On 05 Sep 2012, at 22:24, Stephen P. King wrote:

On 9/5/2012 11:37 AM, Bruno Marchal wrote:

 On 05 Sep 2012, at 14:01, Russell Standish wrote:

For certain choices of "this or that", the ultimate reality is
actually unknowable. For instance, the choice of a Turing complete
basis means that the hardware running the computations is completely
unknowable to the denizens of that computation.

Not really. With comp we know that the *physical* "bottom" is the result of the competition among all universal machines, (by UD-7 or 8) and this leads to (re)define physics by such a competition/ measure on all computations. The initial base ontology is really irrelevant, and it makes no sense to choose one or another, except for technical commodities.

 Dear Bruno,

I am trying hard to be sure that I understand your ideas here. Could you specify the cardinality of "all universal machines"?


How many of them possibly exist?

Aleph_0, like the primes.

Put in another way: there is no ontological hardware. The hardware and wetware are emergent on the digital basic ontology (which can be described by numbers or combinators as they describe the same computations and the same object: you can prove the existence of combinators in arithmetic, and you can prove the existence of numbers from the combinator S and K. So the basic ontology is really the same and we can "know" it (betting on comp). It is really like the choice of a base in a linear space.

So is there or is there not something that corresponds to "resources" (such as memory) for the Universal machines in your thought?

Yes, Stephen, most digital beings have memories, and things like that. All universal machine defines their own way to memorize, and interact. And none, a priori, use any physical resource, only when they are implemented in a special universal one which we bet support us too, but that is a relative situation. Please ask if not clear, or read some good book on computer science. All the (mathematical) machine have memories or equivalent. Keep in mind that they can all emulate each other. So arithmetic (above) can emulate a UNIVAC with transistors and tube, like it can emulate a quantum topological modular functor à-la Kitaev-Friedman.



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