encodings that only one permutation of all possible permutations of a given combination of 1s and 0s is used. This allows us to write for the 20s and 51s combination any permutation of it, 0111011 or 0011111 and so on, but not more than one permutation of it.
As to where we are going with this, anyone familiar with information theory will immediately recognized that the L bit coding recipe is practically inefficient in its requiring many bit symbols for a message compared with the H Shannon entropy coding recipe. This is not surprising given that Shannon devised H initially strictly as an efficient coding recipe, that is, for the minimum number of bit symbols needed to encode a message in bit signal form (with Khinchin the one who developed it later more as a general function for information.)
L as a coding recipe fails miserably at the task of bit symbol minimization. But, of course, we are not trying to engineer an efficient coding system in any practical way with L diversity but rather trying to show how it can be understood as function for information, its efficiency for practical communication quite beside the point. And we do that we next look carefully at the details of the difference in the H and L bit encodings. Let’s do that first for the N=4, (■■, ■■, ■■, ■■), set whose colors are encoded in H coding as [00, 01, 10, 11] and in L coding as [000, 001, 011, 111]. Look closely to see that these are two very different ways of providing N=4 distinguishable bit signals to encode the N=4 distinguishable messages in (■■, ■■, ■■, ■■).
What is special about the L bit encoding of (■■, ■■, ■■, ■■) with [000, 001, 011, 111] is that these N=4 bit signals are all quantitatively distinguishable, each bit signal distinct numerically from the other bit signals in having a different number of 0s and 1s in it than all the others. That is not the case for the H encoding of (■■, ■■, ■■, ■■) with [00, 01, 10, 11], for there it is seen that the 01 and 10 signals have the exact same number of 0s and 1s in them. This understands 01 and 10 to be distinguished not quantitatively but rather positionally or qualitatively by having the bit symbols of 0 and 1 be in different positions in 01 and 10. The bit signals of [00, 01, 10, 11] for (■■, ■■, ■■, ■■) are, thus, nonquantitatively or positionally or qualitatively distinguishable generally rather than quantitatively distinguishable as was the case for the L bit signal encoding of [000, 001, 011, 111].
This quantitative versus qualitative bit signal difference in L and H is even more clear for the N=8 set of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) and its L=N–1=7 encoding of it as [0000000, 0000001, 0000011, 0000111, 0001111, 0011111, 0111111, 1111111]. For there we see that every one of the N=8 bit signals is quantitatively distinguished from every other bit signal. That is, the N=8 distinguishable messages derived from (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) are encoded in the N=8 distinguishable bit signals in [0000000, 0000001, 0000011, 0000111, 0001111, 0011111, 0111111, 1111111] by distinctions between the bit signals that are quantitative. This quantitatively distinguishable bit encoding with L=7 is in contrast to the H=3 bit encoding of that color message set as [000, 001, 010, 100, 110, 101, 011, 111]. In that 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 those bit signals. And that positional, qualitative, distinction is also seen between the 011, 101 and 110 signals, all of which are quantitatively identical, not quantitatively distinguishable.
The quantitative versus qualitative difference between these the two kinds of bit information, L and H, corresponds to our everyday sense of information as being quantitative or qualitative information. My telling you that General George Washington owned slaves is qualitative information for you, while if I tell you that he owned 123 slaves (at the time of his death), that’s quantitative information.
This explains why the H (qualitative) coding recipe is logarithmic in form and why the L (linear) coding recipe is quantitative. H is logarithmic because it is a coding recipe for information communicated or transmitted from person to person. The human mind distinguishes intuitively between the positions of things as between 20s and 51s arranged as 0111011 or as 0011111 in different positions. This property of mind allows us to encode or represent distinguishable messages sent from one person to another with signals that are distinguishable from each other in any way including those that are distinguished from each other positionally. Because the N number of distinguishable messages that can be constructed from H variously permuted, variously positioned, bit symbols is N=2^{H}, a power function, the information in one of those messages specified as the H number of bits in its bit signals is inherently logarithmic via the inversion of N=2^{H} as H=log_{2}N.
Compare this to L=N–1=7 bit encoding of the N=8 (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) set as [0000000, 0000001, 0000011, 0000111, 0001111, 0011111, 0111111, 1111111]. The L coding recipe encodes the colors via the number of 1s in the bit signals distinguishing them as the zeroth color, the 1^{st} color, the 2^{nd} color and so on with ordinal numbers that are sequentially the zeroth color to the 7^{th} color and that in effect are a count of the number of colors and a clearly quantitative description of them as such even though the count starts with 0 rather than 1. Information that comes to us from nature invariably is precisely described numerically or quantitatively as every practitioner of the physical sciences understands and, hence, any reduction of it to bit form signals must be of the L encoded linear type which explicitly represent the numerical amount of the characteristics of a system in nature.
It may seem odd here to start with zero in the counting of the colors in (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■). But recall earlier that N=7 is the number of subset distinctions that any one subset in a balanced set has from the n=other subsets. In that regard, all of the bit signals but the 0000000 zeroth bit signal may be understood as the N=7 distinctions that any one subset, say, the red subset, has with the other color subsets, and with the zeroth color understood as red counted as compared to itself and not having any distinction from itself. However, even with that nuanced subtlety, it is obvious that the L specified bit signals for the N=8 set of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) comprise a count of them.
This sense of linear diversity being a measure of quantitative information as a count of things is more clear in D=L+1 diversity, which can be understood, as D=L+1=8=N, as a count of the subset colors in (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), each with D=8 bits as [00000001, 00000011, 00000111, 00001111, 00011111, 00111111, 01111111, 11111111] and with 00000000 disallowed as signifying nothing. Doing that provides for ordinal numbers from the 1^{st} color and to the 8^{th} color, in effect counting the distinguishable colors in (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) as D=N=8 of them and providing quantitative information about them.
Hence the proper general understanding of information is as diversity: logarithmic diversity for communicated information, as in H, which is indeed most basically a logarithmic diversity measure as made clear with in Eq07 for the Shannon Diversity Index, which is absolutely no different effectively than the H Shannon Entropy of Eq01; and linear diversity, which indeed is linear in form entirely like the counting numbers, 1, 2, 3, 4, 5, etc., which are utterly linear on form. It is not that such quantitative descriptions of countable items cannot be reduced in communication to positional or qualitative distinctions, which we do in the Arabic numerals that write thirteen as 13 rather than 1111111111111 and in binary numbers as 1101. But that should not take away from the elemental linear nature of counting and, hence, of describing and measuring things linearly. This will become precisely physically clear once we touch upon the true nature of entropy understood properly as a linear diversity measure. And we will make it clear immediately next with familiar situations specified by unbalanced sets that illustrate meaningful information the way the human mind intuitively senses it in terms of significance and insignificance.
The true nature of information as we experience it perceptually in what we see is made clear with D beyond any abstract bit signal justification of L and D from their conveyance of the meaningfulness of something in terms of its significance, which extends from thermodynamic systems that clearly explain physical nature as we shall see later to cognitive systems that profoundly explain some of the most elemental aspects of man’s mental nature.
In a nutshell, the D diversity of a set is readily interpreted as the number of significant subsets in the set to provide a far reaching understanding of much in physical and human nature that heretofore was utterly confusing. We will begin with an upgrading of the cognitive sciences first and then later will proceed to physical systems and entropy, and that not just for its own sake, but also because entropy’s clarification also helps to most completely explain our mental machinery.
The sense of significance versus insignificance spelled out with the D diversity index is investigated with a number of examples starting with the Ferguson Police Dept. With its x_{1}=50 White officers and x_{2}=3 Black of its K=53 total, one really needs take no recourse to mathematical analysis to understand that its Black officers are insignificant. This is, in one sense, an equivalent way of describing the force as having “no diversity.”
A diagram always helps, so let’s start with (■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■, ■■■) as the set of “objects” representing the Ferguson Police Dept. That there is no or little diversity is a measurable observation from Eqs010&015 telling us that L=.12, very close to the L=0 measure of zero diversity in a completely uniform set we talked about between Eqs014&016. From this we also know that its D measure is D=L+1=1.12, which rounded off to the nearest integer is D=1, which suggests only 1 significant subset in the (50, 3) number set that represents the Ferguson Police Dept. quantitatively. That it is the White contingent of x_{1}=50 cops who are significant or meaningfully and the x_{2}=3 Black officers who are insignificant or effectively meaningless, and not vice versa, will be now in the detail it deserves.
We will use the K=12, N=3, (■■■■■■, ■■■■■, ■), (6, 5, 1), set with x_{1}=6, x_{2}=5 and x_{3}=1 to illustrate. Note first from Eq013 the D=2.323 diversity index of this set, which rounded off to D=2 suggests 2 significant subsets, the red and the green, with the purple subset with only x_{3}=1 object in it understood as insignificant. To identify the purple subset as the one that is insignificant in a sure way, we need to massage the D diversity equation of Eq010 a bit in order to specify each subset individually as to their significance of lack of it. To do this let us first define two familiar averages in mathematics. The first is the arithmetic average or mean of a set,
021.)
The mean of the K=12, N=3, (■■■■■■, ■■■■■, ■), (6, 5, 1), set is µ=K/N=4 as the average number of objects per subset. And the mean of the K=12, N=3, balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), introduced after Eq08 is also µ=K/N=4. The second average we want to introduce is the root mean square (rms) average, ξ, (xi), defined as
022.)
And the rms average squared, ξ^{2}, is
023.)
The rms average of the K=12, N=3, (■■■■■■, ■■■■■, ■), (6, 5, 1), set is ξ =4.546 with ξ^{2}=20.667=62/3. And the rms average of the K=12, N=3, balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), is ξ =µ=4 with ξ^{2} =µ^{2} =4. Now Eqs021,023&09 allow us to express the D diversity index of Eq010 as a function of the µ and ξ averages as
024.)
In the above, the significance index of the i^{th} subset in a set is ς, (final sigma)
025a.)
For the balanced, (■■■■, ■■■■, ■■■■), (4, 4, 4), set, D as computed from the above is, as earlier obtained from Eq011,
025.) D = 1 + 1 + 1 = 3 = N
What the D=1+1+1 means is that all N=3 subsets, in having the value of unity, are significant. And for the unbalanced (■■■■■■, ■■■■■, ■), (6, 5, 1), set, D is, as was obtained earlier in Eq013,
026.) D= 1.161 + .968 + .194 = 2.323
And what D= 1.161 + .968 + .194 mean is that the subset with x_{1}=6 red objects and a significance index of ς_{1}=1.161 is significant in its being close to unity; the green subset with x_{5}=5 objects in it and a significance index of ς_{2}=.968 is significant in being close to unity; and the purple subset with x_{3}=1 object and ς_{3}=.194 is insignificant in being close to 0.
That the mind truly operates on these significance functions or some brain neurobiology facsimile of them by paying attention to significant items and disregarding the insignificant is made clear with the two more illustrative situations. In the first consider a population of K=392 people in Liberal City, USA of which x_{1}=200 are Caucasian, x_{2}=180 are Black, x_{3}=8 are of an small ethnic group from a remote island in the Pacific Ocean and x_{4}=4 are of another unusual ethnic group from a remote island in the South Atlantic Ocean.
Now we ask the question: How many significant ethnic groups are there in town? And by significant we mean numerically significant, not significant as praiseworthy or admirable. And how many insignificant groups are there? Intuition tells you that there are 2 significant groups, the Whites and the Blacks; and that there are two insignificant groups, the two island population groups. A common indication of significance in a case such as this would be whether one of the small ethnic group would be listed by name on a formal census taken in the town. Almost surely were such a census taken it would list the 2 significant ethnicities, Caucasian and Black, on the census form but use “Other” for the two island groups because they are numerically insignificant. The D Simpson’s Reciprocal Diversity Index in Eq024 gives a measure of significance in two ways. First it computes the bulk measure of significance in terms of D as computed below.
027.)
Rounding off D=2.12 to D=2 indicates 2 significant ethnic groups of the N=4 in town, intuition telling you, the Caucasians and the Blacks with the two islander groups deemed insignificant. This understanding is made all the more clear by the significance indices of the groups of ς_{1}=1.08, ς_{2}=.974, ς_{3}=.043 and ς_{3}=.022. The town clerk who would make up this minicensus would not have to calculate significance from the D diversity index to know that the island groups were too insignificant to be listed by name. The sense of significant versus significant is entirely intuitive, automatic, subconscious.
That
it is, is made all the more clear with the three sets of colored objects displayed
below, each of which consists of K=21 objects in N=3 colors.
Sets of K=21 Objects 
Number Set Representation 
D from Eq024 
rounded 
Significance Indices 
(■■■■■■■, ■■■■■■■, ■■■■■■■) 
(7, 7, 7); x_{1}=7, x_{2}=7, x_{3}=7 
D=3 
D=3 
ς_{1}=1, ς_{2}=1, ς_{3}=1 
(■■■■■■, ■■■■■■, ■■■■■■■■■) 
(6, 6, 9); x_{1}=6, x_{2} =6, x_{3} =9 
D= 2.88 
D=3 
ς_{1}=1.24, ς_{2}=.824, ς_{3}=.824 
(■■■■■■■■■■, ■■■■■■■■■■, ■) 
(10, 10, 1); x_{1}=10, x_{2}=10, x_{3}=1 
D=2.19 
D=2 
ς_{1}=1.04, ς_{2}=1.04, ς_{3}=.104 
Table 028. Sets of K=21 Objects in N=3 Colors and Their D Diversity Indices
The N=3 set, (■■■■■■■■■■, ■■■■■■■■■■, ■), (10, 10, 1), has a diversity index of D=2.19, which rounded off to D=2 specifies D=2 significant subsets of color, the red and the green, with the x_{3}=1 object purple subset insignificant, as might be understood intuitively from its contributing only token diversity to the set and analytically from its significance indices. By contrast the D=3, (■■■■■■■, ■■■■■■■, ■■■■■■■), (7, 7, 7), set has 3 significant subsets, red, green and purple, as does the (■■■■■■, ■■■■■■, ■■■■■■■■■), (6, 6, 9), set whose D=2.88 diversity rounds off to D=3. And the significance indices in both are close to or round off to unity. One can get a stronger intuitive feel for how the human mind determines significance and insignificance intuitively by represented the sets in Table 028 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 with a plaid skirt with the (10, 10, 1), D≈2, pattern on the left
would spontaneously describe it as a red and green plaid, omitting
reference to the insignificant thread of purple. She would do this intuitively
and automatically without any conscious calculation because that is how the
human mind automatically registers what is significant and what is
insignificant. The rounded off D≈2 diversity specifies the 2 significant
colors in the plaid, red and green, that the mind intuitively senses and also
intuitively verbalizes as such. Note how the insignificance of the purple
thread specified in the D=2 measure is manifest linguistically in purple being
disregarded in the description of the cloth as a red and green plaid.
This verbalization of only the significant colors in the plaid, red and green, should not be surprising given that the word “significance” 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 isn’t signified or verbalized or given a word. The human mind operating in this way to barely notice and not verbalize what is insignificant is an important factor in human behavior because we generally think, talk about, pay attention to and act on what we sense to be significant while automatically disregarding the insignificant in thought, conversation and behavior. This is also the case for the census taken in Liberal City, USA: the insignificant ethnic subsets are not signified or given a name on the census.
The significance of what we is affected not just by its size or quantity but also extends to the frequency of our observing an object or objects or an event. Consider as illustration a game where you guess the color of a button picked blindly from a bag of buttons, (■■■■■■■■■■, ■■■■■■■■■■, ■). Now let’s assume that you don’t know the makeup of the buttons in the bag, but only what you observe over time about which color buttons are picked, (with replacement), namely that some of the picks are red, some green and some purple. Over time, as you see purple picked infrequently, purple will come to be insignificant in your mind, so much so that you will not even think about guessing it once you came, yourself, play this guessing game. This sense of significance versus insignificance as determined from the frequency of an event as measured by the D diversity index and its constituent ς_{ }significance indices parallels what we will see occur in thermodynamic systems for entropy via a diversity function we shall develop in a later section.
Now one might think that the human mind is doing tricks of its own in making large (and/or frequently observed) things seem significant and small (and/or infrequently observed) things seem insignificant. One might think, to continue this train of thought, that a count of N=3 subsets is the precise quantification for (■■■■■■■■■■, ■■■■■■■■■■, ■) and its D=2.19 diversity measure from Eq024 a less precise measure of (■■■■■■■■■■, ■■■■■■■■■■, ■) that just happens to work well to fit our intuitive sense of the diversity in it and of the relative significance of its color subsets. But, in hard fact, that is absolutely not the case. Indeed, just the opposite is true: the D diversity measure of this unbalanced set is exact and the count of its subsets is inexact.
We are taught early in grade school that we should only add like things together, galaxies with other galaxies, 2 plus 2 of them equaling 4 galaxies, and kitty cats with other kitty cats, 2 plus 2 of them equaling 4 kitty cats. Admonished by your 3^{rd} grade teacher and forbidden by the rules of mathematics is adding together 2 galaxies and 2 kitty cats to get 4 of anything. This also has to do with counting or adding things together things that are different in magnitude. Explicitly stated following Eq08 was that the sets we have been considering consisted of “unit objects”, all the same size. This mathematical regularity is necessary for our accurately saying there are K=21 objects in (■■■■■■■■■■, ■■■■■■■■■■, ■).
But because the subsets are not the same size, don’t have the same number of unit objects in them, it is inaccurate to say there are N=3 subsets. This is easy to see intuitively if you consider the N=3 subsets to arise as N=3 different color containers of pumpkins that are all the same size and color. That is, the pumpkins are differentiated now and put into N=3 distinguishable subsets because their containers are distinguishable colorwise. Now it makes sense intuitively that quantifying (■■■■■■■■■■, ■■■■■■■■■■, ■) as N=3 containers is inaccurate because if you were selling the pumpkins by the container, it would certainly confuse people. And for that reason, merchants just don’t do that, weights and measures all being standardized and of the same unit magnitude. In this case indeed, the sharp merchant would sell the pumpkins by the pound, all of which pounds contain are the same amount of pumpkin, rather than by the container, all N=3 of which don’t contain the same amount of pumpkin.
Indeed we see this with eggs also, if in a slightly different way. We sell eggs by the count, but the seller tries to keep the eggs sold this way graded all very close the same size, be they pullet, medium, large or jumbo. So the N=3 count of the number of subsets, while handy in reference, is inaccurate or inexact in measure or specification. Note on the other hand that the D diversity of (■■■■■■■■■■, ■■■■■■■■■■, ■), D=1.19 is perfectly accurate because it is a function from Eqs010&024 of the K number of unit objects, all the same size, and of the x_{i} number of objects in each subset, all of which are the same size. Hence the mind when it sense significance in terms of D and its component measures is sensing an exact and accurate mathematical structure. This, indeed, is what we should expect of a biophysical organ like the mind that operates strictly on the laws of physics and chemistry that themselves play only by the rules of accurate and exact mathematics.
This also must be the case with thermodynamic systems that consist of oodles of molecules that contain oodles of energy. Because the amount of energy contained in molecules varies in the MaxwellBoltzmann distribution, as every sound chemical physicist knows, one cannot count the molecules in a straightforward way because all the molecules are not identically the same in that regard. Rather what matters as a proper tabulation of the molecules is their diversity index, which, seeming odd for the less astute, will turn out to be that mysterious thing called entropy. Of course there is much more workup necessary to show this precisely as will be done in a later section.
But for now, as a prelude to that quite further down the line, let’s take a closer look at the D diversity as an exact measure. Consider the K=12, N=3, (6, 5, 1) set, (■■■■■■, ■■■■■, ■), set that has an arithmetic average of µ=K/N=4. Every scientist of whatever stripe who talked about a (6, 5, 1) number set in his experiments in terms of its µ arithmetic average would also give along with it a measure of statistical error. Most commonly used is the standard deviation, σ, whose square, σ^{2}, called the variance is also a statistical error function.
030.)
The variance of the N=3, µ=4, (6, 5, 1) set, (■■■■■■, ■■■■■, ■), is
031.)
Hence, the standard deviation, σ, of this set is σ=2.45. Very often the average of the set, µ=4 would be given along with the standard deviation as µ±σ=4±2.45. Another often used statistical error is the relative error, r,
032.)
For this set, (6, 5, 1), r = .54= 54%. The mean, then, might be given as µ ± r = 4 ± 54% which suggests a 54% error in the mean. Now when we talk about an error in the µ=K/N mean, the error clearly does not lie in the counting of the K unit objects, because they are all the same size. Rather the error resides in the count of the N subsets because they are not, for (6, 5, 1), the same size. That this appreciation of statistical error is sensible is reinforced by considering the statistical error of the balanced, (■■■■, ■■■■, ■■■■), set. It is σ= σ^{2}=r=0. There is no error in its µ=K/N=4 mean ultimately because there is no error in the counting of the N=3 number of subsets in (■■■■, ■■■■, ■■■■), because they are all the same size, and as we tried so hard to make clear up to this point, a count of things the same size is accurate and exact while a count of things, including subsets, not the same size is inaccurate and inexact. And indeed, the nonzero σ, σ^{2} or r statistical error of an unbalanced set is the measure of its inaccuracy.
Now
let’s see how statistical error is an inherent part of the D diversity,
incorporated into it so as to make it accurate. To do that we first solve the
σ^{2} variance of Eq030 for the summation term in it.
033.)
Then inserting this summation term into Eq010 or Eq024 obtains D via µ of Eq021 and r of Eq032 as
034.)
Now we
see that we can understand D as an accurate and exact function not only because
its component parameters of K and x_{i} are all the same size and count
up accurately but also in terms of the r error measure in the µ=K/N mean and N
number of subsets in an unbalanced set is incorporated directly into D
diversity index. In that sense D is a correlate of N, identical to it, D=N, for
balanced sets, and to be used in place of it when accuracy and exactness are
important as is the case in specifying physical systems like thermodynamic
systems where the entirety of physical chemistry academia are to obtuse to see
the error in using N as an accurate quantification of the molecules; and of
using an accurate diversity, which turns out to be and to solve the mystery of
entropy, as we shall see in all necessary detail later down the line.
Now we want to end this topic of discussion of significance as a key factor in meaningful information by returning to the example we started with of the makeup of the Ferguson Police Dept. We calculated earlier from its (50, 3) number set representation that the diversity index of the Ferguson PD was from Eq010, D=1.12, as indicated only one significant ethnic group in the department, certainly the Caucasians. Now we see that we could have also determined this measure of D from Eq034 from the r relative error of the (50, 3) number set, which is r=.887. And we see using Eqs024&025 that can determine the significance of the two ethnic groups on the police force in a more exact way with the ς_{1}=1.06 significance index for the Caucasian policemen indicating that they are significant and a ς_{1}=.06 significance index for the Black policemen indicating that they are (quantitatively) not significant. And indeed, this sense of significance is real because when one thinks “policeman in Ferguson, Missouri”, one necessarily thinks, a white person.
