Slavery, Entropy and God


By Ruth Marion Graf

© ruthmariongraf@gmail.com, 11/22/14

 

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1. Freedom

 

Are we free? It is the question of the ages. Ancient Rome was a slave society and proud of it.  In ancient Greece, the cradle of democracy, it was slaves who worked the fields and mines for the upper class Greek politicians and philosophers. And the Christian serfs who provided the labor for the nations of Europe during of the Dark Ages were nothing but slaves to their landlord masters.

 

Russia nominally got rid of serfdom with the Marxist Revolution of 1917. But the Russian people certainly did not live in freedom under Stalin. Nor do they now. And what of the Chinese? They don’t have any freedom to control their own lives as the pro-democracy street demonstrations in Hong Kong make clear. The Chinese are the obvious slaves of their communist overlords. Though our government and media downplay that fact because China supplies a quarter of our household goods and clothing. 

 

We know that the field Negroes of pre-Civil War America were slaves in the worst 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 you consider your supervisor at work to be a slave-driving SOB. Well, no country on earth does democracy better than America, so we say, so let’s not go too far on the anti-capitalist stuff, right? You don’t find any movies or any shows on TV about abusive bosses, landlords, police or teachers. So we can pretty much take it that there’s no slavery of that kind in real life either.

 

That gets tricky, of course, for if a society did enslave its people in any way, they’d cleverly downplay the fact of it to keep potential rebellion at bay. And they’d also hide the unhappiness that comes from control for the same reason. The slaves from Africa were told again and again, in the fields and from the pulpit, that their enslavement was the best possible life for them, a good thing. If they had television back then this message would have been broadcast 24/7 and in the most entertaining ways possible. People drugged 24/7 with misinformation tend to stay in line, then and now.

 

This between the lines reading of history and current events suggests, after you flush the propaganda down the drain, that mankind is stuck with enslavement worldwide in one form or another, whether as the state capitalism in China and Russia, the autocratic monarchies of Saudi Arabia and Kuwait where they behead people routinely, the pseudo-democratic dictatorships of Egypt and Yemen we support with billions, or as our Ferguson style capitalist democracy in America, the place that locks up more than any nation on earth.  

 

A Google headline recently declared that 37 million people in the world live in slavery today. But that number is for just the obvious kind of enslavement like they have in Pakistan and India. In reality all modern civilizations are hierarchically ordered societies with the upper layers having strong control over the lower ones, most often in exploitive and abusive ways. Of course, some will argue the opposite, especially those at the top levels, that America is truly free and fair. It would be surprising to hear on CNBC or any other place on Wall St. advertising controlled TV that Wall St. controls the elections and the media and the government and that a revolution is in order for freedom’s sake.

 

The only way to objectively show the harsh truth of the cradle to grave enslavement in America of most of the population is to precisely clarify what enslavement is mathematically. This quantitative spelling out of reality will also make clear the part that religion plays in the mess by mathematically disproving the existence of a god creator. We do that by showing mental selection to have the perfectly same form mathematically as the natural selection that created the mind, not God. To do this we must first understand how the mind frames our thoughts and emotions through information compression. And to best understand this most fundamental mental process, we will formulate entropy in a new and clear way as the most quintessentially clear illustration of information compression.    

 

One should not panic at the thought of having to learn this groundbreaking mathematics, for the centrally important explanations of subjugation in Section 2 and of human emotion in Section 3 require only the knowledge of fractions learned in grade school. So there’s no excuse for not turning off your favorite sports or cooking or police drama program and paying attention to what follows because getting something good out of life beyond the wishful thinking of children and the delusions of the subjugated requires this clear mathematical understanding of enslavement, of the massive unhappiness that comes from it and how we can change the world to do something about it.

 

Those who truly find math painful can scroll directly down to Section 4 to a personal story replete with child murders and an escape from a religious cult that sketches out the ideas without the pain of the mathematics. And for the technical heavy hitters we have in Section 5 an unraveling of the mystery of entropy whose properties under pin the mind’s information compression as a prelude to the mathematical explanation of human thought in Section 6. And beyond that in the remaining sections is a mathematically unified understanding of all of nature - physical, biological, human and moral - that replaces superstition based religion, misleading Marxism and ideologically corrupt psychology as a proper guide for leading a happy life.    

