Against the Day (115 page)

“And
that’s what has kept driving Cantor back into the
Nervenklinik
,”
added Humfried, “and he was
only worrying about linesegments. But out here in the fourdimensional
spaceandtime 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 beerhall 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 at 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
smokeclouded 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 redtile
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 snakecharmer, 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 justvanished
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.”

·
    
·
    
·

That winter, in
St. Petersburg, troops at the Winter
Palace fired on thousands of unarmed strikers who had marched there in
respectfulnesss and innocence. Hundreds were killed and wounded. In Moscow the
Grand Duke Sergei was assassinated. More strikes and fighting followed, along
with peasant and military insurrections, on into the summer. The Navy mutinied
at Kronstadt and Sebastopol. There was streetfighting in Moscow. The Black
Hundreds carried out pogroms against Jews. The Japanese won the war in the
East, obliterating the entire Baltic Fleet, which had just sailed halfway
around the world to try to lift the siege of Port Arthur. A general strike in
the autumn cut the country off for weeks from the rest of the world and, as
people came slowly to realize, stopped history. In December the Army beat down
another major uprising. In the East there was fighting all up and down the
railroad lines, banditry, eventually a Muslim rebellion in Inner Asia. If God
had not forgotten Russia, He had turned His attention elsewhere.

For
the rest of Europe, the year that followed was to be remembered as the year of
Russians everywhere, fleeing into mass exile, as the Revolution went collapsing
at their heels—the Peter and Paul Fortress and sooner or later death if
they stayed. Who would have thought the Tsar had so many enemies?

Kit
had begun to notice Russians in the Weenderstraße. Yashmeen was convinced they
were in town to spy on her. They were trying to blend in, but certain telltale
nuances—fur hats, huge unkempt beards, a tendency in the street to drop
and begin dancing the kazatsky to music only they could hear—kept giving
them away.

   
“Say,
Yash, what’s with all those Russians?”

“I’m
trying not to take it personally. My parents were Russian. When we lived on the
frontier, my family and I one day were taken in a raid and sold as slaves. Some
time later, Major Halfcourt found me in a bazaar in Waziristan and became my
second father.”

Not
feeling as surprised as he might’ve been, “And he’s still out there someplace?”

“Whatever he’s been up to, it is of
enough political weight that someone thinks they can use me somehow.”

   
“Are
you in touch?”

   
“We
have our own means, which neither distance nor time can affect.”

   
“Telepathy
or something.”

She
frowned. “Perhaps you think I am a girl with Æther between her ears, easily
influenced by the beliefs of the T.W.I.T.”

“Dang,
Yash, you sure
read my mind
there,” with what he hoped was enough of a
twinkle that she wouldn’t take offense, for her unannounced ferocities, however
playful, continued to cause him some dismay.

She
was fooling with her asever transcendentally interesting hair, always a sign of
trouble down the line. “Even with the Revolution, news comes back. Thousands of
miles, multitudes of tongues, unreliable witnesses, deliberate misinformation
and all, it finds its way back to the T.W.I.T. people at Chunxton Crescent, and
what comes out of their shop can surprisingly often be trusted—even the
War Office admits it’s better ‘gen’ on the whole than their own.”

   
“Anything
I can do, just fire away.”

She
gave him a look. “To the world here, I enjoy a reputation as ‘my own person’
. . .
yet I am also, ever
. . .
his.
My other family have
gone on to destinies I cannot imagine. Only in dreams do I catch glimpses of
them, moments so fugitive, so slight, that afterward there is the sensible ache
here, in my breast, of cruel incompletion. My true memories do not begin until
the moment
he
first saw me in the market—I was a soul impaled,
exactly upon the cusp between girl and young woman, a cusp I could literally
feel as it penetrated me, as if to bisect me— I do hope that is not a
blush, Kit.”

