The Bright Angelic Mills

Volume 9 Number 8
December 1985

from The Underground Grammarian, Box 203, Glassboro, New Jersey 08028

"In a world where wands are waved over uniform produce codes in supermarkets and where kids have personal computers--just why are we spending billions to teach arithmetic in schools?"
Anthony Oettinger

"Wise men say, Callicles, that heaven and earth, gods and men, are held together by the principles of sharing, by friendship and order, by self-control and justice; that, my friend, is the reason they call the universe `kosmos,' which is to say `order,' and not disorder or licentiousness. Clever though you are, you seem not to have paid enough attention to these matters; it has, in fact, escaped you what a mighty power is exercised, both among men and gods, by geometrical equality. And it is your neglect of geometry which brings about your opinion that one should strive for a larger share than that which other men possess."

That Oettinger fellow also asks, "Exactly what is the meaning of penmanship when keyboard skills are becoming more important?" We are abashed. For all the attention and thought we have given to reading and writing, we do have to admit that we have never elucidated the "meaning" of penmanship.

Oettinger is just as expert in history as he is in the art of writing. "In 1100," he tells us, "educated people talked, only menials like clerics wrote. So the snobbery of writing only began around 1300. Before that snobs only spoke." So there.

But that Oettinger fellow is not, as you probably suspect, a taxidriver in Hoboken. We have the word from the Kitchener-Waterloo Record that he is a teacher of "applied mathematics" at Harvard, and a consultant to Ronald Reagan's Foreigh Intelligence Advisory Group of the U. S. Defense Communications Agency. That tells us a lot about the state of our Republic, in which menials like clerics have been made obsolete and replaced by menials like consultants. And his words, along with many others such, were spoken--not penned--to a conference put on by the Canadian Institute for Research on Public Policy.

It is, of course, unlikely that we would be able to explain anything at all to a mind that equates writing with penmanship, thus easing enormously the work of literary criticism by making it possible to prove conclusively that Flaubert, for instance, was by far the very worst writer of his time. There is no hope of rational discourse with a man who holds that the "modern workplace" no longer needs "the people who could write and do arithmetic" in the "dark satanic mills and the Dickensian counting houses," and that even "keyboard skills" will prove dispensable once the computers have learned to understand and produce speech, like the snobs of yesteryear. While Socrates would at least give it a try, we know not how to seek the betterment of the Oettingers of this age, and we have to leave them to that work for which they find themselves best suited, the making of public policy for the rest of us.

Callicles, the principal adversary in Gorgias, was at least amenable to rational discourse and aware of the need to define his terms, although certainly neglectful of geometry. But even he, to say nothing of Socrates, would have been astounded by the proposition that the purpose of learning arithmetic is to be discovered in the bright angelic mills of the modern supermarket, where anyone who can wave a wand finds himself free from the need to cipher.

It is true that those who have learned arithmetic can, usually, calculate; but the idea that we should learn arithmetic in order to calculate is one of the many convenient notions of the schoolers, who will surely be delighted to hear from Oettinger that they will soon be relieved, by pocket wands, we suppose, of the tiresome work of teaching little children to balance their checkbooks.

To those who can not understand mathematics--to say nothing of reading and writing--as anything more than "life skills," Socrates' mild rebuke of Callicles must prove mystifying indeed. For Socrates, and even for Callicles, although he didn't like to think about it, the study of mathematics was nothing less than the soul's discovery of order and proportion, of permanent and essential relationships, of rightness. And the idea of Rightness revealed in mathematics provides understanding of the idea of Justice among men.

It was out of just such an understanding that the poet deemed Euclid alone the beholder of Beauty bare. Socrates would have nodded approval. And it was for his desire to live "out of proportion" that Callicles was rebuked. He was, as it were, an angle of the great polygon who supposed that he could gobble up more than his natural share of degrees without twisting the whole thing out of shape, or, even worse, without caring that he would twist it out of shape.

That such an ancient understanding of the study of mathematics should seem to us at least unusual, if not downright quirky, is, of course, the result of our schooling, and likewise a measure of the shallowness of our education. The schoolers like to think of themselves as "humanists." They suppose that the study of mathematics--and of the hard sciences as well--is in some unspecifiable but nevertheless real way--an inhuman enterprise, and not noticeably conducive to feelings of tolerance and kindness, and the burning desire to feed those of the hungry who happen to be very far away.

There is also the unhappy fact that mathematics, unlike relating to self and others, is both hard to teach and, for those education majors who might be expected to teach it, hard to learn. Ditto for chemistry and physics, of which Socrates, had he studied them, would have some interesting things to say, and that entirely without regard to the daily work of the chemist or the physicist.

Thus the educationists find themselves in a pickle. On the one hand, they choose to see mathematics as a life-skill most particularly useful in the modern workplace, and thus feel obliged to teach it as essential to their great mission, the production of employable workers who might some day be able to compete with the Japanese. On the other, they find the teaching of inhumane subjects a galling diversion from their even greater mission, the inculcation of "right feelings." And so it is that they have sold us on the idea of minimum competence in subjects like mathematics, by which they mean just enough study for the needs of the modern workplace, but not enough to bring on the suspicion that Goodness, Truth, and Beauty are to be discerned not by the feelings but by the intellect.

From this dilemma, Anthony Oettinger will deliver them, and, noble fellow that he seems to be, at no small cost to himself. What work will there be for a teacher of applied mathematics when no one has to apply mathematics any more? His loss, however, will be the schoolers' gain. Those who used to struggle with the teaching of writing will be able to justify the much easier task of teaching basic minimum keyboard skills, and, to replace the few and rapidly disappearing teachers of mathematics, the gym-teachers will stand forth as providers, even to tiny tykes, of just enough dexterity out of which to waive a wand over a checkout counter or a checkbook. It's all in the wrist.

Things equal to the same thing, we seem to recall from somewhere, are equal to each other. Makes sense.

And that, of course, is another way to understand the worth of all sorts of studies not just now popular. Mathematics makes sense, and it makes sense happen in anyone who contemplates it. Wand waving does not make sense happen in the waiver; it merely works. It is interesting that the latter is called progress in the world, and the former, nothing more than betterment in a person.

From v 9 n 8 (Dec 1985)

The Underground Grammarian is published by Richard Mitchell, Glassboro, New Jersey 08028