The Graf Child Murders
& the End of the World


 

By Ruth Marion Graf
©, ruthmariongraf@gmail.com, 10/21/14


1. He Burned the Kids to Death

The prosecution said at his first trial in 1988 that Edward E. Graf Jr. 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 boys about a month before the fire.

 

 

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Edward Graf Jr. on retrial in Waco for the deaths of his two adopted stepsons.

 

Bail was set for his October retrial at a million dollars. Ed’s brother, Craig, was only able to raise $100,000 it was said in the Waco Tribune. So Ed remained in jail during the retrial which is nearing its end as we approach Halloween and I begin writing this piece somewhat in shock because though I am a first cousin of Ed’s, this is the first I have heard of any of this.    

It is somewhat odd to have been so close to the family in my younger days as to have been the baptismal sponsor, the godmother, of his younger brother, Craig, and yet to have been so completely in the dark about the murders these last thirty years until I came across the story entirely by chance on the Internet just before the end of the retrial. I remained in the dark for so long because I was the one of lucky Graf’s who fled this fundamentalist clan when I was a young woman, never to be told by any family member about this hideous skeleton in the closet that makes tangible sense of why it was I fled them all in the first place.

 

I want to give my close up understanding of the kind of life Ed Jr. had as the child of my Uncle Ed and Aunt Sue, not just to explain Ed, himself, and what he did to those boys, but also to make clear how a cruelly strict and unloved upbringing like he and I had are important causally, when not rebelled against, in generating the darkness and incompetence that fills our once exceptional country these days and especially as it affect America’s ability to manage international conflict and keep at bay the worst possible outcome of war in modern times of nuclear annihilation.           

 

Ed’s father was the younger brother of my father, the Rev. Arthur E. Graf, in a family of 11 LCMS Christians (Lutheran Church Missouri Synod). To make the point of just how immersed the Graf clan was in the ministry of the church, my Aunt Emily, Ed Sr. and my father’s sister had two daughters, both married to LCMS ministers, and two sons, one a minister and the other a Lutheran parochial school teacher. Near half of my relatives were an integral part of this LCMS fundamentalist religion in some way.      

 

The word strict as applied to this Lutheran sect and my extended family requires some amplification. Dancing was forbidden when I was growing up. Movies were limited to “Francis the Talking Mule” and music to religious hymns. Punishment for even minor infractions was painfully corporal and as frequent as Sunday church services. That was even for me, a very obedient and generally fearful girl who required nothing more than a glance and a tone of voice to toe the line rather than embarrassing beatings meted out weekly with a hairbrush. Punishment for questioning authority was harsh enough to be accurately labelled as unbelievable. The youngest of the 11 in my father and Uncle Ed’s father’s family, my Aunt Lillian, slapped my grandfather in an argument over a beau when she was sixteen causing her to be immediately carted off to an insane asylum, where she remained, dulled to a point of eternal silence by shock treatment, until she was 65.

 

I cannot speak for the details of Ed’s upbringing, but saw him enough at family gatherings to see the results and develop by parallax to my own experiences a good explanation of why he committed these horrid murders. I ran from the pain and got away with the escape by pure luck while Ed, less lucky, had the pain twist his personality to the point where he had no problem turning it on the boys in the ugliest way.

 

From his and my early life experiences along with that of my, brother, Don, whose life I also know about in depth, I will make the case that much of what happens in family life that is near totally swept under the rug in American mythology is a significant cause of unhappiness, evil and incompetence in people in adulthood, the latter manifest in our massive screw ups with Ebola, with the Secret Service falling down on the job, with the CIA and Obama’s failure to predict the rise of ISIS and with the epidemic of anti-science and anti-common sense Fox News thinking now infecting all of America. I will also try to make clear the ultimate cause of these problems in the social control placed over us in and out of the workplace in pseudo-democratic capitalism, which is also carefully hidden from view by information control in the media, in schools and from the pulpit. I’ll explain and propose a solution to these problems with a firm and scientifically precise mathematical analysis of human thought and emotion introduced with the story of my personal experiences that include the misfortune of my being a Lutheran missionary in my younger days.

 

Nothing is as difficult as exposing the truth about oneself to the public. Whatever feels bad inside tends to feel all the worse when offense from others and personal failures from it bring greater humiliation yet in the public confessing and complaining about them.  But the cost of keeping private matters that most of us 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 with our culture 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, one at the nuclear level that will shackle us to a Fukushima type irradiated atmosphere bring a painfully horrible end to all of us and to our children.

 

 

2. Revolution in the Garden in Eden

 

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.  

(I make note as I am at this point in writing this story on 10/21/14 that the jury on Ed Graf Jr. over in Waco is deadlocked at 10-2, presumably with the majority voting guilty.)

 

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 neat on the way to his in-laws in Texas.

 

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 naïve as a newborn rabbit, we all jumped in our respective vehicles and off we went.   

 

A picture worth a thousand words would do better at this point, but we have to settle for a verbal snapshot of Don standing on one side of a table at the winery where corks are put in wine bottles with a cork hammer. He is banging one such hammer repeatedly on the table top as his insulting voice tone punches are thrown at me again and again, which is making me progressively more uncomfortable and shaky as in victimized days of old with him. He knows me well, which buttons to push. And next to me, progressively more irritated while naively trying to disguise his bubbling up fury for the sake of maintaining some semblance of family civility, is Pete.

 

As the tempo of Don’s attacks increase along with Pete’s less and less well disguised look of impending violence and Don’s hammer banging down harder and harder on the table, I am vaguely aware of the presence of Don’s 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 for it or was seriously in on it somehow, likely carrying out a dark plan that 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.   

 

(As of this moment while writing this, Ed Graf just pled guilty in the courtroom, afternoon, 10/21/14)     

 

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And at that point I knew that this punk rat murderer had been in on June's beating and had possibly been the one to suggest it in a cold calculating way to begin with because he knew from his same torture of me when I was little what the result would be. As June escaped and recovered over time enough to have a happy life as one of the finest mothers this world has ever seen, her son solid proof of that, I can tell this story without tears in my eyes to make the point that what happens in life that is hidden and destroys people's lives and happiness is the reality that must be explained, as we will do mathematically starting in the next section of the Mathematics of Emotion.  Below are a couple of photos of June and Angel Thomas.

 

This is me, Ruth, with my genius grandson, Thomas, 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 run police state and to disarm the world by helping to elect me president as a start, click here

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A few years later in 1986, Pete penned our first article on A World with No Weapons.  

 

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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.  

   

To that end I’ll fast forward from the last story to a more recent one that just happened to us under the banner of one of the largest and most powerful corporations in America, these guys. 

 

Description: Description: http://www.13wmaz.com/images/640/360/2/assetpool/images/110112121819_greyhound%20Bus%20Logo.jpg

 

 

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 from one’s 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.

 

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 of McClesky, Harriger, Brazill and Graf 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 naïve wishful thinking about the future alive. The idea that they could embrace the reality of mankind's bigger problems was farfetched indeed.

Our laptop was in one of the missing bags. This necessitated a trip to the Summit County Library by Pete to check out emails and such. There he ran into 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 naïve and some beaten by life into blind bourgeois thinking) do the opposite, that is, shape reality to fit one’s expectations. That’s done because of the comfort provided by false expectations and wishful thinking, which usually winds up in a personal catastrophe of some sort as time passes. That’s the point I was trying to make to a family man I have some natural empathy with because I have raised five kids myself.

 

I don’t expect any of this to take with you, Mike. Indeed, that was not my purpose in dropping this note off. In the end we expect this hard cold mathematical truth to win out with the public as scientific truth properly presented always does eventually, ideological resistance notwithstanding. At that time, hopefully in the not too distant future, you should at least appreciate that our conversations were quite helpful to a full understanding of the complexities of human emotion. And perhaps then you will understand my motives in talking to you better and take some of the conclusions of this broad mathematical sociopolitical treatise to heart as good advice. I bear no resentment and hope you feel the same.  Peter

Near three months later only one of our bags has been returned and any chance of our recovering the value of what was lost screwed up by Greyhound. Are corporations, is Greyhound, really that uncaring and cruel? It's important to see life as it plays out, not like you want it to despite your falls in the mud of our modern hierarchal slavery. The mathematics makes clear the dangers of great expectations not supported by sensible evidence. An eternal trip to Heaven after you die is the most obvious of these culturally supported emotionally comforting expectations that have little realistic foundation, just rationalizations and honeyed delusions.

People believe in fairy tales. Why? Because it feels nice to be bathed in pleasant expectations no matter how farfetched and delusional they may be. But when false expectations crash, bad decisions based on delusional hope smash a person into unhappiness and depression fully gotten rid of only with a Robin William’s type suicide as the only true escape of an emotional cripple produced by delusional expectations that never had the slightest chance of being realized. The nature of such wishful thinking is made mathematically clear 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 in mathematical language.  

 

3. The Mathematics of Thought and Emotion   

 

Nothing is more critical to correctly understand than human thought and feeling because these mental phenomena are the prime determinants of behavior including those behaviors that have unhappy outcomes like the violent behaviors of mass murder and war. But nothing is more difficult to understand than thought and emotion for two important reasons. First is the inaccessibility of thoughts and feelings to anybody other than the person having them that makes a scientific understanding of them most problematic. And second is the confusion about our thoughts and feeling sowed by ideological, religious and psychobabble cultural propaganda, for any clear understanding of how thought and emotion control behavior inherently explains how propaganda influences thoughts and emotions to control behavior, knowledge of which runs contrary to the primary function of propaganda of mind control.    

 

The best literature, humor, art and humor, when they are not propaganda vehicles themselves, their primary function, also give a strong hint of what people think and feel about things. But these forms of expression even when benign are for the most part too equivocal in meaning to spell out the truth needed to jump start the rebellion against social control in people that makes possible the recovery of happiness.

 

We resolve both problems with clear mathematical representations of thought and emotion that ultimately explain the sexual and aggressive thoughts and emotions that have the greatest potential to foul up men and women’s pursuit of happiness. The quantitative expressions for thought and emotion presented are further elaborated to make clear the highly regulated nature of social interaction in modern societies and the unhappy feelings caused by it that are partially alleviated by aggression on vulnerable innocents when direct retribution on the actual controlling agents is not possible. The greatest danger in the perverse exaggeration of innate Darwinian animal violence in us talking apes caused by this is the tendency of the world’s collective unhappiness from social control manifesting itself in the bloody violence of war, which is especially dangerous when nuclear weapons are available for use.

 

The possibility of ISIS terrorists obtaining nuclear weapons or provoking the use of a nuke to start a larger global nuclear exchange and the renewal of the Cold War by nuclear armed Vladimir Putin from the conflict in the Ukraine should make us all tremble, resignation to divine punishment or the delusional hope of divine intervention notwithstanding. Add to this America’s increasing incompetence in matters large and small as in our screw ups with Ebola, the Secret Service falling down on the job, the CIA and President Obama’s inability to forecast the rise of ISIS and the Fox News anti-science blather that now infects common sense thinking across all of America and you have the perfect recipe for the world’s collective misery boiling over via incompetent decision making to global nuclear war and mankind’s extinction.

 

This problem goes quite beyond Chicken Little’s imagined fears that the sky is falling. The nuclear problem is real whatever the media’s hiding it as an eminent threat. To sidestep this train filled with explosives barreling down the track on us, people of all nations, as led by America, need to move rapidly towards a world with no weapons or we’ll soon be a world with no people. We show this outcome to be highly likely with a mathematical explanation of thought and emotion that solves the problems of inaccessibility and obfuscating propaganda with this hard core analysis sprinkled with a few amusing true life stories in Section 3 that illustrate the dangerous reality of modern life.

 

The threat of nuclear annihilation goes beyond conservative and liberal political quarreling. It’s all of us, right and left, and all of our kids and grandkids who are at risk of lethal nuclear irradiation and incineration. Please read on to see the details of what we hope will be the beginning of a sensible new political party in America that will get done what needs to be done to keep us safe and that will make us all significantly happier as a side effect of the significant lessening of social control in our lives that an elimination of all weapons, guns to bombs, will bring about. This 73 year old grandma mathematician leading the fight for a safer, happier world seems the best option until a more vigorous personality comes along to do the job. We need a woman in the White House and not Hillary Clinton, who is nothing but a self-serving professional actress no better than her “I would never lie to you” jerk husband.   

 

            

 


4. The Generalizations the Mind Makes and Entropy

We begin our mathematical journey with a quantitative development of thought that distinguishes our simple recall of things and events from the generalizations the human mind so strongly tends to make about them. Consider by way of illustration a new Object-X we see 9 of as (). Their sizes vary in square feet as (4, 5, 6, 4, 5, 6, 4, 5, 6) with the mean or average size of Object-X being, from grade school mathematics, 5 square feet.

 

Now when we think about Object-X from this set of them, we can recall one or more of them in terms of their individual size or we can generalize Object-X as generally being 5 square feet in size. For information economy the human mind strongly tends to generalize past observations and experience in what we will call condensed representations of reality. This powerful tendency of the mind to generalize experience including emotions we feel is introduced mathematically in a precise way starting with the sense of an average as a condensed representation that extends to our natural sense of temperature, how we feel cold or hot, as a special kind of average developed in terms of an alternative formulation of entropy, something almost everybody has at least heard of, though few understand.  

 

The mathematics of this may prove a bit difficult for readers who lack a STEM background, that is, one in science, technology, engineering and/or mathematics. Non-STEM readers are encouraged to scroll down through parts of it they find too difficult to follow to the easy to read stories in Section 3 and then on to the simpler math in Section 4 that spells out human emotions like hope, anxiety, disappointment, fear, relief, excitement, dismay, joy, depression, hunger, the joy of food, sex, heartache and anger. The profit in making some effort to read through this entropy section, though, it should be pointed out, is not only in developing an illuminating understanding how people form their thoughts and ideas about things but also of the mysterious concept of entropy.

 

Let’s get right to it. The basic equation for entropy in science developed by the 19th Century mathematical physicist, Ludwig Boltzmann, was honored by inscription on his 1906 tombstone in Vienna.  

 


Boltzmann’s entropy formulation is in modern notation, S=kBlnW. Whatever its considerable merits, though, it has confused students and professors alike over the last 100 years. We will derive entropy in a way that is more clearly understandable intuitively using Simpson’s Reciprocal Diversity Index, a function that was unavailable to Boltzmann in its not being available to science until 1948, over 40 years after Boltzmann’s untimely death by suicide. In brief, our new equation for entropy based on diversity has a .999 correlation to Boltzmann’s S entropy formulation (to be explained later) and as such is indistinguishable from it in all laboratory measures while providing a superior understanding of entropy as a physical quantity.  

 

To explain diversity based entropy and ultimately how the mind generalizes observed reality in thought we begin by explaining diversity. Diversity is a general property of sets of objects that can be divided into distinguishable subsets. These can be animal organisms divided into species; people divided into ethnic groups; or of a set of buttons divided into subsets on the basis of color that we will use to illustrate diversity.  

 

The (4, 4, 4), (■■■■, ■■■■, ■■■■), set of K=12 buttons is divided into N=3 color subsets, x1=4 red, x2=4 green and x3=4 purple buttons, is intuitively sensed as being more diverse than the (6, 6) set of K=12 buttons in N=2 colors, (■■■■■■, ■■■■■■), x1=6 red and x2=6 green buttons. And both of these sets of buttons are less diverse than the (2, 2, 2, 2, 2, 2), N=6 color, set of buttons, (■■, ■■, ■■, ■■, ■■, ■■), x1=2 red, x2=2 green and x3=2 purple, x4=2 blue, x5=2 black, and x6=2 brown buttons. One can give quantitative measure to this sense of relative diversity with Simpson’s Reciprocal Diversity Index, written below as

1.)                                          


The K term is the total number of objects in a set, K=12 for our example button sets. And the xi term in Eq1 is the number of objects in each of the subsets of the set. i=1, 2,…N. For the N=3 color, (■■■■, ■■■■, ■■■■) button set with x1=4 red, x2=4 green and x3=4 purple buttons the diversity index is from Eq1

2.)                                             


We see that the D=3 diversity index of this set is equal to the N=3 different kinds of colored buttons in the set. If we apply Eq1 to the K=12 button, N=6 subset, (2, 2, 2, 2, 2, 2) set of (■■, ■■, ■■, ■■, ■■, ■■) buttons, we calculate its diversity to be D=N=6. And for the K=12 button, N=2 subset, (6, 6) set of (■■■■■■, ■■■■■■) buttons, we calculate the diversity to be D=N=2.

 

The D diversity indices of these three sets fit our intuitive sense of their relative diversity. The D=N equivalence holds for these sets because they are all balanced sets, the number of buttons in each subset of all the sets, whether (4, 4, 4), (6, 6) or (2, 2, 2, 2, 2, 2), being the same. All balanced sets have

3.)                                           D = N      (balanced)

 

From Eq1 we can also calculate the D diversity index of an unbalanced set like the (6, 5, 1), (■■■■■■, ■■■■■, ) set of colored buttons that has K=12 buttons divided into N=3 color subsets as x1=6 red, x2=5 green and x3=1 purple.

