The Information (52 page)

Then again, it is special. It begins a book published in 1955 with the title
A Million Random Digits
. The RAND Corporation generated the digits by means of what it described as an electronic roulette wheel: a pulse generator, emitting 100,000 pulses per second, gated through a five-place binary counter, then passed through a binary-to-decimal converter, fed into an IBM punch, and printed by an IBM model 856 Cardatype.
^♦
The process took years. When the first batch of digits was tested, statisticians discovered significant biases: digits, or groups of digits, or patterns of digits that appeared too frequently or not frequently enough. Finally, however, the tables were published. “Because of the very nature of the tables,” the editors said wryly, “it did not seem necessary to proofread every page of the final manuscript in order to catch random errors of the Cardatype.”

The book had a market because scientists had a working need for random numbers in bulk, to use in designing statistically fair experiments and building realistic models of complex systems. The new method of Monte Carlo simulation employed random sampling to model phenomena that could not be solved analytically; Monte Carlo simulation was invented and named by von Neumann’s team at the atomic-bomb project, desperately trying to generate random numbers to help them calculate neutron diffusion. Von Neumann realized that a mechanical computer, with its deterministic algorithms and finite storage capacity, could never generate truly random numbers. He would have to settle for
pseudorandom
numbers: deterministically generated numbers that behaved as if random. They were random enough for practical purposes. “Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin,”
^♦
said von Neumann.

Randomness might be defined in terms of order—its absence, that is. This orderly little number sequence can hardly be called “random”:

Yet it makes a cameo appearance in the middle of the famous million random digits. In terms of probability, that is to be expected: “00000”
is as likely to occur as any of the other 99,999 possible five-digit strings. Elsewhere in the million random digits we find:

This, too, appears patterned.

To pick out fragments of pattern in this jungle of digits requires work by an intelligent observer. Given a long enough random string, every possible short-enough substring will appear somewhere. One of them will be the combination to the bank vault. Another will be the encoded complete works of Shakespeare. But they will not do any good, because no one can find them.

Perhaps we may say that numbers like 00000 and 010101 can be random in a particular context. If a person flips a fair coin (one of the simplest mechanical random-number generators) long enough, at some point the coin is bound to come up heads ten times in a row. When that happens, the random-number seeker will typically discard the result and go for a coffee break. This is one of the ways humans do poorly at generating random numbers, even with mechanical assistance. Researchers have established that human intuition is useless both in predicting randomness and in recognizing it. Humans drift toward pattern willy-nilly. The New York Public Library bought
A Million Random Digits
and shelved it under Psychology. In 2010 it was still available from Amazon for eighty-one dollars.

A number is (we now understand) information. When we modern people, Shannon’s heirs, think about information in its purest form, we may imagine a string of 0s and 1s, a binary number. Here are two binary strings, fifty digits long: