Talk:Infinite monkey theorem

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. 67.248.112.172 (talk) 21:07, 11 January 2010 (UTC)

Apes?

would using apes by any chance change the probability?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" 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) 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)). —Preceding unsigned comment added by 124.78.192.45 (talk) 10:02, 16 December 2010 (UTC)

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 cardinals a little if you're interested in how these things work Bobathon (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). —Preceding unsigned comment added by 124.78.192.45 (talk) 11:24, 16 December 2010 (UTC)

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. Bobathon (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. —Preceding unsigned comment added by 124.78.192.45 (talk) 12:45, 16 December 2010 (UTC)

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.

—Preceding unsigned comment added by 124.78.192.45 (talk) 13:01, 16 December 2010 (UTC)

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)).

Bobathon (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. —Preceding unsigned comment added by 124.78.192.45 (talk) 13:49, 16 December 2010 (UTC)

Infinities are fun :-) Bobathon (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?? —Preceding unsigned comment added by 62.30.156.106 (talk) 09:57, 16 August 2008 (UTC)

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 67.248.112.172 (talk) 21:21, 11 January 2010 (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. (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). --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 —Preceding unsigned comment added by 72.88.90.206 (talk) 02:46, 22 September 2008 (UTC)

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. RAmen, 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! —Preceding unsigned comment added by 137.14.10.22 (talk) 18:38, 4 May 2008 (UTC)

Zero or one?

The 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"? -- noosphere 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. --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. -- noosphere 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. --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. -- noosphere 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. --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. -- noosphere 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. --Trovatore 07:16, 27 November 2006 (UTC)

For the record, this discussion refers to 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. 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). --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). 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. CMummert · talk 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. Melchoir 19:02, 9 March 2007 (UTC)

Erm...

Would it still count if they typed out Christopher Marlowe instead? 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.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. 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.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.

Ason 11:48, 18 January 2007 (UTC)

I agree. Given infinite time, the probability that the event will occur is 1. That means it is certain. --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. --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. --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. --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. --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. --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? --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. --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. --Aprogressivist 09:27, 19 January 2007 (UTC)

P.S. It seems we have reached the same conclusion. --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. --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. --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. —The preceding unsigned comment was added by Gnassar (talk • contribs) 17:22, 6 March 2007 (UTC).

Well, it's standard in modern probability theory, whether you like it or not. --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. 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 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.  --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. --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.  --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. --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. 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) events, 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.  --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. --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? (Discuss). --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.--70.231.149.0 03:09, 4 February 2007 (UTC)

Ignore

Ignore. 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. Fizzackerly 13:21, 29 January 2007 (UTC)

Big Bang math checks out

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. — ciphergoth 19:30, 14 February 2007 (UTC)

A picture

In case you guys want it, 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. -- 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. Melchoir 23:03, 1 March 2007 (UTC)

…Thanks! 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. 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 added by an anonymous user in October 2005. It lived in the lead section before 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! 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?". — Loadmaster 23:57, 5 March 2007 (UTC)

More than 10^100000 and less than infinity, regardless of all details. 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? — 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". 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. — 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 Google books around here. 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. — 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 sources for anything. --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. Glooper 01:31, 8 July 2007 (UTC)

Um, okay, I'll rephrase the question: What is the 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?
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 (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.
— 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 below (108 keystrokes by my count) you can expect about 3.5×10¹⁵⁹ 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. 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. Quatreryukami 15:46, 7 March 2007 (UTC)

Uh yeah, it kinda sounds not impossible, but definetly improbable. Wikizilla ^{Signme!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? 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. 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. Melchoir 16:50, 19 April 2007 (UTC)

Thought not. I've eventually managed to find out how to add to the RFD page 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).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. LordArros 15:04, 11 May 2007 (UTC)

Perhaps you could point out where in the article it mentions repressed monkeys? — 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. - JJ Effix 17:13, 11 September 2007 (UTC)

"LordArros", the monkeys are a metaphor. 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). --200.222.30.9 16:56, 22 May 2007 (UTC)

Perhaps the quote referred to the expected amount of time, or the amount of time such that the probability that it would happen in that time exceeds some particular number. 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. 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. --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. 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? --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. 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. --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. 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. --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. — 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. --Nathan (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. 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. --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 don't need a tornado. 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. 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 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? 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. 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. :-) 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:
If a hundred monkeys typed
For a hundred years,
One of them would produce
The works of Shakespeare.

Alternately, in question form:

If a hundred monkeys typed
For a hundred years,
Would one of them produce
The works of Shakespeare?

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.

