Talk:Infinite monkey theorem/Archive 1

message: i always considered myself mildly intelligent. i dont understand a word of this article. im going to go and kill myself now. 208.103.186.197 00:38, 5 October 2006 (UTC)
thread_title: i feel dumb

message: "the probability that the first letter is b is 1/50" -- um... what's the 1/50? should it be 1/52, 1/53(to include a whitespace)? or something? Where on earth does 1/50 come from? --Storkk 12:32, 27 August 2006 (UTC)
replies: text: Okay, I skimmed over "Suppose this typewriter has 50 keys." Still, I think the number should be slightly more intuitively chosen. Like 2 x 26 or (2 x 26 + 10). Just my 2¢. --Storkk 12:34, 27 August 2006 (UTC)
thread_title: 1/50 ?

message: The theorem appllies to all complex systems.
As such, we can take the "random" nature of atoms "&-or" matter in an "infinate" universe and restate the theorem.
"Given an infinate universe, and an infinately long time, every possible combination of atoms will arise."
Thus; the universe out of "brute force of possible probabilities" has produced the planet we live on with all its complexity. 
A man ponders this and realises, that if the theorem is true, there must be a copy of himself in this "infinate" universe. Not only that, but there must be infinately many copies, EXACT copies of himself. 
He decides to go and find one of these "exact" copies of himself, (and for simplicity he can travel at any speed, thus arriving practically instantaniously)
He now arrive's at a galaxy that looks "exactly" like the milky way. He approach's a planet that looks "exactly" like the earth. He lands in a country that is "exactly" like he's, and he knock's on the door where he lives. The mans wife answers and informs him that, he had just left a while ago, (exactly the same amount of time ago that he had done),
There is a hair left in a comb on the side, the man analises it in he's dna machine, and it "exactly" matches he's own. (This is a true copy). The stars look the same (they'de have to be) he look's at the history archive and supernova exploded on exactly the same dates as they did back home, back on earth, and in exactly the same places in the sky (theyde have to have done or their realities wouldnt be the same).
The man stops' and ponder's this for a moment, and he come's up with an idea, He call's up 5 of he's identical twin brothers, and they all set off in the 6 directions in all axis. He decide's that if they all set off in different directions then they will find 6 copies of their selves no matter which direction they go.
As they set off to the next "identical" world, he crosses one of hes twin brothers along the way he says hello and they pass and carry on. (this must be exactly half way between worlds).
When he arrive's at the next "idnetical" world, all 5 of hes twin brothers are arriving from different directions at the same time.
"Strange" the man says' to himself, and he ponder's the infinate monkey theorem more closely. 
If the infinate monkey theorem is true, then any direction i go in, there will always be a copy of myself. Not only that but every time i set off to meet him(the copy), he also sets off to meet me, so well never meet. Where does he go? He goes to meet the next "identical" copy of myself (according to the theorem there are infinately many of us). 
But there is a halfway point, i met my brother there, and not only that, but the stars "MUST" be the same upto this halfway point for every copy, as we all have the same view in the nights sky. So as we "account" for more & more complex systems, the need for greater & greater accuracy in replication also increases. The man come's to 2 conclusions.
'1)There are infinate copies of "only 1" set of stars. And NOT an infinate variety, as the theorem states.'
'2)The theorum breaks down at some point of complexity.'
(If the constraints of the universe present a problem, the idea is still valid, we could imagine an infinately fast computer, simulating every atom in an infinate universe, we still get infinately many copies of only 1 universe.)Spintronic 23:13, 19 January 2006 (UTC)
replies: text: This is a fun argument, but atoms don't randomly rearrange themselves all the time, the universe has only been around for a few billion years, not nearly long enough to form even mildly interesting arrangements of atoms, and the universe (we believe) has only a finite number of particles, so there's not an infinite number of anything in it. Deco 23:15, 18 January 2006 (UTC)

text: Er, the infinite monkey theorem does not support evolution. Evolution is a directed process based on a feedback loop with random elements, but attempting to achieve life by merely randomly rearranging constituent parts would take far longer than the age of the universe. You are attempting to argue against something nobody believes anyway (and this article certainly doesn't say any such thing). Deco 19:27, 19 January 2006 (UTC)

text: I'm afraid you're misinterpreting the article. I don't know how DNA evolved, but it did. And I'm not feeding the troll anymore. :-) Deco 00:56, 20 January 2006 (UTC)

text: I don't think you're a troll, but you have a very firm grasp on the wrong end of the stick. The  mathematical statements behind the IMT are simply facts.  Their consequences may be counterintuitive, especially if you compare them to very-large-but-finite-monkey situations (eg imagining an entire universe of monkeys working for the age of the universe) but if you think the theory is wrong you should work harder to understand it. — ciphergoth 13:19, 21 February 2006 (UTC)
thread_title: Theorem breaks down as complexity grows

