1967-1969 Part 1: U-M Classes

Classes in the middle years. Continue reading

To the best of my recollection this was my undergraduate academic schedule at Michigan:

FreshmanFall 1966Math 195Russian 101Chem 103Latin 350
 Spring 1967Math 196Russian 102Chem 106Greek 101
SophomoreFall 1967Math 295Comp ProgEcon 101Greek 102
 Spring 1968Math 296Comm SciSp PersuasionGreek 201
JuniorFall 1968Math 395Econ IntlSp DebateGreek 202
 Spring 1969Math 396TopologyHomerThucydides
SeniorFall 1969ProbabilityStatisticsPsychologyEuripides
 Spring 1970Sp StudyLinguisticsRuss LitAnthropology

The classes for the first semester of freshman year (fall 1966) are discussed here.

The classes for the second semester of freshman year (spring 1967) are discussed here.

The classes for the second semester of senior year (spring 1970) are discussed here.

Here is what I remember from the middle years by subject:

Math: The three-year basic sequence (195-6, 295-6, 395-6) started with a review of calculus. The last semester covered, I think, the calculus of several—more than three—variables. It was during this last class that I realized that I had absolutely no interest in being a mathematician. I could no longer visualize what was being talked about. I am sure that it is valuable for things like string theory, but it was not for me.

In fact, I was lucky to last that long. These six classes were all taught by professors, as opposed to graduate students.1 We were expected (but not required) to do the problems at the end of each chapter of the text. I looked at them, but I never did them. Our tests asked for proofs rather than solutions to problems. The material became more and more difficult as the course numbers got higher. I familiarized myself with the concepts, but I did not actually learn them. That was not my goal; my goal was to pass the tests.

HH

I developed several techniques for pretending to prove that formula A is equivalent to formula B, which is the format for most, but not all, mathematical proofs. It would be best to come up with an actual proof, but this is not like horseshoes or hand grenades. Coming close can count for a lot. I thrived on partial credit.

The first technique is known as proof by induction, a legitimate and powerful method absolutely essential for proving some mathematical concepts. It even has its own Wikipedia page. Any time than something countable—an integer or even a rational number—was mentioned in either formula A or formula B, I would used proof by induction. It was always good for a half-page of paper, and I never got less that seven out of ten points. Occasionally, it actually produced the required proof.

The technique that I invented and perfected was the Wavada Squeeze. You will not find it on Wikipedia yet. Here is how you do it: Start with formula A, and in a column beneath it make as many manipulations of it as you can think of. For example, you could multiply and divide by something: A=((x+3) x A)/(x+3). After ten or so manipulations, you end up with something quite different from what you started with. On a separate sheet of paper perform a different set of manipulations on formula B. Once in a while one of the two will actually show the way to a proof, and that’s great. However, even if neither does, you can maximize your partial credit by writing the the manipulations of B in reverse order beneath the manipulations of A. This will give you a “proof” that A=B with twenty or so legitimate manipulations, and one horrible leap somewhere in the middle. This was usually good for at least five out of ten, which was much better than nothing.

I made the mistake of taking one graduate-level class, Topology. I ended up with a C, which is a terrible grade in a graduate class. I remember entering the classroom on one Monday after a debate tournament. Everyone was busy writing their names on “Blue Books”, which meant that an exam was about to take place. This was news to me. Evidently, it was announced in a class that I had not attended. Usually I tried to make sure that I had a friend in classes to warn me about such events. This class, however, was composed of graduate students in math. None seemed approachable. I got one right out of nine. Showing up clueless in a classroom full of people with Blue Books appeared frequently in nightmares over the decades.

I am embarrassed to say that not only have I forgotten the names of these teachers, but I also have only vague recollections of any of the concepts, never mind the details, of what I supposedly learned. I never considered graduate school in math.

