Brent,

I must go, so I will just comment one line before commenting the other paragraph (tomorrow, normally).


Le 18-janv.-07, à 06:38, Brent Meeker a écrit :

Why isn't the computer (or rock) associated with an infinity of computations? I'm assuming you mean a potential countable infinity in the future.


I don't know if computers or rocks "really exist", nor what you mean exactly by such words, but as far as you can associate a computational state to the computer or to the rocks, it belongs to a (first person actual) NON COUNTABLE infinity of computational histories, including quite dummy one, like a program which dovetails on some loopy local simulation of the rock (or the computer) together with a (infinite) dovetailing on the real numbers. Cf my old conversation with Jurgen Schmidhuber. OK?

That is why comp predicts a priori not only some white rabbits, but continua of white rabbits. QM eliminates them by "destructive interference", and my point is just that if we take comp seriously enough, then we have to justify those destructive interference by classical computer science/number theory alone.

Now, a way to see what happens ( a shortcut!) consists in interviewing a correct lobian machine which looks inward, and, because such a machine has to take into account the modal nuances forced by the incompleteness phenomenon, i.e. the nuance between p, Bp, Bp & p, Bp & Dp, etc., the structure of the space of possible histories appears to be arithmetically quantized in some way. Enough to associate a universal quantum field in the neighborhood of universal machine? Well, that is still an open problem.


Bruno


http://iridia.ulb.ac.be/~marchal/


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