Talk:Infinite monkey theorem: Difference between revisions

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== Do not edit "Direct proof." ==

I'm a complete layman when it comes to mathematics. I have no intuitive sense of math at all. The Direct proof section, however, explains the math in such a way I can understand it. As an encyclopedia is meant to be understood by the casual reader, I encourage the editors to preserve this easy-to-understand explanation. Altering as little as a few words can make the explanation nearly impossible to understand by people like me. [[Special:Contributions/67.248.112.172|67.248.112.172]] ([[User talk:67.248.112.172|talk]]) 21:07, 11 January 2010 (UTC)

== Apes? ==

would using apes by any chance change the probability?[[User:Firl21|Firl21]] ([[User talk:Firl21|talk]]) 15:07, 3 September 2009 (UTC)

:ok the meaning behind this is that apes have diffrent centeres of gravity and diffrent hand sizes. would thoes factors contribute to the probibilty of producing hamlet .

also if the monkey has to prduce 1 of shakespears works wouldnt we multiply the chance by the numbers of shakespears works. and what if the work of shake spear was inside of a string of "jrwosufjsiuhamlet hamlet hamletwjfgijsivso"

[[User:Firl21|Firl21]] ([[User talk:Firl21|talk]]) 15:10, 3 September 2009 (UTC)

::Presumably yes, since the photo on the page is of an ape (chimpanzee) not a monkey. Anyone got a better photo? (Actually the probability is one in either case) [[User:Number774|Number774]] ([[User talk:Number774|talk]]) 11:44, 26 September 2011 (UTC)

=="Probabilities" section is wrong==

If the monkeys filling the known universe were typing "for all time" (meaning, I guess, for an infinite time), then surely the probability of "Hamlet" appearing would eventually reach 1. Challange this assertion, if you think it's wrong. If not, the section should be radically edited.

==proof it's wrong==

The question should be rephrased "What percentage of infinite sets of infinite random strings contain Hamlet?"

Heres an infinite string that doesn't contain Hamlet:

3.14159265... ie the constant pi.

If an infinite number of monkeys all typed pi then Hamlet wouldn't appear anywhere, and this is as equally probable as any other infinite set of infinite strings - as a counter example it proves that the probability isn't one.

We can think of an infinite number of infinite sets of infinite strings that do not contain Hamlet (just from typing digits).

Moreover, lets take an infinite string that does contain Hamlet (denoted H):

a b c d e f H f k k s k d k k....

we can use this to generate a new string by replacing every instance of H with any non-Hamlet string:

a b c d e f * f k k s k d k k....

So for every string that does contain Hamlet, we can generate an infinite number of strings from it that do not - and all these strings are as likely to occur as the ones that do contain Hamlet.

There are an infinite number of infinite sets of infinite strings that do contain Hamlet and there are infinite number that don't. But there are more that don't (like there are an infinite number of integers and an infinite number of integers divisible by 5, but the chance of picking a number divisible by 5 is 1/5 (even though there are an infinite numbers divisible by 5)). <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/124.78.192.45|124.78.192.45]] ([[User talk:124.78.192.45|talk]]) 10:02, 16 December 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

:It doesn't quite work like that. Your 'proof' that there are infinitely many more non-H strings than H strings, if it were true, could be used to 'prove' that there are infinitely many more strings of decimals that don't contain any 3s at all than there are that do. Just take any infinite string containing 3s, and you have an infinite number of ways of replacing all the 3s by other digits. Therefore the percentage of real numbers with 3s in the decimal expansion is zero. Which is obviously silly. You might want to explore the mathematics of [[transfinite_number|transfinite cardinals]] a little if you're interested in how these things work [[User:Bobathon71|Bobathon]] ([[User talk:Bobathon71|talk]]) 10:56, 16 December 2010 (UTC)

::Yes, but if it is possible to generate an infinite string on a keyboard that doesn't contain Hamlet then clearly the probability isn't 1. Someone with the appropriate math skills ought to be able to work out what percentage of these sets contain Hamlet. But it clearly isn't 100%. So the proof given in the article is incorrect. The monkeys could pick a not-Hamlet set of strings. I don't say that there are infinitely more, just that there are infinite of both H and non-H. The number of integers divisible by 5 is infinite not 1/5th of all integers, but the probability of randomly picking a number divisible by 5 IS 1/5. Since we don;t know the percentage of H strings in the list of all possible sets of infinite strings we cannot come to a probability. But it's not 1. With your point about 3's - there are an infinite number of 3less real numbers. But there is still a finite probability of picking a number with a 3 in it (and it too isn't 1) And there are an infinite number of non-H strings (which was my point). <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/124.78.192.45|124.78.192.45]] ([[User talk:124.78.192.45|talk]]) 11:24, 16 December 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

:::No, the probability of an infinite string of digits containing a 3 is precisely 1. You're correct to say that there are an infinite number of strings both with and without a 3, but that doesn't tell you anything at all about the ratio. The probability of the first digit not being 3 is 0.9. The probability of first string of n digits all not being a 3 is 0.9^n. As n tends towards infinity, the probability tends towards zero. The probability of an infinite string of digits all not being 3 is precisely zero, therefore the probability of picking a number with a 3 in it is precisely 1. The argument for H is exactly the same. [[User:Bobathon71|Bobathon]] ([[User talk:Bobathon71|talk]]) 12:12, 16 December 2010 (UTC)

::::0.666666666666...recurring. it exists = so you are saying that this number doesn't exist because it doesn't contain a 3? I follow your logic, but it's trivial to find numbers that contradict the result. How can something with zero probability of existing in fact exist? If zero probability means 'zero apart from a few notable exceptions' then there is a serious problem with probability theory. And we need to rewrite what we mean by zero. <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/124.78.192.45|124.78.192.45]] ([[User talk:124.78.192.45|talk]]) 12:45, 16 December 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

:::::Actually your maths is wrong p(finding 3)= (0.1)+(0.9)(0.1)+(0.9)^2(0.1)+(0.9)^3(0.1)+...

= (0.1)(1 + (0.9) + (0.9)^2 + ...)

= (0.1)(0.9)/(1-(0.9)) (sum of infinite geometric progression)

= 0.9

:::::Your maths only applies to finding a 3 at infinite decimal places - but you could find it at the 1st, or second etc.

The probability of any number containing at least one 3 is 0.9

:::::This result effectively proves that the infinite monkies writing Hamelet is also not 1 since the logic is identical.

<span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/124.78.192.45|124.78.192.45]] ([[User talk:124.78.192.45|talk]]) 13:01, 16 December 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

::::::Ok, this is getting silly. If you don't get it, please learn the subject rather than persisting with faulty arguments.

::::::1. As I said, there are an infinite number of strings that do not contain a 3 and an infinite number that do, but that doesn't preclude the ratio being zero.

::::::2. Your infinite sum is (0.1)(1/(1-0.9)).

::::::[[User:Bobathon71|Bobathon]] ([[User talk:Bobathon71|talk]]) 13:34, 16 December 2010 (UTC)

:::::::Bugger - you are right. But I'm still going to have sleepless nights over this. I was proud of myself for a minute. <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/124.78.192.45|124.78.192.45]] ([[User talk:124.78.192.45|talk]]) 13:49, 16 December 2010 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

::::::::Infinities are fun :-) [[User:Bobathon71|Bobathon]] ([[User talk:Bobathon71|talk]]) 13:52, 16 December 2010 (UTC)

=== Where are all the assumptions?===

Obviously this only holds true if:

* The monkey lives for ever

* As t-> infty the support of the any probability distribution function does not decrease

* The length of time the type writer is broken is not above some limit

The first point is obvious. The second just means that, say your a monkey and you you start pressing the buttons, sooner or later you'd expect the monkey to realize that the "biggest event" happens when you press the return carriage key and thus it is entirely plausible that the monkey would never press any of the other keys again. In fact there are even similar reasons this could fail. It could well be the case that the width of the finger of the monkey are such that it never hits only one key, rather it hits two or more, which in turn could cause this theorem to fail. The last point is about "what if the type writer broke?" surely the time between break downs would have to be strictly less that than the time necessary to type the number of characters in the text?? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/62.30.156.106|62.30.156.106]] ([[User talk:62.30.156.106|talk]]) 09:57, 16 August 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

: Point 2 is very interesting. You might be interested in the real-life experiment they did with 6 monkeys, mentioned in the article. Point 3, however, is flawed. Even if the typewriter is broken down for 95% of the time, 95% of infinity is still infinity. - Minetruly [[Special:Contributions/67.248.112.172|67.248.112.172]] ([[User talk:67.248.112.172|talk]]) 21:21, 11 January 2010 (UTC)

=== [[Randomness = White noise]] ===

People! This is really very simple. This is an argument for that an infinite series of random numbers, can produce shakespeare. Many add "because infinity makes that probable". Now what is a random series of numbers? That is white noise. What the monkey will produce, finitely or infinitely, and it cannot be infinite by logic, but that is another argument, is purely white noise, nothing else. No shakespeare, no guitarsound, no universe, or sudden emergence of abiogenesic consciousness. Just hiss boys. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/84.211.32.31|84.211.32.31]] ([[User talk:84.211.32.31|talk]]) 20:19, 9 February 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

:More about randomness vs assigned meaning would be a good addition to the article (providing it had good sources of course). [[User:Gracefool|··gracefool]][[User talk:gracefool|&#9786;]] 00:38, 13 February 2012 (UTC)

::White noise is defined in terms of randomness, not the other way around. There's an article on randomness. I put in a link to it on the first line. [[User:Bobathon71|Bobathon71]] ([[User talk:Bobathon71|talk]]) 09:52, 14 February 2012 (UTC)

=== [[Infinite monkey theorem in popular culture]] ===

This article may contain content copied from the deleted article [[Infinite monkey theorem in popular culture]], which was edited by Michael Hardy, Calton, Cyberneticorganism, Eyrian, Scrumshus, Eh! Steve, Xanzzibar, CyberSkull, 0nlyth3truth, Ravenhull, SmackBot, Mukadderat, Orgone, RobJ1981, Sceptre, Zenohockey, Vinograd19, Chris the speller, Lovelac7, Tocky, Melchoir, Hughtcool, Scorpion0422, Think outside the box, Aprogressivist, Faustus Tacitus, Trovatore, Aprogressivist, Fagles, and anonymous editors.

==A VERY VERY simple experiment==

Out of curiosity, i decided to test this theory using... wait for it... VB6!!! To keep things simple, i decided to make my program attempt the word 'easy'- only 4 characters. The program randomly generated a letter a-z or a space, and if it was an 'e', then it kept that and went on to the next letter. If the next letter was ''not'' an 'a' however, the program had to go back the start and try again from 'e'. Each time the letters were cleared and started again from 'e', i counted that as an attempt. Using some basic probability, i predicted it would take 531,441 attempts to produce the four letters 'easy'.

Here are my results:

To produce the letter 'e' took 65 attempts.

To produce 'e' and 'a' consecutively took 118 attempts. (must've gotten lucky here)

To produce 'eas' took 25,815 attempts

And to randomly generate 'easy' took a grand total of 669,124 attempts.

I didn't time it, but based on the fact that my timer had an interval of 1/100th of a second, it took about 1hour 50minutes to complete. I went and had dinner and called my girlfriend for a bit while i waited.

The conclusion: The theory is only true because infinity is unbeatable, and I need to get out more.

Wow, proof if ever I saw it. Good job you dont work for the FDA, or wede have all sorts of untested drugs on the market.

Run them multiple times and see if the average is closer to your 531,441 figure. If its consistently high, the difference will grow infinite on larger strings. ([[User:Spintronic|Spintronic]] 15:28, 6 July 2007 (UTC))

:Why is this here exactly? This is not a discussion forum, nor a forum for relating personal experiences related to this topic. I'm glad you had fun playing with visual basic, and I'm sure your girlfriend was happy to hear from you, but this does not belong on Wikipedia. It's not a significant discovery, nor is it terribly academic, nor is it published (nor would it ever be). --[[User:Cheeser1|Cheeser1]] 16:35, 6 July 2007 (UTC)

I think it's a good contribution...and if this isn't a discussion forum, then why does this page come up when I click "DISCUSSION" at the top?

Moron. ~ surge <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/72.88.90.206|72.88.90.206]] ([[User talk:72.88.90.206|talk]]) 02:46, 22 September 2008 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

==Why is the part about a monkey pissing on a keyboard on this page?==

It's the last paragraph. What does this have to do with anything?

-G

:Some researchers gave some monkeys a keyboard to see what they'd do with it and, well, they peed on it. [[Pastafarianism|RAmen]], [[User: Demosthenes_1|Demosthenes]] 21:28, 15 February 2007 (UTC)

Frankly, that was the funniest part of the article! I hope that one of the monkies that was successful in re-creating one of the play remeber to save his work before pooping on it! <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/137.14.10.22|137.14.10.22]] ([[User talk:137.14.10.22|talk]]) 18:38, 4 May 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

== Zero or one? ==

The [http://en.wikipedia.org/wiki/Infinite_monkey_theorem#Probabilities Probabilities] section states:

:''The text of Hamlet, even stripped of all punctuation, contains well over 130,000 letters which would lead to a probability of one in 3.4×10¹⁸³⁹⁴⁶... The mere fact that there is a chance, however unlikely, is the key to the "infinite monkey theorem", because Kolmogorov's zero-one law says that such an infinite series of independent events must have a probability of zero or one. Since we have shown above that the chance is not zero, it must be one.''

Couldn't one just as easily argue that, ''"since we have shown above that the chance is not one, it must be zero"''? -- [[User:Noosphere|noosph]]<font color="green">[[User:Noosphere/Esperanza|e]]</font>[[User:Noosphere|re]] 22:59, 26 November 2006 (UTC)

:Well, you could, if you ''had'' shown the probability is not one. But you haven't. Good thing too, since in fact it ''is'' one. --[[User:Trovatore|Trovatore]] 23:29, 26 November 2006 (UTC)

::Per the above, the probability the quoted argument was referring to was ''"one in 3.4×10¹⁸³⁹⁴⁶"'', which is not one. -- [[User:Noosphere|noosph]]<font color="green">[[User:Noosphere/Esperanza|e]]</font>[[User:Noosphere|re]] 04:14, 27 November 2006 (UTC)

:::That's the probability per trial. The zero-or-one is the probability of at least one success, given infinitely many independent trials. --[[User:Trovatore|Trovatore]] 05:01, 27 November 2006 (UTC)

::::Then where in the Probabilities section is there a demonstration that the probability of at least one success, given infinitely many independent trials is not zero? I only see mention of the probability per trial. -- [[User:Noosphere|noosph]]<font color="green">[[User:Noosphere/Esperanza|e]]</font>[[User:Noosphere|re]] 06:19, 27 November 2006 (UTC)

:::::Well, if you perform infinitely many trials, you've certainly performed one trial. So the chance of success in infinitely many trials can't be less than the chance in a single trial, which is calculated as "one in 3.4×10¹⁸³⁹⁴⁶" (copied from your text above), and that is greater than zero. --[[User:Trovatore|Trovatore]] 06:22, 27 November 2006 (UTC)

::::::That's convincing. But it's not part of the argument given in that section. Perhaps it would make the article clearer if something along the lines of your argument should go in to that section instead of having it claim that ''"we have shown above that the chance is not zero"'' when no such demonstration is present. -- [[User:Noosphere|noosph]]<font color="green">[[User:Noosphere/Esperanza|e]]</font>[[User:Noosphere|re]] 07:05, 27 November 2006 (UTC)

:::::::No proof gives every detail; they'd be unreadable. But in any case the proof by direct calculation, which doesn't need the zero-one law as a black box, is given earlier in the article. The separate proof as an application of the zero-one law is a debatable organizational choice (one of the problems of article-by-committee) but I don't think that leaving out that particular step is its biggest problem. --[[User:Trovatore|Trovatore]] 07:16, 27 November 2006 (UTC)

For the record, this discussion refers to [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem&oldid=111304141#Probabilities this text], which has since changed dramatically. To be precise, I changed it.

