Panic in Level 4: Cannibals, Killer Viruses, and Other Journeys to the Edge of Science (12 page)

I
F PI IS TRULY RANDOM
, then at times pi will appear to be orderly. Therefore, if pi is random it contains accidental order. For example, somewhere in pi a sequence may run 070707070707070707 for as many digits as there are atoms in the sun. It’s just an accident. Somewhere else the exact same sequence may appear, only this time interrupted, just once, by the digit 3. Another accident. Every possible arrangement of digits probably erupts in pi, though this has never been proved. “Even if pi is not truly random, you can still assume that you get every string of digits in pi,” Gregory told me. In this respect, pi is like the Library of Babel in the story by Jorge Luis Borges. In that story, Borges imagined a library of vast size that contained all possible books.

You could find all possible books in pi. If you were to assign letters of the alphabet to combinations of digits—for example, the letter
a
might be 12, the letter
b
might be 34—you could turn the digits of pi into letters. (It doesn’t matter what digits are assigned to what letters—the combination could be anything.) You could do this with all alphabets and ideograms in all languages. Then pi could be turned into strings of written words. Then, if you could look far enough into pi, you would probably find the expression “See the U.S.A. in a Chevrolet!” Elsewhere, you would find Christ’s Sermon on the Mount in his native Aramaic tongue, and you would find versions of the Sermon on the Mount that are blasphemy. Also, you would find a guide to the pawnshops of Lubbock, Texas. It might or might not be accurate. Even so, somewhere else you
would
find the accurate guide to Lubbock’s pawnshops…if you could look far enough into pi. You would find, somewhere in pi, the unwritten book about the sea that James Joyce supposedly intended to tackle after he finished
Finnegans Wake.
You would find the collected transcripts of
Saturday Night Live
rendered into Etruscan. You would find a Google-searchable version of the entire Internet with every page on it exactly as it existed at midnight on July 1, 2007, and another version of the Internet from thirty seconds later. Each occurrence of an apparently ordered string in pi, such as the words “Ruin hath taught me thus to ruminate, / That Time will come and take my love away,” is followed by unimaginable deserts of babble. No book and none but the shortest poems will ever actually be seen in pi, for it is infinitesimally unlikely that even as brief a text as an English sonnet will appear in the first 10
⁷⁷
digits of pi, which is the longest piece of pi that can be calculated in this universe.

Anything that can be produced by a simple method is orderly. Pi can be produced by very simple methods; it is orderly, for sure. Yet the distinction between chance and fixity dissolves in pi. The deep connection between order and disorder, between cacophony and harmony, seems to be tantalizingly almost visible in pi, but not quite. “We are looking for some rules that will distinguish the digits of pi from other numbers,” Gregory said. “Think of games for children. If I give you the sequence one, two, three, four, five, can you tell me what the next digit is? A child can do it: the next digit is six. What if I gave you a sequence of a million digits from pi? Could you tell me the next digit just by looking at it? Why does pi look totally unpredictable, with the highest complexity? For all we know, we may never find out the rule in pi.”

H
ERBERT
R
OBBINS
, the coauthor of
What Is Mathematics?,
the book that had turned the Chudnovsky brothers on to math, was an emeritus professor of mathematical statistics at Columbia University and had become friends with the Chudnovskys. He lived in a rectilinear house with a lot of glass in it, in the woods near Princeton, New Jersey. Robbins was a tall, restless man in his seventies, with a loud voice, furrowed cheeks, and penetrating eyes. One day, he stretched himself out on a daybed in a garden room in his house and played with a rubber band, making a harp across his fingertips.

“It is a very difficult philosophical question, the question of what ‘random’ is,” Robbins said. He plucked the rubber band with his thumb,
boink, boink.
“Everyone knows the famous remark of Albert Einstein, that God does not throw dice. Einstein just would not believe that there is an element of randomness in the construction of the world. The question of whether the universe is a random process or is determined in some way is a basic philosophical question that has nothing to do with mathematics. The question is important. People consider it when they decide what to do with their lives. It concerns religion. It is the question of whether our fate will be revealed or whether we live by blind chance. My God, how many people have been murdered over an answer to that question! Mathematics is a lesser activity than religion in the sense that we’ve agreed not to kill each other but to discuss things.”

