On Fri, Aug 16, 2019 at 12:06:32PM -0500, Jason Resch wrote: > > Thanks for the background and explanation. Is it the case then that any > undecidable (creative?) set is a compact description of universal > dovetailing? > Would Chaitin's constant also qualify as a compact description of the > universal > dovetailing (though being a single real number, rather than a set of rational > complex points)? >
Related to this, on page 218 of Li and Vitanyi's "Introduction to Kolmogorov Complexity and it Applications", right under corollary 3.6.2 is the statement: "Moreover, for all axiomatic mathematical theories that can be extressed compactly enough to be conceivably interesting to human beings, say in fewer than 10,000 bits, [the first 10,000 bits of the Chatin probability Ω] can be used to decide for every statement in the theory whether it is the true, false or independent. ... Thus Ω is truly the number of Wisdom, and 'can be known of, but not known, through human reason' [C.H Bennett and M. Gardner, Sci Am. 241:11(1979),20-34]". Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow hpco...@hpcoders.com.au Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/20190816233116.GX20075%40zen.
