Pi Keeps 'Em Guessing
It might seem as easy as pie to prove that the digits of pi are random; after all, they dance about so unpredictably that scientists and statisticians have long been using them as a handy stand-in for randomly generated numbers. But surprisingly, mathematicians have been completely at sea when trying to prove that the digits of pi--or any other important irrational number for that matter--are truly random. Now two mathematicians are getting closer.
In 1996, David Bailey of Lawrence Berkeley National Laboratory in California, along with two mathematicians at Simon Fraser University in Vancouver, Canada, flabbergasted the math world by coming up with an algorithm for calculating any digit of pi without having to calculate all the digits that precede it--unlike every other known pi recipe. Bailey and Richard Crandall, a computational mathematician at Reed College in Portland, Oregon, realized that they could use this formula, dubbed BBP, to look at the randomness of pi in a new way.
The BBP formula is written in a certain easily recognizable form, and the duo hypothesize that the value of formulas of that sort (except for particularly boring ones) will skitter chaotically among numbers between 0 and 1. If true, this motion ensures that the output of the BBP formula would be random, and that, in turn, would mean that pi's digits are also random. If the hypothesis is true, they write in the Summer 2001 issue of Experimental Mathematics, it would prove not only pi's randomness, but also that of other constants which have BBP-type formulas, such as the natural log of 2.
Bailey and Crandall haven't cracked the problem yet, but mathematician Jonathan Borwein of Simon Fraser University hopes that their insight will finally allow mathematicians to prove that pi's digits are random. "Whenever you recast an old problem in a new language, there's hope that the new language will provide a new impetus," he says. But even Crandall himself says he expects only a "10% chance of a partial solution" to the hypothesis in the next decade.