1. If time continues to infinity, for infinity, then there will never be a time when "All things have happened" right? Because more things happen?

But then you went on and said how monkeys will do this, and spiders will do that, like painting Mona Lisa and writing books.. That I don't understand.

Time continues into infinty and all things do happen, in essence, all things happen and don't happen with each new passing second.

Essentially, because of infinity all things that can ever happen must happen, and at the same time all things that can ever happen haven't happened aswell, as there are another infinty worth of "things" to happen after you've reached any arbitrary lenght of infinity.

If we asked this same question after 8 billion trillion years, we would still say that all things that can happen will happen in the next 9000 billion trillion years, but as each second passes we move away from the old infinity, and into a new one.

All things that could ever happen in our universe (or cosmos or whatever you wish) may occur at some point, say randomly in the 80902838734 billionith trillionth year, but the second after that passes, we continue into a new infinty, where all things that could ever happen, have both happened and not happened as infinity continues. Again that is an excellent thought. It illustrates the duality of infinity, where things happen and don't happen at a given point.

My second point was simply a further illustration of infinity.

If all things that can happen will happen, as is supposed in infinity, there will be all concievable things happening; including spiders painting all the works of art ever painted, or the sea creating shapes on the beach from shells that resemble all things, or the plants in someone's garden growing to resemble Will Smith.

Basically, if it can happen, it will; so if we can concieve of a spider stepping in some ink and walking on a page in a way that replicates the works of Edgar Allen Poe, it will happen, as we have an infinte time scale.

( I hope that makes sense, if not ask!)

That is exactly why I think it there isn't a 100% chance for monkeys to output Shakespear. There is a 1/∞ chance of it not happening.
Well, that is the issue, if infinity is the way we describe, as the OP said, there is a chance in rolling die that we could roll a 6 forever, it will just be so against all odds that it is almost also infinestimal in chance. I don't think the thought experiment is postulating anything like this though, again it is more an illustration of the nature of infinity and not the practical implications of getting monkeys to type Shakespeare.

2. z
That is exactly why I think it there isn't a 100% chance for monkeys to output Shakespear. There is a 1/∞ chance of it not happening.
Actually, there is a 100% chance of it happening. Only it is not certain. I explained this some posts ago.

Time continues into infinty and all things do happen, in essence, all things happen and don't happen with each new passing second.

Essentially, because of infinity all things that can ever happen must happen, and at the same time all things that can ever happen haven't happened aswell, as there are another infinty worth of "things" to happen after you've reached any arbitrary lenght of infinity.

If we asked this same question after 8 billion trillion years, we would still say that all things that can happen will happen in the next 9000 billion trillion years, but as each second passes we move away from the old infinity, and into a new one.
"Until the end of time."

My second point was simply a further illustration of infinity.

If all things that can happen will happen, as is supposed in infinity, there will be all concievable things happening; including spiders painting all the works of art ever painted, or the sea creating shapes on the beach from shells that resemble all things, or the plants in someone's garden growing to resemble Will Smith.

Basically, if it can happen, it will; so if we can concieve of a spider stepping in some ink and walking on a page in a way that replicates the works of Edgar Allen Poe, it will happen, as we have an infinte time scale.

( I hope that makes sense, if not ask!)
This spiders painting arts.. This doesn't exactly make sense, but I think see your point in it; assuming that if there was a spider who could do arts at some point in time, then there would have been a spider who did some art at some point. Simple illustration like you said.

So, a lot of things happen in time, but randomness and certain limitations as to how species grow and evolve alone, it kind of restricts monkeys and spiders from doing such precise art-work that humans have shown to be able to.

4. When we have no concept of an end of time, and it continues forever into infinity, all things must happen, it is just a fact. If one can't grasp this, you haven't understood infinty!
This "all things must happen" is actually not true in its literal form. For example, if the random character generator is set to only generate numbers, then it's obvious that Hamlet will never be written, because none of the letter characters of Hamlet is present.

A more precise statement is that, if a random character generating machine is set for infinite time, then any finite combination of said characters of arbitrary length 100% chance of happening.