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? 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. 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.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. Glooper 01:38, 8 July 2007 (UTC)

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

So can we go home now? My thumbs are nubs.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. --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. --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 — and of course, any which remains should be sourced — but I am convinced that at least some of it should have a place on WP, and should be accessible from this article. Paul August ☎ 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.) --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. Paul August ☎ 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. 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. 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: [1], [2], [3] (that one is a substantive change), and [4]; and there: [5], [6], [7]. I'm going to synchronise the content and remove it from here until the AfD is over. Carcharoth 09:02, 12 August 2007 (UTC)

That's fine. If the article is deleted again, we can copy any appropriate content back here. Paul August ☎ 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. Michael Hardy 18:15, 11 August 2007 (UTC)

New sources

I don't think this website, nor the subpage here are actually quoted in the article (only the PDF of the 'book' seems to be there). Someone may want to add them. Carcharoth 12:55, 12 August 2007 (UTC)

Swift and Pascal bits are missing

The history section mentions Swift and Pascal in passing, but unlike the Aristotle and Cicero bits, the Swift and Pascal references are never explained or quoted. I found the Swift bit in the popular culture article (which I am working on at the moment), but don't know where to find the Pascal bit. The Swift bit should be added:

• 1782 - Jonathan Swift's Gulliver's Travels (1782) anticipates the central idea of the theorem, depicting a professor of the Grand Academy of Lagado who attempts to create a complete list of all knowledge of science by having his students constantly create random strings of letters by turning cranks on a mechanism (Part three, Chapter five): although his intention was more likely to parody Ramon Llull.

And someone should find and add the Pascal bit. Thanks. Carcharoth 14:27, 12 August 2007 (UTC)

Later history section?

Is there a possibility for a rigorously sourced selection of examples from the 'in popular culture' article being integrated to this article under the title 'Later history' or 'Recent history'? At the moment, I'm rigorously sourcing the examples and re-ordering them in date order. I'm also turning up papers that mention not the mathematics or the early history and development of the idea, but rather of the current history and usage of the idea in literature and elsewhere. In other words, rather than being a "here are some examples", it would become "here is a history of the later use of the idea". Carcharoth 14:34, 12 August 2007 (UTC)

New paper on this topic - Monkeying Around with Text

Please see Monkeying Around with Text, Terry Butler, University of Alberta, Computing in the Humanities Working Papers, January 2007. I've used this as a reference over at Infinite monkey theorem in popular culture, and I think it will be useful here as well. Carcharoth 18:26, 12 August 2007 (UTC)

Expanded summary for popular culture section

I've now added a summary for the popular culture section, based on my rewrite of the daughter article Infinite monkey theorem in popular culture. See my edit here. Carcharoth 12:11, 16 August 2007 (UTC)

Stephen Ballentyne

Editors of this page may wish to be wary of including material by the philosopher of mathematics Stephen Ballentyne until there is evidence that such an individual exits and has been published. --Mark H Wilkinson ^{(t, c)} 19:12, 16 September 2007 (UTC)

Yes, even though Ballentyne seems to exist, publishing is key. The edits to this article are confused, and if they are based on a published source, I would be very interested in learning which publisher endorsed it and what exactly it said. Melchoir 04:41, 17 September 2007 (UTC)

Apparently this person is now teaching Religious Studies at Uppingham School.[8] Unless he publishes in a reputable journal, and his point of view is discussed by multiple independent published sources, his opinions are just as non-notable and unencyclopedic as those expressed at the local pub.  --Lambiam 07:04, 17 September 2007 (UTC)

Or that could be another individual entirely. The Ballentyne edits have been introduced by two new user accounts, apparently set up for the sole purpose of pushing this issue ([9], [10]).

At least we're getting a better class of vandal. --Mark H Wilkinson ^{(t, c)} 09:03, 17 September 2007 (UTC)

It's a shame that the Internet appears to be the sole source of verification for published source materials and that no evidence of Ballentyne's published material exists (as yet) on the Internet. My fellow students and I will strive to correct this omission by writing to the editors of the journals and books he has contributed to. It is sad that material about monkeys urinating on typewriters and repetitive computerised random number experiments are present in this article, instead of the dynamic range of mathematical philosophies that exist on the subject. --Merisalis 04:33, 18 September 2007 (UTC)

Funny thing about the internet is that the work of noted academics tends to turn up in Google searches. For example: Prof JF Toland is exceedingly easy to find. --Mark H Wilkinson ^{(t, c)} 10:41, 18 September 2007 (UTC)

Evolution?

Excuse me, what is the relevance of this to the article?

"Various Christian apologists on the one hand, and Richard Dawkins on the other, have argued about the appropriateness of the monkeys as a metaphor for evolution." —Preceding unsigned comment added by 128.122.20.71 (talk) 14:23, 18 September 2007 (UTC)

Evolution is probably the most common and most important context for the infinite monkey theorem in modern popular culture, and there is a section of the article describing how. The Wikipedia:Lead section provides a one-sentence summary of that section.

I've reverted a bunch of recent edits to the lead that had little basis and removed information. I've also reverted the "However" paragraph from the "Real monkeys" section; the section already states that monkeys are not random number generators, and we don't need arguments that experiments are "unnecessary". Melchoir 01:00, 3 November 2007 (UTC)

I don't get it... :P

Infinity is an unending period of time. Why does the term "almost surely" apply? Shouldnt it just be "certainly"? After all, there are no limits. -- Anonymous Dissident^Talk 09:42, 21 December 2007 (UTC)

It's a joke. Your tax dollars hard at work: big rings in the ground and monkeys at typewriters, congratulations.72.201.19.165 (talk) 20:21, 8 December 2011 (UTC)

Imagine that a fair coin is tossed infinitely often. Denoting the two sides as 0 and 1, this gives an infinite sequence of bits, something like

0111001110001111111111010011110100101001110111100010010111001011011100010011101110101110110010001010...

(space limitations do not allow to show the full sequence). What is the chance of getting exactly this sequence? In fact, all possible sequences are just as likely, such as the sequence

1011010001100111000011101111110110011111011011110011000111011011101111110111001011011110010100011011...,

or, for that matter, the sequence

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000....

So if it is certain that the last sequence will not occur, it is just as certain that any other sequence, such as the two above it, will not occur, including the one that actually is the result of tossing the coin infinitely often. Under the normal meaning of the word certain, that is a contradiction.  --Lambiam 18:56, 21 December 2007 (UTC)

I had the exact identical question back in the section entitled (appropriately enough) "Question". Refer to Dcoetzee's answer there. —Preceding unsigned comment added by 75.163.233.26 (talk) 17:35, 29 March 2008 (UTC)

This looks like a case of approaches infinity vs. infinity. Similarly p(x)->1 not p(x) identical to 1. 68.144.80.168 (talk) 12:30, 19 June 2008 (UTC)

It is definitely not surely. If a monkey presses a button at random, that means it is possible that it can repeatedly press the same button each time. The probability of this continually happening is very small, but it can happen. For this reason it is impossible to 'guarantee' that the works of Shakespeare would ever be produced. It only becomes more likely as more time is given. —Preceding unsigned comment added by 79.68.196.135 (talk) 14:31, 27 June 2008 (UTC)

"Huxley" &c.

Does it not seem a little silly to put a picture of Huxley up when the article does not actually owe much to the man? He simply was attributed wrongly, and had a nice little quip about the bishop. The only other illustration contained in this article illustrates the article beautifully. Huxley, however, has little to do with this. I'm just being picky, but it threw me for a second. It seems like unnecessary emphasis on an only mildly meaningful character (in the context of this article).130.101.14.214 (talk) 19:35, 2 February 2010 (UTC)

The "Evolution" section currently begins:

In his 1931 book The Mysterious Universe, Eddington's rival James Jeans attributed the monkey parable to a "Huxley", presumably meaning Thomas Henry Huxley. This attribution is incorrect.

The footnote for this bold statement includes the following citation: Padmanabhan, Thanu (2005). "The dark side of astronomy". Nature. 435: 20–21. .. However, I cannot figure out how that article relates to the Infinite Monkeys, let alone to whether or not "Huxley" invented that formulation. Am I missing something, or has there been an error?

Also:

Borges follows the history of this argument through Blaise Pascal and Jonathan Swift, then observes that in his own time, the vocabulary had changed. By 1939, the idiom was "that a half-dozen monkeys provided with typewriters would, in a few eternities, produce all the books in the British Museum."

Interestingly, when Borges says this, he too attributes it to a "Huxley":

Siglo y medio más tarde, tres hombres justifican a Demócrito y refutan a Cicerón. En tan desaforado espacio de tiempo, el vocabulario y las metáforas de la polémica son distintos. Huxley (que es uno de esos hombres) no dice que los "caracteres de oro" acabarán por componer un verso latino, si los arrojan un número suficiente de veces; dice que media docena de monos, provistos de máquinas de escribir, producirán en unas cuantas eternidades todos los libros que contiene el British Museum.

I would be interested in knowing the history of this attribution. Is there a kernel of truth in it? I guess I'll have to check Respectfully quoted: a dictionary of quotations (the other authority cited in the aforementioned footnote) when I get home, but in the meantime can anyone elucidate this? It seems like we should have some firm sources if we're going to categorically state that the "attribution is incorrect," right? --Iustinus (talk) 23:44, 28 December 2007 (UTC)

Should have specified: since Borges wrote in 39, he's presumably repeating the claim from Jeans. But it's still very interesting that hementions it. --Iustinus (talk) 00:50, 29 December 2007 (UTC)

assumptions

It must be made very clear here what we take on faith in our definition of "infinite". Even if "infinity" as a logical abstraction is comfortable and acceptable in the exact branches of mathematics, bringing it into statistics raises innumerable difficulties, not all of which are mathematical. --VKokielov (talk) 05:05, 4 February 2008 (UTC)

One of the worst Wikipedia articles ?

And it also has an error - in the Direct Proof section, please note the while the individual keystrokes are independent (by assumption), the blocks of 6 letters are NOT, since they overlap. and if they not overlap, there is the possibility of |1QpBAN| |ANAhlp|, which is not accounted for. Either way, the proof is incorrect.

zermalo (talk) 20:02, 17 March 2008 (UTC)

Your claim is not constructive. Please point out which particular sentence you believe is incorrect by directly quoting it here. Melchoir (talk) 01:32, 18 March 2008 (UTC)

I think this is covered pretty well by footnote 1. Does it need to be in the body of the article? Algebraist 14:29, 5 May 2008 (UTC)

Whether or not the text is organized into blocks is irrelevant to the proof. Organizing the text into blocks of, say, 6 implies that we will be making 1/6th as many samples which in turn implies that the time needed will be 6 times longer. The samples are still independant. Let us examine the alternative. No blocks: There are two variations to this problem. Case 1: Will "poem" be replicated. In this case, overlapping samples can be considered independant. 'Nuff said. Case 2: searching for the first instance of "poem". This case is harder, (as samples demonstrate dependance), but we can still fall back on the blocks (or even case 1). 68.144.80.168 (talk) 12:48, 19 June 2008 (UTC)