From what I gather of David A. Williams' ''Probability with martingales'' and of our article [[Kolmogorov's zero-one law]], the probability of "at least one success" '''is not the kind of "tail event" to which the law applies'''. It applies only to the statement that a given text occurs infinitely many times, whose probability is not ''a priori'' bounded below by a positive number. After Williams admits that the zero-one law solution to the monkey problem does not differentiate between 0 and 1, he advocates using the second Borel-Cantelli lemma to prove that the probability is 1 after all. This is done in our article.

Anyway, I removed both references to Kolmogorov in the article, so there is no longer a problem. [[User:Melchoir|Melchoir]] 08:25, 3 March 2007 (UTC)

:Interesting; thanks for tracing that down. The proof sounded reasonable and the conclusion is true, so I hadn't bothered to check the conditions for the application of the zero-one law. This outcome vindicates both Noosphere (that the proof was invalid) and me (that leaving out the step Noosphere objected to was not the biggest problem in the exposition). --[[User:Trovatore|Trovatore]] 08:54, 3 March 2007 (UTC)

::And I'm mostly interested that the outcome vindicates me (in that reasonable-sounding things still demand verification). [[User:Melchoir|Melchoir]] 09:08, 3 March 2007 (UTC)

The paragraph at the top is certainly terse, and the application of the zero-one law is redundant, but that doesn't mean that there is no relationship between the zero-one law and this topic. The original author probably had an interpretation like this in mind: Let the random variable X be such that an observation of X requires randomly generating exactly as many letters as the length of Hamlet. The outcome is X = 1 if the text generated is Hamlet, X = 0 otherwise. In short, break up the typewriter output into consecutive blocks and replace each block with 0 or 1 depending on whether it equals Hamlet.

The calculation in the article showed that the probability that X = 1 is positive, and so the probability that X = 0 is not 1. Now think about infinite sequences of observations of X and put the usual measure on these using the probabilities of X. The set of such sequences that contain infinitely many ones is a tail set (so the zero-one law does apply), although the measure of its complement is easy to compute (it's zero) and so there is no need to apply the zero-one law to find out the measure of this set is 1. Its complement is the set of infinite sequences that contain only finitely many 1s, and this is the countable union of a sequence of measure zero sets, one measure zero set for each possible final ___location of X = 1 in the sequence. There is also no need to apply the Borel-Cantelli lemma, since this is a direct calculation. [[User:CMummert|CMummert]] · <small>[[User talk:CMummert|talk]]</small> 13:02, 9 March 2007 (UTC)

:Yes, in that sense the infinite monkey theorem's result is certainly consistent with what the zero-one law tells us about the problem. The Borel-Cantelli lemma is more relevant to the article than the zero-one law, even though they are both redundant, because the former gets us p=1. [[User:Melchoir|Melchoir]] 19:02, 9 March 2007 (UTC)

== Erm... ==

Would it still count if they typed out [[Christopher_Marlowe#Marlowe_as_Shakespeare|Christopher Marlowe]] instead? [[User:Totnesmartin|Totnesmartin]] 23:06, 28 November 2006 (UTC)

I think the last 3 paragraphs of Intuitive proof sketch should be deleted. They really aren't relative to the theorem as the theorem isn't concerned with capitalization or the possibility of jamming a typewriter.[[User:161.184.194.100|161.184.194.100]] 09:09, 12 December 2006 (UTC)

I think the last three paragraphs are essential to the article, not only because it's hilarious, but also because it shows the reality of the expression. People want to know if it has been proven in reality. [[User:Poopsix|poopsix]] 02:32, 5 January 2007 (UTC)

== Probability section removal ==

I removed the following text from the Probability section:

:''But the problem as stated ignores "boundary" counditions. It is physically impossible to breed and sustain infinitely many monkeys (even if only "theoretical"), and similarly impossible to provide immortality to any of the monkeys, or to keep the monkeys on task for the required time. But of even more consequence, no machine is self repairing, nor has a life cycle sufficient for the problem, thus the probability is 0, not 1.

:''It is impossible to "re-create" an art-form of reasonable complexity with any random-process; if it were not so, there would be no such thing as plagiarism, nor methods of determining document authenticity.

:''Even if one could randomly create meaningful artistic works, there still needs to be judgement processes to determine what is of value that should be kept, and what is worthless that should be eliminated.

:''For a good computer program random text generator on the fastest computers available, the "answer" is that the machine is in all likelyhood going to "crash" before producing the desired results, even if the program takes into acount word probability and grammar logic.''

The first paragraph fails to recognize that we are not talking about a specific incident, but instead an abstract idea. The second is just wrong; it negates the entire article. The third is an opinion statement, and the fourth goes back to talking about a specific incident again.[[User:BlueSoxSWJ|BlueSoxSWJ]] 17:26, 15 December 2006 (UTC)

== guaranteed to occur, or only almost guaranteed to occur ==

2007-01-09, 16.19 Ason:

"(→Probabilities - Removed "almost" in: "To consider that an event this unlikely is almost guaranteed to occur given infinite time can give a sense of the vastness of infinity.")"

2007-01-09, 19.30 Trovatore:

"(but it *isn't* guaranteed. It just has probability one. That's better than any guarantee you'll ever get in this physical life -- but this is mathematics.)"

An even that is unlikely to happen during a definite time, but not impossible, WILL happen if given infinite time.

Actually it will happen an infinite number of times, regardless of how unlikely the event is.

Therefore it CAN be said that the event is guaranteed to occur given infinite time.

If you don't like the word guaranteed, you could say the event WILL occur given infinite time.

Using the word almost, implies that there is a probability that the event will never occur, and THAT is wrong.

Since I think editing wars are counterproductive, I will not edit the article untill Trovatore or someone else has had reasonable, but not infinite, time to comment.

[[User:Ason|Ason]] 11:48, 18 January 2007 (UTC)

: <s>I agree. Given infinite time, the probability that the event will occur is 1. That means it is '''certain'''</s>. --[[User:Aprogressivist|Aprogressivist]] 16:19, 18 January 2007 (UTC)

: The issue is semantically confusing. I need to grok the semantic difference between mathematical "almost sure" and such ambiguous terms as "guaranteed", "almost guaranteed", "certain", etc. --[[User:Aprogressivist|Aprogressivist]] 16:33, 18 January 2007 (UTC)

: Having read up on the [[Probability]] article, it seems consistent to say that the event is '''certain''' to happen. The following three phrases are synonymous: P(''X'') = 1; ''X'' is almost sure to happen; ''X'' is certain to happen. --[[User:Aprogressivist|Aprogressivist]] 16:40, 18 January 2007 (UTC)

::An event that is certain to happen has probability one. The converse, however, does not hold.

::Suppose I pick a real number at random between 3 and 4, with the [[uniform distribution]]. Given any ''particular'' real number between 3 and 4, what's the probability that I pick it? That probability can only be zero. So the probability that I ''won't'' pick it, is 1.

