2001/12/17 by Cristian S. Calude, Calude, Cristian S., Michael J. Dinneen +3
Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.AO #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0112022
16 pages; Experimental Mathematics (accepted)
arxiv created 2002/02/11 · arxiv updated 2009/11/30
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.