The proof is correct, because if the probability of BANANA occurring on a block boundary is 1, then any more likely event has the same probability. There's no need for a precise analysis here. Dcoetzee 01:45, 28 June 2008 (UTC)

Oh, dear! I hadn't noticed the claim. It is wrong, but the errors also really do not matter. See the "Definitely wrong but morally right" section infra. JoergenB (talk) 20:20, 7 October 2008 (UTC)

The Brainiac Experiment

When I came to this page I immediately thought of an experiment conducted on Brainiac testing this idea. They sat several monkeys and several "Brainiacs" down at computers, and the closest they could get to Shakespeare's works was when one monkey typed "alas" in the whole six hours. I would put this on the page, but I don't think I'd do a very good job of it and I'm relatively new to Wikipedia, so please could someone else who knows more about what they're doing add this? Thanks:) Lowri (talk) 17:27, 22 July 2008 (UTC)

Do you have a reliable source for this story? Surely anyone of the "Brainiacs" could have typed To be or not to be; in fact almost any English-speaking "Joe Shmoe" would know that much Shakespeare. What have the computers to do with it?  --Lambiam 00:04, 27 July 2008 (UTC)

Is the story itself not reliable enough? Well, it doesn't matter anyway as their experiment really didn't prove anything, they probably just did it for the "lulz". 193.44.6.146 (talk) 21:24, 31 July 2008 (UTC)

How tiny is very tiny?

In a recent edit, the sentence

"The probability of a monkey typing a given string of text as long as, say, Hamlet, is so tiny that, were the experiment conducted, the chance of it actually occurring during a span of time of the order of the age of the universe is minuscule but not zero."

was changed to:

"The probability of a monkey typing a given string of text as long as, say, Hamlet, is very tiny, but not zero."

The edit summary stated:

"This is redundant and wrong ".

I don't see what is wrong with this, assuming the age of the universe is not significantly more than 10¹⁰⁰⁰⁰⁰ years and that the monkey does not type significantly faster than 10¹⁰⁰⁰⁰⁰ characters per second. Please enlighten me.  --Lambiam 23:41, 12 August 2008 (UTC)

You might want to knock a zero off the second exponent (I'm not sure of the average word length of Hamlet, so I'm being conservative), but otherwise You're right. Algebraist 23:52, 12 August 2008 (UTC)

I see the full edit summary was This is redundant and wrong, especially interesting to be wrong only 2 lines after explaining the perils of reasoning in this exact way...:), referring to 'the perils of reasoning about infinity by imagining a vast but finite number, and vice versa'. Perhaps Diza was imagining an infinite age of the universe? Algebraist 23:55, 12 August 2008 (UTC)

Yes, the shortened version, while true, is a bit of an empty statement - it's a bit obvious. But the original is also vague - we've no idea what "the chance of" is actually referring to, or even what "the experiment" is. The theorem is only meaningful in an idealised, thought-experiment sense. I suspect any re-write eliminating this vagueness would render it too wordy for an introductory paragraph. I can't imagine calculations about the universe or the laws of physics having any place here - there's plenty of scope for them in the main body. I'd say the sentence is both redundant and vague, and the section works better without it.Bob D (talk) 00:14, 13 August 2008 (UTC)

The antecedent of "it" in the original is obviously "a monkey typing a given string of text as long as, say, Hamlet". In the preceding sentences of the lede it has just been explained that the "monkey" is not an actual monkey, but a metaphor for an abstract device that produces a random sequence of letters ad infinitum, which in an infinite amount of time will almost surely produce a given text, such as the complete works of William Shakespeare. At least to me, it appears so obvious that the experiment is to let an abstract device produce a random sequence of letters for an indefinite amount of time that I don't think this needs to be explicated.  --Lambiam 13:05, 17 August 2008 (UTC)

Since 'it' has no reference to a time scale or rate, so there is no meaning to the 'chance of it occurring' within a given time.Bob D (talk) 06:28, 18 August 2008 (UTC)

The "chance of it occurring" in question is, of course, a non-constant function of the typing rate. This does not make it meaningless, nor does it prevent us from observing that it is miniscule in any experiment. Melchoir (talk) 07:01, 18 August 2008 (UTC)

130.000 (or actually more) ?

Take Hamlet from http://www.gutenberg.org/dirs/etext98/2ws2610.txt and pipe it through

perl -pe 's/\[.*?\]//; s/[\s\,\.\-\;]//g'|wc

and you'll see it's just a little less than 130.000 characters.

Not that it matters much, but still :) Rkarlsba (talk) 03:55, 3 September 2008 (UTC)

Definitely wrong but morally right

The section Direct proof contains a fallacious statement (whence of course its proof also is not quite correct). At the same time, the error is of no importance for the thesis of the article; instead of the proposed exactly exponential expression, you get an approximately exponential expression, not with the same but with a rather similar base, and thus the conclusion is not at all involved. Thus, the argument ought to be rephrased. I'm afraid there is no doubt about the results in themselves; they are the most simple cases in studies of growths of dimension sequences related to finitely presented algebras, which were studied in the '70's e.g. by Victor Ufnarovski, Warren Dicks, and myself. The simple, purely combinatoric situations, independently later have been rediscovered by combinatorians (coming to the same conclusion, of course); and I suspect that the simple "one forbidden word" enumeration problem also has been covered by independent discoveries several other times, both before and after the first publication of it that I know about (by Govorov in 1972).

