On 03 Feb 2011, at 12:05, Andrew Soltau wrote:
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.
Not at all. the point is that in step seven, you can still argue for
comp + mat, by postulating that the material universe is too little.
If you believe at the start that the (apparent) universe is enough big
to contain the UD*, then the reversal is done, and we are already in
the "omega point" of arithmetic, and you should then see that physics
is a branch of number theory (indeed the branch of the first person
sharable number's belief, say).
Step 8 is needed only for those willing to save MAT by advocating a
little finite physical reality.
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.
So by conceptual OCCAM let us choose the simplest one. Tipler uses
arithmetic + QM. But the argument shows that arithmetic is enough, and
that we can, or more aptly: we have too, explain QM (or the real
physics, in case QM is false) from it.
And, as I said, the advantage of doing that (beyond the fact that we
have to do it), is that it gives both the quanta and the qualia. QM
typically gives only the collapse, not the wave which is presupposed.
Bruno
http://iridia.ulb.ac.be/~marchal/
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