Would it be sufficient to have some kind of "finite" or "approximate"
measure even if it can not be taken to infinite limits (is degenerative?) in
order to disallow for "white rabbits"? A very simple and very weak version
of the anthropic principle works for me: Any observation by an observer must
not contradict the existence of that observer.
But there are plenty of observations that would not result in my destruction, like seeing a talking white rabbit run by me, anxiously checking its pocket watch. To pick a less fantastical example, it would also not be incompatible with my existence to observe a completely wrong distribution of photons hitting the screen in the double-slit experiment. Why, out of all possible experiences compatible with my existence, do I only observe the ones that don't violate the assumption that the laws of physics work the same way in all places and at all times?
I disagree with David's claim that "The universe doesn't depend on the rock for its existence..." since the notion of quantum entanglement, even when considering decoherence, implies that the mere presense of a rock has contrapositive effects on the whole of the "universe". The various discussions of "null measurements" by Penrose and others given a good elaboration on this.
I think you're talking about a different issue than David was. You're talking about a rock that's a component of our physical universe, while I think David was responding to Chalmers' question about whether random thermal vibrations in a rock instantiate all possible computer simulations, including a complete simulation of the entire universe (complete with all the rocks inside it).
To me the computational question boils down to the question of how does
Nature solve NP-Hard (or even NP-Complete) problems, such as those involved
with "protein folding", in *what appears to be* polynomial time.
What do you mean by "the" computational question? Are you addressing the same question I was, namely how to decide whether some computer simulation is instantiating a copy of some other program? If we imagine something like a detailed physical simulation of some computer circuits running program X, it seems intuitive that this simulation instantiates a copy of program X, but Chalmers' paper suggests we don't have a general rule for deciding whether one program is instantiating any other given program. And as I said, this is relevant to the question of measure, and a measure on observer-moments is probably key to solving the white rabbit problem.
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