::But if you say that it's ''certain'' that I won't pick that number, and generalize that argument to all the reals between 3 and 4, you must now conclude that I am certain not to pick any number at all. But that's a contradiction; we assumed that I ''would'' pick such a number. --[[User:Trovatore|Trovatore]] 19:31, 18 January 2007 (UTC)

::: I don't think your generalisation step is valid. I'll work on that in a moment. Besides, as I noted, '''certain''' and '''almost surely''' are used synonymously in the scope of the Probability article and the Almost Surely article (both mean P(''X'') = 1). It is therefore ''consistent'' to use them interchangeably; if it is inaccurate, it would seem the problem extends beyond the scope of this article. --[[User:Aprogressivist|Aprogressivist]] 21:18, 18 January 2007 (UTC)

::::Look at the probability article more carefully, with particular attention to [[probability#Representation and interpretation of probability values]]:

:::::''The probability of an event is generally represented as a [[real number]] between 0 and 1, inclusive. An ''impossible'' event has a probability of exactly 0, and a ''certain'' event has a probability of 1, but the converses are not always true: probability 0 events are not always impossible, nor probability 1 events certain. The rather subtle distinction between "certain" and "probability 1" is treated at greater length in the article on "[[almost surely]]".''

:::: The only thing I can see in the article that might have led you to the conclusions you state is the stuff about Laplace. Laplace was great, but things have moved on a bit in the intervening 230 years. --[[User:Trovatore|Trovatore]] 21:28, 18 January 2007 (UTC)

::::: I concede that '''certain''' is not synonymous with '''almost surely'''. That being said, to the layperson, I suspect the phrase '''almost surely''' is much weaker than it is to the mathematician; it certainly seems so to me. I think the original sentence ("To consider that an event this unlikely is (SOME_QUALITATIVE) to occur given infinite time can give a sense of the vastness of infinity") losses some of its impact to the layperson if it includes the word "almost". I attempted to compromise between impact and accuracy with 'certain (mathematically "almost surely")'; how does that sound? --[[User:Aprogressivist|Aprogressivist]] 22:10, 18 January 2007 (UTC)

::::::No, I don't agree with compromising on accuracy. It ''isn't'' certain, so we can't say it is. --[[User:Trovatore|Trovatore]] 01:26, 19 January 2007 (UTC)

:::::::Bear in mind that Wikipedia is not a resource for mathematicians alone, but a resource for the layperson, who will not immediately grasp the semantic distinction between '''certain''' and '''almost surely'''. The phrase with '''almost surely''' has not much strength to the lay person if it is accurate to the mathematician; and if it is accurate to the mathematician it is merely repeating what has already been said in the article already. If you don't wish to compromise, it would seem best to me that it be deleted entirely, because it is somewhat redundant to repeat a mention of '''almost surely'''. --[[User:Aprogressivist|Aprogressivist]] 09:27, 19 January 2007 (UTC)

:::::::P.S. It seems we have reached the same conclusion. --[[User:Aprogressivist|Aprogressivist]] 09:30, 19 January 2007 (UTC)

:::It remains to be shown, however, that the infinite monkeys problem is not certain. I do not believe this is correct; I think Ason's original contention stands. More succinctly put, given a particular event with a result of nonzero probability, that result is certain to occur in an infinite number of events. --[[User:Gnassar|Gnassar]] 15:51, 25 February 2007 (UTC)

::::No, that's simply not correct. All you can show probabilistically is that the result has probability 1 of occurring; probability theory has no hope of showing that the outcome is certain. And in fact it is ''not'' certain, if the trials are truly independent (as opposed to just probabilistically independent), because if they are truly independent, then any combination of possible outcomes of the individual trials is a possible outcome of the whole (infinite) experiment. --[[User:Trovatore|Trovatore]] 23:15, 25 February 2007 (UTC)

:::::I don't believe that's the case. There is no "any combination of possible outcomes" of an infinite number of trials. All finite combinations of possible outcomes would occur in an infinite number of trials. But defining the infinite set of "combinations" of an infinite number of trials is an overexpansion of choice. <small>—The preceding [[Wikipedia:Sign your posts on talk pages|unsigned]] comment was added by [[User:Gnassar|Gnassar]] ([[User talk:Gnassar|talk]] • [[Special:Contributions/Gnassar|contribs]]) 17:22, 6 March 2007 (UTC).</small><!-- HagermanBot Auto-Unsigned -->

::::::Well, it's standard in modern probability theory, whether you like it or not. --[[User:Trovatore|Trovatore]] 17:53, 6 March 2007 (UTC)

:::::::Missed that one somehow. Citation? I appreciate your "standard," but it still seems like an overexpansion of choice, like I said. Last I checked, belief in the axiom of choice was not mandatory in modern probability theory. [[User:Gnassar|Gnassar]] 13:13, 1 September 2007 (UTC)

::::::::Give us a ''mathematical definition'' of "''X'' is certain", where ''X'' is an event, and I'll tell you if ''P''(''X'') = 1 implies its certainty. However, please don't make the discussion pointless by defining it as "P = 1". I have some sympathy for your point of view, but I'm afraid it is not the mainstream view, and even mentioning it might be "original research". Perhaps not you, but most mathematicians would agree with the statement that, just like for any natural ''n'' there exists a random variable consisting of a sequence of ''n'' independent identically distributed discrete r.v.s with uniform distribution on {0, 1} (and sample space {0,1}^''n''), there exists a r.v. consisting of an infinite sequence of such i.d.d. discrete r.v.s. The probability of any outcome of this r.v. is obviously 0, so equating P = 1 with certainty then implies that whatever the outcome, it is one that was certain not to happen. If you don't agree with the mathematicians who would think so, please convert them until the mainstream agrees that P = 1 is synonymous with certainty, whereupon we'll proceed to adjust the article text.

::::::::If you can find a [[Wikipedia:reliable source|reliable source]] of a respected mathematician discussing the issue and asserting that it is meaningless (or highly problematic) to ascribe probabilities to single events from this sample space with the cardinality of the continuum, there might be room for a remark noting that mathematician's point of view. &nbsp;--[[User talk:Lambiam|Lambiam]] 15:35, 1 September 2007 (UTC)

:::::::::Maybe I'm missing something, but the sample space is "the set of all texts that an infinite number of monkeys could type in an infinite amount of time." The outcome we want is "at least one monkey types, somewhere in its text, the text of Hamlet." That is not a single event, it can occur |R| different ways, can it not? Maybe I'm wrong. But to me, it appears that it has the same cardinality as the sample space. --[[User:Cheeser1|Cheeser1]] 22:49, 1 September 2007 (UTC)

::::::::::It does not make a principled difference. The standard treatment does not have an infinitude of monkeys, but the following is agnostic about the cardinality, as long as it is enumerable. Assume without loss of anything essential that the monkeys, numbered 1, 2, ..., are hitting the keys in perfect synchrony. Define ''s''_''k'' by: if some monkey with number ''i'' in the range 1 to ''k'' produced a copy of ''Hamlet'' ending exactly on keystroke ''k'' - ''i'', then ''s''_''k'' = 1; otherwise ''s''_''k'' = 0. There are many ways in which ''Hamlet'' could appear, and many ways in which it may not have appeared at any given stage; the latter are all condensed into a sequences of zeros: a single event in a condensed sample space. The argument (for one monkey) can be made even simpler. Suppose that the famous minimalist author I has written a work consisting of the single character 1. (Author O, who wrote an even more minimal work, containing not a single character, is embroiled in bitter copyright litigation.) We wonder if a monkey could have performed the feat. We give the monkey a copy of I's famous typewriter, which has only two keys: 0 and 1. Surely, if one is to believe that a monkey would ''certainly'' eventually produce Shakespeare's play while rattling away on an Underwood, than our monkey would no less surely eventually reproduce I's work of genius. So again, is it ''certain'' that the event 000... does not occur? If it is not, then it is also not certain that the text of ''Hamlet'' will eventually appear. &nbsp;--[[User talk:Lambiam|Lambiam]] 00:12, 2 September 2007 (UTC)

