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What is random?
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Not long ago, the computer network at the offices of American Scientist developed a frustrating problem-turtle file transfers between machines and refusals to print documents, all punctuated by unpredictable periods of normal function. A long diagnosis isolated the problem to a piece of hardware called a hub, essentially a connecting device where computers, printers, scanners and so on meet to communicate. While attempting to verify the device's "illness," one of our editors turned to the hub's manual, which offered one rather useless bit of diagnostic information: The activity light should be flashing randomly. So I watched the pinheadsize green light flash on and off-blinking in a seemingly erratic pattern. It looked random enough, but then I wondered: What is random?
In 1983, Mark Kac asked the same question in this publication (American Scientist 71:405-406). He began by writing: "I am convinced that the vast majority of my readers, and in fact the vast majority of scientists and even nonscientists, are convinced that they know what 'random' is. A toss of a coin is random; so is a mutation, and so is the emission of an alpha particle.... Simple, isn't it?" Well, no. In fact, Kac knew that randomness could be called many things, but not simple. In his essay, he showed that randomness can be quite complicated, and it can be described in more than one way.
During the past 14 years, I thought, a single, simple definition of randomness must have emerged. In search of that definition, I sent an electronic-mail message about it to "Ask Dr. Math" (dr.math@forum.swarthmore.edu)-a Swarthmore College question-and-answer service "for students from Kindergarten through 12th grade (typically ages 5 to 18 in the American school system)." Despite the non-student, non-K-12 nature of my question, my irregular plea apparently touched Dr. Math, who replied: "What an...