Robbins got up from the daybed and sat in an armchair. Then he stood up and paced the room, and sat at a table, and moved himself to a couch, and went back to the table, and finally returned to the daybed. The man was in constant motion.

“Mathematics is broken into tiny specialties today, but Gregory Chudnovsky is a generalist who knows the whole of mathematics as well as anyone,” he said as he moved around. “He’s like Mozart. I happen to think that his and David’s pi project is a will-o’-the-wisp, but what do I know? Gregory seems to be asking questions that can’t be answered. To ask for the system in pi is like asking, ‘Is there life after death?’ When you die, you’ll find out. Most mathematicians are not interested in the digits of pi. In order for a mathematician to become interested in a problem, there has to be a possibility of solving it. Gregory likes to do things that are impossible.”

The Chudnovsky brothers were operating on their own, and they were looking more and more unemployable. Columbia University was never going to make them full-fledged members of the faculty, never give them tenure. This had become obvious. The John D. and Catherine T. MacArthur Foundation awarded Gregory Chudnovsky a “genius” fellowship. The brothers had won other fashionable and distinguished prizes, but there was a problem in their résumé, which was that Gregory had to lie in bed most of the time. The ugly truth was that Gregory Chudnovsky couldn’t get an academic job because he was physically disabled. But there were other, more perplexing reasons that had led the Chudnovskys to pursue their work in solitude. They had been living on modest grants from the National Science Foundation and various other research agencies and, of course, on their wives’ salaries. Christine’s father, Gonzalo Pardo, who was a professor of dentistry, had also chipped in. He had built the steel frame for m zero in his basement, using a wrench and a hacksaw.

The brothers’ solitary mode of existence had become known to mathematicians around the world as the Chudnovsky Problem. Herbert Robbins eventually decided to try to solve it. He was a member of the National Academy of Sciences, and he sent a letter to all of the mathematicians in the academy:

I fear that unless a decent and honorable position in the American educational research system is found for the brothers soon, a personal and scientific tragedy will take place for which all American mathematicians will share responsibility.

There wasn’t much of a response. Robbins got three replies to his letter. One, from a professor of mathematics at an Ivy League university, complained about David Chudnovsky’s personality. He remarked that “when David learns to be less overbearing,” the brothers might have better luck.

Then Edwin Hewitt, the mathematician who had helped get the Chudnovsky family out of the Soviet Union, got mad, and erupted in a letter to colleagues:

The Chudnovsky situation is a national disgrace. Everyone says, “Oh, what a crying shame” & then suggests that they be placed at
somebody else’s institution.
No one seems to want the admittedly burdensome task of caring for the Chudnovsky family.

The brothers, because they insisted that they were one mathematician divided between two bodies, would have to be hired as a pair. Gregory would refuse to take any job unless David got a job, too, and vice versa. To hire them, a math department would have to create two openings. And Gregory couldn’t teach classes in the normal way, because he was more or less confined to bed. And he might die, leaving the Chudnovsky Mathematician bereft of half its brain.

“The Chudnovskys are people the world is not able to cope with, and they are not making it any easier for the world,” Herbert Robbins said. “Even so, this vast educational system of ours has poured the Chudnovskys out on the sand, to waste. When I go up to that apartment and sit by Gregory’s bed, I think, My God, when I was a mathematics student at Harvard I was in contact with people far less interesting than this. I’m grieving about it.”

“T
WO BILLION DIGITS OF PI
? Where do they keep them?” Samuel Eilenberg said scornfully. Eilenberg was a distinguished topologist and emeritus professor of mathematics at Columbia University.

“I think they store the digits on a hard drive,” I answered.

