From: Hal Finney (hal@finney.org)
Date: Wed Feb 12 2003 - 11:47:11 MST
I have been following the discussion between Wei and Eliezer with great
interest. The issue of how probability and decisions should work in the
context of parallel universes is quite difficult. Tegmark alludes to
this in the last section of his paper. I know Wei and have had several
discussions with him on this topic but I still have difficulty fully
grasping his approach.
In the case of the millionth bit of pi, Wei argues that from a certain
perspective, getting information about the value (with a certain intrinsic
error) does not change your estimation of the value - you still see it
as being 0 or 1 with 50-50 probability. This is of course quite counter-
intuitive but Wei shows that if you don't reason like this, you get the
wrong answer in your Bayesian calculations.
My question is, doesn't this apply just as well to all other factual
data about the universe? Take for example the first fractional bit
of pi. The way binary fractions work, any fraction < 1/2 has its first
bit as 0. Since pi's fractional part starts with .14159..., which is
less than 1/2, we know its first bit is 0.
Or do we? Isn't all reasoning inherently uncertain? We don't know
this fact with perfect certainty. There must be some chance of error -
one in a trillion, one in 10^100?
Given this, wouldn't Wei's Bayesian globalist have to say that the value
of the first fractional bit of pi was still uncertain, that there was
a 50-50 chance of it being 0 or 1? And similarly, wouldn't he say the
same thing about every bit of pi, therefore that pi's value was completely
uncertain? And in fact, wouldn't this reasoning apply to every fact about
the universe? Therefore every probability stays stuck at 0.5, or at least
at some a priori probability distribution that was uninformed by facts.
This seems to make "probability" a rather meaningless concept in this
model, or at least it seems to have a different meaning than what we
usually think of it. Maybe "a priori probability" or "initial bias"
would be a better word for it?
Hal
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