Polytropy

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This essay – these notes for an essay, this draft of an essay – is inspired by Robert Pirsig’s first book. I have made sectional divisions where they seemed to occur naturally.

While we who work at universities may be employed by the state, our true work is to serve not the state as such, but what may be called knowledge, or science, or reason. This is a theme of Pirsig, which I take up here.

In the ideal state, there would no conflict between doing our true work and serving the state. This is a theme of Thoreau, whom Pirsig read during his motorcycle trip. In the Conclusion of Walden, Thoreau recalls an early leader of the French Revolution who romanticized illegal violence as requiring the greatest resolution and courage. Thoreau observes that Mirabeau missed the point:

A saner man would have found himself often enough in formal opposition to what are deemed the most sacred laws of society, through obedience to yet more sacred laws, and so have tested his resolution without going out of his way. It is not for a man to put himself in such an attitude to society, but to maintain himself in whatever attitude he find himself through obedience to the laws of his being, which will never be one of opposition to a just government, if he should chance to meet with such.

Pirsig suggests that conventional schools and universities teach students to imitate. I investigate this idea. I think mathematics, at least, done properly, cannot be imitation. In my department, we have our first-year students read and present the propositions of Book I of Euclid’s Elements, as I did as a freshman at St John’s College. Are we then imitating St John’s? If a student just tells her classmates what Euclid says, this would seem to be imitation; at any rate, it is not what we want. After Euclid establishes the hypotheses of a proposition, he continues with legô hoti, I say that –. The student must not merely mimic this; she must utter it on her own behalf.

If Euclid is considered somehow inadequate by modern standards, this can be all the more reason to read him: then students may learn not to accept a piece of mathematics, merely on somebody else’s authority. Pirsig may be found inadequate as well. Still I think all teachers should read him, if only that we may better understand the job we should be doing; but I, at any rate, find the reading of him a pleasure.

The title of this article may be taken to allude to the problem of explaining how one world, one universe, can comprise many things. Pirsig’s solution is to derive everything from Quality, which at least resembles the Tao.

1

Turkish universities enjoy the economy of not deciding whom to admit as a student. The decision is made nationally and mechanically on the basis of scores on multiple-choice examinations.

In the United States, every institution of higher education has to determine its own criteria for admissions; then it has to apply them. Admission to St John’s College requires a number of essays. Since there are few examinations at the College, and grades are not distributed automatically, but classes are general discussions, students have to be self-motivated. Willingness to write all of the application essays is a test for this self-motivation.

In my day at least, one of the St John’s application essays was requested as follows:

Choosing a book that has been important to you, write about some aspect of the book (not the book as a whole).

That was the wording in 1982, as near as I can remember; I see that today the wording is,

Discuss a particular aspect of a book, old or new, that you consider great and that has influenced you.

I chose Robert Pirsig’s Zen and the Art of Motorcycle Maintenance: An Inquiry into Values (1974). I recall addressing an aspect that I touched on again in this blog in June, 2013, in an article called Books hung out with: Pirsig shows, and does not just tell. He not only tells us his philosophy, but shows how to apply it.

As I said in the earlier article, I have read Pirsig’s book countless times. As I said in my most recent article, Surgery and Recovery, I have now read the book yet again. I want now to talk about another aspect or feature of the book: its practical ideas about the university and education.

2

I know somebody who says he never read children’s books as a child. I myself first used the public library, precisely to check out a children’s book: Beverly Cleary, The Mouse and the Motorcycle (1965). Pirsig’s book about motorcycles would have the same publisher: William Morrow. Meanwhile, our second-grade teacher was reading Cleary’s book to us, and I wanted to read it for myself. I went on using the children’s section of the library for some time, be it for more Beverly Cleary books, or books about mathematics, or American history books for a fourth-grade course. A dearth of suitable books of the last kind did make me wonder if I should use the grown-up section.

When I read adult books (in the non-euphemistic sense), I was not enticed by those that my parents’ generation were reading. I did not absolutely refuse them though. I knew that my elders had read Zen and the Art of Motorcycle Maintenance. When later I noticed the book in the library of my high school, I picked it up and was drawn in by the first sentences:

I can see by my watch, without taking my hand from the left grip of the cycle, that it is eight-thirty in the morning. The wind, even at sixty miles an hour, is warm and humid. When it’s this hot and muggy at eight-thirty, I’m wondering what it’s going to be like in the afternoon.

In the wind are pungent odors from the marshes by the road. We are in an area of the Central Plains filled with thousands of duck hunting sloughs, heading northwest from Minneapolis toward the Dakotas. This highway is an old concrete two-laner that hasn’t had much traffic since a four-laner went in parallel to it several years ago. When we pass a marsh the air suddenly becomes cooler. Then, when we are past, it suddenly warms up again.

