Polytropy

Would education solve the world’s problems? A meaningfully positive answer would imply that the appropriate education could actually be supplied to us, or enough of us; and yet education is not a drug that can be administered willy-nilly.

My thoughts here are occasioned by a friend’s remark yesterday (Istanbul time, August 1, 2016), to the effect that the current presidential election cycle in the United States shows that

• liberal education—learning to think—is needed;
• this learning should start in grade school.

I responded as follows (this was on that social medium that I loathe):

Yes, the liberal arts are desirable. At least we who have supposedly been educated in them see them as desirable. We somehow saw them as desirable before we had learned much about them. But apparently most people don’t see this desirability. Can we change this?

The best I can come up with is that people need to be seduced into education. If we pursue the idea of Robert Pirsig in Zen and the Art of Motorcycle Maintenance, that one can only acquire an education after one has learned for oneself the value of that education—if we effectively abandon people in this way, well, it may happen that too many young people don’t bother to learn things when they are at the best age for learning. But trying to force young people to learn does not seem best either, be it by stick or carrot. Young children apparently learn languages easily. I suppose this is because they are social animals: they want to be active members of the group they find themselves in.

There is no examination that can measure the achievement of a liberal education as I think we understand it. At least, there is no examination that can be repeated: for a repeated examination is one that the examinees may try to learn the tricks for, without actually doing the learning that is supposed to be measured.

My late mother described being overwhelmed by mathematics in college, but still wanting to do well for her teacher. It may be a problem if young people are too concerned about pleasing others: this is the theme of the delightful graphic memoir, Dare to Disappoint: Growing Up in Turkey, by Özge Samancı (New York: Farrar Strauss Giroux, 2015). Here though, the person to be pleased (but who will be disappointed, no matter what) is young Özge’s father. Wanting to please teachers seems less problematic than wanting to please parents. At least it seems so, if the student can have enough teachers that she can find something in common, some sympathy, with at least one of them; and the teachers are paid enough to help ensure competence.

Much in these remarks built on a longer email that I had written to a few friends in 2015, and which (after some editing) I shall reproduce below. The remark about examinations comes from my experience in Turkey, where young people do what they can to do well on the national university entrance examinations. These exams are a theme of Özge Samancı’s book, actually. They have enough uniformity that fortunes can be made giving lessons in how to take the exams; but these lessons appear to be detrimental to any interest in learning for its own sake. The state takes elaborate pains to prevent cheating on the exams: presumably this is because people would cheat, if they could.

By the way, my university’s faculty of fine arts has an exam on which cheating is impossible. Candidates are given paper and told to sketch something, and no attempt is made to keep them from seeing one another’s work. Presumably successful copying from one’s neighbor would still display the skill that is being tested for.

I think it is self-evident that being a good person is not a matter of following any rules as such. For one thing, rules conflict, as “Take an eye for an eye” conflicts with “Forgive.” One should obey the good rules; but this begs the question of what is good in the first place. Following a list of rules, because they are supposed to get you into heaven, is at worst like cheating on an exam; at best it is like passing an exam legitimately, but assuming that this very fact means you have mastered what the exam is supposed to be about. As somebody who has to write exams for the mathematics courses that he teaches, I know how much there is that an exam cannot cover, but that I want my students to have learned.

It just so happens that a recent article on Medium called “Habits of highly mathematical people” touts the benefits of mathematics to daily life, even to the point of figuring out how to respond to a presidential campaign. As I understand part of the argument, the mathematics that we do can be so complicated that we must try to express a lot in a few words; but then we need to be prepared to figure out what those words really mean, or are trying to mean. According to the author, Jeremy Kun (who apparently has a doctorate in mathematics, but is otherwise unknown to me), we ought to give the same care to understanding the express goals of a presidential candidate like Donald Trump. Deriding those goals as insane is not enough.

I would say rather that deriding Trump’s potential voters as insane or otherwise incompetent is not enough. No court order is going to take away their right to vote. If one wants them not to vote for Trump, and one is prepared to do something about it, I think one has two options:

1. Employ marketing techniques, such as have been in development since the early twentieth century: techniques used to sell cigarettes, soft drinks, and dictators.
2. Educate.

