Panic in Level 4: Cannibals, Killer Viruses, and Other Journeys to the Edge of Science (7 page)

The Chudnovsky Mathematician: Gregory and David Chudnovsky in Gregory’s New York City apartment, 1992.
Irena Roman

“We are a full-service company,” David said. “Of course, you know what ‘full-service’ means in New York. It means ‘You want it? You do it yourself.’”

A steel frame stood in the center of the room, screwed together with bolts. It held split-open shells of personal computers—cheap PC clones, knocked wide open like cracked walnuts, their meat spilling all over the place. The brothers had crammed superfast logic boards inside the PCs. Red lights on the boards blinked. The floor was a quagmire of cables.

The brothers had also managed to fit into the room masses of empty cardboard boxes, and lots of books (Russian classics, with Cyrillic lettering on their spines), and screwdrivers, and data-storage tapes, and software manuals by the cubic yard, and stalagmites of obscure trade magazines, and a twenty-thousand-dollar engineering computer that they no longer used. “We use it as a place to stack paper,” Gregory explained. From an oval photograph on the wall, the face of Volf Chudnovsky, their late father, looked down on the scene. The walls and the French door were covered with sheets of drafting paper showing circuit diagrams. They resembled cities seen from the air. Various disk drives were scattered around the room. The drives were humming, and there was a continuous whir of fans. A strong warmth emanated from the equipment, as if a steam radiator were going in the room. The brothers were heating the apartment with silicon chips.

“M
YASTHENIA GRAVIS
is a funny thing,” Gregory Chudnovsky said one day from his bed in his bedroom, the junkyard. “In a sense, I’m very lucky, because I’m alive, and I’m alive after so many years. There is 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 were drawn, as always, and the room was stiflingly warm. He lay against a heap of pillows with his legs folded under him. His bed was surrounded by freestanding bookshelves packed and piled with ramparts of stacked paper. That day, he wore the same tattered wool sweater, a starched white shirt, blue sweatpants, and another pair of handmade socks. I had never seen socks like Gregory’s. They were two-tone socks, wrinkled and floppy, hand-sewn from pieces of dark blue and pale blue cloth, and they looked 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 bookshelves along the wall, too, from floor to ceiling. The brothers had wedged the paper, sheet by sheet, into manila folders, until the folders had grown as fat as melons. The paper was also stacked chest-high to chin-high on five chairs (three of them in a row beside his bed). It was heaped on top of and filled two steamer trunks that sat beneath the window, and the paper had accumulated in a sort of unstable-looking lava flow on a small folding cocktail table. I moved carefully around the room, fearful of triggering a paperslide, and I sat down on the room’s one empty chair, facing the foot of Gregory’s bed, my knees touching the blanket. The paper surrounded his bed like the walls of a fortress, and his bed sat at the center of the keep. I sensed a profound happiness in Gregory Chudnovsky. His happiness, it occurred to me later, sprang from the delicious melancholy of a life spent largely in bed while he explored a more perfect world that opened through the portals of mathematics into vistas beyond time or decay.

“The system of this paper is archaeological,” he said. “By looking at a slice, I know the date. This slice is from five years ago. Over here is some paper from four years ago. What you see in this room is our working papers, as well as the papers we used as references. Some of the references we pull out once in a while to look at, and then we leave them in another pile. Once, we had to make a Xerox copy of the same book three times, and we put it in three different piles, so we could be sure to find it when we needed it. There are books in there by Kipling and Macaulay. Eh, this place is a mess. Actually, when we want to find a book it’s easier to go to the library.”

Much of the paper consisted of legal pads covered with Gregory’s handwriting. His handwriting was dense and careful, a flawless minuscule written with a felt-tipped pen. The writing contained a mixture of theorems, calculations, proofs, and conjectures concerning numbers. He used a felt-tip pen because he didn’t have enough strength in his hand to press a pencil on paper. Mathematicians who had visited Gregory Chudnovsky’s bedroom had come away dizzy, wondering what secrets the scriptorium might hold. He cautiously referred to the steamer trunks beneath the window as valises. They were filled to the lids with compressed paper. When Gregory and David flew to Europe to speak at conferences on the subject of numbers, they took both “valises” with them, in case they needed to refer to a proof or a theorem. Their baggage particularly annoyed Belgian officials. “The Belgians were always fining us for being overweight,” Gregory said.