Now we want to switch to another kind of meaningful information, one not necessarily connected with significance from size, but with the emotions evoked by an object or an event that make it meaningful. A good recent example of that, also associated with police officers, is of the thousands of NY City cops who turned their backs on Mayor Bill De Blasio, effectively publically ridiculing him, during the funeral of a police officer shot by a cop hater who later committed suicide. This is a clear case of meaningful information in its powerful emotional implications. The police in a democracy are by law under the authority of the Police Commissioner, who, himself, is appointed by and is under the authority of the mayor, who is democratically elected by and is nominally, thus, under the authority of the people. The disregard of this chain of command by police, this public ridiculing of the mayor, is nothing less than a revolt against the people, a revolt against democracy, as a clear manifestation of a police state, you know, one in which it is the police who control what happens governmentally and not the people. That’s why what happened during the cop’s funeral is meaningful or important, because it affects the lives of every person living in a democracy that is rapidly on its way to becoming an out and out police state, or already is, no matter how much that reality is kept well hidden by means that MIT will make clear after we have thoroughly fleshed out the details of meaningful information. And the emotions on the side of the police also run high when people start gunning them down in response to excessive police force.
To get a good handle on this majorly contentious issue we need to consider meaningful information beyond quantitative significance and that has to do with meaning imbued in an object or event by its emotional associations. And to do that we need to understand the emotions people feel in a systematic way, for the issues that are meaningful to most people, especially in these times in America, tend to be highly contentious and divisive.
That information is inherently affected by emotion is obvious from the intuitively reasonable sense of it in information theory we considered earlier that understands information as the resolution of uncertainty for, generally speaking, uncertainty is experienced or felt as an unpleasant feeling or emotion. Moreover when uncertainty is resolved, by whatever means, a person tends to feel something akin to relief or elation, a generally pleasant feeling or emotion, that “aha!” feeling. Let’s see if we can’t understand this in a more analytical way using the L and D information functions of the (■■, ■■, ■■) set of colored buttons. Consider a button is picked from (■■, ■■, ■■) and a person at some destination away from where the picking too place must guess the color of button picked. The probability of him making the right guess, which we’ll give the symbol, Z, to is
035.) Z=1/N=1/3
And the probability of failing to make the correct guess, understood as the person’s uncertainty in making the correct guess, is
036.) U=1– Z = 2/3
Note first that this form of uncertainty as probability is much more how the human mind configures uncertainty than the log_{2}N=log_{2}3=1.58 bits form of uncertainty specified in information theory. And as we see from the comparison matrix of the K=6 object, N=3 color, (■■, ■■, ■■) set, the U uncertainty is very much a function for information, itself, from its relationship to L and D as measures of information.

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Figure 037. The Comparison Matrix of (■■, ■■, ■■)
In Eq020 we saw that L was the ratio of the Y number of object distinctions to the ε samenesses, here L=Y/ ε=24/12=2. Now we can get a sense of what this means in terms of human cognitive and emotion by considering the comparison matrix as providing a comparison of guesses about which color was picked to actual outcomes of color picked. We do that by understanding the (■■, ■■, ■■) set on the matrix horizontal axis to be the average outcome of picks for every six picks taken; and by understanding the (■■, ■■, ■■) set on the vertical axis to be the average of any six guesses of color, the guesses of color taken to be equiprobable assuming that no one color is a preferred guess given the equiprobable set of color outcomes. And the K^{2}=36
This understands the Y distinctions to be incorrect guesses such as with ■■ (green guessed, red picked); and the ε samenesses to be correct guesses, such as with ■■, (green guessed, green picked). Generally speaking, indeed universally, making a correct guess elicits pleasure, whether of color in this game or guessing the right Jeopardy question while playing along with the TV game or guessing the words that fit correctly in a crossword puzzle. And generally speaking, indeed universally, guessing incorrectly, as in the above instances, elicits a feeling of displeasure of some kind.
Now we can see that the fraction of wrong answers in this guessing game, the ratio of the Y=24 incorrect answers, the distinctions, to the K^{2}=36 times the game is played and a pick made and color guessed, is the probability of guessing wrong, aka the uncertainty in guessing incorrectly, U=Y/K^{2}=24/36=2/3. Later we will make clear how this relationship is general for the matrix of any set of objects used similarly.
038.)
This derives L from Eq020 as a function of U as
039.)
And we can also express U as a function of L from the above and from L=D–1 of Eq015 as
040.)
Now U being an effectively increasing monotonic function of L and D tells us from measure theory that whatever L and D are measures of, namely information, U is a measure of. But, of course, we know that U is, in a powerfully unarguable intuitive way, a measure of uncertainty. And that makes sense too, taking the principle from information theory that information is the resolution of uncertainty and in amount equal to the measure of the prior uncertainty that is resolved to information by the message received.
This is, as we see, just another way of framing that principle from information theory that information is uncertainty resolved. Now let’s make the uncertainty meaningful. We do that by changing the color guessing game a bit to make there be a cash penalty for failing to guess the color picked. Let’s say that the penalty is v=$120. Now from elementary probability theory that dates back three centuries to the days of Blaise Pascal, we know that the expected value of a game like this, E, is
041.) E= –Uv
And specifically for these particular values of U=2/3 and v=$120, the E expected value is
042.) E= –Uv = – (2/3)($120)= –$80
From a purely objective perspective, E= –$80 is the average amount of money the player would lose, the loss specified by the minus sign (–).This expectation of E= –Uv is also understandable as the person’s meaningful uncertainty, his expectation of failure that is meaningful because to fail to win the game costs him money, which is certainly meaningful in this day and age. This kind of meaningful uncertainty is also called worry or fear, fear of losing money, an unpleasant feeling generally, indeed universally unless one is too much of a child not to value money or an adult very much not of sound mind in a modern economy.
Now let’s look at the player being sent the message about which color was picked so that he can use that information to make a correct guess and not lose his money. This is certainly meaningful information for him. And it jibes and make sense that meaningful information is what resolves meaningful uncertainty. That is, the player feels meaningful uncertainty before making his guess when he doesn’t know what color was picked but must guess the right color to avoid the v=$120 penalty. And certainly the message about what color was picked that he can use to avoid the penalty is meaningful information for him.
As to the latter, getting the meaningful information that relieves the meaningful uncertainty has to be pleasant as the relief felt as an emotion gotten from the relief he gets from not having to pay the penalty. Thus we understand the meaningful uncertainty felt ahead of time, E= –Uv, to be unpleasant, and its resolution from getting the meaningful information taken to be in the same amount as the prior uncertainty, Uv, to be pleasurable.
This explains information as what people actually sense, not the material existence of things, but rather those things that appear intuitively to be significant, automatically disregarding the insignificant, and those things that are “highlighted” as it were by emotion in some form and to some significant degree, those things we are apathetic towards or have no emotion about also lacking meaningfulness and being intuitively ignored. Considering that we have developed both of these aspects of meaningful information, significance and emotional association, as a refinement or upgrading of classical information theory principles, and that they also fit tightly with our intuitive sense of meaningful information, more details to be provided in the following sections to better fill in the picture, it is difficult to deny the power of MIT as the basis of a major revolution in science.
We have made clear that meaningful information and the antecedent mental structure of meaningful uncertainty have intrinsic emotional association. With that as a foundation, we want next to begin our spelling out of all of our basic or operational emotions, fear, relief, dismay, depression, hope, anxiety, excitement and elation. And to do that we want to change the game of chance we’ll develop these emotions from to one easier to follow of tossing dice. We’ll start by explaining this game of tossing dice with a focus on that bane of freedom, subjugation.
3. Subjugation
Consider a game you are forced to play on the 2^{nd} Tuesday of every month where if you fail to roll a “lucky number” on a pair of dice, you have to pay a penalty of v=$120. The probability of tossing the numbers 2 through 12 on a pair of dice are:
1.) 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
The lucky numbers are 2, 3, 4, 10, 11 and 12. If you roll one of them you escape paying the v=$120 penalty. The probability, Z, of rolling one of these lucky numbers is just the sum of their individual probabilities.
2.) Z = 1/36 + 2/36 + 3/36 + 3/36 + 2/36 + 1/36 =12/36 =1/3
So you have a 1 chance in 3 of rolling a lucky number and escaping the v=$120 penalty. Put another way you have to pay the v=$120 penalty if you roll a 5, 6, 7, 8 or 9 rather than a lucky number, which occurs with a probability of
3.) U=1 – Z =2/3
The expected value of this game of chance, what you lose on average, is
4.) E = −Uv = − (2/3)($120) = −$80
The negative sign specifies E= −$80 as a loss of money, the average loss incurred when you play the game repeatedly. If you play the game three times, on average you will roll a lucky number and escape the v=$120 penalty one time out of three; and fail to roll a lucky number and pay the v=$120 penalty two times out of three, which adds up to $240, averaging out over the three games an E= −$240/3= −$80 loss per game.
Why would anybody play this game? You do because if you don’t you’re beaten with
a stick until you do play. You can rebel against this expensive piece of coercion
if you dare. If you beat the extortionist in hand to hand combat you’re free from
having to play the game. But keep in mind that he has a distinct advantage because
he has and you don’t have this weapon of a stick as thick as a baseball bat
with a lead weight buried into the end of it. If you lose to him in the fight,
the rules say, the penalty in the lucky numbers game that you have to continue
to every month is upped v=$360, which increases the average penalty you have to
pay to
5.) E = −Uv= − (2/3)($360)= −$240
And consider that also he may also hurt you badly. An important factor in deciding whether or not to fight for your freedom is your probability of winning in the fight. Perhaps you know karate and fear no man, nasty stick in hand or not. But perhaps the extortionist also knows karate, and don’t forget the stick.
We need exact numbers on the probabilities of winning the fight to analyze the situation mathematically. And to get them we’ll change what has to be done to revolt against this abusive exploitation to your winning in a special session of the Lucky Numbers game in which you need to roll the 2 or 12 with probability of 1/18 or about 5.5% to free yourself from ever having to play the monthly v=$120 penalty game again. But also note that this option for revolution comes not only with your continuing to have to play the monthly game at the increased penalty of v=$360 dollars, but also with the extortionist getting three whacks at you with his stick while you’re all tied up in chains, which could break one or more of your bones, ouch.
This
spells out subjugation or enslavement in mathematical welldefined terms. The
extortionist is controlling your behavior in his selfinterest (and against
yours) by taking your money coercively. This is not plantation slavery, but rather
more or less in line with the modern variety in a number of ways including the
very real possibility that there will be some who wind up paying no money at
all, these held up of paragons who are very adept at throwing the dice in just
the right way to avoid the penalty altogether, with it made clear to the rest
of the suckers that their misfortune is, hence, their own fault.
It is important next to show how this form of enslavement and the more general and real workplace slavery most people endure feels bad and ruins any chance of happiness other than in the regrettably unavoidable wishful thinking of the young and in the equally unavoidable delusional thinking of beaten adults who wind up chasing rainbows with great hope placed in a happy retirement or in their magical transport to Heaven after death or, even stupider, in the possibility of their children’s success in this Ponzi scheme slave society run by rats. Note that our (justifiable) ridicule of religion will be firmed mathematically as we proceed, as if that were necessary at all for it is already well documented in all history books that the rise of organized religion correlates perfectly with the rise of empires that rest on the enslavement of most of its population in one way or another.
To explain the emotional outcome of enslavement, we need first to explain emotions generally, both the unpleasant ones that enslavement is sure to bring about and the pleasant emotions that slaves long for but can never attain other than in wishful thinking. It’s important to develop the emotions mathematically and in a systematic way, on the one hand, because of the ephemeral nature of emotion and, in the other, because of the massively confusing ways emotion has been explained by various religions, philosophies, ideologies and in modern times by psychology, an ideologically corrupt prattle of nonsense majorly directed to blaming unhappiness on other than sociopolitical control or a seriously flawed wouldbe science at best.
We will make clear mathematically, for example, that the emotion of sexual pleasure is not a temptation by a Devil like spirit to sin and that the emotion of depression as often comes from the loss of a once happy sexual relationship to a guy is a mathematically welldefined neural signal that is not explained at all correctly by calling it “mental illness,” the most misleading phrase in the English language outside of the Blessed Trinity. To get past the intentional and unintended misleading dogmas of religion and the human sciences in their explanations, we will specify our emotions, good and bad, pleasant and unpleasant, in mathematical terms using the same Lucky Numbers game we have just used to give a clear introduction to subjugation with.
This will give us a scientifically objective understanding of our emotions as markers of meaningful information central to determining behavior, not only to understand the unhappiness caused by modern workplace slavery but also how that unhappiness primes people to aggress on innocent others in order to reduce that unhappiness so caused. Such a reduction in unhappiness by aggressively passing it on to others is seen in a wide spectrum of activities that range from the petty meanness of everyday life to our seemingly neverending mass murders and ultimately to our seemingly neverending warring, which is particularly dangerous for mankind when hydrogen bombs replace sticks as the weapon of choice.
And to repeat the important message directed to changing this whole ugly mess, the only means to eliminating enslavement is by maximizing the balance of power between people as done by taking away just about everybody’s weapons, which will also eliminate war. A path to attaining this is, of this writing, best stated in the story form presentation of the ideas after the math in the present edition of this blog. Then if upon reading this, you find yourself awakened to the realities of enslavement and of the worst that comes and might come from war and would like to encourage me to run for elected office to do something about these tragedies facing America and the world, scroll back to this point once the light turns on and click here.
Now
to explain the function of our emotions as markers for the meaningful
information that controls everything that people do, good and bad, we need to
specify human emotion in a precise and clear way as follows. This is raw
science. We will be staying away from politics and such for the next few
sections.
4. The Mathematics
of Human Emotion
The kind of behavior we’ll consider first along with its associated emotions is goal directed behavior. To generalize goal directed behavior precisely we need to begin by looking at behaviors we can describe numerically. Getting money is one goal that can be quantified numerically in terms of the V dollar amount of money one has as his or her goal to get. And we make the means to get those V dollars mathematical in a form of a Lucky Numbers game that provides a precise V dollar prize for rolling a lucky number, a behavior that has a precise probability of success.
From this foundation we’ll develop mathematical functions for our most basic emotions like hope, anxiety, excitement, disappointment, fear, relief, dismay, relief, joy and depression that we’ll refer to from time to time as our operational emotions. And later, much later, we’ll develop precise functions for our visceral emotions like sex, anger, hunger and the taste pleasures of eating.
The lucky numbers for the prize dice game are 2, 3, 4, 10, 11 or 12. If you roll one of them you win a prize of V=$120. The probability, Z, of rolling one of these winning lucky numbers is seen from Eq2 to be Z=1/3. This obtains the probability of rolling a number other than one of these lucky numbers as we saw earlier of
3.) U=1− Z=2/3
U=2/3 is thus 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
6.) 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 repeatedly you could expect to win V=$120, on average, one play in three for an average payoff of E=$40 per game played. Eqs3&6 enable us to write the expected value of E=ZV in Eq6 as
7.) 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 Eq7 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 Eq7, 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. That is, 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 Eq7 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 Eq7 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 Eq7. 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
8.) 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
9.) 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
10.) 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
11.) 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
12.) 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
13.) 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
14.) 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 Eq8, T=R−E, via the U=1−Z relationship in Eq5,
15.) 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 Eq5, the intensity of the excitement in winning the V=$120 prize is from Eq15
16.) 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.
17.) 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.
18.) 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 Eq8 when the E expectation term in it is expressed from Eq7 as E=V− UV.
19.) 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 Eq19.
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 Section 2. It will be recalled that the player was forced to play it and that the penalty could 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 was given in Eq3 as U= 1− Z =2/3. The expected value first given in Eq4 as Uv=$80 is given below in more proper form with a negative sign as
20.) 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 Eq8,
21.) 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 from Eq3,
22.) 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.
23.) 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.
24.) 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.
25.) T=Uv=(35/36)($1200)=$1166.67
Compare to the relief of T=$116.67 in Eq23 when the penalty was only v=$120. The universal fit of mathematically derived Uv relief to the actual emotional experience of felling relief is remarkable. We also use the Law of Emotion of Eq8 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
26.) 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
27.) 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.
28.) 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 of Eq3 as
29.) E= −Uv = −(1–Z)v = −v + Zv
The − v term in Eq29 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 Eq29 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 Eq29.
Expressing the E expectation as in Eq29 adds an important nuance to the derivation of dismay from the T=R−E Law of Emotion of Eq8.
30.) 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.
31.) 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 consider 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. We shall have much more to say about the operational emotions after we explain meaningful information in a physical system as entropy in the next section. Those who have no interest or knowledge of entropy can skip the next section or two to get to the Section 7, which explains the function of the transitional emotions of excitement, relief, disappointment and dismay in our emotional machinery. And then goes on to show how the Law of Emotion derives an emotion based pricing Law of Supply and Demand in market economies, something that even the most ardent capitalist hater of MIT cannot deny.
5. A Reformulation of Entropy
Entropy is a gateway concept for understanding the human mind, the nature of thought as compressed information being much clarified by correctly understanding the nature of thermodynamic entropy. To explain problem phenomena like entropy, information and thought mathematically, though, we need to start by providing a new foundation for mathematics itself. Its details aside, the currently accepted foundation of mathematics is axiomatic set theory. Mathematicians have recognized a major problem with this for the last 80 years in axiomatic set theory violating Kurt Gödel’s incompleteness theorem, which says that any axiomatic structuring of mathematics is inherently incomplete and hence fundamentally incorrect.
Allowed, though, within the context of Gödel’s theorem is a foundation of mathematics which is empirical. And that is exactly where we will start to solve another central problem in science that has plagued it for over a century, and that is a clear understanding of entropy as a physical quantity. First let’s develop an empirical, really a quite simple thing to do.
When I open my eyes and look around while typing this out on a computer in the Texas Tech University library, I see different kinds of objects that include people, computers and overhead light fixtures and other kinds of things. I can specify what I see as a set of objects divided into subsets of different kinds with each kind having a countable number of objects in it, for example, let’s say 75 people, 200 computers, 100 overhead light fixtures and so on. This representation or mapping of my visual field is empirical in nature in depending on my observation of the environment around me. The different size and shape of each kind of object, though, presents a barrier to mathematical regularity. But that problem is readily remedied by taking all objects of all the distinguishably different kinds to be the same size and shape.
An example of such a set of unit objects, objects of the same size and shape, that are distinguishable so as to be understood as different kinds of unit objects, is this (■■■■, ■■■■, ■■■■) set of K=12 unit objects divided into N=3 distinguishable subsets on the basis of color, x_{1}=4 red objects in one subset, x_{2}=4 green objects in another and x_{3}=4 purple objects in a third subset, with the set as a whole describable in shorthand with the natural number set, (4, 4, 4). Elaborations of the unit object set are the basis for a new way of approaching the frontier problems of science, one of which is yet an intuitively clear sense of thermodynamics entropy.
Let us consider the unit object set in terms of its basic properties. The unit object set has K objects in it divided into N subsets with each subset containing x_{i} objects, i=1,2,...N.
32.)
For the (■■■■, ■■■■, ■■■■), (4, 4, 4), set, K=x_{1} + x_{2} +x_{3} = 4+ 4+ 4=12 objects. Note that each object in this unit object empirically developed set fundamentally distinguishable from every object. The first red object in (■■■■, ■■■■, ■■■■) is distinguishable from the second red object in (■■■■, ■■■■, ■■■■) in being observed to be in a different place. And, of course, from the way we developed the notion of the unit object set to begin with, some of the objects in the set are also distinguished from some other objects categorically or in kind in having different color.
One
way of describing a unit object set in a simpler, compressed, way is with the mean
or average number of objects in each subset of the set, μ, (mu).
33.)
For the K=12, N=3, (■■■■, ■■■■, ■■■■), set, μ=K/N=12/3=4. Describing this set in terms of its μ=4 mean uses just one number, the mean, and is simpler than specifying all of the x_{i} number of objects in each subset, (4, 4, 4), but also leaves out some information in the set. To see that clearly next consider the K=12. N=3, (■■■■■■, ■■■■■, ■), (6, 5, 1), set. It also has an average number of objects in each set of μ=K/N=12/3=4. But what is missing in describing a set with just its μ mean is how the K objects are distributed over the N subsets of the set. Certainly (■■■■■■, ■■■■■, ■), (6, 5, 1), is more unbalanced in its distribution than (■■■■, ■■■■, ■■■■), (4, 4, 4), which has no imbalance, but you couldn’t tell that from the μ=4 of both of them, which gives you no sense of their imbalance. The imbalance in the distribution of a unit object set can be measured by the variance of the set, σ^{2}, a statistical error measure that is the square of the standard deviation, σ, (sigma).
34.)
The variance of the N=3, µ=4, (6, 5, 1) set, (■■■■■■, ■■■■■, ■), is
35.)
Using the same formula of Eq3 determines the variance of the completely balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), to be σ^{2}=0, which denotes that it has no imbalance. And we see that the K=12, N=3, (■■■■■■■■■■, ■, ■), (10, 1, 1), set, which also a mean of μ=K/N=12/3=4 but greater imbalance than the (4, 4, 4) and (6, 5, 1) sets, has a greater variance as measures its imbalance of σ^{2}=18. The μ mean, a compressed, single number, representation of a set, leaves out the information of the distribution of a unit objects set. Often when a set is represented by its μ mean, it is accompanied by a statistical error measure of the distribution, whether as the σ^{2 }variance or the σ standard deviation. Thus we might describe (■■■■■■■■■■, ■, ■), (10, 1, 1), as having a μ=4 mean with a σ^{2}=18 variance or σ=4.24 standard deviation as gives some sense of the distributional imbalance in the set
Another most important property of a set is its diversity as specified
by Simpson’s
Reciprocal Diversity Index. Though introduced to science in 1948 by Edward Hugh
Simpson primarily as a measure of biological diversity, it is readily
understood as a general property of a unit object set. It is, indeed, a most
important property because it can represent the set in compressed form with
just one number that is a function of the μ mean and of the σ^{2} variance measure
of the set’s distribution. It is defined as a function of the K, N and x_{i}
parameters of a set we are familiar with as
36.)
For the N=3 color, (■■■■, ■■■■, ■■■■), set with x_{1}=4 red, x_{2}=4 green
and x_{3}=4 purple objects the diversity index is from Eq36
37.)
For a
balanced set like (■■■■, ■■■■, ■■■■), we see that the D diversity index is just the N
number of subsets in the set. From Eq36 we see the diversity of the N=6 balanced set,
(2, 2, 2, 2, 2, 2), (■■,
■■, ■■, ■■, ■■, ■■), to be D=N=6. And
for the N=2 subset, (6, 6), (■■■■■■, ■■■■■■) objects, we
calculate the diversity to be D=N=2. So in general for any balanced set with N
subsets,
38.) D = N (balanced)
From Eq36 we can also calculate the D diversity index of an unbalanced set like the (6, 5, 1), (■■■■■■, ■■■■■, ■), set.
39.)
For this (6, 5, 1) set and for all unbalanced sets the D diversity index is less than the N number of subsets in the set.
40.) D < N (unbalanced)
We can intuitively understand the D<N for unbalanced sets from the N=3, (6, 5, 1), (■■■■■■, ■■■■■, ■), unbalanced set by interpreting the x_{3}=1 object purple subset in the set to contribute only token diversity. Next we want to show that the single number D diversity index is a function of and includes both the μ mean and the σ^{2} variance measure of a set’s imbalance. We do that by first solving the σ^{2} variance of Eq3 for the summation term in it as
41.)
