Why hasn't anyone run the monkeys-typing-Shakespeare program through a supercomputer? [Archive]

andrewdt85

10-09-2005, 10:07 PM

I discovered this site (http://user.tninet.se/~ecf599g/aardasnails/java/Monkey/webpages/index.html) today, and I saw that they don't have enough funding to accept entries anymore! Darn!

It got me thinking: why haven't scientists gotten together like these guys did and run a program like theirs, but w/ a supercomputer, to figure out the age old question (actually, not a question, but a scientific answer to a bewildering claim!): if you put enough monkeys in a room w/ typewriters and let them type long enough, they will eventually produce the entire works of Shakespeare.

The guys who did this site assumed that a.) the monkeys had infinite bananas, b.) they bred at an alarmingly exponential rate, somehow w/o leaving the typewriters, c.) they typed one letter every second, and I think d.) they never sleep? or stop for anything, even when they eat or poop

Also, apparently we are working w/ an incredible population of monkeys (more than this earth has!) in a room that would have to be serviced by an incredible number of humans (again, more than 6 billion as in our world) to feed them and clean up after them and reload they're typewriters. But all of this is assumed: infinite workers to keep after the monkeys, infinite room, infinite number of monkeys you can use, infinite bananas, infinite time, infinite typewriters and resources for those typewriters, and the monkeys never stop to sleep, procreate (which they do at an incredible rate), or poop, and they always hit one key every second. That's a lot of assumptions!

If I were a scientist, here's what my version of the program would be, one that I would run through a supercomputer: I would allow the number of monkeys to increase as fast as the computer could possibly allow, and I would run the program as fast as possible until every correct sentence of Shakespeare's entire work was written; that is, at some point, these monkeys had typed each of Shakespeare's sentences correctly, and they all add up to his entire work. Then I'd know how many monkeys and how long it would take to do this!

But my question is: what did the original claim say? Was it just originated by mathematicians as a hilarious and fascinating sidenote, now used in conversations about bad writers (I bet a monkey typed this script!)? And what is the original claim: I mean, obviously it's just a mathematical fact and not something that can be done in the scope of human history (the Earth will not be around long enough, we don't have enough resources, etc.), but what were the terms of the original claim: was it claiming the monkeys would type each sentence correctly (as my program would test for) at different points along the way that add up to his works, or does it just claim they would type all the right words at some point, or that some monkey would type each play/work at some point? And speaking of that last one, I have to wonder- is it even possible to run something like this on a supercomputer? I have doubts that we can even compute somethings so unlikely as what I've proposed above, or something like what I just said about a monkey typing an entire play and eventually every play being typed.

BTW, a monkey wrote this whole post. These words are all accidentally put together. This is amazing. So was that. And that.

Dunderman

10-09-2005, 10:15 PM

The original claim was that a single monkey at a typewriter would, at some nonspecified point in the future, have typed out every single book in the French National Library. Given infinite time, you don't need any more monkeys than one.

Q.E.D.

10-09-2005, 10:16 PM

BTW, a monkey wrote this whole post.
Actually, it was an ape. Genus, Homo. ;)

Otto

10-09-2005, 10:18 PM

In his book Why People Believe Weird Things, Michael Shermer writes of a computer program written in 1988 which was able to reproduce the text of Hamlet in about 4 1/2 days. The program selectively retained correct letters and discarded and replaced incorrect ones to obtain the text. Per the same source, were it done completely randomly without retaining correct letters, it would take 2613 trials to hit the correct text, which is more seconds than have elapsed since the solar system was formed.

CalMeacham

10-09-2005, 10:19 PM

There was a scientist who did the whole "monkeys doing random typing" with computers and andom number generators decades ago. I'll have to dig up the rticle, which I've got here somewhere.

One interesting twist he added was to use not random uses of each letter, but to weight each letter with its relative appearance in English. THen he moved onto the relative frequency of pairs of letters, then triplets and so on.

By the time you got to "fifth order" monkeys ina langag you weren't familiar with (he did th same thing in Latin, German, French, mnd other langges), it was hard t tell real text from "monkey" text And for some reason third- and fourth-order monkeys gave a surprising number of obscene words.

