Not Even a Stinking Sonnet

Could an infinite number of monkeys given an infinite amount of time produce the complete works of Shakespeare? The BBC reports that some scholars at the University of Plymouth wanted to test the theory, so they put a computer in the monkeyhouse of a zoo. After a month, "the Sulawesi crested macaques had only succeeded in partially destroying the machine, using it as a lavatory, and mostly typing the letter 's.'"

This is being touted as a refutation of the Shakespeare theory, despite the fact that six monkeys and one month do not represent infinite primates or time. In addition, the project was shuttered just as it started to get interesting: "towards the end of the experiment, their output slightly improved, with the letters A, J, L and M also appearing." If you'd like to see the results yourself, they've been published in a limited-edition book called Notes Towards the Complete Works of Shakespeare.

When I was in college, we did a much more rigorous experiment, with uncountable monkeys allowed to type forever. After 300 years, we peeked at their work -- and were aghast. In thousands of pages they'd created no Shakespeare at all: just reams and reams of Marlowe.

[Via Sara Ryan.]

Comments

[Lazarus Long]

"It was the best of times, it was the BLURST of times? You stupid monkey!"

[Jon B.]

Shakespere was referring to himself, though he rarely gets credit for inventing the theory of evolution.

[SM]

But Marlowe was Shakespeare !!!

[Jim]

Yet another fine use of money. Probably tax dollars at the root, I suspect. I always thought it was just meant to be a logical truism, that given complete randomness you'd eventually get something that looks ordered given enough time and/or a large enough sample size. What a dumb experiment. If someone wanted to do this more efficiently, you could probably just calculate the probablility of random key strokes eventually resulting in a Shakespeare work, or write a small computer program to run a simulation. I suspect (as maybe the only useful bit of info to come out of this study) that in truth you'd never get your "Shakespeare" out of monkeys because animal (and human) behavior is rarely random. Note the early interest in 'S' - maybe they thought it was a worm or something they could eat.

[Daniel Lam]

Note that this was not a scientific experiment. It was a project performed by students in a "MediaLab Arts" course at an "Institute of Digital Arts and Technology" and was funded by the "Arts Council". No testing of anything here, just artsy fartsy expression.

[Xrlq]

Party of me wants to say "thank God I'm not a British taxpayer," but then my memory of that cow flatulence / global warming study in the 1990s brings me back to reality. Your tax dollars at play.

[Sean]

"Gian-Carlo Rota wrote in a textbook on probability (unfinished when he died):

'If the monkey could type one keystroke every nanosecond, the expected waiting time until the monkey types out Hamlet is so long that the estimated age of the universe is insignificant by comparison ... this is not a practical method for writing plays.'"

This study didn't show any flaw, given that its sampling period in proportion to what it was attempting to sample makes the results hopelessly insignificant. It would be less foolish to take a one-second glance out your livingroom window at the street and, upon seeing no cars, conclude that there were no cars being driven on any street in the united states at that time.

As for the fondness of 's', again, the sample size of monkeys is insignificant compared to an infinite number of monkeys. 99% of all monkeys may prefer 's' to all other letters, but this doesn't mean this is all they will ever type (equal probability of all letters is not required, just some non-zero probability of each letter).

And remember, on a tangential note, if you want to build a universal library, you'll need a hell of a lot more pages of nothing but 's' than five.

[JJ]

Why are so many commenters taking this so literally? This is more of a conceptual art project than a scientific experiment. And with those novelty books, they might make back the money.

[Jim]

As an art project, it's fairly stupid then. Yes, I guess the logic still holds as long as the probability of random letters is non-zero. They probably will hit different ones sometimes by mistake, eh? It certain does have value for humor, if nothing else.

[Neb Okla]

Perhaps it is a question of finding the right monkey...

Maybe we could expdite things by teaching a monkey to type Shakespere.

I prefer the notion that all data that ever was or ever will be crated can be found as a string of numerals in Pi.

With such an advance, data compression would consist of indexing the start and end points.

Maybe instead of writing new software - we could just find it! 😉

[JDM]

"With such an advance, data compression would consist of indexing the start and end points."

Wouldn't the indices become larger than the data they pointed at? Maybe they could also be compressed similiarly...

[Neb Okla]

"The six monkeys - Elmo, Gum, Heather, Holly, Mistletoe and Rowan - produced five pages of text which consisted mainly of the letter 's'."

"But towards the end of the experiment, their output slightly improved, with the letters A, J, L and M also appearing."
____________

...anyone else notice that J is next to H, and J, L, and M are adjacent to K.

So far they've got the S down, and they've practiced a bit with A - clearly K and E are next on their list.

Given more time, they'll complete the word "Shakespeare".

It would be amusing if they typed the phrase "the complete works of Shakespeare" in, say, a year. 😀

[Neb Okla]

JDM - Yes, you could compress the indices in much the same way, but you would want to do it in the fewest hops possible.

Maybe someone could come up with an imaginative way to annotate the location of the index such that it doesn't take up much space at all.

[Sean]

JJ,

The reason I saw fit to treat this with some seriousness was in the way it was interpreted and reported. In particular:

Paignton Zoo scientific officer Dr Amy Plowman said: "The work was interesting but had little scientific value, except to show that the 'infinite monkey' theory is flawed."

The article also refers to it as an experiment as well as a project, and gives its genesis in the lecturers and students desire to test, not display.

The general public's knowledge of science, math and statistics is so piss-poor to begin with, that misleading information taking up the limited space that these subjects are allotted in the popular media should not be let to go by without comment.

[SM]

Hey Neb Okla -

"Maybe someone could come up with an imaginative way to annotate the location of the index such that it doesn't take up much space at all"

What do you mean by that ?

[Plutarck]

An infinate number of monkeys would produce the entire works of Shakespeare INSANTLY.

Like, duh.

[Warren]

Let us now peer over the shoulder of one promising candidate?

Now is the winter of our discontent, made glorious summer by this sun of l- 7fwj09uas ef97yf e buowg98hgwh9 gw hu

Ahhh so close, so very very close, and yet so far.

[Sean]

Plutarck,

While there is a bit of redundancy in having an infinite number of monkeys and an infinite amount of time (one monkey would suffice assuming immortality), an infinite number of monkeys would not produce the entire works instantly. At least one would type them out flawlessy in the minimum number of keystrokes, but it would take the amount of time necessary to make those keystrokes. You could also compile the work of several monkeys (perhaps on per work), reducing the time to however long it takes the one typing the longest work, but he still has to hit all the keys.

[Jesse Walker]

But Sean: Given an infinite number of monkeys, isn't at least one of them likely to be a mutant supermonkey able to type millions of words per second?

[Sean]

Jesse,

Even a mutant supermonkey would take slightly longer than an instant, but I did fail to consider the possibilty of illuminated, transcended ubermonkeys, one of whom has already completed the task (although it never seems to get credit).

[Jim]

If you truly ponder the meaning of infinity, then you'd be forced to conclude that you'd get an infinite number of the same Shakespeare works, and an infinite number of any other imaginable works (although it would be such a small subset of the total infinity of random key strokes generated by monkeys). And it would happen relatively instantly (taking in time the amount of time required to type it). The longer you wait, the more you get (but it's infinite already, you say? You'd get more). Doesn't make much sense but then again, we are finite beings in an apparently finite universe so we're not mentally equipped to really visualize such things.

How big a zoo would you need to keep an infinite number of monkeys in? I can only imagine the stench....

[Brad S]

I think the reason for the hubbub about the monkeys producing Shakespeare "study" or whatever you want to call it is that it brings up a very interesting (and potentially significant) philosophical point: given infinite time and randomness, anything conceivable can (and perhaps more significantly, WILL) happen. It follows that there is absolutely no meaning to anything that ever happens. Anything that happens was simply bound to happen eventually, given the randomness of events and the infinite nature of time. It follows that there is no "God", and while there may be natural selection and evolution at work, they are ultimately driven by the random nature of the universe in which they operate.

[Anonymous]

From the Button-Down Mind of Bob Newhart: one monkey got so far as "To be or not to be; that is the g'zorn'nplatt."

[Brad S]

From the typewriter of another monkey: "Romeo, Romeo, wherefore art thou Fsdhg8fjgbc;s23"

[Jesse Walker]

Jim: Don't worry too much about the smell. An infinite number of monkeys will eventually shit roses.

[Ranald H.]

Jeez - now they're all blogging. Figures.

[PLC]

You're all missing the point of the "project" - an infinite number of monkeys would never produce Shakespeare, because monkeys are not random agents. The point was that while mathematically, given infinite random keystrokes on infinite typewriters, you could produce everything ever written essentially instantly, real life is not random and given infinite MONKEYS and infinite TIME, I'm sure you'd never get a single intelligable paragraph.

Also, Brad S - fortunately, the universe if not infinite and the rules of prior causes along with uni-directional time mean that not everything that could happen will happen. For instance, I was never not born.

[Ranald H.]

QED

[PDQ]

"You're all missing the point of the "project" - an infinite number of monkeys would never produce Shakespeare, because monkeys are not random agents."

Actually, I think that that's the basis for at least half the jokes here. Or at least that's why they're funny.

[Sean]

PLC,

As long as the chance of hitting each individual letter is non-zero, eventually all combos will be produced.

[Brad S]

PLC - randomness plus infinite time does not necessarily dictate that anything that can happen will eventually happen TO YOU. It simply means that everything that can happen will eventually happen at SOME POINT, SOMEWHERE to SOMEONE.

[PLC]

Brad S - so you've granted that not everything that can happen will happen (since if everything that can happen will happen, it would necessarily happen to everyone at every instant). Given this, the statement that "everything than can happen will eventually happen at some point, somewhere to someone" becomes absurd on the face of it. Unless you have a ridiculously limited sense of "everything".

The point is - the universe is not infinite, time travels in one direction, and phenomena result from the interaction of quantum randomness, visable scale causal determination, and conscious choice - not simply random acts through time.

[Jim]

Brad,

Actually, if you want to make an allusion that is relavent to our policy makers, it is that given a large enough sample size and enough time, some bad shit is going to happen to someone somewhere. It therefore does not follow that every time something like this happens we have to enact laws to make sure it 'never happens again'. There are 270 million very diverse folks in this country. It shouldn't surprise us that every now and then some wacko shoots up a school, kidnaps a child or blows up a building. Not saying we shouldn't go after people who do such things but it should be sufficient to accept that we're never going to reduce crime or tragedy to nil.

Jesse -

Yes that may happen but in order for that to happen to all of them at the same time that would take infinite time so we'd be waiting a long time for some fresh air...

[PLC]

Sean - "As long as the chance of hitting each individual letter is non-zero..." that's exactly the point - that chance is zero.

[Brad S]

PLC - I stand by the argument that everything that can possibly happen will eventually happen by random chance. And no, that does not necessarily mean that everything happens to everyone at every instant.

I'll give you an example using that bastion of statistics, baseball. People are always amazed whenever a pitcher throws a no-hitter. But statistics tells us that random chance alone should produce at least a few no-hitters every year. To get a no-hitter, a pitcher must get 27 hitters out (for simplicity, I'll ignore the impact of walks, hit batters, errors, etc - a pitcher can walk any number of batters or hit any number of batters with a pitch and still end up with a no-hitter). The league batting average usually hovers right around .270 or so. So, the odds of one batter making an out are about 73%. The odds of two batters in a row making an out are about (73%)^2. The odds of 27 batters in a row making an out (again, ignoring walks, etc) is (73%)^27 = .000204. The reciprocal of that (1/.000204) is about 4900. So, put another way, every 4900 games, by random chance, an average pitcher will throw a no-hitter against an average opponent on an average night. There are 15*162=2430 games played every year. So, roughly once every two years, random chance alone dictates that there is likely to be a no-hitter.

Given random chance and about two years time, we can expect there to be a no-hitter every two years in baseball. Now, the actual rate of no-hitters is higher than that, and I could rattle off a bunch of obvious reasons why that is (against some pitchers the league average is much lower than .270, some pitchers tend to have either really good stuff or really bad stuff on a given night, conditions in a particular ball park or the way a particular umpire calls balls and strikes may favor the pitcher on a given night, etc, etc etc). All this means is that mathematical models rarely fully reflect reality, and in the case of my baseball analogy, it does not. The overriding point I'm trying to make (and that the Shakespeare/monkeys issue tries to make) is that random chance plus the infinite nature of time is a very powerful thing. More things occur by random chance alone than most people want to acknowledge.