I’m happy to be riding back into this country. It is a kind of nowhere, famous for nothing at all and has an appeal because of just that. Tensions disappear along old roads like this. We bump along the beat-up concrete between the cattails and stretches of meadow and then more cattails and marsh grass. Here and there is a stretch of open water and if you look closely you can see wild ducks at the edge of the cattails. And turtles. … There’s a red-winged blackbird.

In my earlier article (Books hung out with), I observed that Pirsig had better relations with inanimate objects than with people. He relates well to nature though, and this is not inanimate. He recalls winter in the marshes.

The blackbirds were gone then. But now in July they’re back and everything is at its alivest and every foot of these sloughs is humming and cricking and buzzing and chirping, a whole community of millions of living things living out their lives in a kind of benign continuum.

Presently he revisits the metaphor.

I have seen these marshes a thousand times, yet each time they’re new. It’s wrong to call them benign. You could just as well call them cruel and senseless, they are all of those things, but the reality of them overwhelms halfway conceptions.

Recovering from a hernia operation, I could lie in bed, reading this, feeling the breeze through the window, seeing the blue sky – and forgetting all of the concrete under the Istanbul sky.

3

Riding out into the countryside from Minneapolis, Pirsig was in the moment, at least for brief snatches: not analyzing it, but just living it. A theme taken up first in Chapter 7 is that we can live in the moment, and in a sense we always do.

All the time we are aware of millions of things around us – these changing shapes, these burning hills, the sound of the engine, the feel of the throttle, each rock and weed and fence post and piece of debris beside the road – aware of these things but not really conscious of them unless there is something unusual or unless they reflect something we are predisposed to see. We could not possibly be conscious of these things and remember all of them because our mind would be so full of useless details we would be unable to think. From all this awareness we must select, and what we select and call consciousness is never the same as the awareness because the process of selection mutates it. We take a handful of sand from the endless landscape of awareness around us and call that handful of sand the world.

Once we have the handful of sand, the world of which we are conscious, a process of discrimination goes to work on it. This is the knife. We divide the sand into parts. This and that. Here and there. Black and white. Now and then. The discrimination is the division of the conscious universe into parts.

We can make this division different ways. An important example comes up in Part II, in Chapter 13.

He avoided splitting the University into fields or departments and dealing with the results of that analysis. He also avoided the traditional split into students, faculty and administration.

Unfortunately the members of my own university’s physics department take the division into departments so seriously that they want physics students to learn their mathematics only from physics courses, and mathematics students to learn their physics only from mathematics courses. I would say in response that members of the physics and mathematics departments ought to be able to teach one another’s subjects, at least at a basic level; but students ought to see the way of thinking of teachers from outside their home department. For Pirsig, and I agree, the important distinction in the university is between the idea and the place where it is realized.

The real University, he said, has no specific location. It owns no property, pays no salaries and receives no material dues. The real University is a state of mind. It is that great heritage of rational thought that has been brought down to us through the centuries and which does not exist at any specific location. It’s a state of mind which is regenerated throughout the centuries by a body of people who traditionally carry the title of professor, but even that title is not part of the real University. The real University is nothing less than the continuing body of reason itself.

In addition to this state of mind, reason, there’s a legal entity which is unfortunately called by the same name but which is quite another thing. This is a nonprofit corporation, a branch of the state with a specific address. It owns property, is capable of paying salaries, of receiving money and of responding to legislative pressures in the process.

But this second university, the legal corporation, cannot teach, does not generate new knowledge or evaluate ideas. It is not the real University at all. It is just a church building, the setting, the location at which conditions have been made favorable for the real church to exist.

Which university do we serve? It is an important question for us in Turkey, where on June 16 of this year (2016) a professor was dismissed from her university for insulting the country’s president in a lecture the previous day. This was at a private university. Mine is public, and so the state has more direct control, though this control may be hobbled by a wish to at least appear to respect laws giving rights to state officers.

Pirsig reminds me that Turkish universities are free of a kind of control that exists in the United States, separately from the state; but this then is a control that may mitigate the evil designs of the state. Having a vendetta against the president of Pirsig’s college in Bozeman, the governor of Montana was cutting funds. In protest of this, Pirsig tried to get the Northwest Regional Accrediting Association to withdraw accreditation. A student told Pirsig that the governor would prevent the loss of accreditation by posting guards. The student had confused a campus with the university itself. It is a confusion often made in Turkey, where there are no accrediting associations in the first place. The government has built lots of buildings in the provinces, and these are called universities; but it is not clear how much of the work of reason is being carried out there. In fact the state itself may be recognizing that this is a problem; but the proposed solution would seem to be to keep salaries low, while awarding bonuses for published papers. This only pushes the need for accreditation onto the journals that publish the papers.