 

The right wing born again 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.” Let’s see if we can’t distinguish freedom from enslavement a bit better than that by doing it in mathematical language that can’t be spun. What freedom really is along with the pain of enslavement that comes having no freedom will be made perfectly clear to all who “believe” in mathematics. Don’t kid yourself. Some people don’t. There are a significant number of fundamentalist Christians and Muslims who’ll tell you that God can make 2+3 be equal to something other than 5 if He wishes. Those so childish as to trust in some god’s imagined power to contravene mathematical logic need read no further.

        

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2. Subjugation

 

Consider a game of chance you must play on the 2nd 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 probabilities of tossing the numbers |2| through |12| on a pair of dice are respectively:

 

1.)      p|2|=1/36;  p|3|=2/36;  p|4|=3/36;  p|5|=4/36;  p|6|=5/36;  p|7|=6/36;  p|8|=5/36;  p|9|=4/36;  p|10|=3/36;  p|11|=2/36;  p|12|=1/36

The lucky numbers in the game are the |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

 

This tells us that you have a 1 chance in 3 of rolling a lucky number and of escaping the v=$120 penalty. Or 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 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. For example, given Z=1/3 and U=2/3, 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 will fail to roll a lucky number and incur the v=$120 penalty two times out of three, which adds up to $240, which averages out over the three games played to an E= −$80 loss per game.

 

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 non-mathematical 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 Section 6. We will put this most important topic of information compression on the back burner until then.  


Returning to the v=$120 Lucky Numbers penalty game, we now ask: why would you play it? You do because the person who forces you to play this game every month will beat you with a stick if you don’t play until you do. You can rebel against this physical coercion that costs you money on average, if you dare. If you beat the extortionist in hand to hand combat, he though having the advantage with this weapon in his hands, you’re free from having to play this game. But if you lose to him in the battle, he will up the penalty in the game to v=$360, which will increase the average penalty per month you pay to

 

5.)                E = −Uv= − (2/3)($360)= −$240  

 

He may also hurt you badly in the fight. An important factor in your 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, stick in hand or not. But perhaps the extortionist also has a black belt, and don’t forget the stick.

 

You need exact numbers on the probabilities of winning and losing the fight to mathematically analyze the situation you’re in. And to get them we’ll change what has to be done to revolt against this abusive exploitation to winning in a special session of the Lucky Numbers game. It entails your rolling a lucky number of |2|, |3|, |4|, |10|, |11| or |12| to free yourself from ever having to play the monthly v=$120 penalty game again, let us say. This way clearly gives you a Z=1/3 chance of successfully rebelling.

 

But also note that if you lose, you not only have to keep playing the monthly game at an increased penalty of v=$360 dollars, but the extortionist also gets three unopposed whacks at you with his stick, which could break one or more of your bones, ouch.

 

We understand this situation to be subjugation or enslavement or tyranny or whatever you might wish to call it in ordinary language, by stating it in unequivocally well-defined mathematical terms. The extortionist is controlling your behavior in his self-interest and against yours by taking your money from you coercively. This is not picking cotton slavery, but it is enslavement in this mathematically well-defined way that all the varieties of modern abusive exploitation take the form of one way or the other.

Much of what follows explains why enslavement feels bad and ruins any chance of real happiness in life. It also explains how religion, innocently or otherwise, supports enslavement. It is already well documented that the rise of organized religion in man’s history correlates pretty much perfectly with the rise of empires, that is, with societies that are fueled by the enslavement of most of the population.

 

To explain enslavement and religion in the most fundamental way in terms of the mental processes involved, we need to explain first how and why emotions feel generally good and bad, pleasant and unpleasant. It’s important to do mathematically and in a systematic way both because of the ephemeral nature of emotion and because of the massively confusing ways emotion has been incorrectly explained in the past whether by religion or philosophy or ideology or in modern times by psychology, a seriously flawed science at best.

 

The Mathematics of Enslavement and Religion will make clear that sexual pleasure is not a temptation by a Devil spirit to commit sin and that depression from loss of a sexual relationship is a mathematically well-defined dynamic not explained at all, except perhaps poetically, by just labelling it as mental illness. To get past the misleading dogmas of religion and the shortcomings of the so-called human sciences as regards human nature, we will specify our emotions, good and bad, pleasant and unpleasant, in mathematical terms using the same Lucky Numbers game we used to illustrate enslavement.

