Against the Day

by Thomas Pynchon

  “Yeah, but how many of those could there be?”

  “Oh you’re all so horrid,” Yashmeen said.

  Günther meanwhile insisted that Yashmeen’s presence here amounted to an affair of honor. “Obviously, we must now a duel fight.”

  “How’s that?”

  “You have insulted me, you have insulted my fiancée—”

  “Oh, Günni?”

  “Ja, Liebchen?”

  “I’m not your fiancée, remember? we talked about this?”

  “Egal was, meine Schatze!—meanwhile, Mr. Traverse, as challenged party you shall have the choice of weapons—how lucky to have provoked your quarrel here, in the dueling capital of Germany. At my disposal, and yours, are matched pairs of the Schläger, the Krummsäbel, the Korbrapier, even, if it should be your vice, the épée—a weapon which, though not up to German standards, is I am told quite all the rage now in England—”

  “In fact,” said Kit, “I was thinking more along the lines of, maybe, pistols? I happen to have a couple of Colt six-shooters we can use—though as for ‘matched,’ well . . .”

  “Pistols! Oh, no, no, impulsive, violent Mr. Traverse—here we do not duel to kill, no! though of course wishing to maintain the honor of the Verbindung, one’s deeper intent is, upon the face of the other, to inscribe one’s mark, so that a man may then bear for all to see evidence of his personal bravery.”

  “Is that what that is on your face, looks like a Mexican tilde?”

  “Unusual, no? Later we worked out the probable frequency the blade must have been vibrating at, given the restoring moment, elastic constants, all in the most gentlemanly way, which I am sure your American gunslinger has no concept of. Oh it is true, ja, there do creep among us certain desperate maniacs, who have come away from their affairs carrying actual bullet scars on their faces, but this takes a degree of indifference to mortality that few of us are blessed with.”

  “Are you saying pistols’d be too dangerous for you, Günni? Where I’m from, when it’s about Honor? why a man’s pretty much obliged to use a pistol. Blades, that’d be just too—I don’t know—quiet? mean? . . . sneaky, even?”

  Günther’s ears quivered. “Am I to understand, sir, that you mean thus to classify the German as a subspecies of some less valiant race, is this correct?”

  “Wait—I’ve insulted you again? you’re . . . calling me out, twice now? Well! That sure ups the ante, don’t it? say, if you’re going to get offended at every little thing, maybe we’d better have all our chambers full, six shots apiece, what do you think?”

  “This cowboy,” Günther in plaintive appeal, “seems unaware that civilized beings are repelled by the stench of powder.”

  “Listen, Porkbarrel, what’s this really about? I told you it wasn’t going to converge, and it never will.”

  “There. Again. Three times, now.”

  “Just the same, about halfway through, you skipped a step. Not to mention in one of your series you grouped some terms together wrong, reversed sign a couple times, even went and divided by zero, yeah you did, Günni, look, right here, you’re lucky somebody took the time to read it that close—basic stupid mistakes—”

  “Four!”

  “—and instead of all this carving on folks, why not consider if this is really the best field of study for you, if all you want’s your face on a souvenir postcard.”

  “You insult Geheimrat Hilbert now!”

  “At least he’s got the right hat.”

  After repeated consultations with the Prussian dueling bible, a small brown volume known as the Ehrenkodex, Kit, Günther and their seconds met down by the river, as soon as there was light to see by. It was one of those profoundly agreeable spring mornings, which more rational souls might choose to celebrate in some less lethal way. The tanneries had not quite cranked up to operating speed, and the air still smelled like the countryside it had passed over. Willows swayed alluringly. Farther off, ruinous watchtowers emerged from the mists. Early bathers came blinking by, wraithlike and curious. Students in dressing-gowns, Tyrolean hats, colored spectacles, carpet slippers, and exotic pajamas with Oriental prints on them, sleepily queued up to stake demented wagers with the bookmakers found haunting such affairs. Now and then someone, edging into consciousness, remembered he was still wearing his Schnurrbartbinde, or nighttime mustache-keeper. Those principally involved stood around bowing back and forth for a while. A vendor appeared with a cart carrying a steaming tub brimful of boiled sausages, and beer arrived as well, both in barrels and in bottles. A photographer set up his tripod and Zeiss “Palmos Panoram” for any who might wish visual mementoes of the encounter.

