The Information (60 page)

It is easy to see that each digit, and each combination of digits, occurs equally often in the long run. Yet the sequence could not be less random. It is rigidly structured and completely predictable. If you know where you are, you know what comes next.

Even apart from freaks like Champernowne’s, it turns out that normal numbers are difficult to recognize. In the universe of numbers, normality is the rule; mathematicians know for sure that almost all numbers are normal. The rational numbers are not normal, and there are infinitely many rational numbers, but they are infinitely outnumbered by normal numbers. Yet, having settled the great and general question, mathematicians can almost never prove that any particular number is normal. This in itself is one of the more remarkable oddities of mathematics.

Even Π retains some mysteries: