On 01/02/11 20:07, Bruno Marchal wrote:
In step 8 you state that 'a “physical universe” really “exists” and
is too little in the sense of not being able to generate the entire
UD*, nor any reasonable portions of it,'. However, if we adopt
Tipler's Omega point scenario, we get infinite computational power as
the universe collapses into the big crunch. Tipler specifically
states that all possible computations will be carried out in such a
scenario, including all possible experiential realities.
Any UD does that, indeed. No need of physical omega point. arithmetic
gives you alpha points for any alpha constructive ordinal, and even
quasi names for above the constructive ordinals. Machine's theologies
are rich. If the rational Mandelbrot is Turing universal (Sigma_1
complete) then it represents already an Omega points.
Yes, but your point in step 8 is that a physical universe is *too
little*, but with omega point it is not too little, it is as rich as
arithmetically possible.
Yes, 'If the rational Mandelbrot is Turing universal (Sigma_1 complete)
then it represents already an Omega points.', but, also, Omega point
represents already the Turing universal rational Mandelbrot. Neither is
necessarily richer than or prior to the other.
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