Edited:

Essentially, because of infinity all things that can ever happen must happen, and at the same time all things that can ever happen haven't happened aswell, as there are another infinty worth of "things" to happen after you've reached any arbitrary lenght of infinity.

If we asked this same question after 8 billion trillion years, we would still say that all things that can happen will happen in the next 9000 billion trillion years, but as each second passes we move away from the old infinity, and into a new one.

All things that could ever happen in our universe (or cosmos or whatever you wish) may occur at some point, say randomly in the 80902838734 billionith trillionth year, but the second after that passes, we continue into a new infinty, where all things that could ever happen, have both happened and not happened as infinity continues. Again that is an excellent thought. It illustrates the duality of infinity, where things happen and don't happen at a given point.

My second point was simply a further illustration of infinity.

If all things that can happen will happen, as is supposed in infinity, there will be all concievable things happening; including spiders painting all the works of art ever painted, or the sea creating shapes on the beach from shells that resemble all things, or the plants in someone's garden growing to resemble Will Smith.

What?

5. "Until the end of time."

This spiders painting arts.. This doesn't exactly make sense, but I think see your point in it; assuming that if there was a spider who could do arts at some point in time, then there would have been a spider who did some art at some point. Simple illustration like you said.

So, a lot of things happen in time, but randomness and certain limitations as to how species grow and evolve alone, it kind of restricts monkeys and spiders from doing such precise art-work that humans have shown to be able to.
If we had an infinite universe, spiders would eventually paint every work of art ever painted, by stepping in paint and wandering around on a canvas. That is the nature of infinity, if it is possible for it to be done, it will.

This "all things must happen" is actually not true in its literal form. For example, if the random character generator is set to only generate numbers, then it's obvious that Hamlet will never be written, because none of the letter characters of Hamlet is present.

A more precise statement is that, if a random character generating machine is set for infinite time, then any finite combination of said characters of arbitrary length 100% chance of happening.

Edited:

What?
Well that isn't really what we're saying. We are asking if monkeys on typewriters (which contain all the neccessary characters for Hamlet or Romeo and Juliet) could replicate the works of shakespeare in an infinite time scope, and the answer is yes.

It has nothing to do with probability per se (hear me out), in an infinite time scale the probability of every thing happening becomes 1, in essence, all things that can happen must happen, because infinity is just that, infinity. It's very hard to grasp this idea, some people just do not accept it; and say things like the OP (where the monkey hits AAAAAA for infinity) but that is more a practical problem, and again, not an illustrative approach to infinity.

And what does the "what" pertain to? I was merely trying to illustrate infinity. Many people get stuck in the practical implications of monkeys bashing keys or whatever other example they have. But given an infinite time period, all possible things must happen, it is just a necessary condition of infinity. Essentially, anything that can happen must happen.

6. If we had an infinite universe, spiders would eventually paint every work of art ever painted, by stepping in paint and wandering around on a canvas.

That is the nature of infinity, if it is possible for it to be done, it will.
Exactly. But this spider scenario isn't obviously possible.

7. It has nothing to do with probability per se (hear me out), in an infinite time scale the probability of every thing happening becomes 1, in essence, all things that can happen must happen, because infinity is just that, infinity. It's very hard to grasp this idea, some people just do not accept it; and say things like the OP (where the monkey hits AAAAAA for infinity) but that is more a practical problem, and again, not an illustrative approach to infinity.
You probably will dismiss this, but I think there is a problem with the "must" in "must happen". Of course, I do agree with you that in essence, all things that have a nonzero probability of happening in certain time in a system will have a probability 1 of happening given infinite time. BUT that doesn't mean that they must happen. (see my posts in page 4 for an example of events having probability 1 that are not necessarily going to happen).

8. Exactly. But this spider scenario isn't obviously possible.
I think it is, we should leave some canvas and paints out and open a box of spiders. See what happens.

You probably will dismiss this, but I think there is a problem with the "must" in "must happen". Of course, I do agree with you that in essence, all things that have a nonzero probability of happening in certain time in a system will have a probability 1 of happening given infinite time. BUT that doesn't mean that they must happen. (see my posts in page 4 for an example of events having probability 1 that are not necessarily going to happen).
Well, whilst I agree with the logic of what you're saying (i.e. that even if there is a 100% probability of it happening over an infinite time period, it is possible for it to not happen).