 

It is very important to mathematically develop a precise sense of our emotions and our thoughts and how they determine human behavior not only to understand the unhappiness caused by subjugation but also how that unhappiness primes people to do violence on innocent others to help alleviate their bottled up unhappiness. Such a reduction in one’s unhappiness by aggressively passing it on to others has a wide spectrum of manifestation, showing itself not only in the petty meanness of day to day life we take so much for granted, but also in our never ending mass murders and wars, the latter particularly dangerous for mankind when the hydrogen bomb replaces the stick as the weapon of choice.

 

A means to eliminating enslavement from maximizing the balance of power between people by the worldwide banning of all weapons, which eliminates war too, is also developed from this mathematics. With this starts a political movement towards A World with No Weapons. If upon reading this you find yourself truly enlightened and would like to encourage me to run for president in 2016 in order to do something tangible about this tragedy for America and mankind, scroll back to this point once the light turns on in your head and click here.
                

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3. The Mathematics of Human Emotion

 

Our understanding of physical phenomena like planetary motion and electricity and magnetism and such, has been couched in mathematical language for the last couple of centuries. No sane person still thinks that angels with instructions from God steer the planets around in their orbits. The change of heart from superstition to gravitation came from early scientists like Kepler and Newton who were able to tack numbers onto physical nature. We can do this for human nature, too, by putting number on to human emotion, thought and behavior.

 

It’s actually not all that difficult if you follow one simple step at a time. The kind of human behavior we’ll first look at along with its associated emotions, pleasant and unpleasant, is goal directed behavior. To generalize it precisely we need to start off looking at behaviors with goals we can describe with exact numbers and with means to achieve those goals we can describe with exact numbers. Getting money is one goal that can be quantified precisely in terms of the V dollar amount of money one has as his goal to get. And we make the means to getting those V dollars mathematical in a form of the Lucky Numbers dice game that provides a V dollar prize for rolling a lucky number that has a precise numerical probability of success.

 

From this we’ll develop simple mathematical functions first for our most basic operational emotions like hope, anxiety, excitement, disappointment, fear, relief, dismay, relief, joy and depression. And following that we’ll develop our visceral emotions like sex, the pleasures of eating, hunger and anger. Later we will develop formulations for thought independent of emotion. And eventually we’ll put it all together to formulate a mathematical cognitive science that explains how the mind’s emotions and thoughts control human behavior. It helps to follow the text with pencil and paper in hand.

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| through|12|, 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 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.

 

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 20th 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 symbol-words 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 well-defined word-symbols 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, E1=Z1V1 and E2=Z2V2 with E1>E2, we choose E1 whether E1>E2 comes about via Z1>Z2 or V1>V2 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 E1 being better than in E2; or, hedonistically, to their being greater pleasure in entertaining E1=Z1V1 than in E2=Z2V2. .

 

Rule #3. If we have a choice between two v penalty games, one with fearful expectation, E1= –U1v1, and the other with E2= –U2v2, one of which games we must play, we choose the game with the smaller expectation (in absolute terms.) Or more exactly, if E1>E2 numerically, we choose to play the E1 game. To clear up any confusion, as between the games in Eqs4&5, we choose to play the E1=–80 game, E1>E2, 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 ramifications of these three basic rules are many, the main point being that they show that it is our expectations that primarily determine the choices we make in what we do in life. We shall have much more to say about them and about all of our emotions after mathematically explaining in Section 5 the nature of the thoughts that go with our emotions to complete the mental machinery that controls our behavior. But before we do that I want to tell a personal story that will serve as a reference point and data base of the mathematical understanding of life that is presented in this work.  

Description: Description: illustration of two red dice Stock Photo - 13443929

4. Revolution in the Garden in Eden

Description: Description: http://bloximages.chicago2.vip.townnews.com/wacotrib.com/content/tncms/assets/v3/editorial/6/0f/60f45d81-a31b-5011-92a9-3f1d33163a93/54348f20498cb.image.jpgDescription: Description: http://bloximages.chicago2.vip.townnews.com/wacotrib.com/content/tncms/assets/v3/editorial/e/c3/ec358722-d8b2-5158-8184-51652edde644/5426157fe5d8e.image.jpg

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, 10-2, 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 mega-death 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 pre-teen 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 over-dominated 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 pre-adolescence 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 semi-worship 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 would-be 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 state-side, 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 son-in-law.

 

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, animal-fucker 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 self-help 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 anti-establishment 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 lizard-like 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 self-interested 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, anti-Vietnam 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 1st and 2nd 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 self-loathing, 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. 