message: "attempting 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."
why don't we try this on wikipedia? also, has anyone ever combined random text generation (though perhaps using a dictionary) with genetic algorithms? something where each revision is human-reviewed, given marks, and then grammar, syntax and phrases from high scoring drafts are kept for future revisions, and where material from unpopular drafts is digarded?
:Yes. See [Darwinian Poetry http://www.codeasart.com/poetry/darwin.html]. Derrick Coetzee 18:21, 31 Oct 2004 (UTC)
replies: text: It has also been tried in music, by John Fulton, a former member of Dillinger Escape Plan. See [Astronaught/Cosmonaught http://remus.rutgers.edu/~jfulton/music.htm]. 207.34.120.71 14:31, 4 October 2005 (UTC)
thread_title: the answer to life, the universe, and everything

message: I reverted an edit that changed a 'graph to 
: There need not be infinitely many monkeys; a single monkey who executes infinitely many keystrokes suffices. This is inherent in the concept of infinity.
by adding the link and the last sentence.  First i must comment that there is a laudable insight in the sentence.  Second, i must add that it doesn't belong in the article.
While i'm confident that i know what i'm talking about here, i see some obligation to bear in mind that i am proposing to correct others who have shown similar confidence, and i don't know the content of the Kolmogorov theorem in question, except by what i would called "inferred reputation".  It is for that reason that i request someone who has studied it in a formal setting to check my understanding that:
: K. addresses limits as a variable approaches infinity rather than transfinite cardinals (or or transfinite ordinals).
I intend in any case to lay out the fact that there is no "concept of infinity" for that equivalence to be inherant in, but three such concepts:
# A dualist philosophical concept that has only a poetic relationship to mathematics, but is nevertheless durable and popular.
# A concept of Isaac Newton and Gottfried Leibniz, fundamental to calculus, which deals with the in-fin-ite simply in terms of the absence of end, and uses "infinity" simply as a shorthand for conditions that specify the non-existence of specific limits, and the existence and numerical value of specific limits, without positing any infitite number.
# A concept of Georg Cantor, of transfinite number, fundamental to discussion of differences in the natures of various infinite collections of abstractions, but almost independent of limit-theory.
I am convinced that this article has suffered seriously by failure to recognize these distinctions, and propose to thoroughly rework the muddled language that has called forth the idea that the seductive concept of  transfinite arithmetic helps to understand this subject.  But not in the next 12 hours. --Jerzy(t) 09:43, 2004 Mar 2 (UTC)
:Jerzy is right.  There are multiple concepts of "infinity" (his list is less than complete, but never mind that) and Kolmogorov was writing about a limit as a finite-value variable approaches infinity, as is done in calculus. Transfinite arithmetic should not be brought in to this article. Michael Hardy 20:37, 2 Mar 2004 (UTC)
replies: text: ... but on the other hand, I don't see that the article has suffered from exclusion of these distinctions, except when that comment about what is "inherent in the concept of infinity" was added. Michael Hardy 20:48, 2 Mar 2004 (UTC)
replies: text: You can state this theorem without reference to limits.  If you choose an infinite sequence of characters at random (ie a random map from the natural numbers to the characters), the probability that the map contains Hamlet somewhere in its length is one.  In other words, in the space of all such maps, the measure of the set of such maps that do *not* contain Hamlet is zero.  This covers the case of a single monkey with infinite time.  For infinite monkeys, we consider a map from pairs of natural numbers to characters instead.  I've just realised that this answers my question below! — ciphergoth 08:26, 30 September 2005 (UTC)
replies: text: That's not entirely true, or at least you haven't proven it. The statement I take issue with is that the probability is one for an infinite sequence. There are an infinite number of infinite sequences that don't contain Shakespeare's works, for example an infinite repetition of the character 'a'. In fact, for any infinite sequence of characters that contains Shakespeare's works (except those cases that consist solely of a repetition of Shakespeare with perhaps a finite number of other characters), you can construct an infinite sequence that doesn't simply by deleting those sections. So there are at least as many infinite sequences without Shakespeare's works as with. I would venture to guess (though I have no proof) that the ratio of sequences without Shakespeare's works to those with them is the same as the ratio of possible sequences the same length as Shakespeare's works to one. This is assuming that there's a definative version of Shakespeare's works. Trevor 19:13, 29 August 2006 (UTC)
thread_title:  Counting to Infinity Before Speaking Harshly 

message: I have removed the following passage about the 1860 debate between T. H. Huxley and the Bishop of Oxford (Samuel Wilberforce), because it is so far as I can see unsustainable:
: Wilberforce began the debate and, after making several scientific points regarding the plausibility of  Darwin's  work, concluded with William Paley’s argument that a watch implies the existence of a watchmaker, and similarly design in nature implies the existence of a Designer.
: Huxley then arose and put forward his now well-known argument that six eternal monkeys or apes typing on six eternal typewriters with unlimited amounts of paper and ink could, given enough time, produce a  Psalm, a Shakespearean sonnet, or even a whole book, purely by chance that is, by random striking of the keys.
:In the course of his presentation  Huxley pretended to find the 23rd  Psalm among the reams of written gibberish produced by his six imaginary apes at their typewriters. He went on to make his point that, in the same way, molecular movement, given enough time and matter, could produce  Bishop Wilberforce himself, purely by chance and without the work of any Designer or  Creator.
No transcript of the Huxley/Wilberforce debate exists, but typewriters were not in commercial production at the time, and though prototypes did exist and might have been known to members of the British Association, it is unlikely that Huxley would have relied on that.  No mention of the infinite monkey theorem can be found in Huxley's own accounts of the debate (for excerpts, see), and the account given here differs markedly from contemporary descriptions.  In my view the association of the infinite monkey theorem with the Oxford debate is an urban myth born of the fact that there really was some by-play about apes - but this was the famous exchange in which Wilberforce asked Huxley which side of his family the ape ancestry was on, and Huxley replied that he'd sooner be descended from a creature of mean intelligence than one of high intelligence who misused it in the way the Bishop had.
seglea 09:38, 30 Aug 2004 (UTC)
thread_title: Huxley/Wilberforce debate

message: A few months back I created the section titled "pedantic usage note" a few months ago after someone objected to the inclusion of that usage note in an earlier part of the article, and seemed to think it was unduly pedantic.  I think it's useful, especially in view of some of the terminological confusion I've seen elsewhere on Wikipedia since then that could have been avoided if those who were confused had seen this fact pointed out.  But now someone has said that if the article admits to being pedantic, then there's probably more pedantry "hidden [sic!]" elsewhere in it, and it should therefore not be a featured article!  I think that criticism has no merit.  I did not remove any pedantry, but I did remove that which may confuse the overly literal-minded: the word pedantic.  Here's how that section now appears:
::Usage note
::To some lay persons, "infinite monkeys" and "infinitely many monkeys" may be synonymous; to the mathematician, the former is incorrect because each monkey individually is finite.
Michael Hardy 21:22, 21 Sep 2004 (UTC)
thread_title: Explanation of my last edit

message: What is the context for the quote by Arthur Eddington?  In particular, what sort of vessel was he talking about, and what manner of extreme probabilities was he illustrating by invoking this concept?  --η[ υωρ] 04:43, 23 Sep 2004 (UTC)
thread_title:  Arthur Eddington 

message: Although this is not how it was originally stated, is it not the case that if an infinite number of monkeys begin typing random characters from a finite alphabet, one of them (indeed, infinitely many of them) will immediately produce any given text? Derrick Coetzee 03:16, 31 Oct 2004 (UTC)
replies: text: This is exactly what I meant. It's just that it's hard to say it precisely without being verbose. Derrick Coetzee 19:51, 31 Oct 2004 (UTC)
thread_title:  Infinite monkeys 

message: 19,928,148,895,209,409,152,340,197,376, roughly equivalent to the probability of buying 4 lottery tickets consecutively and winning the jackpot each time.
This feels at first like a good real-life illustration of something very improbable, but it for me it always invites the question: "which lottery"? The UK national lottery, for instance, has odds of about 14 million to one against winning, and the term "jackpot" is a bit confusing, too, because the prize is often shared among several winners.
I can't think of a better real-world example for now, though: randomly choosing one of the world's six billion people a certain number of times in a row, perhaps? I don't have the maths to know how many times... Mswake 14:43, 31 Oct 2004 (UTC)
thread_title:  Lottery odds 

message: The Zero-One law is really irrelevant here. Kolmogorov's zero-one law is a deep result having to do with (Kolmogorov's own) formulation of probabilities on sequences. Here, however, we have a trivial calculation that can be done with high school mathematics, and was known (in this way or the other) to Pascal. Gadykozma 17:13, 31 Oct 2004 (UTC)
replies: text: I wouldn't go so far as to say the zero-one law is irrelevent; this is certainly a demonstration of it. I've added a simpler proof from basics, though, that should hopefully be very easy to understand. Derrick Coetzee 18:24, 31 Oct 2004 (UTC)
thread_title:  Zero-One law 

message: That isnt a proof. An informal explanation, but not a proof.
:It's intended to be palatable to people with little formal background. I changed the name to Proof sketch to avoid suggesting it's a complete, general proof. Deco 23:12, 2 Nov 2004 (UTC)
thread_title:  Not a proof 

message: This argument assumes that the key-mashings of the monkeys is completely random from one letter to the next.  It's possible that if this experiment were tried then perhaps there would emerge discernible monkeymashing patterns that might actually preclude the creation of long, coherent, flawless texts beyond a certain threshold.  Simple limitlessness is not enough; in this case you also need random variation.  Maybe it would turn out that, out of every X keys hit, a monkey will always wind up hitting two keys that are immediately next to each other after a certain level of fatigue sets in.  Or maybe the monkey eventually develops a preference for a certain set of keys and ignores the rest.  It's possible that an infinite number of monkeys hitting a keyboard is less like pi and more like the repeating decimal .142857...  It's at least possible that there are some regular patterns that would emerge that would ruin this randomness-dependent theorem.
If you can get an infinite set of random key generators, the theorem is sound.  But I'm not convinced that monkeys are perfect random letter generators.  It may monkeybe that there is a slight flaw in this monkeyplan. Mr. Billion 16:26, 12 May 2005 (UTC)
thread_title:  Chaos Monkeys 