[Brad S]

I should amend my prior post to read "random chance dictates that a no-hitter should occur at least every few years". My mistake on the verbiage. The monkeys must be starting to control my typing. 🙂

[PLC]

Brad S - there is nothing at all wrong with you baseball analogy post. However, what that has to do with your prior post against which I was arguing, I cannot fathom. Here's a reminder:

"given infinite time and randomness, anything conceivable can (and perhaps more significantly, WILL) happen." This statement is patently wrong - saying anything conceivable WILL happen means that it WILL happen that I was never born.

"It follows that there is absolutely no meaning to anything that ever happens." No, it does not.

"Anything that happens was simply bound to happen eventually, given the randomness of events and the infinite nature of time."

Firstly, events are NOT random. Secondly, time is NOT infinite. Thirdly, not everything was bound to happen.

Events are inextricably tied to time. It was not "bound" to happen that Roger Clemens would win his 300th game on any particular day. Like-wise, I am certain that it will NEVER happen that anyone will win 25 Cy Young awards. The universe is not a statistician's model. There are actors, there are prior non-random causes, there is UNI-DIRECTIONAL time.

For a more thorough explanation of the point I am making rather poorly, read "Being and Time" by Heideggar. The primary aspect of existence in temporality.

[PLC]

Last sentence should read "The primary aspect of existence IS temporality."

[amr]

The biggest assumption of this "Monkeys and Shaekspeare" hypothesis is the assumption of inependently random keystrokes. I don't belive that monkeys have that in them, that they will hit keys next to other keys. Now, we could rig a computer program what would do near-random typing that sould eventually produce all Shakespeare. And everything else. Given infinite time.

Or, if you have two computers running the same program, it should take half as long.

Also, if you have an infinite number of monkeys, sequence their first keystrokes and this should give you the complete works of shakespeare. I'd guess that there is an independence of "first keys" that is not there for sequential typing.

Finally, did the "studiers" count spaces and carriage returns? Just curious. If the monkeys saw what return does, they may get interested in finding which other keys do cool stuff, like shift and tab. Note that these are cool on typewriters bu boring on computers.

[Anonymous]

The datum that the monkeys at times mistook the computer for a loo makes me wonder whether it was running Windows 98.

-- CTI

[Hank]

Define Monkey

[Brad S]

PLC - once again, I partially agree and partially disagree with your points.

When you say "it WILL happen that I was never born", you are throwing another variable into the pot - the variable of negative actions. If you were born, then you were necessarily not never born. To me, the fact that you were born makes my argument more than the fact that you were not never born makes your argument.

You argue that events are not random, and in most cases I agree with you.

You argue that time is not infinite. To me, that depends upon how you define time. Of course, our lifetimes are not infinite, and human time is not infinite. If you define time as "human time", then time is not infinite. But if you define time simply as the passage of various events, then time is infinite.

I also agree with your point on uni-directional time. If something has not happened in the past, it will necessarily not ever happen in the past (i.e. past time will never reoccur such that things that did not happen in that past time will happen in that past time the second time around). But it does not follow that something that has not happened in the past will not happen at some point in the future. That should be self-evident.

When I say there is absolutely no meaning to anything that ever happens, I'm speaking of large theological issues. For example, there's no meaning to the fact that it takes the earth rougly 365.25 days to orbit the sun. Now, of course there are phenomena in the physical world that cause this to be the case, and furthermore, the fact that it does take the earth 365.25 days to orbit the sun causes certain other things to be. But there is no divine reason why 365.25 days is the right number. Random events happened at some point along the line that caused this to be so. Nothing more, nothing less.

My overriding point is still that time and random chance can be a powerful combination, and I stand by that point.

[Douglas Fletcher]

The bigger question is: if you had an infinite amount of New York Times reporters, how long would it take them to create an unbiased newspaper?

[geophile]

Try reading these posts in reverse order. Trippy.

[Anonymous]

Isn't it fair and balanced enough for you, doug ?