4

To insist on the wrong division of consciousness may be to suffer value rigidity, as Pirsig explains in Part III, in Chapter 26. We pursue things that we assume are valuable: we ought to pause and reconsider how valuable they really are.

Of the value traps, the most widespread and pernicious is value rigidity. This is an inability to revalue what one sees because of commitment to previous values. In motorcycle maintenance, you must rediscover what you do as you go. Rigid values make this impossible.

The typical situation is that the motorcycle doesn’t work. The facts are there but you don’t see them. You’re looking right at them, but they don’t yet have enough value. This is what Phaedrus was talking about. Quality, value, creates the subjects and objects of the world. The facts do not exist until value has created them. If your values are rigid you can’t really learn new facts.

This often shows up in premature diagnosis, when you’re sure you know what the trouble is, and then when it isn’t, you’re stuck. Then you’ve got to find some new clues, but before you can find them you’ve got to clear your head of old opinions. If you’re plagued with value rigidity you can fail to see the real answer even when it’s staring you right in the face because you can’t see the new answer’s importance.

This is what I take away from the book. I never did take a motorcycle out on the road. My uncle talked about letting me use his motorcycle; but he must have figured his sister would never forgive him, if something happened to me; and he would never forgive himself.

I did take a bicycle on the road. I knew how to fix everything that could go wrong with it. At least I thought I could. My ability was perhaps never pushed to the limit. Riding across the mountains of West Virginia along US Route 50, I did fail to recognize the value of a small pain in my leg. Its value was as a sign to take a rest; I ignored this. The small pain turned into a big pain, and this caused me to cut short my trip.

5

These days, I work at fixing things that are more ethereal than a motorcycle or a bicycle: writing and mathematics. An analogy between motorcycles and writing is suggested by one of the reviews quoted in the front matter of the pink Bantam paperback edition of Zen:

This book should live a long life and go through many editions, and it should be properly maintained, and I hope Pirsig tinkers with it …

This is credited only to the Los Angeles Times Calendar. In fact the quotation has always offended me on Pirsig’s behalf. Some authors would rather write a new book than tinker with an old one.

 
Turkish translation of Outlines of a Philosophy of Art, and The Principles of Art

Collingwood was this way. When the Clarendon Press at Oxford gave him the option of editing Outlines of a Philosophy of Art (1925) for a new edition, he preferred to write The Principles of Art (1938). In An Autobiography (1939), he says of Speculum Mentis (1924), It is a bad book in many ways; but then he reads it for the first time since publication, and I … find it much better than I remem­bered. I do revisit my own writing from time to time, and I do tinker with it; but this is blog articles and the like, not published books. I may have some regrets about the language of my older published mathematics articles; but then all I can do is write new articles better.

According to a 2006 interview in the Guardian, Pirsig is disappointed that his books Zen and Lila have not been taken more seriously as philosophy. I take them seriously, though I recognize in them a certain amateurishness. As far as I know, the most professional elaboration of something like Pirsig’s philosophy is to be found in Collingwood. However, he too seems not to be taken seriously by most academic philosophers; at any rate, unlike Pirsig, he is not widely read.

6

The opening sentences of Zen and the Art are a pleasant start to a journey. Mark Richardson alludes to them in opening Zen and Now: On the Trail of Robert Pirsig and the Art of Motorcycle Maintenance (2008):

I can tell from the sign by the bank, without turning my head from the road, that it’s nine thirty in the morning. The sign flashes to show it’s 80 degrees, and the heat’s already coming through my jacket. It’s going to be hot today. That’s okay – on a motorcycle, heat is always welcome.

Pirsig’s opening sentences illustrate what he says in Chapter 16, which is the first in Part III:

Today now I want to take up the first phase of [Phaedrus’s] journey into Quality, the nonmetaphysical phase, and this will be pleasant. It’s nice to start journeys pleasantly, even when you know they won’t end that way. Using his class notes as reference material I want to reconstruct the way in which Quality became a working concept for him in the teaching of rhetoric. His second phase, the metaphysical one, was tenuous and speculative, but this first phase, in which he simply taught rhetoric, was by all accounts solid and pragmatic and probably deserves to be judged on its own merits, independently of the second phase.