 

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Pete all neatened up on the way to the in-laws.

 

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 semi-religious 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 brother-in-law, 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 in-laws 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 father-in-law and brother-in-law 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 in-laws, 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 naďve 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 in-law 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 mini-ordeal, 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 in-laws 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. 

 

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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 mega-death, 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 all-powerful 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 pseudo-western 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, including a stay in Mexico of four years on and off. The photo on the left below of me in Acapulco with June and the youngest of her three kids, Angel Thomas Rogovsky, taken twenty years after the news article on A World with No Weapons was written makes it clear that having a family of her own made a magical difference in June’s life.   

 

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This is me, Ruth, with my genius grandson, Angel T., and his mom, June, down in Acapulco shortly before we returned to campaign for Obama in 2008. We were sold a brave Obama fighting for the people and spent $5000 to help get him elected.

 

 

 

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CBS photo of the kids at the Las Vegas Occupy March four disappointing Obama years later before the Occupy movement was destroyed by 6000 slam-to-the-ground wrist-breaking arrests. To support our movement to end the NSA and Wall St. run police state and disarm the world by electing me as president as a starter, click here

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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 unpleqsant 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.  

 

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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, mid-twenties 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?”

 

“Twenty-seven 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 semi-forgave 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 7-Eleven 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 7-Eleven 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 2nd 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 no-star 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 save-the-world 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 Polish-American 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=R-E 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 R-E part of the T=E-R 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=R-E 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 naďve 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 hotsy-totsy 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=R-E 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 mini-lecture, 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 middle-age 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 hotsy-totsy pretending the shit they take in life is sweet cream butter.

 

There’s a real reason why bleach-blond 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 1st 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 non-mathematical 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=R-E, 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=R-E, to shape your expectations to fit reality. You (and many people to be fair, some naďve 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 starting at Eq66. 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 so-called 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.

 

Well enough of the chit chat. Let’s talk about all things important now back in mathematical language. The next section concerns itself with developing a new function for microstate entropy that replaces the Boltzmann expression for it that has confused science for the last hundred years, confused it because Boltzmann’s entropy is basically incorrect. Resolving that problem in turn leads the way to a clear and complete understanding of information compression and thought, which when combined with our mathematical specifications of emotion completes our understanding of the cognitive machinery of the human mind to provide an explanation for every facet of human behavior.   

 

Description: Description: illustration of two red dice Stock Photo - 13443929

5. A Mathematical Reformulation of Entropy   

 

To explain problem phenomena like entropy and thought mathematically, we need to go very deep into the problem 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, x1=4 red objects in one subset, x2=4 green objects in another and x3=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 xi objects, i=1,2,...N.

 

32.)                                        Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image010.png

 

For the (■■■■, ■■■■, ■■■■), (4, 4, 4), set, K=x1 + x2 +x3 = 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.)                                        Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image011.png

 

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 xi 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, σ2, a statistical error measure that is the square of the standard deviation, σ, (sigma).  

 

34.)                                        Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image012.png

 

The variance of the N=3, µ=4, (6, 5, 1) set, (■■■■■■, ■■■■■, ), is

 

35.)                                          Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image013.png

 

Using the same formula of Eq3 determines the variance of the completely balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), to be σ2=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 σ2=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 σ2 variance or the σ standard deviation. Thus we might describe (■■■■■■■■■■, , ), (10, 1, 1), as having a μ=4 mean with a σ2=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 σ2 variance measure of the set’s distribution. It is defined as a function of the K, N and xi parameters of a set we are familiar with as           

 

36.)                                        Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image014.png



For the N=3 color, (■■■■, ■■■■, ■■■■), set with x1=4 red, x2=4 green and x3=4 purple objects the diversity index is from Eq36

37.)                                        Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image015.png  


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.)                                         Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image018.png

 

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 x3=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 σ2 variance measure of a set’s imbalance. We do that by first solving the σ2 variance of Eq3 for the summation term in it as

  

41.)                                       Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image019.png

 

Then inserting this summation term into Eq32 obtains D via µ of Eq33 as

 

42.)                                        Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image020.png

 

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 σ2 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 x1=1 candy for Jack and x2=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=NK=24=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

x1=4, x2=0

x1=3, x2=1

x1=2, x2=2

x1=1, x2=3

x1=0, x2=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/KN=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 1st through 6th lines in the table would occur 1 time. 

