Computing A Glimpse of Randomness
Abstract
A Chaitin Omega number is the halting probability of a universal Chaitin (self-delimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing, converging sequence of rationals) and random (its binary expansion is an algorithmic random sequence). In particular, every Omega number is strongly non-computable. The aim of this paper is to describe a procedure, which combines Java programming and mathematical proofs, for computing the exact values of the first 64 bits of a Chaitin Omega: 0000001000000100000110001000011010001111110010111011101000010000. Full description of programs and proofs will be given elsewhere.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2001
- DOI:
- 10.48550/arXiv.nlin/0112022
- arXiv:
- arXiv:nlin/0112022
- Bibcode:
- 2001nlin.....12022C
- Keywords:
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- Chaotic Dynamics;
- Adaptation and Self-Organizing Systems
- E-Print:
- 16 pages