  “Very well, I did divide by zero—once only, mea maxima culpa, no effect on the result. I did not omit any step where you said I did. You, rather, incapable appear, of following my argument.”

  “Hogwash Günther, look, between steps, here to here, this function of time, you assume it’s commutative, just glide on past it, when in fact—”

  “So?”

  “You just can’t make that assumption.”

  “I may do as I wish.”

  “Not when this needs a minus sign here. . . .” Thus, despite the restlessness of the crowd, who had been chanting “Auf die Mensur!” for quite some time actually, the young men found themselves in yet another mathematical exchange, which soon bored everyone into wandering away, including Yashmeen, who had in fact left much earlier, on the eager arm of a graduate anthropologist visiting from Berlin, who hoped to define here among the dueling clubs of Göttingen a “control-group” for examining the deeper meanings of facial inscription, especially as practiced among northern tribes of the Andaman Islands—departing, in fact, to shouts of “Stephanie du Motel!” and rude whistling, as the community, being fully up to date on the details of the romance, had found itself divided as to Yashmeen, some regarding her as a brave and modern young woman, like Kovalevskaia, others as a faithless harlot whose mission in life was to lure promising mathematicians into premature demise by duel, as the infamous Mademoiselle du Motel had done to group-theory godfather Evariste Galois back in 1832.

  AMONG THE RUSSIAN VISITORS to Göttingen were some of decidedly mystical inclination. Yashmeen recognized them right away, having met, and on occasion eluded, several at Chunxton Crescent, but here, farther east, there was no avoiding the momentous events unfolding close by. By 1906 there were Russians everywhere, flown and fleeing westward, and many brought copies of young Ouspensky’s book The Fourth Dimension.

  An unkempt individual with a single name, vaguely Eastern, was observed hanging around with Humfried and Gottlob. “He’s all right. He’s a Theosophoid, Chong is. That’s like a Theosophist, only not entirely. He’s here to learn about the Fourth Dimension.”

  “The what?”

  “And the others, of course.”

  “The other . . .?”

  “Dimensions. You know, Fifth, Sixth, so on?”

  “He believes Humfried to’ve been his teacher in a previous life,” added Gottlob, helpfully.

  “How odd. There are educators among the invertebrates?”

  “But look here!” cried Yashmeen, “that’s no Chinese Bolshevik—it’s old Sidney, well blimey if it isn’t old Kensington Sid, with some vegetable dye—I say Sid! it’s I! old Yashmeen! Cambridge! Professor Renfrew! Remember?”

  The Eastern personage gazed uninformatively back at her—then, seeming to reach a decision, began to speak with some intensity in a tongue no one could identify, not even by its language-family. More cognizant listeners understood this as an attempt to distract.

  Dr. Werfner of course had spotted him right away and assumed he’d been sent out as one of Renfrew’s operatives, as did Yashmeen, who assumed he was there to spy on her, for he did seem to show an uncommon interest in the Russians who passed through town. Whenever they sought out Yashmeen to discuss the transtriadic dimensions, Chong was sure to be there.

  “Four is the first step beyond the space we know,” said
Yashmeen. “Dr. Minkowski suggests a continuum among three dimensions of space and one of time. We can look at the ‘fourth dimension’ as if it were time, but is really something of its own, and ‘Time’ is only our least imperfect approximation.”

  “But beyond the third,” persisted one of their Russian visitors, “do dimensions exist as something more than algebraists’ whimsy? Can we be given access to them in some more than mental way?”

  “Spiritual,” declared Gottlob. As far as anyone could recall, it was the first time he had ever used the word.

  “The soul?” Humfried said. “The angels? The invisible world? The afterlife? God?” By the end of this list, he had acquired a smirk. “At Göttingen?”

