The odds of infinity and... monkeys ?

[GSM:Xtreme]

It has been said that a million monkeys typing on typewriters would eventually type the works of Shakespeare. Now, thanks to the internet, we know this to be false. UB Law Class of 2008

While watching an episode of Nova a couple of months ago, I heard this thought about in a different way.

Let's say that the odds of a monkey randomly hitting keys on a keyboard and typing a perfect version of Hamlet can be demonstrated by the equation below:

10^x; where, lim x--> -()()
and yes for goodness' sake I'm using ()() as the sign for infinity...

That is effectively saying the odds are just about zero. But let's use the analogy 100% odds represents all matter in the universe and 0% is absolute nothingness.... that equation would represent less than one sub-atomic particle. (Is that clear? I tried... )

Well, with infinantly many monkeys hitting keyboards for eternity, I think that the x value would be brought back to the realm of real numbers, and thus it may be possible for a version of Hamlet, as well as perhaps Galileo's Principia, and even every Dr. Seuss book to be typed quite perfectly.

What do you think? I'm a little new with calculus and limitations, but I think I hit the nail in the wall here; though, I did mention infinite monkeys instead of millions, as stated in the quote, but the concept is the same.

[Muckraker]

Quote by: GSM:Xtreme While watching an episode of Nova a couple of months ago, I heard this thought about in a different way. Let's say that the odds of a monkey randomly hitting keys on a keyboard and typing a perfect version of Hamlet can be demonstrated by the equation below: 10^x; where, lim x--> -()() and yes for goodness' sake I'm using ()() as the sign for infinity... That is effectively saying the odds are just about zero. But let's use the analogy 100% odds represents all matter in the universe and 0% is absolute nothingness.... that equation would represent less than one sub-atomic particle. (Is that clear? I tried... ) Well, with infinantly many monkeys hitting keyboards for eternity, I think that the x value would be brought back to the realm of real numbers, and thus it may be possible for a version of Hamlet, as well as perhaps Galileo's Principia, and even every Dr. Seuss book to be typed quite perfectly. What do you think? I'm a little new with calculus and limitations, but I think I hit the nail in the wall here; though, I did mention infinite monkeys instead of millions, as stated in the quote, but the concept is the same.

There really is no point in making the statement since the concept of infinite monkeys is impossible. If one of the prerequisite conditions is impossible then the statement is also impossible even if it is theoretically possible.

Infinite monkeys would also require infinite computers with infinite drive space and infinite power consumption.

Also, how exactly would the work of the individual monkeys correlate with each other? Is the implication that a single monkey in the infinite scenario would compose the exact works of Shakespeare or is it that somehow the collaborative work of infinite monkeys over infinite time would have chunks that would exacly match the works of Shakespeare?

Also, if the amount of time is truly infinite, what is the difference between a single monkey with infinite time and infinite monkeys with infinite time? A single monkey would theoretically get the job done at some point as well.

[Domino]

Given infinite time, one could hope that, somewhere, eventually, a leather-bound edition of the complete works of Shakespeare will coalesce from the random collisions of particles in the depths of space.

However, infinite duration does not imply infinite variety. As a simple example, the decimal form of 1/3 is infinitely long, but there isn't a five anywhere in it. If you like, there are infinite, nonrepeating numbers that lack all sorts of digits.

If you had infinite typing monkeys, you could hope that one of them ought to just start right in on whatever text you wish, have it done right quick.

[Tycoon]

If you had infinite typing monkeys, you could hope that one of them ought to just start right in on whatever text you wish, have it done right quick.

And if the same can be said for one particular text, then the same can be said for every particular text. Infinite monkeys typing with unlimited resources would create every possible text ever written and every possible text never written as well. Oh, and an infinite number of copies of each of those texts.

I don't know what else there is to say, other than that you will never have infinite monkeys.

[treme]

Quote by: GSM:Xtreme While watching an episode of Nova a couple of months ago, I heard this thought about in a different way. Let's say that the odds of a monkey randomly hitting keys on a keyboard and typing a perfect version of Hamlet can be demonstrated by the equation below: 10^x; where, lim x--> -()() and yes for goodness' sake I'm using ()() as the sign for infinity... That is effectively saying the odds are just about zero. But let's use the analogy 100% odds represents all matter in the universe and 0% is absolute nothingness.... that equation would represent less than one sub-atomic particle. (Is that clear? I tried... ) Well, with infinantly many monkeys hitting keyboards for eternity, I think that the x value would be brought back to the realm of real numbers, and thus it may be possible for a version of Hamlet, as well as perhaps Galileo's Principia, and even every Dr. Seuss book to be typed quite perfectly. What do you think? I'm a little new with calculus and limitations, but I think I hit the nail in the wall here; though, I did mention infinite monkeys instead of millions, as stated in the quote, but the concept is the same.

yes you're quite right. But how possible is it for a monkey to evolve? Well the odds here on Earth were apparently 1 to 1 :)

[Tycoon]

Yes you're quite right. But how possible is it for a monkey to evolve? Well the odds here on Earth were apparently 1 to 1

What does it have to do with evolution??

[nm420]

Of course such a scenario is simply an analogy. The monkey (it needn't matter if there are one, a million, or an infinite number of them) is supposed to behave as a random typing machine. That is, it will hit any one of the 26 keys on the keyboard (or however many other keys you'd like to add for punctuation, spacing, capitalization) with equally likely probability. The statement is that, if this process is continued unabated, it is a virtual fact (i.e. probability 1) that any arbitrarily chosen (finite) string of characters will be produced. That doesn't mean it's something that will actually be observed, as the expected amount of time it would take to achieve this goal is infinite!

On the other hand, it is virtually impossible (i.e. a zero probability) that any chosen infinite string of characters can be produced by this process. Even something as seemingly "nonrandom" as "aaaaaaa...." could never be replicated.

[Galaxar]

Quote by: Tycoon I don't know what else there is to say, other than that you will never have infinite monkeys.

But if the universe is cyclical, as Nietzsche and others insisted, then there will be an infinite number of monkeys, because there will be an infinite number of cycles of the universe in which monkeys evolve. And surely at least some number (x) of those monkeys will have access to typewriters or similar machines. And since ()()/x = ()(), then over the course of infinite cycles of the universe there will be an infinite number of monkeys with access to typewriters. Ergo, assuming the cyclical theory of cosmology is correct, we already do have an infinite number of monkeys with typewriters or similar devices, and sooner or later they will produce the works of Shakespeare. Of course, they will need hundreds of trillions or quadrillions of cycles.

The average paperback romance novel takes about three weeks.

[Domino]

Few people know this, but Shakespeare actually had infinite monkeys.

[sinequanon]

Quote by: Domino Few people know this, but Shakespeare actually had infinite monkeys.

According to evolution theorists, Shakespeare was an ape which evolved in the indefinite timescale of the experiment. According to evolution theorists, the apes not only eventually wrote the complete works of Shakespeare, but they built the typewriters to do it!

[Galaxar]

Quote by: sinequanon According to evolution theorists, Shakespeare was an ape which evolved in the indefinite timescale of the experiment. According to evolution theorists, the apes not only eventually wrote the complete works of Shakespeare, but they built the typewriters to do it!

Don't tease the apes. They're busy with their keyboards.

[another day]

The problem with this is that just because the test goes on for infinity, does not mean the monkeys will eventually go through an infinite number of possible arrangements of words because their typing won't be systematic.

The presumption with this theory is that the monkeys will be providing completely random typing, but there is nothing to say they won't type the same patterns over and over again, and infact everything to suggest that they will. Even a human cannot provide completely random typing, they settle into routines, patterns and continue those patterns. For this theory to be successful, a better example would be some kind of automatic typing machine that types 'a' and then 'aa' and so forth. It would eventually write the entire works of shakespeare because it would be going through all the possible outcomes, rather then a monkey which being a living creature with a non-systematic brain will likely simply repeat patterns of body movements through it's typing.

Of course it's only an analogy and the random typing machine just doesn't sound as interesting...I'm just being nitpicky.