When I looked at the Monkey Shakespeare Simulator the other day, I remembered how we traced the story/image back to mathematician Emile Borel of 1913 (1), and it occurred to me to wonder what point Borel was trying to make when he invented it as an analogy or illustration.

The only other thing I remembered about Borel was that he was the one who said that events of extremely low probability are the things that don't happen by chance. That doesn't seem to match any blithe prediction of monkeys producing Hamlet.
Borel's paragraph, in French, is found here:
http://www.angelfire.com/in/hypnosonic/Parable of the Monkeys.html

After describing the imaginary set-up of a million monkeys turning out results and these pages being bound (by unreading humans) into books, which turn out to replicate the world's libraries, he says

Telle est la probabilité pour qu'il se produise
pendant un instant très court, dans un espace de
quelque étendue, un écart notable de ce que la
mécanique statistique considère comme la phénomène le plus probable...
The meaning of which is difficult for me to puzzle out, and the English translations are also hard:
Saved from Message-ID Such is the likelihood that there should occur,
even for a moment, a notable deviation in any extended region from what statistical mechanics considers the most likely phenonenon ...
This one I saved from an old Web page, not found now, looks like Babelfish nonsense:
Such is the probability so that it occurs during one very short moment, in a space of some extent, a
notable variation of what statistical mechanics
regards as the phenomenon most probable."
I hope that Isabelle or other fluent French speakers can help here.

However, as best as I can figure, Borel is talking about how unlikely this all is. Isn't he saying, "It's about as unlikely that these randomly-produced pages will turn out to reproduce all the world's literature, as it is for the laws of science to be suspended, even for an instant"?
The chances of the monkeys' work reproducing the world's literature is incredibly tiny. The chances of events deviating from the laws of statistical mechanics is similarly tiny.
I can't find the larger piece of writing this is from, so I don't know what sort of event of "statistical mechanics" he was considering. I wonder if it was the sort of question like, "Since atoms move, could all the atomic particles in my finger and this door happen to move aside at the same instant, so my finger goes into the door?"

So although Borel (apparently) invented this image of the typing monkeys, it would have been some later variant that gave us what we know today, the claim that if this could be set up, the works of Shakespeare would eventually be produced.
The next known use was Eddington (1929) (2), and he too was cautious, using it as an illustration that this unlikely event was more likely than molecules lining themselves up:
... If I let my fingers wander idly over the keys of a typewriter it /might/ happen that my screed made an intelligible sentence. If an army of monkeys were
strumming on typewriters they /might/ write all the books in the British Museum. The chance of their
doing so is decidedly more favourable than the
chance of the molecules returning to one half of the vessel.
So, my point is, it began as a measure of *unlikeliness.* Not as a way to illustrate infinity or anything else.
I see that the third example on the Parable page, Jeans (1930), attributes it to Huxley and uses the words "bound to produce"... And so the image, once launched, gathered steam and changed.

I am reminded that "In 1911 Boas casually mentioned that Eskimos used four unrelated words for snow..." (Pinker 1994)
(1) Émile Borel, "Mécanique Statistique et Irréversibilité," J. Phys. 5e série, vol. 3, 1913, pp.189-196.
(2) A. S. Eddington. The Nature of the Physical World: The Gifford Lectures, 1927. New York: Macmillan, 1929, page 72.

Best Donna Richoux
1 2 3 4 5 6 7 8 9
When I looked at the Monkey Shakespeare Simulator the other day, I remembered how we traced the story/image back to ... (2) A. S. Eddington. The Nature of the Physical World: The Gifford Lectures, 1927. New York: Macmillan, 1929, page 72.

