From: Rolf Nelson (rolf.h.d.nelson@gmail.com)
Date: Fri Nov 02 2007 - 06:22:12 MDT
On 11/2/07, Wei Dai <weidai@weidai.com> wrote:
> Ignoring the non-branching universe for the moment, how do you know that
> each quantum coin flip is actually independent from all of the others?
How do you know *anything*? You have a Bayesian "prior distribution",
which may include anthropic reasoning.
> I'll put this in more formal terms to make it clearer. Let P(x) be the
> probability that x is the output of a uniformly random program.
Obviously if a bounded-rationality agent is aware that it's a
uniformly random program, then once it has seen that x is its output,
it should (if it is sophisticated, and it has nothing better to do
with its time) give x a probability on the order of the amount of
Chaitin's Omega that it doesn't know. So what? You're begging the
question of why it had this prior in the first place. The prior
certainly isn't true of the programs running on my PC; none of my
programs are drawn from uniformly random distributions (not even
Microsoft Word).
> Now is it
> possible that SI can take an arbitrary string x and tell us whether P(x) <
> 1/2^(2^100)?
Underspecified. If by "probability" you only mean "something that
obeys the Probability Axioms, and is also sometimes useful", then
sure. If an agent has bounded rationality, it can consistently say
"there is a 1/2 probability that any number between 1 and 10 is an
even number. There is a 1/2 probability that 5 is an even number.
There is a 1/2 probability that 6 is an even number."
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