[s.m. koppelman]

In Shakespeare's day, there were probably people grumbling about his plays being written with grant money from government-appointed nobles. Especially when it could have been spent on more important things like more ships to send on quests for gold in the New World, or better yet, on a tax cut for businesses that employed 500 or more enslaved peasants.

[JDM]

"My overriding point is still that time and random chance can be a powerful combination, and I stand by that point."

Just because the idea of randomness exists in mathematics, does not mean that it exists in the physical universe. Actions that appear random are not necessarily causeless.

[JDM]

Think of a constrained infinite set, such as one of random odd numbers. The set of keystrokes made by monkeys may be constrained in some way by the physical nature of monkeys that cannot be known which precludes Shakespeare from appearing.

[Spinoza]

"Given more time, they'll complete the word 'Shakespeare.'"

I doubt it.

The keyboard would be all gunked up with feces long before they get the hang of QWERTY, or any such sequential logic.

PLC: "Time travels in one direction, and phenomena result from the interaction of quantum randomness, visable scale causal determination, and conscious choice - not simply random acts through time."

I disagree. Time may SEEM to travel uni-directionally, but as Einstein has proven, that direction is ultimately circular and spiral-shaped. Hence, the quantum leaps of existence and creation. And hence, the infinite big-bang explosions and contractions of the universe. (God breathes.)

BTW: "visable scale" as opposed to "MC-ble scale"?
(Just kidding.)

JIM: "we're never going to reduce crime or tragedy to nil."
(Not if Hillary has her way with School Drugs for everyone, heh-heh-heh.)

[Jon B.]

This is all moot since the number of monkeys in the universe is a finite number without a boundry layer;-)

Spinoza-
BTW I think cyclic universe theories are out of vogue nowadays. Last I heard, the universe wasn't just expanding, it was accelerating. This is why as you get older time seems to pass faster.

[Jim]

PI might be an infinite series, but it has a starting point and any point on it is a finite distance into it. One possible way to compress the index would be to reduce it to a factorial (if you can calculate one that would work).

I think the true flaw in this line of reasoning is assuming the sequence is random. It is definitely predetermined over its whole length and may never have any content that resembles the desired data set.

[JDM]

Jim,

The distances might be finite, but the distance to any given piece can be arbitrarily large, the data at that point is not. No matter how it's compressed, indeces can be chosen which are still arbitrarily large.

Something I thought of: one of the infinite strings of data you could take out of an infinite string of random numbers would be the set of all useful knowledge in one continuous sequence without extraneous numbers in it. You could start the indeces at that point and it would work.

"I think the true flaw in this line of reasoning is assuming the sequence is random."

I agree. To me this is more an argument that randomness in the mathematical sense does not really exist, at least among sequences that can be regenerated. Wouldn't the fact that Pi represents something in the real world preclude its being random?

[Jim]

JDM,

I agree with your first statement - it would be silly to use a huge number to get to a point in a random sequence that had one bit of data.

You'd have to use a computer or something based on quantum-level 'true' randomness to generate random sequences but then you'd have to find the information in it, which would render the effort impractical, methinks. Might as well just type it all in or something. Also, a location in the random sequence with all the useful information in it would be just as unmanageable as 'all the useful information' - just as unmanageable as when your keyword search on the web nets 52,000 entries or whatever. It may be theoretically possible but I don't think it will help anybody.

Pi would be precluded from being random because it is always the same and is a preexisting artifact of the 4 dimensional universe we live in. It never will change. However information changes every day (people actually create it, like the Shakespeare plays in question). We might find coincidences in the sequence of numbers that can represent some existing things, but not necessarily all (or even many) things.

A truly random infinite series of numbers could contain all possible bits of information, but we'd be creating it randomly so that it could in theory capture everything that exists and will be.
There may be no known pattern in the numbers of Pi but it is definite and unflexible. An infinite series of 1's, for example, is never going to contain one whit of Shakespeare. One could argue that the endless sequence of Pi is one infinite pattern, and I think they'd be right. Thus, it is not sufficient for something to be infinite but it must contain all possible sequences (whether generated randomly or not)in order to store all possible information.