Here is the result, and an outline of the proof. A much more general result, covering any finite number of "forbiodden words", was proved and puublished by V. E. Govorov in the Mat. Zametki 12 (1972), pp. 197-204. I concentrate on "BANANA" and 50 letters, however.

Assume given an alphabet of 50 letters, and among these the letters A, B, and N. For any ("European") natural number n, let a_n be the number of strings of length n in the 50 letters, that do not contain BANANA as a subword; let us call "BANANA" forbidden, and the strings without an occurrence thereof allowed. Then, for $0\leq n\leq 5$, clearly $a_{n}=50^{n}$. For $n\geq 6$, $a_{n}$ fulfils the recursion formula

$a_{n}=50a_{n-1}-a_{n-6}$.

The reason is simply this: We may prepend any letter to any one of the $a_{n-1}$ allowed strings of length $n-1$, and in that manner we get $50a_{n-1}$ strings. Obviously, these strings include all the allowed strings of length n. However, some of them are forbidden; namely those beginning with "BANANA". For any one of these forbidden strings, the last $n-6$ letters will form an allowed string, say S (since otherwise already the string ANANAS would be forbidden, before prepending the initial "B"). Thus, out of the $50a_{n-1}$ candidates for allowed strings, exactly $a_{n-6}$ fail.

Now, the most neat way to sum up these recursive properties are by the generating formal power series (as it ought to be called), alias the generating function (as it usually is called). In fact, it is not hard to see that

$\sum _{n=0}^{\infty }a_{n}x^{n}={1 \over 1-50x+x^{6}}\,$,

by means of the usual methods taught in an elementary coursis including combinatoric enumeration by means of formal power series. However, our purpose here is slightly different; we want an estimate of the probability for finding or not finding "BANANA" as a subword of an arbitrary length n string. Assuming that the letters are chosen i.i.d. and with equal probabilities, all the $50^{n}$ strings are equally probable; whence the probability of not having "BANANA" as a subword is exactly $a_{n}/50^{n}$. Now, as also taught in these elementary enumeratoric combinatorics courses, a rational expression for a formal power series, such as the one supra, may be converted to a polynomial expression for the coefficients, in terms of the roots of denominator polynomial of the rational expression; or, more precisely, of the associated "auxiliary equation"

$y^{6}-50y^{5}+1=0\,$.

A sixth degree equation is a bit hard to solve by elementary means (as Abel proved); but it is easy to see that this one does not have double roots (by taking the g.c.d of it and its derivative). This yields, that there are constants $c_{1},\ldots ,c_{6}$, such that for any $n\geq 0$ we have

$a_{n}=\sum _{j=1}^{6}c_{j}r_{j}^{n}\,$,

where the $r_{j}$ are the roots of the auxiliary polynomial. The absolutely largest of these roots, say $r_{1}$, is a positive real number; and thus already for moderately large n the quotient $a_{n}/50^{n}$ will be rather close to $(r_{1}/50)^{-n}$. However, as you may see by simple means, the auxiliary equation does not have any rational root, whence a fortiori

$r_{1}\neq 50-50^{-5}\,$.

Now, I know that arguments involving probabilities often invoke hot sentiments; and I also know that nobody likes being told that someone else knows much more about these subjects. I'm really not trying to bully anyone; but I did write part of my ph.d. thesis about these things, and have published a few articles about this later, whence I would be lying if I told you that this just is a guess. I've really tried to explain why you get the results, perhaps too lengthily; I'm absolutely prepared to discuss them further in detail, here or on my user talk page; but, as I said, the differences are actually not that important. The base of the exponential expression is a number somewhat smaller than 1, that's all that matters here, actually. I'd like to rewrite the text slightly, weakening the claims a bit (and not including the Govorov et al. precise results with proofs, if you don't mind), but providing a correct and sufficient estimate. However, I won't try this, if there are too many "unresolved issues" about the mathematics left. JoergenB (talk) 21:50, 7 October 2008 (UTC)

What's wrong with the direct proof as it stands? Algebraist 11:54, 8 October 2008 (UTC)

The entire point of the simple proof is just to demonstrate a simple case of the theorem and why it's true in that case. It doesn't need to provide an accurate estimate of the probability, only to bound it from below, and then show that that bound tends to 1. A more accurate estimate may be relevant, but for this initial example it's overkill and defeats the point of having a simple example. Dcoetzee 21:45, 8 October 2008 (UTC)

I believe JoergenB meant we should use the phrase "Sketch of proof" if we don't meant to have the exact details to be correct. K61824 (talk) 05:10, 10 May 2009 (UTC)

Link 24: the monkey Shakespeare simulator

This site bombarded me with Java errors and made Firefox crash. Is this a common issue with the site? Should the link be removed if the site is unusable because of this? - 84.27.9.117 (talk) 22:21, 25 October 2008 (UTC)

might be just you. worked fine on ieFirl21 (talk) 15:13, 3 September 2009 (UTC)

Kolmogorov Complexity and monkeys typing on a computer

One of the most interesting sidenotes to the infinite monkey theorem is the fact that the monkeys would be significantly faster if they used a computer instead of a typewriter. I first heard about this in Cover and Thomas, "Elements of Information Theory".

