**Gregory
Volfovich Chudnovsky recently build a super computer in his appartment
from mail-order parts. Gregory Chudnovsky is a number theorist. His appartment
is situated near the top floor of a run-down building on the West Side
of Manhattan, in a neighborhood near Columbia University. Not long ago,
a human corpse was found dumped at the end of the block. The world's most
powerful supercomputers include Cray Y-MP C90, the Thinking Machines CM-5,
the Hitachi S-820/80, the nCube, the Fujitsu parallel machine, the Kendall
Square Research parallel machine, the NEC SX-3, the Touchtone delta, and
Gregory Chudnovsky's apartment. The apartment seems to be a kind of container
for the supercomputer at least as much as it is a container for people.**
**Gregory Chudnovsky's
partner in the design and construction of the supercomputer was his older
brother, David Volfovich Chudnovsky, who is also a mathematician, and who
lives five blocks away from Gregory. The Chudnovsky brothers call their
machine m zero. It occupies the former living room of Grogory's apartment,
and its tentacles reach into other rooms.**
**The brothers claim
that m zero is a "true, general-purpose supercomputer", and that it is
as fast and powerful as a somewhat older Cray Y-MP, but not as fast as
the latest of the Y-MP machines, the C90, an advanced supercomputer made
by Cray Research. A Cray Y-MP C90 costs more than thirty million dollars.
It is a black monolith, seven feet tall and eight feet across, in the shape
of a squat cylinder, and is cooled by liquid freon. So far, the brothers
spent around seventy thousand dollars on parts for their supercomputer,
and much of the money has come out of their wives' pockets.**
**Gregory Chudnovsky
is thirty-nine years old, and he has a spare frame and a bony, handsome
face. He has a long beard, streaked with gray, and dark, unruly hair, a
wide forehead, and wide-spaced brown eyes. He walks in a slow, dragging
shuffle, leaning on a bentwood cane, while his brother, David, typically
holds him under one arm, to prevent him toppling over. He has severe myasthenia
gravis, an auto-immune disorder of muscles. The symptoms, in his case,
are muscular weakness and difficulty in breathing. "I have to lie in bed
most of the time", Gregory once told me. His condition does not seem to
be getting better, and does not seem to be getting worse. He developed
the desease when he was twelve years old, in the city of Kiev, Ukraine,
where he and David grew up. He spends his days sitting or lying on a bed
heaped with pillows, in a bedroom down the hall from the room that houses
the supercomputer. Gregory's room is filled with paper; it contains at
least a ton of paper. He calls the place his junk yard. The room faces
east, and would be full of sunlight in the morning if he ever raised the
shades, but he keeps them lowered, because light hurts his eyes.**
**You almost never meet
one of the Chudnovsky brothers without the other. You often find the brothers
conjoined, like Siamese twins, David holding Gregory by the arm or under
the armpits. they complete each other's sentences and interrupt each other,
but they don't look alike. While Gregory is thin and bearded, David has
a stout body and a plump, clean-shaven face. He is in his early forties.
