The Quest for Randomness
Determining whether numbers truly can have no pattern has implications for quantum mechanics, not to mention the stock market and data security.
Let’s return to the question raised by the Dilbert cartoon: Is it ever possible to be sure something is random? If we make no auxiliary assumptions whatsoever, the strict answer is no. At some metaphysical level, any sequence claimed to be random—no matter how patternless it looked—could have been determined (by God, the initial conditions of the universe, or whatever) to be precisely what it is. However, we can come closer to that ideal than one might have thought possible—in effect, saying “If these numbers aren’t random, then some fundamental assumption has to collapse.”
In this article, the assumption was that any regularities in nature are computable, so that they correspond to low Kolmogorov complexity. In my next column, I’ll discuss quantum mechanics and a famous theorem called the Bell inequality, and how they let us generate random numbers under the sole assumption that it’s impossible to send signals faster than light. Notably, the latter approach won’t suffer from the problem of uncomputability—so unlike Kolmogorov complexity, it will actually lead to practical methods for generating guaranteed random numbers.
Scott Aaronson will continue this discussion in the July–August issue’s Technologue column.