THE MANY MONKEY THEOREM

What's the point?

The theorem is used to illustrate these conflicting points:

  • inevitability
  • impossibility, and
  • some particular degree of probability, partway between impossible and inevitable, which a mathematician would write as

    0 < p < 1.

Borel, 1913

... 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. 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...

Émile Borel, ``Mécanique Statistique et Irréversibilité,'' J. Phys. 5e série, vol. 3, 1913, pp.189-196.

Eddington, 1929

... 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.

A. S. Eddington. The Nature of the Physical World: The Gifford Lectures, 1927. New York: Macmillan, 1929, page 72.

Jeans, 1930

... It was, I think, Huxley, who said that six monkeys, set to strum unintelligently on typewriters for millions of millions of years, would be bound in time to write all the books in the British Museum. If we examined the last page which a particular monkey had typed, and found that it had chanced, in its blind strumming, to type a Shakespeare sonnet, we should rightly regard the occurrence as a remarkable accident, but if we looked through all the millions of pages the monkeys had turned off in untold millions of years, we might be sure of finding a Shakespeare sonnet somewhere amongst them, the product of the blind play of chance. In the same way, millions of millions of stars wandering blindly through space for millions of millions of years are bound to meet with every sort of accident, and so are bound to produce a certain limited number of planetary systems in time. Yet the number of these must be very small in comparison with the total number of stars in the sky.

Sir James Jeans. The Mysterious Universe. New York: Macmillian Co., 1930, page 4. (Not seen; quote courtesy of Dave Woetzel.)

Koestler, 1972

Neo-Darwinism does indeed carry the nineteenth-century brand of materialism to its extreme limits--to the proverbial monkey at the typewriter, hitting by pure chance on the proper keys to produce a Shakespeare sonnet.

Arthur Koestler. The Case of the Midwife Toad, New York, 1972, page 30.

Pirsig, 1974

In a paraphrase of the gist of Henri's Poincare's philosophy:

...What are facts?

Poincare proceeded to examine these critically. ``Which'' facts are you going to observe? he asked. There is an infinity of them. There is no more chance that an unselective observation of facts will produce science than there is that a monkey at a typewriter will produce the Lord's Prayer.

Robert M. Pirsig Zen and the Art of Motorcycle Maintenance: an inquiry into values. New York: Morrow, 1974

But the paraphrase is pretty loose, since Poincare actually wrote:

``Le savant doit ordonner; on fait la science avec des faits comme une maison avec des pierres; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison.''

Henri Poincare La Science et l'Hypothese Paris: Flammarion, 1908. Chapter IX, p. 168.

Douglas Adams, 1979

``Ford!'' he said, ``there's an infinite number of monkeys outside who want to talk to us about this script for Hamlet they've worked out.''

Douglas Adams. The Hitchhikers' Guide to the Galaxy, [chapter 9] London: Pan, 1979; New York: Pocket Books, 1981.

Scott Adams, 1989

Dilbert writes a poem and presents it to Dogbert:

DOGBERT: I once read that given infinite time, a thousand monkeys with typewriters would eventually write the complete works of Shakespeare.

DILBERT: But what about my poem?

DOGBERT: Three monkeys, ten minutes.

Scott Adams, Dilbert comic strip, 15 May 1989.

Houghton, 1993?

Come to think of it, there are already a million monkeys on a million typewriters, and Usenet is NOTHING like Shakespeare.

Blair Houghton. [Quoted in Adam Rifkin, http://www.cs.caltech.edu/~adam/MSGLIST/MsgList and in a 2 December 1993 contribution to the alt.humor.best-of-usenet computer humor newsgroup. (A copy is in http://www.cs.berkeley.edu/~allanl/funny/classic/like.usenet, where it seems to be copied from an earlier telecom@eecs.nwu.edu list-serve posting thanking knauer@ibeam.intel.com (Rob Knauerhase) for contributing it.]

Maybe the best thing of all would be for Blair Houghton to fess up and supply a proper citation for first appearance & exact wording of his version of the topos.

Ostrov, 1994

A cat can collaborate with one intelligent mouse to produce an infinite number of literary works on a computer. Unlike a monkey, who needs a multitude of collaborators to produce one Shakespearian work on a typewriter.