 

The Ω=NK=16 permutations are grouped into W=5 states, [4, 0], [3, 1], [2, 2], [1, 3] and [0, 4] on the 7th line with each state having a given number of permutations as listed on the 8th 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 9th 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 10th line in the table are the number set notations of the states, x1 being the number of candies that Jack gets and x2, 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 7th 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.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image021.png


This formula calculates the W=5 number states of the K=4 candy over N =2 kids random distribution in Table 43 as 

 

45.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image022.png   

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 σ2 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, x1=3 and x2=1, is σ2 =1, its µ mean is µ=K/N=2 and its diversity from Eq42, 

 

46.)                  Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image024.png    

 

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 σ2 variances and D diversities from Eqs34&42 are

 

State

Mean
µ

Variance  σ2

Diversity
D

[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 σ2 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 9th line in Table 43.
 

State

Variance, σ2

Probability of the State

Probability Weighted Variance

[4, 0]

4

1/16

(4)(1/16)=1/4

[3, 1]

1

Ľ

(1)(1/4)=1/4

[2, 2]

0

3/8

(0)(3/8)=0

[1, 3]

1

Ľ

(1)(1/4)=1/4

[0. 4]

4

1/16

(4)(1/16)=1/4

 

 

 

Sum is the average variance2AV=1

Table 48. The Average Variance, σ2AV, of the W=5 States of the K=4 over N=2 Distribution


The average variance is specified as σ2AV, which for the K=4 over N=2 equiprobable distribution is σ2AV=1. Now let’s modify D in Eq43 as a function of σ2 so we can calculate an average diversity, DAV, as a function of the average variance, σ2AV.    

 

49.)                     Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image025.png   

 

This calculates the average diversity, DAV, of the K=4 over N=2 distribution from its σ2AV=1 average variance obtained in Table 48 as  

 

50.)                   Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image026.png

 

We obtain a simpler formula for the DAV average diversity of a K over N equiprobable distribution by developing a shortcut formula for the σ2AV average variance from a textbook expression for the variance of a multinomial distribution (see Wikipedia). For the general case that expression is

 

51.)                            Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image027.png

 

This simplifies for the equiprobable case in which the Pi term is Pi= 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 Pi=1/N probability for the K=4 candy over N=2 children equiprobable distribution to be P=1/N=1/2. This Pi =1/N probability simplifies the variance formula of Eq51 for the equiprobable case to

  

52.)                     Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image028.png 

 

This variance of an equiprobable multinomial distribution is just the average variance of an equiprobable distribution, σ2AV, same thing. Hence we can write the above as  

 

53.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image029.png

 

We demonstrate the validity of Eq53 by calculating the σ2AV=1 average variance of the K=4 over N=2 distribution obtained in Table 46 from Eq53 as  


54.)           
Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image030.png  

 

And now we derive a simple formula for the average diversity, DAV, from Eqs49&53.  

 

55.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image031.png

 

And we demonstrate its validity by calculating the DAV=1.6 average diversity of the K=4 over N=2 distribution from it as

 

56.)               Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image032.png 

 

Now we want to show that the DAV 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.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image033.png

 

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 DAV 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.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image034.png

 

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.)    Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image035.png 

 

Now let’s use this formula for lnW to compare the lnW of some randomly chosen large K over N equiprobable distributions to their DAV average diversity of Eq55.    

K

N

lnW

DAV

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 DAV of Large Value K over N Distributions

The Pierson’s correlation coefficient between DAV 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 DAV versus lnW values in Table 60.  

Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image036.png

Figure 61. A plot of the DAV versus lnW data in Table 60

This high .9995 correlation between lnW and DAV 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 DAV. 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

 

Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image037.jpg


                                                                                                        Ludwig Boltzmann’s 1906 Tombstone in Vienna      

 

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 DAV. 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 σ2 variance and D diversity index as the states that comprise it.

Configuration

States   

Variance, σ2 

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, σ2, 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 σ2AV=1 of the K=4 0ver N=2 distribution from Table 48 and Eq23 and its average diversity of DAV=1.6 of Eq50 are exactly the same respectively as the σ2=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.

 

Earlier we saw the µ mean is a 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 saw that the D diversity was also a compressed representation of a number set, though with more information in it in containing as the mean does not a sense of the distributional imbalance in a set as represented by the σ2 variance in the D diversity seen in Eq11. In an analogous way the Average Configuration of an equiprobable distribution is a compressed representation of the distribution’s many configurations in it including the diversities of all of the distribution’s configurations by way of its D diversity index being the same as the DAV 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 mathematical structure.  We will consider how it acts as a general model for the generalizations the human mind encodes experience with in a later 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 Maxwell-Boltzmann energy distribution pictured below.

