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 [email protected] 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/20190816233116.GX20075%40zen.