message: if you had an infinite number of monkeys, and an infinite amount of time, wouldnt you eventualy get a room full of dead monkeys?
I think the monkeys wouldnt acualy type anything, monkeys would usualy just throw the typewriters around, anyway even if they did make the entire of shakespeare, they wouldnt know what to do with it, they would probably use it as loo roll. And you also  need an infinite amount of paper.
I however am firmly in the believe that Shakespeares works were actualy made by Shakespeare, not an infinite number of monkeys.
</p>By the way an infinite number of monkeys is ALOT OF MONKEYS there is a chance that SOME OF THEM will actually make SOMETHING. There would also be a circus of monkeys producing an oompa loompa style dance, throwing keyboards at one another mysteriously floating due to atmospheric anomlies and all of a sudden they spontaneously combust, and there sub atomic particles will create Shakespeares works, and this will be happening an infinite amount of times. When infinity is used anything and everything can and will happen infinitely, infinity is that mind boggelingly incomprehensibly massive. Many people have a finite veiw of infinity because the concept is just so dificult.
:Sheesh.  As the article says, just one monkey, with an infinite amount of time, is enough.  But the mathematical proposition involved admits a precise statement, and it's not about monkeys. Michael Hardy 19:02, 23 Jun 2005 (UTC)
replies: text: Well, again, if one merely states the mathematical proposition without the fanciful stories, it's not about monkeys at all, of course. Michael Hardy 20:54, 23 Jun 2005 (UTC)

text: Why not just eliminate the monkeys and say that somewhere in the universe at some point in time, the collected works of Shakespeare will spontaneously materialize in some form, due to chaotic particle interaction?
Because that's about physics, and this theorem is not about physics.  (And besides, the word "spontaneously" in this context would be absurd.) Michael Hardy 21:55, 1 October 2005 (UTC)
thread_title:  Problems of the Theory 

message: don't believe it. my friend and i got exotic pet licenses and imported 500 monkeys and were able to get 500 keyboards donated.....well after a year there was not one intelligent thing typed. there were a couple words here and there but i dont know im skeptical of this whole thing. still trying to get rid of the monkeys. leave a line on my talk page if you could use a few dozen--Elysianfields 05:55, 12 August 2005 (UTC)
replies: text: If you're serious, please consult the second paragraph of this article. Also, how much are those monkeys? I happen to be a monkey farmer and specialise in monkeys that have been traumatised by typing experiments. Deco 22:34, 12 August 2005 (UTC)
replies: text: The benefits to humankind outweigh the trauma the monkeys suffer. Michael Hardy 23:34, 12 August 2005 (UTC)

text: Your mistake was to use a finite number of monkeys.  Try again with infinitely many monkeys and let us know how you get on.  (Alternatively you could use one immortal monkey for infinite time but who can be bothered to wait that long?) — ciphergoth 07:00, August 13, 2005 (UTC)
The useful life of the universe (at least as far as the monkeys are concerned) is approximately 1E14 years (see 1_E19_s_and_more), as after that the last stars cool off and the monkeys can neither be kept warm or fed any more bananas (since bananas require sunlight, which comes from stars). 31 million seconds x 1E14 years x 1 keypunch per second = 31E20 keypunches per monkey in the useful life of the universe (i.e. 1E14 years). Probability therefore requires 21E33 monkeys typing through the useful life of the universe just to type “to be or not to be that is the question”. The last 2 lines of this Hamlet soliloquy, “The fair Ophelia! Nymph, in thy orisons Be all my sins remember'd.” would require the work of 18E67 monkeys without punctuation; or 9E70 monkeys to reproduce it with its proper punctuation, but still without capital letters or carriage returns.
An interesting question at this point is, is it truly Shakespeare without the carriage returns? And without the capital letters? What about the stage directions?
Anyway, there is only 1E53kg of mass in the universe (see 1_E51_kg) with which to create these 9E70 monkeys, their typewriters, and (again) all the paper and ribbons and typewriter repairmen required to keep them going, and that’s assuming you can use up all the universe’s hydrogen and helium to make these things, which again begs the question of where you're now going to find the bananas. 
Of course, there's likely fewer than 1E8 monkeys in the universe right now, so... well... you figure out for yourself how long it would take to breed 9E70 from a population of 1E8. Thus, the question of where you're now going to find the monkeys.
Also, you need to keep the monkeys in proximity to each other, because they're taking up all the mass of the universe and otherwise there's no gravity. No gravity would mean that each keypunch will result in the typewriter permanently flying away from the monkey (see Classical_mechanics), and given the low mass-density of the universe (under 1 atom per cubic meter), you've got pretty much no hope of ever getting another letter typed on that particular typewriter by anyone after it flies away, much less 1 keypunch per second. Yes, of course, you could tether each monkey to its typewriter, but first you have to find a tether material to last for 1E14 years. Here's a hint: don't bother trying.
The monkeys also have to be kept as close together as possible to minimize the problem of ripe banana delivery. Unfortunately, keeping 9E70 monkeys in proximity to each other for 1E14 years will mean the probability approaches one that one heck of a poop-throwing fight will wreck the piece of paper that this purported Shakespeare was typed on anyway. 
And at that point, you should also consider this theory from the existentialist point of view. Read up on how hard it is on a monkey to be kept in a laboratory. Now imagine that these monkeys instead are being kept in a universe where the only thing they are able to do - anywhere in the universe - is type on a typewriter, eat a banana, bite a repairman, or throw poop at the universe. I'm sure a large number of these monkeys would commit suicide rather than be fated to such a dismal existence - certainly any who evolve a superior intelligence will! But what do you think these monkeys will do over 1E14 years? Evolve. Boy, this is looking even more doomed.
And what would such a project would entail for the entropy of the universe? Since we're attempting to convert the mass of the universe into monkeys, typewriters, ribbons, paper, typewriter repairmen and bananas, and then transporting them into one location, wouldn't that mean a terrific increase in entropy for the universe as a whole? And let's just hope that collecting all those monkeys (and typewriters!) (and bananas!) together in one place doesn't cause the whole mass of 'em to implode into one big Supermassive_black_hole, or you'll never know what they wrote.
So, the infinite monkey theorem proves to be mathematically a theoretical certainty, but at the same time a real-world complete impossibility. Shows you how useless mathematics is, eh? I'm pretty sure that all this proves that this Emile Borel fellow must have been a bit bananas.
24.213.90.49 01:44, 30 September 2005 (UTC)

text: I have a small point... Probability therefore requires 21E33 monkeys typing through the useful life of the universe just to type “to be or not to be that is the question”.  I don't think this comes out quite right.  You don't need that many monkeys to have them type that, although you might need that many monkeys to make it at all probable... exactly what probability are you aiming for?  Just a non-zero effective probability?  I'm not sure if I can see the math on this part...  I mean, all you NEED for a monkey to type that at the rate of one keypress per second is said monkey at a keyboard and 39 seconds (or only 30 if you're not counting even spaces) .... and, of course, to be really lucky.  -JC 07:14, 21 February 2006 (UTC)
replies: text: Probability requires that before the chances rise to something noticeable.  As you say, there's a non-zero chance of it happening immediately with a single monkey. — ciphergoth 13:20, 21 February 2006 (UTC)
replies: text: What is "something noticeable" though?  If you had that many monkeys, what IS the chance you'd have the result of "to be or not to be that is the question"?  It just says "Probability requires" but never really goes into the mathematical details of such a requirement - it seems very arbitrary that you just "need 21E33" monkeys, when you really only need one monkey for it to be possible...  Either need is the wrong word, or we need to talk a little bit more about exactly what the chances become with that many monkeys and why that number of monkeys was chosen in particular.  -JC 23:12, 21 February 2006 (UTC)
replies: text: I can't work out whether you're pointing up a problem with the article, or just asking a question about what I've said.  If the former, which part of the article is problematic?  If the latter, you'll probably find it most enlightening if you do the sums yourself - they're not hard. — ciphergoth 11:42, 22 February 2006 (UTC)
replies: text: It's not the article.  You only said "to something noticable" - but I want to know what point that is.  It's already a non-zero chance with a single monkey, right?  So why does 24.213.90.49 (John Merrall) say that we "need 21E33" monkeys?  That is my question.  My questions here are in response to John Merrall's post (I hope that much is pretty obvious...) ... -JC 04:44, 23 February 2006 (UTC)
replies: text: If the alphabet has z letters and you have m monkeys each of which types k keystrokes, then the expected number of times that a passage of length l will be typed is around mkz^{-l} (closer to m(k-l+1)z^{-l} but we usually assume that k >> l).  Where that's very small it's also a good approximation of the probability of it being typed even once; where it's bigger you can use the Poisson distribution as an approximation, so the probability of it being typed even once is around 1 - e^{-mkz^{-l}}.  From there you should be able to work out how many monkeys are needed to cross whatever probability threshold you want to set.  I expect that the estimate of how many monkeys you "need" refers to the point at which mkz^{-l} == 1, at which point the probability of the passage being typed is around 70%, but you can now do the sums yourself and answer any such question. — ciphergoth 10:18, 23 February 2006 (UTC)
replies: text: Typical mathematicians! You argue over trivia. The point I was trying to make on 30 Sep 95 (my IP address is probably different but it's still me) was, if you were able to convert ALL the available mass of the universe into REAL monkeys who typed through the useful life of the REAL universe, it would take too long to generate that many monkeys using real-world techniques, the monkeys would all go insane or starve or evolve away from monkeydom, all the typewriters would get broken, you'd run into relativistic problems, and so on. I think it's meaningless to say "there's a small non-zero chance even with one monkey", just like it's meaningless to say "an infinite number of monkeys". You don't have infinite time or mass, monkeys are non-infinite creatures in every sense of the word, and I think this might even illustrate that this idealized mathematical problem (using "let's-pretend" monkeys" and a "let's pretend universe") has no meaning because, in translation to the real world, it falls apart from ignoring the second law of thermodynamics. You might as well be talking about the mathematical chance that your smashed teacup will reassemble itself - if you say the chance is nonzero, I reply that it's so trivially nonzero that it may as well be zero. If this theory proves anything, it's that numbers close to zero behave like zero and can be assumed to be zero in the real world.71.19.38.228 12:51, 21 July 2006 (UTC)
thread_title:  I tried it....it doesn't work 

