On 5/20/2012 9:33 PM, 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.
I see that the set of all programs is countable.
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.
Ok, I was thinking that because the outputs of infinitely many programs were infinite
there would be 2^\aleph_0, but I see that's a mistake.
Brent
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).
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