* By "metaphysical" I mean literally meta-physical, as in laws that apply to the physics of all universes in a multiverse; I do not mean supernatural.
Saturday, October 2, 2010
Infinite != All
Just a minor rant this time, but it's something that has been bugging me for a long time, and that I encounter quite often these days, as more and more speculation flies about the so-called "multiverse". Almost everyone who writes about the multiverse or about any infinite system, including scientists who should know better, falls prey to the same misconception about infinity... They equate infinite to all. That is, they invariably say something like, 'and thus, being infinite, every possible variation of the system must exist'. WRONG! You can have an infinite number of zeroes, in which infinite set not a single other number is ever found. You could conceivably have an infinite number of Mazda Miatas, in which not a single vehicle of any other make or manufacturer is to be found. You could have an infinite number of universes in which, due to metaphysical* constraints we don't yet understand, the fine structure constant only ever took on a single value, or two specific values, or N values, or... Yes, it could conceivably take on all possible values, but that's just one possible form of an infinite set of universes. Without theory or data to suggest a probability distribution function for whatever variable one is considering there is no possible way a priori to say how many or which values of that variable will be obtained in even an infinite number of examples of that variable. Infinite != All.