>From: "Norman Samish" <ncsamish.domain.name.hidden>
>To: <jcolvin.domain.name.hidden>
>CC: <everything-list.domain.name.hidden>
>Subject: Re: Implications of MWI
>Date: Wed, 27 Apr 2005 22:30:31 -0700
>
>Jonathan,
> If it is true that “In infinite time and infinite space, whatever can
>happen, must happen, not only once but an infinite number of times,” then
>what does probability mean? In your example below, there must be an
>infinity of worlds where Colin Powell is president and an infinity of
>worlds
>where your 6-year old niece is president. Are you saying that the Colin
>Powell infinity is bigger than the 6-year old niece infinity?
>Norman
Yes, the concept of assigning different probabilities to different infinite
subsets of an infinite set is what the branch of math called "measure
theory" is all about (see
http://en.wikipedia.org/wiki/Measure_theory ),
that's why you often see people on this list talking about the "measure" of
different worlds or observer-moments. As an example, if the possible
outcomes are the set of real numbers from 0 to 1, and if the probability
function was y=2x, then the probability that the outcome would be within any
given range (say, x=0.24 to x=0.97878...) would just be the area under the
function in that range (note that the area of y=2x from x=0 to x=1 is 1,
just as it should be if it's supposed to represent probability).
Jesse
Received on Thu Apr 28 2005 - 02:17:19 PDT