Eilenberg snorted. He didn’t care about some spinning piece of metal covered with pi. He was one of the reasons why the Chudnovskys would never get permanent jobs at Columbia; he made it pretty clear that he would see to it that they were denied tenure. “In the academic world, we have to be careful who our colleagues are,” he told me. “David is a nudnik! You can spend all your life computing digits. What for? It’s about as interesting as going to the beach and counting sand. I wouldn’t be caught dead doing that kind of work.”

In his view, there was something unclean about doing mathematics with a machine. Samuel Eilenberg was a member of the famous Bourbaki group. This group, a sort of secret society of mathematicians that was founded in 1935, consisted mostly of French members (though Eilenberg was originally Polish) who published collectively under the fictitious name Nicolas Bourbaki; they were referred to as “the Bourbaki.” In a quite French way, the Bourbaki were purists who insisted on rigor and logic and formalism. Some members of the Bourbaki group looked down on applied mathematics—that is, they seemed to scorn the use of mathematics to solve real-world problems, even in physics. The Bourbaki especially seemed to dislike the use of machinery in pursuit of truth. Samuel Eilenberg appeared to loathe the Chudnovskys’ supercomputer and what they were doing with it. “To calculate the two billionth digit of pi is to me abhorrent,” he said.

“‘Abhorrent’? Yes, most mathematicians would probably agree with that,” said Dale Brownawell, a respected number theorist at Penn State. “Tastes change, though. To see the Chudnovskys carrying on science at such a high level with such meager support is awe-inspiring.”

Richard Askey, a prominent mathematician at the University of Wisconsin at Madison, would occasionally fly to New York to sit at the foot of Gregory Chudnovsky’s bed and talk about mathematics. “David Chudnovsky is a very good mathematician,” Askey said to me. “Gregory is a great mathematician. The brothers’ pi stuff is just a small part of their work. They are really trying to find out what the word ‘random’ means. I’ve heard some people say that the brothers are wasting their time with that machine, but Gregory Chudnovsky is a very intelligent man who has his head screwed on straight, and I wouldn’t begin to question his priorities. Gregory Chudnovsky’s situation is a national problem.”

“I
T LOOKS LIKE KVETCHING
,” Gregory said from his bed. “It looks cheap, and it is cheap. I don’t think we were somehow wronged. I really can’t teach. So what does one do about it? We barely have time to do the things we want to do. What is life, and where does the money come from?” He shrugged.

At the end of the summer, the brothers halted their probe into pi. They had other things they wanted to do with their supercomputer, and it was time to move on. They had surveyed pi to 2,260,321,336 digits. It was a world record, doubling their previous world record. If the digits were printed in type, they would stretch from New York to Los Angeles.

In Japan, their competitor Yasumasa Kanada reacted gracefully. He told
Science News
that he might be able to get a billion and a half digits if he could rent enough time on the Hitachi—the half-megawatt monster.

“You see the advantage of being truly poor,” Gregory said to me. “We had to build our machine, but now we own it.”

M zero had spent most of its time checking the answer to make sure it was correct. “We have done our tests for patterns, and there is nothing,” Gregory said. He was nonchalant about it. “It would be rather stupid if there were a pattern in a few billion digits. There are the usual things. The digit three is repeated nine times in a row, and we didn’t see that before. Unfortunately, we still don’t have enough computer power to see anything in pi.”

And yet…and yet…the brothers felt that they might have noticed something in pi. It hovered out of reach, but seemed a little closer now. It was a slight change in pi that seemed to rise and fall like a tide, as if a distant moon were passing over the sea of digits. It was something random, probably. The brothers felt that they might only have glimpsed the human desire for order. Or was it a wave rippling through pi? Would the wave, if it was there, be the first thread in a tapestry of worlds blossoming in pi? “We need a trillion digits,” David said. Maybe one day they would run the calculation into a trillion digits. Or maybe not. A trillion digits of pi printed in ordinary type would stretch from here to the moon and back, twice. Maybe one day, if they lived and if their machines held together, they would orbit the moon in digits, and would head for Alpha Centauri, seeking pi.