Teachers: preachers, propagandists, gurus

Gian-Carlo Rota, “Ten Lessons I Wished I Had Learned Before I Started Teaching Differential Equations,” an address to the Mathematical Association of America at Simmons College on April 24, 1997:

Who cares whether the students become skilled at working out tricky problems? What matters is their getting a feeling for the importance of the subject, their coming out of the course with the conviction of the inevitability of differential equations, and with enhanced faith in the power of mathematics. These objectives are better achieved by stretching the students’ minds to the utmost limits of cultural breadth of which they are capable, and by pitching the material at a level that is just a little higher than they can reach.

We are kidding ourselves if we believe that the purpose of undergraduate teaching is the transmission of information. Information is an accidental feature of an elementary course in differential equations; such information can nowadays be gotten in much better ways than sitting in a classroom. A teacher of undergraduate courses belongs in a class with P.R. men, with entertainers, with propagandists, with preachers, with magicians, with gurus. Such a teacher will be successful if at the end of the course every one of his or her students feels they have taken “a good course,” even though they may not quite be able to pin down anything specific they have learned in the course.

The work of reason produces monsters

Poincaré, “Mathematical definitions and education,” 1906, in Science and Method, translated by Francis Maitland:

Logic sometimes breeds monsters. For half a century there has been springing up a host of weird functions, which seem to strive to have as little resemblance as possible to honest functions that are of some use. No more continuity, or else continuity but no derivatives, etc. More than this, from the point of view of logic, it is these strange functions that are the most general; those that are met without being looked for no longer appear as more than a particular case, and they have only quite a little corner left them.

Cf. Goya’s El sueño de la razón produce monstruoscirca 1799:

Drift and mastery

Horace Traubel’s review of Walter Lippman’s Drift and Mastery, in The Conservator, October 1914:

Lippmann dont quite approve the vagaries of people who love in spite of love. He dont quite agree to having us as ignorantly loyal as we are knowingly courageous. He rather wants us to always understand what we’re about. But sometimes when I’m about the best things I know nothing. And other times when I’m about the worst things I know much. I say for all in all: Dont drift. And I say for all in all: Do master. But then I add a qualifying imbecility. Drift all you must. Master all you can. Master all you must. Drift all you can. I want to be in the stream. I want the big stream to be in me. I want to take account of everything. I want everything to take account of me. I want life so orbic I can put my arms about it in an embrace of revelation. Yet I also want life so atmospherically liberated I couldn’t include it in any finite definitions. I dont want any man or woman to be all hashed up into meaningless inconsecutiveness. Neither do I want any man or woman tied into an all-consistent knot. I want reason. But I dont want too much logic. I want order. But I dont want too much system. Lippmann says: “To own things in common is one of the most educating experiences in the world.” I say so too. I also say: To be something in common is to inherit the earth.

Facts, coy and elusive

Mencken, “Conrad Revisited,” The Smart Set, September 1922:

I put in a blue afternoon last week re-reading Conrad’s “Youth.” A blue afternoon? What nonsense! The touch of the man is like the touch of Schubert. One approaches him in various and unhappy moods: depressed, dubious, despairing; one leaves him in the clear, yellow sunshine that Nietzsche found in Bizet’s music. But here again the phrase is inept. Sunshine suggests the imbecile, barnyard joy of the human kohlrabi—the official optimism of a steadily delighted and increasingly insane Republic. What the enigmatical Pole has to offer is something quite different. If it’s parallel is to be found in music, it is not in Schubert, but in Beethoven—perhaps even more accurately in Johann Sebastian Bach. It is the joy, not of mere satisfaction, but of understanding—the profound but surely not merry delight which goes with the comprehension of a fundamental fact—above all, of a fact that has been coy and elusive.

Inevitably irritated into writing it

The preface to T. E. Hulme’s posthumously published collection of meditations on language and philosophy, “Cinders”:

The history of philosophers we know, but who will write the history of the philosophic amateurs and readers? Who will tell us of the circulation of Descartes, who read the book and who understood it? Or do philosophers, like the mythical people on the island, take in each other’s washing? For I take it, a man who understands philosophy is inevitably irritated into writing it. The few who have learnt the jargon must repay themselves by employing it. A new philosophy is not like a new religion, a thing to be merely thankful for and accepted mutely by the faithful. It is more of the nature of food thrown to the lions; the pleasure lies in the fact that it can be devoured. It is food for the critics, and all readers of philosophy, I suppose, are critics, and not faithful ones waiting for the new gospel.

With this preface I offer my new kind of food to tickle the palate of the connoisseurs.

Only a little dirtied

Readers may be divided into four classes.

1. Sponges, who absorb all they read, and return it nearly in the same state, only a little dirtied.

2. Sand-glasses, who retain nothing, and are content to get through a book for the sake of getting through the time.

3. Strain-bags, who retain merely the dregs of what they read.

4. Mogul diamonds, equally rare and valuable, who profit by what they read, and enable others to profit by it also.

—Coleridge, opening of Lecture II of Lectures and Notes on Shakespeare and Other Poets

You are not helpful!

I think that your fault in a discussion is this: YOU ARE NOT HELPFUL! I am like a man inviting you to tea in my room, but my room is hardly furnished; one has to sit on boxes, and the teacups stand on the floor, and the cups have no handles, etc., etc. I hustle about fetching anything I can think of to make it possible that we should have tea together. You stand there with a sulky face, say that you can’t sit down on a box and can’t hold a cup without a handle, and generally make things difficult. At least that’s how it seems to me.

—Wittgenstein to Sraffa, January 1, 1934

I have heard of Krakens

Melville to Hawthorne, November 1851:

Lord, when shall we be done growing? As long as we have anything more to do, we have done nothing. So, now, let us add Moby Dick to our blessing, and step from that. Leviathan is not the biggest fish; — I have heard of Krakens.

A drawing by British naturalist William Evans Hoyle, 1886:

Thought in the pure enjoyment of itself

Marilynne Robinson on the humanities, The New York Review of Books, November 2017:

I have been reading lately about the rise of humanism in Europe. The old scholars often described themselves as “ravished” by one of the books newly made available to them by the press, perhaps also by translation. Their lives were usually short, never comfortable. I think about what it would have been like to read by the light of an oil lamp, to write with a goose quill. It used to seem to me that an unimaginable self-discipline must account for their meticulous learnedness. I assumed that the rigors and austerities of their early training had made their discomforts too familiar to be noticed. Now increasingly I think they were held to their work by a degree of fascination, of sober delight, that we can no longer imagine.

• • •

Then how to recover the animating spirit of humanism? For one thing, it would help if we reclaimed, or simply borrowed, conceptual language that would allow us to acknowledge that some things are so brilliant they can only be understood as virtuosic acts of mind, thought in the pure enjoyment of itself, whether in making a poem or a scientific discovery, or just learning something it feels unaccountably good to know. There is an unworldliness in the experience, and in what it yields, that requires a larger understanding than our terse vocabularies of behavior and reward can capture. I have had students tell me that they had never heard the word “beautiful” applied to a piece of prose until they came to us at the workshop. Literature had been made a kind of data to illustrate, supposedly, some graceless theory that stood apart from it, and that would be shed in a year or two and replaced by something post- or neo- and in any case as gracelessly irrelevant to a work of language as whatever it displaced. I think this phenomenon is an effect of the utilitarian hostility to the humanities and to art, an attempt to repackage them, to give them some appearance of respectability. And yet, the beautiful persists, and so do eloquence and depth of thought, and they belong to all of us because they are the most pregnant evidence we can have of what is possible in us.