 

Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image038.jpg

Figure 65. The Maxwell-Boltzmann 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 Maxwell-Boltzmann 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 Eq55 the DAV average diversity of the distribution, which along with its K and N values is a central defining property of the system.  

 

66.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image039.png       

 

The Average Configuration of the K=12 over N=6 distribution is a configuration that has this DAV value of diversity, DAV=4.235. The easiest way to find the Average Configuration is with a Microsoft Excel program that generates all the configurations of this distribution and their D measures to find one that has the same value as DAV=4.235. 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 diversity index of D=4.235. 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.

 

Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image040.png

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 Maxwell-Boltzmann energy distribution of Figure 65 is a bit of a stretch, though it might be characterized as a very simple, very choppy Maxwell-Boltzmann distribution. Next let’s consider a larger K over N distribution, one of K=36 energy unit over N=10 molecules. Its DAV is from Eq55, DAV=8. The Microsoft Excel program runs through the configurations of this distribution to find one whose D diversity has same value as the DAV =8 average diversity, namely, (1, 2, 2, 3, 3, 3, 4, 5, 6, 7). A plot of the energy distribution of this Average Configuration is

 

Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image041.png

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 proto-Maxwell-Boltzmann.” Next we look at the K=40 energy unit over N=15 molecule distribution, whose DAV average diversity is from Eq55, DAV=11.11. 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 D=11.11 diversity. A plot of its energy distribution is

 

Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image042.png

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 Eq55, DAV=30. There are nine configurations with a D =30 diversity including (0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 10), which is an Average Configuration of the distribution on that basis. A plot of its energy distribution is

 

Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image043.png

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 that show a clear resemblance to the classical Maxwell-Boltzmann 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 Maxwell-Boltzmann of Figure 65. As we progressively increase the K and N of our example 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 Maxwell-Boltzmann distribution of Figure 65.

 

This demonstration of the Average Configuration having the shape of the empirical Maxwell-Boltzmann energy distribution along with the dynamic picture presented of the Average Configuration as the average over time of a dynamic system of rapidly changing configurations from repeated collision further supports, in conjunction with the .9995 lnW-DAV Pearson’s correlation, diversity based entropy as a proper form of entropy. The question, at this point in our analysis, though, is whether diversity based entropy is the correct form of entropy with the lnW based Boltzmann entropy understood as incorrect; or both formulations of entropy are equally valid with each providing a different perspective that gives different meaningful information on what entropy is.

 

Before we provide the argument that decides between these two possibilities, we must first investigate a second diversity index that also has a very high correlation with Boltzmann S=klnW entropy and as such must also be considered as a valid replacement or adjunct function for the S entropy. This derivation is somewhat tedious, though very clear, and is given attention here because it thoroughly resolves the conundrums that presently plague microstate thermodynamic including its developing the proper microstate form of temperature. And that temperature measure once developed also provides a quintessentially illuminating example of the mind’s very basic tendency and ability to form generalizations about the phenomena it is exposed to in the world.

 

And as a side effect of solving the two century’s old mystery of entropy, the exercise also gives great confidence in this mathematics we will also be using to explain human nature in terms of people’s thoughts, emotions and behaviors particularly as they present a significant danger to the human race in terms of the violence of modern people and its expression in war, the next global one possibly nuclear and terminal.     

 

To develop that alternative diversity index we begin by expressing the μ=K/N mean of Eq2 in terms of K expressed in Eq1.

 

71.)                    Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image044.png

 

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 xi of a number set as the ratio of the xi 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)                    Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image045.png

 

For the K=12, N=3, (6, 5, 1), number set that has x1=6, x2=5 and x3=1, the weight fractions of the set are p1=x1/K=6/12=1/2, p2=x2/K=5/12 and p3=x3/K=1/12. We can write these pi weight fractions of (6, 5, 1) in shorthand form as (1/2, 5/12, 1/12). Note that the pi weight fractions of a number set necessarily sum to one.

 

73.)                   Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image046.png

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 pi weight fractions, which sum to one (1), and then dividing that sum of 1 by the number of pi in the set, which is N. For example, the weight fractions of the N=3, (6, 5, 1), set are p1=6/12, p2=5/12 and p3=1/12, which sum to 1. Then dividing this sum of 1 by N obtains 1/N as the average weight fraction, denoted asDescription: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image047.png.    

