http://www.perlmonks.org?node_id=77935


in reply to the secret of PI

If someone could be able to give a proof that \pi's digits follow a casual distribution, you could find in it every possible finite sequence of digits. Thus, you could find on \pi the source for Perl 6, all nodes of PerlMonks (even those that are not written yet) and so on...

Furthermore, such a true casual number exists: we are able to define it and we know some of its properties, but it is demonstrated that we can't compute it. This number is called \Omega, and it's defined as the probability that an Universal Turing Machine halts given random input.

\Omega has other interesting properties. If we could know \Omega we would be able to solve the halting problem for every Turing Machine, finding a solution to, for example, the Goldbach's conjecture and Collatz's game.

If you want to read more about this mystic number and related topics, visit the home page of this wise man.