Phaedrus is Pirsig’s former self, before he underwent court-ordered electroshock treatment. Pirsig has in fact tinkered with his book to the extent of adding a new introduction, in which he confesses his error of thinking phaedrus in Greek meant wolf. He has also reset the words of Phaedrus in a sans-serif font, to make it clear that Phaedrus comes back to life in the end. In any case, as one learns from Richardson’s book (pp. 187–9), there was no character called Phaedrus in Pirsig’s first draft of Zen. Pirsig just talked about himself as himself. The first person being excessive, Pirsig ditched the manuscript and created Phaedrus.

The real Pirsig had undergone electroshock treatment, but had not actually lost his memory.

7

In Chapter 16 of Zen, Pirsig will go on to describe his classroom experiment of withholding students’ grades. I do not recall just how this struck me, when I read it in high school. However, when I learned about St John’s College, I admired its withholding of grades. Meanwhile, my high school hired a new and enthusiastic physics teacher, who volunteered to teach an after-school AP physics course: it is hard to believe now, but apparently the school had not had such a course before. Many students came to the first meeting of the new course; but they stopped coming when they thought the course would not appear on their transcripts. Ultimately the course did appear on the transcripts of the few of us who remained; but this mattered little to me. I just wanted to learn what I could.

From my late father-in-law’s bookshelf, I recently preserved a copy of the Halliday and Resnick text that our physics teacher was enthusiastic about. In school I did not buy the book; I remember consulting a borrowed copy.

I also remember, from school, our being shown a good film in which two physicists demonstrate the importance of frame of reference. One of them speaks normally into the camera until the other walks up to him and is upside down in relation to him: in fact the first physicist turns out to be hanging from the ceiling. Later the authors try to roll a billiard ball back and forth to one another, but the ball follows a curved path: the table and camera turn out to be mounted on a rotating platform. This is what I have remembered; but I have also assumed that the two physicists were Halliday and Resnick. It turns out they were Hume and Ivey.

I have been amused to find on Amazon a review of Halliday and Resnick by somebody called Notslar who says,

Don’t buy this book. You cannot learn physics from it. Halliday and Resnick’s first edition triggered the current era of ignorant low-skill hacks writing what publishers wanted to sell … These books pretend to be rigorous and focused on concepts. The pretense and tone of au­thor­ity of Halliday and Resnick was their only accomplishment.

Notslar claims the authority of a research physicist and professor for almost three decades. Some such people love to be controversial. I know a mathematician like this, who says, Euclid ruined mathematics by introducing that pernicious axiomatic method. To me this was the creation of mathematics. At least the author of the bizarre opinion does not hide behind a pseudonym.

From reading Halliday and Resnick and other textbooks in high school, I went on to a college with no textbooks as such, and no grades. After St John’s, when I returned to the conventional classroom as a graduate student and a teaching assistant, I had a hard time adjusting to the format, where all students faced the same way. I had to quiz the students and grade their responses, and this bothered me. I am glad that one of the students did respond to my request to know what they thought about grades. He said he appreciated grades, because they let you know how you were doing in a course.

I do not recall how that boy turned out as a student. What Pirsig found among his own students was,

the brighter, more serious students were the least desirous of grades, possibly because they were more interested in the subject matter of the course, whereas the dull or lazy students were the most desirous of grades, possibly because grades told them if they were getting by.

Pirsig’s explanation is inadequate. An aspect of brightness is being able to assess one’s own performance. An aspect of weakness is not understanding how one is doing, or even overestimating it: this is not laziness, but ignorance. It is only the bright student who can afford to be lazy about grades, since she already knows that hers will be good.

8

Apparently there is a name for overestimating your abilities: the Dunning–Kruger Effect. It is so called, because Dunning and Kruger experimentally observed this phenomenon in 1999. Here I quote Wikipedia as of June 19, 2016.

I have issues with the use, in psychology, of the terminology of physical science. A phenomenon is an appearance: something objective, like a sunrise. The Greek source of our noun is a passive participle of the verb phainô, which means to make visible or to shine. (Despite the similar appearance and meaning, the adjective phaidros shining, which is the original source of Phaedrus’s name, is traced to a different proto-Indo-European root in Beekes’s Etymological Dictionary of Greek of 2010).

Collingwood has a fine account of what is objective, in the Preface of Speculum Mentis:

I may here call attention to one or two words which, though I think my use of them is natural and correct, may be a stumbling-block to others besides the malicious. When I call a thing subjective I mean that it is or pertains to a subject or conscious mind. When I call it objective, I mean that it is or pertains to an object of which a mind is conscious. I do not call a real rose objective and an imaginary one subjective, or the rose objective and its color subjective, or the molecules in it objective and the beauty of it subjective. A real rose I call real, and an imaginary rose I call imaginary; and I call them both objective because they are the objects of a perceiving and an imagining mind respectively. Similarly, the molecules are objective to a scientist and the beauty to an artist.

