a list compiled by Alex Kasman (College of Charleston)
|While playing poker, a math professor and a biology professor discuss the many-worlds interpretation of quantum physics, with the mathematician offering what he sees as a mathematical argument proving that such parallel universes cannot possibly exist.
Septimus Whitlock, the math professor in the story, is annoyingly (and entertainingly) smug:
Aside from the exposition of his argument, which is laid out carefully and slowly, there is not much going on in this story. Unfortunately, I am afraid the argument is not actually valid, rendering this story somewhat pointless. (Hmmm...I guess I sound like a smug mathematician myself now. Perhaps that much of the stereotype is really true.)
There are a few "red herring" ideas that the story passes through on its way to its main argument. Let me mimic that style by mentioning a few little points here. The argument seems to be based on the idea that there are infinitely-many parallel universes. I do not think that is necessarily the case in the Everett Many-Worlds interpretation of quantum physics. (In particular, those who believe in an entirely discrete universe, as some do, could end up with a description for which at any one moment there are only finitely-many universes.) But, okay, certainly some people also do consider the case in which each of infinitely-many possible outcomes are realized and so the story could be arguing against those. Another small problem with this story is that it claims physicists use the term "zero sum" for "small enough to be negligible." I have never heard anyone use it that way before, and I think the author may be mistaken. (The term "zero sum" is usually used in game theory to describe situations in which one player's gain always comes at the cost of an equal loss to someone else.)
But, the main argument of this story is that the idea of probability simply makes no sense when there are infinitely many universes because one would (according to Septimus) lose the ability to talk about the fraction that have a certain property. For example, if there are infinitely many universes, what would it mean to say that a particular flip of the coin produces "heads" in exactly half of them? Since there are infinitely-many, wouldn't it just be infinity over infinity?
In fact, mathematicians have already figured out how to provide sensible answers to such questions. For a sophisticated view of the subject, check out any literature on what we call Measure Theory. But, ironically, a simple example exists within the very subject that Septimus was discussing. Consider this:
In a course on probability we usually start by talking about a finite probability distribution: "Suppose a bag contains 5 white buttons, 3 black buttons and 2 blue buttons. What is the probability of choosing a white button?" The answer turns out to be 1/2 because 5/(5+3+2)=5/10=1/2. Eventually, though, even introductory probability courses begin talking about continuous probability distributions in which there are infinitely many possible outcomes. For instance, if the distance that a baseball will fly is a normally distributed variable, one can ask for the probability that the distance will be less than one standard deviation from the mean. Since there are infinitely many possible distances that it could travel, one cannot simply divide the number of positive outcomes by the number of all possible outcomes as we did in the finite case. Yet, as anyone who has worked with bell-curves knows, there is a notion of a probability being 1/2 (or 1/4 or e-100 or whatever) for a normally distributed random variable. That's because we are able to put a measure on an infinite set and can still say what fraction of it we have for any given subset.
So, although I am in no way arguing in favor of the Many-Worlds interpretation of QM, I also must say that neither Septimus Whitlock nor Guy Hasson has demonstrated that it is impossible using a logical argument.
|More information about this work can be found at www.aphelion-webzine.com.|
|(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)|
Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books
let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.
(Maintained by Alex Kasman,
College of Charleston)
(Maintained by Alex Kasman, College of Charleston)