http://en.wikipedia.org/wiki/Infinite monkey theorem "Borel exemplified a proposition in the theory of probability called Kolmogorov's zero-one law by saying that the probability is 1 that such a monkey will eventually type every book in France's National Library. Strictly speaking, what Borel was illustrating was only a special case of Kolmogorov's zero-one law, the more general statement of which had not yet been given"
On that basis, Emile wasn't offering a philospohical view - he was illustrating a mathematical law. My stab at translation of his remarks is :
"Such is the probability that there would occur, in a very brief moment in part of a large space, a notable difference from what statistical method would regard as the most likely outcome"
The Wikipedia article points out that there are earlier uses of a monkey-type analogy, notably Darwin's bulldog in 1860 with his reference to six eternal monkeys. And the random creation of what turn out to be sensible and meaningful texts is shown to be foreshadowed in Gulliver's Travels.
I would have to take issue with your "The chances of the monkeys' work reproducing the world's literature is
incredibly tiny." The chance of one* monkey's work producing even a single intelligible word is vanishingly remote. But infinite monkeys on infinite typewriters are *certain to produce the world's literature past, present and future in all languages dead, living and yet to be invented. (I'm following the convention here that we disregard the idea of real monkeys with limited attention spans and real typewriters with jammable keys.
But ifBorel's comments seem to be from the realm of higher mathematics, the 'infinite monkey thing' has a life of its own now. To see how random actions can produce meaningful results, it makes more sense to imagine a computer programme that can produce random letters, punctuation and spaces. Running over an infinitely long period of time, such a programme must inevitably produce every possible combination of letters, punctuation and spaces. It must, therefore, produce everything that human beings can* write and therefore everything we *have written or are going to write. My love letters to my wife would pop up somewhere, though there's no guarantee any more than two people would know what they are.
A quasi-random programme would produce results more quickly - if it were set to produce letters at the frequency they are found in English - our old friend Etaoin Shrdlu - and to insert spaces to create word lengths conforming with the observed distribution, then using a set of Crays networked and running for a billion years, we're almost certain to see the victory speech of the next President of the United States.

John Dean
Oxford
Amateur attempt: It is no more probable (than in the monkey parable) that, within a short time and in a limited space, there would be any significant variation from the most likely outcome predicted by statistical science. CDB ( or not CB, that is the gzornenplatz)
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When I looked at the Monkey Shakespeare Simulator the other day, I remembered how we traced the story/image back to ... we know today, the claim that if this could be set up, the works of Shakespeare would eventually be produced.

Hi, Donna,
I don't understand the French or the English, either. But I recall both analogies in the mathematician George Gamow's book, One, Two, Three...Infinity . There he said that it was theoretically possible for all the molecules of air in a room, moving randomly, to suddenly all wind up in one corner of the room, leaving the inhabitants of the rest of the room to suffocate. Possible, but not very likely. He also referred to the monkeys, saying, as I recall, that they not only could but would produce the complete works of Shakespeare...it's just that you'd need an infinite number of monkeys and an infinite length of time. That seems to contain both elements of what you're describing: in principle, a monkey can write Shakespeare; in practice, it ain't gonna happen.
Perhaps in the popular mind there isn't an adequate distinction between "an infinite number of monkeys" and "a lot of monkeys".

Gary Williams
When I looked at the Monkey Shakespeare Simulator the other day, I remembered how we traced the story/image back to ... we know today, the claim that if this could be set up, the works of Shakespeare would eventually be produced.

Hi, Donna,
I don't understand the French or the English, either. But I recall both analogies in the mathematician George Gamow's book, One, Two, Three...Infinity . There he said that it was theoretically possible for all the molecules of air in a room, moving randomly, to suddenly all wind up in one corner of the room, leaving the inhabitants of the rest of the room to suffocate. Possible, but not very likely. He also referred to the monkeys, saying, as I recall, that they not only could but would produce the complete works of Shakespeare...it's just that you'd need an infinite number of monkeys and an infinite length of time. That seems to contain both elements of what you're describing: in principle, a monkey can write Shakespeare; in practice, it ain't gonna happen.
Perhaps in the popular mind there isn't an adequate distinction between "an infinite number of monkeys" and "a lot of monkeys".