  KIT MEANWHILE HAD BEGUN to frequent the Applied Mechanics Institute. Since Prandtl’s recent discovery of the boundary layer, things over there had been hopping, with intense inquiry into matters of lift and drag, powered flight poised like a new-feathered bird at the edge of history. Kit had not thought much about aerodynamics since his brainless sojourn in the Vibe embrace, when in the course of golfing parties out on Long Island he had become acquainted with the brambled guttie, a gutta-percha ball systematically roughened away from the perfectly spherical by molding little knobs all over the surface area. What he could not help noticing then, even though he was not all that crazy for the game, so inordinately populated by the likes of Scarsdale Vibe, was a particular mystery of flight—the undeniable lift of heart in seeing a struck ball—a tee shot especially—suddenly go into a steep ascent, an exhilarated denial of gravity you didn’t have to be a golfer to appreciate. There being enough otherworldliness out on the links already. Finding himself more and more drawn to the microcosm on the other side of the Bürgerstraße, Kit soon understood that the brambling of the golf-ball surface had been a way to keep the boundary layer from detaching and falling apart into turbulence which would tend to drag the ball down, denying it its destiny in the sky. When he mentioned this in conversations at the saloons along the Brauweg frequented by engineering and physics students, some immediately suggested implications for the Earth, a brambled spheroid on the grand scale, in its passage through the Æther, being lifted not in the third dimension but on a euphoric world-line through Minkowski’s “four-dimensional physics.”

  “What happened to vectorism?” Yashmeen teased.

  “There are vectors,” Kit replied, “and vectors. Over in Dr. Prandtl’s shop, they’re all straightforward lift and drift, velocity and so forth. You can draw pictures, of good old three-dimensional space if you like, or on the Complex plane, if Zhukovsky’s Transformation is your glass of tea. Flights of arrows, teardrops. In Geheimrat Klein’s shop, we were more used to expressing vectors without pictures, purely as an array of coefficients, no relation to anything physical, not even space itself, and writing them in any number of dimensions—according to Spectral Theory, up to infinity.”

  “And beyond,” added Günther, nodding earnestly.

  IN HILBERT’S CLASS one day, she raised her hand. He twinkled at her to go ahead. “Herr Geheimrat—”

  “‘Herr Professor’ is good enough.”

  “The nontrivial zeroes of the ζ-function . . .”

  “Ah.”

  She was trembling. She had not had much sleep. Hilbert had seen this sort of thing before, and rather a good deal of it since the turn of the century—since his own much-noted talk at the Sorbonne, he supposed, in which he had listed the outstanding problems in mathematics which would be addressed in the coming century, among them that of the zeroes of the ζ-function.

  “Might they be correlated with eigenvalues of some Hermitian operator yet to be determined?”

  The twinkle, as some reported later, modulated to a steady pulsation. “An intriguing suggestion, Fräulein Halfcourt.” Usually he addressed her as “my child.” “Let us consider why this should be so.” He peered, as if she were an apparition he was trying to see more clearly. “Apart from eigenvalues, by their nature, being zeroes of some equation,” he prompted gently.

  “There is also this . . . spine of reality.” Afterward she would remember she actually said “Rückgrat von Wirklichkeit.” “Though the members of a Hermitian may be complex, the eigenvalues are real. The entries on the main diagonal are real. The ζ-function zeroes which lie along Real part = 1/2, are symmetrical about the real axis, and so . . .” She hesitated. She had seen it, for the moment, so clearly.

  “Let us apply some thought,” said Hilbert. “We will talk about this further.” But she was to leave Göttingen shortly after this, and they would never have the chance to confer. As years passed, she would grow dim for Hilbert, her words those of an inner sprite too playful to frame a formal proposition, or to qualify as a fully habilitated Muse. And the idea itself would evolve into the celebrated Hilbert-Pólya Conjecture.

  One morning Lew walked into the breakfast parlor at Chunxton Crescent to find Police Inspector Vance Aychrome, angelically revealed in early sunbeams through the stained-glass dome overhead, relentlessly despoiling a Full English Breakfast modified for the Pythagorean dietary here, including imitation sausages, kippers and bloaters, omelettes, fried potatoes, fried tomatoes, porridge, buns, baps, scones, and loaves in various formats. Robed acolytes crept timidly between the tables and the great kitchen with caddies, tureens, and trays. Some wore mystical facial expressions as well. Late risers, sandals twinkling, sought to avoid the Inspector, preferring to fast rather than compete with his all-but-entitled insatiability.

  “One fancies a wee fry-up at this hour,” Aychrome somehow between huge mouthfuls greeted Lew, who, smiling grimly, went looking for some coffee, a fool’s errand around here on the best of mornings, which this already wasn’t. These English were a people of many mysteries, none more peculiar than their indifference to coffee.