 

4.)                                            

 

For this (6, 5, 1) set and for all unbalanced sets, the D diversity index is less than the N subsets of a set.  

 

5.)                                            D < N      (unbalanced)

 

We can understand the D<N in Eq5 for the unbalanced, N=3, (6, 5, 1) set by considering the x3=1 object purple subset in (■■■■■■, ■■■■■, ) to contribute only token diversity to the set.

 

Next we develop the D diversity index as a statistical function. To do that, we first formally specify the mean or arithmetic average of a set of objects as μ, (mu).   

6.)                                          

 

The average number of buttons in the N=3 subsets of the (6, 5, 1), K=12, N=3, (■■■■■■, ■■■■■, ) set is μ=K/N=12/3=4 buttons. The mean of a set is very often accompanied by a measure of statistical error. A commonly used statistical error is the standard deviation, σ, (sigma). It is the square root of another statistical error that is most useful to us in our derivations called the variance, σ2.  

 

7.)                                          

 

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

8.)                                            

The variance can be understood as a measure of the imbalance in a set. To see this, let’s consider another unbalanced K=12, N=3 color set of buttons, the (10, 1, 1), (■■■■■■■■■■, , ), set. It is intuitively sensed as more unbalanced than the (6, 5, 1), (■■■■■■, ■■■■■, ), set. And we see by calculating its σ2 variance from Eq7 that the variance of (10, 1, 1), (■■■■■■■■■■, , ) is greater than the σ2=4.67 of the (6, 5, 1), (■■■■■■, ■■■■■, ), set as σ2=18.


Another commonly used statistical error measure is the relative error, r, which is the σ standard deviation divided by the μ mean.    


9.)                                            

 

And a form of the relative error very useful to us is its square, r2, which we call the perfect error

 

10.)                                       

 

For the σ2=4.67, µ=4, (6, 5, 1), (■■■■■■, ■■■■■, ) set, r2=4.67/16=.29 and for the σ2=18, µ=4, (10, 1, 1), (■■■■■■■■■■, , ) set, r2=18/16=1.125. From this we see that r2 is also a measure of the imbalance of a set. This sense of r2 as set imbalance is further reinforced with the balanced, (4, 4, 4), (■■■■, ■■■■, ■■■■), set from Eqs6,7&10 whose perfect error is r2=0, which specifies no imbalance for this completely balanced set. 

 

We now see from the D diversity index for (4, 4, 4) in Eq2 of D=3, for (6, 5, 1) in Eq3 of D=2.32, and for (10, 1, 1) from Eq1 of D=1.41, and from the perfect errors of these N=3 subset sets respectively of r2=0, r2=.29 and r21.125 that their D diversity indices are inversely proportional to their r2 perfect errors. This inverse relationship is developed analytically by first solving the σ2 variance of Eq7 for the summation term in it as

  

11.)                                      

 

Then inserting this summation term into Eq1 obtains D via µ of Eq6 and r2 of Eq10 as

 

12.)                                       

 

 

 

We will use this expression of the D Simpsons Reciprocal Diversity Index for our development of diversity based entropy and ultimately of the mind’s way of generalizing what it senses in the world around us. But before we do that, we want to use the notion of diversity to develop the more fundamental notion of distinction. The reader is asked to bear up with this seeming digression from our main themes, for it will prove in the end very useful in our explaining human emotion later down the line.

 

To develop the concept of distinction analytically, we first note a discrepancy in the D Simpson’s Reciprocal Diversity Index as a good measure of our intuitive sense of the diversity in a set, specifically  when we apply D to a completely uniform set like the N=1 color, (■■■■■■■■■■■■), set. It obviously has no diversity or (0) diversity. But from Eq1 this uniform set has a D diversity index of D=1. This discrepancy is easily rectified, though by defining a new diversity index, L, called the Exact Diversity Index.      

 

13.)                                        L = D 1

 

The Exact Diversity Index does specify the zero diversity in the uniform, D=1, set, (■■■■■■■■■■■■), as L=D1=0. In reducing the D diversity indices of all of the button sets we’ve been considered by 1, L=D1 also, as with D, provides a useful quantitative measure of the relative diversities of sets.  

Set of Objects

Number Set

D, Simpson’s Diversity Index

L, Exact Diversity Index

(■■, ■■, ■■, ■■, ■■, ■■)

(2, 2, 2, 2, 2, 2)

6

5

(■■■■, ■■■■, ■■■■)

(4, 4, 4)

3

2

(■■■■■■, ■■■■■, )

(6, 5, 1)

2.32

1.32

(■■■■■■, ■■■■■■)

(6, 6)

2

1

(■■■■■■■■■■, , )

(10, 1, 1)

1.41

.41

(■■■■■■■■■■■■)

(12)

1

0

Table 14. Sets and Their D and L Diversity Indices


The Exact Diversity Index, L, has other advantages over D in explaining how the mind operates in its having a foundation in the primitive mental operation of our distinguishing, or making a distinction, between things. It does this in two rather fascinating ways. In the N=D=6 set of (
■■, ■■, ■■, ■■, ■■, ■■), every color subset is intuitively distinct or distinguishable color-wise from the 5 other subsets in the set. And this subset distinction is perfectly specified by its Exact Diversity Index of L=D1=5. In the N=D=3 color (■■■■, ■■■■, ■■■■) set, every subset is distinguished from 2 other subsets and that amount of subset distinction is specified by its L=D1=2 diversity. And for the N=D=2 set, (■■■■■■, ■■■■■■), each of the N=2 subsets in the set is distinguished from one (1) other subset and its Exact Diversity Index is L=D1=1. And we see in Table 14 that the L=0 measure for the uniform, N=D=1 set, (■■■■■■■■■■■■), specifies that the red subset of the set is distinct from no or (0) other subset in the set. Hence L is a measure both of the diversity in a set and of its subset distinction. This is significant because our minds operate to a great extent by distinguishing between things both in our perceptions and in our thoughts.

 

Also significant is that L is also a measure of the distinction we intuitively make, not just between subsets of objects, but also between individual objects. In the N=3 subset, (2, 2, 2), (■■, ■■, ■■) set of colored buttons we intuitively distinguish an individual red object, , from an individual  green object, , and both of these from an individual purple object, . We can quantify these distinctions between objects by comparing the objects in (■■, ■■, ■■) systematically to each other in a comparison matrix.

 

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

Figure 15. The Comparison Matrix of (■■, ■■, ■■)


The K=6 set of objects, (
■■, ■■, ■■), has K2=36 comparison pairs in its matrix. Y=24 of them, such as , are distinctions between objects or mismatches in color. And ε=12 of them, such as ■■, are likenesses between objects or matches in color. It is clear for this matrix, as it must be for the comparison matrix of any set of objects that

 

15a.)                                Y + ε = K2

 

Now from Eqs1&13 we calculate L=D-1=2 for (■■, ■■, ■■). On the one hand, L=2 is the number of distinctions that any one subset in (■■, ■■, ■■) has from the other subsets in the set. But we also see that L is the ratio of the Y number of object distinctions in the matrix of Figure 15 to the ε (epsilon) number of likenesses in the matrix, L=Y/ε=24/12=2. Or more generally, 

 

15b.)                                    

 

Hence the L Exact Diversity Index is not only a measure of the number of subset distinctions in a set but also a simple function of the set’s Y object distinctions. In that sense both L and D=L+1 are measures both of diversity and distinction in a set. L as expressed in Eq15b is also valid for unbalanced sets like the K=6, N=3, (3, 2, 1), (■■■, ■■, ), set. From Eqs1&13, we calculate the diversity of (3, 2, 1), (■■■, ■■, ) as D=2.57 and L=1.57 and we also see the validity of Eq15b for it by looking at its comparison matrix. 

 

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

Figure 16. The Comparison Matrix of (■■■, ■■, )


We count in the matrix K2=36 comparison pairs consisting of Y=22 distinctions and ε=14 samenesses, which calculates the Exact Diversity Index as L=Y/ε=22/14=11/7=1.57. This makes it clear that L is a most elemental diversity index in deriving from the mind’s most primitive senses of distinction and likeness.

 

The matrix underpinning of diversity in terms of distinction and sameness, it is next easy to point out next, provides the mathematical foundation for the equations for the basic human emotions of hope, fear, anxiousness, excitement, relief, dismay, depression, hunger, anger, sex and love we will develop in later sections. Let’s take another look at the comparison matrix of (■■, ■■, ■■) in Figure 15 to see how.

          

 

■■

■■

■■

■■

■■

■■

 

■■

■■

■■

■■

■■

■■

Figure 15. The Comparison Matrix of (■■, ■■, ■■)


For this analysis let’s consider the (■■, ■■, ■■) set of objects as a bag of K=6 colored buttons from which one is picked blindly or randomly. A game can be played in which a person makes a guess at which color will be picked.  She knows the (■■, ■■, ■■) contents of the bag, which will tell her that each color has an equal probability of being picked randomly from the bag. Because of that it is assumed that she will guess each color with the same probability or frequency. The (■■, ■■, ■■) set on the vertical axis of the matrix is understood, hence, as a representation of her guessing all the colors with equal frequency. And the (■■, ■■, ■■) set on the horizontal axis of the matrix is the average outcome of the picks from the bag, all equally likely.  

 

This interprets the K2=36 comparison pairs in the matrix as K2=36 guess-outcome pairs. The Y=24 distinctions between color guessed and color picked such as are understood as incorrect guesses. And the ε=12 likenesses between color guessed and color picked are correct guesses. Assumed now is that every incorrect guess feels unpleasant and that every correct guess pleasant, much as the way that guessing or getting a correct answer feels good or pleasant to some extent and guessing incorrectly or making a mistake feels bad or unpleasant to some extent when one plays along at home with TV game shows or does a crossword puzzle any other kind of guessing game. This sense of pleasure in being right and of displeasure in being wrong in such games is universal and is a way to introduce the ephemeral phenomena of pleasure and displeasure in a firm analytical way. We will elaborate on this in great detail in the sections on emotion we will take up later.

  

Another major property of mind is its sense of the probability or likelihood that something will happen in the future. We can also develop that mathematically from the Y distinction and ε likeness matrix functions for it is intuitively obvious that the ratio of Y wrong guesses to the K2 total number of guesses is, when projected to future guessing, the probability of failure in guessing correctly or equivalently the uncertainty in guessing correctly.

 

16a)                        

 

This ratio that we have given the symbol, U, to is readily understandable as a measure of the displeasure in the uncertainty in guessing as a lumped or collective measure of the displeasures of the Y incorrect guesses in the matrix. And the ratio of the ε correct guesses to the K2 total guesses is as projected to future guessing the probability of success in guessing.

 

16b.)                         

 

The Z probability of correct guessing in the above is measure of the pleasure of the expectation or hope of success as a lumped measure of the pleasure in the ε individual correct guesses in the matrix projected to future guessing. Details aside for now as will be taken up later, this distinction and likeness based matrix foundation of the pleasures and displeasures of correct and incorrect guessing will spell out all the human emotions in a firm mathematical way. 

 

This is a very important breakthrough in science for the human emotions have been without question the most difficult phenomena to give clear explanations for over the last five millennia in which knowledge has been set down in written form. Previous attempts at explanation include the evil spirit theory of the emotions in which characters like Satan are responsible for the pleasant feeling of sex as temptation to sin. And in modern times we have the psychobabble mental illness theory of unpleasant emotion, which is almost as foggy causally as the more primitive supernatural good and bad spirit sourcing of human feeling. This treatise is a significant improvement in explanation in couching its representations in form mathematical language.

 

We hold off on delving further into this most important topic of our emotions, reserving it for a later section, because the feelings aroused by discussing our feelings can be so intense themselves and potentially unpleasant when they run against the rationalizations and delusions people have in this area, that it is preferable to first explain entropy and how the mind generalizes as the starting point for considering our emotions so that our conclusions on this most important topic of emotion become inarguable.     

The fundamental expression for entropy in physical science is Boltzmann’s S entropy  


17.)                S=kBlnW


The primary problem with this equation is that even when it is explained thoroughly in all its details, it makes little sense intuitively. Or put in more technical terms, however good its numerical fit to laboratory data, it doesn’t explain what entropy is as a physical quantity. The diversity based entropy that has a .999 correlation to Boltzmann and is, hence, numerically indistinguishable from it, on the other hand, makes perfectly clear sense intuitively of entropy as a physical quantity.

 

Ludwig Boltzmann is almost as much a saint or god of science as Isaac Newton, his ideas not to be questioned anymore than a Christian would question the sanctity of the Virgin Mary, the very thought of it put out of mind right from the get go with no further consideration of the possibility that he, Boltzmann, could be in error in any way. But it is most important in this age of bloody ISIS beheadings and nuclear missiles in the waiting to destroy us all that this mathematics that explains both thermodynamic entropy and the workings of the mind including its violent inclinations be understood and accepted. For that reason, we will preface the full argument for diversity based entropy with an immediate, brief exposition of the quantitative equivalence of it and Boltzmann’s S entropy.

 

Thinking in set terms of K objects distributed over N subsets that we have already considered, we express the lnW term in Boltzmann’s S=kBlnW entropy using Stirlings Approximation as a function of K energy units distributed over the N molecules of a thermodynamic system as 

 

17a.)

 

And we will express the average energy diversity of that K energy unit over N molecule thermodynamic distribution as

 

18.)                

 

While both of these functions brought out of nowhere can make little immediate sense, they are readily developed in the most logically unarguable way shortly. What is important is that they have a Pearson’s correlation coefficient minimally of .999, more so for the high K energy unit and N number of molecules values associated with realistic thermodynamic systems. With the kB term in S=kBlnW a constant, this makes Boltzmann’s S entropy and the DAV average energy diversity as entropy near identical and effectively quantitatively indistinguishable. Anybody with a computer with Microsoft Excel can test that correlation for themselves. The correlation comes out exceedingly huge and approaching unity as a near perfect correlation no matter the specifics of how one tests it for large K and N values, K>N.

 

Assuming the above high correlation is correct so to show that diversity based entropy is valid from the perspective of its quantitative equivalence to Boltzmann’s S entropy, (something we’ll derive next as firmly as the Pythagorean Theorem is derived in Euclidian Geometry), we want to ask which of the two might be correct in that case. While the actual derivation of Eqs17a&18 that follow is needed to provide the answer to that question beyond any doubt, it is worthwhile to give a prefatory view as to how that decision might be made.

 

We look to a parallel problem that faced Johannes Kepler in deciding between the Ptolemaic system and the Copernican system of explaining our solar system, both of which had a valid numerical fit to measurable reality. The argument is well synopsized in Tycho and Kepler, Kitty Ferguson, 2002, Walker and Co., NY.       

 

It, (Kepler’s), is one of the finest analyses ever written about scientific methodology, pointing out a difference between the Ptolemaic and Copernican models that … remains even today the primary reason for deciding in favor of Copernicus. In principle, Ptolemaic astronomy was not “incorrect.” It could plot and predict the courses of the heavenly bodies just as correctly as Copernican astronomy. So could the Tychonic model (of Tycho Brahe). But wrote Kepler, “If in their geometric (mathematical) conclusions two hypotheses coincide, nevertheless in physics each will have its own peculiar additional consequences.” In other words, when one begins asking the ‘why’ questions, seeking the physical causes for the motion, Ptolemaic and Tychonic astronomy could no longer hold their own. To Kepler the search for physical consequences had become paramount.

 

And that physical cause was, of course, gravitation. In a similar vein we will show that the physical cause of the increasing entropy seen in the 2nd Law of Thermodynamics is the random dispersion of energy or increase in its average diversity, something Boltzmann’s S=kBlnW entropy gives not the slightest hint of, or of any other sensible physical cause for that matter.       

 

To derive the conclusion favorable to diversity based entropy rather than Boltzmann’s S entropy in the most direct and simple way, we will consider a thermodynamic system to be an equiprobable or random distribution of K discrete (or whole numbered) energy units over N molecules and to be well modeled by an equiprobable or random distribution of K candy bars to N children. Specifically let’s consider the random distribution of K=4 candy bars to N=2 children, Jack and Jill, as done by their grandpa tossing the candy bars to them blindly over his shoulder. Such a distribution is understood as equiprobable because each of the N=2 children has an equal, P=1/N=1/2, probability of getting the candy bar thrown on any given toss by grandpa.   


For ease in explanation we’ll have the K=4 candy bars be different kinds: a Snickers bar, S; a Hershey bar, H; a Butterfinger candy bar, B; and a Tootsie Roll, T. We could as well use all the same kind for the K=4 of the candy bars and get the same mathematical results, but using different brands makes the argument easier to follow.

 

There are Ω=NK=24=16 permutations or different ways of candy bar distribution possible in this action as listed in {braces} below with the candy bars Jack gets on the left of the comma in the {braces} and the candy bars that Jill gets listed to the right of the comma.

