On 26 Sep 2011, at 21:44, meekerdb wrote:

On 9/26/2011 9:08 AM, Bruno Marchal wrote:
Suppose that you are currently in state S (which exist by the comp assumption).

But what does "you" refer to?

Your first person view. Or the owner of your first person view, restricted to that view, without salvia amnesia, if you want.

The comp assumption seems ambiguous. Is it the assumption that "you" are instantiated by a specific computation?

No. Something like that can be part of the consequence, but this is clearly not assumed. In fact the UD shows that "you" is instantiated by an infinity of computations.

Or is it the assumption that your brain could be replaced, without you noticing, by a physically different computer, so long as it computed the same function (at some level).


These seem slightly different to me and are only identical if QM is false and the world is strictly classical and deterministic. At a practical level the brain is certainly mostly classical and so I might say 'yes' to the doctor even though my artificial brain will have slightly different behavoir because it has different counterfactual quantum behavior. But this difference seems to present a problem when trying to identify "you" within the inifinite bundle of computations instantiating a particular state in the UD computations.

Why? If my "original brain" is described by QM (without collapse) it might be said to self-multiply naturally. But that self-multiplication will be contagious on the UD in that universe, so this will not change the relative proportion. On the contrary, the UD itself forces a multiplication to be lived from inside. As to identify yourself in the UD*, this is just impossible in any third person ways. But the indeterminacy is on the first person experiences, not on their description in the UD. So the statistics are lived from inside. A computation is winning, if indeed you feel to be alive through its UD instantiation.
Ambiguities remain, but they are part of the measure problem.

Of course if you replace the whole universe with an emulation, instead of just my brain, then my emulated brain in the emulated universe can have the same behavior as my natural brain in this universe.

Yes, and that is why the reasoning will work in the limiting case where your "generalized brain" is the entire universe described at some level. The UD will generate all the digital approximation of that universe, and at some level of approximation, you will not see the difference, because we are assuming comp.

The UD generates an infinity of computations going through that state. All what I say is that your future is determined by all those computations, and your self-referential abilities. If from this you can prove that your future is more random than the one observed, then you are beginning to refute rigorously comp. But the math part shows that this is not easy to do. In fact the random inputs confer stability for the programs which exploits that randomness, and again, this is the case for some formulation (à-la Feynman) of QM.

How is this?

Consider the iterated self-duplication experience, like with the random movie, where you expect to see (correctly) a random movie. The movie will seem random because the limiting case is described by a Gaussian (accepting the p = 1/2 for a single duplication). Other considerations make such a randomness occurring below you substitution level, so it might be that the only way to stabilize the computations above the substitution level comes from some phase randomization, similar to Feynman explanation of why QM minimize the path action. We need a notion of negative (amplitude) of probability, extracted from comp, for such a procedure to work, but this is already provided by the logic of self-reference when we add the non-cul-de-sac assumption (Dt) to the provability modality (Bp), with p sigma_1. This can be made enough precise to make sense of how the quantum can be explained by the digital viewed from the digital creature themselves. No doubt that a lot of work remain to be done, but that is exactly what I wanted to show.



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