Black-and-gray curly hair grows thickly on the top of David's head, and
he has heavy-lidded deep-blue eyes. He always wears starched white shirt
and, usually, a gray silk necktie in a foulard print. His tie rests on
a bulging stomach.**
**The Chudnovskian supercomputer,
m zero, burns two thousand watts of power, and it runs day and night. The
brothers don't dare shut it down; if it did, it might die. At least twenty-five
fans blow air through the machine to keep it cool; otherwise something
might melt. Waste heat permeates Gregory's apartment and the room that
contains m zero climbs to a hundred degrees Fahrenheit in summer. The brothers
keep apartment's lights turned off as much as possible. If they switched
on too many lights while m zero was running, they might blow the apartment's
wiring. Gregory can't breathe city air without developing lung trouble,
so he keeps the apartment's windows closed all the time, with air-conditioners
running in them during the summer, but that doesn't seem to reduce the
heat, and as the temperature rises inside the apartment the place can smell
of cooking circuit boards, a sign that m zero is not well. A steady stream
of boxes arrives by Federal Express, and an opposing stream of boxes flows
back to mail-order houses, containing parts that have bombed, along with
letters from the brothers demanding an exchange or their money back. The
building superintendent doesn't know that the Chudnovsky brothers have
been using a supercomputer in Gregory's apartment, and the brothers haven't
expressed an eagerness to tell him.**
**The Chudnovskys, between
them, have published a hundred and fifty-four papers and twelve books,
mostly in collaboration with each other, and mostly on the subject of number
theory or mathematical physics. They work together so closely that it is
possible to argue that they are a single mathematician-anyway, it's what
they claim. The brothers lived in Kiev until 1977, when they left the Soviet
Union and, accompanied by their parents, went to France. The family lived
there for six months, then emigrated to the United States and settled in
New York; they have become American citizens.**
**The brothers enjoy
an official relationship with Columbia University: Columbia calls them
senior research scientists in the Department of Mathematics, but they don't
have tenure and they don't teach students. They are really lone inventors,
operating out of Gregory's apartment in what you might call the old-fashioned
Russo-Yankee style. Their wives are doing well. Gregory's wife, Christine
Pardo Chudnovsky, is an attorney with a midtown law firm. David's wife,
Nicole Lanne- grace, is a political-affairs officer at the United Nations.
It is their salaries that help cover the funding needs of the brother's
supercomputing complex in Gregory and Christine's appartment. Malka Benjaminovna
Chudnovsky, a retired engineer, who is gregory and David's mother, lives
in Gregory's apartment. David spends his days in Gregory's apartment, taking
care of his brother, their mother, and m zero.**
**When the Chudnovskys
applied to leave the Soviet Union, the fact that they are Jewish and mathematical
attracted at least a dozen K.G.B. agents to their case. The brother's father,
Volf Grigorevich Chudnovsky, who was severely beaten by the K.G.B. in 1977,
died of heart failure in 1985. Volf Chudnovsky was a professor of civil
engineering at Kiev Architectual Institute, and he specialized in the structual
stability of buildings, towers, and bridges. He died in America, and not
long before he died he constructed in Gregory's apartment a maze of book
shelves, his last work of civil engineering. The bookshelves extend into
every corner of the apartment, and today they are packed with literature
and computer books and books and papers on the subject of numbers. Since
almost all numbers run to infinity (in digits) and are totally unexplored,
an apartmentful of thoughts about numbers holds hardly any thoughts at
all, even with a supercomputer on the premises to advance their work.**
**The brothers say that
the "m" in "m zero" stands for "machine", and that they use a small letter
to imply that the machine is a work in progress. They represent the name
typographically as "m0". The "zero" stands for success. It implies a dark
history of failure-three duds (in Gregory's apartment) that the brothers
now refer to as negative three, negative two, and negative one. The brothers
broke up the negative machines for scrap, got on the telephone, and waited
for Federal Express to bring more parts.**
**M zero is a parallel
supercomputer, a type of machine that has lately come to dominate the avant-garde
in supercomputer architecture, because the design offers succulent possibilities
for speed in solving problems. In a parallel machine, anywhere from half
a dozen to thousands of processors work simultaneously on a problem, whereas
in a so-called serial machine- a normal computer-the problwem is solved
one step at a time. "A serial machine is bound to be very slow, because
the speed of the machine will be limited by the slowest part of it", Gregory
said. "In a parallel machine, many circuits take on many parts of the problem
at the same time". As of last week, m zero contained sixteen parallel processors,
which ruminate around the clock on the Chednovskys' problems.**
**The brothers' mail-order
supercomputer makes their lives more convenient: m zero performs inhumanly
difficult algebra, finding roots of gigantic systems of equations, and
it has constructed colored images of the interior of Gregory Chudnovsky's
body. According to the Chudnovskys, it could model the weather or make
pictures of air flowing over a wing, if the brothers cared about weather
or wings. What they care about is numbers. To them, numbers are more beautiful,
more nearly perfect, possibly more complicated, and arguably more real
than anything in the world of physical matter.**
**The brothers have
lately been using m zero to explore the number pi. Pi, which is denoted
by the Greek letter, is the most famous rati in mathematics, and is one
of the most ancient numbers known to humanity. Pi is approximately 3.14
- the number of times that a circle's diameter will fit around the circle.
