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

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