Given that the Information entropy of the English language is about 1.5 bits per character, Shakespeare's works could probably be compressed by a factor of at least three. Thus, the probability that the monkeys come up with a compressed version of Hamlet (or a computer program which prints Hamlet) is much higher than the probability that they produce the full text.

I just find that interesting... what do others think about it? If there are enough people that motivate me (write to j dot b dot w at gmx dot ch) I'll create a Wikipedia account and write it down properly. —Preceding unsigned comment added by 128.178.83.79 (talk) 11:00, 19 December 2008 (UTC)

Yes, that's interesting - I've added your paragraph (with minor changes) to the Probabilities section as a footnote to the text.Bobathon (talk) 13:48, 11 January 2009 (UTC)

It may be appropriate to create a section for this somewhere within the article - it has a significant bearing on all calculations relevant to this subject (though clearly not on the final "finite but non-zero" conclusion)Bobathon (talk) 13:54, 11 January 2009 (UTC)

Note

There are some broken equations in the Solution section. Could somebody more knowledgeable than I fix that? Thanks! –Juliancolton ^{Tropical Cyclone} 02:53, 25 February 2009 (UTC)

Weasel misconception

I have corrected a misconception in the article which stated that "Dawkins has his Weasel program produce the Hamlet phrase METHINKS IT IS LIKE A WEASEL by typing random phrases but constantly freezing those parts of the output which already match the goal". The bold text is incorrect; in the context of this article, it's not a big deal, but it is part of the toolkit used by those who oppose evolution, and is plainly wrong.

The current Weasel program article does not clearly address the issue, but it is well covered in the discussion. The correct letters appear to lock because the program chooses the best match from mutated progeny (so mutations which make a good letter bad will usually not be the next parent). However, a video shows that the program does not lock correct letters, and the words used by Dawkins in The Blind Watchmaker make it obvious that his simulations apply random mutations to all locations. Johnuniq (talk) 08:55, 2 May 2009 (UTC)

How was the specific probability calculated?

Just wondering, how was the number 3.4 × 10^183,946 obtained? This needs to be explained somewhere, or else the number should be removed for being unverifiable original research. ··gracefool☺ 18:54, 8 May 2009 (UTC)

It's just 26^130000. Algebraist 20:00, 8 May 2009 (UTC)

How do you work that out? ··gracefool☺ 10:38, 9 May 2009 (UTC)

It was clear from the immediately preceding text that 26^130000 was the number that should have appeared there, so I just checked (using Google calculator) that it was. Algebraist 18:37, 9 May 2009 (UTC)

To calculate n = 26^130000 we take log of both sides: log(n) = 1300000*log(26) = 183946.5352

Therefore n = 10^0.5352 * 10^183946 = 3.429 * 10^183946 Johnuniq (talk) 00:29, 10 May 2009 (UTC)

Thanks. So including punctuation the figure is about 10^360783 (26 letters x2 for capitalisation, + 12 for punctuation characters = 64, log(64)*199749 characters). That makes a big difference to the number! ··gracefool☺ 01:18, 10 May 2009 (UTC)

I've added this stuff to the article. ··gracefool☺ 05:36, 25 June 2009 (UTC)

I once slapped the keyboard at random and got "iloveyouall". Professor M. Fiendish, Esq. 04:51, 13 September 2009 (UTC)

"Almost surely"

The phrase "almost surely" has ABSOLUTELY NOTHING to do with the monkey metaphor! It's a precise mathematical term with a precise meaning that has NOTHING to do with metaphors. Please fix the article so that it makes sense! —Preceding unsigned comment added by 174.20.91.244 (talk) 18:04, 15 August 2009 (UTC)

Broken external link

The first external link (to the Baltimore Examiner) is broken, and just redirects to the homepage of the Washington Examiner. 170.148.198.156 (talk) 09:52, 9 November 2009 (UTC)

You meant the first link in the External Links, correct? I couldn't find it either. Looks like it got lost when baltimoreexaminer merged into washingtonexaminer. Lots of googling no go. Worse news, see here: http://web.archive.org/web/*/http://www.baltimoreexaminer.com/opinion/The_million_monkey_room.html Looks like baltimoreexaminer never let IA archive their stuff, so it'll be real hard to find again.  :-( —Aladdin Sane (talk) 10:43, 9 November 2009 (UTC)

Probability section fails

That whole section is wp: or, not to mention wrong. It assumes that the monkey is only striking keys that produce letters the monkey could strike any of the function keys or numbers etc. It cites no sources except the bottom where it takes a quote. The main trouble is that this section falsely presents a low probabilty by restricting the origional terms of the theory to the life of the known universe rather then infinity which is how it is supposed to be. Any probability repeated with a time frame of infinity will be come 1, the life of the universe isnt even a warm up phase compared to infinity. This section needs to be removed entirely it is not helpful Smitty1337 (talk) 23:04, 21 April 2010 (UTC)

