Maddenation
Monkeys, Typewriters, Shakespeare
I’ve found links to this on a couple of other blog sites, so I figured why not put it here as well. You know the old hypothesis that given an infinite number of monkeys clacking away on an infinite number of typewriters (one per monkey would be enough, I suppose, but when both monkeys and typewriters are infinite, does that even suggest a 1:1 correlation? Seems like it should, but mathematically I guess it doesn’t) for an infinite amount of time (minus appropriate breaks for eating, sleeping, and other bodily functions, of course), you would eventually get the entire works of Shakespeare? You’ve heard this before? Well, researchers at Plymouth University in England gave six monkeys one computer to mess with for one month, and this is what the monkeys came up with.
So the question is, does that disprove the hypothesis? Can’t you just hear the monkeys clamoring at the injustice: “We need more time! One month isn’t nearly enough! And could we please each have our own computer next time!?” And what good is the hypothesis anyway? What is it trying to tell us? That Shakespeare wasn’t that great after all? That infinity is really really big? And do the monkeys have to produce Shakespeare’s works with all the words in the correct order, or could one monkey be working on Act I of, say, The Merchant of Venice, while another monkey is working on Act II. And could a monkey leave out small bits that would be filled in by another monkey? Do the monkeys have to realize they’ve written Shakespeare’s complete works, or will an outside judge tell them when to stop? The questions go on and on and on…
This makes me think of a lot of Jorge Luis Borges stories, but mostly The Library of Babel. Read it and weep.
Patrick • News • 05/10/03 • 4 comments
Comments
Dad • 05/11/03 • 2:19 PM:I like John Allen Paulos’s comment on this subject, from his book, Innumeracy. He says monkeys would be better off trying to evolve into something that has a better chance of writing good plays. Given an infinite amount of time, this is really the best option. In fact, as Darwin would point out, this has already happened! You wouldn’t even need to supply the typewriters, as they would be invented along the way.
Paulos also poses an alternate question: “What is the probability that Shakespeare, by randomly flexing his muscles, might accidentally have found himself swinging through the trees like a monkey?”
I think from a mathematical point of view, you needn’t engage an infinite number of monkeys in this exercise, but merely one immortal monkey working for an infinite amount of time. Of course that begs the question: If you did have an infinite number of monkeys working, how long would it take to produce the works of Shakespeare? (Or Hamlet, for example.) One could suppose that one of those monkeys would type out the works in the minimum amount of time, with no “typos.” On the other hand, what about his neighbor who begins with a few lines of gibberish and then proceeds to produce the whole works? What if the gibberish is in the middle somewhere? As a purist (whatever that means) I would have to insist on the complete works, in order, with all punctuation intact.
Regarding Borges’s Library of Bable, I am reminded of a column Martin Gardener wrote many years ago. He spoke of an advanced civilization who came to earth and wanted to take back all the information contained in all the libraries of the world. They did this by digitizing the information and producing a single decimal number of unimaginable length. Then, because they had also evolved nearly infinite precision capability, they measured off a fractional distance on a unit-sized metal bar that was exactly equal to the decimal they had produced. Thus, they were able to reduce all written human knowledge to one tiny mark on a small stick.
You think that’s far-fetched? Think about Avagadro’s number, the number of atoms in one mole of and element. With 6 E+23 atoms available, and assuming you could put a mark between any one of them, this would produce fractions with that many digits. That’s a lot of data! Say you use 10 binary digits for each character (much more than you need), assume 10 characters per word, 1000 words per page, and 1000 pages per book. Then assume a million books per library and a million libraries in the world. Those assumptions work out to “only” E+22 digits. Avagadro’s number is 60 times that!
And then there’s Godel’s theorem about there being unprovable truths and undisprovable lies in any formal system. So, as Borges was no doubt aware, those searching for the “meaning of life” in the library of Babel, would never know for sure when they had found it.
One final shot, and then I must abandon this comment. Is our universe, which might have “waited” an indefinite amount of time before the “big bang” the result of an infinite number of “sub-atomic-monkeys” banging away at the firmament?
David • 05/13/03 • 2:24 PM:At the risk of ending all discussion, I will add a comment.
Interesting stuffs. I love it. Great questions. I’m going to use the article with the monkeys tomorrow as my bellringer. We’re studying evolution right now and it’ll fit right in. Awesome.
As for Dad’s comments - whoa! good work. I will always remember you telling me that Gardener story about precision. That’s deep!
Let’s make one change in wording and possibly understanding about evolution - you cannot ‘will’ evolution, nor can the monkeys ‘try’ to evolve into something else. They could ‘hope’ that natural selection and random variation and mutation goes the ‘right’ way, and let nature do it’s thing. I suppose you could attempt to recreate the same environmental pressures that existed during Earth’s history and evolved primates into humans.
I wonder what the chance of it happening twice is? Probably next to nothing. Not to mention - more accurately - we’re talking about a common ancestor here, that we both evolved from (we did NOT evolve from the apes that exist now - but from other common ancestor apes that are long extinct) - so once again, the understanding of evolution is off (I realize, Dad, that you’re just making a point and summarizing some other people’s views). Maybe I’m just picking on words here, if so, sorry.
Very interesting. Thanks Pat and Dad for offering these thought provoking ideas/questions
Dad • 05/20/03 • 10:38 PM:Dave,
See? You didn’t end discussion! Thanks for correcting the evolution comment. Yes, I was merely repeating the words of another, and he was just making an amusing point, but clarification of such a profound concept as evolution is always useful. Next time I will know better.
This raises another issue that is either nit-picking or very important. I think much of our so-called knowledge comes from offhand remarks or carelessly written words of others. Thus, when someone says casually that we evolved from monkeys, this is mostly taken to be true and widely accepted, whereas it is really bad science that is not accepted at all by real knowledgeable biologists. Often too, people knowledgeable in one subject say things about another field that isn’t necessarily right. They are believed because of their reputation, but often they are talking beyond their experitise. The lesson is always be careful about what you say, but especially about what you accept as fact.
Finally, the question about the probability of our particular evolutionary history repeating itself is a great one. I agree with you that it’s probably next to nil, but who knows? This is related to the question whether or not we are alone in the universe. Carl Sagan found it hard to believe that with “billions and billions” of stars, some with planets, etc. there wouldn’t be life elsewhere. But his logic is flawed, and his “facts” are merely conjetures. Yes, it is hard to believe that intelligent life didn’t occur anywhere else in this big universe, but so far we can’t provide any evidence that it did. Why would God create life more than once? Is He experimenting? In the case of intergalactic conflict, would God be on our side? If life sprang up more than once, doesn’t that kind of diminish God’s roll? If there were another intelligent civilization, would it be better than ours? Would they have written Shakespeare?
Patrick • 05/21/03 • 12:37 AM:They would if you gave them an infinite number of typewriters and infinite time to do it (or if you gave them a printed copy of Shakespeare’s collected works and told them to write a copy for themselves).
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