Here is a circle, with its diameter:**

**Pi goes on forever,
and can't be calculated to perfect precision:**
**3.1415926535897932384626433832795028841971693993751....**
**This is known as the
decimal expansion of pi. It is a bloody mess. No apparent pattern emerges
in the succession of digits. The digits of pi marches to infinity in a
predestined yet unfathomable code: they do not repeat periodically, seeming
to pop up by blind chance, lacking any perceivable order, rule, reason,
or design - "random" integers, ad infinitum. If a deep and beautiful design
hides in the digits of pi, no one knows what it is, and no one has ever
been able to see it by staring at the digits. Among mathematicians, there
is a nearly universal feeling that it will never be possible, in principle,
for an inhabitant of out finite universe to discover the system in the
digits of pi. But for the present, if you want attempt it, you need a supercomputer
to probe the endless scrap of leftover pi.**
**Before the Chudnovsky
brothers built m zero, Gregory had to derive pi over the telephone network
while lying in bed. It was inconvenient. Tapping at a small keyboard, which
he sets on the blankets of his bed, he stares at a computer display screen
on one of the bookshelves beside his bed. The keyboard and the screen are
connected to Internet, a network that leads Gregory through cyberspace
into the heart of a Cray somewhere else in the United States. He calls
up a Cray through Internet and programs the machine to make an approximation
of pi. The job begins to run, the Cray trying to estimate the number of
times that the diameter of a circle goes around the periphery, and Gregory
sits back on his pillows and waits, watching messages from the Cray flow
across his display screen. He eats his dinner with his wife and his mother
and then, back in bed, he takes up a legal pad and a red felt-tip pen and
plays with number theory, trying to discover hidden properties of numbers.
Meanwhile, the Cray is reaching toward pui at a rate of a hundred million
operations per second. Gregory dozes beside his computer screen. Once in
a while, he asks the Cray how things are going, and the Cray replies that
the job is still active. Night passes, the Cray running deep toward pi.
Unfortunately, since the exact ratio of the circle's circumference to its
diameter dwells at infinity, the Cray has not even begun to pinpoint pi.
Abruptly, a message appears on Gregory's screen:**
**LINE IS DISCONNECTED.**
**"What the hell is
going on ?" Gregory exclaims. It seems that the Cray has hung up the phone,
and may have crashed. Once again, pi has demonstrated its ability to give
a supercomputer a heart attack.**
**"MYASTHENIA GRAVIS
is a funny thing", Gregory Chudnovsky said one day from his bed in his
junk yard. "In a sense, I'm very lucky, because I'm alive, and I'm alive
after so many years". He has a resonant voice and a Russian accent. "There
are no standard prognosis. It sometimes strikes young women and older women.
I wonder if it is some kind of sluggish virus".**
**It was a cold afternoon,
and rain pelted the windows; the shades are drawn, as always. He lay against
a heap of pillows, with his legs folded under him. He wore a tattered gray
lamb's-wool sweater that had multiple patches on the elbows, and a starched
white shirt, and baggy sweatpants, and a pair of handmade socks. I had
never seen socks like Gregory's. They were two-tone socks, wrincled and
floppy, hand-sewn from pieces of dark-blue and pale-blue cloth, and they
look comfortable. They were the work of Malka Benjaminovna, his mother.
