in reply to the secret of PI
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.


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Re: Mystic numbers (Re: the secret of PI)
by japhy (Canon) on May 04, 2001 at 16:43 UTC  
by jcwren (Prior) on May 04, 2001 at 18:23 UTC  
Re (tilly) 1: Mystic numbers (Re: the secret of PI)
by tilly (Archbishop) on May 04, 2001 at 19:20 UTC  
by jynx (Priest) on May 05, 2001 at 03:02 UTC  
Re: Mystic numbers (Re: the secret of PI)
by Anonymous Monk on Aug 19, 2003 at 23:27 UTC  
by larsen (Parson) on Aug 20, 2003 at 08:05 UTC 