Nesbitt

Actuarial Science: I passed part 1 of the actuarial exams in May of 1969. I took two classes from Cecil Nesbitt2, a very famous actuary, in the fall semester of 1969 with the half-hearted purpose of passing part 2—probability and statistics. I was not a bit impressed with the quality of the other students, when compared with the guys (and girl) in my math sequence.

My attendance in both classes was extremely spotty. I did not do any of the assigned problems. Nevertheless, I thought that I had passed part 2 in November, but i was wrong. The exam was offered again in May, but I was not upset enough about this failure to study more in the spring session. The result is described here.

Cecil Nesbitt’s Wikipedia page is here.

Cameron

Greek: For the first two Greek3 classes the teacher was H.D. Cameron.4 I can clearly visualize the professor who taught the 200-level classes as well, but I am embarrassed to report that I cannot remember his name. He also taught the Thucydides class.

My clearest recollection of those last two classes in the sequence involved the final exam. With less than one hour remaining before the Greek final, I realized that I had misread the exam schedule and studied for a different subject. The exam for that subject was a day of two later. So, I ended up taking the Greek test with practically no cramming.

Thank goodness it a Greek course was the one to which I gave insufficient attention; I got an A anyway. If I had neglected the other subject (I forget what it was), I would have been in a world of hurt. This kind of thing was also a subject of many future nightmares.

In all honesty the university should not have allowed me to take these four classes. My high school Greek class was good enough that I could almost certainly have placed out of Greek. However, there was no placement test for Greek at U-M. I am thankful for the lack; I received four easy A’s.

The Homer and Thucydides classes were more difficult. All of the other students in both classes were graduate students who took nothing but Greek classes and spent all of their daylight hours in the classics department. I was lucky to survive.

I enrolled in a course that translated the plays of Euripides. I had to get special permission from the professor to join. However, after a week or two I dropped the class. It was just too demanding for my schedule.

If I had applied to graduate school in 1970, I would have tried for a masters in the classics. These were the only classes that I enjoyed the most.

Gronbeck

Speech: I took only one real speech class, persuasion. It was taught by Bruce Gronbeck.5 The other two speech classes were gift A’s to compensate for the time that my participation in debate consumed.

I went to the persuasion class every time that I was in town. I gave all the speeches and turned in the assigned paper. I found the material presented boring, but the speeches were quite interesting.

I have several vivid recollections. We talked about some of the speeches as a class. In one situation I remarked that I thought that the speaker had seemed sincere. Prof. Gronbeck asked me why I thought that, and I was stumped. Nobody else really had a better answer. As Jean Giraudoux famously noted, “The secret of success is sincerity. Once you fake that you’ve got it made.”

Jim Pitts is #20 in the middle row.
Jim Pitts is #20 in the middle row.

Jim Pitts, the captain of the basketball team, was on the roster for the class, but he never attended, not even for the assigned speeches. Prof. Gronbeck told Dr. Colburn about this, and a few days later Jim appeared, and he was prepared to give a speech. No speeches were scheduled for that day, but he was allowed to deliver his speech, which was about abortion.

Jim took the floor with about twenty 3″x5″ cards held in very large hands. The use of a deck of cards in a speech is always a bad idea unless you plan to demonstrate how to throw them. Jim’s first line was “The chances of getting an abortion in this country are 1. Slim and 2. None.” On the fourth card he could not read the handwriting of whoever wrote the speech. A few cards later the cards were in the wrong order, which always seems to happen. When he finished the speech, Prof. Gronbeck thanked him, and no one else said anything. The class then continued as usual.

That was Jim’s last speech, but he never missed any basketball games that year.

Prof. Gronbeck wanted to hold a one-on-one debate, and I volunteered. My opponent, who was from Germany, chose as the topic the reunification of her country. She was against it. It wasn’t much of a debate. I had to go first, and we only got one speech each. She made no attempt to refute anything that I had said.

