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Math Humor; This one's for Grundtvig
Topic Started: Jan 27 2015, 08:01 PM (189 Views)
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Thomas Ruggles Pynchon
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Since Grundtvig mentioned some genuine knowledge of Bernhard Riemann, I figured I throw out a snippet from my favorite novelist Thomas Pynchon's Against The Day. I'm not in any way a "math person," but I am interested in the history of ideas and I think this vignette is both pretty funny and accurately rendered, at least as the turn-of-last-century pulp fiction it's intended to tweak. Pynchon's style has been termed historiographic metafiction. It is set in the University of Göttingen math department a few years before the outbreak of WW1.

Dramatis Personae:

Kit Traverse: A Coloradan from the mining frontier and student of Josiah Gibbs whose practical-minded interest in higher math comes from the emerging field of electrical engineering.

Yashmeen Halfcourt: A mysterious Central Asian devotee of the Riemann Hypothesis studying number theory.

Gottlob and Humfried: Two knuckleheaded students included mainly for comic relief.

We begin:

The lads collapsed into laughter, before whose loudness and puerility any young woman of the day might have been excused at least a dip in confidence. But not the self-possessed beauty who now approached. No, though being openly stared at -- more in wonder, mind you, than indignation -- Yashmeen Halfcourt continued to glide, through the Turkish smoke and beer fumes, in her bearing a suggestion that she might, with or without a partner, begin to dance a polka. And that hat! Draped velvet toques had always been Kit's undoing.

"Swell that you're all on such close terms with her -- so! Who'll introduce me?"

Amid a great creak and scrape of beer-house furniture, Kit's companions had swiftly vanished.

"Converging to zero," he mumbled, "what a surprise ... Good evening, miss, were you looking for one of those boys that suddenly ain't here anymore?"

She sat down, took a look at him. The Eastern eyes, the tension of whose lower lids had found a perfect balance between heat and appraisal, certainly were promissory of heartbreak.

"You are not English." Her voice unexpectedly just a little screechy.

"American."

"And is that a revolver you're carrying?"

"This? No, no this is the, what they call the Hausknochen? Get in off the street and up the staircase with." He produced a gigantic key whose transgression of scale, beyond all parameters of the tasteful, had in its time provoked unease even in the most collected of spirits. "Everybody around here packs one of these."

"Not everybody. All they've given me is this." She held up and jingled at him a silvery ring with a little pair of latchkeys. "Feminine, yes? This, plus of course a set of signs and countersigns before I'm even allowed to use them, as I am chaperoned without mercy. How is a person expected to prove Riemann's Hypothesis when half her time is taken up getting in and out of rooms?"

"Another one of those Zetamaniacs, eh? Sure a lot of you folks pouring into town, it's like a silver camp in Colorado here, eternal renown in em hills, so forth."

Yashmeen lit up an Austrian cigarette, held it between her teeth, grinned. "Where have you been? This has been going on everywhere, since Hadamard -- or Poussin, if you like -- proved the Prime Number Theorem. The first nugget out of the ground, as you'd say. Is it the problem that offends you, or those of us trying to solve it?"

"Neither one, it's an honorable pursuit, just kind of obvious, is all."

"Don't patronize me." She waited for a protest, but he only smiled. "'Obvious'?"

Kit shrugged. "I could show you."

"Oh please do. While we're at it, you could also show me how your Hausknochen works ... "

He guessed he was hearing things, but before long, having translated themselves without inconvenience out the door, down the street and up the stairs, here they were, actually up in his room with two bottles of beer he'd located in the patent Kühlbox. He sat just taking in her image, presently venturing,

"They tell me you're kind of famous?"

"Women at Göttingen form a somewhat beleaguered subset." She looked around. "And what is it you do here again?"

"Drink beer, work on my sleep allowance, the usual."

"I took you for a mathematician."

"Well ... maybe not your kind ... "

"Yes? Come, don't be too clever."

"All right, then." He squared his shoulders, brushed imaginary beer foam off his almost-matured mustache, and, expecting her to disappear just as quick as beer-foam, winced in apology. "I'm a sort of, hm ... Vectorist?"

Despite the shadow of an intent to flinch, she surprised him instead with a smile which, for all its resemblance to the smiles one gives the afflicted, was still able to turn Kit's extremities to stone. That is, it was some smile. "They teach vectors in America? I'm amazed."

"Nothing like what they offer here."

"Isn't England where you ought to be now?" as to a naughty child one expected to become, in a short while, naughtier.

"Nothing but Quaternions over there."