A sunrise being objective, I can write down its times on a succession of days at my flat. You could do the same thing wherever you are, and we could compare notes. With superficial similarity, we could also write down individual self-evaluations. These being subjective, how to compare them would not be so clear.

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In Chapter 19 of Zen, Pirsig recalls how Phaedrus was faced with the question of whether Quality was subjective or objective. This was a dilemma. After several pages,

Phaedrus, following a path that to his knowledge had never been taken before in the history of Western thought, went straight between the horns of the subjectivity-objectivity dilemma and said Quality is neither a part of mind, nor is it a part of matter. It is a third entity which is independent of the two …

Pirsig may be factually correct here about what his former self thought. To his knowledge, he was taking a new path; but his knowledge was poor. I think Collingwood and others were on that path, if only in reaction to the positivism that said the objective was the only reality. No, said Collingwood, the subjectivity of the observer is just as real.

Pirsig himself continues, two pages later:

I don’t know how much thought passed before he arrived at this, but eventually he saw that Quality couldn’t be independently related with either the subject or the object but could be found only in the relationship of the two with each other. It is the point at which subject and object meet.

That sounded warm.

Quality is not a thing. It is an event.

Warmer.

It is the event at which the subject becomes aware of the object.

And because without objects there can be no subject – because the objects create the subject’s awareness of himself – Quality is the event at which awareness of both subjects and objects is made possible.

Hot.

Now he knew it was coming.

This means Quality is not just the result of a collision between subject and object. The very existence of subject and object themselves is deduced from the Quality event. The Quality event is the cause of the subjects and objects, which are then mistakenly presumed to be the cause of the Quality!

Now he had that whole damned evil dilemma by the throat. The dilemma all the time had this unseen vile presumption in it, for which there was no logical justification, that Quality was the effect of subjects and objects. It was not! He brought out his knife.

The sun of quality, he wrote, does not revolve around the subjects and objects of our existence. It does not just passively illuminate them. It is not subordinate to them in any way. It has created them. They are subordinate to it!

If Phaedrus was the prophet of the sun of Quality, Pirsig’s choice of name for him was fortuitous. But Collingwood was already there before Phaedrus was born. In his first book, Religion and Philosophy (1916), Collingwood wrote:

When a man makes a statement about the nature of God (or anything else) he is interested, not in the fact that he is making that statement, but in the belief, or hope, or fancy that it is true. If then the psychologist merely makes a note of the statement and declines to join in the question whether it is true, he is cutting himself off from any kind of real sympathy or participation in the very thing he is studying – this man’s mental life and experiences. To take an example, a certain mystic says, God is a circle whose centre is everywhere and whose circumference is nowhere. The psychologist, instead of answering, Of course, or, Really? or, I don’t quite see what you mean, replies, That is an example of what I call the Religious Paradox.

Collingwood adds a footnote here: This instance is not imaginary. I have not been able to find the referent. Apparently Josiah Royce defined a religious paradox, but this is that a divine revelation can be recognized as authentic only by somebody who has already seen God. One of my St John’s classmates was supposed to resolve this paradox when a tutor asked her, How do you know when God is talking to you? The friend’s response may have been, Well, He may speak to you, but He doesn’t speak to me!

Collingwood continues in Religion and Philosophy with a sentence that he quotes in An Autobiography:

The mind, regarded in this external way, really ceases to be a mind at all. To study a man’s consciousness without studying the thing of which he is conscious is not knowledge of anything, but barren and trifling abstraction. It cannot answer ultimate questions, because it has renounced the attempt; it cannot enter into the life it studies, because it refuses to look with it eye to eye; and it is left with the cold unreality of thought which is the thought of nothing, action with no purpose, and fact with no meaning.

10

It may be convenient to label as the Dunning–Kruger Effect such examples as a satirical opinion piece in The Onion: Dispatches from the Tenth Circle (2001), called I bet I can speak Spanish (originally published September 16, 1999):

Hello, amigos! ¡El soy quando agunto! ¡Ella balloona balunga espanyo!

Did that sound Spanish to you? I bet that means something. And guess what? I’ve never had one lesson! It’s just that I have a natural gift for Spanish. I was able to pick it up all by myself, outside the system, if you will.

We know people who think they are smarter than they are. Sometimes they are comic, sometimes tragic. Since 1999, we have been able to diagnose them with the Dunning–Kruger Effect.

Some time before 1999, I came to regret a failure to recognize an instance of what would become the Dunning–Kruger Effect. Between St John’s and graduate school, in 1987–8, I tutored some students at my old high school. I met one of them at his house, and he put on some music. I questioned the wisdom of this. The boy said music helped him study though; and since I also liked the music itself (it was Neil Young), I let it go. This was a mistake. If this boy had been able to judge when he was studying well, he would not be failing his course.