Well,
sort of, but more from perplexity than desire. Today she wore an ancient coin,
pierced and simply suspended from a fine silver chain around that everfascinating
neck
. . . .
“It’s an Afghani dirhan,
from the early days of the Ghaznivid Empire. He gave it to me, for luck.” Over
its nine or ten centuries of circulation, thieves had nipped and shaved silver
from around the outer border, but the inner circle survived, crowded with
ancient writing. It was the outward emblem of a hidden history of assault and
persistence, the true history of its region and perhaps of this young woman,
through this life and who knew how many previous. “Thank you for the offer,
Kit. If anything arises, I shall certainly seek your advice. I am ever so
grateful,” with eyes adance in the luxury of believing little beyond the
assumption that he would allow her to get away with this, yet expect no favors
in return. He ate it all up like a fairground icecream cone, even if he had to
pretend indifference. You sure never got this in New Haven. They didn’t know
how to flirt like this even in New York. This is the world, Kit reflected, and
a couple nights later, around three a.m., as an extra smack of the bamboo
stick,
She
is
the
world.

Meanwhile
Yashmeen, a fine one to scold the trivial, had taken up with a wealthy coffee
scion named Günther von Quassel. On their first date, Günther, a devotee of the
less than universally respected Ludwig Boltzmann, had tried to explain to her
the Riemann problem by means of statistical mechanics.

   
“Here.
Tell me please, as
n
grows infinitely large, what the
n
th prime is?”

Sighing,
though not with desire, “Its value—as any Gymnasium child at all acquainted
with the Prime Number Theorem knows—approaches
n
log
n.
”

   
“So.
Looking at the entropy of a system—”

“Some
sort of. . . steamengine word, isn’t it? Am I a boiler engineer, Günni?”

“Except
for the usual constants,” writing as he spoke, “one may express the entropy as
. . .
the summation, of
p
(
E
_k
)
, times log
p
(
E
_h
)
.
All in
order so far?”

   
“Of
course, but this is only statistics. When do we get to the mathematics?”

   
“
Ach,
die Zetamanie. . .
your
Prime Number Theorem is
not
statistical?”

But
she was looking at what he’d scribbled down, the two somethinglogsomethings.
“This
E
_k
.
. .
?”

“The
energy of a given system, you use the
k
to index if there is more than one, and there usually is.”

   
“And
is there insanity in your family, Günther?”

“You
do not find it odd that the
N
th
prime for very large
N
may
be expressed as one measure of the chaos in a physical system?”

   
None
of which kept Yashmeen from pursuing the attachment.

“
As
a crime
,” Humfried pointed out, “often of the gravest sort, committed in
a detective story, may often be only a pretext for the posing and solution of
some narrative puzzle, so romance in this town is often pursued as little
beyond a pretext for running in and out of doors, not to mention up and down
stairs, while talking nonstop and, on auspicious days, screaming.”

Yashmeen
one day overheard Günther confessing to his intimate Heinrich, “There is only
one girl in this town I have ever wanted to kiss.” It was doctoralcandidate
talk, of course, though Yashmeen in her Riemannian obsession appeared to be
unaware of the Göttingen tradition that required successful Ph.D.’s in
mathematics to kiss the statue of the little goosegirl in the fountain of the
Rathaus square, getting soaked and with luck delirious in the process.

Yashmeen
grew exercised. “Who is this person?” she demanded of Heinrich, who assumed she
was teasing.

   
“All
I know is, he says that she waits every day near the Rathaus.”

   
“For
whom? Not for Günther?”

   
Heinrich
shrugged. “Geese were mentioned?”

“Real geese, or University students?”
as she went storming out into the Platz, where she began to loiter menacingly.
For days. Günther happened

by, or did not happen by, but never
in the company of any imaginable rival. Naturally she failed to pay much
attention to the fountain nearby, or the little statue. One day she did hear
him singing—

Her idea of banter

Likely isn’t Cantor,

Nor is she apt to murmur low

Axioms of Zermelo,

She’s been kissed by geniuses,

Amateur Frobeniuses,

One by one in swank array,

Bright as any Poincaré,

And
. . .
though she

May not care for Cauchy,

Any more than Riemann,

We’ll just have to dream on . . .

Let

it occur in spots in

Whittaker and Watson—

Unforeseen converging,

Miracles emerging,

Epsilonic dances,

Small but finite chances,

For love . . .

Concerned for her mental stability,
everybody felt obliged to put in their two pfennigs, including Kit. “Yash, you
want to forget this customer, he’s not for you. I mean, what if he is tall,
muscular, even in some strange German way some’d think presentable—”

   
“You
forgot brilliant, amusing, romantic—”

“But you are being used by your
racial memory here,” declared Humfried indignantly, “you are out looking for
some Hun.”

   
“Are
you saying I want to be overrun and conquered, Humfried?”