 

Ω=16 permutations

{SHBT, 0}

{SHB, T}

{SH, BT}

{T, SHB}

{0, SHBT}

 

 

{SHT, B}

{SB, HT}

{B, SHT}

 

 

 

{SBT, H}

{ST, BH}

{H, SBT}

 

 

 

{BTH, S}

{HB, ST}

{S, BTH}

 

 

 

 

{HT, SB}

 

 

 

 

 

{BT, SH}

 

 

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 19.The Ω=16 Permutations and other Properties of the Random Distribution of K=4 Candy Bars to N=2 Children


All Ω=16 permutations are equiprobable, the probability of each one from grandpa’s random or equiprobable toss being 1/Ω=1/16. To make clear what we mean by equiprobable permutations, consider that if grandpa repeats his random tossing of the K=4 candy bars to the N=2 grandkids 16 times, on average each of the Ω=16 permutations listed in the table will happen 1 (one) time.

 

The Ω=NK=16 permutations are grouped into W=5 states, [4, 0], [3, 1], [2, 2], [1, 3] and [0, 4], with each state having a certain number of permutations in the 8th line in the table. The [1, 3] state consists of 4 permutations, for example, as tells us that there are 4 ways that Jack can get 1 candy bar and Jill, 3.

 

And below 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 candy bars, the [2, 2] state, is 3/8=.375. And below on the 10th line in the table is listed the number set notation of each state, x1 being the number of candy bars that Jack gets and x2, the number that Jill gets for any given state.

 

The W number of states for a random distribution of K=4 candy bars to N=2 kids is W=5, listed as [4, 0], [3, 1], [2, 2], [1, 3] and [0, 4] on the 7th line in the table. There is a shortcut formula for W in standard mathematical physics.  

 

20.)               

 

We see this formula calculating the W=5 number states of the K=4 over N =2 candy bar distribution of Table 19 as 

 

21.)                   

The W term of Eq20 is the W in Boltzmann’s S=kBlnW entropy of Eq17, the W=5 in Table 19 being understandable as the number of states for an equiprobable distribution not just of K=4 candy bars over N=2 children but also of K=4 energy units over N=2 molecules in a mini-thermodynamic system. As was made clear above but worth repeating, the kB in S=kBlnW is a constant, Boltzmann’s constant, which does not impact the argument. 

 

It should be obvious now that some of the W=5 states in the K=4 over N=2 candy bars are more diverse distributions than others. The [2, 2] state that has both children getting the same number of candy bars in a K=4 toss, for example, has greater diversity in being a balanced state as opposed to the [1, 3], [3, 1], [0, 4] and [4, 0] states which are unbalanced.

 

The σ2 variance of a state understood as a number set can be calculated from Eq7. And the D diversity of a state can then be calculated from the variance and the µ=K/N=2 mean of the K=4 over N=2 distribution and of all its states from Eq12. For example, the variance of the [3, 1} state, x1=3 and x2=1, is σ2 =1 and the diversity of that state is from Eq12, 

 

22.)                      

 

 

The σ2 variances and D diversities of the W=5 states of the K=4 over N=2 distribution are from Eqs7&12

 

State

Variance, σ2 

Diversity, D

[4, 0]

4

1

[3, 1]

1

1.6

[2, 2]

0

2

[1, 3]

1

1.6

[0, 4]

4

1

Table 23. The Variance, σ2, and Diversity, D, 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 of the variances of the states in weighting the variance of each state by the probability of that state occurring, as is listed on the 9th line in Table 19.
  

State

Variance, σ2

Probability of State

Probability Weighted Variance

[4, 0]

4

1/16

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

[3, 1]

1

¼

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

[2, 2]

0

3/8

(0)(3/8)=0

[1, 3]

1

¼

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

[0. 4]

4

1/16

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

 

 

 

Sum is average variance2AV=4/4=1

Table 24. 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 Eq12 as a function of σ2 to be the average diversity, DAV, as a function of the average variance, σ2AV.    

 

25.)                  

 

 

 

This calculates the average diversity, DAV, of the K=4 over N=2 distribution from its σ2AV=1 average variance obtained in Table 24 as  

 

26.)   

 

 

 

To show that Boltzmann’s S=kBlnW entropy has a .999 correlation to the DAV average diversity of an equiprobable distribution, we need to calculate the DAV and the σ2AV of distributions with larger K and N values than our K=4 and N=2 distribution. Calculating σ2AV by probability weighting as we did for the K=4 and N=2 distribution in Table 24, though, is extremely tedious for K and N much larger than that.

 

Fortunately we can develop a shortcut formula for σ2AV from a textbook expression for the variance of a multinomial distribution. For the general case that expression is

 

27.)                           

 

This simplifies greatly for the equiprobable case in which the Pi term in the above is Pi= 1/N as tells us that each the N containers for K equiprobably distributed items has an equal, 1/N, chance of getting those items whether the K items are candy bars equiprobably distributed to N children or K energy units equiprobably distributed over N molecules. (We saw this Pi=1/N probability for the K=4 candy bar over N=2 children equiprobable distribution to be P=1/N=1/2).

 

This Pi =1/N probability for the equiprobable case simplifies the variance formula of Eq27 via substituting 1/N for Pi to

  

28.)                      

 

This variance of an equiprobable multinomial distribution is entirely the same as the average variance of an equiprobable distribution, σ2AV, that we generated in Table 24 for the K=4 over N=2 equiprobable distribution. Hence the variance formula of Eq28 is that of the average variance, σ2AV.    

 

29.)               

 

We quickly demonstrate the correctness of Eq29 by calculating its σ2AV=1 average variance in Table 24 of the K=4 over N=2 distribution from Eq29 as  


30.)           
  

 

Now from Eqs25&29 we derive the simple formula for the average diversity, DAV, we first introduced without derivation in Eq18.  

 

31.)               

 

 

 

 

And we demonstrate the correctness of this formula by using it to calculate the DAV=1.6 average diversity of the K=4 over N=2 distribution of Eq26 as

 

32.)                

 

We could also have calculated this DAV average diversity for an equiprobable distribution directly from the D diversities of its W states, though because DAV is an inverse function of the σ2 variance, to do so we would sum all of the probability weighted inverses of the D diversities of the W states and then invert that sum to obtain DAV. Certainly Eq31 is a much more efficient way to calculate it.

 

Now we want to develop an easy to use formula for the lnW term in Boltzmann’s S=kBlnW for large K over N distributions in order to determine the extent of the correlation between lnW and DAV of Eq31. The lnW term is from W of Eq20

 

33.)               

 

 

A formula that provides ease in calculating lnW for large K and N is Stirling’s Approximation, which approximates the ln (natural logarithm) of the factorial of any number, n, as

 

34.)               

 

This gives an excellent approximation of lnW of Eq33 as the function introduced earlier without derivation of Eq17a. 

 

17a.)   

 

To demonstrate the accuracy of Stirling’s Approximation, note that it computes lnW for a K=145 over N=30 random distribution as lnW≈75.71 as compares well to the lnW=75.88 value for this distribution calculated directly from the exact function for lnW of Eq33. And the larger are the K and N values, the better the Stirling’s Approximation.

 

Realistic thermodynamic systems have very large values of K energy units and N molecules so we compare the lnW of large K and N as computed from Eq17a to their DAV average diversity of Eq31 in the table blow.   

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 35. The lnW and DAV of Large Value K over N Distributions

The Pierson’s correlation coefficient between DAV and lnW for these large K over N random distributions is .9995, close to a near perfect 100% correlation as can be appreciated visually with the near perfect straight line scatter plot below of the DAV versus lnW values in Table 35. 

Figure 36. A plot of the DAV versus lnW data in Table 35

The .9995 correlation between lnW and DAV, (which is even greater yet for K and N larger than in the Table 35, K>N), tells us that Boltzmann’s S=kBlnW entropy can be substituted for by DAV because the fit of DAV to relevant laboratory data must be as valid as the lnW based Boltzmann’s S=kBlnW entropy.

 

On the one hand, the direct proportionality between the two functions suggests from measure theory that S=kBlnW and DAV are measures of the same thing, namely entropy. Parallel examples clarify and reinforce this conclusion. The relationship between Fahrenheit temperature, F, and Centigrade temperature, C, is one of direct proportion, F=(1.8)C + 32; and both are a measure of the same thing, namely, temperature. At an even more basic level, the relationship between feet and meters is one of direct proportion, Feet = .3048 Meters; and both are a measure of the same thing, namely, distance. This would have us understand both S=kBlnW and DAV as equally valid measures of entropy, with nuances peculiar to system circumstances dictating, perhaps, which measure is better to use.  

 

On the other hand, the quantitative equivalence between S=kBlnW and DAV, because the two functions are derived from quite different assumptions as any textbook on Boltzmann statistical mechanics makes clear, may be understood in parallel to the derivation of the same astronomical values from Ptolemaic astronomy and Copernican astronomy, which have quite different, contradictory assumptions. Hence it is helpful for deciding which understanding of entropy is correct to repeat Kepler’s reasoning as laid out in the Kitty Ferguson book, Tycho and Kepler.

 

It, (Kepler’s), is one of the finest analyses ever written about scientific methodology, pointing out a difference between the Ptolemaic and Copernican models that … remains even today the primary reason for deciding in favor of Copernicus. In principle, Ptolemaic astronomy was not “incorrect.” It could plot and predict the courses of the heavenly bodies just as correctly as Copernican astronomy. So could the Tychonic model (of Tycho Brahe). But wrote Kepler, “If in their geometric (mathematical) conclusions two hypotheses coincide, nevertheless in physics each will have its own peculiar additional consequences.” In other words, when one begins asking the ‘why’ questions, seeking the physical causes for the motion, Ptolemaic and Tychonic astronomy could no longer hold their own. To Kepler the search for physical consequences had become paramount.

 

In regard to “physical consequences” we next will draw a physical picture of the DAV diversity based entropy, one that is much more sensible than that for the Boltzmann S entropy found in any standard text on statistical mechanics. This is also the gateway to a fuller understanding of the human mind’s generalizing the phenomena it is exposed to in life.

 

We start with an introduction of a property of a distribution called a configuration. A configuration is well defined as the collection of all states in a distribution that have the same number set representation. For example, the states of [0, 4] and [4, 0] in the K=4 over N=2 distribution have the same number set, (4, 0), which is understood as a configuration of the K=4 over N=2 distribution. Note that we write a configuration in parenthesis, (4, 0), in contrast to the brackets we used for the [4, 0] and [0, 4] states of the (4, 0) configuration.

 

We see that the K=4 over N=2 equiprobable distribution has 3 configurations, (4, 0), (3, 1) and (2, 2), which the W=5 states of the distribution of Figure 19 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 37. The Configurations of the K=4 over N=2 Distribution and Their States

A quick look back to Table 23 makes it clear that a configuration has the same σ2 variance and same D diversity 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 38. The Variance, σ2, and Diversity, D, of the Configurations of the K=4 over N=2 Distribution

 

Now note carefully in the above table that the average variance of σ2AV=1 of the distribution in Eq30 and its average diversity of DAV=1.6 in Eq32 of the K=4 over N=2 distribution are 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 28. On that basis the (3, 1) configuration is a generalization or condensed representation of the full set of the three configurations, (4, 0), (3, 1) and (2, 2), that make up the K=4 over N=2 distribution given the name of the Average Configuration of the equiprobable distribution.

 

Much as the µ mean is a condensed representation of a set of N numbers, as with K=24, N=6, (6, 4, 2, 1, 5, 6), number set being represented in condensed or reduced form by its μ=K/N=4 mean, so the Average Configuration of an equiprobable or random distribution is a condensed representation of the distribution’s many configurations. To wit we see the (3, 1) Average Configuration representing in condensed form the entire K=4 over N=2 distribution of all its configurations of (4, 0), (3, 1) and (2, 2).  

 

Both kinds of condensed representation, the µ mean of a number set and the Average Configuration of an equiprobable distribution, leave out information from their larger set of numerical parameters, the µ mean not including the N numbers or xi, of the number set it represents; and the Average Configuration not including the many configurations specified by number sets that make up the equiprobable distribution.  

 

To understand the Average Configuration as a condensed representation in greater detail requires our first making it clear that the D diversity measure of Eq1 is itself a condensed representation of a number set, but one that contains more information than the μ=K/N mean condensed representation of a number set. Indeed, as shown below, the D diversity algebraically manipulated from Eq12 is itself a function of the μ mean but one that includes the σ2 variance as a measure of the amount of imbalance in a number set.   

 

38a.)                                          

 

 

To repeat for clarification, the D diversity is a condensed representation of a number set that leaves out the information of the individual numbers of a number as does the μ mean but includes a measure of the imbalance in a number set via its inclusion of the σ2 variance, which the μ mean does not include as μ=K/N.

 

This is well demonstrated with a comparative consideration of the μ mean and D diversity of two K=12, N=3, number sets: the (10, 1, 1), (■■■■■■■■■■, , ) set, which has μ=K/N=12/3=4 and D=1.41; and the (6, 5, 1), (■■■■■■, ■■■■■, ) set, which also has μ=K/N=12/3=4 but a different diversity index of D=2.323. This shows in an obvious way that the D diversity is a condensed representation of a number set that has more information in it than the μ mean, specifically the information via the σ2 variance of the imbalance in a number set.  

 

This allows us to understand the Average Configuration as a two-fold condensed representation. First in a thermodynamic system as equiprobable distribution it includes the D diversity of the energy of N molecules in the system in whatever configuration the system finds itself at any moment in time. And secondly, the primary property of the Average Configuration is the probability weighted average of the diversities of all the configurations the system runs through over time as DAV, the diversity of the Average Configuration.

 

This condensed representation of a thermodynamic system as an equiprobable distribution of K energy units over N molecules will serve as a mathematical model for the generalizations the human mind makes about the objects and events we experience in the world including the emotions associated with that experiencing of objects and events, as will be considered later in detail. To develop that understanding of thought and to make the best decision between diversity based entropy and Boltzmann S entropy we must delineate the properties of the Average Configuration as completely as possible. Doing that centrally includes showing that the Average Configuration to exhibit the Maxwell-Boltzmann energy distribution pictured below, a standard observed property of every realistic thermodynamic equiprobable distribution.

 

Figure 39. The Maxwell-Boltzmann Energy Distribution


Showing that the Average Configuration of a K over N distribution exhibits the Maxwell-Boltzmann distribution goes a long way in supporting diversity as the correct formulation and understanding of entropy rather than Boltzmann’s S=kBlnW formulation. While we developed the Average Configuration for the random distribution of K candy bars over N children it is also valid for the random distribution of K discrete energy units over N molecules of a thermodynamic system. Indeed, the equiprobable distribution of K candy bars over N children from grandfather tossing the candy bars to the children blindly over his shoulder when done repeatedly is a perfect mathematical model for the equiprobable distribution of K energy units over N molecules that comes from repeated collisions between molecules and the random energy transfers those collisions bring about for the simplest thermodynamic system of gas molecules moving about and repeatedly colliding in a container of fixed volume.

 

A 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 39. 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 the DAV average diversity of the equiprobable distribution, its defining property, from Eq31.

 

40.)                       

 

The Average Configuration of the K=12 over N=6 distribution will have a D diversity with the same value as the average diversity of the equiprobable distribution, 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 diversities whose D 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 for this Average Configuration of (4, 3, 2, 2, 1, 0) vs. the number of its molecules that have that energy is shown below.

 

Figure 41. 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 39 is a bit of a stretch, though it might be characterized as a very simple, 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 Eq31, 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

 

Figure 42. 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 distribution variance is from Eq31, DAV=11.11. Our 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

 

Figure 43. 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 Eq31, 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

 

Figure 44. 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


All of the other configurations of this distribution bear similar resemblance to the Maxwell-Boltzmann of Figure 39. As we progressively increase the K and N of our example equiprobable distributions we see that the plot of their energy per molecule versus the number of molecules with that energy progressively more and more approach and eventually fit the shape of the realistic Maxwell-Boltzmann distribution of Figure 39.

 

This understanding of the empirical Maxwell-Boltzmann energy distribution as a measure of the Average Configuration, which itself is an agglomeration of all the configurations the equiprobable or random distribution takes over time very much supports diversity based entropy as the proper form of entropy but also provides an intuitively sensible microstate picture of a thermodynamic system. Specifically it depicts a K energy unit over N molecule system as consisting from an extrapolation of the picture presented in Table 19 of Ω=NK energy distribution permutations that develop from Ω=NK sequential collisions between molecules over time. The random energy transfers from the collisions produce on average all of the various Ω=NK equiprobable permutations from the Ω=NK sequential collisions, those permutations represented by the Average Configuration that consists of the average properties of the system that include its average variance, its average energy diversity and its Maxwell-Boltzmann energy distribution.

 

This easy to intuitively digest picture of a thermodynamic system developed in terms of the Average Configuration in conjunction with the .9995 correlation of energy diversity and Boltzmann’s S entropy minimally suggests an alternative interpretation of entropy to Boltzmann’s S entropy formulation and in the extreme can be understood as overthrowing Boltzmann statistical mechanics in a major scientific revolution.

 

This is not in any way to disparage Boltzmann’s genius, for it is a simple matter to understand his error. Boltzmann proved his S=kBlnW entropy equation with its quantitative fit to the thermodynamic data. But this fit to data only came about by a fluke or chance correlation of S to mathematical diversity, something Boltzmann couldn’t possibly have appreciated because the Simpson diversity index wasn’t developed by Simpson and available to science until 1948, long after Boltzmann died. Credit for genius where credit is due, though, for the correct specification of entropy given here as energy diversity would have been quite impossible without Boltzmann developing his S entropy formula first.