"Oh dear, not the Quaternion Wars again. That is so all fading into history now, not to mention folklore ... Why should any of you keep at it this way?"

"The believe -- the Quaternionists do -- that Hamilton didn't so much figure the system out as receive it from somewhere beyond? Sort of like Mormons only different?"

She couldn't tell how serious he was being, but after a decent interval she stepped closer. "Excuse me? It's a vectorial system, Mr. Traverse, it's something for engineers, to help the poor prats visualize what they obviously can't grasp as real maths."

"Such as your Riemann problem."

"Die Nullstellen der ζ-Funktion," saying it the way some other girl might say "Paris" or "Richard Harding Davis," but with a note as well warning that though she might possess an active sense of humor, it did not extend to Riemann. Kit had seldom, if ever, in those years up and down the New York-New Haven Trail, from debutantes to nymphs of the Tenderloin, run into anything as passionate as this stretching of spine-top and untilting of face. Her neck so uncommonly slender and long.

"Hate to tell you, but it's not all that hard to prove."

"Oh, a Vectorist proof, no doubt. And only excessive modesty has kept you from publishing."

Rummaging through the domestic clutter for a piece of paper with some blank space still on it, "Actually, I've been looking for a way, not to solve the Riemann problem so much as to apply the ζ-function to vector-type situations, for instance taking a certain set of vectorial possibilities as if it was mappable into the set of complex numbers, and investigating properties and so forth, beginning with the vector systems in the prime-numbered dimensions -- the well-known two and three, of course, but then five, seven, eleven, so forth, as well."

"Only primes. Skipping the fourth dimension, then."

"Skipping four, sorry. Hard to imagine a less-interesting number."

"Unless you're --"

"What?"

"Sorry, I was only thinking out loud."

"Aw." Was this amazing girl flirting? How come he couldn't tell?

"Death to reveal, I'm afraid."

"Really?"

"Well ... "

Which is how Kit first heard about the T.W.I.T.* back in London, and of the ghostly neo-Pythagorean cult of tetralatry or worship of the number four, currently the rage in certain European circles, "not to mention ellipses and hyperbolĉ," -- loosely allied, in fact, as a sort of correspondence group, with the T.W.I.T. These days, among those inclined to studies of the mystical, the fourth dimension, owing to the works of Mr. C. Howard Hinton, Professor Johann K. F. Zöllner, and others, was enjoying a certain vogue, "or should I say 'vague'?" remarked Yashmeen.

"O.K. Here's the Riemann proof --" He wrote down, without pausing, no more than a dozen lines. "Leaving out all the obvious transitions, of course ... "

"Of course. How eccentric-looking. What were these upside-down triangles again?"

All at once there came a horrible metallic banging and rattling from down at the street entry, accompanied, from beneath the window, by some tone-deaf beer-society in vulgar song. She stared at Kit, lips compressed, head nodding emphatically. "So -- it's all been a trick. Hasn't it, yes. A squalid trick."

"What?"

"Arranging for your little beer-mates to show up just as I was about to find the screamingly obvious fallacy in this ... 'proof' of yours -- "

"It's only Humfried and his pals, trying to get a Hausknochen in the lock. If you want to hide someplace, I'd suggest that closet, there."

"They ... live here?"

"Not here, but none of them more than a couple-three blocks' distance. Or do you Riemann folks say 'metric interval'?"

"But why should your friend use his key?"

"Um actually, as it turns out, every Hausknochen fits pretty much every lock around here."

"Therefore -- "

"Social life is unpredictable."

Shaking her head, eyes on the floor, "Auf wiedersehen, Herr Professor Traverse." By mistake the door she chose to exit by was not the back door, though it looked -- and from its swing, weighed -- about the same, indeed seemed to be located in the same part of Kit's rooms, as the back door, and yet, strangely, was not the back door. How could this be? Actually, it was not even a door to begin with, but something designed to allow the human brain to interpret it as a door, because it served a similar function.

On the other side of it, she found herself out on the corner of Prinzenstraße and Weenderstraße, known to mathematicians here as the origin of the city of Göttingen's coördinate system. "Return to zero," she muttered to herself. "Begin again." She didn't find this sort of excursion especially out of the ordinary -- it had happened before, and once she had learned that no harm was likely to come of it, she was able to shrug and get on with her day. It was no more upsetting than waking from a lucid dream.

Back in quotidian space, Kit, having observed Yashmeen apparently walk through a solid wall, had scarcely time to register puzzlement before up the stairs and into the room came thumping Humfried and his creature, Gottlob. They were indeed seldom noted apart, being driven by a common fascination with the details of others' lives, no matter how trivial. "All right, where is she?"