I don't really know how to move away from this problem. It is my understanding of infinity that if it has a nonzero probability it will and must happen, or else it wouldn't have an nonzero probability.

There is, as you claim, a separation between probability and actual chance, in so much as a probability of 1 happening in an infinite time scale doesn't necessarily mean it will happen (as per OP's example of hitting A for eternity or rolling 6 forever on dice). It's a tough one to answer, I just think that infinity describes a situation where probabilities move closer and closer to 1 as time passes, and eventually, if it can happen, it will.

9. I think it is, we should leave some canvas and paints out and open a box of spiders. See what happens.
As precise art-work as Mona Lina would not happen, however.

Not to mention the paint would dry out, and hundreds (of thousands) of Spiders would die to old age before anything even closely similar to a Mona Lisa would appear on the canvas.

And still.. dude, leaving a canvas, paints and a box of spiders for an infinity on a table (or on the ground?) Doesn't make any sense to me in any way, even as a simple illustration of what COULD happen in an infinity.

10. As precise art-work as Mona Lina would not happen, however.

Not to mention the paint would dry out, and hundreds (of thousands) of Spiders would die to old age before anything even closely similar to a Mona Lisa would appear on the canvas.

And still.. dude, leaving a canvas, paints and a box of spiders for an infinity on a table (or on the ground?) Doesn't make any sense to me in any way, even as a simple illustration of what COULD happen in an infinity.
You're getting caught in the practical mindset. Both my illustration and the monkeys are just a representative display of the nature of infinity, not the practicality.

11. Impossible, it's impossible to work on anything for an infinite amount of time. Actions require two set points in time, infinity has no two points of time for 2 reasons.
1; It never started or ended
2; It's not a number, two points of time cannot be placed on something that cannot be measured (as far as we know).

12. Impossible, it's impossible to work on anything for an infinite amount of time. Actions require two set points in time, infinity has no two points of time for 2 reasons.
1; It never started or ended
2; It's not a number, two points of time cannot be placed on something that cannot be measured (as far as we know).

13. When you give infinite time for probabilities, everything is possible because infinity basically means something is sure to happen.
Even we can pass the speed of light ? You are missing a point. Universe that we live inside works with an algorithm. So everything is not possible even in an infinite time. Besides that there is no time in universe. Time is just an illusion because humans are biological things and they are mortal. We are able to observe people and ourselves while getting old. But that doesn't mean time is exist. It is just an unit of measure for mankind. So we are already in an infinite time. The only difference among the time and mankind is immortality of time and mortality of humans. You have to use the word "biologically" infinite or immortality. Even the mankind can obtain immortality. That doesn't mean you can do basically anything. You are just an algorithm of algorithm so you are belong to algorithm of the universe. If the algorithm of universe won't allow you to the thing that you want then you never ever can do. Maybe if you can find an another universe with an another algorithm that works for you then it is possible to do the thing you want otherwise it is impossible. I talk theoretically i didn't practice it I'm just talking about the way that universe works and the rules that universe comply.

Edited:

Time continues into infinty and all things do happen, in essence, all things happen and don't happen with each new passing second.

Essentially, because of infinity all things that can ever happen must happen, and at the same time all things that can ever happen haven't happened aswell, as there are another infinty worth of "things" to happen after you've reached any arbitrary lenght of infinity.

If we asked this same question after 8 billion trillion years, we would still say that all things that can happen will happen in the next 9000 billion trillion years, but as each second passes we move away from the old infinity, and into a new one.

All things that could ever happen in our universe (or cosmos or whatever you wish) may occur at some point, say randomly in the 80902838734 billionith trillionth year, but the second after that passes, we continue into a new infinty, where all things that could ever happen, have both happened and not happened as infinity continues. Again that is an excellent thought. It illustrates the duality of infinity, where things happen and don't happen at a given point.

My second point was simply a further illustration of infinity.

If all things that can happen will happen, as is supposed in infinity, there will be all concievable things happening; including spiders painting all the works of art ever painted, or the sea creating shapes on the beach from shells that resemble all things, or the plants in someone's garden growing to resemble Will Smith.

Basically, if it can happen, it will; so if we can concieve of a spider stepping in some ink and walking on a page in a way that replicates the works of Edgar Allen Poe, it will happen, as we have an infinte time scale.

( I hope that makes sense, if not ask!)

Well, that is the issue, if infinity is the way we describe, as the OP said, there is a chance in rolling die that we could roll a 6 forever, it will just be so against all odds that it is almost also infinestimal in chance. I don't think the thought experiment is postulating anything like this though, again it is more an illustration of the nature of infinity and not the practical implications of getting monkeys to type Shakespeare.
But what if it can't happen. If even the one thing can't happen algorithm will pass it. But it will stuck in there in an infinite amount of time like a bug in the terms of computer science. And it will not be deleted until the problem solved. So your theory "everything is possible" is unsuccessful cause that bug blocked your theory in an infinite time and made it false.

14. But what if it can't happen. If even the one thing can't happen algorithm will pass it. But it will stuck in there in an infinite amount of time like a bug in the terms of computer science. And it will not be deleted until the problem solved. So your theory "everything is possible" is unsuccessful cause that bug blocked your theory in an infinite time and made it false.
What?

If something can't happen it wont happen.

Also there is no algorithm or "bug". The monkeys just sit typing away until they hit the right string of randomness that replicates the works of Shakespeare from beginning to end.

Maybe I don't understand what you are saying, but the theory that everything is possible is not susceptible to "bugs" because if it can happen it will. So everything that is possible will happen. My examples are just another way of thinking about infinity.

I've said it about 3 times in this thread already, it is not meant to be a practical point, but an illustrative one. I doubt PRACTICALLY monkeys, even in an infinite time scale could replicate the works of shakespeare before they got bored and started throwing their shit at eachother. But illustratively, it shows what the concept of infinty IS in itself.

15. What?

If something can't happen it wont happen.

Also there is no algorithm or "bug". The monkeys just sit typing away until they hit the right string of randomness that replicates the works of Shakespeare from beginning to end.

Maybe I don't understand what you are saying, but the theory that everything is possible is not susceptible to "bugs" because if it can happen it will. So everything that is possible will happen. My examples are just another way of thinking about infinity.

I've said it about 3 times in this thread already, it is not meant to be a practical point, but an illustrative one. I doubt PRACTICALLY monkeys, even in an infinite time scale could replicate the works of shakespeare before they got bored and started throwing their shit at eachother. But illustratively, it shows what the concept of infinty IS in itself.
Actually practically it would be guaranteed given an infinite timescale and infinite amount of monkeys.

16. This debate isn't whether or not Infinite time exists, it's whether or not a machine typing out random letters could reproduce the works of Shakespeare.

17. This debate isn't whether or not Infinite time exists, it's whether or not a machine typing out random letters could reproduce the works of Shakespeare.
Actually it isn't whether or not a machine typing out random letters could reproduce the works of Shakespeare. Of course it can happen. The debate is whether, given infinite time, that event would be certain or not.

18. Actually it isn't whether or not a machine typing out random letters could reproduce the works of Shakespeare. Of course it can happen. The debate is whether, given infinite time, that event would be certain or not.
Ehhh? Aren't you proving it right by what you're saying? If it's possible to write the entire length of Shakespeare's works by accident, it's definitely possible given infinite time. If there are infinite iterations one must be the right answer as the number of permutations is finite.

19. Actually it isn't whether or not a machine typing out random letters could reproduce the works of Shakespeare. Of course it can happen. The debate is whether, given infinite time, that event would be certain or not.
I thought it was discussing whether monkeys are random character generators or not.

20. I thought it was discussing whether monkeys are random character generators or not.
Fuck now that's missing the point.

21. This thread, filled with Karl Pilkingtons. Infinity means forever, I don't even know why this is a debate.

22. The whole point of the metaphor is to give an idea of the nature of infinity. Monkeys typing Shakespeare is something incredibly unlikely, but physically possible. For something to not happen in a given time-frame, it requires there to be an end-point, a point where you can say "no, it hasn't happened".
Infinity doesn't have an end, there is always more time for it to happen.