Then inserting this summation term into Eq32 obtains D via µ of Eq33 as
42.)
Both the µ mean and the D diversity are compressed representations of a number set. Their importance as such is better made clear with a larger unit object set like, in natural number set form, the N=10 set of (1, 2, 2, 3, 3, 3, 4, 4, 8, 10), whose mean is µ=4 and whose diversity, which includes the µ mean and the σ^{2} variance measure of set imbalance, is from Eq36, D=6.9. Representing the ten numbers in the set with the one number µ=4 mean or the one number D=6.9 diversity is a much more simple and succinct representation of the number set relative to listing all ten numbers in the set. In that sense, both the µ mean and the D diversity are generalizations of a number set, both of them simplified or compressed representations of sets that parallel the generalizations that our minds make of many object, many event, situations we experience as give a crisp mathematical sense of what we mean by a thought or an idea. As we shall see our emotions also come about as compressed information.
But for the moment we next want to use the D diversity index to clearly explain for the first time in science thermodynamic entropy, which has been a confusion and a mystery of sorts for the last 200 years. We take up this task for two primary reasons. One is that a mathematical structure that is developed in the exercise for a thermodynamic system that gives an additional, fuller sense of a mathematical generalization that explains thoughts and ideas. This is also the gateway to explaining emotion as a special kind generalizations of the mind. Another is the very solving of the difficult entropy problem, which greatly adds to the authority of the unit object set mathematics as matters to acceptance of its understanding of emotion, a very difficult problem because of the ephemeral nature of human feeling that is further greatly complicated by adherence to erroneous religious and philosophical understandings of emotion, the origin of sexual feeling, for example, ascribed to the Devil as temptation to sin.
To apply the D diversity to the task of explaining entropy, we first want to make two important, if simple and obvious, points. The first has to do with the distinction between things. Consider the K=12 objects in (■■■■■■, ■■■■■■). As we introduced above, on the one hand they are distinguished by color. A red object, ■, is readily intuitively distinguished from a green object, ■. This is called categorical distinction or distinctions of kind. But we also, in actual experience, between two objects of the same kind. We do this in a very intuitive way in such being in different places. Consider two red ink disposable ball point pens out of the same fresh package, one of which I am holding in my right hand, and one in my left. Clearly these are two different objects even if of the same kind. From that perspective, we might represent a set of 4 red objects, (■■■■) as (abcd) to make it clear that though they are all red objects, objects of the same kind, they are yet fundamentally distinct from each other.
And we also want to generalize on the nature of sets and how they can be divided into subsets to include the placement of objects into different containers as subsets. Thus we may think of dividing up (abcd) thought of as K=4 red candies between two children, Jack and Kill, diagrammed as (a, bcd), as a unit object set with K=4 objects in it divided into N=2 subsets with x_{1}=1 candy for Jack and x_{2}=3 candies for Jill. Note that this unit object set has from Eq33, a mean of µ=K/N=4/2=2 pieces of candy on average for each kid and a diversity from Eq5 of D=1.6.
Now let’s consider a random or equiprobable
distribution of K=4 red candies to the N=2 children, Jack and Jill, as done,
say, by their grandfather tossing the candy blindly over his shoulder, one at a
time to the kids. Such a random distribution is understood as equiprobable
because each of the N=2 children has an equal, P=1/N=1/2, probability of
getting a candy thrown on any given toss.
There are
Ω=N^{K}=2^{4}=16 permutations or different
ways of candy distribution possible as given in the {braces} below with the
candies Jack gets on the left of the comma in the {braces} and the candies that
Jill gets listed to the right of the comma.
Ω=16 permutations 
{abcd, 0} 
{abc, d} 
{ab, cd} 
{a, bcd} 
{0, abcd } 


{abd, c} 
{ac, bd} 
{b, acd} 



{adc, b} 
{ad, bc} 
{c, abd} 



{bcd, a} 
{bd, ac} 
{d, bca} 




{bc, ad} 





{cd, ab} 


States 
[4, 0] 
[3, 1] 
[2, 2] 
[1, 3] 
[0, 4] 
Permutations per state 
1 
4 
6 
4 
1 
Probability of a state=permutations per state/Ω 
1/16 
4/16=1/4 
6/16=3/8 
4/16=1/4 
1/16 
Number set notation of a state 
x_{1}=4, x_{2}=0 
x_{1}=3, x_{2}=1 
x_{1}=2, x_{2}=2 
x_{1}=1, x_{2}=3 
x_{1}=0, x_{2}=4 
Table 43.The Ω=16 Permutations and Related Properties of the Random Distribution of K=4 Candies to N=2 Children
All of the Ω=16 permutations are equiprobable, the probability of each permutation
being 1/Ω=1/K^{N}=K^{N}=1/16. So if grandpa repeated his
random tossing of K=4 candies to the N=2 grandkids 16 times, on average
each of the Ω=16 permutations shown in Table 43 on the 1^{st}
through 6^{th} lines in the table would occur 1 time.
The Ω=N^{K}=16 permutations are grouped into W=5 states, [4, 0], [3, 1], [2, 2], [1, 3] and [0, 4] on the 7^{th} line with each state having a given number of permutations as listed on the 8^{th} line in the table. The [1, 3] state consists, for example, of 4 permutations as tells us that there are 4 ways that Jack can get 1 candy and Jill, 3.
And on the 9^{th} line in the table is the probability of each state coming about. For example, the probability of each child getting 2 of the K=4 candies tossed, the [2, 2] state, is 6/16=3/8=.375. And on the 10^{th} line in the table are the number set notations of the states, x_{1} being the number of candies that Jack gets and x_{2},_{ }the number that Jill gets in 3 each state.
_{ }
The number of states for a random distribution of K=4 candies to N=2 kids is W=5, namely, the [4, 0], [3, 1], [2, 2], [1, 3] and [0, 4] states listed on the 7^{th} line in the table. There is a textbook shortcut formula for calculating the W number of states for any distribution of K objects over N containers.
44.)
This formula calculates the W=5 number states of the K=4 candy over N =2 kids random
distribution in Table 43 as
45.)
The formula is especially useful for calculating the W number of states of very
large K over N distributions, as, for example, from grandpa distributing K=145 candies
randomly to N=25 kids in the neighborhood, whose W number of states is from Eq44,
W=1.45EXP31. Now we want to show that the diversity of the states has an
interesting functional relationship to the W number of states.
It is intuitively obvious that some of the W=5 states in the K=4 over N=2 candy bars are more diversely distributed than others. The [2, 2] balanced state of both of the children getting the same number of candies in a random toss of K=4 candies to them has greater diversity than the unbalanced [1, 3], [3, 1], [0, 4] and [4, 0] states. We can measure the diversity of these states from Eq11 with the σ^{2} variance of a state, expressed as a number set, calculated from Eq44 and the µ mean from Eq43. The variance of the [3, 1} state of the K=4 over N=2 distribution, x_{1}=3 and x_{2}=1, is σ^{2 }=1, its µ mean is µ=K/N=2 and its diversity from Eq42,
46.)
The µ mean of all of the W=5 states of the K=4 over N=2 distribution is µ=K/N=4/2=2 and their σ^{2} variances and D diversities from Eqs34&42 are
State 
Mean

Variance σ^{2} 
Diversity

[4, 0] 
2 
4 
1 
[3, 1] 
2 
1 
1.6 
[2, 2] 
2 
0 
2 
[1, 3] 
2 
1 
1.6 
[0, 4] 
2 
4 
1 
Table 47. Set Properties
of the W=5 States of the K=4 over N=2 Distribution
The
average of the σ^{2} variances of the W=5 states in the K=4 over
N=2 distribution is a probability weighted average that weights the
variance of each state by the probability of that state occurring as listed on
the 9^{th} line in Table 43.
State 
Variance, σ^{2} 
Probability of the State 
Probability Weighted Variance 
[4, 0] 
4 
1/16 
(4)(1/16)=1/4 
[3, 1] 
1 
¼ 
(1)(1/4)=1/4 
[2, 2] 
0 
3/8 
(0)(3/8)=0 
[1, 3] 
1 
¼ 
(1)(1/4)=1/4 
[0. 4] 
4 
1/16 
(4)(1/16)=1/4 



Sum is the average variance=σ^{2}_{AV}=1 
Table 48. The Average Variance, σ^{2}_{AV}, of the W=5 States of the K=4 over N=2 Distribution
The average variance is specified as σ^{2}_{AV}, which for
the K=4 over N=2 equiprobable distribution is σ^{2}_{AV}=1.
Now let’s modify D in Eq43 as a function of σ^{2} so we can
calculate an average diversity, D_{AV}, as a function of the average
variance, σ^{2}_{AV}.
49.)
This calculates the average diversity, D_{AV}, of the K=4 over N=2 distribution from its σ^{2}_{AV}=1 average variance obtained in Table 48 as
50.)
We obtain a simpler formula for the D_{AV} average diversity of a K over N equiprobable distribution by developing a shortcut formula for the σ^{2}_{AV }average variance from a textbook expression for the variance of a multinomial distribution (see Wikipedia). For the general case that expression is
51.)
This simplifies for the equiprobable case in which the P_{i} term is P_{i}= 1/N as tells us that each the N containers in a K over N distribution has an equal, 1/N, chance of getting any one of the K objects distributed. For example, we saw such a P_{i}=1/N probability for the K=4 candy over N=2 children equiprobable distribution to be P=1/N=1/2. This P_{i} =1/N probability simplifies the variance formula of Eq51 for the equiprobable case to
52.)
This variance of an equiprobable multinomial distribution is just the average variance of an equiprobable distribution, σ^{2}_{AV}, same thing. Hence we can write the above as
53.)
We demonstrate the validity of Eq53 by calculating the σ^{2}_{AV}=1 average variance of the K=4 over N=2 distribution obtained in Table 46 from Eq53 as
54.)
And now we derive a simple formula for the average diversity, D_{AV}, from Eqs49&53.
55.)
And we demonstrate its validity by calculating the D_{AV}=1.6 average diversity of the K=4 over N=2 distribution from it as
56.)
Now
we want to show that the D_{AV} average diversity of the W states of a
K over N equiprobable distribution is for large K and N distributions near
perfect directly proportional to the logarithm of the W number of states,
lnW, the formula for which is given below from Eq44 as
57.)
For the K=145 over N=25 distribution, lnW=71.75. For the very large K and N equiprobable distributions that have the near perfect direct proportionality to D_{AV} we want to demonstrate, it is easier to calculate lnW for large K and N using Stirling’s Approximation. It approximates the ln (natural logarithm) of the factorial of any number, n, as
58.)
This approximation is excellent for large n. For example, 170! =706.5731 it well approximated with the above as 706.5726. Stirling’s Approximation for lnW in Eq26 takes the form of
59.)
Now
let’s use this formula for lnW to compare the lnW of some randomly chosen large
K over N equiprobable distributions to their D_{AV} average diversity
of Eq55.
K 
N 
lnW 
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 60. The lnW
and D_{AV} of Large Value K over N Distributions
The
Pierson’s correlation coefficient between D_{AV} and lnW for these
distributions is .9995 indicating a functional relationship very close to perfect
direct proportionality as can be appreciated visually from the near straight
line scatter plot below of the D_{AV} versus lnW values in Table 60.
Figure 61. A plot
of the D_{AV} versus lnW data in Table 60
This high .9995 correlation between lnW and D_{AV} is greater the greater the K and N values, K>N, of the distribution and for all manner of randomly selecting the distributions to be tested. For values of K on the order of EXP20, the correlation for K>N distributions is .9999999≈1 indicating effectively a perfect direct proportionality between lnW and D_{AV}. It should be emphasized now that though we developed this relationship for the random distribution of K candies over N children, this pure mathematical relationship applies to the random distribution of any kind of K fundamentally distinct unit objects over any kind of N distinguishable subset containers of these K units.
Of particular interest for science is the application of it to thermodynamic systems given the presence of lnW in Boltzmann’s famous equation for entropy honored by inscription on his tombstone, which in modern notation is
62.) S=klnW
It has caused confusion for myriad students and professionals alike since it was first introduced to science over a hundred years ago. This confusion is quite cleared up by understanding entropy in terms of the equivalence of the lnW term in S=klnW to D_{AV}. A thermodynamic system of N gas molecules at a fixed temperature and, hence, with a fixed K number of discrete energy units, develops, from the random collisions of the molecules as they move about in a container of fixed volume, a random distribution of the K energy units over the N molecules. As such, the K candies over N children random distribution provides a perfect mathematical model for it. Rather than a new state of the random distribution of K energy units over N molecules coming about from something akin to the repeated blind toss of K candies to N children, it comes about from repeated molecular collisions that transfer the energy units of some molecules to others in a random way.
To apply to randomly distributed thermodynamic systems what we developed for randomly distributed candies, we must use the sense of a set as we developed it empirically, namely with its K unit objects being fundamentally distinguishable from each other. This is contrary to one of the basic axioms of Boltzmann statistical mechanics, which is of indistinguishable discrete energy units. That is, we substitute for that our sense of the discrete energy units being distinguishable. This is hardly farfetched considering that the energy units reside in or on the individual N molecules of the thermodynamic system, which even Boltzmann considered to be distinguishable. That is, if two energy units reside on distinguishable molecules, they can certainly be understood to be distinguishable in their residing in different places.
So far we have seen that this assumption that is in contradiction to Boltzmann physics is reasonable from the high correlation of the diversity based entropy we derived to the Boltzmann S entropy. If the Boltzmann entropy is correct from its fit to laboratory data, so also must be, from the same empirical perspective, the diversity based entropy even if the elementary assumptions for the two as regards distinguishable versus indistinguishable energy units are mutually contradictory. Further that fact, makes it clear that though there is a high quantitative correlation between the two, they cannot both be correct. That is, they cannot be two valid and mutually supportive ways of understanding the same phenomena, entropy.
A
powerful argument that diversity based entropy model is the proper
understanding of entropy is developed by our first considering now another
property of a random or equiprobable distribution that is related in a simple
way to the W states of a thermodynamic system of Eq44. This property of a
distribution is called a configuration. A configuration is the collection
of all the states in a distribution that have the same number set
representation. For example, the states of [0, 4] and [4, 0] of the K=4 over
N=2 distribution have the same number set, (4, 0), understood as one of the configurations
of the K=4 over N=2 distribution. Note that we write a configuration in
parenthesis, (4, 0), in contrast to the brackets used for states, as in the [4,
0] and [0, 4] states of the (4, 0) configuration. The
K=4 over N=2 equiprobable distribution of Table 43 has 3 configurations, (4,
0), (3, 1) and (2, 2), which the W=5 states of the distribution of Table 43 belong
to as
The 3 configurations of the K=4 over N=2 Distribution 
(4, 0) 
(3, 1) 
(2, 2) 
The W=5 states of the K=4 over N=2 Distribution 
[4, 0] 
[3, 1] 
[2, 2] 
[0, 4] 
[1, 3] 

Table 63. The Configurations of the K=4 over N=2 Distribution and Their
States
A
look back to Table 43 makes it clear that a configuration has the same σ^{2}
variance and D diversity index as the states that comprise it.
Configuration 
States 
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 64. The Variance, σ^{2}, and Diversity, D, of the Configurations of the K=4 over N=2 Distribution
Now note carefully in the table that the average variance of σ^{2}_{AV}=1 of the K=4 0ver N=2 distribution from Table 48 and Eq54 and its average diversity of D_{AV}=1.6 of Eq50 are exactly the same respectively as the σ^{2}=1 variance and D=1.6 diversity of the (3, 1) configuration of this distribution as seen in Table 64. On that basis the (3, 1) configuration is a compressed representation of the entirety of the three configurations, (4, 0), (3, 1) and (2, 2), of the K=4 over N=2 distribution and as such is called the Average Configuration of the distribution.
The Average Configuration is a quintessential example of compressed information in its being a compression of all of the configurations of a random distribution. Earlier we saw that the µ mean is a compressed representation of a set of N numbers, as with the K=24, N=6, (6, 4, 2, 1, 5, 6), number set being represented in compressed or reduced form by its μ=K/N=4 mean. And we made mention that the D diversity was also a compression of a number set, though with more information in it in its containing, as the mean does not, a measure of the distributional imbalance in a set in the σ^{2} variance in the D diversity seen in Eq42.
In an analogous way the Average Configuration of an equiprobable distribution is a compression of the distribution’s many configurations in including a measure of the diversities of all of the distribution’s configurations in its D diversity index being the D_{AV} average of the diversities of all of the configurations. In that sense the Average Configuration is a mathematical generalization that compresses much information into a single piece of information. We will consider how it acts as a general model for the generalizations the human mind encodes experience with in the next section.
For now, though, let’s stick to explaining how the Average Configuration represents in compressed form the entire equiprobable distribution of K energy units over N molecules in a thermodynamic system. Consider a system of N=2 molecules with K=4 energy units distributed over them as modeled by the random candy tossing dynamic in Table 12. As collisions occur between N=2 gas molecules moving about in a container of fixed volume, there are random energy transfers that happen between the molecules and over 16 collisions, on average, we would expect, in parallel to the 16 candy toss dynamic specified in the paragraph just following Table 43, the [4, 0] state to appear 1 time, the [3, 1] state 4 times, the [2, 2] state 6 times, the [1, 3 state], 4 times and the [0, 4] state 1 time, .
In this process the (3, 1) Average Configuration is what is sensed by a sensing device that gathers information on the system slower than the assumed more rapid collisions that take place. That is, the Average Configuration of the system is the thermodynamic system as measured. This conclusion of the mathematical argument can be tested empirically because observed in an actual thermodynamic system is the MaxwellBoltzmann energy distribution pictured below.
Figure 65. The MaxwellBoltzmann Energy Distribution
The K=4 energy units over N=2 molecule distribution has too few K energy units
and N molecules for its Average Configuration of (3, 1) to show any resemblance
to the MaxwellBoltzmann distribution of Figure 65. We need equiprobable
distributions with higher K and N values to show it starting with a K=12 energy
units over N=6 molecule distribution. To find its Average Configuration we
first calculate from Eq53 the σ^{2}_{AV} average variance of
the distribution, which is a defining property of it.
66.)
The Average Configuration of the K=12 over N=6 distribution is a configuration that has this σ^{2}_{AV} value 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 their σ^{2} measures to find one that has the same value as σ^{2}_{AV} =1.667. It is the (4, 3, 2, 2, 1, 0) configuration, which is the Average Configuration of the distribution on the basis of its having a variance of 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 67. 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 65 is a bit of a stretch, though it might be characterized as a very simple, very choppy MaxwellBoltzmann distribution. 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 Eq53, 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 68. 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 Eq53, 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 69. 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 Eq53, 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 70. 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
We are at this level considering K and N values high enough to show a good resemblance
to the classical MaxwellBoltzmann distribution. And all of the other
configurations of this K=145 energy unit over N=30 molecule distribution also bear
a reasonable resemblance to the MaxwellBoltzmann of Figure 65. As we
progressively increase the K and N values of distributions, the plot of their
energy per molecule versus the number of molecules with that energy more and
more approaches and eventually fits the shape of the realistic
MaxwellBoltzmann distribution of Figure 65.
This demonstration of the Average Configuration having the shape of the empirical MaxwellBoltzmann energy distribution in conjunction with the .9995 Pearson’s correlation of D_{AV} to lnW supports an understanding of entropy as a diversity based physical quantity to be reasonable. The next question to ask is then whether diversity based entropy is the correct form of entropy with the lnW based Boltzmann S entropy taken to be incorrect; or whether both formulations of entropy are equally valid with each giving different but valuable information on what entropy is. It is easy to show the possibility of both being correct to be untenable given that the two entropy formulations, diversity based and Boltzmann, are based on two contradictory basic assumptions as to the distinguishability of the K discrete energy units in a thermodynamic system, the Boltzmann argument assuming they are indistinguishable and the diversity argument assuming they are distinguishable. Only one formulation, hence, diversity or Boltzmann, can be correct.
Before we further argue which, we will next investigate another diversity index that also has a very high Pearson’s correlation with Boltzmann S=klnW entropy and as such must also be considered as an alternative to the Boltzmann S entropy. To develop this new diversity index we begin by expressing the μ=K/N mean of a number set of Eq2 in terms of K as expressed in Eq1.
71.)
Next we will express 1/N in the above in terms of the weight fraction of a number set. It is just a fractional measure of the x_{i} of a number set as the ratio of the x_{i} number of unit objects in each of the N subsets in a set to the K total number of unit objects in the set.
72)
For the K=12, N=3, (6, 5, 1), number set that has x_{1}=6, x_{2}=5 and x_{3}=1, the weight fractions of the set are p_{1}=x_{1}/K=6/12=1/2, p_{2}=x_{2}/K=5/12 and p_{3}=x_{3}/K=1/12. We can write these p_{i}^{ }weight fractions of (6, 5, 1) in shorthand form as (1/2, 5/12, 1/12). Note that the p_{i} weight fractions of a number set necessarily sum to one.
73.)
The weight fractions of (6, 5, 1) as (6/12, 5/12, 1/12) sum to one. The (1/N) term in Eq40 can now be shown to be the average weight fraction of a number set. We develop the average of a number set’s_{ }weight fractions in exact parallel to the way we develop the μ mean or arithmetic average of a number set, namely by adding up the p_{i} weight fractions, which sum to one (1), and then dividing that sum of 1 by the number of p_{i} in the set, which is N. For example, the weight fractions of the N=3, (6, 5, 1), set are p_{1}=6/12, p_{2}=5/12 and p_{3}=1/12, which sum to 1. Then dividing this sum of 1 by N obtains 1/N as the average weight fraction, denoted as.
74.)
This appreciation of 1/N allows us to express the μ mean of Eq40 in terms of the average weight fraction,, as
75.)
This form interprets the μ mean of a number set as the sum of “slices” of x_{i} with each “slice” the “thickness” of, the average weight fraction. This form for μ computes the μ=K/N=12/3=4 mean of the K=12, N=3, (6, 5, 1), number set as
76.)
This alternative formulation of the μ mean or arithmetic average of a number set is the first step in obtaining the aforementioned new diversity index. The second step entails our introducing a new kind of number set average called the biased average, φ, (phi). In parallel to the μ arithmetic average of a number set as the ratio of K to the N number of subsets in a set as μ=K/N, the φ biased average is defined as the ratio of K to the D diversity of a number set as
77.)
For the K=12, (6, 5, 1), set, which has D=2.323 from Eq8, φ=K/D=12/2.323=5.167. Note that this φ=5.167 biased average of (6, 5, 1) is greater than its μ=4 arithmetic average. Next we want to express the D Simpson’s Reciprocal Diversity Index of Eq36 via Eq72 as a function of the weight fractions of a set.
78.)
This has us specify φ=K/D of Eq77 in a way parallel to μ in Eq71 as a function of the p_{i} weight fractions of a number set of Eq78 as
79.)