Communication Science: For some reason in those days the academic department at U-M that dealt with computers was called “Communication Science”. I took two courses. The first was the introductory programming class. My instructor was Господин Muchnik, whom I already knew as a student in my first-semester Russian class. We learned to program in MAD, which stood for Michigan Algorithm Decoder, a programming language used nowhere else in the world.

Card

There were no terminals. We had to record our programs and our data on eighty-column IBM cards. This required use of a machine to punch the cards. Each card corresponded to a line of code or a row of data. There was no backspace or delete key. If you made a mistake when you punched the, you had to eject the card and throw it away. The university had a dozen or more of these machines for students, and they were located on the other side of campus. If they were all in use, you just had to wait or come back later.

When you finally had your program and data punched, you inserted the deck of cards into the pre-compiler, a small machine that found syntax errors in MAD programs. When you fixed all of the errors that it found, you were ready put a rubber band around your deck of cards to submit a job to the computer. The operator would accept the job, assign it a number, and give you a card with your job’s number and a phone number for a recording that announced the number of the job that the computer was currently on. It might be hours or even days befor the announced number was greater than the number of your job. When it finally happened, you walked back to the computing center to retrieve your output and your deck.

Card_Punch

The first few times that you did this, the output consisted of a list of errors. If there were only a few errors, you would wait for a keypunch machine to be available, fix the errors, and resubmit the deck. This process went on until you either despaired or were euphoric when you finally got some results.

For our final project we could do any program that we wanted. The only requirement was that it be at least one hundred lines of code. My project read in a bridge hand of thirteen cards and output the opening bid using the standard American system taught by Charles Goren. I did it over the Thanksgiving holiday when there were no lines for the keypunch machines, and shorter waits for the jobs. I got it to work well pretty quickly.

Needless to say, I really liked programming, and I was good at it.

The other Comm Sci class that I took was a strange amalgam of language theory and the history of computer languages back to the Turing machine. I did not get a lot out of it.

Economics: You cannot debate as much as I did without doing quite a bit of research into economics. By the time (sophomore year) that I enrolled for the introductory class at U-M I had already read hundreds of articles and several books on economics. The format for the class was lecture plus recitations. I enjoyed the lectures, although my memory of who gave them cannot be correct. I found the recitations tiresome and overly simplistic.

I studied for the final with my debate partner, Gary Black, a senior. I helped him more than he helped me. I was more than a little peeved when he got a low A, and I got a high B.

I took one more economics class. I did not like anything about the way the course in international economics was taught. I put in as little effort as possible. I think that I got a C.

Daniel Kahneman.
Daniel Kahneman.

My enduring impression about the field of economics was that it was 99 percent unproven theories. I was right. The next fifty years proved conclusively that most of what I was taught was just wrong. In fact, Daniel Kahneman, a psychologist, won a Nobel Prize in Economics in 2002 for demonstrating that the basic behavioral assumption underlying all economic analysis is nonsense.

Psychology: As a senior I signed up for the introduction to psychology in the honors program. I was allowed to take one class pass-fail, and this was the one that I selected. Grades lower than C were unheard of in honors classes. So, I correctly determined that I could pass this class with virtually no effort.

The teacher was a female graduate student, and she insisted that we understand the principles of feminism. Most of us had never heard of the word. I remember very little else about the class, except that it was full of freshmen with first names like Hill or Twink. Twink told us that in the home in which he grew up no one ever questioned Freud’s teachings. I found that astounding, but I suppose that it is no more astounding than believing in the Book of Mormon or, for that matter, the Bible.

I could take this guy, too.
I could take this guy, too.

Twink was a fairly big guy, maybe 6’3″. Once I was walking somewhere with my friend, Tom Rigles, who had already heard me tell stories about him. Tom said that he did not imagine him being so big. I casually remarked that I could take him. Rigles scoffed at me. As God is my witness, I could take Twink then, and if he is still alive, I could take him now.