I agree that OR is an issue but I support the section (WP:IAR or whatever) since it is verifiable and useful to readers. The restriction to 26 letters is just a commonly-made simplification – if the monkey had more than 26 choices the probability would be lower than the effectively zero value shown in the article. No one is denying that in some metaphorical sense randomly striking keys would eventually produce a sentence, but it is valuable to learn that in practical terms the outcome is impossible. The concept has sometimes been used to assert that freak things will eventually occur by blind chance (i.e. physical things in a practical universe). Whereas that is true for many very rare phenomena, it is not true in this universe for an event such as randomly typing a particular book. Also, note that there is a very reliable reference that supports the conclusion of the section. Johnuniq (talk) 02:02, 22 April 2010 (UTC)

this section shows the odds at 3.4 × 10183,946 . if we assume 1 letter per second and 130,000 total seconds thats 2166.66 hours or 90 days roughly 1 quarter of a year, per full book attempted (and this is generous because it doesn't assume failure on letter 3 throws the book out and starts over right there). if the 3.4 × 10183,946 attempts required to get 1 right is all that's statistically probable, then the monkey should write one copy every 76.5 x 10183,946 years which divided by infinity will happen infinite times so in 76.5 x 101839460 years we'd have the 10th copy (collectors edition i presume). I'm being absurd to get my point across, this theorem is meant to prove a point, not be taken literally, the point is that anything that has a probability that is not zero no matter how excessively large the denominator is on that fraction, the concept of infinity makes that number minisucle to the point of if it "can" happen it will happen repeatedly in 345235324532452345234523453245234523452345234532 years (not even .00001% of infinity of course). this is all OR of course which is why i'd never push to say such on the article, but neither should some silly probability section give a false notion of unlikelyhood when infinity makes the chance 100% (eventually) Smitty1337 (talk) 10:33, 22 April 2010 (UTC)

From the reliable source: As Kittel and Kroemer put it, "The probability of Hamlet is therefore zero in any operational sense of an event…". The numbers used for input to the calculation are shown in the "Direct proof" section. Don't you find it interesting that the chance of randomly typing Hamlet is essentially zero, even if you have as many monkeys as there are particles in the universe, and each types 1,000 keystrokes per second for 100 times the life of the universe? Johnuniq (talk) 11:20, 22 April 2010 (UTC)

The trouble with making that statement is that it is without context. The probability may be operationally zero, as the sourcer says, and that is infact true, but the problem is that any probability given infinite repetition will become 1, and if not stopped upon successful completiion, then technically the book will be made and remade infinite times. the statement is true but by itself its misleading because its just the probability without moving to the next logical step of infinite repeatition, and everything above it is wp: or Smitty1337 (talk) 00:43, 23 April 2010 (UTC)

From a Darwinian approach to the question "How long would monkeys type the works of Shakespeare"?, the solution is the period intelligent man has evolved from primates. A monkey , trapped on earth a million years ago with nothing but to mutate itself into an intelligent being, discover words, concoct writing, invent the typewriter and finally produce among its descendants a literary genius would take a few million years. This period has been historically tested and is much much less than the predicted statistical outcome with the assumption that the monkey will genetically remain stagnant without hope for increased brain capacity but just random act in his eternal life. —Preceding unsigned comment added by 149.136.17.253 (talk) 20:16, 1 September 2010 (UTC)

You have missed the point entirely, as the article says right in the lead, its a metaphorical moneky, as in one monkey, not a series of generations, there is no evolution involved in this article and its only meant to imply a concept of probability and infinity. Smitty1337 (talk) 18:29, 2 September 2010 (UTC)

Sorry to engage in forum talk, but while of course you are correct, I think 149.136.17.253 probably knows that, and the point they made is interesting because it highlights how human commonsense can fail when extrapolated too far. Our brains provide a model of the world whereby we are happy to talk about an ideal monkey typing for millions of years (which is fine), but in the time frames under discussion lots of things will change in ways that we struggle to appreciate (the Atlantic ocean is expected to disappear in 200 million years or so, due to plate tectonics; can't find it on en.wiki). Johnuniq (talk) 02:35, 3 September 2010 (UTC)

None of this is right at all. A correct neuron configuration is required to type out a William's Shakesphere Play. Given infinite time, the neuron configuration of the brain will never reach precisely the right locations and synapses as that so the monkey will be typing out an entirely play by chance because it is deterministically a zero probability. In order for an action to occur, a neuron must be fired, and certain neurons specifically. —Preceding unsigned comment added by 209.159.183.114 (talk) 13:33, 20 November 2010 (UTC)

"Experiment"

"Popular interest in the typing monkeys is sustained by numerous appearances in literature, television, radio, music, and the Internet. In 2003, an experiment was performed with six Celebes Crested Macaques. Their literary contribution was five pages consisting largely of the letter 'S'."

1. This wrongly suggests that it was a scientific experiment, rather than a student art project.
2. I don't see that this is significant enough to mention in the lead. Feezo (Talk) 03:05, 8 February 2011 (UTC)

   I agree that the sentence should be removed from the lead. I suppose the mention in the "Real monkeys" section is warranted, although it adds little of value to the article other than to show that the topic is of general interest. Johnuniq (talk) 05:46, 8 February 2011 (UTC)

Weird sentence in the lede

"The theorem illustrates the perils of reasoning about infinity by imagining a vast but finite number, and vice versa. " - what's "perilous" about it? What, I'm gonna get shot if I think about infinity by imaging a vast but finite number? What the hell is this sentence even supposed to mean? Nonsense.Volunteer Marek (talk) 21:24, 11 April 2011 (UTC)