Gary Williams
(snip long post I made today about Emile Borel and his use of the monkeys/typewriter image in 1913. The French paragraph is here:

http://www.angelfire.com/in/hypnosonic/Parable of the Monkeys.html

and I ask anyone interested to find my post. - DR)
monkey theorem "Borel exemplified a proposition in the theory of probability called Kolmogorov's zero-one law by saying that the ... random creation of what turn out to be sensible and meaningful texts is shown to be foreshadowed in Gulliver's Travels.

Thanks for these tips on earlier use, which I will pursue. Now that you say "six eternal monkeys," I think that has shown up in a discussion here before.
So I shift my quest from finding the original purpose, to Borel's purpose.
I would have to take issue with your "The chances of the monkeys' work reproducing the world's literature is incredibly ... a single intelligible word is vanishingly remote. But infinite monkeys on infinite typewriters are certain to produce the world's literature

(snip)
However, if you don't mind, I want to set aside all discussion of infinity, for the time being. Once this group starts talking about infinity, there's no end to it...
Borel wasn't talking about infinity, he specifically said a million monkeys, and a fixed amount of time ("at the end of a year"). I want to focus on finding out what the point was that he was trying to illustrate.

Date: 1885
a branch of mechanics dealing with the application of the principles of statistics to the mechanics of a system consisting of a large number of parts
having motions that differ by small steps over a
large range

1884 - Gibbs coins the term "statistical mechanics"for the kinetic theory's treatment of thermodynamic issues.
Maybe Murray or someone can explain what issues are dealt with in statistical mechanics.
That page whose URL I no longer have said that a million monkeys working for a year works about to be approximately 80 trillion characters produced. The page says this "would probably not be enough to prove correct" but it doesn't explain what it thinks the proposition is* that it would fail to prove. I'm afraid they may have it wrong, they may think Borel claimed the world's library would be produced by the monkeys, and they're saying, no, it's not enough. I think that that was *Borel's point.
the 'infinite monkey thing' has a life of its own now.

Indeed. As does a gazillion words for snow.

Best Donna Richoux
Students: Are you brave enough to let our tutors analyse your pronunciation?
However, if you don't mind, I want to set aside all discussion of infinity, for the time being. Once this group starts talking about infinity, there's no end to it...

I haven't noticed an end to any of this group's preoccupations... But OK, back to Email Borel
Borel wasn't talking about infinity, he specifically said a million monkeys, and a fixed amount of time ("at the end of a year"). I want to focus on finding out what the point was that he was trying to illustrate.

In which case I have to repeat the assertion from Wikipedia that he was looking to illustrate "a
special case of Kolmogorov's zero-one law". He wasn't philosophising, he was illustrating a mathematical proof.
As to what he was saying about the mathematics, it's useful to translate what Borel says immediately before the passage you quoted (taken from the site you urled):
"Concevons qu'on ait dressé un million de singes à frapper au hasard sur les touches d'une machine à écrire et que, sous la surveillance de contremaîtres illettrés, ces singes dactylographes travaillent avec ardeur dix heures par jour avec un million de machines à écrire de types variés. Les contremaîtres illettrés rassembleraient les feuilles noircies et les relieraient en volumes. Et au bout d'un an, ces volumes se trouveraient renfermer la copie exacte des livres de toute nature et de toutes langues conservés dans les plus riches bibliothèques du monde."
Which is, roughly, " Imagine we trained a million monkeys to hit the keys of a typewriter at random and that, under the supervision of illiterate foremen, these monkey-typists worked enthusiastically for ten hours a day with a million typewriters of various kinds. The illiterate foremen would gather the blackened pages and bind them in volumes. And at the end of a year, these volumes were found to contain an exact copy of the books of every description and every language contained in the richest libraries of the world."
And thence to "Such is the probability". I think he's taking it for granted (which would have been OK with a mathematical audience but perhaps risky with a general audience) that we will know what volumes of monkey typing bound by illiterates would contain. Clearly, gibberish. Or gibbonish. But I mustn't orang my readership.
The monkeys would have produced, in a year, the equivalent of 17 million books the size of the Bible. Which wouldn't even equal the total number of books held in aforesaid libraries. So the chance that they, by pure chance, had the same content, is infinitesimal. And that, I think, is all Email is trying to say.
It has something to do with "statistical mechanics" (mécanique statistique)... :