 

The nature of generalization in human thought can now be considered in relation to the defining parameter of the Average Configuration, its diversity as the average diversity of the equiprobable distribution, DAV. It should be clear from the foregoing analysis that the D diversity of one of the W states of a given configuration is a condensed representation of that state and its configuration that exists at any one moment in time, as we discussed earlier from Eq38a, a kind of a complex average of it. It is also clear that DAV in turn is an average of the D “averages” of all of the W states of the system. As such DAV is a condensed representation of a thermodynamic system or equiprobable distribution of K energy units over N molecules.

 

Our mind averages the objects and events it perceives over time in the same way, namely as two-fold averages of them over space and over time. As an example, when we use the word “dog” in the broadest way, we are talking about a generalization of all the dogs in the world observed or observable at any moment in time averaged in terms of their characteristics of size and shape and further so over all the times they are observable, actually or potentially. And that is the same for all the other “common nouns” we use, like fish, house, and so on. They are all as with all most basically generalizations or averages of observables over space at any moment in time and over time.

 

The nuances to this understanding of the “ideas” we hold in our minds as generalizations or averages over space-time are many and include constructions of possibility from imagination and generalizations communicated to us by others. What is important to understand, though, is the basis of such generalizations most fundamentally in what the mind, someone’s mind, observed in reality, whether in perception or in emotion experienced as we will consider in greater detail in Section 4 on the Mathematics of Emotion.            

 

We next want to cement this understanding of how the mind develops its generalizations with a detailed consideration of how our brain senses temperature, a most elemental property of the thermodynamic systems we have been considering. To do that we must solve the problem of entropy completely, which requires us to investigate yet another diversity function that has a very high correlation with Boltzmann S=kBlnW entropy and as such must also be considered as a valid replacement for it. This will also revamp the science of thermodynamics in an entirely thorough way, which as a side effect will give greater confidence yet in the mathematics we are using to explain human nature correctly and how its culturally altered form presents a significant danger to the human race in terms of the violence it engenders in people, individually and collectively in war.   

 

To develop that alternative diversity function we begin by expressing the K number of objects in a set with N subsets in a formal way as

 

45.)                  

 

For the (6, 5, 1) number set, for example, which has x1=6, x2=5 and x3=1, we see K= x1+x2+x3=6+5+1=12. Eq45 allows us to define the μ mean of Eq6 as 

 

46.)                   

 

Next we want to express 1/N in terms of what we are calling 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 objects in each of the N subsets to the K total number of objects in the set.

 

47)                   

 

For the K=12, N=3, (6, 5, 1), number set that has x1=6, x2=5 and x3=1, the weight fractions 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.

 

48.)                  

 

The weight fractions of (6, 5, 1) as (6/12, 5/12, 1/12) sum to one. The (1/N) term in the rightmost summation of Eq46 can now be understood as the average weight fraction of a number set. We take the average of a number set’s weight fractions by adding up its pi to one (1) and then dividing that sum 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. Dividing this sum of 1 by N obtains 1/N. So the average weight fraction, which is given the symbol,, is for any number set,   

49.)               

 

This allows us to express the μ mean in Eq46 in terms of the average weight fraction,, as

 

50.)         

 

This interprets the μ mean of a number set as the sum of “slices” of its xi with each “slice” the “thickness” of, the average weight fraction. This form for μ computes the μ=K/N=12/3=4 mean of the K=12, N=3, (6, 5, 1), number set as

 

51.)          

 

All of the above is spelled out as preface to our defining a new kind of average of a number set called the biased average, φ, (phi). In parallel to the μ arithmetic average of a number set being the ratio of K to N as μ=K/N, we specify the φ biased average as the ratio of K to the D diversity of a number set as

  

52.)            

 

For the K=12, (6, 5, 1), set, which has D=2.323 from Eq4, φ=K/D=5.167. Note that this φ=5.167 biased average of (6, 5, 1) is greater than its μ=4 mean or arithmetic average. Next let’s express the D Simpson’s Reciprocal Diversity Index of Eq1 via Eq47 as

 

53.)               

 

 

 

This has us specify φ=K/D of Eq52 in a way parallel to μ in Eq50 as a function of the pi weight fractions of a number set of Eq47 as

 

54.)           

 

 

 

 

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 =1/N average weight fraction, as was the case for μ in Eq50. The above form for φ in obtains the φ=5.167 biased average of (6, 5, 1) as

 

55.)           

 

This makes it clear how the φ biased average is biased in its exaggerating the contribution of the larger subsets in a set to the set’s φ biased average. With regard to our perfecting our formulation of diversity based entropy, the φ biased average is just an introduction to another diversity related biased average called the square root biased average, ψ, (psi), which will be shown to be the proper foundation of microstate entropy and temperature.

 

In parallel to the φ biased average as the sum of slices of the xi of a set of thickness pi in Eq54, 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. So in parallel to Eq54 for the φ biased average, we write ψ as

 

56.)              

 

We place a question mark on this introductory definition of the ψ square root biased average to indicate that there is something not quite right with it as it stands. What isn’t right is that the pi1/2 weightings don’t add up to 1 as they must to form any kind of an average of the xi of a set, that proviso being in the intrinsic nature of what an average is. This problem is 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 these 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, though, by normalizing the pi1/2 to get them to add up to 1 as is done by dividing each of them, (.7071, .6454, .2887), by their 1.6412 sum. This obtains normalized pi1/2 of (.4308, .3933, .1759), which do add up to 1 and, hence, can properly weight the xi of the (6, 5, 1) set to form its ψ square root biased average as

 

57.)                ψ = (.4308)(6) +(.3933)(5) + (.1759)(1)= 4.727

 

The sum of pi1/2 function that divides the pi1/2 to normalize them is expressible as

 

58.)            

 

This revises the ψ{?} questionable function for ψ in Eq56 by dividing the pi1/2 in the numerator to obtain the ψ square root biased average correctly as

 

59.)        

 

 

Next note that we can express ψ in an alternative way via the pi=xi/K weight fraction relationship of Eq47 as 

 

60.)           

 

 

The φ=K/D biased average as the ratio of the K number of objects in a set to the set’s D diversity index implies that the D diversity index can be understood as the ratio of K to the φ biased average.

 

61.)            

 

In parallel we define a diversity index that is the ratio of K to the ψ square root biased average and that we’ll call the Square Root Diversity Index.  From Eq60

 

62.)       

 

 

 

Next we show that the average G diversity of a thermodynamic distribution, GAV, also has a high correlation to the lnW term in Boltzmann’s S=kBlnW entropy and as such that it along with DAV is a candidate to replace Boltzmann’s S=kBlnW as the correct diversity based function for entropy. This is a somewhat tricky correlation to compute, however, because the form of G  in Eq62 is not amenable to developing a simple function for its average value, GAV, as we did for the average diversity, DAV, in Eq31 as DAV=KN/(K+N−1). 

 

But GAV is the G diversity index of the Average Configuration much as was DAV was the D diversity index of the Average Configuration. Hence we can obtain GAV for the K over N distributions for which we have the specific number sets of the Average Configurations, the K=4 over N=2 distribution and those in Figures 41-44. Below we list those K over N equiprobable distributions along with their lnW values from Eq33 and the D and G of these distributions’ Average Configurations, the DAV and GAV respectively from Eq31 and Eq62.


       

K

N

lnW

DAV

GAV

4

2

1.61

1.6

1.76

12

6

8.73

4.24

4.57

36

10

18.3

8

8.85

45

15

26.1

11.11

12.33

145

30

75.88

25

26.49

 

Table 63. The lnW, DAV and G­AV of Distributions in Figures 101-107


The correlation between the lnW and DAV of the above distributions is .996. Though quite high, this is less than the .9995 correlation between lnW and DAV that we saw in Table 35 for high value K over N distributions. What is noteworthy is that the correlation between lnW and GAV for the K over N distributions in Table 63 is also quite high as .994, very little different than the .996 correlation between lnW and DAV for these distributions.

 

As the correlation of DAV with lnW went from .996 for the low value K over N distributions to .9995 for the high value K and N distributions back in Table 35, so we can assume reasonably from the closeness in the lnW correlations for DAV and G­AV of .996 and .994 respectively that for high value K and N distributions the correlation of GAV to lnW would also be in the range of .999 or near 100%. Thus we see that either diversity function, DAV or GAV, can replace Boltzmann’s S=kBlnW entropy from both having a high correlation to lnW. What will have us choose GAV over DAV starts with specifying these two average diversity functions by extension from Eqs61&62 as

 

64.)                             

 

65.)                           

 

In standard theory, via the equipartition theorem, temperature is a simple function of the average kinetic energy, μ=K/N, where K is total number of energy units and N the number of molecules. But a μ=K/N temperature specification must be seriously questioned from the perspective of the reality of how temperature is actually measured physically with a thermometer.

 

Let us understand the K energy units of a thermodynamic system of N gas molecules to be distributed over them with xi energy units, 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 on each molecule. This has 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 39 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 rather than DAV=K/φAV, 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 as dS=dQ/T, where S is entropy, Q is heat, dimensionally energy, and T is Kelvin temperature.

 

What is remarkable is that our neurophysiology detects the temperature of our surroundings in a way entirely the same as a thermometer, generalizing the energy that impinges on the skin’s surface as an average of molecular energies over space and, in the short term, over time.

 

The above analysis also tells us, we repeat, 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 this Eq64, 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 it.          

 

 

5. The Mathematics of Emotion

Description: illustration of two red dice Stock Photo - 13443929

We’ll use the notion of condensed representation developed in the entropy section to understand our operational emotions of desire, hope, anxiousness, disappointment, excitement, fear, dismay, security, depression and relief in a firm mathematical way as also further provides an analytical foundation for our visceral emotions of hunger, food taste, anger, cold, warmth, sex and love and the like.

 

In a dice game called Lucky Numbers we’ll use to develop the operational emotions, the lucky numbers rolled on a pair of dice are |4|, |7| and |10|. If you roll one of them you win V=$12. There are 36 ways a pair of dice can fall with 3 of those 36 ways resulting in a |4| with probability of 3/36=1/12; 6 ways out of 36 for a |7| with probability of 6/36=2/12; and 3 ways out of 36 for a |10| with probability of 3/36=1/12. Hence the probability, Z, of rolling a lucky number of a |4|, |7| or |10| is the sum of these probabilities as    

 

66.)                Z=1/12 +2/12 +1/12 =4/12=1/3

This calculates the probability of rolling a number other than a |4|, |7| or |10| lucky number as 

67.)                 U=1− Z=2/3

U is also understood as the improbability or uncertainty in rolling a |4|, |7| or |10|. The amount of money one can anticipate winning on average in this V=$12 prize game is

68.)                E=ZV=(1/3)$12=$4  

E is the expected value of the game, the average amount you win per game. If you play the dice game repeatedly you can expect to win V=$12 on average or one time in three for an average payoff of E=$4 per game played.

The E expected value is understandable as a condensed representation. Consider that you play the Lucky Numbers game twelve times with payoffs of ($12, 0, 0, 0, 0, $12, $12, 0, $12, 0, 0, 0). The average payoff per game has been arranged to be $4, that is, to be the E=$4 expected value.

This way of generating the E expected value as the average or condensed representation of observed experiences projected to future play is valuable because it is the way that the mind intuitively operates to predict future events in terms of similar events in the past condensed as their average value. The mind does this in many ways as in the way we develop expectations from the words we use via condensed representation. 

The word dog, for example, conjures up a picture of what to expect when one encounters a dog, which is through a pictorial averaging of all the dogs a person has ever come across including in books and movies. It 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.

With the Lucky Numbers game we take a shortcut in developing the E expected value not as a condensed representation of past experiences but from elementary probability theory. But the human mind’s most basic foundation of expectation as a condensed representation of past experience should be kept in mind when we are deriving emotion from the E expected value. We will get into condensed representation as the basis of expectation later after we first develop the emotions efficiently and clearly through the following firm mathematical analysis.

Eqs67&68 enable us to write the expected value, E, of Eq68 as

69.)                E=ZV=(1−U)V=V−UV 

 

The E expected value as E=V− UV has two components, V and – UV. The V term in E=V− UV is the amount of money one anticipates or desires or wishes to win. It is also a measure of the pleasure felt in the thought of getting V dollars, the intensity of that pleasure being proportional to V. If we raise the prize to V=$120, the pleasure in its anticipation is proportionately greater.

 

This V pleasure in anticipating a V dollar win is accompanied in E=V−UV by the −UV term in Eq69 that is a measure of the displeasure of anticipating failure to win the V dollars. It goes variously under the everyday name of anxiousness or anxiety or fear or concern or worry. And we’ll also give it a technical name of meaningful uncertainty, that is, uncertainty, U, made meaningful by association with V dollars in –UV, dollars or money being generally a meaningful or valuable item for all adults 

 

That this feeling of anxiety is unpleasant is indicated by the minus sign of –UV, the displeasure of it being greater the greater the U uncertainty in winning and the greater the V number of dollars one is uncertain about winning. In the roll of the |4|, |7| or |10| for V=$12 with uncertainty U=2/3, the displeasure of the –UV anxiety is measured in dollar terms as 

 

70.)           −UV= − (2/3)($12)= −$8

 

This –UV= −$8 is seen from Eq69 to reduce the pleasure in the V=$12 sized wish for the money to

 

70a.)        E=V−UV=$12−$8=$4 

 

The –UV anxiousness about winning is more unpleasant when the prize is larger as with one of V=$120.    

 

71.)        −UV= −(2/3)($120)= −$80

 

Also note that the −UV feeling of anxiousness is greater when the U uncertainty in winning is greater as when only a roll of   the |4| with probability of Z=1/12, and uncertainty of U=1− Z=11/12 is the lucky number that wins the V=$120 prize.

 

72.)         −UV= − (11/12)($120)= −$110

 

This appreciation of −UV understands E=ZV=V−UV as a reduction in one’s pleasurable desire to win V=$120 by the –UV anxiousness about winning, which also results in a Z fractional reduction of V in one’s overall E=ZV hopes or hope of getting the V=$12 prize.

 

The pure V wish to get the cash prize is, by itself, in isolation from the −UV uncertainty or improbability of getting the V dollars, wishful thinking, the V term in E=V−UV when the –UV term of realistic difficulty in getting the V prize is ignored being the measure of the pleasure felt in pure wishful thinking about getting the V dollar prize.

 

Young children’s expectations are dominated by desire for what they want, V in cash representation in Eq69, independent any worry or anxiety, the –UV term in E=V−UV in Eq69, because parents provide what children desire with minimal uncertainty felt by the child. This sense of expectation in children of E=V–UV without the –UV worry as E=V gradually develops to E=ZV=V−UV as the children grow up and become aware of the difficulty or uncertainty in getting what they wish for when they have to provide what they wish for themselves. That is, the perfectly reasonable wishful thinking of a child takes on sharp negative overtones when it persists into adulthood.

 

The other broad category of behavior that people do besides trying to get something of value is to avoid losing something of value. That category, which extrapolates even more broadly as avoiding bad things happening, is well illustrated with a dice game one is forced to play that exacts a v=$12 penalty (lower case v) if you don’t roll a |4|, |7| or |10| lucky number. The probability of incurring the penalty by failing to roll a |4|, |7| or |10|, that is, the uncertainty in avoiding the penalty, is U= (1− Z)=2/3. And the E expected value of paying the v=$12 penalty is  

73.)                E= −Uv= −(2/3)($12)= −$8

This is the average penalty you would pay if you were forced to play the game repeatedly. It tells us, for example, that if you play three of these penalty games, on average, you will escape the v=$12 penalty one time out of three by rolling the |4|, |7| or |10| and you will pay the v=$12 penalty two times out of three, $24 in total for an on average penalty per game of E= − $8. The U=1− Z uncertainty of Eq67 allows us to write E in Eq73 in an alternative way as   

74.)              E= −Uv = −(1–Z)v = −v + Zv

 

The − v term in Eq74 is the anticipation of incurring the entire v penalty, which we will call dread of the penalty for want of a better word. The displeasure in the dread of paying the v penalty is specified by the negative sign of − v with the intensity of its displeasure greater, the greater the v dollar penalty dreaded. Were the penalty raised to −v= − $120, the dread and its displeasure would be proportionately greater than that for the –v= −$12 penalty.

 

The −v dread in E= − v + Zv of Eq74 is reduced by the +Zv term in it as the (pleasant) hope one has that one will escape the penalty by rolling a |4|, |7| or |10|, the probability of which is Z=1/3. This Zv term is understandable emotionally as the sense of security one has that one will avoid the penalty, the greater the Z chance of escaping the penalty in +Zv and the greater the v penalty, the greater the sense of security when one is forced to play the penalty game that one will escape the penalty.

 

The Zv hope in E= − Uv = − v + Zv of avoiding the –v penalty reduces the displeasure of the − v dread of the penalty to bring about the overall –Uv fearful expectation of incurring the penalty. This − Uv fear of something unpleasant happening goes by a number of other names in everyday language including anxiety, worry, distress and concern. This plethora of common names for –Uv fear has us give it a technical name as we did −UV anxiety of meaningful uncertainty. That is, both –Uv fear and –UV anxiety are forms of meaningful uncertainty. Note for E= −Uv that the intensity of displeasure in the feeling of fear is greater the greater is the U probability of incurring the v penalty and the greater is the v penalty, as fits universal emotional experience.