And what for monkey's sake does the "vice versa" refer to? Reasoning about "finity" by imagining a minuscule but infinite number? Seriously.Volunteer Marek (talk) 21:26, 11 April 2011 (UTC)

almost surely

"almost surely" implies the change the money wont type the play is considerable, but the chance is actually infinitesimal or zero. 173.183.79.81 (talk) 22:35, 14 April 2011 (UTC)

It's a technical term; it's not up to us to change it. It's explained in the text, which is really all we can do. --Trovatore (talk) 22:45, 14 April 2011 (UTC)

typing for infinity

If the apes could type for infinity, and there was a small amount of probability that they could type the works of some author, is it also possible there is a small chance they write something that hasn't been written yet (assuming nobody saw the writings and somehow copied them)? Could the typing somehow predict a future? If they could, they could also predict another piece of writing that will never happen, or never has happened, creating something new, couldn't they? I may be asking something that has been gone over already, but I don't think so. — Preceding unsigned comment added by 66.165.17.192 (talk) 03:47, 3 July 2011 (UTC)

anything about the article ? Arjun^codename024 05:21, 3 July 2011 (UTC)

For the record, there is no "predictive" value to monkeys typing for billions of years, because any process which found some coherent text in the randomness (say, a collection of poetry about probability) would in effect be "writing" that text by searching for it. Overall, readable random texts are way way way less frequent than unreadable ones, unless you have an evolution-like process that keeps the readable stuff and ditches the unreadable, in which case it's a somewhat different puzzle.

However, if we're talking about an infinite length of time, then yes, even one monkey will indeed produce every possible finite sequence of text with probability 1, including readable books that no human had ever written — an infinite number of such books, in fact. There's nothing special about Shakespeare here, it's just used to illustrate this surprising idea. ± Lenoxus (" *** ") 00:32, 13 October 2011 (UTC)

Nothing surprising about it when you consider how long infinite time is. ··gracefool☺ 03:22, 3 November 2011 (UTC)

Lenoxus has it right, but in other words: You can't predict the future with randomness, because to recognize it as something apart from randomness, you have to already know the information in question. If there was no Shakespeare, you couldn't recognize Hamlet as being something special, any more than any of the other millions of readable books likely to be typed before that. If there were a specific prediction, eg. "The World Trade Center will be destroyed on September 11, 2011", how would you tell its accuracy over a million other predictions of the same thing happening on a different date? ··gracefool☺ 03:22, 3 November 2011 (UTC)

The picture in the article is wrong also

That's a chimpanzee, not a monkey. And that's a camera, not a typewriter (I think). — Preceding unsigned comment added by 71.98.215.115 (talk) 05:45, 10 September 2011 (UTC)

It's a very old typewriter: zoom in on it to see the detail (the base, the keys, the paper holding structure at the top). As for the ape historically 'monkey' was used for both apes and monkeys. Certainly when this phrase arose it would be common usage. Even now it is still used informally like that.--JohnBlackburne^words_deeds 12:15, 26 September 2011 (UTC)

Title of first (non-lead) section

Why is the first section under the TOC headed Solution? Solution of what? Problems have solutions, but the theorem is not stated as a problem. I've looked through the history and it appears to have been that way for quite a while so I don't want to change it rashly, but surely we can do better than that. Suggestions? Maybe the inelegance of this word indicates a more structural difficulty with the article, and suggests moving the proof sketch further down? --Trovatore (talk) 20:13, 12 October 2011 (UTC)

Yes, it is odd, although I don't think moving it would be particularly helpful. Perhaps "Analysis"? Also, in "proof of this theorem", the "this" should be replaced with "the infinite monkey". Johnuniq (talk) 00:31, 13 October 2011 (UTC)

Similar concepts

Why aren't there links to similar concepts? Someone could include a link to Bogosort or something, which I believe is a great example.98.119.209.61 (talk) 09:09, 15 November 2011 (UTC)

Good question! I'll add some later, if I can remember to. In the meantime, feel free to be bold. Evanh2008, Super Genius Who am I? You can talk to me... 09:43, 15 November 2011 (UTC)

Why the link at the top about "not to be confused with..."?

Why exactly is there a link at the top of the article staying this should not be confused with the hundreth monkey effect? They are totally unrelated things and in my opinion, are not easily confused. If this statement stays, then I think we should also add the following statement: "Not to be confused 12 Monkeys." I mean, there is a number at the front of the statement and it says monkeys... a reader might be confused. Krohn211 (talk) 19:09, 1 December 2011 (UTC)

I agree: if this title were ambiguous it should link to a disambiguation page but it clearly isn't. Further I can't see anyone confusing this with the hundredth monkey effect which seems not to be widely known: from the article it's a discredited crank theory, not part of mainstream science. I've moved it to 'See also' but I have no objection to it being removed altogether.--JohnBlackburne^words_deeds 19:35, 1 December 2011 (UTC)

I am not a heavy wikipedia user so I don't know the goal of the "See Also" section. From my understanding, this section is meant for related topics and I don't believe this is a related topic. If it were up to me, I'd remove all references to it from this article. Looking at the history I can't tell who put this there in the first place. Since I didn't put it there, I don't want to be the one to remove it. But if I had a vote, I'd say remove it altogether. Krohn211 (talk) 03:53, 2 December 2011 (UTC)

The above issue was fixed in this edit by JohnBlackburne. Johnuniq (talk) 06:45, 2 December 2011 (UTC)