On Mon, May 21, 2012 at 07:42:01AM -0400, Stephen P. King wrote: > On 5/21/2012 12:33 AM, Russell Standish wrote: > >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. > > Hi Russell, > > Interesting. Do you have any thoughts on what would follow from > not holding the continuity (Cantor's continuum?) hypothesis? >

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No - its not my field. My understanding is that the CH has bugger all impact on quotidian mathematics - the stuff physicists use, basically. But it has a profound effect on the properties of transfinite sets. And nobody can decide whether CH should be true or false (both possibilities produce consistent results). Its one reason why Bruno would like to restrict ontology to machines, or at most integers - echoing Kronecker's quotable "God made the integers, all else is the work of man". > > > >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). > > > Does the symbol "=>" mean "implies"? I get confused ... > Yes, that is the usual meaning. It can also be written (DP or not COMP). Of course in Fortran, it means something entirely different: it renames a type, much like the typedef statement of C. Sorry, that was a digression. > -- > Onward! > > Stephen > > "Nature, to be commanded, must be obeyed." > ~ Francis Bacon > > > -- > 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. -- ---------------------------------------------------------------------------- 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.