"Where's who, and speaking of where, Gottlob, where's 'at twenty marks you owe me?"

"Ach, der Pistolenheld!" screamed Gottlob, attempting to hide behind Humfried, who as usual was looking for food.

"No, no, Gottlob, control yourself, he will not shoot at you, here, see, this interesting sausage --" Eating half of it immediately and offering the rest to Gottlob, who shook his head vigorously no.

Humfried had been obsessed for a while now with a connection he thought he saw between automorphic functions and the Anharmonic Pencil or, as he preferred, das Nichtharmonischestrahlenbündel, though he had decided to write all his papers in Latin, which no one had done since Euler.

Gottlob, on the other hand, had come to Göttingen from Berlin to study with Felix Klein, on the strength of Klein's magisterial Mathematical Theory of the Top (1897), approached by way of functions of a complex variable, and also to get away from the sinister influence of the late Leopold Kronecker, keepers of whose flame regarded the complex domain with suspicion if not outright abhorrence -- only to find at Göttingen a dwarf variety of the same monumental quarrel between Kronecker and Cantor then raging in the capital, not to mention the world. Fundamentalist Kroneckerites had been known to descend on Göttingen in periodic raids, from which not all of them returned.

"Ach, der Kronecker!" cried Gottlob, "he needed only to step out into the street, and mad dogs ran away or, knowing what was good for them, at once regained their sanity. Only five feet tall, but he enjoyed the abnormal strength of the possessed. Each time he appeared, one could count on weeks of panic."

"But ... folks say he was very sociable and outgoing," said Kit.

"Perhaps, for an insane zealot who believed 'the positive integers were created by God, all else is the work of man.' Of course, it is a religious war. Kronecker did not believe in pi, or in the square root of minus one --"

"He did not even believe in the square root of plus two," said Humfried.

"Against this, Cantor with his Kontinuum, possessing an equally strong belief in just those regions, infinitely divisible, which lie between the whole numbers so demanding of all of Kronecker's devotion.

"And that's what kept driving Cantor back into the Nervenklinik, added Humfried, "and he was only worrying about line-segments. But out here in the four-dimensional space-and-time of Dr. Minkowski, inside the tiniest 'interval,' as small as you care to make it, within each tiny hypervolume of Kontinuum -- there likewise must be always hidden an infinite number of other points -- and if we define a 'world' as a very large and finite set of points, then there must be worlds. Universes!"

In fact, a mystical Cantorian cult of the very, indeed vanishingly, negligible, ever seeking escape into a boundless epsilonic world, was rumored to be meeting weekly at Der Finsterzwerg, a beer-hall just outside the old ramparts of the town, near the train station. "A sort of Geographical Society for the unlimited exploration of regions neighboring the Zero ... "

As Kit had rapidly discovered, this sort of eccentricity abounded in Göttingen. Discussion ran far into the night, insomnia was the rule, though if one did wish to sleep for some reason, there was always chloral hydrate, which had its own circle of devotees. He saw Yashmeen now and then, usually across the smoke-clouded depths of some disreputable Kneipe by the river, but seldom to talk to. One evening he happened to be walking along the promenade on top of the old fortifications, and near the statue of Gauss passing to Weber a remark forever among the pages of silence, noticed her gazing out over the red-tile roofs of the town, and the lights just coming on.

"How's 'at old Zeta function?"

"Something amuses you, Kit?"

"Every time I see one them Zetas, it makes me think of a snake up on its tail being charmed by a snake-charmer, ever notice that?"

"These are the reflections that occupy your time?"

"Let me put it a different way. Whenever I see one, it reminds me of you. The 'charmer' part anyway."

"Aaah! Even more trivial. Do none of you ever think beyond these walls? There is a crisis out there." She scowled into the stained orange glow of the just-vanished sun, the smoke rising from hundreds of chimneys. "And Göttingen is no more exempt than it was in Riemann's day, in the war with Prussia. The political crisis in Europe maps into the crisis in mathematics. Weierstrass functions, Cantor's continuum, Russell's equally inexhaustible capacity for mischief -- once, among nations, as in chess, suicide was illegal. Once, among mathematicians, 'the infinite' was all but a conjuror's convenience. The connections lie there, Kit -- hidden and poisonous. Those of us who must creep among them do so at our peril."

"Come on," Kit said, "let a trivial fellow buy you a beer."

(Against The Day pp. 589-94, Penguin hardbound edition, 2006)

*T.W.I.T. = True Worshipers of the Ineffable Tetractys.
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