Talk:Infinite monkey theorem

Various Aspects

Found this via Arthur Eddington. Could we have a source, puhLEEyuz? And if it does indeed take an infinite number of monkeys an infinite amount of time to hammer out Hamlet, then wouldn't it be provable that a finite number of monkeys couldn't do it -- even with an infinite amount of time? <>< tbc

No --- the same theorem of probability says any finite number of monkeys would do the job in some finite amount of time. If you specify a particular finite number of years, the probability that the job would be done before then is less than 1. It approaches 1 as time approaches infinity. The source seems to be Borel's book on probability, published in about 1910. There's also a nice short story that appeared in the New Yorker in (I think) 1940, based on this idea. Borel's book also has a nice account of the Borel-Cantelli theorems. I don't like the title of this article, since it may be misread as referring to "infinite monkeys". It's not the monkeys that are infinite; each monkey is finite. Rather it is the number of monkeys that it asserted to be infinite. (Unnecessarily so, if one allows an infinite amount of time.) One should speak of infinitely many monkeys, not of "infinite monkeys". 131.183.142.18 22:07 Jan 30, 2003 (UTC)

The title of this article as it now stands Borel's dactylographic monkey theorem does not express the concept as it it commonly known. Indeed typing the above expression into google returns zero results. If the origin of this concept resides with Borel then this should be stated within the body of the article, and the title of the article should be where people would expect to find it as per Wikipedia:Naming conventions (common names). Mintguy

This article is nice! I was just about to link dactylographic in the article to dactylography, as uncommon words should be linked for explanation, but decided to look it up first: dactylography: n. Chiefly US the scientific study of fingerprints for purposes of identification. Why do the monkeys have to have anything to do with fingerprint identification? And if this is true, maybe a short explanation of this could be put into the article. Thanks, snoyes 02:42 Mar 7, 2003 (UTC)

It seems to be a false friend - the French term "dactylographier" means "to type." - Montréalais

Is the theorem really a case of Kolmogorov's 0-1 law? The law tells us that the probability infinitely many copies are typed is either 0 or 1, but doesn't tell us which. Conversely, we know the probability at least one copy is typed is nonzero, but Kolmogorov's law no longer applies since the probability something eventually occurs isn't in the tail sigma-algebra. As I learned it, this theorem was a consequence of the second Borel-Cantelli lemma. Kevinatilusa

Re: "grotesquely incorrect". It's just grammar, chill out. Clearly, I did not mean an infinitely large keystroke. Daniel Quinlan 00:00, Dec 11, 2003 (UTC)

Counting to Infinity Before Speaking Harshly

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:

1. A dualist philosophical concept that has only a poetic relationship to mathematics, but is nevertheless durable and popular.
2. 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.
3. 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)

... 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)

'Net Shakespeare Simulator

I am not an enthusiast of this activity; in fact, i think those who install it should dedicate their processor cycles to something more socially valuable, like downloading pornography. But we should document it in a way that does more justice to the limitations that it imposes upon itself.

The article invites the inference that the "records" of a dozen or so characters reflect the longest two or three words that both WS and the monkey-engine have put together. My strong impression (from an admittedly brief visit to the site) is that in fact they represent the longest matches between the engine and any string that begins a WS work (or is it a WS play? Do the sonnets count? (Does his "second-best bed" will count?!)) I'm not going to be the one to get the details right, or state them fluently, but i think the present description is inadequate. --Jerzy(t) 01:28, 2004 Mar 31 (UTC)

It's just the plays; a list of exactly which plays heads the FAQ on the site. And you're right about it just being beginnings.
I've had another shot at the paragraph in the article: better now? --Paul A 12:50, 3 Apr 2004 (UTC)

I think that's great! The only phrase that bothers me is

how long it takes the virtual monkeys to produce a complete Shakespearean play

I may be indulging my taste for excessive precision by mentioning it, but i find it a little confusing in that it fails to distinguish between the collective nature of the project (in the sense that any monkey can complete a play) and the individual nature of the completion of any single play by one monkey. I especially fear my excessiveness in this case, in that i have no alternate wording to suggest for making the distinction clearly (tho i'll sleep on it).
One question does occur to me, tho, and its answer might help: isn't one user of the program letting their machine simulate one monkey, and if so, might that focus offer a less tricky wording? --Jerzy(t)

Each user of the program is letting their machine simulate the whole room-full-of-monkeys; one user simulates the room for a while, then the next user simulates it for a while, and so on. (In practice, because it's a random process that doesn't depend on past events, the set-up allows different users to simulate conceptually-subsequent slices of the room's history simultaneously. Ignore that sentence if it's giving you trouble.)

Conceptually, each monkey's pages of typing are added to a single communal pile that is then submitted a page at a time to be checked for matches. (Incidentally, the matching rules require not only that the output match the beginning of a play, but that the play begin at the top of a new page. If a monkey starts typing out a play halfway down the page, it doesn't count.) Consequently, the goal is for the entire play to appear out of the combined output, not out of the output of any one monkey.--Paul A 08:13, 5 Apr 2004 (UTC)

Wow, way f'g cool. The elaborate design described suggests more effort than i thought on the part of the origninators, is moderating my disdain for the project. Tnx for Paul's dogged effort of research and description! --Jerzy(t) 14:39, 2004 Apr 5 (UTC)

What about older precursors, like Galileo or the hermeticists?

The emphasis of this article on modern thinkers is pretty odd, considering that this is infact a recurring conundrum throughout human history. Not just Galileo, but the umpteen hundred beautiful names of god in Islamic tradition. Oh, I just remembered, maybe something on Arthur C. Clarke too... --Cimon

Huxley/Wilberforce debate

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[1]), 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)