Hard-to-describe numbers

who thought that one number could be so powerful?

consider a number so rare that most of math’s difficult enigmas can be solved simply by reciting the number. this number might be represented somewhere in the universe, but even if a person stumbled upon it, they would not be able to identify it. have i successfully made this number sound like an incantation from some numerology text?

well, charley bennett wrote a proof of this number’s existence in his 1979 paper “on random and hard-to-describe numbers” (requires acrobat). the paper is a dense read, even for those versed in computability theory, but if you get stuck, you can skip to the end, where you’ll find gems like this one:

“to know it in detail, one would have to accept its uncomputable digit sequence on faith like words of a sacred text. it embodies an enormous amount of wisdom in a very small space, inasmuch as its first few thousand digits, which could be written on a small piece of paper, contain the answers to more mathematical questions than could be written down in the entire universe…”

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