11

While in high school myself, I had happened to see the exercise sheet of a student at another school. The exercises required balancing chemical reactions, which meant supplying the missing coefficients in expressions like

_CH₄ + _O₂ → _CO₂ + _H₂O.

This means solving the “equation”

x CH₄ + y O₂ → z CO₂ + t H₂O,

and this means solving the linear system

here there is an equation for each chemical element in the reaction.

On the student’s worksheet that I saw, the answers were all wrong. I was appalled. Perhaps finding answers is a challenge; but checking whether they are correct should be easy. It is therefore hard to imagine that the student suffered from the Dunning–Kruger Effect to the extent of believing her answers correct.

More likely, the student did not care whether her answers were correct. I accepted equation-balancing as a puzzle; but not everybody can be amused by such puzzles.

12

Lack of care is a theme of Pirsig. In Chapter 2 he shows why he had to learn motorcycle maintenance for himself. Professionals damaged his motorcycle, without ever being able to discover why the engine seized, because they did not care to do a good job.

While at work I was thinking about this same lack of care in the digital computer manuals I was editing. Writing and editing technical manuals is what I do for a living the other eleven months of the year and I knew they were full of errors, ambiguities, omissions and information so completely screwed up you had to read them six times to make any sense out of them. But what struck me for the first time was the agreement of these manuals with the spectator attitude I had seen in the shop. These were spectator manuals. It was built into the format of them. Implicit in every line is the idea that Here is the machine, isolated in time and in space from everything else in the universe. It has no relationship to you, you have no relationship to it, other than to turn certain switches, maintain voltage levels, check for error conditions … and so on. That’s it. The mechanics in their attitude toward the machine were really taking no different attitude from the manual’s toward the machine, or from the attitude I had when I brought it in there. We were all spectators.

Students are spectators when they come into class as if it were a cinema. They watch what the teacher does at the board. Maybe they write it down; or maybe they just photograph it with their mobiles. Or they may check their mobiles for messages from their friends, in which case they are not even spectators. Pirsig continues:

And it occurred to me there is no manual that deals with the real business of motorcycle maintenance, the most important aspect of all. Caring about what you are doing is considered either unimportant or taken for granted.

Of course there is no manual for caring. There might be a manual for how to fake caring; but only a psychopath would have a use for it.

13

I imagine that most poor students easily convince themselves that they have done enough work for one study session, so that they can spend the rest of their time as they please. But then they will have to face their examination results or report cards, to see if their earlier opinions will have held up.

Pirsig suggests that a student might need to learn from the school of hard knocks before having the motivation to study in a course without grades. A problem with requiring this motivation is that we learn some things better when we are young, but when we are young, we lack the experience to know what is worth learning. We may then need to trust our teachers. In this case, we teachers must make ourselves trustworthy.

Richard Rodriguez describes education as

a nurturing never natural to the person one was before one entered a classroom.

Education in the United States had been particularly wrenching for Rodriguez, who was the son of Mexican immigrants with no interest in reading. I take the quotation from David Bartholomae and Anthony Petrosky, Ways of Reading: An Anthology for Writers (5th ed., 1999), which I bought because of the enthusiasm of a Johnnie who was reading it in a writing class.

Education had wrenched me like Rodriguez; at least it wrenched me from my neighborhood. All of my friends there continued to attend the public schools of Alexandria, Virginia; but since those schools were found to be intellectually inadequate for me, I was sent to St Albans School for Boys in Washington. A neighborhood friend said I became a snob afterwards. I knew that my new school put me in a different world. When I was there, I imagined a battle between the boys there and the children I knew at home. I was not sure which side to root for.

When the time came, St Albans did not root for me to go off to St John’s College. It is amusing now to learn that the new president of the College, Mark Roosevelt, is a St Albans alumnus.

As for the anthology in which I read Rodriguez, I do not recall specifically why I bought it, because I do not recall being specifically interested in my own writing at the time. I had not moved to Turkey yet. After moving here, I wrote emails about life in the country; but it took me a while to realize that these emails might be worth saving and perhaps reworking. I especially regret not having kept an email I wrote in 2001 about an early spring trip with Ayşe and her parents to İznik (the ancient Nicaea) and then Ayvalık.

14

Students ought to be able to judge their own work. In mathematics especially, they can do this. One can always make a mistake; but the standards in mathematics are universal, and one ought to be able to train oneself to meet them. Writing is different. The best way I can assess my own writing is to read it again after I have forgotten writing it. So I should like to know more about Pirsig’s rhetoric class.