I don’t think that the psych class had a final exam, but we were required to write a paper. I had picked up a book called Games People Play by Eric Berne. The night before the papers were due, I skimmed the book and wrote and typed the paper. It was the third and last paper of my entire undergraduate career

I disliked all the “social science” courses that I took. If you had predicted in 1970 that I would voluntarily take almost nothing but social science courses for six years in graduate school, I would have told you that you did not know what you were talking about.


Ted

1. Ted Kaczynski, the notorious Unabomber, was a graduate assistant in the math department at U-M during the sixties. The offer of the teaching position was the main reason that Ted chose Michigan over Cal Berkeley and the University of Chicago.

2. My best friend since 1972, Tom Corcoran, worked as an actuary. One year I was shopping for a birthday card for him. I looked through about twenty humorous cards until I found one that actually mentioned Cecil Nesbitt! I was absolutely astounded.

3. I learned classical Greek in high school and college. Decades later I tried to teach myself modern Greek in preparation for a Hellenic vacation. The alphabet was the same, and the grammar was similar. However, the vocabulary and pronunciation were drastically different.

4. Professor Cameron in 2020 is emeritus in the classics department and curator of the university’s Museum of Zoology.

5. Professor Gronbeck died in 2014. A very lengthy obituary can be read here.

April Fools

Also May, June, July, etc. Continue reading

I long ago realized that the common view of human beings as rational decision-makers is hooey. Three things that I have recently encountered have reinforced this for me to the extent that I have been considering applying for membership to another species. The elephants that are featured on my World Wildlife Federation calendar look like an inviting possibility.

I have almost finished Daniel Kahneman’s Thinking, Fast and Slow. One of the many astounding things that his research has uncovered is how incompetent most people are at using probabilities to make decisions. I already knew that many people are poor at calculating the probability of the occurrence of certain types of events, but I never would have guessed that even when they are given the probabilities they are unable to apply them to make utilitarian decisions. One of the many things that he discovered was that people routinely overweight the likelihood of unlikely events, and the effect is substantial. The research studies produced the following table:

Probability (%) 0 1 2 5 10 20 50 80 90 95 98 99 100
Decision weight 0 5.5 8.1 13.2 18.6 26.1 42.1 60.1 71.2 79.3 87.1 91.2 100

So, when people make decisions they exaggerate the possibility of a 1 percent likelihood by a factor of 5.5, and they exaggerate the difference between a certainty and 1 percent failure by a factor of 8.8! The former helps to explain why so many people waste their money playing the Lotto and gambling in casinos. It’s not just that they are fixated upon the payoff (as they are), that fixation makes them think that they have a much better chance of winning than they actually have.

The misjudgment of the difference between 99 and 100 percent results can make people continue to devote resources to projects that are almost certain to fail long after that likelihood has been manifest even to them. This helps explain why people keep pouring money and effort into failing businesses and projects with little chance of success. That 1 percent chance of the project succeeding looks much bigger to them.

I remember distinctly that I had an experience with a project like that. I developed a software system for nursing homes that allowed them to compute what they would be reimbursed by the state of Connecticut while they still had a chance to change policies. We installed it at one of our customers, and the proprietor loved it. I abandoned the project when I discovered that an accounting firm that numbered almost every nursing home in the state as a client already provided this kind of service. When I realized that my chances of competing with them were slim, I abandoned the project, moved on, and never looked back. Many others are apparently just incapable of admitting defeat early.

I have absolutely no idea why anyone would think that something that is 50 percent likely should be valued at only 42.1. Although Kahneman does not address that one, I believe that the assessment is probably correct. Sue has told me that she does not like to take finesses in bridge, which ceteris paribus have a 50 percent chance of succeeding, because she does not like the idea of losing that trick.

In short, most humans should not be trusted with a decision about any matter with a likelihood between 1 percent and 99 percent.

