Again: how was it managed? The paperboy’s paper is dispensed with. It becomes a point; its flight, a line. That curve itself is seen to be a row of dots, or so we might conceive a string of pearls if we were mathematically inclined. Next, each dot is said to represent the top of a slat, a vertical fixed like a post in the plane of the paperboy’s feet. A picket fence, in short, has unfolded from his throw. If you prefer: it’s a Venetian blind on its side, on edge. But no, the tip of each post is the elbow of an angle, the corner of that old friend, area, again, and thus this simple little daily act is actually, in our new poetry and picture book, exactly like a perfect fan of cards. Plato’s intuition has been confirmed: the world we know and swim in is everywhere it flows a qualitative expression of serene, unchanging quantitative laws. The ambiquity of “point” makes many of these verses possible. Who knows? it may be the peak of a witch’s cap, the climax of the geometer’s cone. Point: it is truly a word to wonder at, this minute mark like a prick, this place in space less large than a hair’s end or the sound of a silent clock, this piercing part and particular of discourse, this dimensionless speck which has been spelled, alone in English, sixteen different ways already—should we not salute it?
So yonder man is carried to prison. Shakespeare measures matters in quite another way. This sort of sexuality is seen as poaching … poaching in a peculiar river. The term is technical, and requires that we feel for the fish with our hands beneath an overhanging bank. “Fish must be grop’t for, and be tickled too,” Bunyan writes. When Hamlet tells Horatio how
Up from my cabin,
My sea-gown scarf’d about me, in the dark
Groped I to find them …
he is using “groped” less precisely, more generally, than in this passage from Measure for Measure. Tickling is apparently essential to it, for Maria awaits Malvolio, whom she plans to dupe, with the words: “… here comes the trout that must be caught with tickling.” And what was thought as peculiar then was, in particular, private property.
For instance.
We hate to think that through much of our life we window-shop and rarely purchase. Therefore, I suppose, it does dismay us to discover that of all the time we spend on sex—in thought, dreams, deed, in word, desire, or feeling—there is so little spending done to show for it that nothing’s bought. Yet notice how predictably I’ve put it. I should be ashamed. First I spoke of spending time, and then I spoke of sperm—our sacred future—in the same way. Well, time is money, don’t we say? and maybe our seeds are simply many pennies. Both, at least, are quantities—methods of accounting, blueprints, masterplots—and perhaps Protagoras really meant to tell us that man is the measurer of all things, not merely the measure, for I honestly believe it is his principal concern.
Certainly man will seem, in impoverished circumstances, to be interested only in getting himself fed, and of course if he feeds he will belch and break wind, he will wipe his behind with leaves, he will stopper his heart, allow his belly to rust, his skin to scale, and eventually he will inflate his bladder to embarrassment; but we cannot accurately measure man’s nature in terms of what he must do (he must breathe, for example—all of us manage—yet few of us take much pleasure or even an interest in it); no, we have to observe him in the latitudes; in just those moments when the world unpins his shoulders from the mat; moments in which, if we were speaking of clocks, we would sense a wobble in the works. And if we think it’s satisfaction that man wants, a simple easing of his needs like the release of stool or the fall of pants, remark how he collects in order to arrange (shells, coins, stamps); overeats to set a standard (ice cream, clams, corn, pie, cake, melons for a prize); makes rules as rapidly as clubs; commits to memory even fractional statistics, decimal notations (how fast six furlongs has been run, what Willie Mays is batting, what the market’s done); turns the simplest “good day” into a social rite as empty, bored, and automatic as prayer or genuflection, any sign of the cross; passes laws and calls them measures; lays out all the acres of his days in stingy tracts with the ruthless greed of a plot developer. He arranges everything he hears, feels, sees, in decorous ranks like pallbearers beside him, and says he’s “informing” his visual field. He lives a lot like a pin in a map—he calls it “growing up”—and there he indicates the drains. No, he does not copulate, he counts; he does not simply laugh or sneer or shout, he patiently explains. Regardless of the man or woman whom he mounts, throughout his wildest daydreams and even in the most persistent myths of his pornography, he will imagine in amounts. As our poet warns us, in the following boast:
Some glory in their birth, some in their skill,
Some in their wealth, some in their body’s force;
Some in their garments, though new-fangled ill;
Some in their hawks and hounds, some in their horse;
And every humour hath his adjunct pleasure,
Wherein it finds a joy above the rest:
But these particulars are not my measure …
Some writers are worthwhile, even if the other virtues they possess are invisible, because, like cooling soup, all the scum is on the surface.