Students were submitting their writing to the teacher, who secretly recorded grades. This made the students nervous, but they got over it.

The phenomenon of relaxation and friendliness was explained later by a couple of students who told him, A lot of us got together outside of class to try to figure out how to beat this system. Everyone decided the best way was just to figure you were going to fail and then go ahead and do what you could anyway. Then you start to relax. Otherwise you go out of your mind!

Why did not the students try assessing one another’s work? Why did not Pirsig encourage them to do this? He had them do it once, with two student essays; why did he not make this happen all the time? Perhaps he was too much the lone wolf that he describes himself as being. He understood learning from nature, or learning from motorcycles, or learning from his own solitary experience; but not learning directly from other persons.

Pirsig had been inspired to withhold grades by thinking about students who had nothing to say. A student wanted to write about the United States, but did not know what. Pirsig suggested narrowing the scope, but the girl still could not think of anything to say until Pirsig had her describe the front of the opera house of Bozeman.

I sat in the hamburger stand across the street, she said, and started writing about the first brick, and the second brick, and then by the third brick it all started to come and I couldn’t stop. They thought I was crazy, and they kept kidding me, but here it all is. I don’t understand it.

Neither did he, but on long walks through the streets of town he thought about it and concluded she was evidently stopped with the same kind of blockage that had paralyzed him on his first day of teaching. She was blocked because she was trying to repeat, in her writing, things she had already heard, just as on the first day he had tried to repeat things he had already decided to say. She couldn’t think of anything to write about Bozeman because she couldn’t recall anything she had heard worth repeating. She was strangely unaware that she could look and see freshly for herself, as she wrote, without primary regard for what had been said before. The narrowing down to one brick destroyed the blockage because it was so obvious she had to do some original and direct seeing.

I can well imagine that an assignment to write about a brick can be readily satisfied. I am dubious of Pirsig’s diagnosis of why an attempt to write about the United States would fail. Was the student really trying to imitate?

He experimented further. In one class he had everyone write all hour about the back of his thumb. Everyone gave him funny looks at the beginning of the hour, but everyone did it, and there wasn’t a single complaint about nothing to say.

In another class he changed the subject from the thumb to a coin, and got a full hour’s writing from every student. In other classes it was the same. Some asked, Do you have to write about both sides? Once they got into the idea of seeing directly for themselves they also saw there was no limit to the amount they could say. It was a confidence-building assignment too, because what they wrote, even though seemingly trivial, was nevertheless their own thing, not a mimicking of someone else’s. Classes where he used that coin exercise were always less balky and more interested.

As a result of his experiments he concluded that imitation was a real evil that had to be broken before real rhetoric teaching could begin. This imitation seemed to be an external compulsion. Little children didn’t have it. It seemed to come later on, possibly as a result of school itself.

That sounded right, and the more he thought about it the more right it sounded. Schools teach you to imitate. If you don’t imitate what the teacher wants you get a bad grade. Here, in college, it was more sophisticated, of course; you were supposed to imitate the teacher in such a way as to convince the teacher you were not imitating, but taking the essence of the instruction and going ahead with it on your own. That got you A’s. Originality on the other hand could get you anything – from A to F. The whole grading system cautioned against it.

He discussed this with a professor of psychology who lived next door to him, an extremely imaginative teacher, who said, Right. Eliminate the whole degree-and-grading system and then you’ll get real education.

I want to say, first of all, that of course originality can get you anything. If something is really new, there is no telling whether it is going to be good or bad.

Perhaps the most a teacher can ask of students is that they learn what is already known to be good. Are the students then imitating? Not if they have recognized for themselves what is good. As Pirsig’s epigraph from Plato’s Phaedrus says,

And what is good, Phaedrus,
And what is not good –
Need we ask anyone to tell us these things?

The answer to Socrates’s question is ultimately No; but we may ask what others think is good, and we may find that we agree.

15

At the time of writing, Pirsig had raised two children; I have raised none. But it seems to me that little children are imitators par excellence. They may have a lot going on inside themselves, but they need a technique, a language, for getting it out, and they learn this language by imitating people around them.

We have a problem in mathematics courses when students want only to imitate: when they want exam problems to be just like homework exercises, or even exactly the same. We teachers want the students to be able to handle new problems.

We may supply the tools to be used in handling the new problems. The students may baulk at using those tools. Here is what I mean.

For some years I have tried to develop a set theory course in which students could really learn something. I started out using the course to develop some of my own ideas about the foundations of mathematics. When it transpired that most students could not get fired up about foundations, I tried to make the course more computational. I taught the arithmetic of Cantor normal forms of ordinal numbers. There are a few rules for manipulating these normal forms, and with these rules, one should be able to solve every problem.