* * *
Since Sandy Hook there has been much discussion about reinstating the ban on “assault weapons” and high-capacity magazines. Although I strongly believe in one form of gun control (a national ban on handguns), the arguments presented both in favor of and against assault weapons make me see red. Those in favor of the ban argue that the fact that a weapon that could hold so much ammunition allows a shooter to kill more people than if he needed to reload. I seriously doubt that that is true. The shooter carried two handguns and a shotgun in addition to his rifle, and he had ten magazines for the rifle. It does not take more than a few seconds to eject a magazine and put in a new one. Furthermore, at short range the handguns would be almost as accurate as a rifle. So, maybe he needs to bring four handguns instead of two. Does anyone think that this lunatic would have been deterred by the fact that it would have taken him ten minutes instead of five to fill up twenty-six body bags?

Of course, assault weapons with large magazines are not needed for hunting (other species), but the most salient argument that gun enthusiasts proffer is that if there were a dictatorship, as in, say Syria, and the populace needed to resist, it would need weapons. It is definitely true that the assault weapons would be more useful in such an endeavor than shotguns or handguns. Unfortunately, as the 70,000 dead Syrian rebels have discovered, the air power and tanks that are available to the government render any type of firearm fairly useless.

S.S.

S.S.

Needless to say, the solution to the Sandy Hook problem proposed by the NRA and a few others of arming thousands (millions?) of Fearless Fosdicks hired to patrol the hallways of the schools is so ridiculous as to preclude a serious examination. They can hire Steven Seagal (with his “millions of hours” of training) to do that in Arizona if they want. In Connecticut, the Land of Steady Habits, we prefer that there be no guns at all in the schools.

F.F.

F.F.

The point is that assault weapons kill very few people in the United States, and removing them (assuming that that is even possible) would cause very little, if any, harm, and do very little, if any, good. From a practical point of view this is just not a critically important issue. In short, this is a distraction from the real problems.

* * *
What is an important issue is what has happened to our labor force. Since the collapse of the economy engineered by the geniuses hired by the brokerage firms (I refuse to call them banks) and the previous administration’s misguided policy of trying to establish an “ownership society,” the ratio of employment to the total population has tanked. The Obama administration’s policies have had essentially no effect in the last four years. And yet, the unemployment rate has decreased markedly in that time. How is that possible? There is only one possible answer: lots of people have left the labor force.

Some of them have retired, of course. Another group has gone back to school. However, I was surprised to learn from a podcast produced by the radio show This American Life that fourteen million Americans are now receiving disability payments from the federal government. These people are not getting rich off of this program, but some private companies are:

  • States have been paying private companies to comb the welfare rolls looking for people who could qualify for disability. These companies are paid thousands of dollars for each person whom they successfully move from the temporary state program to the permanent federal one, and they have high success rates.
  • Law firms such as Binder and Binder (thirty thousand disability clients in 2012 alone) contact people whose applications for disability have been rejected by the Social Security Administration. They represent the claimant in a hearing before a judge. Incredibly, no one represents the government, and the lawyers who win receive 25 percent of the awarded backpay, which amounts to about $1 billion per year.

The result of this bizarre system is that, as hard as it is to believe, since 2009 the economy has created about 150,000 jobs per month, but in the same period about 250,000 people per month have applied for disability. The system that was designed to help cripples has become the safety net for people for whom the modern economy has no use. I know a few of these folks; you probably do, as well. I doubt that the current approach is optimal, but I have yet to hear or read of a better approach. It is difficult not to think of Soylent Green at this point.

Epiphanies

Changing one’s mind. Continue reading

In his famous book Thinking, Fast and Slow, Daniel Kahneman posits that the mind uses basically two systems of decision-making. The first is employed nearly all of the time in the thousands of quotidian decisions that confront people. The judgments are generated so fast and require so little effort that we often do not even think of them as thinking. The second system is more analytical and deliberate. When we say that we are paying attention, we mean that System 2 is in charge. The funny thing about this arrangement is that humans all identify with the second system even though the first one is clearly the mental workhorse. The commonly heard sentence “I don’t know why I did that” really means “System 2 does not know why System 1 did that.”