This has us interpret the φ biased average as the sum of “slices” of x_{i} with each “slice” the “thickness” of p_{i}, that is, of the thickness of the actual p_{i} weight fraction rather than of the =1/N average weight fraction, as was the case for μ in Eq71. The above form for φ in obtains the φ=5.167 biased average of (6, 5, 1) as
80.)
This makes it clear how the φ biased average is biased in its exaggerating the contribution of the larger subsets in a set in this average. This third step in our obtaining the new diversity index that underpins the correct diversity based entropy and correct microstate form of temperature is the development of another biased average of a number set called the square root biased average, ψ, (psi). In parallel to the φ biased average as the sum of slices of the x_{i} of a set of thickness p_{i} in Eq79, the ψ square root biased average is the sum of slices of the x_{i} of a set of thickness, p_{i}^{1/2}, the square root of the weight fractions of a number set. In parallel to Eq79 for the φ biased average, we introduce the ψ square root biased average functionally as
81.)
We tagged a question mark onto ψ in this introduction to it to indicate that there is something not quite right with this expression for ψ. What isn’t right is that the p_{i}^{1/2} weightings of the x_{i} of the set don’t add up to 1 as they must to form any kind of an average of the x_{i }of a set, this proviso being in the intrinsic nature of what an average is. This problem is well illustrated with the (6, 5, 1) set, which while its p_{i} weight fractions of (1/2, 5/12, 1/12) do add up to 1, the p_{i}^{1/2} square roots of its p_{i} weight fractions, (.7071, .6454, .2887), don’t add up to 1. Rather their sum is .7071+.6454+.2887=1.6412. Because they don’t add to 1 they can’t be used to weight the x_{i} in forming an average of them.
This problem is readily resolved by normalizing the p_{i}^{1/2} to get them to add up to 1. This is done by dividing each of the p_{i}^{1/2}, (.7071, .6454, .2887), by the 1.6412 sum of the p_{i}^{1/2}. This obtains normalized set of p_{i}^{1/2} of (.4308, .3933, .1759), which do add up to 1 and, hence, properly weight the x_{i} of the (6, 5, 1) set to obtain its ψ square root biased average as
82.) ψ = (.4308)(6) +(.3933)(5) + (.1759)(1)= 4.727
Note that this ψ=4.727 square root biased average of (6, 5, 1) is less than the μ=4 arithmetic average of the set, but not as less as the φ=5.167 biased average of (6, 5, 1) of Eq49. Also note that the sum of the p_{i}^{1/2} that divides each the p_{i}^{1/2} to normalize them is expressed in general form as
83.)
This function for the sum of the p_{i}^{1/2} revises the ψ{?} questionable function we introduced for ψ in Eq81 by dividing its summation term to obtain the ψ square root biased average correctly as
84.)
And next we express ψ from the above in an alternative way via the p_{i}=x_{i}/K weight fraction relationship of Eq72 as
85.)
Now the φ=K/D biased average of Eq46 solved for D makes clear that the D diversity index is expressible as the ratio of the K number of unit objects in a set to its φ biased average.
86.)
This suggests, in parallel, that the ratio of K to the ψ square root biased average of Eq85 is also a diversity index, the Square Root Diversity Index, G
87.)
(Do not confuse the G square root diversity index with the G free energy of classical thermodynamics.) Every one of the W states of a K energy unit over N molecule random energy distributed thermodynamic system has a G diversity index and the system as a whole has an average G diversity index, G_{AV}, which is also the G of its Average Configuration. We will show next that this G_{AV} also has a very high correlation to the lnW term in Boltzmann’s S=k_{B}lnW entropy. To show this correlation of G_{AV} to lnW, though, is not as straightforward as was the correlation of D_{AV} to lnW because G_{AV} is not a simple function of the K energy units and N molecules of a thermodynamic system as D_{AV }in Eq55 as D_{AV}=KN/(K+N−1).
Because G_{AV} is the G diversity index of the Average Configuration much as D_{AV} was the D diversity index of the Average Configuration, we can obtain G_{AV} for the K over N distributions for which we know the specific number set form of the Average Configuration, as we do for the K over N distributions in Figures 6770. We list these G_{AV} below along with the lnW values of those Average Configurations obtained from Eq57. And we also include their D_{AV} diversity indices for comparison sake.
Figure 
K 
N 
lnW 
D_{AV} 
G_{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 88. The lnW, D_{AV} and G_{AV} of Distributions in Figures 6770
The correlation between the lnW and D_{AV} of the above random distributions
is .997. Though quite high, this is less than the .9995 correlation between lnW
and D_{AV} we saw in Table 60 for large K and N distributions, the difference
attributed to the fact that the degree of correlation is a function of the
magnitude of the K and N parameters. The Pearson’s correlation between lnW and
G_{AV }for the distributions in Table 88 is also quite high as .995, not
much different than the high .997 correlation between lnW and D_{AV}
for these distributions. As the correlation of D_{AV} with lnW goes from
.997 for the low value K over N distributions in Table 88 to .9995 for the high
value K and N distributions back in Table 60, so it is reasonable to assume
from the closeness in the lnW correlations for D_{AV} and G_{AV}
of .997 and .995 respectively that for high value K and N distributions the
correlation of G_{AV} to lnW would also be in the range of .999 and
greater yet for greater K and N values, approaching 100%.
This tells us from both D_{AV} and G_{AV} having a very high correlation to lnW that either diversity function, D_{AV} or G_{AV}, could underpin a diversity based entropy that replaces Boltzmann’s S=k_{B}lnW entropy. To answer this question we see that we can specify the D_{AV} and G_{AV} diversities by extension from Eqs86&87 respectively as
88a.)
89.)
G_{AV} in the above is the average of the G square root diversity indices of all configurations (and, alternatively, W states) of the thermodynamic system and as such the G of the system’s Average Configuration. And ψ_{AV }is the biased square root average energy per molecule of the Average Configuration, also understandable as the average of the ψ biased average of all configurations (or W states) of the system. Now we will argue that this ψ_{AV} is the proper microstate temperature of a thermodynamic system as
89a.)
In standard physical theory, via the equipartition theorem, temperature is taken to be a simple linear function of the mean kinetic energy, μ=K/N, of a thermodynamic system where K is the total number of energy units and N the number of molecules. But a μ=K/N microstate temperature must be seriously questioned from the reality of how temperature is actually physically measured with a thermometer.
Let us understand the K energy units of a thermodynamic system of N gas molecules to be distributed over them with energy units, x_{i}, i=1,2,…N, for each of the N molecules that move about in a container of fixed volume. Because the molecular energy units are divided equally from the equipartition theorem over kinetic, rotational and vibrational energy, the velocity of the molecules, as a function of the kinetic energy, is proportional to the square root of the x_{i} number of energy units each molecule has.
This snapshot of the system sees each of the molecules collide with the thermometer that measures the temperature of the system at a frequency equal to the molecular velocity, which is proportional to the square root of the x_{i} number of energy units on the molecule. Hence the smaller energies of the slower moving molecules in the MaxwellBoltzmann energy distribution of Figure 65 collide with the thermometer less frequently and are, hence, recorded less frequently as part of the temperature than the higher energies of the faster moving molecules that collide with the thermometer and are recorded more frequently.
This necessarily specifies temperature to be an average of molecular energies weighted toward the higher energies of the faster moving molecules because of their greater velocities that cause them to have a higher frequency of collision with the thermometer and, hence, to be measured more often by it than the lower energy, slower moving molecules. As the velocities of the molecules are directly proportional to the square root of the x_{i} energy of the molecules, the true average molecular energy that is temperature is the square root of the x_{i} energy weighted average, which is the square root biased average energy per molecule of the thermodynamic distribution, ψ_{AV}.
This idea of microstate temperature as the ψ_{AV} square root biased energy per molecule average may seem so different from the theoretically accepted µ arithmetic energy per molecule as to be immediately rejected. But the two averages are actually very close in value for systems of K>>>N systems found at room temperature that comprise the bulk of experimental data. This can be readily deduced from D_{AV}=KN/(K+N−1) of Eq55 for when K>>>N, we see that N is very close to 0 in the denominator and D_{AV}, hence, very close to N in D_{AV}=KN/(K+N−1), which makes very close in value to µ . And as the ψ square root biased average was seen to be closer in value yet to µ than we can also say that ψ_{AV} is very close to µ as to be near indistinguishable from it at room temperature and, hence, entirely reasonable as microstate temperature.
From the above arguments, we accept the diversity of the distribution as a function of the ψ_{AV} temperature to be G_{AV}=K/ψ_{AV}, which has us choose the G_{AV} diversity index as the proper diversity candidate to replace Boltzmann’s S entropy. Next we will give further arguments for the suitability of G_{AV} as entropy and for its superiority to S=klnW. First we see that G_{AV}=K/ψ_{AV }is quite reasonable as entropy from a dimensional analysis of G_{AV} as energy, K, divided by temperature, ψ_{AV}, in Eq89 as perfectly fits the dimensions of entropy in the macroscopic Clausius definition of entropy in differential form as
90.)
In it, S as entropy is Q heat, dimensionally energy, divided by T temperature. The G_{AV} diversity formulated entropy has these same dimensions of energy divided by temperature. Now we want to show how entropy both as S and as G increases in thermal equilibration as a simple manifestation of the 2^{nd} Law of Thermodynamics, spelled out below in difference form as
90a.) ΔS > 0
The system we will use to illustrate the 2^{nd} Law is comprised of two subsystems. Subsystem A has K=12 energy units divided over N=3 molecules. And Subsystem B has K=84 energy units divided over N=3 molecules. We will understand the equilibrium point of both N=3 subsystems to be, upon thermal contact, when they each have the same number of K energy units as transforms both to K=48 energy unit over N=3 molecule subsystems. Using an “i” subscript for the “initial” thermodynamic state of a subsystem and an “f” subscript for the “final” or equilibrium state of a subsystem and taking the liberty of expressing temperature for these supersmall subsystems as µ=K/N obtains: µ_{Ai} = 4, µ_{Af} =16; µ_{Bi}=28, µ_{Bf} = 16. To determine the change in entropy for the thermal equilibration has us next express that classical form for entropy change of in Eq90 as
90b.) ΔS=Cln(µ_{f}/µ_{i})
In the above ln is the natural logarithm and C a positively signed constant. This obtains
90c.) ΔS_{A}= 1.39C; ΔS_{B}= –.56; ΔS = ΔS_{A} + ΔS_{B} = .83C
Given C as a positively signed constant, this tells us from ΔS = .83C that the entropy change is positive as confirms the 2^{nd} Law of Thermodynamics. But it doesn’t tell us in any intuitively sensible way why the entropy increase happens. Now let’s go to a G diversity entropy analysis. From Eq53 we see that the average variance of K=12 energy unit over N=3 molecule Subsystem A is σ^{2}_{AV }=2.667 and its Average Configuration, (6, 4, 2). And for Subsystem B of K=84 energy units divided over N=3 molecules, from its Eq53 average variance of σ^{2}_{AV }=18.667 we see that the Average Configuration is (34, 26, 24).
The G diversity based analysis considers the two subsystems as one whole system once thermal contact is made between them. At the very beginning of thermal contact the whole system is specified as (6, 4, 2, 34, 26, 24). And at thermal equilibrium it is its Average Configuration obtained from its Eq53 average variance of σ^{2}_{AV }=13.333 to be (11, 14, 15, 16, 17, 23). The G diversity of the initial state of the whole system of (6, 4, 2, 34, 26, 24) has from Eq87 a value of G_{i}=4.39; and that of the final, equilibrium, state is G_{AV}=G_{f }=5.85. The change in diversity is, hence,
90d.) ΔG = G_{f} – G_{i} = 5.85 – 4.39 = +1.46
We see that this measures the change in entropy as a positive change or increase as also fits the 2^{nd} Law of Thermodynamics. Note that understanding the 2^{nd} Law as an increase in energy diversity or energy dispersal is quite intuitively sensible. For that reason we will rewrite the 2^{nd} Law in terms of it as
90e.) ΔG > 0
Note that we could also express this thermal equilibration microscopically in terms of the change in lnW. From Eq57 we calculate (lnW)_{Ai}=4.51, (lnW)_{Bi}=8.20 and (lnW)_{Af}=(lnW)_{Bf}=7.11. This calculates the change in entropy for the A and B subsystems and for the system as a whole as
91f.) (lnW)_{Af} – (lnW)_{Ai}=7.11 – 4.51 = 2.60; (lnW)_{Bf} – (lnW)_{Bi}= 7.11 – 8.20 = –1.09; Δ(lnW)=[ (lnW)_{Af} – (lnW)_{Ai}] +_{ } [(lnW)_{Bf} – (lnW)_{B}] = +1.51
Again the change in entropy measured by lnW is positive, an increase, as fits the 2^{nd} Law of Thermodynamics. But what it means physically is anybody’s guess. On the other hand, the qualitative sense of entropy as energy dispersal is entertained in a number of Wikipedia articles on entropy including Entropy, (energy dispersal). The article states that though energy dispersal, aka diversity, is qualitatively sensible, there is no mathematics of it. But there is now in the above rendition of entropy in terms of G diversity, which is just another term for dispersal.
A brief review of the salient points of both formulations of entropy make clear why it is that the diversity measure is the correct measure. The most obvious is Boltzmann’s erroneous sense of what his indistinguishable energy units are. Distinction is a very subtle concept. We don’t see distinction in our visual field. Rather we see by distinguishing things. A related major difficulty in understanding distinction is that it comes in two flavors, both very important. Consider the (■■■■, ■■■■, ■■■■) set of objects we introduced this section with. One kind of distinction we make automatically is between the different colored subsets in the set. That is, we distinguish ■■■■ from ■■■■ and ■■■■. And we distinguish between some of the objects in the set and others on the basis of color as with distinguishing between ■ and ■. These distinctions on the basis of color are called categorical distinctions or distinction of kind. They extend really to any two objects or groups of objects that we think of as different kinds of things.
Some objects are categorically indistinct or indistinguishable as with ■ and ■, the first two objects in the ■■■■ subset of (■■■■, ■■■■, ■■■■). One reason this division we are making between categorically distinguishable objects and categorically indistinguishable objects is because the two have quite different mathematics. Their statistical functions are different. Specifically, without getting into the details, which are available in myriad textbooks, there is a combinatorial statistic for categorically distinguishable objects and a quite different combinatorial statistic for indistinguishable objects.
This division of two types of groups of objects, categorically distinguishable and categorically indistinguishable, extends all the way down to the molecular level. Consider six noble gas atoms, He (Helium), Ne (Neon), Ar (Argon), Kr (Krypton), Xe (Xenon) and Rn (Radon). These are categorically distinct. They are different kinds of atoms. If I could hold them in my hands and distribute or arrange them in three different baskets in various ways, the number of ways is determined by the combinatorial statistic for categorically distinguishable objects. Now consider a group of six He (Helium) atoms. The number of observably different ways I could distribute or arrange them in three baskets is determined by a different combinatorial statistic, one for indistinguishable objects.
But in hard material fact, each of the six He (Helium) atoms is different than the others. Let’s go back to (■■■■, ■■■■, ■■■■) for a minute. While the first two red objects in the red subset are categorically indistinct, they are most certainly distinguished from each other by us in being in different places. This is called in contrast to categorical distinction as between different colored objects, fundamental distinction. All six He (Helium) atoms are fundamentally distinct from each other both because they are materially different atoms and because of the most obvious criteria of their being in different places at any moment in time.
Now there are two statistical considerations we can have towards are group of six He (Helium) atoms. We can treat them as categorically indistinct and use that combinatorial statistic to describe them statistically. Or we can treat them as fundamentally distinct, in which case we treat them with the very same combinatorial statistic used for categorically distinct objects. Very often when the statistics of objects have bearing on their physical dynamics, the objects are treated as being materially or fundamentally distinct. And that’s exactly what Ludwig Boltzmann does (or did) for the molecules he uses to develop his statistical mechanics and his S=klnW entropy function. To wit, the Avogadro’s number of He (Helium) atoms in a mole of Helium are treated mathematically by Boltzmann as being distinguishable. Indeed, that’s one of the foundational axioms of Boltzmann statistical mechanics.
Now the above considerations include categorically distinct objects, categorically indistinct objects and fundamentally distinct objects. But we have not yet talked about fundamentally indistinct objects. Perhaps if we did, as suggested by the similarity of treatment of categorically and fundamentally distinct objects, (which both are described with the same combinatorial statistic), we would describe categorically indistinct objects with the same combinatorial statistic, the one also used for categorically distinct objects. But the problem here is that there are no such things as categorically indistinct objects. If categorically indistinct objects reside in different places, they are inherently and unarguably fundamentally distinct. But for objects to be fundamentally indistinct would require them to be in the same place, in which case they would be the same material object, and even at that, there would be only one of them or it. That is to say, it is impossible to have or even sensibly imagine a set of categorically indistinct objects.
Now let’s take a very close look at the discrete energy units, whole numbered and countable, that is assumed in both Boltzmann’s take on entropy and in ours. As they must be in any reckoning all the same kind of thing and hence not specifiable in categorical terms any more than a group of He (Helium) atoms are, they must be describable only in fundamental terms. As such they must be fundamentally distinct because they (and nothing you can think of) can be fundamentally indistinct. If that logic is too much to grasp for those who accept Boltzmann statistical mechanics like a religion because it has provided a microstate explanation for this most foundational part of science of thermodynamics when no other explanation existed, understand that each molecule contains energy units that reside on or in that particular molecule which is in a particular place, and accordingly all of the energy units of a particular molecule are in a different place than the energy units that reside in or on other molecules that are in different places. So at least the energy units of one particular molecule are fundamentally distinct from the energy units on any other molecule.
And upon collision where there is energy transfer of an energy unit from one molecule to another, surely an energy unit transferred from a molecule is distinguishable in terms of place from all of the energy units on that same molecule that were not transferred upon collision. If these seems too prosaic and fitted to the argument in some sophistic way, we go back again to the notion that while there is categorical lack of distinguishability and fundamental distinct, if you can count things, they must be distinguishable. And discrete energy units are by definition of being discrete or whole numbered able to be counted in principal. Hence Boltzmann’s discrete energy units must be discrete.
If so why did he make them indistinguishable? He did that in order to use the indistinguishable combinatorial statistic needed to make his model fit the data. But in the end the fit is epistemologically chimerical and nothing but mathematical serendipity, the chance equivalence of two functions that have nothing to do with each other, one of which lacks not only physical reality, but also any mathematical legitimacy. This is not to down grade Boltzmann’s genius. The science of physics rests on a mathematical fit of data to theory, the power of mathematical exactness triumphant in Newton’s Laws of Mechanics and Gravitation and Maxwell’s Equations for Electromagnetism. But in this case, while the numbers added up, the underlying concepts are misfit like water and oil. If there were no Boltzmann, this diversity based formulation of entropy would have been impossible for us. But giving him full credit for his amazing breakthrough approach to the truth, let us not respect what is missing from it as sensible explanation and revere him like the foolish do God.
There is much to be gained from understanding entropy correctly in terms of its lending its basic ideas to the other great conundrum in science, a clear understanding of the workings of the human mind, best and only really done mathematically. Specifically we must understand our organ of information processing, the mind, in terms of a mathematically understanding of information. Part of this is done in terms of the operation of information compression of the mind considered in the next section. But in a later section more importantly we shall take information as it is affected by the significance we give things we are exposed to visually and verbally. It is a simple matter, most intuitive, to understand the D and G diversity measures as applied to thermodynamics systems as specifications of the number of energetically significant molecules with the low energy ones that collide with the measuring device of the thermometer and the afferent sensory parts of the human CNS understood as energetically insignificant. More on this in due time.
6. The Mind’s Compression of Information
The E expected value can be understood as a compression of information on events perceived in the past. Consider that you play the Lucky Numbers game twelve times with penalties incurred of (−$120, 0, −$120, −$120, −$120, −$120, 0, 0, −$120, −$120, −$120, 0). You could either remember them as twelve individual pieces of information or compress them as the average penalty, that is, the E=−$80 expected value. Of course knowing the probabilities of rolling dice is a short cut to obtaining the E expected value of the game and what to expect in the game when you play it in the future. But the more primitive dynamic of compressing information gotten from the past to get the expected value and use it for future expectation is the more general way that the mind stores information and process it for the future. Knowing this is a principle key to understanding how the mind stores information from experience as our thoughts and our emotions and uses it for the future.
A nonmathematical example makes sense of this compression of information process a bit more intuitively. The word “dog” conjures up a picture of what to expect when one encounters a dog as a pictorial average or morph of all the dogs one has ever come across in the past including in books and movies. The mind does this quantitatively also, the size of a dog in our minds being a rough average of the sizes of all the dogs we have ever come across. The averaging of all dogs sensed over all times is roughly what we intjuit9vely expect a dog’s size to be in future encounters with a dog.
Of course, it is not as simple as that, but working out the important nuances of information compression that are a major part of our mental machinery requires an understanding of quantitative information compression that goes beyond the arithmetic average. We obtain that from our development of entropy as a compression of information in Section 5, which we then will use in Section 6 to explain compression as it applies to and explains the totality of cognition in subsequent sections. We will put this most important topic of information compression on the back burner until then.
In the last section we developed the concept of compressed information in terms of the µ mean, the D diversity index and the Average Configuration. Now let’s consider information compression in terms of two of the main properties of the Average Configuration, the G_{AV} average square root energy diversity and the ψ_{AV} average of the ψ square root biased average energy per molecule. The latter property, ψ_{AV}, derives from the ψ the square root biased average energy per molecule of a system of N molecules. This is an average of the thermodynamic system at a particular moment in time when the system is in a particular one of its W states. This ψ biased average is a compression of x_{i} energies of all of the N molecules, of the discrete energy units on all the molecules, though as the square root biased average rather than the simple µ arithmetic average. Then this ψ average is itself as ψ_{AV} averaged over all the W states of the system as weighted by the probability of each state. Hence ψ_{AV }is a double average of molecular energy, first over every one of the N molecules at a particular moment in time and then over every state of the system over time.
What is remarkable about this ψ_{AV} double average is that it is a measure of temperature not only as taken by a Mercury in glass thermometer but also as sensed by the human body, which collectively measures the energies of all of the environment’s molecules that impinge upon the skin’s surface and senses them as temperature by averaging the energies over all N molecules at any moment in time and then also over time assuming (reasonably) that the collisions of the molecules on the skin are rapid relative to the brain’s integrating sensory impression of them. This is noteworthy because it understands the mind’s sense of temperature as a compression of information.
The mind compresses everything it senses in its memory of it. Consider a human observer who could see every dog in the world at every moment in time. Then the person’s sense of a dog upon recall would be akin to the ψ_{AV} sense of temperature in averaging all the world’s dogs at any one moment and then averaging this at time average over time as time passed. This sense of what a dog is, though, would be tempered by recency, that is, with the set of dogs in the world most recently observed having greater weight in the average than those observed in the more distant past.
This is not only how we think about objects observed that are common nouns for us, but also for particular dogs, like the family pet, Fido. Our sense of what Fido is, is a compression of all of his various characteristics or properties over time, some of which change quickly and some slowly, again with recency coming into play in our temporal averaging of Fido’s characteristics.
