From: Matt Mahoney (matmahoney@yahoo.com)
Date: Fri Mar 06 2009 - 08:14:02 MST
--- On Fri, 3/6/09, Stathis Papaioannou <stathisp@gmail.com> wrote:
> 2009/3/6 Matt Mahoney <matmahoney@yahoo.com>:
>
> > Remember that probability is a model of belief, not of
> reality. In quantum mechanics, the square of the modulus of
> the wave function fits our model of probability only in the
> absence of other knowledge. For example, if constraints such
> as conservation of mass-energy, electric charge, momentum,
> and angular momentum restrict the possible combinations of
> observations we could make, we call that entanglement. As
> another example, the probability of observing a radioactive
> decay over one half-life interval is 1/2 only if that
> interval is in the future. But if you knew the quantum state
> of the universe, you would know everything about the future
> and probability would be a meaningless concept.
>
> If you knew the quantum state of the universe you would know
> everything that happens from the point of view of an observer outside
> the multiverse. However, as an observer inside the multiverse you
> would not know whether you would end up experiencing the atom decay or
> not decay.
It is impossible for an observer inside the universe to know its state.
> To give another example, a computer program with an
> observer that branches into two processes, one where the observer sees
> heads and the other where he sees tails, will be completely
> deterministic viewed from outside, but it will seem to the internal
> observer that he has a 1/2 chance of seeing heads or tails, even if he
> has full access to the source code and the data.
The program will estimate a probability that depends on how it was programmed. It cannot have full access to the source code and data by the above theorem.
> > The reason we expect a coin to come up heads with
> probability 1/2 is because of the way our brains compute
> probabilities based on past experience.
>
> Yes, and the same psychopathology applies in the equivalent situation
> where there are multiple copies, half of which see heads and the other
> half tails.
Nevertheless, it is possible to describe universes where probabilities estimated by the number of copies is inconsistent with the beliefs of its inhabitants, even when those beliefs are consistent with experiment. For example, under a Solomonoff prior, copies are weighted according to the length of the program describing them.
-- Matt Mahoney, matmahoney@yahoo.com
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