Rolled Out On: 7/20/2006 1:34 AM

You make a good point, but I think your examples are seriously off base. Or at least the monkey one is.

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 would eventually 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 got forever.

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 decrease as n increases. So you start of with something pretty close to 100% chance you will not get 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?

Rolled Out On: 7/20/2006 1:39 AM

I'd just like to apologize for my previous comment. I should've put some sort of "DANGER: MATH!" warning in there.

Rolled Out On: 7/20/2006 7:31 PM

No, would and could mean two totally different things. "Practically assured" doesn't mean "will happen". Just like that girl told me it was practically impossible to catch whatever she had.

The probability that it will happen is equal to the probability it won't happen. As Yoda said "Do or do not. There Is No Practically assured". Or something like that.

Then again, we're arguing about something we can never test nor wait for the results. Looks good on paper though, eh?

Rolled Out On: 7/20/2006 8:07 PM

Well I admit the probability will never actually get to 1, but it will get infinitely close. 99.9999999999% is close enough for me. Ok, maybe 99.99999999999%

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).

Rolled Out On: 7/20/2006 8:22 PM

I am assuming when we insert the word 'Monkey' we're actually just saying 'some random force'. Now, granted the noise on a TV is primarily black and white with very little grey, yes the sample size probably doesn't cut it. So I'll give a better analogy.

An infinite number of quantum based computers produce a random 32 bit number, one after another for an infinite time. Eventually, you can take those numbers, convert them into RGB and have a perfect digital representation of "The wizard of Oz" with every 4th frame spliced in pictures of ferrets reenacting historical events.

I'm not actually saying it cannot happen, I'm just saying it isn't guaranteed. Close enough, true, and if I were to be a betting man I'd bet a gajillion dollars (being that during this infinite amount of time, the penny I put into savings should cover it after interest and all).

Sorry I offended you with Andy Griffin. Would Father Knows Best have been a better choice?

Rolled Out On: 7/20/2006 8:24 PM

Oh, and sorry you weren't on the blogroll. That has been corrected.

Rolled Out On: 7/21/2006 2:24 PM

Matlock is the only true Griffith.