[Spinoza]

Making these quantum leaps from simians to physics reminds me of that tossed bone in "2001 A Space Odyssey." (Turn up the dramatic music.)

Yet, regardless of fashionable thinking, Jon, if you attempt to refute Einstein, you're going to have to do better than that.

The big-bang was not a one-time deal. The infinite explosions and contractions of the universe are macrocosmically and microcosmically reflected all around us -- in the pulsations of a quasar, the rhythm of your lungs, the workings of the pistons inside a combustion engine, to name just a few.

The universe may indeed be accelerating as it expands, but it still does so in spiral form, eventually turning back in upon itself. As reflected in thousand-year-old Vedic philosophy, you, too, will eventually assume the fetal position and start all over again.

[Neb Okla]

SM, when referring to my comment about seeking a better way to index a given start and end-point in Pi said...

"What do you mean by that?"

What I mean by that is that the suggestion was made (probably accurately) that at some points, the values of the indexes would become very cumbersome.

An example though might be something comparable to scientific notation where we can use a relatively short string of characters (2 x 10^8000) to represent a much larger string of characters.

[Neb Okla]

Also, PLC said:

"For instance, I was never not born."

What about before you were born?

I was not born before my birthday, how about you? Maybe you were born-again?

[Neb Okla]

I'm somewhat disturbed by the notion of some people in this group that the universe is so random that anything can happen given enough time.

We are limitied by physics.

Monkeys will never shit roses due to physics, and also due to physics it may not be possible for a monkey to ever type anything meaningful.

For example, what if something about a monkey's brain prevents it from typing a "b" and an "e" sequentially? This would preclude the sentence "to be, or not to be".

Mother nature seems to have built-in safeguards against humans having too much fun.

[Jesse Walker]

I recommend to all the R.A. Lafferty story "Been a Long, Long Time," which deals specifically with monkeys, Shakespeare, and the fabled experiment.

Beyond that, I agree with Neb: Maybe we could expedite things by teaching a monkey to type Shakespeare. Of course, that would just give fodder to the creationists.

[Sean]

Neb,

Are you saying that monkey's wouldn't make typos? Even given a limited amount of intentionality (e must never follow b), accidents happen. Perhaps the redundancy of an infinite number of monkeys and infinite time is not so redundant after all.

[Neb Okla]

Sean: What if, due to the physical design of a monkey, it is impossible for a monkey to even mistype an "e followed by a b". Consider ergonomics here - the typewriter was designed for humans to use, not monkeys, so it is concievable that such a limitation might exist.

Just as monkeys are very good at climbing trees - there are some things that probably reqire four dexterous appendages *AND* a tail that a human would have no hope of accomplishing - even given an infinite number of humans and an infinite amount of time.

[Todd]

>Wouldn't the indices become larger than the data
>they pointed at? Maybe they could also be compressed
>similiarly...

Looks like someone failed their discrete math/ information theory classes.

[JDM]

Neb,

The count of an infinite series is infinite by definition. Therefore wouldn't the indeces into an infinite series be infinite by definition? An infinite sequence of digits representing an index compressed to 1% of its original length is still infinite.

[JDM]

Todd,

The "maybe they could also be compressed similarly" was tongue in cheek. My intuition says that it wouldn't work with an infinite random series. Number theory is sometimes counter-intuitive though. If you're young enough (or specialized enough) to remember number theory, which is it?

[Jim]

Spinoza,

As much as I'd like to think we live in a cyclic, repeating universe, there's the second law of thermodynamics to contend with. Disorder and entropy always increases net (even if it creates some order along the way like people to speculate about it). I don't think that's been refuted yet.

[Steve]

Nothing is random. Everything is cause and effect. One thing affects another and that affects another etc - the "network" is virtually incomprehensible. We have free will, yet our free will and decisions are still the result of cause and affect. Our fate is the result of our free will and it still comes down to cause and effect, which is all the same. Theoretically everything can be predicted when you are linked to the source, like seeing a passing ocean wave - you see it coming and going, except you are part of the wave. Time is a man made measure of progress. When connected to the source, such a concept does not exist, and is not relevant.

[Hirsch Claudia]

EMAIL: [e-mail]
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DATE: 01/22/2004 12:10:14
Newness is relative.