In David Deutsch's Beginning of Infinity chapter 8, he criticises
Schmidhuber's Great Programmer idea by saying that it is giving up on
explanation in science, as the hardware on which the "Great Program"
runs is unknowable.

David, why do you say that? Surely, the question of what hardware is
implementing the Great Simulators simply becomes uninteresting, much like
the medieval arguments about the number of angels dancing on the head
of a pin. It is unknowable, and it doesn't matter, as any universal
machine will do.

The second question I have to David is why you say "The whole point of
universality is lost if one conceives of computation as being somehow
prior to the physical world."?

I do appreciate that mathematically, hypercomputers exist, an example
being the infinity hotel example you give in your book. So a
consequence of something like Schmidhuber's theory is that
hypercomputers can never exist in our physical world.

I suppose you would say that if physics were generated by machine, why
the class of Turing universal machine, and not some hyper-(hyper-)
machine? Whereas in a physics-first scenario, physics can only support
Turing computation.

Surely though, we can reverse the question in the physics-first case -
why can't physics support hypercomputation?


I'm copying this to the everything-list, as people there are
interested in this topic too.

Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics
University of New South Wales

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