The latter might be the better option, theoretically; but education takes time and effort, and the present time is late in the game for citizens already of voting age. Thus arises my friend’s lament. I would guess that potential Trump voters have already had all of the education they want. Teachers are authority figures. Trump stands up to the authorities, to the people who tell you what you are not supposed to say. This is what people like about Trump.

I prefer to talk about education though, rather than to talk about Trump. I look forward to being back in the mathematics classroom in September: it will be a distraction from the horror show that is the current election season in America. (The aftermath of the attempted coup in Turkey is dismaying as well, one reason being that the authorities are not interested in allowing the people to stay informed through the medium of a free press.)

I do want to acknowledge the argument that Trump attracts voters for economic reasons: that his voters are the “losers of modernity,” and what they need is not education is such, but a job and a stake in society. I take this expression, “losers of modernity,” from what seems to me a fine refutation of the argument: another Medium article, “Why Is Trump Attracting Voters?” by Eric Tillman (whom I know from Twitter as a scholar of Turkey). There would seem to be plenty of brown-skinned “losers of modernity” in America, and few will vote for Trump. Many light-skinned “losers of modernity” will not vote for Trump either. The losers who will vote for him are perhaps those who have been driven crazy by having a black man in the White House for the last eight years. “And now they want to put a woman in the White House? Everybody knows America was created by and for white men!” (Nobody said this is so many words, as far as I know; but I imagine many people thought it.)

In short, it seems that Trump appeals not to the poor as such, but to the racist. But it is a grave matter to accuse somebody of racism. I do think I have encountered it face to face a few times.

In one example, when I was young, a member of our (all-white) neighborhood gang came running up to say, “Let’s go beat up some black people!” I do not know how seriously he meant this, but he was quite exercised. He wanted revenge. A white friend of his had been beat up by some black people.

The same neighborhood friend had once remarked to me, “It’s every parent’s dream to have a child go to college.” This surprised me. It had never occurred to me that I might not go to college. My parents and grandparents had gone to college. I had never thought about whether the friend’s parents had gone, but probably they had not.

When I went off to college in Maryland, I made friends with a classmate who read the conservative National Review. He also had a girlfriend back home in California whose name was Charlene. I suggested that this sounded like a black name. However ill-founded, perhaps my inference was not unusual: in 2008 or earlier, a white girl named Charlene raised on Yahoo the question, “When you hear the name Charlene, do you assume the girl is black?” In 1984, my classmate was offended, though he managed to keep smiling. “David, that’s not very nice!” he said. I had thought I was teasing him; apparently I was insulting him.

Such are two of various examples that I may think of, when I think of personal racism.

It may be precious now to turn from this to thoughts on education inspired by my own formal schooling. What I am turning to is an email that I wrote on Sunday, May 24, 2015, at the Nesin Mathematics Village. I had been inspired by a talk the previous evening called “Education on the Deck of the Titanic,” given by Alexandre Borovik as part of Antalya Algebra Days XVII. By my memory, the content of Sasha’s talk overlapped with that of an “extended abstract” now on Sasha’s webpage with the title, “Makers and Users.” As Sasha says at the end, regarding mathematics education at least, the Right wants to rearrange the deck chairs on the Titanic; the Left wants to provide the disadvantaged with better chairs. At any rate, below is an edited version of what I had to say to three people whom I had talked with that evening.

The Beatles sang, “All you need is love.” In that spirit, I am going to propose that all you need for education is love. Teachers should love their students and should love learning. It is hard to make this more precise. I may note that in Greek there are words for (at least) four kinds of love: ἔρως, φιλία, ἀγάπη, and στοργή. One hears of awful cases where teachers fail to understand what love for students means. Such teachers abuse their power over students.

Of course my comments on education will be based on my own experience of being educated (and being an educator). I have already written an article about my college: “St John’s College,” The De Morgan Journal 2 no. 2 (2012), pp. 63–73. Being a student at St John’s College was the most valuable educational experience of my life. My article spells things out in more detail. After Sasha’s talk, I learned that another American attending Antalya Algebra Days had been interested in attending St John’s College, but figured her parents would never allow it. She attended a more traditional American liberal-arts college instead, and this was a women’s college to boot. She was satisfied with it. Now we are alike in being math professors living abroad.

A feature that makes St John’s special is that nearly the only choice for the student there is the initial decision to attend in the first place. All students follow the same course of study, based on so-called Great Books. Everybody has read, is reading, or will read the same things. This means everybody is willing to sit down and talk about them. This is why, in conversation after Sasha’s talk, I could propose that there might be books that all students should read. The classics on the St John’s program are examples.