 

The above development of fearful expectation, E=− Uv = − v + Zv, gives us functions for three more elementary emotions: the − v dread of incurring a v penalty; the Zv sense of security one feels in the possibility of escaping the penalty; and the probability tempered E= −Uv fear of incurring the penalty. These add to the V desire of getting a V prize, the –UV anxiousness about getting it and the Z probability tempered hopes of getting a prize we consider earlier to give a complete set of our anticipatory emotions.

 

We emphasize that −UV, ZV, V, −Uv, Zv and –v are the best denotations for our anticipatory emotions rather than the more familiar names for them for them of anxiety, hope, desire, fear, security, dread and so on. 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 everyday language to describe the mental states of ourselves and others. Words for externally observable things like “wallet” are clear in meaning because if any confusion in meaning arises, one can point to a wallet to make clear what is meant by the word. With emotions, however, as nobody feels the emotions of another person, the familiar words we use for the emotions have no referent one can point at to clarify its meaning.

 

The mathematical symbol-words of −UV, ZV, V, −Uv, Zv and –v for the above emotions, on the other hand, are clear in meaning because they have countable referents of money gained or lost as V and v and of probability, Z and U, as their components. And the fit of these well-defined mathematical words to emotional experience, pleasant and unpleasant, is universal. That is, all people would feel these −UV, ZV, V, −Uv, Zv and –v anticipatory feelings when playing the V prize and v penalty Lucky Number games. Hence quibbling over the “correct” names to call −UV, ZV, V, −Uv, Zv and –v or any of the other mathematical terms we will develop for the human emotions is not a valid criticism of this analysis.

 

Mathematical language is superior to everyday language for describing emotion not only in the unequivocal meaning of its symbol words, but also in the firm logical relationships of mathematics as seen in Euclidean Geometry and Newtonian Mechanics. This logic and clarity of mathematics in geometry and the physical sciences points up the value of putting the human sciences on a mathematical foundation. Indeed, this is entirely necessary given the inability of current psychology to provide any clear understanding of normal emotion and but poor explanations consequently for abnormal emotions. And that makes a scientific understanding of socioeconomic control as a major cause of unhappiness very difficult.

 

So far we have considered just anticipatory emotions, what is felt prior to rolling the Lucky Numbers dice to win money or avoid losing it. Next we will consider the emotions felt after the dice are thrown and the outcome of rolling the dice occurs. In the V prize game rolling a lucky number and winning V dollars produces a pleasant emotion we’ll call delight, an “up” feeling specified mathematically as R=V. The greater the V amount of dollars won, the greater the R=V delight. The R symbol is used to specify R=V delight in winning V dollars as a realized emotion, one that comes about from something that actually happens or is realized rather than from expecting something to happen.

 

In the v penalty Lucky Numbers game, the realized emotion felt when the penalty is incurred from failure to roll a lucky number is R= − v. This is the goto unpleasant feeling of sadness or most generally of depression, a “down” feeling that is more unpleasant the greater the v money loss. Note that depression here is not defined as a disease or mental illness but rather as an unpleasant emotion whose origin lies clearly in losing something of value. It is also possible in the V prize game to fail to win the money. In that case, as nothing is realized, no money changing hands, there is no realized emotion, which is specified by R=0. And it is possible in the v penalty game to not lose any money, which also has no realized emotion as specified by R=0.

 

This is not to say there are no emotional consequences from the R=0 failing to win the V prize or the R=0 escaping the v penalty. Specifically they constitute a third class called transition emotion, symbol, T, that is neither E expectation nor R realized emotion but the arithmetic difference between R and E.

 

75.)                  T = R−E  

     

This equation is called the Law of Emotion because it holds generally for E=ZV hopeful expectation and for E= −Uv fearful expectation and for all manner of realized outcomes of R=V, R= −v and R=0. With hopeful expectation of winning a V prize as E=ZV, when a lucky number is not rolled, the V prize not won and the realized emotion R=0, the T transition emotion is

 

76.)                  T = R −E = 0 −ZV = −ZV     

 

This T= − ZV emotion is the disappointment felt when one’s hopes of winning the V prize, E=ZV, are dashed or negated. 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 not won and the greater the Z probability the player felt he had to win it. In the dice game for the V=$12 prize won by rolling a |4|, |7| or |10| with probability Z=1/3, the intensity of the disappointment is

 

77.)                 T = −ZV = −(1/3)($12) = −$4

 

The T= −$4 cash value of the disappointment indicates that the intensity of the displeasure in it is equal in magnitude if not in all its nuances to losing $4. The T= − ZV disappointment over failing to win a larger, V=$120, prize, is greater as 

 

78.)                T= − ZV= − (1/3)($120)= − $40

 

Eqs77&78 fit with the universal emotional experience of disappointment being greater the more you hoped you’d get but didn’t. The T= − ZV disappointment is also great when the Z probability you felt of winning the V prize is great. Consider a 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

 

79.)                     E = ZV = (35/36)($120)= $116.67

 

And the disappointment from failure when the ZV hopes are dashed or negated to –ZV is also great as

 

79a.)                   T= −ZV = − (35/36)($120)= − $116.67

 

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 people feel much less disappointment when they have a very low expectation of success to begin with. As an example, consider the T= − ZV disappointment in a dice game where to win you must roll snake eyes, the |2|, as the only lucky number. With such a low probability of winning felt of Z=1/36, the disappointment is much less as  

 

80.)                   T= ZV= − (1/36)($120)= −$3.33

 

This amount of disappointment is much less than for the dice games of Eqs78&79a because of the low expectation of winning of E=ZV=(1/36)($120)=$3.33 to begin with. We see in the broader picture that though there is no realized emotion when one fails to win in a V prize game, R=0, there is still felt the T= − ZV transition emotion of disappointment.

 

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 Eq75, T=R−E, via U=1−Z,

 

81.)                T = R−E = V −ZV = (1− Z)V = UV

 

This T= UV transition emotion is the thrill or excitement of winning a V prize under uncertainty. It is a pleasant feeling as denoted by the positive sign of UV with its pleasure greater, the greater is the V size of the prize and the greater the U uncertainty of winning it felt beforehand. When one is absolutely sure of getting V dollars as in a weekly paycheck with no uncertainty, U=0, there is still the R=V delight in getting the money. But with uncertainty present, U>0, there is an additional thrill or excitement in winning the money as in winning the lottery or winning a jackpot in Las Vegas or winning V=$120 in the dice game by rolling a lucky number of |4|, |7| or |10|. In the latter case with an uncertainty of U=2/3 from Eq67, the intensity of the excitement in winning is from Eq81

 

82.)                T=UV=(2/3)($120)=$80    

 

That this additional pleasure of excitement in getting V dollars over and above R=V depends on prior U uncertainty is made clearer if we look at trying to win V=$120 by rolling the dice in a game where rolling only the |2| with probability Z=1/36 and uncertainty U=35/36 wins the prize. Here if you do win, as with winning in any chance game when the odds are very much against you, there’s that much more of a thrill or feeling of excitement in the win.       

83.)                T=UV=(35/36)($120)=$116.67

By comparison consider a game that awards V=$120 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 quite expect to win the money. While there is still the R=V=$120 delight in getting the money, there is much less thrill because like getting a paycheck, the player was almost completely sure of getting the money in this particular Z=35/36 dice game.

 

84.)                T=UV=(1/36)($120)=$3.33

This relationship between the uncertainty of getting something of value and the excitement or thrill felt when you do get it is clear in the thrill children feel in unwrapping their presents on Christmas morning. The children’s uncertainty about knowing 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 on top of the pleasure from the gift itself, that special thrill in opening the presents under the Christmas tree not being felt if the youngsters know ahead of time what’s in their wrapped packages and have no uncertainty about it.

It is also universal that winning a V=$120 prize is more thrilling than winning a V=$12 prize when the U uncertainty in winning is the same in both cases. We see the UV excitement in the V=$12, |4|, |7| or |10| lucky number game to be significantly less than for the V=$120 prize in Eq82 as

85.)                T=UV=(2/3)($12)=$8

We get a fuller picture of our emotional machinery by deriving the T=UV thrill of a win from the T=R−E Law of Emotion of Eq75 with the E=ZV expectation expressed from Eq69 as E=ZV=(1− U)V=V− UV.   

86.)            T = R− E =V−(V−UV) = − (−UV)=UV           

This derivation of T=UV as T= − (− UV)=UV sees the T=UV excitement as the negation or elimination of − UV 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 from the hero’s initial and/or continuously meaningfully uncertain situation, which the audience feels vicariously. When the hero’s meaningful uncertain situation is resolved by success towards the end of the movie, it vicariously brings about thrills and pleasurable excitement for the audience by negating or eliminating the anxiousness they felt about the hero’s situation. Though the emotions felt by the audience are vicarious, the essence of the dynamic is essentially the same as is spelled out above in Eq86. 

Now let’s consider the T transition emotions felt in the v penalty exacting game. With a fearful expectation of E= − Uv, when the v penalty is avoided by rolling the |4|, |7| or |10|, the realized emotion is R=0 and the T transition emotion from the Law of Emotion of Eq75 is

87.)            T = R−E = 0 − (−Uv) = Uv           

This T=Uv emotion is the relief gotten 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 the pleasure of relief greater, the greater is the v loss avoided and the greater the U improbability of avoiding the loss. The T=Uv relief felt when a |4|, |7| or |10| lucky number is tossed in the v=$120 penalty game is with U=2/3 from Eq66  

88.)                T=Uv=(2/3)($120)=$80

But if one plays a v=$120 penalty game where rolling only the |2| with uncertainty U=35/36 avoids the penalty, there is greater relief in rolling the |2| and avoiding the loss because you felt prior to the throw with U=35/36 that most likely you would lose. 

89.)                T=Uv=(35/36)($120)=$116.67

But if you play a v=$120 penalty game that avoids the penalty with any number |3| through |12| and an uncertainty of only U=1/36 of avoiding the penalty, there is much less sense of relief because you felt pretty sure you were going to avoid the penalty to begin with.

 

90.)                T=Uv=(1/36)($120)=$3.33

Note also that the larger the v penalty, the more relief there is in avoiding it as with a v=$1200 penalty, the relief in escaping it the |2| lucky number game with U=35/36 being that much greater than for the v=$120 penalty game of Eq88.

 

91.)               T=Uv=(35/36)($1200)=$1166.67

The universal fit of mathematically derived Uv relief to the actual emotional experience of felling relief is remarkable. Lastly we use the Law of Emotion of Eq75 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   

92.)                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 |4|, |7| and |10| lucky number v=$120 penalty game with Z=1/3 from Eq66 is

93.)                T= − Zv = − (1/3)($120)= − $40

But if you have a small Z probability of avoiding a v=$120 dollar loss as in the dice game with only rolling the |2| providing escape to probability, Z=1/36, there is little of this − Zv dismay when you fail because you had such low Zv hope of escape to begin with. 

94.)                T= − Zv = − (1/36)($120)= − $3.33

This low dismay from failure given low expectation is why many people develop 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 v=$120 penalty game where the numbers on the dice of |3| through |12| are the lucky numbers that avoid the v penalty to probability, Z=35/36. Then if you roll the |2|, the only losing number, and must pay the penalty, the intensity of the dismay when you lose is great because you did not expect to lose to begin with. 

95.)                T= − Zv = − (35/36)($120)= − $166.67

Great dismay from a high Z=35/36 probability felt of escaping the v penalty is felt as shock from a person’s surprise at failure when what was expected from the high Z=35/36 probability was success in avoiding the penalty.

In brief review we now list the primary emotions that people experience in goal directed behavior demonstrated with a dice game whose goals are getting money and avoiding losing it: ZV, V, −UV, −Uv, −v, +Zv, −ZV, −Zv, UV, Uv, R=V, R= −v. We differentiate between V and R=V with the former understood as the pleasant wish or desire for V dollars, an expectation emotion, and the latter as the pleasant emotion of actually getting V dollars; and similarly between –v and R= −v. Whatever everyday language names we want to assign to these emotions, they are a complete set of what we will call the operational emotions. They will be augmented to a complete set of all the human emotions after we later include the visceral emotions, pleasant and unpleasant, like hunger, food taste, cold, warmth, anger, glory, sex and love.  

For now, though, we want to explain the purpose of the T transition emotions of disappointment, excitement, relief and dismay in our emotional machinery. Recall that they derive from the T=R−E Law of Emotion and the E expected value function in it, which depends in a very direct way on the Z and U probabilities whether as E=ZV in the V prize game or E= −Uv in the v penalty game. In our analysis up to this point, the player’s sense of the values of the Z and U probabilities were understood to be calculated correctly from the mathematics of throwing dice. But that need not be the case. A player may suppose any probabilities for success and failure, which will affect his or her E expectations, be they hopes or fears, and in turn from the T=R−E Law of Emotion, the T transition emotions experienced upon success or failure. 

Let’s illustrate this with a Christian girl who makes a bet with her non-believing father-in-law that she will play the v=$120 penalty game with |4|, |7| and |10| as the lucky numbers three times and win it each time to avoid the penalty. If she succeeds he promises to go to church every Sunday for the rest of his life and if she fails she must pay him the penalties incurred. The daughter-in-law with God on her side for sure success supposes a probability of Z=1 for each roll instead of the actual Z=1/3 and a zero probability of failure, U=1−Z=0, instead of U=2/3 of Eq67. Her supposition of Z=1 and U=0 generate a fear of losing of

96.)          E= −Uv= −(0)$120=0

This total optimism is at variance with the correct fear of losing she should have of 

97.)                E= −Uv= −(2/3)$120= −$80

As luck would have it, the first time the daughter-in-law rolls she does get one of the lucky numbers and escapes the v=$120 penalty. This gives her no sense of T=Uv relief because her perfect faith told her she couldn’t lose. This fits mathematically with her Z=1, U=0, supposition of the probabilities involved. She doesn’t feel the T=Uv=$80 relief of Eq88 that derives from the correct Z=1/3, U=2/3, probabilities, but rather feels no relief as derives from her Z=1, U=0, supposition as

98.)                T=Uv=(0)$120=0

On the second roll, however, she fails to roll a lucky number and must pay the professor the v=$120 penalty. Her dismay as the −Zv in Eq92 is great. 

99.)                T= −Zv= −(1)$120= −$120   

Note again that this emotion of dismay felt by her depends on her supposition of Z=1 and U=0 probabilities rather than on the correct Z=1/3, U=2/3, value. Her faith in God is not broken by this outcome, however, for she assumes the Devil must have intervened in some way and that God will surely guide the dice in her favor on the third roll so she can minimize the penalty money she must pay to her now smiling father-in-law. 

On the third roll, the girl again misses a lucky number to get the on average outcome, which while not a surety is the most probable outcome. This ups the penalties she must pay to the professor by another v=$120 while generating another dose of the T= −$120 dismay of Eq99 in her. At this point her two heavy doses of T= −$120 dismay begin to emotionally question her faith in God, at least in His Divine power to overrule elementary probability theory. What she does not realize is that the T transition emotions she felt in her dice rolling are working on her mind subconsciously to alter her previous expectation based on the Z=1 and U=0 incorrect suppositions she was making about probability. This works on a formula that is a simple variation, as we shall show later, of the T=R−E Law of Emotion.

100.)              ENEW = EOLD + T        

The daughter-in-law’s original or old expectation was from Eq96, EOLD=0. The T transition emotion in the formula is the average of the T transition emotions felt, the T=Uv=0 relief felt once of Eq98 and the T= −Zv= −$120 dismay of Eq99 felt twice.

101.)              T= (0 −$120 −$120)/3= −$240/3= −$80

Now inserting into Eq100 from Eq96, EOLD=0 as her initial fear of losing and from Eq101, T= −$80 will generate her new fear of losing of 

102.)                 ENEW = EOLD + T= 0 −$80 = −$80

This is the correct expectation seen in Eq97 evaluated from the correct Z=1/3 and U=2/3 probability values that she should have had to begin with. This tells us that dismay from failure, T= −Zv, increases fearful expectation in subsequent play, E= –Uv. And from E= −Uv= −v+Zv of Eq74 we see that –Zv dismay from failure also decreases the Zv feeling of security in subsequent play.

 

Note that for the average T transition emotion to be T= −$80 in this example in a predictable way would have taken a much larger number of repeated rolls. This would have made the mathematics and the story significantly more tedious to tell, which is why we made the outcomes of the daughter-in-law’s three rolls artificially fit the average. 

 

That clarified, it should be obvious that the daughter-in-law is engaging in wishful thinking in basing her E= −Uv=0 expectation of paying the penalty on U=0, no uncertainty of losing given the divine intervention of God. Let’s explain this by reference to wishful thinking we have already considered in the V prize game where we made clear that it entails ignoring the realistic –UV meaningful uncertainty in the E=V−UV expectation. Now let’s write the E= –Uv fearful expectation in the v penalty game a little differently as

 

103.)              E= 0 −Uv.   

