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.## Advertising

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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