This sense of compressed information is necessary for understanding the interplay between our emotions and our thoughts, both of which take the form of compressed information. We made clear in Section 2 that the E expected value of a Lucky Numbers Game, such as E= −$80 in Eq4 in the penalty incurring game, and by extension E=$40 in Eq6 in the prize awarding game, are most basically compressions of information from past experience. Now when we expressed the E expectation in Eq7 for the prize awarding game as E=V−UV, we specified V as our wish or desire for the V amount of dollars. In the quantitatively couched goal directed behavior of rolling the dice to obtain the goal desired or wished for, the “thought” of receiving the V prize is a very precise picture in one’s mind, varying little in image as receiving money generally has little variation in it. But that is not the case for many of our desires whose goals are qualitative rather than quantitative and lie beyond getting money. In those cases where variation is the norm, what is wished for is formed by our imagination as a compression of information that impinges on the mind from the past.
That is to say, that we think, especially about the future, in terms of ideas and concepts that are inherently statistical in nature as compressed information. When these ideas, thoughts, concepts are expressed in quantitative form, there is greater clarity in what they mean and in predictions about the future that stem from them. Freedom and enslavement, the one desirable and desired, the other dreaded, are two examples of immediate interest, both of which are information compressions whose meaning can be quite fuzzy unless they are couched in precise mathematical terms. As both freedom and enslavement are highly emotional terms, this will become more clearly as we continue
7. The Function of the Transition Emotions
For now, though, we want to continue on in our systematic explanation of our emotional machinery by explaining the purpose and function of the transition emotions of T= −ZV disappointment of Eq9, T=UV excitement of Eq15, T=Uv relief of Eq21 and T= −Zv dismay of Eq25. Recall that they all come about from the T=R−E Law of Emotion of Eq8. 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 Eq7 to
91.) E’=Z’V=(1/2)($120)=$60
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 Eq8 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
92.) 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’
93.) 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
94.) ∑T’_{ }= −$60 −$60 +$60 = −$60
And the average of these T’ transition emotions per game is
95.) ∑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
96.) T_{AV} =E– E’
Or solving for E_{NEW},
97.) E_{NEW} = E’ + T_{AV}
For the example case developed above, this obtains an E_{NEW} expectation of
98.) E_{NEW }= $60 −$20 = $40
Now this revised E_{NEW}=$40 is just the E=ZV=$40 of Eq10 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
99.) 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
100.) T’=R−E’=$120−0=$120
Note that this is an excitement greater than the T=$80 of Eq16 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
101.) ∑T’_{ }= 0 + 0 + $120 = $120
And the average of these T’ transition emotions per game is
102.) ∑T’/3 = T’_{AV}= $120/3 = $60
And from the Law of Emotion Inversion of Eq97 we obtain the correct expectation felt in the next play of the game of
103.) 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 Eq97 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 in Section 3 and of the Laws of Emotion of Eqs8&97 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 principal of absence of empirical verification is to fail to understand the underlying basis of empirical validity in universality.
8. The 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.
104.) Z_{1}=Z_{2}=Z_{3}=Z=1/3
And the U uncertainties for each toss are
105.) 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).
106.) 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
107.) u=1–z = 26/27
The expected value of this triplet roll game to win the V=$2700 is in parallel to Eq6,
108.) 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 Eq8 with R=0 in parallel to Eq9,
109.) 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 Eq15
110.) 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
111.) 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
112.) 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 Eq112. 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
113.) E_{1}=R_{1}=Z_{2}Z_{3}V = $300
Now we use the Law of Emotion of T= R−E, of Eq8 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 Eq113; 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 Eq108. And with U_{1}=(1−Z_{1}) from Eq105 we obtain T_{1} as
114.) 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 Eq110 from making the triplet toss and winning the V=$2700 prize can be written, given R=V for success, as
115.) 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 Eq119 to obtain T_{1} as
116.) 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 Eq115 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 Eq114 is much less than the T=$2600 excitement of Eq110 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 Eq112. 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,
117.)
R_{2}= E_{2 }=Z_{3}V=(1/3)($2700)=$900
The transition emotion that comes from rolling 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 Eq113, is
118.)
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 Eq117 as T_{2}=U_{2}R_{2} makes it clear from its
parallel form to the excitement of T=uR of Eq115 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 Eq8 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 Eq117, the Law of Emotion, T=R−E, obtains a T_{3 }transition
emotion of
119.) 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 Eq115 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 Eq8 is further validated from the three partial excitements, T_{1}, T_{2} and T_{3} of Eqs114,118&119 summing to the T=uV=$2600 excitement of Eq110 that arises from making the triplet roll in one fell swoop as you might from throwing three pair of dice simultaneously.
120.) 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.
121.) 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 Eq109 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 Eq120 and in ultimate failure in Eq121 universally fit emotional experience and as such are a convincing validation of the Law of Emotion, T=R−E, of Eq8. 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 Eq108. Much as we saw that sequential increases in expectation produced a T transition emotion of excitement in Eqs114,118&119, 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
122.) 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
123.) T_{0}= E=R_{0}=zV=UzV=UR_{0}
Again by parallel to T=uR excitement of Eq115, 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 Eqs114,118&119. 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 Eq20 and with u=26/27 from Eq107 as the improbability of rolling three lucky numbers, the fearful expectation of incurring the v=$2700 penalty is
124.) E= −uv= −(1−Z_{1}Z_{2}Z_{3})v= −(26/27)($2700)= −$2600
The Law of Emotion, T=R−E, of Eq8 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
125.) 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}
126.) 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
127.) 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 Eq15 and the T=Uv relief of Eq21. 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 Eq114 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.
9. 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 this commodity of the 1^{st} lucky number to the player. Question: what is 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 Eq111, 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 Eq113 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
128.) 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 Eqs114&116.
129.) 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 Eq129 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 Eq129 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 Eq127 in the v penalty as
130.) 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 Eq129. The two forms of the Law of Supply and Demand of Eqs129&130 provide a strong empirical validation of the Law of Emotion of Eq8 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 Eq129 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 Eq15 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.
131.) W=T=UV
Now in recalling Eq16 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
132.) 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
133.) 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 Eq21 with W=T assumed from earlier considerations as
134.) 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.
10. 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 Eq134 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.
135.) 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 Eq135 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 Eq135 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 Eq135 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 Eq135 evaluated for the v*=1 life saved and its prior U*=.999 scarcity of air or uncertainty in getting it as
136.) 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
137.) 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 Eqs135&137 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 Eq20 of losing money in the Lucky Numbers v penalty game.
The W*=T* equivalence of Eq135 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 Eq135, 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 Eq155 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 Eq135 to obtain
138.) W*=T*=U*v*= −(−U*v*)=0
This expression of Eq135 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 Eq135 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 Eq135, 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 Eq20 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 Eq135 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 Eq135 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, Eq135 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 Eq135 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 the analysis in The Mathematics of Slavery, God, Entropy and Armageddon 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,
139.) ERROR = (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.
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
140.) ERROR = (0_{ }–(−U*v*) )
The system is turned on whenever the 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 Eq138, 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 Eq135 Law of Supply and Demand are also negative feedback control or homeostatic systems.
Temperature regulation also demands that skin the 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 Eq135 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 Eq135 to fit universal experience.
Obtaining food to keep an individual from losing his or her v*=1 life from lack of it also follows Eq135, 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 Eq135 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 relived 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 Eq135 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 Eq135. And Eq155 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 Eq135, 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 Eq135 we can substitute W* for the V dollar term in E=ZV to obtain our hopes of pleasure as
141.) 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 Eq7 as the hopes of getting V dollars. In the latter, the pleasurable desire is for V dollars while in the former of Eq141 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,
142.) 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 supply 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 Eq155. 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,
143.) 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 Eq135 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 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.
11. 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.
144.)
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
145.)
You could also get a savings account with a quarterly or daily compounding of the interest. This modifies the interest formula in Eq145 a touch to
146.)
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
147.)
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
148.)
An alternative formula for the daily compounding case is
149.)
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 Eq133 but as
150.)
Eq149 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 Eq149, in differential form as
151.)
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. Eqs149&150 apply not only to the exponential growth of money in a daily compounded savings account also 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.
152.) 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 Eqs149&151, to be keep 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, Eq149 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 organism 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 Eq151 that takes the reality of limited growth into account. It is, with K as the carrying capacity,
153.)
This Verhulst equation or logistic equation spells out growth over time in differential form is expressed as a time equation as
154.)
Eq153 and Eq154 translate into each other much as do Eq149 and Eq151, 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 155.
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 Eq149 as
156.)
156a.) g_{1} = b_{1} – d_{1}
157.)
157a.) 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
158.)
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.
161.)
If the g grow 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.
162.)
163.)
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}.
164.)
This expresses Eq152 via x_{20}=K−x_{10} as
165.)
This expression for x_{1} is
further simplified by dividing the numerator and denominator of the right hand
term by to get
166.)
We can simply Eq156 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
167.) F_{1} = g_{1} – g_{2}
168.)
Noting the sameness in form of the above to the Verhulst time equation of Eq154 tells us that we can write it in a differential form that has the same form as the Verhulst differential function of Eq153.
169.)
Next we define the fitness of the #2 population, F_{2} to be
170.) F_{2 }= g_{2} – g_{1 }= –F_{1}
This allows us in parallel to Eqs168&169 for x_{1} to write for the x_{2} size of population #2,
171.)
172.)
A
graph of Eqs168&171 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 173. 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 Eqs167&170 expanded with Eqs156a&157a.
174.) F_{1 }= g_{1 }− g_{2 }= (b_{1}−d_{1}) − (b_{2}−d_{2})
175.)
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 Eqs168172 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 Eq153 to
176.) 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 in the Section 10 that derive from Eq135. 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 Eqs149,151&152 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.
Talking about the emotions related to sex, love (parental and romantic) and violence, however, and what the mathematically prescribed outcomes of these emotions should or shouldn’t be is fraught with problems because sex, love and violence are very much tied up with values and morality. And these consideration can get all the more confused and contentious 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.
For the above reasons, before we dive into these problems with considering violence and sex, epistemologically and morally, we are required to first consider in depth and with precise mathematical argument the nature of information, both how it is used by the human mind to determine behavior and also how as misinformation it can be used to produce behavior influencing notions about reality that are entirely off the mark and yet are believed as correct by so many.
This also has us delay discussion of many important nuances and ramifications of evolution not considered in this section. Rather we will leave them for later sections as we proceed by the most direct path to get to the heart of matters most meaningful to take up: of enslavement; of the religious dogma that essentially support it; of the violence that enslavement indirectly causes; of the worst aspects of such redirected aggression in being a significant cause of war; of the worst incarnation of that dynamic in the possibility of the coming of nuclear war; and of what can be done to avoid man’s extinction from a nuclear Armageddon. All of that begins with a clear understanding of information in the next section and propaganda in the section after that.
12. Propaganda
Some
of this material is repeated. Our sense of significance versus insignificance
is automatic or subconscious as made clearer yet with the three sets of colored
objects below, each of which have K=21 objects in them.
Sets of K=21 Objects 
Number Set 
D from Eq37 
D, rounded off 
(■■■■■■■, ■■■■■■■, ■■■■■■■) 
(7, 7, 7); x_{1}=7, x_{2}=7, x_{3}=7 
D=3 
D=3 
(■■■■■■, ■■■■■■, ■■■■■■■■■) 
(6, 6, 9); x_{1}=6, x_{2} =6, x_{3} =9 
D= 2.88 
D=3 
(■■■■■■■■■■, ■■■■■■■■■■, ■) 
(10, 10, 1); x_{1}=10, x_{2}=10, x_{3}=1 
D=2.19 
D=2 
Table 185. Sets of K=21 Objects in N=3 Colors and Their D Diversity Indices
The N=3 set, (■■■■■■■■■■, ■■■■■■■■■■, ■), (10, 10, 1), has
a diversity index of D=2.19, which rounded off to D=2 specifies D=2 significant
subsets of color, the red and the green, with the x_{3}=1 object purple
subset sensed as insignificant, as might also be understood from its contributing
only token diversity to the set. By contrast the D=3, (■■■■■■■, ■■■■■■■, ■■■■■■■), (7, 7, 7), set
has 3 significant subsets, red, green and purple, as does the (■■■■■■, ■■■■■■, ■■■■■■■■■), (6, 6, 9), set
whose D=2.88 diversity rounds off to D=3. One can get a stronger intuitive feel
for how the human mind determines significance and insignificance intuitively by
represented the sets in Table 185 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 with a plaid skirt with the (10, 10, 1), D≈2, pattern on the left
would spontaneously describe it as a red and green plaid, omitting
reference to the insignificant thread of purple. She would do this intuitively
and automatically without any conscious calculation because that is how the
human mind automatically registers what is significant and what is
insignificant. The rounded off D≈2 diversity specifies the 2 significant
colors in the plaid, red and green, that the mind intuitively senses and also
intuitively verbalizes as such. Note how the insignificance of the purple
thread specified in the D=2 measure is manifest linguistically in purple being
disregarded in the description of the cloth as a red and green plaid.
This verbalization of only the significant colors in the plaid, red and green, should not be surprising given that the word “significance” 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 isn’t signified or verbalized or given a word. The human mind operating in this way to barely notice and not verbalize what is insignificant is an important factor in human behavior because we generally think, talk about, pay attention to and act on what we sense to be significant while automatically disregarding the insignificant in thought, conversation and behavior.
The sense of significance versus insignificance as spelled out by the D diversity index is also clear in the Ferguson Police Dept. having x_{1}=50 of its K=53 officers White and only x_{2}=3 of them Black. This is described colloquially as “no diversity” and the few blacks on the force as insignificant as quite perfectly fits the D diversity index measure of the number of significant ethnic groups here to be from Eq36, D=1.12 as rounds off to tell us there is only D=1 significant ethnic group on the force.
The significance of something we see as affected by its size or quantity is not the only thing affected by magnitude. Our sense of significance also extends to our frequency of observing an object or event. Consider as illustration a game where you guess the color of a button picked blindly from a bag of buttons, (■■■■■■■■■■, ■■■■■■■■■■, ■). Now let’s assume that you don’t know the color or number of buttons in the bag, but only what you see over time in watching the buttons be picked (with replacement), namely that some picks are red, some green and some purple. Over time, as you see purple picked infrequently, purple will come to be insignificant in your mind and so much so that you will not even think about guessing it as the color picked when your turn comes to play this guessing game. This sense of significance versus insignificance determined from the frequency of the sensing of an event as measured by the D diversity index perfectly parallels what occurs with the G_{AV} square root biased diversity entropy measure of Eq89 interpreted as the number of energetically significant molecules in a thermodynamic system in a given state.
The mind’s automatic mechanism of sensing quantitative significance and insignificance enables the ruling class in a modern society to use the mass media they control to make the realistically significant seem insignificant and the realistically insignificant seem significant via the politicians, journalists, ministers, actors and other media they pay to perform. The ruling class does this to control the thoughts of those on lower rungs of the social hierarchy, which we’ll explain mathematically in a later section. The purpose of bamboozling of what the American people feel is significant and what it dismisses as insignificant is to get them to accept their abuse and exploitation in the social hierarchy most expedient way, that is, through mind control rather than through out and out economic or penal coercion.
To that end common life situations of workplace control and degradation are seldom broadcast on TV in fiction or factual form including news reports while people are bombarded instead with feel items and frivolous entertainment including sports broadcasting, which takes up a large fraction of TV fare. What affects the public’s subconscious acceptance of this often subtle misinformation on the realities of life is how often bogus points of view are repeated in the media to be made to seem significant and thus take up a significant portion of a person’s thoughts, conversation and feelings, all of which affect a person’s behavior.
To understand the inculcation of bogus significance by the repetition of disingenuous talking points and the relative absence of any correction of them, consider the N=2 (■■■■■■■■■■■■■■■, ■), (15, 1), set as representing N=2 polar opposite interpretations of an issue with the number of objects in each subset representing the relative frequency of broadcast of each interpretation. We will assume the red interpretation to be ruling class misinformation on a situation and the green interpretation to be the reality of the situation. The broadcast of the interpretations with relative frequencies of 15:1 makes for a D diversity measure of D=1.132, which rounded off to D=1, imprints on the minds of the audience that the misinformation is significant and the hard truth of the matter insignificant.
From an analytical perspective, then, we see that the significance determining mechanism of the mind functions off both the relative number and size of objects in a situation and on the relative frequency with which situations, real and contrived, are projected into the mind.
A combined illustration of both kinds of insignificance and significance deception is found in the Republicans getting the public to support the war in Iraq in 2003 by describing the invading force in that war as a “coalition.” The invading force consisted approximately of K=163,700 soldiers from N=32 nations distributed 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). This set’s D number of significant contributors to the invading force as calculated from Eq134 is D=1.26, which rounds off to D≈1 significant nation in the socalled coalition, the United States, which is at odds with the general sense of a coalition as a genuine plural entity rather than a collection of subordinates dominated by one nation.
The deceit in calling it a coalition as one of the rationalizations for entering this costly, bloody, unnecessary war is clear enough to be recognized by the astute as raw political deceit without the need for the D Simpson’s Reciprocal Diversity Index to clarify the contributions of N−1=31 of the N=32 nations as insignificant, though using D as a measure of significance allows us to call the politicians and those who supported them in entering the war liars with mathematical precision. Very much also affecting the public’s acceptance of this clever propaganda was how often the above spin on entering war was repeated over and over again to the public to make the lies about the coalition and the supposed WMD’s seem significant and reasonable.
The D diversity index understood as the number of significant objects or events is one of the cornerstones of propaganda. It works by repetition of mistruth and is evident as such in obvious totalitarian governments, religious dogmatists and talking points blabbering Fox News conservatives who repeat “black is white” assertions in a concerted way so often as to make the possibility of their being some truth in them seem significant and reasonable.
In the propagation of religious doctrine the need for near complete unanimity in talking point assertions to make observably insignificant divine characters like angels and God and unseen divine places like Heaven seem significant is why heretics with opposing views have always been anathema to those who have been made to believe in such nonsense and those in such circles who know better but preach the nonsense for reasons of personal benefit. While heretics against ideological thinking are not quite burned at the stake, their ideas are generally ridiculed or denied outlet in the media and made to seem insignificant.
A case in point is the documentary film maker, Michael Moore, whose primary sin was disgust with the mayhem and slaughter of schoolyard mass murder and George Bush’s vanity driven war in Iraq that, for no good national purpose and as driven with repeated out and out lies reinforced by most major media outlets back in 2003, unnecessarily took the lives of 5000 mostly young American soldiers and crippled 30,000 more, not to speak of the horror it wreaked on a million Iraqis to this day from the instability asshole Bush’s invasion of the country caused, itself totally downplayed and swept under the rug in happy, smiley media land. Indeed as regards Moore’s insightful and prophetic castigation of the war in public at the Oscar nominations in 2003 and later in his documentary, Fahrenheit 9/11, this went as far as active encouragement (as by the likes of right wing snake, Glenn Beck, who is held up as a paragon of righteousness and allowed to have endless radio and TV access), for people to out and out kill Moore. Nor are the billions of dollars wasted in our Middle East wars much of which goes into the pockets of ruling class owned and run companies like Halliburton and their local and foreign cronies, which is a primary reason our economy has been so gutted to the personal destruction of so many millions of American families, a hard fact never mentioned.
The question should arise for anybody who has read this far of what to do about this situation in America of near complete physical control via the police, near complete economic control via Wall Street and near complete information control via our Wall Street controlled mainstream media? In the short term the answer is: Run. To keep your selfrespect and the possibility of any happiness in life alive: Run. The best you can do in the short run is to avoid all of the above agencies of control, including avoiding the media drubbing anybody who watches TV and enjoys it gets unavoidably.
Throw the TV set out, out, out. This singular path to maintaining sanity is limited, though. On its own, it takes you down in the end too. You have to fight back somehow. And you do that with the only true solution to the mess human existence has culturally evolved into by shooting for A World with No Weapons, not just for eliminating war and nuclear Armageddon but also for reviving a balance of power that takes personal relationships back to relatively uncontrolled precivilized days.
Keep in mind, as I made clear in the middle of my story in Section 4 that this can only be accomplished by the USA effectively conquering the world in alliance with other sane nations whose leaders also see that A World with No Weapons is the only solution to mankind’s subjugation and the mass murder of war. And understand that this can only happen with somebody in the White House who carries that destiny for the country on their shoulders actively. Other than in the event that somebody other than me, who I don’t know about, has come up with the idea of A World with No Weapons independent of us, I’m the only suitable candidate in 2016.
True the protestors for the Mike Brown and Eric Garner horrors, bravo to them, and old line Occupy guys and gals would prefer a world where we don’t need politics and don’t need leaders of any kind, the joys of individual anarchy cannot be achieved in any tangible way with the present humanoids at the top in charge. And the only way to displace them in our media glossed capitalist police state is to try to change things with the ballot box. It’s hardly guaranteed even if we could come up with majority vote, but it’s the only real path to any salvation, excepting the always chancy panacea of Heaven after death. Encourage me by dropping a line to ruthmariongraf@gmail.com and sending a donation for democratic revolution by clicking here.
Next we consider my true story that counters the propaganda about life endlessly shown in the media.
MATHEMATICS TO BE CONTINUED (someday, when we are not so beset by the never ending turmoil of avoiding the agents of control.)
13. Revolution in the Garden in Eden
Edward Graf Jr. at his retrial for the burning deaths of his two stepsons.
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, which was nearing its end when I first came across the story on the Internet of how my cousin had burned his kids alive. I was in shock because though I’m Ed’s cousin and was close enough to his family to have been his brother, Craig’s, baptismal sponsor back when, 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 completely in the dark about the killings for the last thirty years because I was the one lucky Graf who escaped this fundamentalist clan as a young woman, never to be told by any family member about this hideous skeleton in their closet that made hard core sense 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, that would have locked him up for life with no chance of parole, Ed Graf suddenly pleaded guilty to the murders as part of a most unusual last minute plea bargain and was released on parole a few days later. A letter to the Waco Tribune that appeared on its front page soon after makes clear the outrage caused by his being freed: “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 personal experience as a former member of the Graf clan. I rebelled against its control and abuse and threw the pain of my suffering back in the face of those who caused it while Ed just absorbed the worst of it without resistance and passed his unhappiness from it on to the innocent two youngsters he burned alive.
This release of unhappiness as aggression toward innocent victims who had nothing to do with causing your unhappiness is utterly common whether as the petty meanness we all know and endure from those who have power over us to the mass murders so common these days in our daily headlines to the butchery of war that will one day reach its maximum horror in the megadeath of nuclear conflict. This correct view of life that cuts through the standard American Dream picture presented of it in ruling class controlled mass media should suggest to readers astute enough to recognize the obvious that I would make a good presidential candidate in 2016 as the only person who understands the disastrous place America is going competently enough to have the will to do something about it. After hearing what I have to say, you can support my efforts and potential candidacy by clicking here. We either pull off a miracle or fall off a cliff manufactured by our stupidity and failure of nerve.
