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).
Yes.
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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