  “All right,” he called out, “who’s taken the bloody Spong machine again,” not that it mattered—coffee around here was apt to taste like anything but coffee, owing to folks’s tendencies to use the only grinder in the house to prepare curry powder, incense, even pigments for indecipherable works of art, so he ended up, as usual, with a chipped mug full of pale, uneventful tea, and took a seat across from Aychrome, gazing in some fascination. Assuming he was not here only to deliver another gentle suggestion from Scotland Yard to back off of the Gentleman Bomber case, Lew took from an inner pocket a Tarot deck thinned to the twenty-two Major Arcana and dealt them one by one onto the table, between the remains of a vegetarian haggis and a platterful of pea fritters, until Aychrome began to nod frantically and wave about a finger dripping with what Lew hoped was only treacle. “Ggbbmmhhgghhkkhh!”

  Indeed. The card was not Renfrew/Werfner’s number XV after all, but XII, The Hanged Man, whose deeply veiled secret meanings always seemed to place it in a particularly critical area of investigation. Lew had got to thinking of it as his own personal card, because it had been the first “future” card that Neville and Nigel had turned over for him. Last time he’d checked, its position in the Icosadyad was occupied by one Lamont Replevin, of Elflock Villa, Stuffed Edge, Herts.

  When at last Aychrome’s mouth seemed relatively unengaged, “So, Inspector,” as chirpily as possible given the hour, “nothing too political I hope.”

  “Hmm,” as if to himself, “bit of this . . . kedgeree, I think . . . yes lovely . . . and where was that marmalade pot . . . ah very nice indeed.” Lew was thinking about leaving the man to his appetite when Aychrome, as if just bitten by an insect, fixed him with a pop-eyed stare, wiped his mustaches, and barked, “Political! well I should say so, but then it’s all political, isn’t it.”

  “According to the dossier, this Replevin is an antiques dealer.”

  “Oh beyond a doubt, except that there’s a sheet on the subject half a mile long. The Lombro work alone is most suggestive, yes, most suggestive indeed.”

  Lew was aware that Inspector Aychrome was a zealous disciple of the criminological theories of Dr. Cesare Lombroso, notably the po
pular one that deficiencies of moral intelligence were accompanied by an absence of corresponding tissue in the brain, and a consequently warped cranial development which could be observed, by the trained eye, in a subject’s facial structure.

  “Some faces are criminal faces, is the long and short of it,” declared the Metropolitan veteran, “and woe unto them that ignore it or can’t interpret it properly. This one,” handing across a “mug” photo, “as you can see, has International Mischief written all over his map.”

  Lew shrugged. “Seems like a wholesome enough fellow.”

  “We’ve had men watching the place, you see.”

  “Why?”

  Aychrome gave the room a quick melodramatic once-over and lowered his voice. “Germans.”

  “Beg pardon?”

  “The subject Replevin runs a shop in Kensington, dealing, according to his file, in ‘Trans-Oxanian and Græco-Buddhist antiquities,’ whatever those may be when they’re at home, which is visited by a constant stream of suspect characters, some of whom we already know, bad hats just from their facial types alone, forgers and counterfeiters, fences and collectors . . . but our main worry at the Yard is the high proportion of German traffic between here and Inner Asia that always seems to find its way through Replevin’s establishment. Most of the archaeology out there is being done by German teams, you see, a perfect excuse for these visitors to keep entering the country with dozens of their huge heavy crates labeled, helpfully, ‘Antiquities.’ And then Sands calls in about the Inner Asian show—this Shambhala state of affairs—and as if that wasn’t enough, the Gas Office are on the doorstep stark mental with what they’re overhearing.”

  “‘Gas Office.’”

  Gripping a knife and fork expressively in either fist, the Inspector was happy to explain. Lamont Replevin, it seemed, was a practicing devotee of communication by means of coal-gas—that is, gas-mains city and suburban figured, in his map of London, as networks of communication, every bit as much as pneumatic or telephone lines. The population who communicated by Gas, who indeed were unwilling to communicate in any other way, appeared pretty substantial and, according to Aychrome, was growing daily, as secret interconnections continued to be made among urban and local or village gas-mains, and the system expanded, net-wise, as if destined soon to cover all Britain. For those blessed with youth, money, and idle time, it amounted to little more than a faddish embrace of the Latest Thing, though many corresponded by gas for emotional reasons, including those so vehemently discontented with the post office that they might have been out seeking to chuck bombs into post-boxes, were it not for the many Suffragettes queued up ahead of them. Scotland Yard, taking the lively interest one might expect, had set up a department to monitor Gas traffic.