This made me think about epiphanies, which I would define as occasions in which someone’s System 2 decided that because of some new information it must override an area that had previously been assigned to System 1. I suppose that it could work the other way, too, when someone decides that he/she is just not going to worry about something any more. Going native, becoming an artist, or joining a monastery might qualify.

I experienced a very striking epiphany in 1973. I read a book with a theme that was somewhat similar to Kahneman’s entitled I’m OK,You’re OK. I learned soon enough that the divisions that the author, Thomas A. Harris, described among Parent, Adult, and Child aspects of one’s thinking were not perfectly accurate. In fact, however, I found the medical research by Michael Gazzaniga that served as the basis for the Transactional Analysis described in the book even more compelling. The idea that the same human body possessed more than one thought process and, moreover, that the separate processes actually competed for control of the body’s functions affected me (and by me I mean my System 2) greatly. More than anything else, I found it very liberating. There was no reason for me (System 2) to feel guilty about something that he (System 1) had done. Of course, I could work hard to prevent him from doing it again, but if I had no idea of what was coming, no jury, not even a jury of a dozen nuns, could convict me.

A few years later I had an epiphany of a different sort. Once again a book, James Randi’s The Magic of Uri Geller, was the instigator. In those days I was quite interested in slight-of-hand tricks. I had watched an astounded Charlton Heston on television — at the Amazing Kreskin’s direction — name the color of every card in a deck simply by holding the corner of each card between his fingers for a second. Even after I discovered how Kreskin did this incredibly simple trick, and I learned that Kreskin’s “mental powers” consisted of nothing more than memory and counting, I still thought that there must be some people who had paranormal abilities. This was not a thoroughly researched heartfelt conclusion. It just seemed reasonable that some of the thousands of people who claimed psychic abilities probably had powers that science could not yet understand. I mean, bats and dolphins have mental abilities that are beyond ordinary humans. System 1 often bases its conclusion on those types of impressions.

Randi’s book thoroughly exposed Geller, who was formerly a stage magician, and his assistant, formerly a stage magician’s assistant (!), as frauds. It also made it quite clear that the academics who had tested him and other such claimants did not understand how easy it was for one human being to fool another’s senses. They wrongly thought that they were smart enough to recognize tricks, and they may have wanted him to succeed.

The exposé induced me to pay more attention to the subject of credence. Reading Randi’s book turned me into a skeptic about everything. Shortly thereafter my belief in just about everything invisible — psychic powers, ghosts, souls, guardian angels, etc. — fell aside.

Recently I have been thinking about how one might induce an epiphany in someone else. Religious cults have developed a very effective technique. The first step is to smother someone with love and affection. The idea, in Kahneman’s terms, is to convince them to set aside System 2 processing for everything that has to do with the cult. System 1 quickly associates the cult with stimulation of the brain’s pleasure centers and thus forms a strongly favorable impression. Many become True Believers.

How can one reverse the process? How can one persuade another person to use System 2 in dealing with something (not necessarily a cult) that the target person had previously relegated to System 1? This is a thorny question. System 2 is inherently lazy, and employing it requires real effort that is difficult to sustain. I hope that Kahneman addresses this at some point in his book.

The dissertation that I abandoned long ago was going to focus on a very small aspect of this subject. A long string of well-known studies of some very specific questions involving judgments in situations in which the probabilities of outcomes had been specified showed that people consistently changed their minds about the advisability of certain options after a discussion with others. The direction of the shift is predictable. On some questions it shifts in the direction of taking risks. On others it shifts in a more conservative direction. The effect is not perfect, but it is strong.

I speculated that some of the people who changed their minds probably did not understand the concept of probability well enough to calculate the best course. The discussion might have provided enough context so that System 2 decided that it had enough information to take over and make a different decision.

I wonder if I was right. I probably will never know.