:::::::::::Okay, a million monkeys and an infinitude of time. There are still |R| possible ways a single monkey could produce Hamlet, just like there are |R| possible ways a monkey could produce a sequence of 0s and 1s containing a 1. That was my point. It's not a "single event" as you claim, it's a set of many events. And "certainty" was not at issue, was it? The issue is "almost certainty" (ie probability of 1). All I was doing was pointing out that this is not a "single event." I don't need to be told that typing an infinte sequence of 0s is possible - I'm not grotesquely stupid. The fact that it has probability 0 should also be just as obvious. --[[User:Cheeser1|Cheeser1]] 01:12, 2 September 2007 (UTC)

:::::::::Apparently I haven't been getting email notifications for quite a while... sorry about that. I like the reliable source standard, which is why I asked for a citation in the first place -- I'm not sure I can find a "respected mathematician" discussing the issue in either direction, so I'd be interested in why this could go unchallenged without meeting a similar standard to the one I've been asked to meet for the opposing viewpoint. A citation, if you have one, would go a long way. In the meanwhile, a quick google for '"nearly certain" probability' gave me this as my first link: http://www.aetheling.com/docs/Rarity.htm which pretty clearly discusses "nearly certain" events as events whose probability ''approaches'' 1. [[User:Gnassar|Gnassar]] ([[User talk:Gnassar|talk]]) 13:20, 22 June 2011 (UTC)

(exdent) That is precisely the original issue of this thread: whether we can state in the article, without some qualification like ''almost'', that the success event is ''guaranteed'' to occur, with possible synonyms like that it ''WILL'' happen, or is ''certain''. This (d)evolved into a mathematical argument involving the axiom of choice, although I think it is more a matter of following the Wikipedia policy principles than of mathematical truth. However that may be, the mathematical issue is of some interest by itself, and moves into deep foundational issues. The simplest way to study the issue is by considering an infinite sequence of coin tosses: is it guaranteed to be certain that heads WILL eventually come up? In the jargon of [[probability theory]], success (heads eventually comes up) and failure (tails, tails, always tails) are just two (complementary) [[event (probability theory)|event]]s, of which the latter is atomic (a one-point subset of the sample space of outcomes). It has measure 0, just like the non-atomic subset of ''Hamlet''-free infinite monkey typescripts. If the claim "P = 1 means certainty" is to stand up, it should apply equally in either case; however, it is more readily seen to be problematic in the coin toss example. The immediate issue at hand appeared to be whether the ''infinite'' failure event should be considered an event ''at all'', which is a foundational issue applying equally to the monkey hammering away and the coin being tossed. Since failure is unobservable, one can reasonably maintain that it is a non-event. Standard mainstream probability theory, however, ''requires'' that the complement of an event also be considered an event. &nbsp;--[[User talk:Lambiam|Lambiam]] 06:59, 2 September 2007 (UTC)

:As I stated, I was trying to clear one particular thing up: there is not a single outcome that does not produce Hamlet, there are many. You said "single." Like I already said, that's what I was trying to clear up. The term that should be used is "almost surely" (which is in use now), as far as I'm concerned. --[[User:Cheeser1|Cheeser1]] 08:37, 2 September 2007 (UTC)

==Merging "Infinite monkey theorem in popular culture" article==

Should the article [[Infinite monkey theorem in popular culture]] be merged with this article? [[Talk:Infinite_monkey_theorem_in_popular_culture#Merge|(Discuss)]]. --[[User:Aprogressivist|Aprogressivist]] 16:15, 18 January 2007 (UTC)

:This is a social meme that has grown into a Wikipedia Math FA aritlce. If it cannot be moved to the "Media" group in the FA listings, then I would rather '''this''' article be merged into the other.--[[User:70.231.149.0|70.231.149.0]] 03:09, 4 February 2007 (UTC)

== Ignore ==

Ignore. [[User:Qpw|Qpw]] 13:47, 25 January 2007 (UTC)

== Appeals To Intuition ==

Although I applaud the efforts of whoever it was in writing the intuitive proof of the theorem, I have to say I find the version given here rather unappealing. Essentially it demonstrates that although every finite sequence within an infinite sequence is possible (and indeed highly likely), no finite sequence is almost sure. In that sense it actually disproves the theorem.

An equally appealing disproof of the theorem which exploits the same probabalistic argument would run along the lines of: As the monkey types, the probability that the next key to be hit is the first letter of the target sequence doesn't change, and is always strictly less than one. Therefore it's always possible the monkey will hit a key other than the first letter of the target sequence and therefore there's no certainty that the monkey will start typing the target sequence, and therefore no certainty that it will produce the complete target sequence. Therefore although it's possible the monkey will produce the target sequence, it's not certain that it will. Even allowed infinite time, the probability that the next key to be hit is the start letter of the sequence doesn't change and remains less than one, and therefore the monkey could type forever and never hit the starting letter key.

To be honest I'm not sure how to reword the appeal to inuition to make it more robust, but I'm not sure, as it stands, if it persuades a casual reader of the proof of the theorem. [[User:Fizzackerly|Fizzackerly]] 13:21, 29 January 2007 (UTC)

== Big Bang math checks out ==

[http://en.wikipedia.org/w/index.php?title=Talk:Infinite_monkey_theorem&oldid=76882664#Question_regarding_math_in_opening_paragraph This discussion] which for some reason has been removed from this page thrashes out the math for this in some detail; it checks out. I'll remove the fact tag unless someone wants to dispute the linked math. &mdash; [[User_talk:Ciphergoth/Please don't use this|ciphergoth]] 19:30, 14 February 2007 (UTC)

==A picture==

In case you guys want it, [[:Image:A Thousand Monkeys.png|here's a screen cap]] that I upoloaded for [[Last Exit to Springfield]]. It shows Mr. Burns' room that is filled with a thousand monkeys working at a thousand typewriters. I figured I'd let someone more familiar with the page put it on if they want to. -- [[User:Scorpion0422|Scorpion]] 20:38, 15 February 2007 (UTC)

== Cicero ==

Searching "considers this possible will also be able to believe" on Google Web, Books, and Scholar returns only Wikipedia and its mirrors. I for one would like to know where the quotation comes from. [[User:Melchoir|Melchoir]] 23:03, 1 March 2007 (UTC)

:…Thanks! [[User:Melchoir|Melchoir]] 00:13, 2 March 2007 (UTC)

== 1970?? ==

A couple of days ago, I deleted a truly bizarre assertion that the version of this proposition that involves infinitely many monkeys orginated in about 1970. /BEGIN ATTITUDE/Aside from the fact that only a lunatic would think that,/END ATTITUDE/ check out [[Nevil Shute]]'s novel ''[[On the Beach]]'', published in 1957, via Google Books. [[User:Michael Hardy|Michael Hardy]] 05:01, 5 March 2007 (UTC)

:Thanks for the info! The article history indicates that "1970" was not part of the article when it was featured in October 2004. It was [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem&diff=25282638&oldid=23806719 added by an anonymous user in October 2005]. It lived in the lead section before [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem&diff=58101200&oldid=57960215 Ciphergoth moved it into the body in June 2006], where it then remained for another 8 months or so. This all just goes to show what kind of edits accumulate upon featured articles without careful supervision. When I overhauled the article a few days ago, it was in one of the many paragraphs that had been tagged as needing citation, and I had hoped to save as many as possible. But no sources turned up, and now we know why: it was wrong! [[User:Melchoir|Melchoir]] 07:14, 5 March 2007 (UTC)

== So what is the answer? ==

While the article contains a short discussion of probabilities, it fails to provide an actual answer to the question, "given ''n'' typing monkeys, how long will it take to produce the complete works of Shakespeare?". — [[User:Loadmaster|Loadmaster]] 23:57, 5 March 2007 (UTC)

:More than 10^100000 and less than infinity, regardless of all details. [[User:Melchoir|Melchoir]] 00:26, 6 March 2007 (UTC)

:More than 10¹⁰⁰⁰⁰⁰ ''what''? Assuming ''n'' monkeys typing at rate ''r'', there is an exact answer. What is it? And why is the answer not in the article? — [[User:Loadmaster|Loadmaster]] 18:58, 7 March 2007 (UTC)

::"All details" includes the unit of time; more than 10^100000 seconds, years, universe ages, whatever. There are, of course, exact answers, but none of the sources I've read see a need to calculate them to any greater precision. Math books are content with "less than infinity", and physics books are content with "greater than any reasonable period of time". [[User:Melchoir|Melchoir]] 21:41, 7 March 2007 (UTC)

::That's not much of an answer is it? "Less than infinity" is any real number - utterly useless as a meaningful answer. I'll say it again: given ''n'' monkeys typing at rate ''r'', the article does not provide an answer to the question, "how long will it take them to produce the complete works of Shakespeare?" Surely this is relevant to the article. The closest answer provided is in "Probabilities", which only mentions the text of ''[[Hamlet]]''. — [[User:Loadmaster|Loadmaster]] 18:51, 8 March 2007 (UTC)

:::If you're so sure that this is a worthwhile calculation, then you must be confident that it's in the literature. Why don't you go look for it? Surely I'm not the only one with access to [http://books.google.com/books?q=monkeys+typewriters+probability Google books] around here. [[User:Melchoir|Melchoir]] 19:31, 8 March 2007 (UTC)

::::Non sequitur. Wikipedia could very well be the first place to provide a definitive answer to the question. — [[User:Loadmaster|Loadmaster]] 23:31, 11 April 2007 (UTC)

:::::It could, but it's not supposed to. That's one of the basic ideas of Wikipedia -- it is a [[tertiary source]], and is not supposed to provide new [[primary source]]s for anything. --[[User:Trovatore|Trovatore]] 23:49, 11 April 2007 (UTC)

OK, so you want an answer? How long will it take...?

A single monkey, typing at a rate of r characters a second could take anywhere between C/r seconds, (where C is the amount of characters) and eternity. For your information, probability is not certain, and not restricted by a time limit. There is no single ANSWER, because it all depends on what the monkeys type and when. The monkeys might very well type the damn thing first go, (unlikely, but possible) and with infinite monkeys, one of them would almost certainly take C/r seconds to type the thing. But you can't just have some finite amount of time that is accurate.

Because that would be like asking, "how many times do I have to flip a coin before I get a head?"

If the coin lands on a head first then the answer is one. If it keeps landing on tails, which is a possibility, it could well take a few flips to get a head. You just don't know until you do it. Obviously there may be some sort of average time (or a most probable time) that you can calculate using fancy probability, but in all honesty, I fail to see the point of such an exercise. Besides, the concept is the important thing, not a calculation or formula.

[[User:Glooper|Glooper]] 01:31, 8 July 2007 (UTC)

: Um, okay, I'll rephrase the question: What is the ''[[expected value|expected]]'' amount of time elapsed before the monkeys produce the complete works of Shakespeare? Or, to put it another way: supposing the typing is completely random and all possible letter sequences will eventually be generated, how long will we ''expect'' to wait for one subsequence to match the works of Shakespeare?<br/> The answer is most certainly ''not'' "an infinite amount of time", because by then they would have generated all possible sequences an infinite number of times each. We're only interested in knowing how long we'd have to wait ([[probability|probabilistically]] speaking) until the ''first'' matching subsequence were generated. In the worst case, we'd have to wait until ''all'' possible ''n''-letter sequences were generated, but that's still a finite amount of time, and places an upper bound on the waiting time.<br/> — [[User:Loadmaster|Loadmaster]] ([[User talk:Loadmaster|talk]]) 16:04, 17 January 2008 (UTC)

::If my quick calculation is correct, the expected time to get a specified sequence of n keystrokes from (uniformly distributed, independent) random taps on an r-key typewriter is (rⁿ-1)/(1-1/r) keystrokes. So if you give the monkey a 26-letter keyboard, plus caps lock, return, period, and comma, and demand that it produce the [[#Poem- source?|poem]] below (108 keystrokes by my count) you can expect about 3.5{{e|159}} keystrokes before it succeeds. So if your monkey manages to hit a key every [[Planck time]] (faster than that may well be contrary to the laws of physics), then the expected time is about 6 hundred million [[googol]] years. I'll leave the actual Shakespeare case to someone who feels like counting all those characters. [[User talk:Algebraist|Algebraist]] 14:59, 5 May 2008 (UTC)

== This is... ==

most definatly a joke. Even with all the external sourcing... I can't help but LOL at it. [[User:Quatreryukami|Quatreryukami]] 15:46, 7 March 2007 (UTC)

Uh yeah, it kinda sounds not impossible, but definetly improbable. [[User:Ootmc|<font color="#0000FF">'''Wiki'''</font><font color="#83F52C">'''zilla'''</font>]] ^{[[User:Ootmc|<font color="#FFFF00">'''Signme!'''</font>]][[User talk:Ootmc|Complaints Dept.]]} 01:26, 2 April 2007 (UTC)

== External links ==

I gave my reasons for deleting some of those links and moving and incorporating the others. Are there reasons to keep them now? [[User:Melchoir|Melchoir]] 21:51, 7 March 2007 (UTC)

*No. See [[WP:EL]] and [[WP:NOT]]. Most of them don't rise to the level of [[WP:RS]], and the sources given cover the necessary info. I deleted most of them again. [[User:SandyGeorgia|Sandy<font color="green">Georgia</font>]] ([[User talk:SandyGeorgia|Talk]]) 02:30, 8 March 2007 (UTC)

== Redirection from ''De Natura Deorum'' ==

Why does the link ''De Natura Deorum'' on the works of Cicero page get redirected to this page ?

Is this page really relevant ?

:Not relevant enough. That redirect should be deleted. [[User:Melchoir|Melchoir]] 16:50, 19 April 2007 (UTC)

::Thought not. I've eventually managed to find out how to add to the RFD page [[User:Simonadams|Simonadams]] 17:29, 20 April 2007 (UTC)

== Real Monkeys section ==

I believe some parts of the Real Monkeys section are fundamentally flawed because the monkeys where not sufficiently repressed from the start by years of education. Many humans, if given the chance, without being fired or punished, would react the same way towards a keyboard. Let us not defame monkeys and act like we're civilized when we're really repressed.(This is all sarcasm in case some hominids don't get it).[[User:Septagram|Septagram]] 02:24, 5 May 2007 (UTC)

== Is this Article a joke? ==

This is completely ridiculous. Especially the part about real monkeys. Repressed Monkeys? For Christ's sake, they're monkeys! Monkeys can't be repressed. This is a great example of why people don't take Wikipedia seriously - not only that, but some admin must be having fun with this page too, because this is definitely not one of Wikipedia's best articles. [[User:LordArros|LordArros]] 15:04, 11 May 2007 (UTC)

:Perhaps you could point out where in the article it mentions ''repressed monkeys''? — [[User:Loadmaster|Loadmaster]] 21:50, 11 May 2007 (UTC)

:The punch line was killed a long time ago. This article used to read really well! It needs a lot of fixing... maybe when i'm bored one day. - [[User:JJ Effix|JJ Effix]] 17:13, 11 September 2007 (UTC)

"LordArros", the monkeys are a ''metaphor''. [[User:Michael Hardy|Michael Hardy]] 17:31, 11 September 2007 (UTC)

== Mistake (At least I think so) ==

"The age of the universe is dwarfed by the gulf of time it would take a monkey to type ''Hamlet'', so in a physical sense it would never happen."

