On Sun, May 20, 2012 at 12:06:05PM -0700, meekerdb wrote: > On 5/20/2012 9:27 AM, Stephen P. King wrote: > > > >4) What is the cardinality of "all computations"? > > Aleph1. >
Actually, it is aleph_0. The set of all computations is countable. OTOH, the set of all experiences (under COMP) is uncountable (2^\aleph_0 in fact), which only equals \aleph_1 if the continuity hypothesis holds. This is the origin of Bruno's claim that COMP entails that physics is not computable, a corrolory of which is that Digital Physics is refuted (since DP=>COMP). -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