On the other hand, while some of those books might simply be a pleasure to read, many of them require serious devotion. They are the result of deep struggle with life. They are not easy. They may not repay a reading of them done simply for the sake of passing a course.

In Zen and the Art of Motorcycle Maintenance, Robert Pirsig proposes a model of education in which students receive no grades for their work. Students should pursue a course of study because they have found it desirable, not because of any external obligation. I read Pirsig’s book before attending St John’s. At the College, teachers assign grades to students, but students see them only on request. I myself never saw my grades until after graduation, when I was applying to graduate school. (I did this after working on a farm in West Virginia. This was a terrific educational experience too, and I have written about it in an article published only on my website.)

I admire Pirsig’s book, but I think the author misses an important feature of education. One can learn something without knowing by personal experience that learning it is desirable. Now, it may be possible to learn under pain of corporal punishment: see the latter part of Section 4 of my article “Abscissas and Ordinates,” Journal of Humanistic Mathematics 5 (2015), no. 1, pp. 233–264. (See also Section 1 of that article for my general view of mathematics education. I think anybody who uses analytic geometry in teaching should read the whole article.) If one is not going to learn out of immediate personal desire, it seems best to me to learn because one somehow respects or admires or emulates one’s teachers. Studying to avoid the whip is not good; studying to earn the appreciation of one’s teachers may not be so bad.

Perhaps it is best to learn because one understands it as one’s role in the community that one is happy to be a part of. Here again is something that Pirsig may miss. Pirsig is the individualist, the lone wolf, and this is a reason why I like him. But education is not just something one achieves for oneself. It means joining an educated community; it means helping others join that community. At St John’s, I may have been the most mathematically skilled person in the classroom. My job then was to try to learn to convey my own understanding to others, and to learn others’ ways of understanding in the first place. So described, this is everybody’s job.

At some colleges or universities, a student’s high-school work might allow her to skip certain courses. Such skipping would make no sense at St John’s, where the books that one reads are an inexhaustible source of understanding, and the supposed teacher in the class, the one who gets a salary for being there, is only the most advanced learner. (This is the doctrine of the College itself.)

I went to public school through the third grade in Alexandria, Virginia, the city whose public schools my father had attended. But my school seemed to be not challenging enough, and so from fourth through twelfth grades, I attended an elite private school in Washington, D.C.

I think well of St Albans School for myself. But then I seem to have difficulty recovering bad memories of anything. I knew somebody at the school who was four years older than I, but who now feels bitter resentment towards it. I won prizes from the school, for general academic achievement as well as for specific subjects like mathematics, physics, and chemistry, but also English and writing. Naturally the teachers would love me. Perhaps they loved that other boy too. This was a Christian school, belonging to the Protestant Episcopal Church, the Anglican church in the United States. Christians are supposed to love everybody. But that other boy was not scholarly; he had non-scholarly friends; and that gang were somehow not appreciated.

The school was on the close of the Washington National Cathedral, whose towers looked down on us. While we had obligatory chapel services, I would say there was no indoctrination in religion. Speaking as an atheist, I appreciate the school for projecting the message that religion is a matter of personal conscience. We engaged in the collective ritual of going to chapel and listening to sermons; but what we made of it was up to us. We had some required classes about religion (and these were the only courses at the School in which I ever got a grade of C, because I refused to take them seriously as courses). In the course called Christian Ideas, I said in class it should be called Christian Facts; but then the teacher invited me and a few others to meet him regularly for discussions of philosophy. The course on the Bible taught us that this collection of documents was the human product of different views of religion. There was some kind of sex course in an earlier year, though I think the School had not quite worked out what it should consist of. The School headmaster was a priest; he observed that the decision of whether to have sex was our own to make, only it ought to be a real decision, made before we found ourselves in the heat of passion. The School told us in many ways that we were privileged, if only because we were attending the school in the first place; but I think this came with a message of noblesse oblige: privilege required responsibility.

In a proper democracy, everybody is privileged to help steer the course of the society; and everybody should recognize the responsibility of doing so. Education should inculcate this sense of things.

So I wrote in 2015. I would add only that how to inculcate the democratic virtues is a difficult question. It may not be sufficient to throw money at the problem; but it is probably necessary.