Actually, the probability does not get better after any amount of time, unless the monkey knows what he wants to write and learn from his mistakes, which is unlikely. So, in reality, the chances of the monkey typing Hamlet in his first try are neither more nor less than in his 5678495th try, but equal. Thus, hypothetically speaking, there is no natural (Or mathematical) law that says the monkey won't type Hamlet in one week, or less (If he types continuously). --[[User:200.222.30.9|200.222.30.9]] 16:56, 22 May 2007 (UTC)

:::: Perhaps the quote referred to the [[expected value|expected]] amount of time, or the amount of time such that the probability that it would happen in that time exceeds some particular number. [[User:Michael Hardy|Michael Hardy]] 17:32, 11 September 2007 (UTC)

:That statement in the lead reflects Kittel and Kroemer's interpretation, and probably that of the other physicists in the article as well. Anyway, there is a natural law that says the monkey won't type Hamlet in one week: An event with a probability of 10^-200000 is simply not going to occur. [[User:Melchoir|Melchoir]] 18:13, 22 May 2007 (UTC)

Why not? As long as the chances are not zero, then it's possible. Doesn't matter if its chances are 99,9999999% or 0,0000000001%, it's possible (or at least that's what I remember of the law of probabilities). But either way, you didn't answer why the chances the monkey managing to do it in his 5678495th try are greater than in the first. --[[User:200.222.30.9|200.222.30.9]] 18:27, 22 May 2007 (UTC)

:Possible in a philosophical sense, yes. Possible in any sense accessible to experiment or having an impact on reality, no.

:Yes, the chances are the same each time. [[User:Melchoir|Melchoir]] 19:09, 22 May 2007 (UTC)

Ah, then the chances are equal, at least we agree with that (Which means the text of the article is wrong, since it says "it'll take a long time," and you agreed that time does not matter). The only thing I still didn't get is why possible in the philosophical sense is not possible in the literal sense. I mean, what's stopping the monkey from typing it in, so long as it's possible? Yes, we don't usually see that, but since it's possible, maybe it's because we're unlucky? --[[User:200.222.30.9|200.222.30.9]] 00:04, 23 May 2007 (UTC)

:Given that the article deals with probability, its statements have to be interpreted probablistically. If you want to be precise about it, you could say that there is some time T such that typing for T gives you a 50% probability of having typed Hamlet at least once; and T dwarfs the age of the universe. Or you could say that the expected time of the first occurence of Hamlet is T', and T' dwarfs the age of the universe. Or some other measure; it's all too pedantic for the lead paragraph.

:Nothing stops the monkey; but it's still not going to happen. And as bad as it looks, I'm going to have to say that further philosophical discussion on that issue isn't relevant to the content of the article. [[User:Melchoir|Melchoir]] 01:23, 23 May 2007 (UTC)

It's not philosophy, it's logic, if the chances of the monkey typing it right are not zero, then it's possible. If time does not improve the chances in any way, then the time the monkey takes to type Hamlet can be any time, (T, if you will) as long as it is greater than the time his fingers take to type in the words (T is any number, as long T is greater than t, with t being the time his fingers would take to type Hamlet, if he typed continuously).

I'm not discussing philosophy, I'm discussing a perceived mistake on an encyclopaedia article. I understand your argument, but I still believe that, even if it is not thoroughly wrong, it's at least a little POV. Since it states that certainly it is impossible, when there is doubt. That's my last try, if you are still not convinced, just leave my comment here, so a person may see the discussion and decide for themselves. --[[User:200.222.30.9|200.222.30.9]] 03:32, 23 May 2007 (UTC)

:Philosophy, logic, whatever -- it has no bearing on reality. I could construct an argument that there is a nonzero probability that I will wake up tomorrow with the ability to fly, walk through walls, see ten years into the future, solve the halting problem, and raise the dead.

:A POV case would require a reliable source that claims that a monkey might actually type Hamlet after all. [[User:Melchoir|Melchoir]] 07:40, 23 May 2007 (UTC)

Okay, I said this would be my last try, but you just attacked my argument with the most vile of persuasion tactics: straw man. I didn't say there is a non-zero probability of you waking up flying. There is a natural law that states says you can't wake up flying, it's called cause and effect. So the probability of you waking up flying is zero, unless someone can give you that ability (Which is impossible with our current technology level).

But there is no natural law that says that, if the probability is not zero, and time does not improves the chances, then the monkey can't get it right in the first time. If the monkey can type Hamlet in one trillion quadrillions of years, then it can type Hamlet in one week, because, as you agreed, time is not a factor in the equation. So unless a mystical force decrees the monkey won't type it in one week, it's possible.

The reliable source that states that it's possible is the article itself: ''"which would lead to a probability of one in 3.4×10¹⁸³⁹⁴⁶"''. As far as I know, 1 in 3.4×10¹⁸³⁹⁴⁶ is higher than zero. --[[User:200.222.30.9|200.222.30.9]] 15:18, 23 May 2007 (UTC)

:You are both right, but are talking at cross purposes to each other. Yes, the probability that ''at any given moment'' the monkey will type the correct combination of letters is the same as at any other point in time. And yes, that probability is excruciatingly small. However, we are making the (reasonable) assumption that ''each attempt will be different than any previous attempt'', i.e., that the attempts form a randomly distributed sequence. Therefore, by probability theory, we have a 50% expectation that the one chosen sequence of ''Hamlet'' will appear only after 50% of all the possible sequences are produced. Again, this assumes that each generated sequence is different than all previously generated sequences. Yes, the monkey ''could'' type ''Hamlet'' on the first day, but the odds are almost zero that this would happen. The odds are much higher ''if you wait for a longer total time'' during which many different sequences are generated. And the time required before you can expect to see the ''Hamlet'' subsequence is ''immense''. — [[User:Loadmaster|Loadmaster]] 16:35, 23 May 2007 (UTC)

::I just went ahead and rephrased it (slightly). The time T thing is the most correct way of putting it, but hopefully my phrasing is accurate enough to satisfy the pedants (not meant in a derogatory way, I'm one too... read "perfectionist" if you find that less offensive), but is still succinct enough to fit well in the introduction of the article. --[[User:N.MacInnes|Nathan]] ([[User_talk:N.MacInnes|Talk]]) 17:10, 23 May 2007 (UTC)

:Not to derail too far, but there's no strawman here. Every time I concentrate on flying, there is a positive probability that the air molecules around me will accidentally lift me off the ground and propel me in the direction I'm facing. Since I will attempt to fly only a finite number of times during the course of my life, there is a positive probability that it will work every single time. It is no more an effect without a cause to be able to fly without technological assistance than it is for a monkey to be able to type Hamlet without knowing a word of English. [[User:Melchoir|Melchoir]] 17:59, 23 May 2007 (UTC)

Not to derail too far, but that only would work if you were in a tornado, or something of the kind, then it's possible the air would make you fly, but the expression you used was that you'd "wake up tomorrow with the ability to fly". You didn't simply say you would fly, you said you'd have the ''ability'' to, whenever you wished, fly. And the monkey may have no intention to, but, with the typewriter he, doesn't need knowledge of english to cause the words to appear on the paper, the cause is the monkey's finger pressing the keys, not the monkey's intentions.

But I'm tired of discussing this, so I'll settle with what I have now. Au revoir. --[[User:200.222.30.9|200.222.30.9]] 19:13, 23 May 2007 (UTC)

:Whether I have an intrinsic ability to fly, or I just keep getting lucky, is not a question vulnerable to experiment -- they have the same results. And I [[kinetic theory|don't need a tornado]]. [[User:Melchoir|Melchoir]] 19:57, 23 May 2007 (UTC)

Everybody is essentially right here. If you want to be pedantic, it's more accurate to say that the amount of time you would have to wait to ensure ''a priori'' that the monkey would type ''Hamlet'' with non-negligible probability (say 50%) would dwarf the age of the universe. However, once it's typed, it's typed with certainty - and that could happen at any point and happens at each distinct point with equal probability. The original statement is subtlely incorrect - it shouldn't say the monkey ''would'' take such a long time, but that chances are small ''a priori'' that it would succeed in a significantly shorter time. And yes, it's also possible with negligible probability for the random motion of gases to suddenly cause you to fly. [[User:Dcoetzee|Dcoetzee]] 01:44, 24 May 2007 (UTC)

Note: Both the term straw man and the term cause and effect were used incorrectly in the previous discussion [[Special:Contributions/68.144.80.168|68.144.80.168]] ([[User talk:68.144.80.168|talk]]) 12:07, 19 June 2008 (UTC)

== Question ==

I have a question in a related area. -- Supposing you flip a coin an infinite number of times; the probability you will end up with the particular sequence 'all heads' is zero and so is 'all tales'. The probability is also zero for any ''particular'' sequence of both heads and tales. But the probability that you will end up with ''some'' sequence containing both heads and tales is 100%.