74.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image048.png

 

This appreciation of 1/N allows us to express the μ mean of Eq40 in terms of the average weight fraction,Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image047.png, as

 

75.)          Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image049.png

 

This form interprets the μ mean of a number set as the sum of “slices” of xi with each “slice” the “thickness” ofDescription: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image047.png, 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.)           Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image050.png

 

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.)             Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image051.png

 

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.)                Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image052.png

 

This has us specify φ=K/D of Eq77 in a way parallel to μ in Eq71 as a function of the pi weight fractions of a number set of Eq78 as

 

79.)            Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image053.png

 

This has us interpret the φ biased average as the sum of “slices” of xi with each “slice” the “thickness” of pi, that is, of the thickness of the actual pi weight fraction rather than of the Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image047.png=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.)            Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image054.png

 

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 xi of a set of thickness pi in Eq79, the ψ square root biased average is the sum of slices of the xi of a set of thickness, pi1/2, 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.)               Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image055.png

 

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 pi1/2 weightings of the xi of the set don’t add up to 1 as they must to form any kind of an average of the xi 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 pi weight fractions of (1/2, 5/12, 1/12) do add up to 1, the pi1/2 square roots of its pi 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 xi in forming an average of them.

 

This problem is readily resolved by normalizing the pi1/2 to get them to add up to 1. This is done by dividing each of the pi1/2, (.7071, .6454, .2887), by the 1.6412 sum of the pi1/2. This obtains normalized set of pi1/2 of (.4308, .3933, .1759), which do add up to 1 and, hence, properly weight the xi 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 pi1/2 that divides each the pi1/2 to normalize them is expressed in general form as

 

83.)             Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image056.png

 

This function for the sum of the pi1/2 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.)         Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image057.png

 

 

And next we express ψ from the above in an alternative way via the pi=xi/K weight fraction relationship of Eq72 as 

 

85.)            Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image058.png

 

 

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.)             Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image059.png

 

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,

 

87.)              Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image060.png

 

 

 

 

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, GAV, which is also the G of its Average Configuration. We will show next that this GAV also has a very high correlation to the lnW term in Boltzmann’s S=kBlnW entropy. To show this correlation of GAV to lnW, though, is not as straightforward as was the correlation of DAV to lnW because GAV is not a simple function of the K energy units and N molecules of a thermodynamic system as DAV in Eq55 as DAV=KN/(K+N−1). 

 

Because GAV is the G diversity index of the Average Configuration much as DAV was the D diversity index of the Average Configuration, we can obtain GAV 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 67-70. We list these GAV below along with the lnW values of those Average Configurations obtained from Eq57. And we also include their DAV diversity indices for comparison sake.  


       

Figure

K

N

lnW

DAV

GAV

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, DAV and G­AV of Distributions in Figures 67-70


The correlation between the lnW and DAV of the above random distributions is .997. Though quite high, this is less than the .9995 correlation between lnW and DAV 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 GAV for the distributions in Table 88 is also quite high as .995, not much different than the high .997 correlation between lnW and DAV for these distributions. As the correlation of DAV 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 DAV and G­AV of .997 and .995 respectively that for high value K and N distributions the correlation of GAV 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 DAV and GAV having a very high correlation to lnW that either diversity function, DAV or GAV, could underpin a diversity based entropy that replaces Boltzmann’s S=kBlnW entropy. To answer this question let’s specify the GAV diversity by extension from Eq87 as

 

89.)                            Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image061.png 

 

We know what GAV is, don’t we. It is the average of the G diversity index of all W states of the system. Now let us ask the same question of ψAV. It is the biased square root average energy per molecule of the Average Configuration, also understandable most basically as the average over all W states of the biased square root average energy per molecule. Now we will argue as follows that this is a measure of the microstate temperature of a thermodynamic system.

 

In standard physical chemistry theory, via the equipartition theorem, temperature is taken to be a simple function of the arithmetic average 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 dependent temperature must be seriously questioned from the perspective of 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, xi, 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 x­i 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 xi number of energy units on the molecule. Hence the smaller energies of the slower moving molecules in the Maxwell-Boltzmann 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 develops temperature as 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. As the velocities of the molecules are directly proportional to the square root of the xi energy of the molecules, the average molecular energy, which is temperature, is the square root of the xi energy weighted average, which is the square root ψ average energy per molecule of the thermodynamic distribution, ψAV. From this we see that the diversity of the distribution measured in terms of the ψAV temperature is GAV=K/ψAV, which has us choose the GAV diversity index of the distribution as the proper correction of Boltzmann’s S entropy.