Hilary Ostrov, 1994. http://haven.uniserve.com/~hostrov/cats.html

Jeff Carrie, 1994

MacDonald :

My dear man I wish you were brighter
you speak like a monkey at a typewriter

Jeff Carrie. MacDavis! http://www.ee.umanitoba.ca/~carrie/MACDAVIS/24.html

David Arthur Manning, 1995?


If a hen and a half can lay an egg in a half in a day in a half,
     how many days would it take a furry eyed chihuahua to pick the
     seeds out of twenty bell peppers using the keys from that
     hypothetical monkey's typewriter who is randomly striking out keys
     in order to type out the Complete Works of William Shakespeare.

http://www.dtcc.edu/~m63/texts/finger

Joshua Coxwell, 1995

A potential source of confusion is the idea of evolution having a ``target;'' we have normally combined this activity with others, such as Selection in Action, to address this. Cumulative SelectionOne of the most frequent arguments one hears against the theory of evolution is that complex forms and behaviors simply couldn't have evolved by ``random chance'' alone. The point we must often get across to students is that evolution does not, in fact, work this way; change is cumulative. Richard Dawkins, in his book The Blind Watchmaker, dispels the myth of random chance by using the very metaphor that opponents of evolution often turn to: the monkey at the typewriter. This program models his suggestion that, were a monkey allowed to type random letters, he would produce a work of Shakespeare very quickly if letters he happened to type in the right places were preserved with each attempt. With this program, students type in a phrase of their choosing and observe how long a random phrase takes to ``evolve'' into their target phrase. Below are some sample investigations...

Joshua Coxwell, http://biology.uoregon.edu/Biology_WWW/BSL/Cum_Sel.html

Anon, 1995

Animals have no spiritual development. Their species do not advance or grow in intellect. As animals were thousands of years ago, so they are today. If a monkey is left with a typewriter for a hundred years, he will not produce a single intelligent sentence. Compare and contrast this static existence with the life of man, which is one of perpetual growth of character and pursuit of spiritual goals....

Why a Jewish Burial? http://www.jer1.co.il/orgs/pirchei/bur3.htm

Michael XXX, 1995

However, humans have been around for quite some time, and like the monkey-typewriter cliche, people have stumbled upon elaborate methods to trigger the spiritual emotion. These methods...

95mjp@williams.edu Religion as a function of the brain http://www.cs.williams.edu/~95mjp/religion.html

Fahey, 1995

Imagine the utter dismay and consternation in the scientific community if, after having come all that way, the finger of the key-thumping monkey was off, just a measly once and by hitting a key just one row too high on the QWERTY keyboard, so that Malcolm is ``drown'd'' rather than ``crown'd'' at Scone. It is an interesting question whether the monkey, by hitting one row too high but coming up with a perfectly acceptable word, has screwed up Macbeth worse than if it had missed either to the left or the right and typed ``xrown'd'' or ``vrown'd.'' I betcha you are now looking down at your keyboard to see where the letters c, d, x, and v are located

Noel Fahey, Home Page. http://www.homesteader.com/jnf/com_tips.htm

Stanley, 1995

The most succinct answer is possibly the observation of the French playwright Moliere.

``Writing is like prostitution. First you do for the love of it, Then you do it for a few friends, And finally you do for money.''

The June 1980 Esquire magazine had a monkey sitting at a typewriter. The lettering across the cover asked, ``Is anyone out there not writing a screenplay?''

Jack R. Stanley. SCRNWRIT FAQ Chapter I - Art vs. Commercialism http://emsplum.eecs.uic.edu/ScrnFAQ/ScrnFAQ.I.html

R. R. Collier, 1995?

Finally, other people were reminded of the library in Jorge Luis Borges' story ``The Library Of Babel'', where a vast universe is described which contains all possible books (assuming a finite alphabet and a fixed book size the number of all possible books is mindbogglingly huge, but finite) -- in random order. Most books in such a library would appear written by the `monkey and typewriter' brigade, but all the coherent books, whether actually written or not, are in there as well.

R.R.Collier. http://pantheon.cis.yale.edu/~shadow/smalgods.htm

Buettner, 1995

Imagine that you're in a cave a mile underground and you just dropped and broke your flashlight.
Now, imagine complete darkness. Not close-your-eyes darkness or that of a moonless night but a darkness so absolute that your can wave your hand an inch in front of your face and see nothing. The only sound is your heart thumping and blood coursing through your ears. You're in a place so timeless that the centuries tick past like seconds. If you were lost, your chances being found or feeling your way out are about as good as a monkey banging on a typewriter and accidentally writing Hamlet. You drop to your knees and run your fingers over the limestone like a pianist playing rock and roll. Nothing. One thought goes through your mind: I'VE GOTTA GET OUT OF HERE!