Lines of computer code flickered on the screen beside his bed.**
**This was an apartment
built for long voyages. The paper in the room was jammed into the bookshelves,
from floor to ceiling. The brothers has wedged the paper, sheet by sheet,
into manila folders, until the folders had grown as fast as melons. The
paper also flooded two freestanding bookshelves (placed strategically around
Gregory's bed), five chairs (three of them in a row beside his bed), two
steamer trunks, and a folding cocktail table. I moved carefully around
the room, fearful of triggering a paperslide, and sat on the room's one
empty chair, facing the foot of Gregory's bed, my knees touching the blanket.
The paper was piled in three-foot stacks on the chairs. It guarded his
bed like the flanking towers of a fortress, and his bed sat at the center
of the keep. I sensed a profound happiness in Gregory Chudnovsky's bedroom.
His happiness, it occurred to me later, sprang from the delicious melancholy
of a life chained to a bed in a disordered world that breakes open through
the portals of mathematics into vistas beyomd time or decay.**

**(..)**

**The race toward pi
happens in cyberspace, inside supercomputers. In 1949, Geoerge Reitwiesner,
at the Ballistic Research Laboratory, in Maryland, derived pi to two thousand
and thirty-seven decimal places with ENIAC, the first general-purpose electronic
digital computer. Working at the same laboratory, John von Neumann (one
of the inventors of the ENIAC) searched those digits for signs of order,
but found nothing he could put his finger on. A decade later, Daniel Shanks
and John W. Wrench, Jr., approximated pi to a hundred thousand decimal
places with an I.B.M. 7090 mainframe computer and saw nothing. The race
continued desultorily, through hundreds of thousands of digits, until 1981,
when Yasumasa Kanada, the head of a team of computer scientists at Tokyo
University, used a NEC supercomputer, a Japanese machine, to compute two
million digits of pi. People were astonished that anyone would bother to
do it, but that was only the beginning of the affair. In 1984, Kanada and
his team got sixteen million digits of pi, noticing nothing remarkable.
A year later, William Gosper, a mathematician and distinguished hacker
employed at Symbolics, Inc., in Sunnyvale, California, computed pi to seventeen
and a half million decimal places with a Symbolics workstation, beating
Kanada's team by a million digits. Gosper saw nothing of interest.**
**The next year, David
H. Bailey, at the National Aeronautics and Space Administration, used a
Cray 2 supercomputer and formula discovered by two brothers, Jonathan and
Peter Borwein, to scoop twenty-nine million digits of pi. Bailey found
nothing unusual. A year after that, in 1987, Yasumasa Kanada and his team
got a hundred and thirty-four million digits of pi, using a NEC SX-2 supercomputer.
They saw nothing of interest. In 1988, Kanada kept going, past two hundred
million digits, and saw further amounts of nothing. Then, in the spring
of 1989, the Chudnovsky brothers (who had not previously been known to
have any interest in calculating pi) suddenly announced that they had obtained
four hundred and eighty million digits of pi - a world record - using supercomputers
at two sites in the United States, and had seen nothing. Kanada and his
team were a little surprised to learn of unknown competition operating
in American cyberspace, and they got on a Hitachi supercomputer and ripped
through five hundred and thirty-six million digits, beating the Chudnovskys,
setting a new world record, and seeing nothing. The brothers kept calculating
and soon cracked a billion digits, but Kanada's restless boys and their
Hitachi then nosed into a little more than a billion digits. The
Chudnovskys pressed onward, too, and by the fall of 1989 they had squeaked
past Kanada again, having computed pi to one billion one hundred and thirty
million one hundred and sixty thousand six hundred and sity-four decimal
places, without finding anything special. It was another world record.
At that pouint, the brothers gave up, out of boredom.**

**On a cold winter day,
when the Chudnovskys were about to begin their two-billion-digits expedition
into pi, I rang the bell of Gregory Chudnovsky's apartment, and David answers
the door. He pulled the door open a few inches, and then it stopped, jammed
against an empty cardboard box and a wad of hanging coats. He nudged the
box out of the way with his foot. "Look, don't worry", he said. "Nothing
unpleasant will happen to you. We will not turn you into digits."
A Mini Mag-Lite flashlight protruded from his shirt pocket.**