23. Ehhh? Aren't you proving it right by what you're saying? If it's possible to write the entire length of Shakespeare's works by accident, it's definitely possible given infinite time. If there are infinite iterations one must be the right answer as the number of permutations is finite.
No. Not possible, certain.

Edited:

This thread, filled with Karl Pilkingtons. Infinity means forever, I don't even know why this is a debate.
Actually, there is an argument that has not been refuted: the possibility of the monkey (or monkeys) typing "AAAA...." (or any letter) forever, and never typing Hamlet.

24. In order to confuse you who don't get it more, the works of the monkeys will type an infinite amount of the works of Shakespeare.

25. In order to confuse you who don't get it more, the works of the monkeys will type an infinite amount of the works of Shakespeare.
1. NO, they won't.
2. That is not what is being discussed.

26. No. Not possible, certain.

Edited:

Actually, there is an argument that has not been refuted: the possibility of the monkey (or monkeys) typing "AAAA...." (or any letter) forever, and never typing Hamlet.
Well if they do type A forever, then just wait a bit longer and see if they start typing something else.

27. Well if they do type A forever, then just wait a bit longer and see if they start typing something else.
This. I don't understand what part of this people aren't getting. Infinity is infinity.

28. This. I don't understand what part of this people aren't getting. Infinity is infinity.
And forever is forever. No matter how many times the monkey types "A", it's always a nonzero chance to type another A. Hence the possibility is there.

29. And forever is forever. No matter how many times the monkey types "A", it's always a nonzero chance to type another A. Hence the possibility is there.
Well if it's a monkey that's only capable of pressing A, then it isn't possible for it to type Shakespeare. But that's completely ignoring the point of the metaphor.

30. Well if it's a monkey that's only capable of pressing A, then it isn't possible for it to type Shakespeare. But that's completely ignoring the point of the metaphor.
No. I'm talking about probabilities. The whole thing is a metaphor for a random string generator. Let's say it's using the 26 letter English alphabet, no symbols or other crap.
So now the chance for the first letter to be A is 1/26. The chance for it to produce AA is (1/26)^2. For AAA it's (1/26)^3. For n amount of "A"s, it's (1/26)^n. So for infinite "A"s, the chance would be (1/26)^infinite = 1/infinite. Usually we mark this by zero because it usually doesn't matter. But it's actually not zero. It's an infinitesimally small number. Which means that it could still happen.
It helps if you think about it like this: No matter how many "A"s have happened before, the chance to type another A is always 1/26, ie. a nonzero chance.

Here's some more reading on 1/infinity:
http://mathforum.org/library/drmath/view/62486.html
http://en.wikipedia.org/wiki/Infinitesimal

31. Well if it's a monkey that's only capable of pressing A, then it isn't possible for it to type Shakespeare. But that's completely ignoring the point of the metaphor.
No, he is capable of typing other letters as well, but that does not mean that the possibility of typing always another "A" isn't there.

No. I'm talking about probabilities. The whole thing is a metaphor for a random string generator. Let's say it's using the 26 letter English alphabet, no symbols or other crap.
So now the chance for the first letter to be A is 1/26. The chance for it to produce AA is (1/26)^2. For AAA it's (1/26)^3. For n amount of "A"s, it's (1/26)^n. So for infinite "A"s, the chance would be (1/26)^infinite = 1/infinite. Usually we mark this by zero because it usually doesn't matter. But it's actually not zero. It's an infinitesimally small number. Which means that it could still happen.
It helps if you think about it like this: No matter how many "A"s have happened before, the chance to type another A is always 1/26, ie. a nonzero chance.
Actually, the probability is 0, but that doesn't mean the possibility isn't there. It's like picking a random real number between 0 and 1 and hoping it is 1/pi: The probability that you will pick 1/pi is indeed 0, but that doesn't mean that picking 1/pi isn't a possibility, so if you say "I am certain that I won't pick 1/pi" you would be wrong, you're almost certain. This example is mathematically the same as the random letter generating machine writing Hamlet and the "AAAA..." case.