What does De Sade do, for example? He measures his thing; he organizes orgies; he makes change; he not only contrives novel entanglements, he classifies them, tagging participants, numbering the blasphemies, designing relationships, keeping count of screams. In short, he commands; he orders—on paper nowhere better—for no one slips from his pyramid of bodies with an “oops!”—not in his books—no one misses the mark or fails to come up to it or interrupts the action, that is to say, the argument; because there was nothing De Sade disliked more than the sense that matters were getting out of hand (do not be surprised to find a revolutionary loving order, they can’t wait to issue edicts and pass laws), and where were they more likely to but during fornication? It’s an unprotected time. Both soul and body are in danger, and Plato was neither the first nor last philosopher to suggest that lust was another name for chaos. Take off your clothing—did not the Dukhobors?—and you attack the state.
We have strict statutes and most biting laws,
The needful bits and curbs, to headstrong weeds,
Which for this fourteen years we have let slip;
… ….…
[Now] liberty plucks justice by the nose;
The baby beats the nurse, and quite athwart
Goes all decorum.
This is the judgment of the duke in Measure for Measure, and this judgment motivates the plot. Take off your clothes. Be gymnastic. Public. Be perverse. Attack the deepest laws. De Sade, however, was no Galileo, even though his record as a prisoner was longer. The scientist represented motion geometrically because he wished to understand it. He did not so dangerously confuse his model with the world. But De Sade saw persons as pieces of earth in order to treat human beings like dirt. Sodomy was still a revolutionary act, but lust was some exasperation of the nerves, nevertheless, like a humming in tightly strung wires.
That light travels in straight lines; that a body set in motion will continue unchanged unless something else hinders it; that all things seek equilibrium or act to maintain themselves in any given state; that men seek only their own pleasure or act always to preserve their own lives; that we perceive only sense data; that we are machines: all of these are opinions so plainly desirable for the translation of data into abstract systems, as are both atoms and the void, that it seems unlikely they are more than rules of representation like the principles of perspective in painting.
It was Hobbes who understood clearly the consequences of Galileo’s model as a universal measure. The advantage of thinking of matter in atomic terms was ultimately the resemblance of atoms to points, and as points stood for intersections, the corners of shapes, so atoms could be augmented by others and shrewdly arranged until the assemblage appeared as a visible object. If there were laws for the behavior of these, then might not men, considered as a house built of atomic bricks, be treated as moving bodies too; and finally, co
uld not groups of them be regarded just like even larger bodies also on the move? In this way impressive sovereignties, in the drama Hobbes composed for them, became solarized systems, like vast constellations, crashing through space, and the erratic rattle of humans against one another and the side of the State was no more confused in fact than the dance of shot in a metal bowl. Chaos, like darkness, had been snuffed out.
Chaos, of course, is an enemy of art, an inversion of one of its essential qualities; but chaos, as George Santayana has pointed out, is simply any order incompatible with a chosen good, like a set of files that’s indexed alphabetically by middle name: and a world in which events leaf out at random—the honest card or crap game, for example—is still one where the odds can be stated with precision. The disorders of the streets, the fickleness of crowds, gangs, or mobs, like the heavy rushes of a bull, are often more predictable than the moves of a chess master, and we usually feel that even the quirks of great winds would be perfectly understandable if we knew their backgrounds better—who their parents were and how they were raised. The straw which a mighty storm has driven through a post, the house which has been moved a mile and set down like a tray, seem whimsical acts because, like putting the shot, so much energy has been expressed in them they ought to have been meant, and we believe, in our less faithful moments, they were not.
