20 Nov '04 12:01

One day, a mischievous deity chooses a number uniformly at random from [0,1], and imparts to you knowledge of

We'll say that you 'understand' the number if you can provide a mathematical definition which uniquely determines the number. For example, people 'understand' numbers like 7, pi, the Riemann zeta function evaluated at e, and even weird numbers like omega, which is a constant derived from Turing's halting problem: http://mathworld.wolfram.com/ChaitinsConstant.html

After a while you decide immortality isn't all it's cracked up to be, and so try to end it all by understanding the number. You don't care how long it takes - if you have to persuade generations of mathematicians to help you out until a definition is produced, then so be it.

What is the probability that, despite your best efforts, there is no way you can avoid living forever?

*exactly*what this number is, without telling you any of its special properties. In doing so, he says "This is the ineffable number. If you come to understand the number, I shall strike you dead instantly. However, unless and until that time comes, you will not die."We'll say that you 'understand' the number if you can provide a mathematical definition which uniquely determines the number. For example, people 'understand' numbers like 7, pi, the Riemann zeta function evaluated at e, and even weird numbers like omega, which is a constant derived from Turing's halting problem: http://mathworld.wolfram.com/ChaitinsConstant.html

After a while you decide immortality isn't all it's cracked up to be, and so try to end it all by understanding the number. You don't care how long it takes - if you have to persuade generations of mathematicians to help you out until a definition is produced, then so be it.

What is the probability that, despite your best efforts, there is no way you can avoid living forever?