Nothing is as difficult as exposing the truth about oneself in a public way. Whatever feels bad inside tends to feel all the worse when offense from others and personal failures from those offenses brings greater humiliation yet in the public confessing of it. But the cost of keeping private matters that most of us just do keep hidden from others can be enormous, for only raw truth no longer disguised and hidden from view is able to make clear that we as a people and a nation have significant problems that must be attended to lest we fail as a nation in stopping the catastrophic end for all people that is otherwise in store for us from the world’s next global war at the nuclear level that shackles us to a Fukushima irradiated atmosphere bring a painfully horrible end to all including our children. I will also explain these ideas after I finish my story in a clear and precise way with groundbreaking mathematics.
I
was born four months before America entered WWII as part of the last wave of
women whom fundamentalist tradition was set to control as tightly and painfully
as the foot bound women of imperial China. My father was a minister in rural
parishes that stretched over time from Cullman, Alabama, where I was born, to
Serbin, Texas, north of Austin, with his superior pastoring especially
including his masterful ability to garnish funds from parishioners, elevated
him to a position at Lutheran seminary where he taught Stewardship, a fancy
name for how to extract cash from parishioners' wallets and purses.
My mother was a shrewd, bulldog faced character right out of Stephen King's, Carrie,
who told us that Jesus talked to her personally every day and that the fossils
in Dinosaur National Monument in Utah were plaster fakes buried secretly in the
ground by people who hated God as cover for her raising children, including
this little girl, with near weekly, 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 in coming home from school to her every day, 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
horror continuously muffled by my ever smiling father's explicit and implicit
endorsement of my mother’s insane cruelty as something blessed to be revered
and respected.
Some of the worst of it was my role as fodder for my brother, Don, two years older than me. He was the recipient of the same sort of corporal punishment as I got until he firmed into the role of my mother's toad and her henchman towards me. My hearing her spank Don brought 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 she gave him to his younger sister, me.
That
was quite acceptable in those days when fundamentalist Christian women came in
only two varieties: the obedient wounded in childhood who rose to power in
adulthood with the rod like my mother; and the pretty pastry kids like me that
monsters, like my mother, and their henchmen, like my brother who was allowed
to feed on his little sister to prop up an ego wounded by my mother’s punishing
him to get him to respect this piece of maternal shit who could never get a
child’s love or attention without beating up on it.
I was lucky. I was not so destroyed as to be unable to hate my mother for they
left enough in dumbbell me by pampering on the margins to make me a pretty if
awkward young girl, for the minister's daughter is a public figure and if
thought pretty a valuable status symbol especially helpful for stewardship and
the minister rising in the pastoral ranks.
All that mattered to this young girl growing up was the thought and hope of
love. The most daring books in our home library were Zane Grey novels. My
imagination translated the heroes in the better of them into would lovers
scooping me up on their horses and taking me in my thoughts far away from my
family problems while squirting me in my preteen private parts with some warm
liquid of unknown composition.
Beyond this seeping in of sexual instinct under repression my attitude towards
men was also shaped, no doubt, by my bastard brother, Don, who sustained his
imperious position over me with daily punches on my arm and tales of a wolf on
the prowl near my bedroom always about to pounce that my mind, so dumbed down
by constant disapproval and punishment from my mother actually believed. I was
the model he practiced on in learning to control and humiliate people 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 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 for
him. It takes more weapons and courage to be the knight in shining armor that
rescues a damsel in as much distress as I was in than any seventeen year old
kid 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 after that the humiliation of being seventeen and dragged along on Sunday family trips by my parents devoid of some kind of male admiration. It was on one of these family jaunts to Wichita Falls, TX that I first have a memory of Edward E. Graf Jr. It is brief. At age six, eleven years my junior, my sense of him was that he was puny and glossed with a reputation for being smart, whatever that means in actuality.
A few years later, shortly after I got married, I ran into him again after we went back to Wichita Falls for a visit with Aunt Sue and Uncle Ed after Don’s wedding down in Galveston. I remember him more critically then when he was nine or ten as being awkward to the point of what girls called back then, punky, and his mother, Sue, as an overweight, unattractive, southern Christian lady, who talked to Ed Jr. like some school teachers talk to their charges, continuously in a controlling tone. He certainly did not strike me as a “killer” in any sense of the word at that time. But you see here 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 the results of his less than perfect childhood began to show adult level pathology, but this is getting way ahead in the story. Better for now to continue on in the parallel story of another Graf with a less than perfect childhood, my story.
The fellow my wounded heart connected with in marriage, or was connected with by my parents, was a seminary student in my father's class at Concordia Theological Seminary up in Springfield, Illinois. What I later found him out to be, a toad who filtered all his thoughts before he spoke them, I had absolutely zero way of knowing when I met him, for my father, like most ministers of this ilk did just that 24/7 as an integral part of being a minister, which is 95% an acting profession. After two years of college at age twenty I married this Len Schoppa, a classic Texas phony. The error in it was marked inadvertently by my brother Don’s not bothering to attend my wedding whether because he really did need to study desperately for an important law school exam as he said or out of total lack of respect for me on this most important day in any woman’s life and/or for Len. It was a fairy tale omen of worse things to come with Len and, indeed, with 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 that was not satisfied in this very Christian marriage. Further,
the subtle miseries of a loveless arranged marriage manifested themselves daily
in the severe migraine headaches I'd had torture me since early grade school.
Can you imagine the preposterousness of living your life with the goal of
converting the Japanese to Christianity? Really. For my husband it was all
dominance games with 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 WWII. For me it was being unwittingly used as the pretty young wife
of the pastor whose vacant, submissive personality fit so well the docility
culturally expected of Japanese women. I was very efficient window dressing in
the game. Many fell in love with me like the girl young Elizabeth Taylor played
in Tennessee William's Suddenly Last Summer with Len reveling over and
beating them into subordination as the one who had the woman they were falling
in love with. And down went to him, all these poor bastards, one of them
committing suicide as a result of these love triangles I was completely unaware
of.
I hesitate to say anything in any depth about my relationship to the three kids
I bore for this common predator, they at the same time being the only love I
had ever had in my life; or the unbearable pain I felt in seeing the terrible
job I was doing as a mother as was so clearly revealed by the lack of spark in
their eyes as they approached adolescence. Makes you wish you were dead. If I
could kill myself and offer up the pain of a torturous exit to make up for what
I was incapable of giving them when they were growing up, I’ve thought at
times, I'd take a razor to my throat without hesitation. As bad as what you
become in life, 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 smack in
the middle of their preadolescence turned out to be an intended amelioration 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 idiot form rather like Sandy Dennis in 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 from
semiworship by a vast gaggle of Japanese men who extended beyond our mission
church fellows to the classes of college boys I taught English to at Hokkaido
University. This support was raised even further when fate brought me a side
role in my life as a commercial model on Japanese TV. One of our social
contacts through the mission church was a television producer who signed me up
to pitch Japanese bean soup on television. For six years I became known all
over Japan in this guise and was stopped by strangers on the street and at
restaurants when we dined out and asked, "Aren't you the Koiten Soup
Girl?"
The next wouldbe Zane Grey hero that came into my life was a Japanese college
boy, a ski bum sort, who took the missionary's wife bait Len dangled in front
of all the young men, off to bed. This happened on church related ski trips up
in Hokkaido that Len didn't come on because he didn't ski. It was real love as
close as I'd been to it and a great relief from the emotionally empty love life
I had in this mom and dad arranged marriage to the missionary. Physical love
when you want it is fairly close to Heaven when you’re in the middle of it as
much as not having it is hell.
Perhaps affairs like this are easy to hide for the smart women on the Unhappy
Housewives of New York type shows, but in a crowd of 30 LCMS missionary
couples in Japan we were but one of at the time, once the slightest suspicion
arose about Mrs. Schoppa and her ski partner, the gossip landed like rain
falling from the sky on the doorstep of the Rev. Leonard Schoppa. The climax in
the confrontation between us had surprising twists and turns.
I
didn't hesitate to confess. I was 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. What surprised me was his
falling to the floor when I told him, yes, I did it, and writhing on the rug
like a big piece of bacon frying in a pan turned up too high; and while
twisting all about like that confessing in a blurt to having had sex with farm
animals when he was young, sheep, pigs and even the large dog his parents had
named, "Lassie." What that had to do with my having had an affair the
last six months with one of our converts just could not register in my head and
rather in retrospect a few days later got me to think that the rumor that he
had had sex with his retarded cousin Larry a few of the good old boys in
Harrold, Texas, had joked about, must have been true. Farm animals, my eye.
Once you have a sense of that, parallax with pastor personalities generally
makes it clear they're all closet fags of one sort or another. That’s the
faking fundamentalist ministers, from Len to Ted Haggard to my own father, whom
when I thought about it could possibly have married a woman as ugly and bearish
as my mother if he had any normal feelings about women. While beauty may be in
the eye of the beholder, past some point of garbage smelling, nobody with
healthy normal emotions wants to get near it. Truly, the truest unspoken
generalization ever made on TV was that all fundamentalist conservative men are
queer by Joel McHale at the 2004 White House Correspondents’ Diner. I mean, who
looks prissier and weirder, queer in the original sense of the word, than Ted
Cruz and Rand Paul and chubby cream cheese Rush Limbaugh. And back closer to
home again, it would take a very kind woman not to see my brother, Don,
quintessentially conservative in his religious and political bent, as faggy.
That’s not to say he never married, did twice. But on the other hand both
divorced him. And the guy has to be a pretty unattractive thing to be left when
he’s a high powered lawyer with lots and lots of money in the bank, two women
leaving him, no less.
The headline of Minister’s Wife Has Affair with College Boy Parishioner quickly
spread beyond our Lutheran missionary circle to all the Christian missionaries
in Japan and shortly within the year brought about the recall of all but one of
the 30 LCMS missionaries back to the States. The scandal hit home stateside,
too, for my father was way up there in the LCMS church hierarchy, even as a
candidate for LCMS Bishop of Texas, at just about this same time, (he lost).
Not to speak of half my male relatives being ministers of teachers in the LCMS.
So I was not exactly welcomed back with smiles and flowers after Len and I were
effectively tossed out of Japan as the first of the 29 missionary couples to be
sent back to America. Rather the word was put out by my immediate family who
were all, including brother Don, directly affected by the scandal all that I
was mentally ill. For why else would a girl from such a good Christian family
do something so dirty and sinful and to such a wonderful fellow as Len, as all
ministers are painted up to be, especially one your soninlaw.
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 snake and that they
were all snakes, and snakes with a mind to bite down on me as punishment for my
sin and to get me back with Len, the thought of whom at this point,
animalfucker and God knows what else, made me feel like vomiting. Ted
Haggard's wife remained loyal to her homosexual fundamentalist minister after his
Tuesday night affairs with a gay prostitute were revealed, but she knew at some
level what she was getting into to begin with and hung around to brave the
backlash as a heavily invested business partner.
I must backtrack a bit in the story now to introduce a new character in the
form of a Japanese baby girl we adopted who was my excuse for avoiding Len in
the extreme at night by sleeping on the couch to avoid his touch and his
nearness, which caused the same feeling as being close to manure. You just
wanted to get away from it.
More about the girl. At Len's insistence to make us look like the Holy family
to the Japanese we adopted her. She was the product of a pretty young
prostitute from Yokohama, whom I met before she gave the baby up, and a Norwegian
seaman, hence a strikingly adorable child with this mix of Asiatic and Nordic
features. If you wonder when I’ll get back on track to the theme of child
murder, it is a part of this story about baby Junko. Junko, later in the
States, June, saved my sanity when she came on the scene, for besides my excuse
for my sleeping on the couch to be close to her and make sure she didn't cry at
night, she was not the product of the snake and his snaky mission church set
up. I loved her in a special way that had no poison in it. What was done to her
says much of this clan of fundamentalist German Lutherans that Edward Graf Jr.
came out of.
Len
knew, of course, that the excuse of keeping June from crying at night was crap,
but he bought it anyway because all that mattered to the snake was appearances,
how he looked to others, and nobody knew about why I really slept on the couch
other than me and him.
Anyway, whatever hell was awaiting me back in the States if I didn't go back
with Len, it was impossible to do that, rather like my cutting off my finger
with a kitchen knife. So I ran away in my mind even if not in physical reality.
And they all ran after me, Len, the family and a couple of dozen minister
friends of my father who harassed me morning, noon and night, on the phone and
coming and ringing the bell at the front door to talk to me. I ran away only in
my mind, I should make clear, because I couldn't leave my kids behind and
actually run away. Frightened and with no real solution to my problems, I ran
away in my fantasy thinking.
And oddly, the fantasy came true. In the guise of a fellow appearing on the
scene just in the nick of time. Back then around 1970 you didn't just up and
get a divorce if you wanted one, at least not if you were a good Christian
woman. At least I didn't, coming from where I was coming from. I 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, things that
gave hope in a general way, just what I needed in my personal life at this 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 rocking. We lived in student housing on campus in
San Anselmo in Marin County barely speaking to each other.
At this point I was going slowly mad. It was like being locked up in a cage. I avoided the other ministerial student's wives, a sweetly phony kind I couldn’t stand with their endlessly smiling for no good reason. It was not at all what I had come to the Bay Area for.
So a great relief it was to go 40 miles away for a weekend of environmental education with my oldest boy's seventh grade class. It is 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, he said, as some sort of marriage therapy Len 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 had agreed to this, perhaps as evidence of just how stupid I was back then.
The collection of people who were out at this Youth Hostel we'd be staying at
in the Point Reyes National Seashore included not only all the other kids in my
son, Lenny's, classroom but also genuine users of a youth hostel, many of them
guys with long hair and girls with torn jeans and flowers in their hair, the
kind that favored organically produced cheese. They were mostly a sweet kind of
looking people, not that strong, but 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. He was different in that way
and also because he wasn’t just very smart, but very tough too. And that's how
he looked, like a very smart, very tough guy in his late twenties, not afraid
of anybody as I could see by the way he moved about, confident in a maximum
way, almost excessive way you might think. Later he would tell me that a dream
he had across from the coast of Africa got him to prefer death, actually, to
losing his freedom in life. 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.
Later he would tell me that on first sight of me he thought I looked like a
model in 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 – 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 without knowing my situation, he spelled things out perfectly.
When I told him about my husband as the night went on and my going to a therapy
session with Len's two psychiatrist professors, he said don't go, it's possibly
a trap, that two psychiatrists can commit a person involuntarily. 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 to be called a fool, and I bet especially in front of
me, retorted by making it clear 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 the Australians were big guys. When it became clear that their differences
with Pete were irreconcilable and the remarks going back and forth picked up
steam, Pete raised his eyebrow and lowered his tone a bit 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 for honor, not unlike my heroes in the Zane Grey novels.
We separated during an environmental tour of the seashore and later that
afternoon when we met again I opened up to him. When he asked why I was so sad,
I said, "Look at my son, look at his eyes." To me, anyone could see
he hadn't turned out well, not very confident with kids his own age. It killed
me. 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, you could tell, and that
made me feel a bit better. Our conversations went on and on again Saturday
night too, touching a lot on politics for Pete was heavily into the radical
antiestablishment politics of the day.
We school parents and our kids were all due to leave the next morning on
Sunday. At some point during our last exchange, he touched my upper arm,
squeezing it in a firm way as I was about to go, something I could feel down to
my knees. As we were about to get into our blue Toyota, I suddenly asked him,
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
classes 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 the minute I arrived and we were
alone. The thought came into my head at that moment was 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 it was something
deeply pleasurable enough, what he was doing, that you can't help want to do
again once you've done it once. A little more aggressive and forceful than you
might think a honeymoon encounter should be. But like the best pepperoni pizza
you’ve ever eaten, if it was kind of shoved down your throat a bit to begin
with, once you've tried one slice, it's hard to not want another. And he quite
felt the same way about me, maybe even doubly so judging from the second and
third slices he wanted right away.
I stayed overnight with him and by the time morning came and I knew I had to
get back to the kids and Len, 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,
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 bull talked about in popular psychology magazines of guys needing
to make a commitment, Darwin says all much better than Freud or God. When the
sex clicks in that super pleasant way, you say hello to each other forever. And
when it doesn't, as I knew after a decade of connection to Len by “I do” at the
altar, when it feels sour, there's no future in it. My experience in Japan was
great teen sex. But this by comparison was a pleasure leash around your hips
and your brain that you didn't get away from because you just don’t want to get
away from anything that pleasant. Either a guy's got the testosterone and heart
required without needing a prescription for it, girls, 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 brave ones who resist critical compromise whatever the cost and the risk,
have been gelded, castrated, made cute little boys out of, and most of that
bunch, not very cute.
What
was truly amazing and unarguable as to the power of love that comes from
natural instinct, I thought, was that starting 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 if you think about it. 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, the pompous jerk. 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 in your life that call for it.
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. 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 the leader of a Puerto Rican gang of ten and his gang on East 11th St. in Manhattan where he lived just before he came to California and met me. By the time he left New York City he had acquired four bullet holes in him and a number of knife scars and had never backed down in a fight, even when confronted with a gun.
I've
heard the story of his fight with Len that day Len went out to the youth hostel
many times over the years and without going into all the words and punches
thrown, Pete in the end got Len down in a position where he could have ripped
Len's eyes out of his head, and felt like doing that he was so angry, 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 like that, though, because whatever the details
of their fight, Len got the point and was quite scared enough of Pete after
that to never come over again and bother me. He was a knight in shining armor
with a weapon or two.
But
that was hardly the end of the pain Len was capable of causing because very
immediately after my filing for divorce a few days later, he got visitation
rights and it was impossible not to see that he loved coming over to take a
bite out of me psychologically with the courts backing him up, something 50
million women in America in the same situation 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. We were all, me and the kids,
window dressing for the creep. But there's nothing you can do about it without
severe legal repercussions. Even Pete had to swallow his urge to crack Len’s
skull when he came round, which caused him severe if not unbearable pain every
time Len came for the kids every other weekend.
All of Len’s legal maneuvers 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 repeatedly
like I was a disobedient eight year old. As this phase dragged on it became
clear that much of Len's legal strategy 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 anytime we had
contact or discussions and who seemed half in the dark about what Len was doing
himself.
Part of the endless harassment to get me to leave the evil Pete and go back to
the worthy Len was near daily phone calls and house calls from a dozen or so
LCMS ministers. It was 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 came with a large roast beef in tow.
Fortunately
Pete was right there in the living room two feet from the front door at the
moment. The interaction between the three of us was short and to the point. My
mother, whom Pete described once as looking remarkably like the
"Basilisk", a mythical lizardlike monster, threatened us both with punishment
from God and repeating to 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 long haired 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, that God and she could both go fuck
themselves and for her to get the hell out of the house. When she hesitated he
more or less pushed her out the front screen door and to make his point
further, our point by this time, he tossed her roast beef in the garbage can
that was sitting on the porch not far from the front door.
"Seemed
to me more like a squabble with a dyke over their mutual girlfriend,” Pete said
the minute she cleared the driveway with her bag in 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 kind of, punishments made that picture
of my mother 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 the most common hidden crime in America. I'm sure,
that I don’t know how to prove it, that Adam Lanza’s mother screwed his ass
into the painful hell he lived in that drove him to take all those kids there
with him for some twisted revenge on his pious fraud mother. To hell with 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 and
waked up by the unhappiness on real faces you can’t miss.
One
thing for sure is that the Columbine and Virginia Tech and Newtown mass murders
were all perpetrated by unhappy kids. And it’s hard to make the connection that
a lot of that unhappiness comes from absent, neglectful and predatory mothers.
I am sure fathers too, but whatever the current psychobabble nonsense of
parental equality drummed up by the cultural propaganda chorus to insure
capitalism has a willing female labor force, poor mothers in an especially big
way are the problem through sins of commission and omission because we still
are what we are instinctively the primary immediate parent responsible for the
kid whatever the myth. Pity the children.
When my mother saw how forceful Pete was and during that brief time how much my
kids liked and respected him, she and Len and Don changed gears with who they
wanted to get custody of the kids. First Len said explicitly that, of course,
I'd get the kids, the strategy ion that for them being that he'd get to keep
his feet in the game with every visitation and that eventually he and his
retinue would influence them to influence me to go back to being Mrs. Ruth
Schoppa. But after my mother's visit, the legal papers changed sharply and
abruptly to Len asking for custody of our three biological kids, something I am
sure my brother, Don, had a hand in this legal maneuver as my mother's henchman
in all such matters.
Then the strategy was to take the kids away in order to break my heart, which
it did, and get me to stay with Len. With grandparents on both sides on Len’s
side, indeed, their tone quickly became, “We're going with daddy; and you
should go back with him, too.” Nothing more to be said.
This thing of losing custody of your children is talked about so flat tone in
our mass media as to be the equivalent of something as casual as choosing this
or that cut of meat at the grocery store. But it's damn not. It killed me.
Almost. At that point nearly turning me into the crazy person they said I was
because of the kids deciding under their influence to leave me. I still refused
to go back to the bunch of bastards. That wasn't going to work, fuck you all
and your horrible games, I thought.
Soon after the kids went with Len, Pete and I bought an $800 trailer to live in
with June, whom I still had custody of. They left her behind, not fighting for
custody of her, to keep up Len's connection to me, for the theme was
relentlessly, come back, Ruth.
Len
still had visitation rights with little June, who was three years old by this
time, every other weekend, and those comings and goings were so very difficult.
Almost too sad to talk about, on the third or fourth one of these visitations,
when he brought June back, she wouldn't speak anymore. Wouldn't talk, wouldn't
smile, wouldn't do anything but crawl around on the floor making sounds like a
kitty cat. Whatever had been June seemed dead, just not there anymore and
replaced with something truly out of a horror film, but one you’re in instead
of one you’re watching
After a half 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 an obviously fake and contrived manner,
"What did you do to her?" This doubled the scariness of
what had happened to her 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
whatever might have happened to her, but accusatory towards me in a way that
had been prepared for. Whatever they had done to produce this horror, they wanted
to use it on me, on us, on me and Pete, to destroy me and us by destroying her
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, picking up stakes with the trailer and
driving off to someplace unknown, to them and to us for we had no idea where we
were going, just out of there where he knew where we were. Screw the legal
agreements as to visitation. I'd rather be locked up for violating court
ordered visitation than ever let him get his hands on her again.
Soon we crossed from California into Oregon, leaving the state upping the
potential charges for violating visitation access 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 anger. Pete said if he ever came across Len after what had happened, he'd
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 June after that. We both spoiled her in anything and
everything she wanted to get her to smile and that works. It kept her looking
the most beautiful child in the world, whatever it cost in time and energy and
however much it made her one selfinterested child.
Pet never quit. He was a real revolutionary, true and blue like in the novels,
a revolutionary to the death as he vowed long before he met me. I should talk
about that some to make it clear why he had this extremely dedicated and
radical disposition that may seem so out of place in this post 9/11 era. When
Pete came of age in graduate school, his thesis advisor, a big man in science
by the name of Dr. Posner, stole his research. Pete said at first he couldn't
believe it. Posner stole it and published it without Pete's name on the
scientific paper published. Then he told Pete, to a great extent because Pete
was and looked like a late 60s rebel at this time, antiVietnam war and the
rest of it, practically told Pete that he wouldn't sign Pete's PhD thesis
unless Pete kissed his ass.