 

This stipulates 0 or no penalty as the wish or desire in this game, paying no penalty. Wishful thinking occurs in the v penalty game by thinking that will happen for sure as by ignoring the realistic –Uv uncertainty stipulated in elementary probability theory as the Christian girl did by supposing no uncertainty, U=0, which renders the fearful expectation in Eq38 as E=0.   

To demonstrate the generality of the ENEW = EOLD +T formula of Eq100 let’s turn now to another anecdote, this one about the husband of the Christian girl, the professor’s son. Junior is a total pessimist in situations that in any way involve risk or chance. Delusional in the opposite way of his born again wife, Junior turned out to be a psychological eunuch who submits to even unfair authority obediently to please his wife. Personality issues aside, when Junior plays the dice game that awards a prize of V=$120 for rolling the |4|, |7| or |10| lucky number, he fearfully supposes the probability of winning to be less than the realistic Z=1/3 probability that generates an expectation of

104.)              E=ZV=(1/3)$120=$40

Specifically he supposes that the probability of winning is only Z=1/12, uncertainty U=1−Z=11/12, which generates a hopeful expectation in him of only 

105.)              E=ZV=(1/12)$120=$10

Now we will have Junior play twelve of these games. From the realistic probability of winning of Z=1/3 we will take it that he succeeds in four of the twelve games, winning the V prize, and fails to win eight times. Assuming he retains his deflated probability suppositions for the entire 12 games, the excitement he feels in each of the four times he wins is from T=UV of Eq16 with his supposition of uncertainty of U=11/12,

106.)              T=UV=(11/12($120)=$110

And the disappointment he experiences each of the eight times he doesn’t win is from T= −ZV of Eq11 with his supposition of Z=1/12,             

107.)              T= −ZV= −(1/12)$120= −$10

His average T transition emotion per game for the twelve games is, thus, 

108.)              T= [4($110) −8($10)]/12=$360/12=$30

His average transition emotion is T=$30 of excitement. After twelve games and these emotional outcomes Junior comes to feel that his chances of winning in a game are greater than he initially supposed because of the predominance of the T=UV=$110 excitements over the T= −$10 disappointments. Specifically his mind operates according to Eq100 to increase his E=ZV expectation in subsequent play via EOLD=$10 from Eq40 and T=$30 in Eq108 to 

109.)              ENEW = EOLD + T= $10 + $30 = $40

We see that Eq109 generates the correct E=$40 expectation of Eq104 from trial and error experience. Generally speaking predominant T=UV excitement increases E=ZV hopes and from E=V−UV decreases –UV anxiousness about winning. To see the general pattern, recall that predominant T= –Zv dismay from failure increased one’s E= −Uv fear of losing in the penalty game and from E= −v+Zv decreased one’s Zv security. This tells us from Eq105 without our having to going through mathematical examples of it that predominant T=Uv relief from success in the v penalty game decreases one’s E= −Uv fear and increases one’s Zv security in subsequent plays; and that predominant T= −ZV disappointment from failure in the V prize game decreases one’s E=ZV hopes and increases one’s –UV anxiousness.

This makes clear the function of the T transition emotions, namely to bring one’s E expectations realistically in line with actual experience. This seems unnecessary in these dice games where simple mathematical calculations give immediate correct knowledge of the Z and U probabilities without the need for prior experience. But man’s mind did not evolve to play dice games but rather to survive, reproduce and compete in an often uncertain environment where probabilities of success in such activities were centrally important for success in life. Under those circumstances a priori exact values for the probabilities of success are seldom known and can only be supposed and shaped by actual trial and error experience with cultural transmission of the probability values from other individual’s experiences also taken into account.              

The importance of having realistic expectations that reflect experience lies in man making decisions on what to do on the basis of his expectations. If a person has the opportunity to play a prize awarding dice game for V=$120 either with |4|, |7| and |10| as the lucky numbers (Z=1/3 and E=$40) or with |4| and |7| as the lucky numbers, (Z=1/4 and E=$30), he or she chooses the E=$40 game because in its having a higher average payoff, there is greater pleasure in its expectation. Or similarly if a person must choose between playing one of two v penalty games, one with an expectation of E= −$60 and the other E= −$80, he chooses the former in this Hobson’s choice as “the lesser of two evils” because in incurring a lesser penalty its expectation is less unpleasant. Clearly, having unrealistic expectations that don’t fit actual Z and U probability values make one choose badly with consequences of less pleasure and more displeasure than could have been had.

Now we have given a thumb nail sketch of how the mind works in terms of three classes of emotions, E expectations, R realized emotions and T transition emotions, and how they relate to each other through the formulas of Eqs75&100. Its simplicity, mathematical clarity and generality strongly suggest that is truly how the mind works. Calling it a “theory of the mind” as implies the possibility of competing theories is as misleading as calling the Law of Gravity a theory of how our solar system works rather than a clear and correct description of it. Whatever may seem missing in the larger picture of how the mind works will be filled in.

We also want to make clear that this mathematical explication of the emotions is effectively empirical in being universal. Our specification of disappointment as the −ZV negation or dashing of ZV hopes, for example, is universal in that all human beings feel disappointment when they fail to achieve a desired goal. Such universal agreement is the fundamental factor in empirical validation. When ten researchers all read the same data off a laboratory instrument, that data is taken to be empirically valid because all ten agree on what they see. This criterion for empirical validity of universal agreement extends to the emotions of the dice game laid out as what all people would feel if they played it.

 

6. The Law of Supply and Demand


Though this is somewhat of a veering off from our main line of thought, as the Law of Supply and Demand is the foundation of all free market economics denied by nobody sane, deriving it from the Law of Emotion proves the controversial conclusions of this analysis.  We begin our derivation with first explaining the emotions people feel from partial success. To do that, we alter our dice game to one where you must roll a lucky number of |4|, |7| or |10| not once but three times to win the prize, one of V=$2700. These three rolls may be with three pair of dice rolled simultaneously or with one pair of dice tossed three times in succession. As the probability of rolling a lucky number in any one of the three pairs or three rolls is from Eq1, Z=1/3, so the probability of rolling a lucky number on the 1st pair of dice or the 1st roll is Z1=Z=1/3; on the 2nd pair of dice or roll, Z2=Z=1/3; and on the 3rd pair of dice or roll, Z3=Z=1/3.

 

110.)             Z1=Z2=Z3=Z=1/3

 

And the uncertainties in each toss are

 

110a.)                        U1=U2=U3=(1−Z)=2/3

 

Hence the probability of rolling a lucky number of |4|, |7| or |10| on all three rolls is the product of the Z1, Z2 and Z3 probabilities, which is given the symbol, z, (lower case z).           

 

111.)           z = Z1Z2Z3 = Z3 =(1/3)3 = 1/27


And the improbability or uncertainty of making the triple roll successfully is

 

112.)              u=1–z = 26/27

 

The expected value of this game as a measure of the player’s hopes of winning the V=$2700 is  

 

113.)              E = zV =V−uv=Z1Z2Z3V = (1/27)($2700) = $100

 

The displeasure of disappointment from failure to make the triplet roll is from the T=R−E Law of Emotion of Eq75 with R=0

 

114.)              T=R−E = 0−zV= −zV= −(1/27)($2700)= −$100  

 

And the pleasure of the excitement or thrill in making the triplet roll with R=V=$2700 is

 

115.)              T=R−E = V−zV=(1−z)V= uV= −(−uV)=(26/27)($2700)=$2600  

 

Next we derive the emotion felt from rolling a lucky number on a 1st throw of three sequential throws. After a 1st toss that rolls a lucky number, the probability of winning the V=$2700 prize by tossing lucky numbers on the next two rolls is

 

116.)                Z2Z3 =(1/3)(1/3) = 1/9    

 

And the hopeful expectation of making the triple roll after a lucky number is rolled on the 1st toss is, as increased from E=Z1Z2Z3=$100         

 

117.)               E1 = Z2Z3V = (1/9)($2700) = $300        

 

Next we want to ask what is realized when the 1st toss is successful. It is not R=V=$2700, for the V prize is not awarded for just getting the first lucky number. And it is not R=0, what is realized when the player has failed to make the triplet roll and win the V=$2700 prize. Rather what is realized when the 1st roll is of a lucky number is the E1=$300 increased expectation in Eq117. This understanding of the E1=$300 expectation as what is realized has us specify E1 understood as a realization in terms of the R symbol as

 

118.)               E1=R1=Z2Z3V = $300      

 

Now we use the Law of Emotion of T= R−E, of Eq75 to obtain the T transition emotion that arises from a successful 1st toss. This understands the T term in T=R−E as T1; the R term in it as R1=Z2Z3V from Eq118; and the E term in it as the expectation had prior to the 1st toss being made, E=Z1Z2Z3V of Eq113. And with U1=(1−Z1) from Eq110a we obtain T1 as   

 

119.)             T1 = R1–E = E1– E= Z2Z3V –Z1Z2Z3V = (1−Z1)Z2Z3V =U1Z2Z3V =(2/3)(1/3)(1/3)($2700) =$200

 

Now we ask what kind of emotion this T1=U1Z2Z3V transition emotion is. We answer that question by noting that the T=uV excitement of Eq115 from making the triplet toss and winning the V=$2700 prize can be written, given R=V, as

 

120.)               T=uV=uR          

 

And we see that we can write Z2Z3V=R1=E1 from Eq103 in the T1=U1Z2Z3V transition emotion of partial success in Eq119 as  

 

121.)               T1 =E1−E=U1Z2Z3V =U1E1=U1R1                  

 

The parallel in form of T1=U1R1 to the T=uR excitement of Eq120 identifies T1 as excitement, the excitement felt in rolling the 1st lucky number, excitement that is felt even though no money is awarded for just rolling the 1st lucky number. Note that the intensity of this partial success excitement of T1=$200 of Eq119 is much less than the T=$2600 excitement of Eq50 that accrues from making the triplet roll and getting the V=$2700 prize.

 

The above development of excitement from partial success from the T=R−E Law of Emotion is borne out from observation of situations that go beyond the dice game. Excitement from partial success, indeed, is routinely observed on TV game shows like The Price is Right where a contestant is seen to get visibly excited about entry into the Showcase Showdown at the end of the show, which offers a large prize, by getting the highest number on the spin-off wheel first, which offers no prize in itself. This and other observed examples of the partial success excitement we just derived from the Law of Emotion is a form of empirical if not perfectly measurable empirical validation of The Law of Emotion.    

 

We further validate the Law of Emotion by deriving from it the excitement felt in rolling the 2nd lucky number in the triplet roll once the 1st lucky number has been rolled. We saw that what is realized from getting the 1st lucky number is an increase in the expectation of winning the R=V prize from E=zV=$100 in Eq113 to E1=Z2Z3V=$300 in Eq118. What is realized from rolling the 2nd lucky number after the 1st is a greater expectation yet of making the full triplet roll and winning the V=$2700 prize,

 

122.)        R2= E2 =Z3V=(1/3)($2700)=$900

The transition emotion that comes from rolling 2nd lucky number after having gotten the 1st is specified as T2 and from the Law of Emotion, T=R−E, with T as T2, R as R2=Z3V in the above and E as E1=Z2Z3V in Eq118, the expectation prior to the 2nd lucky number being rolled, is       

123.)       T2 = R2−E1 = E2−E1=Z3V− Z2Z3V =(1−Z2)Z3V = U2Z3V = (2/3)(1/3)($2700) = $600

Expressing T2 = U2Z3V via Z3V=R2 of Eq57 as T2=U2R2 makes it clear from its parallel form to the excitement of T=uR of Eq120 that T2=U2R2 is the excitement felt when the 2nd lucky number is guessed after the 1st lucky number has been rolled. 

And we can also use the Law of Emotion, T=R−E, of Eq75 to derive the excitement felt in getting the 3rd lucky number after getting the first two to win the V=$2700 prize. What is realized in that case is finally the V prize, R=V. Given the expectation that precedes getting the 3rd lucky number of E2=Z3V from Eq122, the Law of Emotion, T=R−E, obtains a T3 transition emotion of  

124.)      T3 = R−E2 = V –Z3V = (1−Z3)V = U3V = (2/3)($2700) = $1800

Expressing T3 = U3V from R=V as T3=U3R and its parallel form to T=uR excitement of Eq120 identifies T3 = U3R as the excitement of rolling 3nd lucky number after the first two are rolled to obtain the V=$2700 prize. Note that the intensity of the T3=$1800 excitement from rolling the 3rd lucky number and getting the V=$2700 prize is significantly more pleasurable than the T1=$200 and T2=$600 excitements for the antecedent partial successes.

 

Such significantly greater excitement in actually winning the prize than from achieving prefatory partial successes is what is observed in game shows like “The Price is Right” where actually winning the Showcase Showdown has the winner jumping up and down and running around screaming showing much more excitement than the excitement had from the prefatory partial success of getting into the Showcase Showdown by getting the highest number on the spinning wheel. Again this fit of observed excitement in the approximate relative amounts suggested by the above derivations from the Law of Emotion constitutes an empirical if not perfectly measurable empirical validation of the Law of Emotion.      

 

Also note that the Law of Emotion, T=R−E, of Eq75 is further validated from the three partial excitements, T1, T2 and T3 of Eqs119,123&124 summing to the T=uV=$2600 excitement of Eq115 gotten from making the triplet roll in one fell swoop as you might from throwing three pair of dice simultaneously.      

 

125.)              T1 + T2 + T3 = $200 + $600 + $1800 = $2600 = T = uV             

 

It is also instructive to calculate what happens when you roll the first two lucky numbers but then miss on the 3rd roll and fail to get the V=$2700 prize, R=0. To evaluate the T3 transition emotion that arises from that we simply use the T3=R−E2 form of the Law of Emotion in Eq124 that applies after the first two lucky numbers are gotten, but with the R realized emotion as R=0 from failure to obtain the V=$2700 prize. 

 

126.)            T3 = R−E2 = 0 – Z3V = – Z3V = −(1/3)($2700)= −$900

 

This T­3 = −Z3V= −$900 is the measure of disappointment felt in failing to make the triplet roll after getting the first two lucky numbers and experiencing the prefatory partial success excitements in doing so. Note that this T3= −Z3V= −$900 disappointment is a significantly greater disappointment than the T=−zV=−$100 disappointment of Eq114 that comes from failure to roll the lucky numbers in one fell swoop.  

 

Note that the −$800 (negative) increase in the T3= −$900 disappointment relative to the T= −$100 disappointment felt without partial success is equal to T1+T2=$200+$600=$800 sum of the two partial success excitements of Eqs119&124 gotten from rolling the first lucky numbers before failing in the 3rd roll.  This understands the additionally unpleasant −$800 disappointment from failure in the 3rd roll rescinding or negating the prefatory $800 pleasant excitements that were followed by ultimate failure. This fits universal emotional experience of an increased let down or disappointment when initial partial success is not followed by ultimate success in achieving a goal as the letdown disappointment gotten when one counts their chickens before they hatch and they fail to hatch.   

The sequential scenarios that end in success in Eq125 and in ultimate failure in Eq126 universally fit people’s emotional experience and as such are a convincing validation of the Law of Emotion, T=R−E, of Eq75. The linear sums and differences of the transition emotions in these two instances also importantly show that our emotions reinforce each other positively and negatively in a linear fashion via simple addition and subtraction of the emotion intensity values.  

One can do the same analysis for a v penalty game. Consider a dice game one is forced to play that exacts a penalty of v=$2700 unless the player rolls three lucky numbers, a lucky number being a |4|, |7| or |10|, whether simultaneously with three pair of dice or sequentially on one pair of dice. In parallel to the E expectation of Eq73 with u=26/27 in Eq112 as the improbability of rolling the three lucky numbers, the fearful expectation of incurring the v=$2700 penalty is

127.)             E= −uv= −(1−Z1Z2Z3)v= −(26/27)($2700)= −$2600 

 

The Law of Emotion, T=R−E, from Eq75 generates a uv emotion of relief in avoiding the v penalty, R=0, when one successfully rolls the lucky numbers on three pair of dice simultaneously as   

 

128.)           T=R−E=0−(−uv)=uv=$2600

 

With this game played with three sequential rolls of the dice, the increased expectation of avoiding the v=$2700 penalty after rolling a lucky number on the 1st toss of the dice, E­1, understood as what is realized from the toss, R1, with the improbability of escaping the penalty then as 1−Z2Z3, is    

 

129.)              E1=R1= −(1−Z2Z3)v= −(1−(1/9))$2700= −(8/9)($2700)= −$2400       

 

Hence the transition emotion, T1, is via the Law of Emotion, T=R−E, expressed as T1=R1−E, is 

 

130.)              T1=R1−E= E1−E=−(1−Z2Z3)v−[−(1−Z1Z2Z3)]=(1−Z1)Z2Z3v=U1Z2Z3v=$200

 

T1=U1Z2Z3v is understood in parallel to the partial excitement of U1Z2Z3V of Eq119 as the feeling of partial relief gotten from rolling the 1st lucky number. The rest of the analysis for the triplet v penalty perfectly parallels that for the triplet V prize game, except that the partial emotions felt are those of relief in escaping a money loss rather than excitement in achieving a money gain.