message: The monkeys can't type out the contents of the British Museum; most of the exhibits are not text.  Is British Library meant here?
For now, I'll remove "others replace the National Library with the British Museum or the Library of Congress" altogether, since I don't think it does any useful work anyway. — ciphergoth 09:29, August 14, 2005 (UTC)
:"all the books in the British Museum" is what the story by Russell Maloney said (cited in the article, in the "popular culture" section). Michael Hardy 01:46, 15 August 2005 (UTC)
thread_title:  British Museum 

message: This edit by User:80.176.134.178 seems to consist of chopping out bits of the article at random.  This is a strange form of vandalism - why go to all the effort, when it's just as easy to detect and fix?
:No, it is not always easy to detect such vandalism. Subsequent editors might often edit the article without viewing its edit history. This way, they'll inadvertently legitimise the vandal's edit. -- Sundar \talk \contribs 13:32, August 30, 2005 (UTC)
::Even then, it's not too difficult to view all changes since the vandalism, revert to the version preceding it, and merge the new changes back in by hand. I think these people try too hard. Deco 21:45, 30 August 2005 (UTC)
thread_title:  Weird vandalism by [[User:80.176.134.178]] 

message: What does this sentence mean?
:The theorem graphically illustrates the perils of reasoning about infinity by imagining a vast but finite number. If every atom in the Universe were a monkey producing a billion keystrokes a second for the entire history of the Universe, it is still very unlikely that any monkey would get as far as "slings and arrows" in Hamlet's most famous soliloquy.
I thought the whole point of the theorem is that eventually, they would write Shakespeare. Don't the quoted sentences (particularly the "very unlikely") directly contradict the "almost surely" of "A single immortal monkey who executes infinitely many keystrokes will almost surely eventually type out any given text"? zafiroblue05 | Talk 01:04, 1 April 2006 (UTC)
replies: text: No, it doesn't contradict it.  An infinite number of keystrokes will invariably eventually type any given text.  However, a very, very large, but finite number, isn't necessarily enough (to have a sufficient chance of it, anyway).  This sentence is indicating that even a huge, huge, huge number of monkeys (that is, as many as there are atoms in the entire Universe) producing huge amounts of keystrokes in a huge amount of time... still have a very small likelihood of having even one type as far as "slings and arrows" in the soliloquy (that is a bit far in the soliloquy, but this is compared to the entire works of Shakespeare!  The required number of monkeys or keystrones for any kind of suitable chance of typing that soliloquy is so vast...  </br> Although I will admit that the theorem doesn't illustrate such perils.  In fact, it encourages them, because people think of an infinite number of monkeys as simply a lot of them, all typing along merrily...  So I think this sentence should be rephrased to say "It is important to realize, however, the perils of reasoning..." and so on.  -JC 06:56, 1 April 2006 (UTC)
replies: text: Hmmm, I see. I think I just read "the entire history of the Universe" as basically being infinite time right there - maybe it should read "since the Big Bang," or something like that... zafiroblue05 | Talk 17:36, 1 April 2006 (UTC)
replies: text: Have edited as you suggest - good suggestion, thanks! — ciphergoth 19:03, 1 April 2006 (UTC)
thread_title: Question

message: From the article: 
"not only did the monkeys produce nothing but five pages (PDF) consisting largely of the letter S, they started by attacking the keyboard with a stone, and continued by urinating and defecating on it."
I don't care if I live until the end of time, that has to be the funniest sentence I'll ever read. J Shultz 08:49, 12 April 2006 (UTC)
thread_title:  This is poetry 