32. No. I'm talking about probabilities. The whole thing is a metaphor for a random string generator. Let's say it's using the 26 letter English alphabet, no symbols or other crap.
So now the chance for the first letter to be A is 1/26. The chance for it to produce AA is (1/26)^2. For AAA it's (1/26)^3. For n amount of "A"s, it's (1/26)^n. So for infinite "A"s, the chance would be (1/26)^infinite = 1/infinite. Usually we mark this by zero because it usually doesn't matter. But it's actually not zero. It's an infinitesimally small number. Which means that it could still happen.
It helps if you think about it like this: No matter how many "A"s have happened before, the chance to type another A is always 1/26, ie. a nonzero chance.

Here's some more reading on 1/infinity:
http://mathforum.org/library/drmath/view/62486.html
http://en.wikipedia.org/wiki/Infinitesimal
Even if it pressed A 10^100^100^100 times, it would still have an infinite number of chances to type out all of Shakespeare's works after that, thus guaranteeing it.

33. Even if it pressed A 10^100^100^100 times, it would still have an infinite number of chances to type out all of Shakespeare's works after that, thus guaranteeing it.

34. The way I understand it is something like this.

Imagine that the time-frame is a year. At the end of the year, you can look back and see whether the conditions were met. You can't wait a month and say that it didn't happen, because the conditions could still be met in the remain 11 months.
Infinite time doesn't have an end, you are always infinitely far from the end of the time-frame, so there is no point that you can say that "it didn't happen". You can only ever say "it hasn't happened yet" until either it does happen, or you reach the end of infinity.

35. No, he is capable of typing other letters as well, but that does not mean that the possibility of typing always another "A" isn't there.

Actually, the probability is 0, but that doesn't mean the possibility isn't there. It's like picking a random real number between 0 and 1 and hoping it is 1/pi: The probability that you will pick 1/pi is indeed 0, but that doesn't mean that picking 1/pi isn't a possibility, so if you say "I am certain that I won't pick 1/pi" you would be wrong, you're almost certain. This example is mathematically the same as the random letter generating machine writing Hamlet and the "AAAA..." case.
Did you read those sites I linked? Especially the first one. The case is exactly same for your example. 1 out of infinite possibilities.
What we would usually mark by a zero, is not actually zero because we define zero as the probability of an event not happening. It's infinitesimally small. 1/infinity.
As the amount of different possible cases approaches infinity, the probability for a certain case approaches zero. But it doesn't reach it because the number of cases never "reaches infinity", infinity is not a number, it's a concept. Just as an infinitesimally small is a concept, "so small that it cannot be distinguished from zero by any available means", but not an actual number.

Also you fucked up the quotes.

36. given infinite time the monkeys could possibly learn english in that time and read shakespeares works then reproduce them

37. So what you're saying is, that there is an infinitely small chance that after infinite time has passed, the monkey will have typed an infinitely long string that doesn't contain any Shakespeare?

38. So what you're saying is, that there is an infinitely small chance that after infinite time has passed, the monkey will have typed an infinitely long string that doesn't contain any Shakespeare?
There is no "after infinite time". It's not a number, you can't treat it as such.
I'll try to explain my post a bit more:
As the amount of different possible cases (meaning things they type. At the first keystroke, if we assume 26 letter alphabet, there's 26 possibilities. At the second, there's 26^2 possibilities. And so on) approaches infinity (this meaning more time passing, meaning more letters typed),
the probability for a certain case approaches zero. But it doesn't reach it because the number of cases never "reaches infinity", infinity is not a number, it's a concept.
(So if you're allowing yourself to talk about "infinite cases", you must allow yourself to have an "infinitesimal chance" for each of them. You have so many cases that it's impossible to measure their amount, thus you have a chance for each of them that is so small that it's impossible to measure. )
Eh, I don't know if that makes it any clearer. Hope so.

39. An infinite number of monkeys would instantly produce the iteration.

A single monkey in infinite time would produce the iteration in time.

40. Nope. Read above post. Thanks.
Nope, you don't get what infinity means.