There was no uncertainty about what was going on in this game between the two
of them. It was just a pure power play, teaching Pete who was boss, a kind of
rape. So what did Pete do? He told Posner and 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, he said, a genuine miracle came, an unexpected change in his life
for the better. He said he was reborn, sort of as a young god, with a whole new
level of confidence in his life. He joked that his sex life, which wasn't the
worst even before this, took off to new heights where women started near
fighting to see who could sit on his lap at clubs on 1^{st} and 2^{nd}
Avenue in New York City. On his way from New York to California not long before
we met he said he'd had sex with three different women on the Greyhound bus
ride while going cross country. He said it was a new life that was impossible
to turn back from even though he'd lost his PhD as the price paid. (He got it
back ten years later as I’ll tell later when his biophysical research on bone
growth was validated by a research team in Czechoslovakia who gave him credit
for the discovery he made.)
Anyway, the point is that he was a fighter in all things and that he led the
fight to bring June back to life, always telling me to never lose hope. This
was all a hard task because June hardly ever spoke a word over the next three
years after what was done to her. But what she did do was draw a lot, an
amazingly gifted artist even though so little. And when she was about six years
old, she started drawing pictures, cartoon frames like I was doing at the time,
hers about strange looking creatures, people that Pete thought might have hurt
her back then because the pictures had this dark look to them, a lot of them
set in the middle of an endless rain storm.
At
about this time, Pete had taken a special course in the Montessori Method of
teaching reading to deaf children and he used it to teach June how to read and
all the talk back and forth loosened June’s tongue until it gradually got her
talking again.
Not only did her talking seem a miracle in itself but it came also to explain
what had been done to her by them. I should point out that June never used a
pillow when she went to bed. She didn't like pillows. Very strange we thought,
but no big deal. Eventually June told us that they had beaten her up because
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 and partially smothered
her and told her if she ever told anybody, they'd smother her. And that put
that level of fear in her. I'm not exaggerating in this. That’s what got her to
stop talking when she was three.
She also talked about things done to her that seemed quite sexual. But Pete
never took that part too seriously because once you start thinking and talking
in that way about somebody you hate, especially from the 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. What was amazing was that after two weeks of intense focus on what had
happened to her, her lightening up was marked and, lo and behold, she started
playfully throwing a pillow on our bed up in the air. And however much it seems
too much to fit the story just as one might like to tell it, she started using
a pillow to sleep with after that.
The cartoons June was drawing she got the basics of from a comic book I was doing about my life back then. I needn’t have to exaggerate how much the combination of losing three of my kids and the other one being turned into an incubus by the beating they put on her shattered me. Frequent sex, believe it or not, and constant comforting reassurance from Pete helped. But he said, “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 then in the 60s, were big. “Can you draw?” Well I couldn’t. And neither could Pete. But like I said, Pete was stubborn about anything and said, “It can’t be that hard, you just follow the lines and put them down on paper as you see them.” He tried that doing a drawing of June’s pretty face, and it came out startlingly well. “If I can draw and I always hated drawing, you can draw. Just follow the lines and tell the story of your life, childhood and marriage exactly as they happened.”
And I did. I entitled it Minister’s Daughter, Missionary’s Wife. Parts were very raw. I talked, did commix frames, openly about the abuse I’d gotten from my parents, some of it from my mother readily interpretable as sexual abuse. And I talked in a set of a few frames about an incident I had with one of my own kids. I might as well repeat it here. It is the truth and it does shed some light on the emotional grip I was in all my life.
When my first born came along, Lenny, 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 past 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 Lenny. 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, very difficult back then, it turned me on sexually. 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 and 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 telling about to you all, 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, which is the whole point of my telling this story about the Graf clan, way over the top. And if something like that was possible for me, forget that I totally resisted it afterwards, what wasn’t possible with others in the family who were all raised the same way, with beatings and by the minute rigid rules about everything you were supposed to do and not supposed to do, rules that hid the sadism and control freak nature of their enforcers.
Two more points to make. Years later we sent the comic book to Robert Crumb, who was the premier commix artist of the 60s, hands down in 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 and he made that clear. The very last page of the 20 page comic book we stapled together had me poisoning my mother with black widow spiders. He didn’t like that because he was a pacifist. But in reality, that was more or less what we did, poison her reputation by sending out 1000 copies of Minister’s Daughter, Missionary’s Wife to 800 Lutheran ministers and to all of my and Len’s family and their friends, relatives and neighbors.
Because the story was so believable from my telling the worst truths about myself, the book caused my jerk of a minister father to be near instantly retired early, fired, from the ministry as a pastor 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 professions being most basically scam artist sales jobs. And the book caused Len to come down with throat cancer six weeks after we sent the book out. Or if you don’t like the cause and effect supposition between emotional travail and some cancers, by some positive miracle for me and a curse on him, he came down with cancer by odd coincidence after we sent it out.
The very 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. And it works. At least it did for me. For I felt a thousand times better after writing it up, sending it out and hearing from this and that channel the harm it did to these people who had done so much over so many years to make my life one crazy miserable mess. I couldn’t write about these things back then. I can now.
Things picked up after that, which will take us to the child murderer, Ed Graf, again fairly soon in this story. As we entered the year, 1979, almost ten years after Pete had dropped out of graduate school, he found out that primary research work he had kept out of the plagiarizer’s hands had been validated by a newly invented electron microscope technique and that he had been credit for the initial discovery in the scientific journal, Calcified Tissue Research.
This had us head back to Rensselaer in Troy, New York, (RPI), where news of this not only got Posner removed from his PhD committee, but also got him, as a genius prodigal son who had figured out how immature bone in babies transforms to rock hard adult bone, a position on faculty in the Dept. of Biomedical Engineering there. This sudden leap in status took us down to Texas to see my family, really to see my three kids after six long years away from them, Pete with his once long and scraggly 60s hair now cut as neat as Robert McNamara’s for the occasion.
Pete all neatened up on the way to the inlaws.
Our first stop was in Vernon, TX, where Len and my two oldest kids were living. Then we were off to Waco where the youngest, Nathan, was at some semireligious thing at Baylor and where my parents were still living. Uncle Ed and Aunt Sue were also living in Waco with their grown kids, Ed Jr. and Craig. Because I was doing my best to make nice in this Texas trip for the sake of the three kids, we went along with my mother’s suggestion for us to visit Uncle Ed and Aunt Sue, especially to connect with recently married Craig Graf, my godson in colloquial speak, with a wedding present in hand for him and his new bride.
Ed Jr. stood out for a couple of reasons when we went over to Ed and Sue’s. For one thing, he was still living with his parents in his thirties. And this was with no particular recession on hand to rationalize this, at least back then, not usual living situation for families. Another is that he was immediately upon introduction afraid and apprehensive about me and Pete, really you’d have to say generally afraid and apprehensive because despite Pete’s moderately imposing presence, he was charismatic enough that almost everybody liked him on first sight. Most odd is that right in the middle of a make nice, hi, how’re you doing, exchange, Ed Jr. did a 180 degree about face and ran out the back door into the vegetation I remember growing so lushly in their back yard. Also odd is that neither Uncle Ed or Aunt Sue breathed a word, made a sound, stirred the slightest bit, about this odd action that was a total misfit in the context of this long belated family visit.
I doubt Ed was seeing a psychiatrist or getting any such professional help because LCMS Lutherans just didn’t do that back then, or probably even now for that matter. It wasn’t just that they settled such things by prayer, so to speak, but also that avoiding scandal as I think I’ve made clear was a number one on the list for all this vast of pious frauds. This attitude no doubt was instrumental to some degree in the suicide of Pastor Rick Warren’s son. All the fundamentalist Christians are always 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 Ted Haggard or suicides or child murders.
Anyway, it was clear, though we thought little about it afterward, that Ed Jr. had a problem. We thought little about it afterward because without my going through the full menagerie of my relatives, most of them ostensibly had a problem that was observably unmistakable, minimally ugliness and/or obesity on a grand scale, as showed on Uncle Ed and Aunt Sue, whatever the more perverse undercoat that produced Ed, the Child Murderer. I couldn’t possibly know their Graf deviations from the norm like I did for my Graf parents.
Last on the menu of this Texas trip was to go see my brother, Don Graf, in Lubbock, 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. 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 fairly well concealed hate stemming not just from my leaving Len and church way back then but also from the devastating effects of the comic book on them, though their hate I was reading was heavily lathered with forced politeness and formal hospitality for I was now the duly married wife of Dr. Peter Calabria at a high grade university.
It would turn out to be the high point (or low point) of the week, the dramatic climax, this invite to Don’s place to breakfast at his house. We brought a box of chocolate doughnuts. Attorney Don’s trophy wife, Ruby, was all smiles and asking friendly flirty Southern gal questions of us as we entered as though everything was “just fine.” Also joining the Peter Calabria’s and the Don Graf’s at the breakfast table, surprise, surprise, was Ruby’s father, a large sized Texas pig farmer and Ruby’s sister and her brotherinlaw, an enormous Texas speedway owner with the classic back of the neck fat roll and 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 large sized 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 record in street violence 10 wins and no losses, a record with some blood spattered on it that made him think, correctly or not, sane or crazy, that if he stepped into the ring with Muhammad Ali, he’d beat him.
Don’s wife, Ruby, was friendly enough to make me wonder how much of her friendly gab was tinsel and how much personal stimulation from Pete. Brother Don, despite being a senior partner at the oldest and largest law firm in West Texas, McClesky, Harriger, Brazill and Graf, was not impressive in appearance or demeanor, that description given with no sour grapes of any kind, though it’s hard to tell whether one is being fair given how much I disliked this pansy ass creep who has to wear cowboy boots to Sunday breakfast to keep up the pretense of his mother blessed Texas superiority.
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 in 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 and tales of the wolf upstairs in my bedroom, with Pete leading the way as recklessly brave as a teenage matador and I still as naïve as a newborn rabbit, we all jumped in our respective vehicles and off we went.
A picture worth a thousand words would do better at this point, but we have to settle for a verbal snapshot of Don standing on one side of a table at the winery where corks are put in wine bottles with a cork hammer. He is banging one such hammer repeatedly on the table top as his insulting voice tone punches are thrown at me again and again, which is making me progressively more uncomfortable and shaky as in victimized days of old with him. He knows me well, which buttons to push. And next to me, progressively more irritated while naively trying to disguise his bubbling up fury for the sake of maintaining some semblance of family civility, is Pete.
As the tempo of Don’s attacks increase along with Pete’s less and less well disguised look of impending violence and Don’s hammer banging down harder and harder on the table, I am vaguely aware of the presence of Don’s inlaw henchmen out of the corner of my eye about fifteen feet or so away from the main action at the corking table. Pete seems unaware of this peripheral danger, and said this to be the case after the standoff was over. His supreme or excessive physical confidence from ghetto living on the Lower East Side after he dropped out of school blocked out any feelings of fear instinctively as his faced welled up in a twist of violent hatred of Don for what he was doing to me repressed by an odd misplaced effort at being mannerly. He looked, though, as I remember so well, and it kept me sane and intact through this miniordeal, like he was about to leap on Don and strangle him to death. At this point in this upward spiraling tension or thereabouts, 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 declared over. Back in our car on a dirt road that circled this winery that was muddied from rain the night before, I look hard 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 news. I hope I didn’t make a bad impression,” and wondered for ten seconds if he meant it all. Another ten seconds after that, though, Pete said as I realized too before he said it, “Punk faggot piece of shit couldn’t pull the trigger,” meaning, as I didn’t have to be told by now, that Don was supposed to provoke Pete into a fight the other two would join in on either to beat him up and/or call the sheriff to come in on after the fact to have Pete locked up and destroyed that way. No wonder my mother pushed so hard and smoothly to get us to come to Lubbock.
Don and his inlaws at this point are in Don’s car in front of us on this puddle infested road. And as we slowly meander down this muddy path, suddenly their car comes to a stop. And, of course, as we are behind them, so does ours. We wait tensed. It is a long minute and a half until Donald Lee Graf jumps out his car and runs over to Pete’s driver’s side window, sputtering nervously, “We got stuck in the mud, honestly!” And I blurt out from the passenger side without thinking, surely because I sensed the 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 nodding, he ran back to his car, jumped in and drove away. At that I knew the bastard did it, was the one who killed baby June’s soul or gave the order or suggestion for it or was seriously in on it somehow, likely carrying out a plan that had originated first in my mother’s dark heart.
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 humiliating him to us, by this point, the two prime enemies he had in his life. Her male relatives seeing what a coward punk her meal ticket lawyer husband was must have taken Ruby past the critical point of putting up with his bad odor as she had for years for the sake of rising up out of the pig farmer daughter class by marrying a lawyer.
It’s funny, I recently read an old piece from The New Yorker magazine about the Nuremberg Trial where the author, name escapes me at the moment, talking about Goebbels escape from execution by taking cyanide says that Goebbels was the exception to the rule that all bullies are cowards. Don wasn’t.
Pete’s stay at the university in the early eighties didn’t last long. While a favorite of his students in teaching – he received a standing ovation from three classes of the engineering thermodynamics he taught and had the highest student evaluations in the school of engineering for the ten years they had been conducted – he found his position in the hierarchy and the degree of control little different than he was a graduate student. While obtaining considerable pleasure in paying back the four professors who had screwed him in his graduate school days in various ways, revenge actually improving one’s life and mood considerably as one finds out when one tries it, Pete was a serious revolutionary who felt that being part of privileged academia and changing the world for the better were contradictory incompatibles.
So he left the university and in a dramatic way after a couple of years so we could devote all of our attention to the difficult problem of how to solve not only the problem of hierarchical control and the unhappiness it generated but also the problem of violence enhanced by weapons, especially nuclear weapons. From his own experiences, both fending off aggression from institutional superiors and defending himself aggressively against those who would attack him and our family, which by this time had expanded to four of us, it was clear to him that aggression up to and including the more violent kinds of it, was part of human nature. The greater part of his thinking on this, which derived from his own experience with bosses and living in rough neighborhoods and driving a cab in New York City for a year after he first left graduate school was supported by a book we both read on animal aggression called On Aggression by Konrad Lorentz, winner of the 1973 Nobel Prize for studies on animal behavior.
The culmination of these considerations was a newspaper article he penned a few years after leaving school, our first article on the idea of aiming mankind towards A World with No Weapons in order to preserve the human race and maximize the happiness people are able to squeeze out of life.
Knickerbocker News, Albany, NY, May 1986
What would a world with no weapons be like? It would be divided into two sectors, mostly a large number of relatively small nations or city states of about a million people each that have no weapons at all, not the city state as a whole nor any of the people in them including the police, who must enforce any rules the city states wish to enforce on its citizens. This proviso gives maximum freedom for the citizens, for as we see again and again, popular uprisings against tyranny are brought down and the will of the people defeated by police power that depends first and foremost on the weapons that police 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. No guns and no jails in A World with No Weapons as make for the great imbalance in power between the ruled and the rulers that makes tyranny possible.
This provides freedom in the real sense even if at a loss of order and efficiency. Freedom in this sense is each city state making its own rules relative to the second group that exists in A World with No Weapons, the Guardians of Freedom. Their control over the city states is limited to two broad rules, no weapons and no invasions of other city states. Anyone holding a weapon whose sole use is for resolving conflict is put to death. This rule exists also for anybody who uses a tool like a knife in fighting with another person. That is to say, the maximum weapons that is allowed in a conflict 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 is also shown especially to the young or in equivocal circumstances where a reprieve is possible by the rolling of a lucky number in a Lucky Numbers game (to be considered in detail in the next section) where the number of lucky numbers assigned and the probability of escaping the death penalty is a function of the circumstances of the breaking of the no weapons rule. The rule of invasion of another city state is also punishable by death. These are the only two rules in A World with No Weapons. The city states decide all their own rules otherwise, few it should be obvious given that the only way allowed to reinforce them is through the muscle power of those the group wishes to enlist as police.
There is obviously lots of uncertainly in such an existence and lots of excitement for each protect themselves for the most part. But there is also lots of freedom and from my own experience in living the life of a rebel and a renegade, the intoxicating pleasure of freedom greatly outweighs the lack of protection of armed police, too much of the actions of which nowadays are unjust and use excessive force as part of their daily routines.
The other great question is: How do you get to this World with No Weapons, for those who hold the advantage of power must be reluctant to give them up. It is only the consequence of continuing on the way we are that decides the future as one with no weapons, in the end squabbles between nations leading to nuclear war and mankind’s annihilation. If that is not understood, the inevitability of the nations of the world going to that most undesirable place of megadeath, no effort will be made in that direction.
To make it clear what the alternative to A World with No Weapons is, three hard facts about the future must be clarified with mathematical precision. First is that violence is innate in mankind, especially the males, who in sight of defeat in a conflict have little motive to restrict their choice of weapon to thwart defeat and its punishing consequences. If the Japanese or Germans had the atom bomb in WWII, they absolutely surely would have used it on us. And future hostilities, worldwide in scope would be no different. Does anybody think that Russia on the verge of defeat in international conflict would no defend itself with the 7000 nuclear weapons it possesses? Or how about us on the verge of defeat? Enough of Pollyanna delusional thinking.
And an allied impediment to clear thinking 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 loving a child. That thought is utterly an impediment to we people doing something real to stop nuclear annihilation, the thought that just wishing it and praying to something that’s not there is going to save us. And the second religious delusion is that even if the world does go to and, everybody or at least 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, will all be happy in Heaven after it happens. 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 we have about him arise as an odd fuck up in human nature twisted by exploitive cultures over the centuries.
This is to say in sum that however idealistically unrealistic A World with No Weapons may seem at first, it’s the only salvation to the horrible end for all of nuclear annihilation. Neither God nor Heaven nor some childish trust in the basic goodness of mankind that obviates evolutionary competition is going to save us from the worst. If there was another way, surely we would set aside A World with No Weapons as a tangible alternative. But there isn’t. We are heading for hell on earth without concerted political effort to get rid of the weapons, period.
And how, say the yet resisting naysayers, do we get there? It 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 all of us getting to A World with No Weapons and continuing to live. And we have the stick to hit reluctant nations with in terms of our military might. Winning at this game definitely requires the carrot that these mathematics say will come from their laying down their weapons. If it didn’t sexist pure military might could never work. The idea matters and matters a lot in this case.
But also the military might matters also because some won’t like giving up their weapons and will only do it when there is a gun to their heads. That’s cool. If the US has to 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 that the main problem will be China, which might have to have a few of its towns taken out in a joint effort by Russia and America. I’d hope not, of course. Personally I have nothing against the Chinese. It’s just that there’s less cultural cohesion between them and us than between us and pseudowestern Russia culturally.
What is gained, it should be stressed isn’t just a reprieve from nuclear destruction. The sense of freedom achieved by the grand plan in terms of the true balance of power achieved with and in A World with No Weapons is not a small thing. And that has to be appreciated by understanding that there really isn’t much freedom in the world right now, not even in our blessed land of free and fair America beyond the use of such slogans used to keep people in line with delusional promises that really never materialize in the clutch of reality.
We spent much of the next twenty years trying to explain our ideas scientifically with hard mathematical analysis and proofs, that necessary to counteract the endless cultural propaganda that talks of the land we live in as though it were a delightful Garden of Eden if only you obey the powers that be. Our research meanderings took us far and wide in adventures not worth cluttering up these pages with at present. I’ll try next to introduce the mathematical analysis we achieved in a soft story like form now by fast forwarding to a tussle we had with of one of the largest and most powerful and unpleasant corporations in America, Greyhound, that will get us up to date with on the ground reality before we start the mathematics of thought, emotion and behavior that makes clear the mess the world is in and why it needs to get rid of weapons to get us out of that mess.
Certainly you could imagine a life more pleasant. A Greyhound bus trip is the reality. Anybody who’s been on one knows of its pains.
Our recent Greyhound round trip started out OK, more or less. The driver dropped us off in downtown Tunica, Mississippi, 20 miles beyond Tunica’s casinos we had come to Mississippi for and a $50 taxi ride to get back to.
“You should have told me you wanted the casinos,” he says to us two unmistakably northerner tourists who had never set foot anyplace in Mississippi before and hadn’t the foggiest idea where anything was.
The Greyhound depot in downtown Tunica is at a McDonalds. As we spit out our reasons for coming to Tunica to a couple of farmer looking McDonalds patrons curious about all the luggage we had dragged in, a heavy set black woman in a smart uniform approached us with a warm smile and offered to drive us out to the casinos.
As we lift our three large bags, all of our worldly goods, into the trunk of her car in the parking lot, this woman tells us, “I’ll have my manager drive you.” The McDonalds manager who come out a minute two later is a softly pretty, midtwenties black girl with a remarkably sweet tone with whom we discretely exchange political ideas during the ride out. I and Pete, my mate of 40 years, are both struck by her sensitivity.
When we get to the Sam’s Town casino, Pete says thanks and hands her $20 “to put some gas in the car.” A few steps away from the car we hear a last minute shout of, “If you need any help gettin’ back, call this number.” So considerate, both of these women were. We were touched.
In contrast casino patrons are some of the funnier looking people you’ll ever see whether in Tunica, Las Vegas or Atlantic City. There are no James Bonds in tuxedos or Ms. Pussywhipple in low cut dresses to be seen at the gaming tables. This casino was ugliness at the deepest levels for there must be no people in the world more obese and instinctively unattractive than Mississippians. Politeness that tried to describe them as otherwise would be an out and out lie.
Much as we were aware of their, to us, funny appearance, so did many of them communicate their awareness of our superior looks in one way or the other to make us feel for the week and a half we were there like the James Bond and Ms. Whipple they’d seen in the movies and other casino propaganda.
Interestingly we weren’t there to gamble. Smart people never gamble at casinos, never. One long time casino owner in Las Vegas said flat out on CBS “60 Minutes” that he never saw anybody come away a winner. The reasons are simple though a bit hard for dull minds to digest, which is how casinos get to steal billions year after year from stupid people who think they can win. One older fellow I talked to in Las Vegas made it clear why. (Only a woman could get away with asking these questions of a slot machine gambler playing at a rate of $2 every ten seconds.)
“How long have you been playing the slots?”
“Twentyseven years.”
“Do you win?”
“Not ever.”
“Why do you play?”
His last response was given with a look of go away and don’t bother me anymore: “Tranquility.”
Passing over for the moment the pathology of spending that much money to distract one from their unhappiness, so common an affliction if the billions spent on gambling in America is any indication, let’s now explain mathematically why one must lose at casino gaming and that as an introduction to a clear mathematical understanding of human feelings.
We’ll use roulette play to illustrate and for simplicity sake assume the gambler bets V=$100 on red at every play. Of the 38 spaces on the roulette wheel where the ball may land, 18 of them are red, a land on which wins the gambler V=$100, and 20 of them not red, which loses V=$100. With the probability of winning, Z=18/38=9/19, and of losing, U=20/38=(1 ̶Z)=10/19, the expected value or average outcome of the gamble is from elementary probability theory,
A. E=ZV ̶ UV=(Z ̶ U)V=((9/19) ̶ (10/19))V=( ̶ 1/19)(100)= ̶ .526(100)= ̶ $5.26
This means that if the $100 bet on red is made repeatedly, on average the gambler will lose $5.26 for every bet made. If he kept playing again and again, from the quite reliable Law of Large Numbers of mathematics, he’d be quite sure to lose about $5.26 per play on average. The other possibility is to play not a lot and have luck on your side enough to start off winning. If you quit then while you’re ahead, and never come back to play again, you come out a winner. But there’s also a firm mathematical reason why people who do win to begin with come back and play some more and eventually give it all back and then some from the Law of Large Numbers.
