From: "Norman Samish" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> CC: <everything-list@eskimo.com> 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).

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