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?
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 ...
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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