 

This sense of entropy as GAV=K/ψAV is also quite reasonable from a dimensional analysis of entropy, GAV as energy, K, divided by temperature, ψAV, which perfectly fits the dimensions of entropy in the macroscopic differential Clausius definition of entropy of

 

90.)                   Description: C:\Users\TheBOX\Documents\Net_Files\INDEX_files\image062.png

 

In the above, S is entropy, Q is heat, dimensionally energy, and T is Kelvin temperature.

 

Now let us look in broad review at the two interpretations of entropy. One, the Boltzmann S entropy, is most essentially a function of the W number of states as lnW. The energy diversity based entropy, GAV, is a function of the G energy diversities of the W states as an average of it over time. The two are obviously both closely related to W. But the W in itself whether in linear form or in logarithmic form as lnW makes no sense out of entropy as a physical quantity. That is because W is just a count of the number of states that the thermodynamic system cycles through over time that, in itself, can have nothing to do with the microstate chemical reactions and thermochemical processes that are so much unarguably affected by entropy. But the G diversity of any one of the W states of the system is a physical quantity that can affect chemical reactions and thermochemical processes because it is a measure of the system at a moment in time rather than as with W, a measure of the system over time, and distinctly and undeniably not a measure of it at any one moment at time, that measure being that 1 particular state of all the W states of the system is what exists at any one moment, which is not a variable in itself, as distinct from its energy diversity, that has any reality at any one moment in time.

 

For that reason, given from the earlier argument of mutually contradicting assumptions as to energy units being distinguishable or indistinguishable, only S=klnW or GAV can be the correct formulation and understanding of entropy, not both as different but equally valid interpretations, it must be GAV. Important from an intuitively digestible perspective, the above analysis tells us that entropy should be specified as energy diversity or the dispersal or spread of K energy units over N molecules, which understands and explains entropy in a much more intuitively clear way as a physical quantity than Boltzmann’s lnW based S=kBlnW entropy whose lnW term has absolutely no meaning as a physical quantity. The quantitative fit of the GAV energy diversity characterization of a thermodynamic system to the qualitative description encouraged in the Wikipedia article, Entropy (energy dispersal), is quite remarkable and a conclusively strong argument in favor of it given its .9995 correlation to the Boltzmann S entropy as satisfies its validity from its empirical fit to all laboratory data no different than the Boltzmann S entropy.     

 

      

 

Description: Description: illustration of two red dice Stock Photo - 13443929

6. Information Compression and Thought

 

The two most complete compressions of information in physical nature are the GAV average square root energy diversity and the ψAV average square root biased average energy per molecule. We explain the latter first. ψ is the square root biased average energy pre molecule of a system of N molecules at a particular moment in time when it is in a particular one of the system’s W states, indeed, when it is in a particular one of the system’s Ω=KN permutations. This is a compression of all of the N molecules xi energies as the number of discrete energy units on each molecule, as the average value of the energy, not the µ arithmetic average, but the square root biased average, ψ. Then this average is averaged over all W states of the system as weighted by the probability of each state. Hence ψAV 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 as ψAV

 

What is remarkable about this double average is that it is the measure of temperature not only as taken by a thermometer like a Mercury in glass thermometer, but also as sensed by the human body, which must collectively measure all of the molecules that impinge upon the skin’s surface and average that first immediately at any moment in time but then also over time assuming that the collisions of the molecules on the skin’s surface are rapid relative to the brain’s integrated sensory impression of them. This is remarkable because temperature is such an elementally important sense of the environment that the brain or mind has.

 

Consider in parallel a human observer who could see every dog in the world at every moment. Then his or her sense of a dog would be very much akin to ψAV in averaging all the dogs in the world at any one moment, and averaging this average as time passed, though with the nuance that the sense of the dogs as to what a dog is, would be affected by recency, with the set of dogs in the world most recently observed having greater weight than those in the past.

 

This is not only how we think about objects that are common nouns for us, but also for particular dogs, and people, too. Take the family pet, Fido. Fido changes at every moment and certainly in observable ways in terms of size and shape over extended periods of time. Yet he or she is always Fido in our compressed representation of the dog.

 

 

TO BE CONTINUED