message: I proved it wrong. I managed to prove it all wrong.  The statement goes that an infinite number of monkeys, typing away for infinity will reproduce the works of Shakespare.   My proof that this is untrue is the following... Be prepared to be shocked.... and awed.... at my genius.... it's just a 3 letter word.... 
MSN (think about it...)
Reuben —Preceding unsigned comment added by 217.22.182.184 (talk • contribs) 
: See this edit.  But you don't have to look that far - look right here... — ciphergoth 22:35, 12 April 2006 (UTC)
replies: text:  The above "disproof" of the hypothesis is false because, although we'll all agree that most MSN users including myself are akin to monkeys, we are not infinite in number. So, sorry, this doesn't invalidate the Infinite Monkey Theorem at all, user 217.22.182.184, and in fact, merely proves that you are firstly a one-time MSN user for how else would you know the nature of MSN users, and secondly, you are a monkey and have managed to edit wikipedia, which is an interesting proof of the IMT. Rolinator 08:19, 14 April 2006 (UTC)
replies: text:  Indeed it suggests a misunderstanding of the term infinite. You cannot be almost infinite. Nil Einne 12:04, 12 August 2006 (UTC)
replies: text:  ... sigh ...  It suggests many misunderstandings: There is no need (as the article says!) for more than one monkey to be involved.  Moreover, if they were infinite in number, then there would be infinitely many monkeys, but not infinite monkeys. Michael Hardy 22:24, 12 August 2006 (UTC)
thread_title: Proved it wrong

message: Why at the beginning it is specified "due to the nature of infinity"? It seems useless, non mathematical and difficult to understand.--Pokipsy76 15:14, 11 June 2006 (UTC)
thread_title:  "Due to the nature of infinity"? 

message: I started making a small edit and ended up making a big one - sorry!  Call it being bold :-)
As we now tell it, Borel didn't posit the Theorem, and it seems we don't know who did; it seems to be just a part of popular culture.  
Given that, there's no reason to give such prominence to Borel.  So I've moved that into a section of its own, credit the original image of many monkeys, many typewriters, and a great deal of time to him, but point out that he and Eddington were actually making the opposite point - that even given resources that seem vast on a human scale the probability of typing Shakespeare is miniscule, and the probability of a significant violation of the Second Law is even smaller than that.
We then implicitly credit the extension of the idea to infinitely many monkeys and infinite time, and the resulting reversal of the conclusion that given this Shakespeare is almost surely produced, to popular culture, since we don't actually know who posited this.  Overwhelmingly, the popular culture version of the Theorem which is what the article is about references Shakespeare, so I follow that example.  If someone can show that the earliest examples of this idea which reference infinite resources don't reference Shakespeare but some other work, I'd be very interested.  I wish we had a citation for "After about 1970".
I think this change improves the flow of the article and de-clutters the introduction, but let me know what you think. — ciphergoth 22:24, 11 June 2006 (UTC)
replies: text: Did you remove the text concerning the explanation that the monkeys are just a metaphor for an abstract mechanism for generating random strings? This may seem completely obvious, but I think there has been enough confusion on this point that it's worth spelling out. Deco 21:48, 21 July 2006 (UTC)
thread_title:  Greatly cut down introduction 

message: This is actually not the only difficulty. There is also a chance that you won't find any, even if you've got the perfect shakespeare locator. That's what you gotta love with probability, "at infinity", every single event will have a measure of zero, but that doesn't mean that it doesn't exist.
A chance you won't find a successful monkey IS the difficulty of finding the successful monkey in the first place. I think (and I have put) this sentence back in the article as it is another way to visualize the IMT. 09:18, 29 November 2006 (UTC)
thread_title:  The only difficulty remaining is in locating the successful monkey. 

message: I've restored the "almost"s to the "almost surely"s that appear throughout the article.  I cannot imagine why they were removed; without them the article is inaccurate.  Also the Infinite Monkey Theorem is very different from the Random Walk theorem. — ciphergoth 15:49, 16 September 2006 (UTC)
thread_title:  Almost surely 

message: The article states: If every atom in the Universe were a monkey producing a billion keystrokes a second from the Big Bang until today, it is still very unlikely that any monkey would get as far as "slings and arrows" in Hamlet's most famous soliloquy.
In my opinion this is just wrong. That part of the text would be less than 100 characters; In addition, there are less than 40 relevant keys for text on a typewriter keyboard. This means the probability of the monkey typing the correct beginning of the soliloqui is plain and easy \frac{1}{{40}^{100}} or better \frac{1}{{4}^{101}}. The number of atoms in the unverse is said to be maximum 6*10^{79}. The age of the universe is said to be maximum 13,9 billion years, that's 4.39^{17} seconds. A billion keys is 10^{9}. If you miltiply that, you get a total of 25*10^{105} or 2,5^{106} keystrokes for our many monkey-friends. This means, they type in 100 characters 2,5^{104} times.
This means: In one of 4^{101} trys, our moneys type in the right 100 characters. I just calculated, that our monkey has a total of 2,5^{104} trys. I am not totally sure, if i calculated correctly (please tell me if i am wrong), but as far as i can see this is far away from "very unlikely". Nerdi 17:42, 18 September 2006 (UTC)
replies: text: 40100 and 4101 are two very different numbers. If you really want base 4, 40100 is not far from 4266 —David Eppstein 18:07, 18 September 2006 (UTC)