No, we can put order anywhere we like; there’s not a trout we can’t tickle, a fish for which we can’t contrive a net; we can find forms in ink blots, clouds, the tubercular painter’s spit; and to the ants we can impute designs which Alexander would have thought himself vainglorious to dream of. But to think of order and chaos in this relative way is not to confuse them, or put conditions out of the reach of judgment. There are clashes between orders, confusions of realms. Not every arrangement is equally effective. And we must keep in mind the relation of any order to the chosen good.
Descartes said that Euclid was too abstract and too dependent on figures: “It can exercise the understanding only on condition of greatly fatiguing the imagination.” I know many books of that kind. Algebra, on the other hand, was overly rule-bound: “there results an art,” he said, “full of confusion and obscurity calculated to embarrass, instead of a science fitted to cultivate the mind.” Orders vary in both their vices and their virtues, in kind as well as in degree. Some are futile, others cheap. Among the worst are the illusory: politics and witchcraft, astrology and diets. Among the noblest are a few measurements of measure like Valéry’s Eupalinos. It does not matter whether we are “arranging” things to fall into an order, the ordering is an act of mind which brings together like two hands that buzzing blooming confusion of which James spoke, and some sublimely empty abstract system like that which Euclid once devised, or the inventors of the diatonic scale … brings them together till they clap. The result is a quantity qualified—that’s Plato’s recipe for the world—and in the past the most successful systems have had their source in music and in mathematics, while we have found our models, as often as not, to be examples of physics and astronomy, religious books, long poetical plays or lengthy epical poetry.
Let us count.
One. We find, perhaps, on a lottery ticket, the most primitive use of number, inasmuch as the number is not even a name there, not even an elementary designation like “Peewee,” “Nitwit,” or “Gramps.” The paper provides a place for their printing; it carries the figures, and these, by themselves, are mere grunts. Why do we number them at all? Why not print “Dimple” on one, “Nymphet” and “Spider” … then “Zealously,” “Viper,” and “Young”? We don’t care for sequence here, only for difference. In manufacturing such tickets, however, we want signs which can be simply produced, and a scheme for their production which will ensure there is no duplication. The ordinary number system pays that bill promptly. It can generate new and unique names indefinitely (no other is so efficient). Not even a language like Latin or English, each capable of a multitude of novel arrangements, can match its easy-going power.
Two. There are dog tags, Social Security, insurance, draft, or other numbers which name documents or people marking them uniquely. These numbers are true names. They are almost too pure, for they tell us nothing else, and the figures themselves simply come from a convenient pool of signs.
Three. The next level is the ordinal use. The sequence of numbers has a little meaning now. The numbering of the pages of a book is not quite an example, because it will tell me that some leaves are missing, or that, in my copy of Under the Volcano, a whole gathering has been repeated. For the first time, nevertheless, it makes sense to speak of measure. Take the scratch test for hardness: suppose I have five rocks. I scratch them turn and turn about as Beckett’s Molloy sucked stones, and then I arrange them serially in terms of who scratches whom and who is scratched by whom, assigning any figures I like so long as they reflect that scratching order: 1 through 5, perhaps, or 0, 4, 25, 92.3, and 112. Either list will do. Of course I could have called one Ruth, another Lou, and so on, but the names wouldn’t tell me whether Ruth scratched Lou or Lou, Ruth, and that won’t do. Even so, the stone labeled 5 in its sequence is not thereby that many times harder than 2, although this is a mistake which is frequently made.
Four. Counting is the cardinal use. What is the number of shoes in the store? Order alone is not enough here, and I must always proceed in whole units—that is assumed. The consequence of my counting, of course, is a sum, but the figure any particular shoe happens to receive is without significance. In the case of labeling hardness, I might have gone 0, 10, 25, instead of the 0, 4, 25, I used, but I could never have run 4, 0, 10, or 9, 6, 21. This floating or fastening of names is important in some metaphors.