Are you quite sure "mécanique statistique" and "statistical mechanics" are the same thing? And were the same thing 100 years ago? Bear in mind also that the quoted passage is from a book called "Mécanique Statistique et Irréversibilité'' which is not to say that the passage in question as to do with the title matters directly. "Mécanique" means clockwork and engineering as well as mechanics.
There's maybe an interesting sidelight here:
http://www.talkorigins.org/faqs/abioprob/borelfaq.html

A quote from a different Borel book goes :"When we stated the single law of chance, "events whose probability is sufficiently small never occur," we did not conceal the lack of precision of the statement. There are cases where no doubt is possible; such is that of the complete works of Goethe being reproduced by a typist who does not know German and is typing at random. Between this somewhat extreme case and ones in which the probabilities are very small but nevertheless such that the occurrence of the corresponding event is not incredible, there are many intermediate cases."
And later "When we calculated the probability of reproducing by mere chance a work of literature, in one or more volumes, we certainly observed that, if this work was printed, it must have emanated from a human brain. Now the complexity of that brain must therefore have been even richer than the particular work to which it gave birth. Is it not possible to infer that the probability that this brain may have been produced by the blind forces of chance is even slighter than the probability of the typewriting miracle?"
I cannot help but wonder if Mme Borel was frightened by a typewriter when she was carrying young Email.

John Dean
Oxford
The monkeys would have produced, in a year, the equivalent of 17 million books the size of the Bible. Which ... by pure chance, had the same content, is infinitesimal. And that, I think, is all Email is trying to say.

I was with you up to this point.
The probability is NOT infinitesimal, and that's part of Borel's point, I think.
The probability of a million monkeys producing the 17 million intellegible volumes excerpted from the world's libraries is finite. (I.e., it is possible indeed, easy to calcualate and name a number which guaranteed to be SMALLER than that probability, but larger than zero.)

It is finite but very small. That's not the same thing as infinitesimal.

It is sufficiently small that we need not worry about it happening during the lifetime of the universe, but it's still finite. It COULD happen, in principle, even if that's not the way the smart money is going to bet. It's not impossible in theory, though it is near to impossible enough for all practical purposes and the odds of all the air in this room deciding to up and huddle in one corner are even slimmer.

Roland Hutchinson Will play viola da gamba for food.

NB mail to my.spamtrap (at) verizon.net is heavily filtered to remove spam. If your message looks like spam I may not see it.
When I looked at the Monkey Shakespeare Simulator the other day, I remembered how we traced the story/image back to ... to me to wonder what point Borel was trying to make when he invented it as an analogy or illustration.

Borel's paragraph, in French, is found here: http://www.angelfire.com/in/hypnosonic/Parable of the Monkeys.html After describing the imaginary set-up of a million monkeys ... espace de quelque étendue, un écart notable de ce que la mécanique statistique considère comme la phénomène le plus probable...

Till Isabelle or another expert comes along, here's my very free crack at it, making no attempt to preserve the author's style:

"This is the probability of any significant deviation, for even the shortest time and in a large space, from what statistical techniques show to be the most probable occurrence..."
The next known use was Eddington (1929) (2), strumming on typewriters they /might/ write all the

(OT: Had to comment on 'strumming on a typewriter'! Love it.)
So, my point is, it began as a measure of *unlikeliness.* Not as a way to illustrate infinity or anything else.

That point is very well taken: thank you for the clarification, which I'll now bash people's ears with. Great posting.
Mike.
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