Infected with Order, Carl Zimmer

Discover, January 31, 1994

No one likes to be the bearer of bad tidings. But Alan Ferrenberg, a physicist at the University of Georgia, has discovered that bad news is a great way to draw people to talks. This past year Ferrenberg got the rapt attention of fellow physicists by showing them how science’s supply of random numbers is badly contaminated with order.

Random numbers are as crucial to science as they are to a game of craps; they form the basis for computer simulations of everything from collapsing stars to expanding universes, from the aerodynamics of fluids to the vagaries of stock market fluctuations.

Computers allow researchers to simulate a complex phenomenon by reducing it to a huge number of simple and understandable interactions, each of which has a certain known probability of having a certain outcome. A computer uses a program called a random-number generator to simulate the outcome of each interaction according to the known probabilities.

A physicist who wants to model the journey of a neutron through a block of uranium, for example, can calculate the exact probability that the neutron will be absorbed in any given encounter with a uranium nucleus. If the chances happen to be 1 in 6, the physicist could roll a die, use the result to decide whether or not the neutron had been absorbed, and then go on to the next encounter. But if the probability is anything other than 1 in 6, or if a few million encounters have to be simulated, dice are no longer an option. Instead the physicist needs a computer program that can quickly generate a string of truly random numbers.

A random-number generator consists of a series of simple steps. For example, an early generator produced numbers as follows: Start with some four-digit “seed” number, square it, take the middle four digits as your first random number, and then use it as the seed for the next. But it turns out that this generator is loaded, although more subtly than dice. If at some point the generator produces a number such as 3,300, with two zeros at the end, every following number will also end with two zeros. Instead of picking four-digit numbers at random from a pool of 10,000, the generator now locks onto only 100 of them.

Some number sequences can appear random for trillions and trillions of numbers before discernible patterns start to emerge. And if hidden flaws lurk in the numbers, the simulations may be skewed. Yet researchers have grown confident in–and dependent on– the newest generators, which can pass brutal tests for randomness and run at blinding speeds on computers. That’s why Ferrenberg’s results were so disturbing.

He was test-driving a new simulation program when he discovered the flaw. Essentially, his work involved simulating the magnetism of materials, which means knowing how the spins of atoms will line up under various conditions. He knew what the solution would be in a simple case. So he tried his program to see if it would produce the same result as the known solution. To his consternation, the result was decidedly off the mark.

Ferrenberg combed through his program for two weeks looking for bugs and then ran it again; the answer that came back was still wrong. A colleague, Joanna Wong, suggested that his number generator was flawed. At first he didn’t believe her, but by the time he’d eliminated all other possible sources of error, he was convinced she was right. Soon he was spending all his time testing generators. Ferrenberg realized that his program could function as an extremely demanding test of random-number generators, and that it could detect errors hidden from gentler scrutiny. He tried other popular generators and found that they sometimes gave bad answers as well.

Ferrenberg’s result doesn’t mean all computer simulations are bunk; a simulation may well be unaffected by the particular pattern that infects its random-number generator. Nevertheless, Ferrenberg has stirred up a lot of anxiety among the people who use generators to make a living. One astrophysicist, for example, called Ferrenberg’s office because of concern that his simulation of galactic jets–fountains of hot gas that spew from the cores of some galaxies–might be badly flawed.

Mathematicians, on the other hand, are fatalistic. After all, numbers produced by mathematical generators are already related to one another by the generator itself; it’s no surprise that after a while patterns emerge. As computer pioneer John von Neumann stated bluntly more than 40 years ago, “Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin… There is no such thing as a random number.”