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.

#### Comments

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Let me put it this way: It is many times more unlikely that one monkey can produce the entire works of Shakespeare in one go as soon as he sits down at the typewriter than it is for the infinite monkeys to somehow

*avoid*producing the entire works of Shakespeare over a long enough period of time.

Mainly I just didn't like your comparing the Andy Griffith show being randomly produced (impossible) to the infinite monkeys (extremely likely).

Naturally, the TV with white noise will never produce Andy Griffith, because the white noise is an analog signal with natural limits that do not resemble man-made TV signals, so it'll never get there. That's not unlike saying if you flip an infinite number of coins an infinite number of times, you'll never get a royal flush. Of course not, no coin flip will come out as "Ace of Diamonds." I'm hoping that's what you're going for. That is a matter of "sample space."

But the infinite monkeys banging on typewriters for infinity

wouldeventually type out the complete works of Shakespeare. I'm sure you could picture even one monkey managing to bang out the string "abc" somewhere in the midst of gibberish. "abcd" would be less frequent. But given an infinite amount of time, any finite string can be reproduced, with a probability of 1. Even with one monkey and one typewriter. He's able to reproduce every character used by Shakespeare, and he's gotforever.I'm not a math major, but unluckily for everyone reading this I have a probability book handy. You're flipping a coin for infinity, will you ever flip one million heads in a row? Let's say you decide to flip it 1 million times a row as a "trial", with a 5 minute break between "trials". You're a coin flippin' fool. This is almost a binomial experiment. (Each trial can be reduced to two outcomes: success or failure, you either flipped a million heads or you failed to do so. The outcomes of each trial are independent of each other. The probability of success is the same for each trial. There are also supposed to be a fixed number of trials, but we can look at large numbers.)

The formula for a binomial distribution is nCx * (p)^x * (1-p)^(n-x), where nCx is the number of ways a success can occur, p is the probability of success, x is the number of successes, and n is the number of trials. Now let's look at the case where you never flip a million in a row. What's the probability of never getting a million in a row for a large number of trials? There's only one possible way to get no successes, so nCx = 1. p will be a very small fraction, but x, the number of successes, is 0, so (p)^x = 1. So the probability of not being successful is simply (1-p)^(n-0) or (1-p)^n. Now p is a tiny fraction, so 1-p is very close, but slightly less than 1. Which means as n increases, 1-p will

decreaseas n increases. So you start of with something pretty close to 100% chance you willnotget 1 million heads in a row if you only do 1 or 2 trials, but do enough and eventually the probability of not succeeding. Then you get into limits, but eventually you're practically assured you'll get a weird result like that.What the hell was the subject again?