Five. If you are number six in a simple count, it does not mean that you are in some way twice the fellow who was three. Addition is an additional property which we reach with luck and often genius only at this stage. Time and space are additive, hardness and heat are not. It is clear, by this time, isn’t it? that my knowledge of the relations between numbered things depends wholly upon my knowledge of the relations between numbers. The Pythagoreans said grandly of justice that it was “4.” Presumably this told us something of justice (actually it told us everything about justice, for the number was not only the logos [word] for justice, it was also the logos [or theory] of justice), but not even the zealots imagined that justice informed us about the number. Mathematical models (and this is important) are designed to tell us things about the data they shape, but the data are not expected or even allowed to snitch in the least on the system.
Rules of representation, I repeat, establish a link between the thing to be ordered and the order to be imposed. Let the face of this paper be the face of the earth. That is a rule of representation. The face of this paper is not the face of the earth, but neither is distance rectangular. Nevertheless, assuming one may enable me to find my way, assuming another may enable me to measure it.
Not all measurement, we have to notice, is direct. The scratch test is, but temperature taken with a thermometer is not. We measure the dance of the mercury because it undulates with the heat. My uncle’s sweat, collected in a cup, would serve as well if only he were as reliable in his response as the metal.
Suppose I were to say, of a married couple, that in their life together the wife played left tackle. Have I made a good model? Where are the other twenty players? who are the coaches, trainers, where are the stands? Tennis would serve a loving couple better. Then I might be able to observe how the wife stayed on the baseline, seldom coming to the net; how she characteristically lobbed her return to his drives; what sort of spin she put on her serves, and so forth—if that’s what she did. Or if I were to compare a football match to a chess game, I might carelessly see the two quarterbacks as the opponents—a mistake. The opponents have to be the coaches, since in chess the players are never pieces. And unless my measurements are meant to be skimpy, I have to assume that the moves of the athletes are fixed; that they act only as ordered. W
ell, my measurements are skimpy, my suit a poor fit, for when is that ever true?
Facts are not so stubborn as we sometimes like to think. The world may be a plenum, but it’s also hollow as bamboo, both stiff as straw and limply flexible as string. We can often talk things into being only what we want to say about them.
Perhaps you know the game in which two players suddenly and simultaneously show one another either an open hand, two fingers, or a fist. The open hand is paper, and it is said to be superior to stone, which the fist represents, because paper covers stone, although the stone can blunt the scissor-shaped fingers, and they, in turn, can cut the paper when they meet. This unusual arrangement comprises a viciously circular pecking order. Imagine that only untouchables gave orders to kings. The superiority of each symbol to the other is inferred from the presumed properties of its name. Scissors cut paper, paper covers stone, stone blunts scissors. Totem names are like our numbers: metaphors seriously meant and socially applied, as instanced in this passage from Lévi-Strauss’s essay on social poetry and measurement, The Savage Mind:
The following clans stand in a joking relationship to each other among the Luapula: the Leopard and Goat clans because the leopards eat goats, the Mushroom and Anthill clans because mushrooms grow on anthills, the Mush and Goat clans because men like meat in their mush, the Elephant and Clay clans because women in the old days used to carve out elephant’s footprints from the ground and use these natural shapes as receptacles instead of fashioning pots. The Anthill clan is linked with the Snake clan and also with the Grass clan because grass grows tall on anthills and snakes hide there. The Iron clan jokes with all clans with animal names because animals are killed by metal spears and bullets. Reasoning of this kind allows the definition of a hierarchy of clans: the Leopard clan is superior to the Goat clan, the Iron clan to the animal clans and the Rain clan to the Iron clan because rain rusts iron. Moreover the Rain clan is superior to all the other clans because animals would die without it, one cannot make mush (a clan name) without it, clay (a clan name) cannot be worked without it, and so on.
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