Against the Day (114 page)

“Swell that you’re all on such close
terms with her—so! who’ll introduce me?”

Amid a great creak and scrape of
beerhouse 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 them Zetamaniacs, eh? Sure are a lot of you folks pouring in to town, is
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 can 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 for a bit, 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 almostmatured
mustache, and, expecting her to disappear just as quick as beerfoam, 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, 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 rather fading
into history now, not to mention folklore
. .
. .
Why should any of you keep at it this way?”

“They
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 ζFunktion,
”
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 YorkNew Haven Trail, from
debutantes to nymphs of the Tenderloin, run into anything as passionate as this
stretching of spinetop 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 ζfunction to vectortype 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 vector systems in the primenumbered dimensions— the wellknown 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 lessinteresting 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
neoPythagorean cult of tetralatry or worship of the number four, currently the
rage in certain European circles, “not to mention ellipses and
hyperbolae,”—loosely allied, in fact, as a sort of correspondent 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 К. 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 eccentriclooking.
What were these upsidedown 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 tonedeaf beersociety 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 beermates
to show up just as I was about to find the screamingly obvious fallacy in this
. . .
‘proof’ of yours—”

“It’s
only Humfried and some 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 couplethree 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 coordinate 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 had been 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, Gott

lob. 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 Pen

cil 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 cap

ital, 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,
and all else is the work of man.’ Of course, it is a religious war. Kronecker
did not believe in pi, or 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,
professing an equally strong belief in just those regions, infinitely
divisible, which lie
between
the whole numbers so demanding of all
Kronecker’s devotion.”