That is confusing to me. How can you have a 100% chance for ''some'' sequence that is both heads and tales when any ''particular'' sequence of heads and tales has a 0% probability? Or, I should ask, am I just entirely wrong in my presumptions? [[User:75.70.166.110|75.70.166.110]] 06:42, 31 May 2007 (UTC)

:That is all entirely correct. This is another funny property of infinities: because the number of possible sequences is uncountably infinite, each can have zero probability while their union has probability 1. Put simply, the law that the sum of the probabilities is the probability of the union does not hold over infinite sets. [[User:Dcoetzee|Dcoetzee]] 11:38, 31 May 2007 (UTC)

Ah, ok. I think that clears things up for me. - Well, at least to the extent that my feeble mind is able to grasp the infinite. :-)

[[User:75.70.76.166|75.70.76.166]] 16:16, 31 May 2007 (UTC)

== 1909 Borel reference ==

The Statistical Mechanics subhead under History asserts that the typing monkeys first appeared in

Emile Borel's 1909 ''Elements de la theorie des probabilites''. I just read through that book and

could not find them. Maybe I skipped them; on what page are they supposed to appear? More likely, I suspect, they are

not in that book. They do show up in his 1914 ''Le hasard'' and in the 1913 journal article cited in the main article.

Jim Reeds

== Poem- source? ==

Hello-

For years, I have known the theorum by this poem:

<br />

If a hundred monkeys typed<br />

For a hundred years,<br />

One of them would produce<br />

The works of Shakespeare.<br />

<br />

Alternately, in question form:<br />

<br />

If a hundred monkeys typed<br />

For a hundred years,<br />

Would one of them produce<br />

The works of Shakespeare?<br />

<br />

I have always believed that the enduring appeal of the theorum was partly the allure of the consideration of the paradox of the seeming impossibility and the seeming eventuality, all captured with the pithy charm of this brief poem.<br />

However, here at this article, I am surprised that I do not see this poem at all. I have searched a bit and I have not been able to find this poem anywhere. I am pretty sure I did not make it up myself. I will continue to look for this poem (either version), and thus provide a reference. But can anyone else help with this reference?

[[User:Pjrowan|Pjrowan]] 13:25, 12 June 2007 (UTC)

:While I've never seen this poem and have no idea who wrote it or whether it's notable, I can at least note that the first is inaccurate. The chance of a hundred monkeys producing even this poem in a hundred years is very close to zero. [[User:Dcoetzee|Dcoetzee]] 21:46, 12 June 2007 (UTC)

Besides not notable and inacurate (my subjective opinion) not good :)

Maybe...

Monkeys have fingers and therefor can type.

But know they not language they simply hit keys.

rather hit they the keys know not what they do.

Write Shakespeare first.

And, then, perhaps, times two.[[User:75.70.76.166|75.70.76.166]] 07:22, 20 July 2007 (UTC)

== Monkeys wrote this article ==

They did. Honest. We stuck them in a temporal looping machine with a few typewriters and they gave us this article. [[User:Glooper|Glooper]] 01:38, 8 July 2007 (UTC)

-Alert the internet! [[User:Ball of pain|Ball of pain]] 22:04, 12 July 2007 (UTC)

So can we go home now? My thumbs are nubs.[[User:Typing monkey|Typing monkey]] 06:58, 22 July 2007 (UTC)

Well, if the first person actually knew anything about probability, then he would realize that since the probability of typing is 1 in 541,000 ish, then it actually, on average I have calculated would only take 368,366 tries to produce "easy" with 27 possible keystrokes. Learn your math. Either that or read the first couple of paragraphs on the monkey page to find out what your stupidity was.

== Contradiction ==

The lead section speaks of an experiment with monkeys and a ''typewriter'', while the last section speaks of the same experiment but with a ''computer keyboard''. One of them is probably wrong. --[[User:CesarB|cesarb]] 02:00, 26 July 2007 (UTC)

:It's pretty clear that the specific section has the details. The lead is a typo, probably due to the fact that the "general" theorem is phrased in terms of a typewriter, while this was a test of a corollary involving a keyboard. I've fixed it, since it's more of a typo than a true contradiction. --[[User:Cheeser1|Cheeser1]] 02:08, 26 July 2007 (UTC)

== I've added text from the deleted article: Infinite monkey theorem in popular culture. ==

I've added text from the deleted article "[[Infinite monkey theorem in popular culture]]", which was deleted via [[WP:AfD]]. I'm not sure whether this is the best place for all this content &mdash; and of course, any which remains should be sourced &mdash; but I am convinced that at least ''some'' of it should have a place on WP, and should be accessible from this article. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 17:40, 6 August 2007 (UTC)

:Hi Paul, just checking, where did you get the text? If you got it from the history of ''this'' article there's no problem, but if you took it from the deleted article there could be a GFDL issue.

:(Of course when I say "no problem" I mean "no GFDL problem" -- by my lights the most unfortunate part of the deletion was that it took away a useful modality for ghettoizing this collection of trivia. But then this article has always been mostly about a middlebrow cultural meme anyway, so I'm not going to fight about that aspect of it.) --[[User:Trovatore|Trovatore]] 21:55, 6 August 2007 (UTC)

::Hi Trov. I got the content form the deleted article, so there may well be some GFDL issues to resolve. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 22:38, 6 August 2007 (UTC)

::The content almost certainly originated from this article in the first place, so someone might want to find the split point, and compare what went out, with what came back in. That will help address some GFDL concerns, and will help find out what was added to the content while it had its own article. [[User:Carcharoth|Carcharoth]] 01:16, 7 August 2007 (UTC)

:::To deal with any potential GFDL concerns, I've posted the complete history of the deleted article at the top of the page. [[User:Dcoetzee|Dcoetzee]] 01:38, 7 August 2007 (UTC)

This is now becoming problematic, following the restoration of [[Infinite monkey theorem in popular culture]], as the same content is now being edited at two different locations. Here: [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem&diff=149674958&oldid=149584298], [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem&diff=next&oldid=149674958], <s>[http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem&diff=next&oldid=150200261] (that one is a substantive change)</s>, and [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem&diff=next&oldid=150576182]; and there: [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem_in_popular_culture&diff=next&oldid=150529203], [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem_in_popular_culture&diff=next&oldid=150539474], [http://en.wikipedia.org/w/index.php?title=Infinite_monkey_theorem_in_popular_culture&diff=next&oldid=150541673]. I'm going to synchronise the content and remove it from here until the AfD is over. [[User:Carcharoth|Carcharoth]] 09:02, 12 August 2007 (UTC)

:That's fine. If the article is deleted again, we can copy any appropriate content back here. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 16:07, 12 August 2007 (UTC)

== Current AfD discusion ==

The deleted article has been relisted at AfD: [[Wikipedia:Articles for deletion/Infinite monkey theorem in popular culture (second nomination)]]. There you can express your opinion on whether to '''keep''' it or '''delete''' it. You should not just say '''keep''' or '''delete''' but also explain your rationale. [[User:Michael Hardy|Michael Hardy]] 18:15, 11 August 2007 (UTC)

== New sources ==

I don't think [http://www.vivaria.net/experiments/notes/publication/ this website], nor the subpage [http://www.vivaria.net/experiments/notes/documentation/ here] are actually quoted in the article (only the PDF of the 'book' seems to be there). Someone may want to add them. [[User:Carcharoth|Carcharoth]] 12:55, 12 August 2007 (UTC)

== Swift and Pascal bits are missing ==