 

The fit of the analysis based on the Law of Emotion to universal emotional experience validates it and the underlying Lucky Numbers mathematics. Further validating them next is the Law of Emotion deriving the universally accepted Law of Supply and Demand.    

 

The Law of Supply and Demand of Economics 101 states that the price of a commodity in a free market economy is an increasing function of the demand for it and a decreasing function of the availability or supply of the commodity. An alternative equivalent expression of it determines the price as an increasing function of the demand for and the scarcity of the commodity, the latter as the inverse of the commodity’s supply or availability.

 

Now let’s consider the triplet lucky number V=$2700 prize game with the 1st lucky number in the triplet sequence as a commodity that can be purchased. This assumes, of course, that some agent who runs the game and pays off the prize money exists to sell such a commodity to the player. What is the fair price of the 1st lucky number, that is, of the pair of dice being placed on the table for the player with a |4|, |7| or |10| showing on it that counts in getting the V=$2700 prize?

 

As this changes the probability of winning the V=$2700 from z=Z1Z­2Z3=1/27 in Eq111 to Z2Z3=1/9 in Eq116, it is certainly a valuable commodity for the player, but what is the fair price of it? It is an amount of money that maintains the E=$100 average payoff in Eq106 of the game played when all three of the lucky numbers must be gotten by random throws of the dice. 

 

Once the 1st lucky number is obtained by purchase from the agent, the average payoff for the player increases from E=$100 of Eq113 to E1=$300 of Eq118. Hence the fair price for the 1st lucky number, W1, must be such that its subtraction from the player’s improved E1=$300 average payoff by purchase must be equal to the original E=$100 average payoff.    

 

131.)                E1−W1= E

 

Solving for W1 obtains the fair price as

 

132.)               W1 = E1−E

 

This W1 fair price is shown to be a function of variables we have already encountered from the algebraic manipulation of E1−E done back in Eqs119&121 as   

 

133.)                W1 = E1−E = Z2Z3V – zV = U1Z2Z3V = T1 = U1E1 =$200

 

The W1=$200 price for the 1st lucky number that increases the average payoff to E1=$300 is equal to the original average payoff of E=$100, which is what understands W1 as its fair price. From the perspective of economic optimization the player as buyer would want to pay as little as possible for it and the agent as seller would want to charge as much as possible for it. But W1=$200 is its fair value or fair price in maintaining the original average payoff or expected value of E=$100.

 

The W1=U1E1 fair price formula of Eq133 is a primitive form of the Law of Supply and Demand in its specifying it in terms of the emotions people feel that control the price they’ll pay for a commodity. W1=U1E1 is the Law of Supply and Demand for price understood as an increasing function of scarcity and demand with the scarcity of the 1st lucky number as the uncertainty in rolling it on the dice, U1=2/3, and the demand for the 1st lucky number in terms of its value to the player as the E1=Z2Z3V=$300 average payoff it provides, the greater the value of a commodity, the greater the demand for it being an intuitively reasonable assumption. This derivation from the Law of Emotion of the Law of Supply and Demand, a firm empirical law of economics universally accepted as correct, is a powerful validation of the Law of Emotion and the mathematics of Lucky Numbers on which it is based. 

 

There are a number of fascinating nuances in this understanding. Note the equivalence in Eq133 of the W1=$200 fair price for the 1st lucky number and the T1=W1=$200 pleasurable excitement in rolling the 1st lucky number on the dice. This equivalence of T1 excitement and W1 price tells us that the price paid for a commodity is a measure of the pleasurable excitement the commodity generates for the buyer. This fits economic reality quite well as seen from TV commercials for automobiles and travel ads and foods that hawk them by depicting them as exciting.

 

The value of the 1st lucky number can be calculated not just in terms of the W1 money one would spend for it but also in terms of the time spent in acquiring the money needed to purchase it. That is, W1 is understood as a measure of the amount of time spent to get the 1st lucky number when time is taken to be directly proportional to money, as is certainly the case for most people in the dollars per hour wage or per month salary they get their money from.

This extends the W1=U1E1=T1 Law of Supply and Demand to showing that people spend their time to obtain commodities that pleasurably excite them, whether as the time spent working to get the money to be spent on the commodity or as time spent directly to get the commodity like time spent growing a pleasant tasting food like strawberries in one’s backyard.  

We can also derive a parallel primitive Law of Supply and Demand from the v penalty game requiring the toss of three lucky numbers. The W1 fair price of the 1st lucky number is again W1=E1−E, but with E1−E from Eq130 as  

134.)                W1 = E1−E = U1Z2Z3v = T1 = $200

This form of the primitive Law of Supply and demand tells us that people also spend their money for commodities that provide T1=U1Z2Z3v=W1 relief in addition to commodities that provide T1=U1Z2Z3V=W1 excitement as seen in Eq119. The two forms of the Law of Supply and Demand of Eqs133&134 provide a strong empirical validation of the Law of Emotion of Eq75 that derived them from the observed fact that people do spend their money and time to get things that provide relief and excitement as is readily seen in the complete spectrum of TV ads, all of whose products are pitched in ads as providing either relief, as with antacids and other medicine and insurance, or excitement, as with exciting cars, foods and vacations.  

Next we want to express the primitive Laws of Supply and Demand we see in Eqs133&134 as simply as possible. In both we note the equivalence of the W1 fair price with T1 partial success excitement or relief. This implies that the simplest forms of T excitement and relief in Eqs115,128,81&87 should also be a measure of the fair price, W, of what is achieved that is generating this excitement and relief. Hence we write from Eq115

135.)              W=T=uV= −(−uV)

This specifies W as the price of all three lucky numbers needed to win a V prize. And we write from Eq128

136.)              W=T=uv= −(−uv)

This specifies W as the price of all three lucky numbers needed to avoid a v penalty. And we write from Eq81

137.)              W=T=UV= −(−UV)

This specifies W as the price of one lucky number needed to win the V prize. And we write from Eq87

138.)              W=T=Uv= −(−Uv)

This specifies W as the price of one lucky number needed to avoid the v penalty.

Now while we have super-simplified the pricing Law of Supply and Demand in form, the intuitive meaning of it seems blurred for what is the fair price of a commodity used to avoid a v penalty than perhaps as intuition suggests the cost of the penalty. Regardless of this objection reasonably raised, these simple form are instrumental to deriving our visceral emotions of hunger, anger, pain, sex and love in an upcoming section. So we will now demonstrate that they are correct functions for fair price on the basis of the earlier argument that the W fair price of a lucky number is equal to the increase in average payoff generated by getting that lucky number.

We’ll show that with the simplest of Eqs135-138, namely Eq135, generating a V=$120 prize from the rolling of one lucky number. From E=ZV with Z=1/3 the average payoff is

139.)              E=ZV=(1/3)$120=$40

We also see from Eq82 that the excitement gotten is

82.)                T=UV=$80

This from Eq135 tells us that the fair price for the lucky number is W=T=$80. If we pay this each time for three games the total price paid is $240. This has us win $120 each game for a total of $360 for the tree games. The net winnings are thus $360−$240=$120, which is what is won on average in three games if the game is played strictly from the throw of the dice with no lucky numbers purchased. Hence W=T=$80 is, indeed, the fair price of the lucky number and W=T=UV is a most simple form of the law of supply and demand with U as the uncertainty or scarcity of the lucky number and V its value as a measure of the demand for it. This should also make clear that without our having to go through the details of it, all four of Eqs135-138 are valid forms of the Law of Supply and Demand. We will use these simple forms shortly to develop the visceral emotions of hunger, anger, pain, sex and love.      

More immediately Eqs135-138 tell us in a clear way that people not only spend money and time to attain the pleasures of relief and excitement specified as W=T=UV, W=T=Uv, W=T=uV and W=T=uv but also in order to negate or eliminate the antecedent displeasures of fear and anxiousness seen in Eqs135-138 as W=T= −(−UV), W=T= −(−Uv), W=T= −(−uV) and W=T=−(−uv).

 

This has us revise and expand our generalization of a few paragraphs back now to people spending their money and time and being motivated not just on the pursuit of the pleasures of excitement and relief but also by the avoidance of the displeasures of anxiousness and fear. Understanding behavior to be motivated by the pursuit of pleasure and the avoidance of displeasure is the essence of hedonism. It should be made clear that this sense of hedonism is not an encouragement for people to seek pleasure and avoid displeasure, but rather a conclusion drawn from the foregoing mathematical analysis that people just do behave so as to achieve pleasure and avoid displeasure as the essence of human neurobiology. To generalize hedonism you need, of course, to also take into consideration the visceral emotions we have that motivate our behavior like hunger, the pleasure of eating, feeling cold and the pleasure of warmth, pain and relief from it, sex and love and the displeasure of their frustrations and failures. That last topic will be the subject of our next section. 

 

7. Mixed Emotions and Behavioral Selection

Our expectations determine our behavioral selections, what we decide to do. To show how, let’s expand the lucky number game in two ways. In the first, we will have the roll of a lucky number of |4|, |7| or |10| give a prize of V=$240 and the failure to roll a lucky number a penalty of v=$60. The expected value in this case is a combination of the E=ZV hopeful expectation of Eq4 and the E= −Uv fearful expectation of Eq73.  

140.)              E = ZV – Uv

For the above game, the amount of money one can expect to win on average, the expected value of the game, E, is  

141.)              E1 = Z1V – U1v = (1/3)$240 – (2/3)$60 =$80 − $40 = $40

We use the subscript, 1, with the variables Z, U and E because this is Game #1 used to illustrate behavioral selection. One can also play a Game #2 whose lucky numbers are |3|, |6|, |11| and |12|. Their probabilities of being roiled are 2/36, 5/36, 2/36 and 1/36, which sum to the probability of rolling a lucky number in Game #2 of

142.)                  Z2 = 2/36 + 5/36 + 2/36 + 1/36 = 9/36 = 1/4

And the improbability or uncertainty of rolling one of the |3|, |6|, |11| and |12| lucky numbers in Game #2 is

143.)                 U2 = 1 – Z2 = 3/4

With a prize of V=$240 for a successful roll and a penalty for failure of v=$60, the expected value or average payoff for Game #2 is

144.)              E2 = Z2V – U2v = (1/4)$240 – (3/4)$60 =$60 − $45 = $15

Now to best develop an understanding of behavioral selection let us consider competitive play between two people. Player #1 is given Game #1 to play with lucky numbers, |4|, |7| and |10|, and Player #2 is made to play Game #2 with lucky numbers, |3|, |6|, |11| and |12|. Each player is paid the V=$240 prize by the other when he rolls a lucky number. And each player pays the penalty of v=$60 when he fails to roll a lucky number to the other player. The two take turns rolling the dice with every pair of rolls producing on average a win for Player #1 that is the difference in the expected values of Eq141 and Eq144 of 

145.)                E1 – E2 = (Z1V – U1v) – (Z2V – U2v) = $40 − $15 = $25

And the outcome for Player #2 after every pair of rolls is

146.)              E2 – E1 = (Z2V – U2v) –  (Z1V – U1v) = $15−$40  = −$25

That is, Player #2 loses $25 in every pair of rolls in this competition. Now we assigned these two games to the two players. What if each had a choice of games to play? To emphasize which game selection would be optimal for either player, let’s go back to the games as they were assigned and give Player #1 a bankroll of $100 to play with and Player #2 a bankroll of $900 with an added rule to this game that the first player to wipe out the other’s bankroll wins the competition. If the average wins and losses hold true Player #1 player in consideration of winning the expected value of $25 in every pair of rolls will be the winner of this competition as made clear in the graph below of average outcomes.

Figure 147. Two Player Lucky Number Competition


After 36 pairs of rolls with average outcomes Player #2 in blue goes broke and Player #1 in red wins the competition. This might be called competitive selection in the sense that the parameters of the game select Player #1 as the winner on the basis of the positive sign of the E1 –E2=$25 expected value difference in Eq145.

And another kind of selection is also illustrated here, behavioral selection or intelligent selection. We mandated Player #2 playing Game #2 in order to show which game was superior. But if Player #2 had a choice between the two games, he would obviously choose to play Game #1 because of its greater expected value or average return. This behavioral selection can also be thought to arise because of the greater pleasure it gives in expectation and/or as is functionally and emotionally related because playing Game #2 resulted in a loss, on average in every pair of rolls and ultimately in Player #2 having his bankroll wiped out, and in feelings of displeasure from loss that we showed earlier.

The emotional or hedonistic basis of behavioral selection is obvious. We do what is pleasant and avoid doing what is unpleasant, generally selecting a more pleasant option over a less pleasant as made clear above and select a less unpleasant penalty game over a more unpleasant penalty when we must choose one of them, as we will make clear in with the following example of such a Hobson’s choice illustrated with the two Lucky Numbers games of Game #1 and Game #2 but with the v in both for failure raised to v=$100. This example considers only one individual who must play either of these two v=$100 penalty modified Lucky Number games. The expectation aroused for Game #1 where the lucky numbers are |4|, |7| and |10| with probability of Z=1/3 and the penalty is raised to v=$150 is a variation of Eq141 as  

148.)              E1 = Z1V – U1v = (1/3)$240 – (2/3)$180 =$80 − $120 = −$40

And in similar fashion, that for the penalty modified Game #2 is as an altered Eq144

149.)              E2 = Z2V – U2v = (1/4)$240 – (3/4)$180 =$60 − $135 = ‑$75

Now the individual will choose Game #1 on the basis of its lower cost and hedonistically or emotionally for a number of interrelated reasons. One the one hand it is because there is less displeasure in the fearful expectation of U1v=−$120 of Game #1 in Eq148 than in the U2v=−$135 of Game #2 in Eq149. There is specifically a difference of

150.)                U1v−U2v =−$120 – (−$135)= +$15

This is the origin of the positive emotion for choosing the lesser of two evils, why that selection operation feels positive or pleasant, which is the neurobiological instrument for getting one to select to do something that is itself a penalty or loss for you. We can also see that there is more positive expectation in Game #1

151.)               Z1V – Z2V = $80 − $60 =+$20

The combination of the two is just E1 of Eq148 minus E2 of Eq149, this E1−E2 difference, though, differing from its arrangement in Eq145 by showing the E1 E2 expectation to be a compound function of combined relative pleasure and displeasure as

152.)               E1 – E2 = (Z1V – U1v) – (Z2V – U2v) = (Z1V – Z2V) – (U1v – U2v)

The first E1 E2 expression was developed in Eq145 as the difference in expected value, quite impossible to argue with, and the second entirely equivalent expression represents what people actually feel in comparing the relative pleasure and displeasure content of competing possible behaviors for selection to be executed. The equivalence of the two expressions shows the mind to work in a remarkably ordered way in three basic modes: choose greater pleasure over less; choose less displeasure over more; and always choose pleasure over displeasure. This is in effect a mathematical definition of hedonism, the basic mechanism that determines the world’s behavior. To understand war, the danger of impending nuclear war and how and why the elimination of all weapons from the earth for people is the only remedy for it, that basic understanding of what makes us tick - the carrot and the stick - must be understood and accepted, mathematically and intuitively.  

There are two broad variations of the competition between relative pleasures and displeasures that should also be mentioned. One of them is sacrifice where displeasure the displeasure of some form of penalty, the general nature of which we’ll consider thoroughly in the next section, is suffered in the present for the pleasure of ultimate success and its reward expected in the future. And the other is coercive restriction where pleasure is forgone in the present because of fearful expectation of a consequent penalty be it a punch, a stay in prison or deprivation of survival needs like housing via lack of income from being fired from one’s job. The equations that explain this are grade school simple and readily extracted from Eqs140152.

To keep the introduction of this section’s material simple, we kept the values of the V prizes and v penalties of games compared equal. The more general case is when any game or situation has rewards specific to it and also with any associated penalties. This generalizes Eq152 to

153.)               E1 – E2 = (Z1V1 – U1v1) – (Z2V2 – U2v2) = (Z1V1 – Z2V2) – (U1v1 – U2v2)  

This leads readily to understanding why people fail in many cases. And that’s because they select doing something on the basis of E1 E2 being positive from their suppositions about the value of the variables in Eq152 they may be in error from inexperience or from obtaining bad information from others, intentionally disingenuous or unintentionally in error.  But that gets way ahead of the time and we must wait to discuss the darker aspects of man’s emotional nature until we well lay out well its broadest general principles.    

 

8. Survival Emotions

Many of our most basic emotions are associated with surviving or staying alive. We derive the pleasant and unpleasant emotions that drive survival behavior from the primitive Law of Supply and Demand, specifically of the form of it in Eq138.

 

154.)              W=T = −(−Uv) =Uv

 

We do that by applying it not to avoiding the loss of v dollars but to avoiding the loss of one’s v*=1 life. That is, the penalty for failing at a survival behavior like getting food to eat or air to breathe is the loss of your own v*=1 life respectively by starvation or suffocation. The other terms in Eq138 are also asterisked to show that they are associated with avoiding the loss of one’s V*=1 life rather than the loss of v dollars. 

