On 2/26/2012 3:50 PM, Bruno Marchal wrote:


On 26 Feb 2012, at 06:48, Stephen P. King wrote:

On 2/26/2012 12:26 AM, Stephen P. King wrote:
Hi Folks,

As I was reading an interesting paper, I ran across an equally interesting quote from Richard Feynman:

‘It always bothers me that, according to the laws as we
understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of spaces, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?’

Bruno's idea explains this by showing that an infinite number of computations "run" though each and every event in space-time (please correct my wording!).


You intuit well that this need rewording. You are still talking like an Aristotelian.

Dear Bruno,


I am using the Aristotelian stance as it is the only one that I see as 1p-consistent in these discussions. The Platonist stance would have us taking as articles of faith concepts that are not surveyable (see the previously referenced Laplace draft that I linked previously). I understand that you want to cover this as 3p by using the Yes Doctor and the Teleportation discussion, but this is too context relative to truly be 3p - as it assumes a measure and a particular level of substitution that is functionally invariant. This is the "book-keeping" problem.


Let me put it is this way. There is no space, there is no time, there are no events. Only the arithmetical truth. They represent all computations, including the one which emulates the Löbian numbers' dreams. Physical reality/realities is deep relatively persistent first person realities.

I agree with that claim only at the deepest neutral level. My argument is that this alone is problematic as you need to show exactly how the observation of time (measure of change) occurs at the 1p level. You see to think that the transitivity of numbers alone covers this, but that is wrong headed as there exist in Platonia all possible strings of numbers and as Kitada argues, this generates an inconsistency that can only be overcome by adding a Hamiltonian process to 'regularize" the inconsistency (making it an oscillator). it would help us if you understood the problem of time, as it seems that you do not. Sorry.



So it is not infinite number of computations which run in space-time, it is space-time observations which emerges from arithmetical self-observation.

You misunderstand me. I am considering that for each and every 1p there is an infinite number of computations that (via universality can act as Universal Virtual Reality Machines capable of generating its content - D. Deutsch's idea) and, per universality, there are an infinite number of functionally equivalent physical systems that can implement these computations. This is consistent with both your idea and Pratt's. The Stone-type duality here lets us identify the computations with Boolean algebras side of the duality and the physical systems are identified with the Stone spaces. This gives us a natural explanation of how your result is predictive in the physical sense in that it demands that the physical world appear as "atoms in a void". We can then generalize the topological spaces via the Pontryagin duality to cover all types of observables. The open problem that I see is whether or not there is a generalization of the Boolean algebra side of the duality; there should be something like a Pontryagin duality for Boolean algebras.


Would Feynman be happy with this answer?

Onward!

Stephen

Adding to my question: Could we equally say that an infinite number of physical processes are running each and every instance of a computation?

Good question, and I guess the answer is yes, especially if QM is bot computationalistic correct (= obeying S4Grz1, X1*, and Z1*) and empirically correct (= non refuted for ever (that's different from non refutable)).


It is computationally correct but we have to be sure that we obey the Kochen-Specker and Gleason theorems, which demand that our Q-logic is not restricted to 2 dimensional systems. Otherwise we are unable to predict large physical structures (e.g having Hilbert spaces of dimension < 2). Did you see my query about the LOOMIS–SIKORSKI THEOREM?

Onward!

Stephen

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