This return to the gaming tables after you first win is driven by the peculiarities of human emotion. To make sense out of those emotions and, indeed, to describe all of our human emotions with mathematical exactness, we next introduce a gambling game that is a bit easier to work with mathematically than roulette, a dice game called Lucky Numbers.
In
this Lucky Numbers game you win V=$100 if you roll a 2, 6, 7 or 8 on
the dice and you lose V=$100 if you roll any other number. The probabilities of
rolling the 2, 6, 7 and 8 lucky numbers are respectively 1/36, 5/36,
6/36 and 5/36. And the probability of rolling one of these lucky numbers and
winning is the sum of those probabilities, Z=17/36. And of losing, the
probability is U=(1 ̶Z)=19/36. This has the expected value or average
outcome of this game, using the same function as in EqA
B. E=ZV ̶ UV=(Z ̶ U)V=((17/36) ̶ (19/36))V=( ̶ 2/36)V=( ̶ 1/18)V= ̶ .555(100)= ̶ $5.55
You get the picture. This is as losing a game as playing red in roulette. What makes it a better game for analyzing the human emotions, though, is that we can easily split it up into two games, two rolls of the dice. First you roll the dice with the object of getting a Lucky Number. If you do, you win V=$100. If you don’t, you don’t lose anything. You just don’t win the V=$100. However, you are required to next roll the dice with the object of avoiding a v=$100 penalty. (Note the small case v symbol for the penalty.) If you roll a lucky number, you avoid the v=$100 penalty. If you fail to roll a lucky number, you pay the v=$100 penalty.
This splitting of the game into one roll to win a V=$100 prize followed by one to avoid paying the v=$100 penalty is more amenable to developing a mathematical representation and understanding of human emotion starting at Eq66 in Section 4. It also makes clear why initial winners always return to the casino to give it all back and it explains violent emotion sufficient to make clear why nuclear war and the annihilation of the human race is a sure thing unless we make planet Earth into A World with No Weapons. The invasion of the Ukraine now pits two nations with over 7000 nukes each, the US and Russia, against each other with just a hundred going off needed to make the planet uninhabitable for human life.
To make the case for why we must eliminate all weapons worldwide, we begin by showing how the Lucky Numbers game played to win a prize of V dollars explains the emotions of hope, anxiousness, excitement and disappointment and when played to avoid a penalty of v dollars explains the emotions of fear, security, relief and dismay. The v number of dollars lost in the penalty game is then translated to the cash value of a life that is kept from being lost via survival, combat and replication to mathematically explain all of our survival, combat and reproductive emotions like hunger, violence, sex and love. We’ll take a break from the math now, though, and get back to the story because all mathematics and no adventure story makes for dull reading.
If we weren’t in Tunica for gambling, what were we there for? Just for a hopefully cheap place to live. We came to Mississippi from Silverthorne, Colorado up in the Rockies. We generally live from cheap motel to cheap motel. When one place turns unfriendly and curtails our freedom, we leave for the next place. When the high country turned sour, we threw a dart into the map and it landed on Tunica. Not really. Actually we saw the low prices of the casino hotel rooms and that was the draw. Not so cheap as we thought, though, and after two weeks we left and headed by bus for Lubbock, TX.
On that trip to Lubbock, TX, the Greyhound bus we were on stalled out five miles short of Abilene. No big deal for us seasoned Greyhound travelers, so we thought. But I might have guessed the trip could be seriously strange from the tone of the black woman bus driver we drew for the ride at Dallas.
There she ushered in every one of the passengers with a scowling, snarly, “Don’t put any luggage on the seats!” as if each was an impossible child who just smeared feces on the bathroom wallpaper and needs to be told in a scowling, snarly voice, “Don’t do that!” We semiforgave the unnecessary rudeness by understanding the driver to be just another American worker filled with the grind of her nine to five workload dispelling her bottled up resentment on whatever victim was available, with all that made worse in this case by the color of her many generations tortured skin.
After the engine sagged out, the bus crawled on three cylinders into an Abilene Greyhound depot set in a 7Eleven with 8 gas pumps out in front. And right next door was an Allsups grocery with a half dozen gas pumps. That would matter because my mate of 40 years, Pete, is asthmatic. At its worst asthma can kill you. It does in 3500 people a year in America.
But we paid that level of danger little attention as our trip stopped cold at three in the morning because as dangerous as extended exposure to gas fumes could be for Pete’s affliction, the key word is “extended” for we did not think the bus would be stuck in this gas pump graveyard for 7 hours.
It
being early in the morning and the summer night warm after a while Pete conked
out on a patch of grass between the 7Eleven and the Allsups for an hour or so
and when he awoke, ouch, his chest hurt. He got alarmed immediately in an
instinctive way as asthmatics do at the onset of anoxia and pain as described
mathematically starting at Eq155. He had standard asthma medicine with him, but
it provides only limited relief when you’re continuously exposed to the lung
antagonist. So the question on his mind was: “How much longer are we going to
be here?” And accordingly he asks the bus driver in as polite a tone as one can
muster at the onset of an asthma attack, “How much longer until the new bus
comes? I’m asthmatic and all these gas pumps are causing me pain.”
She replies in her scowling, snarly voice, “Why didn’t you tell me that when we
first got here!” not having any sense of the medical dynamic and eager also to
make the point that Pete might be at fault for whatever was happening, or worse
that maybe he was lying about something. This put the game into 2^{nd}
gear, with Pete in this state needing to defend himself against a bus driver
out of a Stephen King novel. “My medicine will keep things cool. I just want to
know how long it will be until we’re out of here.”
Her response to this is to call 911 and a few minutes later the rescue fire truck and the ambulance arrive. Pete has a PhD in Biophysics and taught in a Dept. of Biomedical Engineering and consequently knows a lot about his medical condition of 40 years. The ambulance driver had a brain and quickly got the picture that what was needed was not a trip to the hospital but for a replacement bus to come and get Pete away from the gas pumps. So he went over and told that to the bus driver, who then told the ambulance driver to tell Pete that before he could get on any Greyhound bus, he’d need to go to get a doctor’s official permission to get on the bus, which at 5AM meant a trip to the hospital. The ambulance driver came back to Pete and told him this with his hands stretch out palms up, “There’s nothing I can do about it. She makes the rules for the bus.”
We both jumped in the ambulance and off to Hendrix Hospital we went. The trip was stupid and costly for there was nothing the hospital could do beyond the few puffs Pete had already taken from his inhaler. The doctor had a thick brass crucifix tacked on his shirt collar. Texas Christianity is nothing but excessive. There are more than a few hotels down there with a stone carving of the Ten Commandments at the entrance.
We got back to the bus station hours later just a couple of minutes before the replacement bus was ready to take off and that only by repeatedly telling the hospital staff to skip this and that procedure that had nothing to do with Pete’s problem. Back at the bus depot uninsured Pete quickly took down the number of the broken bus and got the name of the bus driver, Mattie Sneed, to make sure that Greyhound would pay the cost of this ridiculously unnecessary trip to the hospital. When the replacement bus finally pulled into the Lubbock bus station, Mattie Sneed dashed off out of sight the minute she brought the bus to a stop.
We stayed in Lubbock for a month or so trying as ever to recoup some of the $27,000 inheritance my mother had left me but which my brother had managed to keep most from me, over $25,000, for the last nine years since my mother had died. As soon as the will was probated, Don told me up in his law office that I'd never see a penny of it unless I left Pete, whom I’ve made clear, I hope, was as much a leftist idealist as Don was a nut job on the right. I took him to court in Lubbock actually thinking quite stupidly that justice might prevail in some way because so little of the money had been paid out, I thought, how could a judge not see the game he was paying. Don made his case that Pete was a bad person and that my mother really wanted the money to be paid for treatment for my mental illness, you know, the one that made me leave my first husband, the minister. I thought I couldn’t lose because how could the judge possibly justify hos withholding the inheritance of a 70 year old woman with little money for such a silly reason of health, mental or otherwise, when I had zero record of ever having had or been treated for a mental illness. And as far as my physical health went, I had Medicare from Social Security. So what was he withholding the money for, Your Honor? I lost, didn’t get a penny. For such is the power of the courts in this country when the judge and the defendant, here Don, are all good Christians and have known each other since law school.
Discouraged again and with the summer heat and the mustiness in our nostar
motel getting to Pete's asthma already aggravated by the Abilene experience, we
headed by bus back to the Colorado Rockies where the cooler cleaner air there
had to be much better we figured. But our ordeal with Greyhound was not quite
over. I hate to think of the painfully critical moment of the trip to write it
up as just the recollection of it makes my stomach pitch and rattle.
"No luggage!" Pete shouts to me in controlled horror as he approaches me from an inner door at the Denver Greyhound Station, "They lost all our luggage!" And as we live from motel room to motel room as idealistic savetheworld radical fugitives from modern civilization, lost were all our worldly possessions.
It immediately struck me that something didn’t add up. How could they so neatly lose all three of our bags and not one of anybody else's on the bus coming into Denver? Quickly my dark mood pointed blame at Greyhound and that black woman bus driver, Mattie Sneed. I said to Pete, "She must have stuck our name into the Greyhound computer, and when our name came up on it this trip, the ticket agent in Lubbock made it a point to mishandle our bags so as to get them lost." Such is the nature of paranoia when you’re on the down end of the game. Kicked in the head in unexpected ways like the seeming unlikely effective theft of $25,000 by my brother, you begin to suspect skullduggery in instances where accident is the cause.
And who knows when which is which when much that is done intentionally that is painful is attributed by the perpetrator as an innocent act. When I asked my brother, for example, for money to ease our difficulties in losing 2/3 of our worldly possessions in the Greyhound luggage loss, he wrote back that “mother didn’t leave the money for that” and wished me a “blessed” birthday. Surely if one was looking for a way to beat up on a sister to pay her back for rejecting him, this story gives the perfect recipe.
By the time we got to the Frisco Greyhound depot up in the Rockies, I had become moderately unglued. It did not strike me as implausible that a corporation with power to screw people would do it if they had reason enough. The notion of fairness from capitalism was shot down by the mortgage scam, wasn't it? And Greyhound has a lot of power with its total monopoly of the bus industry and no place else for abused passengers to go, for those on the lower rungs of the social hierarchy of economic and political/police power who can't afford airplane fares are (really) often treated like dogs by Greyhound. All the passengers on a Greyhound bus are niggers.
The trip to the motel in Silverthorne was emotional. I tried hard to deflect rumblings of worse to come. Pete, ever caught up in the latest advances of his mathematical analysis of human emotion, seemed to translate the tension of the luggage loss into enthusiastic distraction with the minutiae of analysis.
The owners of the motel were a PolishAmerican family, rather dull and plain like the folks you might see in polka dancing TV shows and caught up irreversibly in the nickel and dime game of survival of petty status seeking that in the end lethally affects almost all American families destructively save the model families waved in our face in the media 24/7 as some sure realization of the American Dream.
To us the wife was always pleasant with her leprechaun smile that quickly put you at ease. He, Mike, her husband, was the flip side of the happy immigrant family, burnt to toast by his immigration experiences. I felt sorry for what happened to him to make him such a hater of America, and of Americans, not such a nice guy at times when he played the power of motel owner in a sneak ass way, which got us to leave once. But Pete always held him at bay with a mixed kind of attitude always thinking Mike was a bit crazy or possibly on meds.
An entirely negative attitude towards Mike, though, was off base. The stress of the luggage being lost got Pete to open his usually reticent mouth for he was sensibly unwilling to talk openly about stuff as inescapably revolutionary as the intention of giving all the money folks long prison sentences because they're the ones who have the real cash power to control everything that goes on the country and much beyond. You can derive the moral reasons for this mathematically, but it's not a tune you want to be humming too loud in public. Anyway this time around at the motel, the tension of the luggage problem opened Pete's mouth and almost immediately Mike took up the conversation and surprisingly to both of us came off as a smart friendly fellow, at first.
To find out what happened next, you have to wade through some technical verbiage. It is what popped up sharply as soon as Mike told Pete he had a degree in electrical engineering, or maybe something close to it. For the previous month Pete had been looking over the emotion equations we'd developed from casino games to see that our Law of Emotion, T=RE of Eq75, was a near perfect analog of Kirchhoff's Law for RC circuits. Mike could follow this because he was an EE or such. Of further importance is that Kirchhoff's Law also effectively represents negative feedback control, 1st order. And Pete realized from this unexpected technical conversation with Mike that the RE part of the T=ER Law of Emotion has the form of the error function in negative feedback control theory. This makes great sense when the "error" in one's goal directed activities is the difference between where you're at and where you go to achieve your goal.
Lots of ramifications and nuances of it perfectly tell you exactly how your emotional machinery works, in terms of standard and near ubiquitous negative feedback control. But as the conversation, which for Pete generated these mathematical ideas, went on it became clearer that Mike has but a limited sense of science as a field of discovery and not enough education to understand the breakthrough Pete had made in cognitive science. And Mike may also, I venture, have had too limited experience in life to metabolize the sociopolitical implication of the mathematical conclusions. Mostly he had experienced the less enjoyable parts of life, enough so to make him act in that silly, foppish way that made us think him a bit nuts and on meds.
From these and whatever other causes, Mike could not light up in excitement, even after it was made mathematically clear, unavoidably clear, to him the connection between functions for our emotional circuitry and the basic equations for an electronic circuit. A person who was honestly emoting would have, for this is no fairy tale. Kirchhoff's Laws just do have the same essential form as our Law of Emotion, T=RE of Eq75. And that sameness tells us that much as Kirchhoff's Law controls the behavior of an electronic circuit, so does the Law of Emotion control the flow of emotion in people and thence control their behavior. The ultimate importance of the Law of Emotion lies in its predicting emotion and behavior, especially the emotions and behaviors of world leaders soon to blow the planet in the next world war coming to nuclear hell. If we don't get rid of all the weapons in the world with lots of us working collectively to make a weapons free world possible the worst is going to happen. We must get together against this painful common enemy.
In the end Mike was not a believer in mathematics even when the biggest chunk of it was the electronic engineering math he said he was well schooled in. To be fair, these were cash struggling people hoping at this point to make up for earlier losses in their lives, but with as much of a chance of doing that as when you're behind in a casino game and the odds for recouping are implacably against you. This immigrant family was just happy to keep afloat day by day and keep their impossibly naïve wishful thinking about the future alive. The idea that they could embrace the reality of mankind's bigger problems was farfetched indeed.
Our laptop was in one of the missing bags. This necessitated a trip to the Summit County Library by Pete to check out emails and such. There he ran into hotsytotsy Mary the librarian. When using this library previously, a primary focus was his keeping his mouth shut with this ladies brigade whose greatest practical virtue was keeping their privates and minds scrubbed clean.
But having run into Mary fifty times in the previous three summers we were up in this area and filled with the aforementioned excitement of the mathematics of the T=RE Law of Emotion of Eq75, he began to rail about the fascinating connection of emotion with gambling probabilities to her. He told me after he got back that he was surprised, and happily so, that Mary seemed to understand what he was saying. At least she conveyed that impression with the possibly genuine smiles on her face and the nodding of her head while he was talking, the first time he’d ever seen such.
At some point in his minilecture, though, he was torn away by his need to get onto one of the library computers and told Mary that he’d talk to her more as soon as he had finished up his business. But in the excitement of the moment when he was done he forgetfully just dashed out of the library. The next morning he went back to the library with the intent of making up his error to Mary and tells her he has a couple of hours to explain the math to her in its details.
At this very moment he is talking to her, though, Janet, another librarian we also had contact with on our summer visits to the Rockies, jumps into the game. Janet is a slight notch advanced over Mary in her Colorado style middleage woman bagginess. Jealous of Mary getting the attention from Pete that she, Janet, has missed from Pete never talking to any of them, she butts in, “Mary can’t talk to you. We already listened to you last year about how the mind works and that’s enough.” Pete had opened his mouth about it once for two minutes.
Pete, truly astonished, says, “You’re kidding, aren’t you?” for the women at the library as every patron of it in Summit County knows spend all of their down time in idle chit chat and gossip. Janet retorts: ”I’m the head librarian here and I’m not kidding. Mary needs to fix up the bulletin board. It’s been needing it for weeks now.”
Pete, almost laughing at this point then says to Mary whose face has fallen to the floor, “That’s a pretty rough job you’ve got here.” And Mary caught humiliatingly in the middle of this social tug of war replies loudly with strain in her voice, “I’ve got the best boss in the world!” And with that implicit order from her boss, Mary hides from Pete forever after.
And that’s life in the real world, ladies and gentlemen, today’s 9 to 5 wage slaves in fear of losing their job obsequiously letting their bosses know that they truly love them and love the fucking they take from them, which they make maximal effort to disguise from the rest of the world as they prance around hotsytotsy pretending the shit they take in life is sweet cream butter.
There’s a real reason why bleachblond Mary and the rest of the librarians and the female workers of every stripe in the country come like clockwork to look so unhappy and baggy as all eventually do, media depictions of middle aged women to the contrary notwithstanding. Time for revolution, ladies. Get smart, dummies.
Back at the motel we felt pity for the immigrant family who owned the 1^{st} Interstate Inn and Pete dropped off this note to Mike.
Dear Mike: Permit me to thank you for the discussions we had when Ruth and I first got back here. They definitely helped me to clarify the details of the mind’s emotional machinery as components of a negative feedback control system. Also permit me, if I may, to correct your misplaced sense of me as a liar, which was obvious in you during our second chit chat.
Lies can be enormously helpful for winning in business and in law. A well placed lie can win the money in a business deal and can win the case in court. In scientific R&D (research and development), however, the ideas valued are not those of the best liar. What I was telling you in the motel office was simple out and out truth. I’ll try to make that clear briefly in nonmathematical terms since you seemed to be unable or unwilling to follow the rigor of the mathematical argument.
The intensity of the emotion of disappointment felt upon failure to achieve a desired or expected or hoped for goal is proportional to the initial expectation. If there is no expectation of success to begin with, there is no disappointment in failure. If there is little expectation of success, there is little disappointment upon failure. And so on in mathematical scale. This is a universal emotional dynamic: everybody including me and you feels this way.
The intensity of the emotion of relief felt from avoiding a penalty one expected to get is proportional to one’s fearful expectation of the penalty. If there is no expectation or fear of a penalty and one avoids it, there is no particular relief in the avoidance of the penalty because one did not expect to get it to begin with. And if there is very little fearful expectation of a penalty, there is but a small amount of relief in avoiding it. And so on in mathematical scale. Again this is an emotional universal.
There are a handful of such relationships between the expectation of an outcome, E, the actual outcome, R, and what we call T emotions like disappointment, relief, depression and excitement. All of them are readily expressed in a unified way with a single mathematical function, T=RE, whose general truth is as obvious as that of the disapproval and relief mental operations I just spelled out for you. To see this, though, you need to take 90 seconds or so to look at and consider this simple law before you make a judgment on its validity, something you were unwilling or unable to do despite your engineering background; which surprised me because my PhD, teaching and research were done at Rensselaer Polytechnic, one of the top engineering schools in the country and I know from personal experience that generally speaking engineers, whether at the BS or PhD level, do tend to trust mathematics.
Permit me also to reply to your attitude towards me as though I were a scoundrel of some sort when I tried to give you some sound advice as an immigrant. My mother came to America as an immigrant and, though, I am a generational one step ahead of you, I am the son of an immigrant and know whereof I speak in these matters. Contrary to your feelings as displayed, I was not trying to destroy your hopes in life or intentionally make you feel bad.
The human mind operates according to that simple function, T=RE, to shape your expectations to fit reality. You (and many people to be fair, some naïve and some beaten by life into blind bourgeois thinking) do the opposite, that is, shape reality to fit one’s expectations. That’s done because of the comfort provided by false expectations and wishful thinking, which usually winds up in a personal catastrophe of some sort as time passes. That’s the point I was trying to make to a family man I have some natural empathy with because I have raised five kids myself.
I don’t expect any of this to take with you, Mike. Indeed, that was not my purpose in dropping this note off. In the end we expect this hard cold mathematical truth to win out with the public as scientific truth properly presented always does eventually, ideological resistance notwithstanding. At that time, hopefully in the not too distant future, you should at least appreciate that our conversations were quite helpful to a full understanding of the complexities of human emotion. And perhaps then you will understand my motives in talking to you better and take some of the conclusions of this broad mathematical sociopolitical treatise to heart as good advice. I bear no resentment and hope you feel the same. Peter
Near three months later only one of our bags has been returned and any chance of our recovering the value of what was lost screwed up by Greyhound. Are corporations, is Greyhound, really that uncaring and cruel? It's important to see life as it plays out, not like you want it to despite your falls in the mud of our modern hierarchal slavery. The mathematics makes clear the dangers of great expectations not supported by sensible evidence. An eternal trip to Heaven after you die is the most obvious of these culturally supported emotionally comforting expectations that have little realistic foundation, just rationalizations and honeyed delusions.
People believe in fairy tales. Why? Because it feels nice to be bathed in pleasant expectations no matter how farfetched and delusional they may be. But when false expectations crash, bad decisions based on delusional hope smash a person into unhappiness and depression fully gotten rid of only with a Robin William’s type suicide as the only true escape of an emotional cripple produced by delusional expectations that never had the slightest chance of being realized. The nature of such wishful thinking is made mathematically clear in this work. A fall from happiness caused by false expectations, especially the big falls, kills the best part of a person from sheer stupidity. And we will all collectively suffer a nuclear fall from accepting delusional dogmas and ideologies that people imagine has their country and religion providing some sort of real security for them.
Suffering workers in today’s capitalist police state societies put up with the crap they’re given with the false expectations they’re fed. One of the biggest is the hope of recompense in Heaven or Paradise or from rebirth. And another is that if they endure suffering and sacrifice life will be better for their kids. No way. Life as a wage slave is assured for all whatever one’s level in the social order.
Another expectation sold the workers is that they can have happy “golden years” in retirement to recompense for the pains and humiliations endured as workers. No way. Old age is the time in your life when you die, unavoidably, inescapably and generally uncomfortably. Being old and retired is much less fun than what you see in any AARP TV commercial. In sum and importantly, temporarily comforting false expectations about this life and the socalled afterlife drown out real expectations, including the bad ones you should be concerning yourself with, the most compelling of which is a justified fear of an indescribably horrible death for all of us in a nuclear war that is sure to happen (Ukraine is much worse than an interesting news story after Russia’s invasion of it) unless we all work indescribably hard as though our lives depended on it to bring about A World with No Weapons.
If this has awakened you to the realities of police state enforced capitalist enslavement and you would like to encourage me to run for elected office to do something tangible about things, click here.
TO BE CONTINUED