Infinite does not equal All

In a lot of Sci-Fi that I either read or listen to, there is this underlying thought that there are an infinite number of time lines with infinite possible outcomes (of course, somehow they all say each time line is based on decisions that a human makes, but hey…). Many stories make the age old mathematical faux pas that Infinite Probability = All Possible Outcomes.

This just ain’t true.

For example, take the following set of even numbers

2…4…6…8…10…12…∞

This set contains an infinite number of numbers. As in, a whole metric boatload on numerals plus one. And then some.

But, as large as the set is (infinite), it doesn’t contain all numbers. You won’t find a 3. Or a 2,783,762,091. So while a mind boggling amount of possibilities might exist, it doesn’t mean every possibility must exist. The best fallacy I can point to is the whole “Infinite Monkeys” concept. Just because you have an infinite amount of randomness doesn’t mean you will eventually produce a particular result.

For example, take a TV and tune it to an off line channel and observe the random spots and white noise. Random, right? Now, would you believe for a moment that if you stared long enough that the random patterns would eventually produce the entire Andy Griffith television series, in order, commercial free, except having Barney Fife look like Fabio instead of Don Knotts? With sound? That’s the same concept as having an infinite number of monkeys banging away at typewriters and producing the entire works of Shakespeare.

Of course, if one believes the universe is a random occurrence anyway, then technically the entire Andy Griffith television series has been randomly produced. Which might explain a few things about the show, now that I think of it.

Just a geeky observance. If there are any math majors out there that think I’m wrong, I’d be happy to listen and learn.

posted by by Robb Allen @
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