Steve Buettner, MAYAQUEST UPDATE FOR 3/21/95: St. Herman's Cave http://mayaquest.mecc.com/Update24.html

Tom Solomon, 1996

Remember that old saying, ``give a million monkeys a million typewriters and a thousand years and they'll give you Shakespeare?'' Well, some say USENET is their first draft. It's nowhere near Shakespeare, but many of the Frequently Asked Question files (FAQS) are excellent sources of information. An extremely eclectic range of topics are covered--from computer programming to training a puppy, meteorology to Courtney Love.

Sweet Briar College Library, Home Page. http://www.cochran.sbc.edu/

A pale repackaging of Houghton's version.

Russo, 1996

In a novel, two characters discuss the glitch in a computer which causes it to scroll an endless series of meaningless symbols:

He sighs. ``It casts serious doubt on the old theory that an infinite number of monkeys at an infinite number of typewriters would eventually write the Great American Novel, doesn't it?''

Richard Russo, Straight Man. Random House, 1996. p. 129.

Robert Wilensky, 1996

We've all heard that a million monkeys banging on a million typewriters will eventually reproduce the entire works of Shakespeare. Now, thanks to the Internet, we know this is not true.

According to a personal communication from Prof. Wilensky, he uttered this more elegant reformulation of Houghton's version at the Industrial Liason Program meeting at the EECS Department, University of California, Berkeley, in the spring of 1996.

Wilensky's version began appearing as a very frequent email and web-page epigraph starting in 1997, often attributed to Prof. Silensky, with varying institutional affiliation: California University, Cambridge University, and so on.

(Note how the monkeys, who merrily strummed and typed with ardor in the early part of the century, have moved (dare I say evolved?) to more frustrated banging by the century's end!)

Appendix: Works of Literature

These are some pieces of writing based on the typing monkeys:

  • Russell Maloney. ``Inflexible Logic.'' Short story, originally appeared in The New Yorker magazine, 1940, and anthologized in James R. Newman, The World of Mathematics.
    A gentleman overhears a friend saying ``we know that if six chimpanzees were to set to work pounding six typewriters at random, they would, in a million years, write all the books in the British Musueum'' and decides to put it to the test. His friend's authority: ``It may be nonsense, but Sir James Jeans believes it ... Jeans or Lancelot Hogben.'' The chimps type out works by Dickens, Pareto, Donne, Anatole France, Conan Doyle, Galen, Sumerset Maugham, Proust, and so forth. A mathematician from Yale, distraught at this violation of the laws of probability, assassinates the chimpanzees and their patron.
    According to the anthologizer, James R. Newman: ``...a famous statistical whimsy. Eddington gave currency to it in one of his lectures but I am far from certain that he made it up.''

     

  • Raymond F. Jones. ``Fifty Million Monkeys.'' Astounding Science Fiction. October, 1943.

    Not seen; cited in a netnews posting to alt.folklore.urban and alt.usage.english by Simon Slavin, 31 May 1998.

     

  • Isaac Asimov. ``The Monkey's Finger.'' Startling Stories. February, 1953, pp. 77-83.

    A science fiction writer is replaced by a monkey.

     

  • David Ives. Words, Words, Words One act play, collected in All in the Timing, New York: Vintage, 1995.
    The characters are three monkeys, the subjects of a psychologist's experiment, the object of which seems to be to reproduce Hamlet. Their names are Milton, Swift, and Kafka; Kafka ends up doing the job. Which is more implausible: that a monkey should type Hamlet or that Kafka should type Hamlet?

     

  • Jorge Louis Borges. The Library of Babel. Short story. Describes a library with all (infinitely many) possible books. No monkeys, no typewriters, but some correspondents see a connection.

     

  • Vikram Chandra. Red Earth and Pouring Rain. Boston: Little Brown, 1995. Novel, with an elaborate system of nested ``framing devices,'' the outermost one of which is that a monkey (encouraged by the monkey god Hanuman) types the story.

 

 

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