text: 40100 is about 10160. The age of the universe is about 4.19 1017 -> 2.5 10106 keystrokes. When your machine write an exponenent, it is the exponent of 10 multiplying the mantissa. pom 18:27, 18 September 2006 (UTC)
replies: text: At the very least, though, the term "universe" needs to be qualified. To my knowledge there is no consensus upper bound on the number of atoms in the universe, nor even on the question of whether that number is finite. If the passage specified that it's talking about the visible universe, it might be defensible (though it's kind of OR-ish). --Trovatore 20:04, 18 September 2006 (UTC)
replies: text: That's an estimate for the number of atoms in the entire Universe, as predicted by current theory: see .  I think the idea of an infinitely massive Universe is pretty much dead in current cosmology, since it contradicts the Big Bang; what makes you think there's still doubt on that score? — ciphergoth 21:37, 20 September 2006 (UTC)

text: The math is worked out in "Question regarding math in opening paragraph" above.  Interesting that this keeps coming up - I hadn't expected that paragraph to be so controversial! — ciphergoth 21:46, 20 September 2006 (UTC)
replies: text: The citation does not really state that 6e79 is a hard upper bound. Also it's a bit of an informal, chatty kind of site; I can't take it as establishing a scientific consensus. As I understand it, if the average density of matter in the universe is below the critical density, then the universe has infinite volume. Therefore, if it has positive average density, it must have infinite mass. I don't think this contradicts the big bang; if you run the equations backwards from such a universe, you still wind up with infinite initial density a finite amount of time in the past. --Trovatore 22:03, 20 September 2006 (UTC)

text: 8.34 \times 10^{-38},\,
etc. Michael Hardy 21:15, 18 September 2006 (UTC)

text: The radius of the visible Universe is estimated at 1.7e26 m (18 thousand million lightyears) plus or minus 20 percent or so. 
and the calculations go on from there. Note the use of the term "visible Universe". It's true that in the rest of the passage, the author simply calls it "the Universe", but this is apparently convention among astrophysicists (at least, so our observable universe article would have you believe.
So I think this citation provides no support at all for the claim that there's a consensus upper bound on the number of atoms in the whole universe. --Trovatore 23:10, 20 September 2006 (UTC)
thread_title:  mistake (no mistake, done) 

message: Ciphergoth offered a website which he claimed put an upper bound on the number of atoms in the universe. If you look at the part of the site most directly addressing the question, which is here, you'll see that it says the following:
:The radius of the visible Universe is estimated at 1.7e26 m (18 thousand million lightyears) plus or minus 20 percent or so. 
and the calculations go on from there. Note the use of the term "visible Universe". It's true that in the rest of the passage, the author simply calls it "the Universe", but this is apparently convention among astrophysicists (at least, so our observable universe article would have you believe.
So I think this citation provides no support at all for the claim that there's a consensus upper bound on the number of atoms in the whole universe. --Trovatore 23:10, 20 September 2006 (UTC)
thread_title: ciphergoth's cite; finiteness or infiniteness of universe

message: Although the site only keeps a record up to 24 letters, I felt like checking it out real quick, and my record was 41 letters. This wikipedia article states that it generates AT MAXIMUM 24 letters; should this be changed?
After 2.55116e+79 pages in this session, a monkey typed:
        GLOUCESTER. Now is the winter of our disc?l7QU"G 2&)]4c9JWg2cW'B1ZmV5vqB...
the first 41 letters of which match "KING RICHARD III":
_________________________________________________________________________________
GLOUCESTER. Now is the winter of our discontent
Made glorious summer by this sun of York;
And all the clouds that lour'd upon our house
202.45.98.254 13:27, 25 September 2006 (UTC)
thread_title: Regarding Internet Simulator

message: We can simplify the introduction by considering the other infinity instead.  If a single monkey is placed in front of a typewriter for an infinite time, the monkey will probably die before it types a single word of Shakespeare.  Now, if you wait long enough then another monkey-like creature might eventually rise from the ashes and start to type Shakespeare, but it's a bit counter-intuitive; that's why our monkeys are abstract devices rather than real monkeys.
However, if you place an infinite number of real monkeys in front of an infinite number of real typewriters, then even though most will just urinate on the keyboard before wandering off, infinitely many of them will immediately type the works of Shakespeare in chronological order.
Thus if we consider infinite monkeys and finite time rather than vice versa, we can remove the caveat about the monkeys being abstract machines.
We'd have to add a paragraph to the proof sketch to handle this of course.
— ciphergoth 22:55, 26 October 2006 (UTC)
thread_title:  Changing the emphasis 

message: There are alarmingly few inline citations for this Featured Article, and I have not been able to find sources for the claim that "The theorem as it is now stated, with infinite resources, arose in popular culture after around 1970". Lastly, the Infinite Monkey Project in the last paragraph is also unsourced. I think this article is far from being a FARC candidate (at least I hope so), but the possibility of it losing its featured status is real. Kavadi carrier 14:41, 9 November 2006 (UTC)
thread_title:  Problems with this FA