 

155.)                  W*=T*= U*v*= −(−U*v*)

 

Rather than describing the asterisked terms in the most general way immediately, it is easier to introduce them with specific survival behaviors and save the generalizations of what these variables until we have paid out some primary kinds of survival behaviors. Let’s start with breathing air. Consider Eq155 with the U* in it as the immediate uncertainty or lack of probability of getting air or the scarcity of air. First we’ll take up then U* is very great as when a person is underwater drowning or having a critical asthmatic attack or has a pillow placed forcibly over his or her face. In this case of suffocation the U* scarcity of air as great can be represented as U*=.999 understood intuitively as the probability of losing one’s v*=1 life under such circumstances.

 

The T*=U*v* transition emotion in Eq155 is experienced when a behavior is done to obtain air under this U*=.999 circumstance. In parallel to T=Uv relief of Eq87, T*=U*v* of Eq155 is the pleasurable feeling of great relief in getting air to breathe when one is suffocating. While not all have had this experience of suffocation in one form or another followed by escape many people have had it and all of them will attest to the great intensity of the pleasant relief felt. One measure of this great relief is with Eq155 evaluated for the v*=1 life saved by the relieving behavior and its prior U*=.999 scarcity of air or uncertainty in getting it.  

 

156.)              T*=U*v*=.999.  

 

We can also put a cash value on this relief by putting a cash value or price on your own v*=1 life that you don’t want to lose, let’s say a high value of v*=$100,000. That calculates a cash value for the T*=U*v* relief from suffocation that parallels the cash value of the T=Uv=$1166.67 relief from avoiding the loss of v=$1200 in Eq90 of

157.)              T*= –(–U*v*)=U*v*=(.999)$100,000=$99,900

 

Of course the value put on one’s own v*=1 life of $100,000 is arbitrary as is the T*=$99,900 value of the intensity of the relief felt from alleviation of suffocation. But they convey the central aspect of such relief being as great as you would feel if your life were spared some threatening disaster, which is what suffocating to death unarguably is.

 

The –U*v* term in Eqs155&157 negated or resolved by the behavior of escaping suffocation to T*= –(–U*v*)=U*v* relief is a measure of the unpleasant panic fear instinctively felt in suffocation that parallels the −Uv fear in Eq73 of losing money in the Lucky Numbers penalty game. 

 

Eqs155&157 also specify from W*=T* of Eq155 the W*price one would pay to save one’s life, namely W*=T*=$99,900. If the value of what one would pay to save his or her life was v*=$100,000, then the price one would pay for escape from suffocation and death as W*=T*=$99,900 is entirely reasonable assuming the person suffocating does not have the lives of a love and/or family to concern himself and his bankroll with.

 

The W*=T* equivalence of Eq155 also makes clear that the W*=T*=U*v function that governs the emotional dynamic is an expression of the Law of Supply and Demand with the demand for some commodity, good or service, that provides escape from suffocation and the loss of one’s v*=1 life being measured as the instinctively great value a person places on his or her life and the supply of what is needed to preserve that life as measured inversely by the scarcity in this case of air to breathe or the uncertainty in getting it of U*.    

 

The W* = T*­=U*v*= −(− U*v*) Supply and Demand Law of Eq155 also holds when there is no scarcity of air, no uncertainty in the body’s cells getting oxygen, no probability of losing one’s v*=1 life from lack of oxygen, U*=0, which is the situation for most people most of the time. Inserting U*=0 into Eq88 obtains

 

158.)              W*=T*=U*v*= −(−U*v*)=0

 

This formula quite perfectly fits normal breathing having no unpleasant fearful feeling, −U*v*=0, no noticeable relief in breathing air, T*=U*v*=0, W*=$0 a person is willing to pay for air to breathe under the normal circumstances of plenty of air available to breathe, W*=U*v*=0. The mathematically derived conclusions for U*=.999 suffocation and U*=0 normal breathing universally fit observable human experience.  

 

And so does the intermediate situation with air in short supply but not critically scarce as say U*=.2 as might be found in COPD or Chronic Obstructive Pulmonary Disease. In this case the –U*v* displeasure is felt as pulmonary distress but less horribly unpleasant than the panic fear of U*=.999 suffocation. Also significant is the T*= −(−U*v*)=U*v* relief felt when oxygen is supplied to a COPD sufferer with bottled oxygen. And we also see in this common ailment for older people that they are willing to pay a W*=U*v* price for relief, a lot if necessary though not every last penny a person has as a person would if their life was critically threatened with U*=.999 level suffocation. Again we may reasonably understand the U*=.2 as an approximate probability of death for untreated COPD.                    

 

The U*=.999 case of suffocation provides a clear example of how emotion facilitates survival through negative feedback control. In parallel to the E= −Uv fearful expectation of Eq87 of losing v dollars in the Lucky Numbers penalty game, the –U*v* panic fear from suffocation provides an expectation of losing one’s v*=1 life. Each situation generates the unpleasant sense of fear that motivates avoidance of the fearful situation, the E= Uv fear, avoidance of playing the penalty game if at all possible and the E*=U*v* fear, avoidance of the suffocating situation.

 

An important difference between the two fearful expectations is the origin of the uncertainty variable in them. In E= Uv, the U uncertainty or probability of losing v dollars from failing to roll a lucky number is a mental calculation that derives from elementary probability theory or from an observed failure rate of repeated tosses. In E*= U*v*, the U* uncertainty of getting oxygen to the body’s cells or probability of losing one’s v*=1 life derives from a physiological measure of the amount of oxygen in the blood stream. To understand how this U* measure motivates behavior that obtains the oxygen needed as a feedback control system let’s write the E* expectation U* is the primary variable of as,

 

159.)              E*= –U*v*= 0 – U*v*

 

Expressing the instinctive panic fear felt from getting insufficient air to breathe appreciates the 0–U*v* term in the above as the “error function” in classic feedback control theory where the error is what one wants to get rid of or “zero out” in the parlance of negative feedback control theory, that accomplished by reducing the –U*v* fear term to zero with appropriate behavior that returns one to normal breathing, thus returning the E* expectation of losing one’s v*=1 life by suffocation to zero, E*-0.

 

This confluence of biological control theory with the Law of Emotion derived Law of Supply and Demand understanding of breathing under difficult circumstances is another strong validation of Lucky Numbers. This analysis of emotional control as negative feedback control extends also to all emotion functions derived for obtaining money and avoiding its loss and also to the visceral emotional systems we’ll consider next. This and the overall understanding in Lucky Numbers of behavior as emotion mediated phenomena makes it clear that man has been designed to operate in an automated machine like fashion, whether by the passive design of Darwinian evolution or the intelligent design of an unseen creator God with an excellent sense of systems engineering, which of the two is more improbable, a heated debate between professional biologists and the Duck Dynasty crowd these days. 

 

Temperature regulation as avoidance of extremes of heat and cold is like breathing centrally important for avoiding the loss of one’s v*=1 life. Temperature in the range of 68o −82o Fahrenheit is optimal for man. If the temperature falls below 68o, the heat needed by the body to function well is in short supply or scarce with the uncertainty of the body getting the heat needed specifiable as U* >0 in Eq155, whatever numerical estimate we may wish to insert being an increasing function of how cold and life threatening the temperature is. That is, the colder the skin temperature is, the greater the U* scarcity of heat and from W*=T*=U*v*= −(−U*v*) of Eq155, the greater is the –U*v* unpleasant feeling of cold.

 

The –U*v* unpleasant sensation of cold is not quite a feeling of patent fear as was the –Uv fear of losing money in Eq73 but it has the same effect as fear in making one want to avoid the cold as though you did fear it. The range of the discomfort of cold extends to extreme cold represented as a U*=.99 scarcity of heat as a feeling approaching pain that makes one moan little differently than if one were being hit with a club as those who have experienced such cold will attest to. 

Negating the –U*v* displeasure of cold by getting warm provides via Eq155 the T*= −(–U*v*)=U*v* pleasure of the feeling of the relief of warmth, a pleasure greater in intensity as U*v* the greater the displeasure of the −U*v* antecedent cold, as fits universal experience. As further validates this understanding of temperature regulation, a person is quite willing to pay a W*=U*v* price from Eq75 to alleviate the −U*v* displeasure of cold and obtain the U*v* pleasure of warmth, the amount of money willing to be paid being proportional to the U* scarcity of heat in –U*v* felt as antecedent cold.

 

And by understanding the W* money spent to get warm when one is cold to be directly proportional to the time spent to make that money, Eq155 also tells us as fits universal experience that a person is willing to spend time to get warm directly as by cutting wood to burn in a fireplace and/or by getting or making clothes to put on to stay warm.

 

It is also universal experience that the pleasant feeling of warmth is not felt when a person is in the optimal 68o−82oF temperature to begin with. Being continuously in the optimal temperature range represents a situation of no scarcity of heat, U*=0, which dictates no unpleasant sense of cold via –U*v*=0 nor any pleasant feeling of warmth T*= U*v*=0.    

 

Temperature regulation also requires that the temperature be less than the high end of the 68o-82oF optimal range. Above that there is a scarcity of coolness required by the body to operate optimally, U*>0, with −U*v*>0 displeasure from Eq155 manifest as feeling hot and with the pleasurable alleviation or negation of such unpleasant overheating as −(−U*v*)= U*v*, that by appropriate cooling felt as pleasantly cool relief, T*= −(−U*v*)=U*v*>0. And it is clear from Eq155 as fits experience that a person is willing to pay for air conditioning to stay cool, W*=U*v*>0. Temperature regulation as feedback control has been understood as such for decades and is also derivable from Eq155 in the same way that we did for regulation of breathing.  

 

Obtaining food for the body to keep an individual from losing his or her v*=1 life from critical lack of it also follows Eq155, but not in as simple and direct manner as with breathing and temperature regulation because of the complicating factor of the intermediate storage of the food in various organs and tissues of the body, short term in the stomach and long term in fat and the liver. We dodge that problem by minimizing the effect of storage on the emotions involved as follows. 

 

When one hasn’t eaten for some time, the glucose or blood sugar in the blood vessels of the body becomes in short supply or scarce for the body’s cells, U*>0. Then the emotion of feeling hungry arises as −U*v*>0 of Eq155. This −U*v* feeling of being hungry, quite unpleasant as hunger in high intensity, is negated or relived to the T*=−(−U*v*)=U*v* pleasure of eating that includes both the deliciousness of food taste and the relief of the filling of the stomach. 

 

The T*= −(−U*v*)= U*v* equivalence in Eq155 tells us that the intensity of the pleasure of eating, T*=U*v*, is greater, the greater the antecedent −U*v* hunger. This is readily validated by those who have had genuine hunger and experienced marked pleasure in eating to relieve the hunger even with just a piece of stale bread or cracker, which tastes very delicious under that circumstance. And almost all of us have experienced the fact that feeling hungry before eating makes the food taste better. Eq155 also tells us that people are willing to spend W* dollars to obtain food and also to spend time to that end whether to get the money needed to purchase food or, as our primitive hunter-gatherer ancestors did by gathering plants and hunting animals to spend time directly to get food. .

 

When blood sugar levels are high and the stomach full, U*=0, that is, there is no scarcity of food chemicals for the body’s cells and under normal circumstances, hence, no feeling to eat, −U*v*=0. Under these circumstances, eating food pretty much lacks the T*=U*v*>0 pleasure produced when one does have a −U*v*>0 appetite. In such a state, absent the abnormal, constantly present hunger that is pathologically responsible for modern man’s epidemic obesity, there is neither a pleasure nor displeasure motivation to eat.

 

Lastly as a survival behavior we want to consider physical trauma like a fracture that causes pain. Pain is signified as –U*v* with U*>0 the uncertainty or scarcity of a normal healthy condition mechanically that threatens incurring the penalty of losing one’s v*=1 life. In this way pain is in obvious parallel to the scarcity of air, warmth or food, all unhealthy circumstances that threaten the loss of one’s v*=1 life,. Behavior that eliminates or negates the −U*v* pain as with not putting mechanical pressure on the fracture as −(−U*v*)=U*v*>0 produces U*v*>0 relief from the pain, which is felt as pleasant in proportion to the antecedent pain that pampering the fracture relieves.      

 

Now let us make it clear that the unpleasant emotions of suffocation, hunger, cold and physical trauma and the pleasant emotions of their alleviation, both sets of which derive from W*=T*= U*v*= −(−U*v*) of Eq155 are different from the emotions of the behaviors that obtain the commodities needed for these basic survival activities. When one is hungry, for example, eating proceeds in a direct and immediate fashion when food is readily available. But one must have possession of food first before one can eat. Explaining the functional relationship between the emotions for getting food and the emotions for eating food is best done with a concrete example of a food procurement behavior. We shall use a behavior we are familiar with in playing a dice game that gives food as a reward for rolling a lucky number of |4|, |7| or |10|.     

 

Eating this food gotten as a prize alleviates a hunger of –U*v* to produce the eating pleasure of T*= −(−U*v*)=U*v*. This behavior to get the food has a Z=1/3 probability of success and an improbability or uncertainty of U=(1−Z)=2/3. One’s expectations in this game are not via E=ZV an expectation of getting V dollars but rather of getting the W*=T*=U*v* pleasure of eating the food. Because this T* pleasant emotion gotten has an implicit dollar value from W*=T*=W*v* of Eq155 we can substitute W* for the V dollar value in the E=ZV expectation expression to obtain our hopes of pleasure as

 

160.)              E=ZV=ZW*=ZT*=ZU*v*=(1−U)U*v*=U*v*−UU*v*

 

This E* expectation r hopes of obtaining T*=U*v* food pleasure to probability Z stands in comparison to E=ZV=V−UV of Eq69 as the hopes of getting V dollars. In the latter, the desire is for V dollars while in the former of Eq160 the desire is for T*=W*=U*v* food pleasure as the negation of one’s −U*v* hunger. Then much as the pleasant desire for V dollars is reduced by the –UV meaningful uncertainty about getting the money to one’s probability tempered hopes of E=ZV, so is the U*v* pleasant desire of eating the food reduced by −UU*v* meaningful uncertainty in getting the food to the probability tempered hopes of ZU*v*.

 

This latter term is the intensity of pleasure felt in one’s hopes of satisfying one’s hunger by a particular behavior of getting food, here by playing the dice game to get food to eat. And this is exactly how the mind works in seeking pleasure by a particular behavior characterized by some Z probability of success in achieving that pleasure. We can also develop a T transition emotion felt when one rolls a lucky number and gets the food. From the Eq75, Law of Emotion, T=R−E, what is realized following a successful throw of the dice is eating the food and the R=U*v* pleasure of eating it. But also because there is U uncertainty in getting the food, there is a thrill or excitement in obtaining the food to eat of 

 

161.)              T=R−E= U*v*− (U*v*−UU*v*) =UU*v*   

 

When there is no uncertainty in getting the food as in reaching into the refrigerator to pull out a ham sandwich, there is no excitement involved in the act of getting the food to eat. Contrast this to a hunt for food for people who have no immediate food store or a search to gather berries to eat under the same circumstances of otherwise having nothing to eat. Then upon making the kill for meat or the finding of berry bush, there is great excitement.

 

In that sense UU* in UU*v in the above is a compound improbability, the U* improbability of your body’s cells getting what they need in food chemicals because your blood stream is low on blood sugar and the U uncertainty or improbability of your getting food to eat in order to replenish your blood stream with the blood sugar it needs supply the body’s cellular needs.

 

The T=UU*v* excitement in getting the food, hence, is a function of the U=2/3 uncertainty in getting the food and of the T*=U*v* pleasure in eating the food, itself a function of the –U*v* antecedent hunger via T*=U*v*= −(−U*v*) of Eq155. One gets both the R=U*V* pleasure of eating the food and the T=UU*v* thrill of obtaining it under uncertainty, which is what our hunter gatherer ancestors surely felt when searching for vegetative food or hunting for animal food with uncertainty, U. One can picture such a group having an exciting meal or feast following a successful hunt or search. In contrast if there is no U uncertainty in getting food, from T=UU*v*=0, there is no excitement or thrill in getting the food despite the R=U*v* pleasure in eating it, much as when one needs but to open the door of one’s refrigerator to grab an apple to eat if one is hungry.

 

Note also in the food prize dice game the disappointment that is felt, assuming the game can only be played once, when the lucky number is not rolled and food is not obtained under a condition of –U*v* hunger. In that case with E*=ZU*v* and R=0 for no prize realized, from the Law of Emotion, T=R−E,  

 

162.)             T=R−E*= 0−ZU*v*= −ZU*v*

 

This tells us that beyond the factor of your Z confidence in getting the food, the more –U*v* hungry you are and the more U*v* pleasure anticipated, the greater is the T= –ZU*v* disappointment in failing to get the food. And it also is the case that if there is no hunger for the food, there is no disappointment in not getting it, assuming the food can’t be stored for later consumption. 

 

In a coming section we will consider the various behaviors used to alleviate –UU*v* survival anxieties or needs. These include not only direct and obvious behaviors like hunting or searching for food when one is hungry, but also complex, many part, behaviors analogous to the sequence of rolling three lucky numbers to obtain a V prize, social behavior that obtains food by getting help from another and aggressive behavior that gets food via aggressing on another and stealing his food. And in a later section we will also consider reproductive behavior in terms of the E=ZV function but as E*=Z*V* where V* represents obtaining V*=1 life as that of one’s child.  

TO BE CONTINUED