oldest theory disproved(ot but great)

[Chun-tzu]

Actually, at some point, statistically, the improbable becomes the impossible. The example (monkey/shakespeare theory) is flawed because it fails to recognize that random activity can only go so far in producing anything. I forget the actual statistical figure sometimes given, but after a certain improbability we can state with certainty that a given random event will never occur.

In the real world, yes. The example isn't so much flawed, as it is completely theoretical. Of course there will never be an infinite string of anything, because the universe is finite. There are many theories that we will never be able to prove. That hardly invalidates them. What would math be without theories?

 

[Wicht]

In the real world, yes. The example isn't so much flawed, as it is completely theoretical. Of course there will never be an infinite string of anything, because the universe is finite. There are many theories that we will never be able to prove. That hardly invalidates them. What would math be without theories?

Statistics (and math) is only a worthwhile science as it relates to the real world, IMO. Otherwise it ceases to be science and becomes fantasy. At least IMO.

My beef with the monkey theory is it gives an impossibility and then is used to try and prove something concrete.

 

[Christian]

Monkeys, numbers, and you.

 

[Chun-tzu]

Statistics (and math) is only a worthwhile science as it relates to the real world, IMO. Otherwise it ceases to be science and becomes fantasy. At least IMO.

My beef with the monkey theory is it gives an impossibility and then is used to try and prove something concrete.

The monkey theory is not an impossibility, nor does it try to prove anything.

The works of Shakespeare are one combination of letters and punctuation. Let's say all his works total up to one million letters and punctuation marks. Now generate a completely random series of one million letters and punctuation marks.

The odds of producing any given sequence, including the works of Shakespeare, are equal. You are no less likely to get the works of Shakespeare than you are to get any other SPECIFIC combination, such as one million zeroes.

It is completely possible. It is extremely unlikely, but it is no less likely than any other result. There are so many possible results, though, that the probability of getting that specific combination (or ANY specific combination) approaches zero. And yet when you generate that string, one of those zillion+ nearly impossible combinations becomes actuality.

 

[Mark Chance]

The monkey theory is not an impossibility, nor does it try to prove anything.

It is impossible. Nowhere does there exist an infinite number of monkeys, an infinite number of typewriters, or an infinite amount of time.

To support this point, I quote Chun-tzu:

The example requires an infinite number of monkeys at an infinite number of typewriters, OR a single monkey at a typewriter for an infinite amount of time, either of which is inherently impossible.

 

[Chun-tzu]

It is impossible. Nowhere does there exist an infinite number of monkeys, an infinite number of typewriters, or an infinite amount of time.

OK, I will concede the above.

The odds of producing the complete works of Shakespeare, completely randomly, is not an impossibility. This is the essence of the monkey theory.

 

[Mark Chance]

The odds of producing the complete works of Shakespeare, completely randomly, is not an impossibility. This is the essence of the monkey theory.

On a theoretical level, you are quite right.

On a practical level, however, the situation changes, as you've already noted.

The problem comes about when people confuse the two levels and start claiming what it is possible only in theory is actually possible (or, worse yet, what is possible only in theory is actually a fact!).

 

[Wicht]

The odds of producing the complete works of Shakespeare, completely randomly, is not an impossibility. This is the essence of the monkey theory.

Are you a statistician? Because I have read the articles of a few of them that would disagree with you.

I think the key thing is - In the real universe it is an impossibility to randomly produce anything that long with that much structure. The problem is that it is far more probable for an almost infinite amount of other things to be produced and many of them are far more likely.

Try it - initiate a computer program that randomly produces letters and numbers (coupled with punctuation) in a completely equal way and see how many full sentences you form in say, a month of running the program.

A few problems, IMO should become apparent. In the structure of language some letters are far more likely to appear than others, "e" for example. Punctuation is less likely and some letters, like "z" or "x" only come up every now and then. But in a completely random environment, one is as likely as the other. If you tailor your program so that only one "z" appears for every hundred "e"s you are more likely to begin to approach the sctructure of a language, but you have also taken out the randomness of it.

The flaw in the monkey theory is that probability breaks down when structure is involved.

 

[Chun-tzu]

Are you a statistician? Because I have read the articles of a few of them that would disagree with you.

I wouldn't be surprised if you understand statistics and probability better than I do. Nothing you had stated to this point, however, has convinced me that the chances of randomly producing Shakespeare are completely zero, instead of virtually zero. Further, in the world of academics, many disagree within any given field.

I think the key thing is - In the real universe it is an impossibility to randomly produce anything that long with that much structure. The problem is that it is far more probable for an almost infinite amount of other things to be produced and many of them are far more likely.

To me, this says that we currently have no means of truly random generation. This does not mean that it is impossible. Yes, in the real world, we can't do this or test this. Yet. It hardly seems far-fetched to me that computers or artificial intelligence or some other field of mathematics, physics, or something else entirely will progress to a point where we gain new insights into this question.

 

[MeepoTheMighty]

"It was the best of times, it was the BLURST of times?" Bah, you stupid monkeys!