The brothers’ mail-order supercomputer made their lives more convenient. It performed inhumanly difficult algebra, finding roots of gigantic systems of equations, and it constructed colored images of the interior of Gregory Chudnovsky’s body. They used the supercomputer to analyze and predict fluctuations in the stock market. They had been working with a well-known Wall Street investor named John Mulheren, helping him get a profitable edge in computerized trades on the stock market. One day I called John Mulheren to find out what the brothers had been doing for him. “Gregory and David have certainly made us money,” Mulheren said, but he wouldn’t give any details on what the brothers had done. Mulheren had been paying the Chudnovskys out of his trading profits; they used the money to help fund their research into numbers. To them, numbers were more beautiful, more nearly perfect, possibly more complicated, and arguably more real than anything in the world of physical matter.

T
HE NUMBER PI
, or
, is the most famous ratio in mathematics. It is also one of the most ancient numbers known to humanity. Nobody knows when pi first came to the awareness of the human species. Pi may very well have been known to the builders of Stonehenge, around 2,600
B.C.E
. Certainly it was known to the ancient Egyptians. Pi is approximately 3.14—it is the number of times that a circle’s diameter will fit around a circle. On the following page is a circle with its diameter.

Landscape with a circle and its diameter. This drawing shows a rough visual approximation of pi.
Drawing by Richard Preston

Pi is an exact number; there is only one pi. Even so, pi cannot be expressed
exactly
using any finite string of digits. If you try to calculate pi exactly, you get a chain of random-looking digits that never ends. 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. If you try to express pi in another way, using an algebraic equation rather than digits,
the equation goes on forever.
There is no way to show pi using digits or an equation that doesn’t get lost in the sands of infinity. Pi can’t be shown completely or exactly in any finite form of mathematical representation. There is only one way to show pi exactly, and that is with a symbol. See the illustration on the following page for a symbol for pi.

The pizza pi I baked and drew, here, is as good a symbol for pi as any other. (It tasted good, too.) The digits of pi march to infinity in a predestined yet unfathomable code. When you calculate pi, its digits appear, one by one, endlessly, while no apparent pattern emerges in the succession of digits. They never repeat periodically. They seem 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 caught a glimpse of the pattern by staring at the digits. There is certainly a design in pi, no doubt about it. It is also almost certain that the human mind is not equipped to see that design. Among mathematicians, there is a feeling that it may never be possible for an inhabitant of our universe to discover the system in the digits of pi. But for the present, if you want to attempt it, you need a supercomputer to probe the endless sea of pi.

Pi.
Drawing by Richard Preston

Before the Chudnovsky brothers built m zero, Gregory had to derive pi over the Internet while lying in bed. It was inconvenient. The work typically went like this:

Tapping at a small wireless keyboard, which he places on the blankets of his bed, he stares at a computer display screen on one of the bookshelves beside his bed.

The keyboard and screen are connected through cyberspace into the heart of a Cray supercomputer at the Minnesota Supercomputer Center, in Minneapolis. He calls up the Cray through the Internet. When the Cray answers, he sends into the Cray a little software program that he has written. This program—just a few lines of code—tells the supercomputer to start making an approximation of pi. The job begins to run. The Cray starts trying to estimate the number of times the diameter of a circle goes around the periphery.

While this is happening, Gregory sits back on his pillows and waits. He watches messages from the Cray flow across his display screen. The supercomputer is estimating pi. He gets hungry and wanders into the dining room to eat dinner with his wife and his mother. An hour or so later, back in bed, he takes up a legal pad and a red felt-tip pen and plays around with number theory, trying to discover hidden properties of numbers. All the while, the Cray in Minneapolis has been trying to get closer to pi at a rate of a hundred million operations per second. Midnight arrives. Gregory dozes beside his computer screen. Once in a while, he taps on the keys, asking the Cray how things are going. The Cray replies that the job is still active. The night passes and dawn comes near, and the Cray is still 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’s going on?” Gregory exclaims.

Moments later, his telephone rings. It’s a guy in Minneapolis who’s working the night shift as the system operator of the Cray. He’s furious. “What the hell did you do? You’ve crashed the Cray! We’re down!”

Once again, pi has demonstrated its ability to give the most powerful computers a heart attack.