On a recent exam, I allowed students to use cheat sheets. What the students turned out to have written on their cheat sheets was not the general rules just mentioned, but the answers to specific problems from previous exams. Evidently the abstraction of the general rules had been too great a barrier for them.

I still do not understand why this should be so. My current hypothesis is that the students expend minimum effort, because their courses cost them no money, and foolish politicians have allowed students to take courses again and again until they pass. Students try to take as many courses as possible, all at once, just in case they get lucky and manage to pass some of them. Also, their parents, like Rodriguez’s parents, may not have attended university and may not have learned that their studying needs solitude and quiet.

I asked my set-theory students to able to prove identities of ordinal arithmetic using transfinite induction. Such proofs frequently use the notion of a normal function, which corresponds to a continuous function in calculus. There is a theorem about normal functions corresponding to the rule of calculus that, for continuous functions f,

if lim_n→∞ a_n = a, then lim_n→∞ f (a_n) = f (a).

Students should have enough practice that they know this theorem automatically, the way they would know the knight’s move in chess.

If you were going to play in a chess tournament, you would not take along a rule book; you would have learned to apply the rules without thinking. Instead of learning our theorem of normal functions though, students wrote it out verbatim on their cheat-sheets; but they could not apply it properly.

16

In Chapter 12, Pirsig described relations with his former university colleague:

Another time Phaedrus was upset about some failing students. Walking home with DeWeese under some trees he had commented on it and DeWeese had wondered why he took it so personally.

I’ve wondered too, Phaedrus had said, and in a puzzled voice had added, I think maybe it’s because every teacher tends to grade up students who resemble him the most. If your own writing shows neat penmanship you regard that more important in a student than if it doesn’t. If you use big words you’re going to like students who write with big words.

Sure. What’s wrong with that? DeWeese had said.

Well, there’s something whacky here, Phaedrus had said, because the students I like the most, the ones I really feel a sense of identity with, are all failing!

DeWeese had completely broken up with laughter at this and left Phaedrus feeling miffed. He had seen it as a kind of scientific phenomenon that might offer clues leading to new understanding, and DeWeese had just laughed.

At first he thought DeWeese was just laughing at his unintended insult to himself. But that didn’t fit because DeWeese wasn’t a derogatory kind of person at all. Later he saw it was a kind of supertruth laugh. The best students always are flunking. Every good teacher knows that. It was a kind of laughter that destroys tensions produced by impossible situations and Phaedrus could have used some of it because at this time he was taking things way too seriously.

It may well be that a writing teacher, or perhaps a psychology teacher, will grade up the students who seem to have the same way of thinking as the teacher. This should not make sense in mathematics. I like my students; but likability and demonstrated mathematical ability are two different things.

17

I said there was no manual for caring. There is no manual for enthusiasm either, although Pirsig tries to create one with his book. He explains in Chapter 26:

I like the word gumption because it’s so homely and so forlorn and so out of style it looks as if it needs a friend and isn’t likely to reject anyone who comes along. It’s an old Scottish word, once used a lot by pioneers, but which, like kin, seems to have all but dropped out of use. I like it also because it describes exactly what happens to someone who connects with Quality. He gets filled with gumption.

The Greeks called it enthousiasmos, the root of enthusiasm. which means literally filled with theos, or God, or Quality. See how that fits?

A person filled with gumption doesn’t sit around dissipating and stewing about things. He’s at the front of the train of his own awareness, watching to see what’s up the track and meeting it when it comes. That’s gumption.

Pirsig jokes about creating a college course: Gumptionology 101 – An examination of affective, cognitive and psychomotor blocks in the perception of Quality relationships. Me, I hope only that our students can learn the existence of what Einstein calls the temple of science. Some come to the temple as if to a chessboard, to show off their skills. Others just want to make use of science. But then there are still others.

What has brought them to the temple [Einstein said] … no single answer will cover … escape from everyday life, with its painful crudity and hopeless dreariness, from the fetters of one’s own shifting desires. A finely tempered nature longs to escape from his noisy cramped surroundings into the silence of the high mountains where the eye ranges freely through the still pure air and fondly traces out the restful contours apparently built for eternity.

From the Niesen, Bern, Switzerland, July 5, 2008,
during Logic Colloquium 2008

Pirsig quotes Einstein in Chapter 10. It may be that the system has drilled into our students the idea that their scores on the national university entrance exam determine who they are. By this measure, our students are dummies, fit only to study mathematics.

The prime power staircase, approxi­mating a straight line;
under the Riemann Hypothesis, the ap­prox­i­ma­tion is very good

In high school, our students have not actually seen mathematics. I can only try to offer them a breath of the still pure air of its high mountains.