Infinitely many monkeys?

[Piers]

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No they won't, they will all die from lack of food and water. And then an empty room sits for eternity, until the typewriters rust away and the room is reclaimed by nature.

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Yes your right, that’s much more likely.

[borisp]

Just to be clear, I understand that this fairy tale has no bearing on reality. That is my point; for statements such as those that are often tossed around by armchair philosophers to be meaningful in any rigorous sense, one must usually clarify their content beyond "sound bite" status.

And "infinite" is not the same as "uncountable."

[vhawk01]

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people are getting too wrapped up in monkeys are neglecting the issue.

i think this is a starting point:

an uncountable number of trials with a nonzero probability of a success results in an uncountable number of successes and an uncountable number of failures.

I am pretty certain that statement is true. they don't really talk about an infinite numbers of trials in probability class so I guess i am not 100%, instead they focus on useful things like the law large numbers. which actually might do more for this post. http://en.wikipedia.org/wiki/Law_of_large_numbers

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I don't think any of us are getting too wrapped up in monkeys. Such a thing might not even be possible.

[almostbusto]

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And "infinite" is not the same as "uncountable."

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i know, i used uncountable for a reason.

[Piers]

Its possible we agree. I think hypotheticals that are designed to make a serious point about the real world should be held to a higher standard than ones that are not.

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Once upon a time there was a town with just husbands and wives. But, there was something magical about it. It just so happened that when a wife cheated on her husband, he would grow an ugly pair of horns out of his h

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For a scenario designed to put a story around a mathematical problem anything is fine.

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infinitely many monkeys, typing away at infinitely many typewriters, must eventually produce the works of Shakespeare

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Here the author is using a hypothetical scenario to make a serious point about the universe; maybe a step in an argument concerning the chance of unlikely events occurring.

Nickpicks like the difficulty in feeding an infinite number of monkeys (so what is infinity here?), or controlling their breeding so they continue being monkeys (how do things drift over time) and such like are fair game. Its quite possible some such points are pertinent to the point being attempted. Certainly the author should expect to have to handle such attacks, and maybe gain understanding as a result.

[MelchyBeau]

do you mean countably infinite, i.e. There is a one to one correspondance with the natural numbers. when I hear uncountably infinite the best example I can think of is the real numbers.

[borisp]

Piers, yes I think we do agree. (Although I see the term probability applied in too loose a context more often than with infinity.)

MelchyBeau, the infinity in the original post is intended solely to mean "not finite." I think Piers is just pointing out that uncountable versus countable is a relevant distinction.

The original post is essentially:

Suppose there is an infinite set X. Defining a property P that satisfies "If a subset E of X is infinite, then there exists e in E such that P(e) is true" is logically equivalent to selecting finitely many elements from X for which P is false.

In reality, there are finitely many monkeys. So hypothesizing an infinitude of monkeys would certainly result in some strange monkeys.

[LA_Price]

A better understanding of the idea of infinity is described in the works of Benoit Mandelbrot. For instance the question How Long is the coast of England?

The problem with the monkey example is our own language description, concept of time, idea of "independence", etc.

A better way to phrase the statement would be if a monkey could type an infinite number of random letters in a second, they would eventually end with the works of shakespeare.

[Sephus]

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if a monkey could type an infinite number of random letters in a second, they would eventually

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it would take less than a second.

[surftheiop]

If the monkeys type infinetly fast doesnt that mean its imposible to produce only one copy of shakespeares work? The istant it started typing wouldnt infinite copies be produced?