Read Online Panic in Level 4: Cannibals, Killer Viruses, and Other Journeys to the Edge of Science by Richard Preston - Free Book Online
Authors: Richard Preston
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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.
P I WAS BY NO MEANS the only unexplored number in the Chudnovskys’ inventory, but it was one that interested them. They wondered whether the digits contained a hidden rule, an as yet unseen architecture, close to the mind of God. A subtle and fantastic order might appear in the digits of pi way out there somewhere; no one knew. No one had ever proved, for example, that pi did not turn into a string of nines and zeros, spattered in some peculiar arrangement. It could be any sort of arrangement, just so long as it didn’t repeat periodically; for it has been proven that pi never repeats periodically. Pi could, however, conceivably start doing something like this: 122333444455555666666…. That is, the digits might suddenly shift into a strong pattern. Such a pattern is very regular, but it doesn’t repeat periodically. (Mathematicians felt it was very unlikely that pi would ever become obviously regular in some way, but no one had been able to prove that it didn’t. )
If we were to explore the digits of pi far enough, they might resolve into a breathtaking numerical pattern, as knotty as The Book of Kells, and it might mean something. It might be a small but interesting message from God, hidden in the crypt of the circle, awaiting notice by a mathematician. On the other hand, the digits of pi might ramble forever in a hideous cacophony, which was a kind of absolute perfection to a mathematician like Gregory Chudnovsky. Pi looked “monstrous” to him. “We know absolutely nothing about pi,” he declared from his bed. “What the hell does it mean? The definition of pi is really very simple—it’s just the circumference to the diameter—but the complexity of the sequence it spits out in digits is really unbelievable. We have a sequence of digits that looks like gibberish.”
“Maybe in the eyes of God pi looks perfect,” David said, standing in a corner of the bedroom, his head and shoulders visible above towers of paper.
Mathematicians call pi a transcendental number. In simple terms, a transcendental number is a number that exists but can’t be expressed in any finite series of finite operations. *2 For example, if you try to express pi as the solution to an algebraic equation made up of terms that have integer coefficients in them, you will find that the equation goes on forever. Expressed in digits, pi extends into the distance as far as the eye can see, and the digits don’t repeat periodically, as do the digits of a rational number. Pi slips away from all rational methods used to locate it. Pi is a transcendental number because it transcends the power of algebra to display it in its totality.
It turns out that almost all numbers are transcendental, yet only a tiny handful of them have ever actually been discovered by humans. In other words, humans don’t know anything about almost all numbers. There are certainly vast classes and categories of transcendental numbers that have never even been conjectured by humans—we can’t even imagine them. In fact, it’s very difficult even to prove that a number is transcendental. For a while, mathematicians strongly suspected that pi was a transcendental number, but they couldn’t prove it. Eventually, in 1882, a German mathematician named Ferdinand von Lindemann proved the transcendence of pi. He proved, in effect, that pi can’t be written on any piece of paper, no matter how big: a piece of paper as big as the universe would not even begin to be large enough to hold the tiniest droplet of pi. In a
“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.
P I WAS BY NO MEANS the only unexplored number in the Chudnovskys’ inventory, but it was one that interested them. They wondered whether the digits contained a hidden rule, an as yet unseen architecture, close to the mind of God. A subtle and fantastic order might appear in the digits of pi way out there somewhere; no one knew. No one had ever proved, for example, that pi did not turn into a string of nines and zeros, spattered in some peculiar arrangement. It could be any sort of arrangement, just so long as it didn’t repeat periodically; for it has been proven that pi never repeats periodically. Pi could, however, conceivably start doing something like this: 122333444455555666666…. That is, the digits might suddenly shift into a strong pattern. Such a pattern is very regular, but it doesn’t repeat periodically. (Mathematicians felt it was very unlikely that pi would ever become obviously regular in some way, but no one had been able to prove that it didn’t. )
If we were to explore the digits of pi far enough, they might resolve into a breathtaking numerical pattern, as knotty as The Book of Kells, and it might mean something. It might be a small but interesting message from God, hidden in the crypt of the circle, awaiting notice by a mathematician. On the other hand, the digits of pi might ramble forever in a hideous cacophony, which was a kind of absolute perfection to a mathematician like Gregory Chudnovsky. Pi looked “monstrous” to him. “We know absolutely nothing about pi,” he declared from his bed. “What the hell does it mean? The definition of pi is really very simple—it’s just the circumference to the diameter—but the complexity of the sequence it spits out in digits is really unbelievable. We have a sequence of digits that looks like gibberish.”
“Maybe in the eyes of God pi looks perfect,” David said, standing in a corner of the bedroom, his head and shoulders visible above towers of paper.
Mathematicians call pi a transcendental number. In simple terms, a transcendental number is a number that exists but can’t be expressed in any finite series of finite operations. *2 For example, if you try to express pi as the solution to an algebraic equation made up of terms that have integer coefficients in them, you will find that the equation goes on forever. Expressed in digits, pi extends into the distance as far as the eye can see, and the digits don’t repeat periodically, as do the digits of a rational number. Pi slips away from all rational methods used to locate it. Pi is a transcendental number because it transcends the power of algebra to display it in its totality.
It turns out that almost all numbers are transcendental, yet only a tiny handful of them have ever actually been discovered by humans. In other words, humans don’t know anything about almost all numbers. There are certainly vast classes and categories of transcendental numbers that have never even been conjectured by humans—we can’t even imagine them. In fact, it’s very difficult even to prove that a number is transcendental. For a while, mathematicians strongly suspected that pi was a transcendental number, but they couldn’t prove it. Eventually, in 1882, a German mathematician named Ferdinand von Lindemann proved the transcendence of pi. He proved, in effect, that pi can’t be written on any piece of paper, no matter how big: a piece of paper as big as the universe would not even begin to be large enough to hold the tiniest droplet of pi. In a
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