He finally looked into whether or not you could generate Shakespeare, even using his relative frequency tables of fifth-order or higher correlations. He concluded that the answer was probably "no", because the "random" numbers his computers were generating weren't truly random -- they were th results of those quasi-random-number-generating programs that computers use, and he concluded that there robably wasn't enough "noise" to give you really random numbers.

Of course, with faster computers and better algorithms (not to mention tables of more believable random numbers) now available, maybe you could get a better shot at producing something beyond "To be, or not to be. That is the gesornenplatz..."

andrewdt85

10-09-2005, 10:27 PM

Actually, it was an ape. Genus, Homo.
Did you just call me gay?
<punches Q.E.D.>

KarlGauss

10-09-2005, 10:30 PM

Did you just call me gay?
<punches Q.E.D.>
No, but you just confirmed your simian status.

Colibri

10-09-2005, 10:55 PM

It has recently been confirmed, however, that it took a single Ring-tailed Lemur only a day-and-a-half to produce the script for Deuce Bigelow: European Gigolo.

Otto

10-09-2005, 11:13 PM

Yeah right, there was no script for Deuce Bigelow: European Gigolo!

guizot

10-09-2005, 11:51 PM

If the "Shakespeare/monkeys" idea is to say that, in theory, anything which normally results from human agency can/will happen randomly, given enough time--well, so what? The fact that they're monkeys is beside the point. You could say the same thing about any animal, providing you give them a way to type. Or something non-animal, for that matter.

To have a website that attempts to show this, or to sit around making conditions for the monkeys (or an algorithm) so that they are more likely to succeed in producing Shakespeare, is just a capricious way to kill time. And if you do insert recognition to the algorithm, what you're doing, in a way, is injecting human language capabilities that monkeys don't have, and which is contrary to the point of the original premise, isn't it? Shakespeare didn't produce his oeuvre because he liked to randomly write down letters, and then got really really lucky; he could do so, obviously, because of his human capacity for language.

Operation Ripper

10-09-2005, 11:59 PM

No, but you just confirmed your simian status.

Oh snap!

Alessan

10-10-2005, 03:08 AM

Here's (http://brunching.com/randommonkeys.html) a serious academic take on this very subject.

Small Clanger

10-10-2005, 06:05 AM

Here's (http://brunching.com/randommonkeys.html) a serious academic take on this very subject.The text of Hamlet, except that Horatio is named "Elvis." :D

Randomness and infinity are very tricky concepts, and computers can't really do either.

chrisk

10-10-2005, 06:46 AM

There was a scientist who did the whole "monkeys doing random typing" with computers and andom number generators decades[/i[ ago. I'll have to dig up the rticle, which I've got here somewhere.

One interesting twist he added was to use not random uses of each letter, but to weight each letter with its relative appearance in English. THen he moved onto the relative frequency of [i]pairs of letters, then triplets and so on.

By the time you got to "fifth order" monkeys ina langag you weren't familiar with (he did th same thing in Latin, German, French, mnd other langges), it was hard t tell real text from "monkey" text And for some reason third- and fourth-order monkeys gave a surprising number of obscene words.

He finally looked into whether or not you could generate Shakespeare, even using his relative frequency tables of fifth-order or higher correlations. He concluded that the answer was probably "no", because the "random" numbers his computers were generating weren't truly random -- they were th results of those quasi-random-number-generating programs that computers use, and he concluded that there robably wasn't enough "noise" to give you really random numbers.

Of course, with faster computers and better algorithms (not to mention tables of more believable random numbers) now available, maybe you could get a better shot at producing something beyond "To be, or not to be. That is the gesornenplatz..."

This was written up as a case study in one of my university textbooks. That book is, I believe, currently at my office, so when I get into work tomorrow I'll look it up and post a few more details, especially the funky code name he gave the program. :)

I don't remember it going into detail about any 'randomness gap', or mentioning the dirty words, though I think it's not surprising. At a certain level, the system would be able to model the language well enough to come up with new combinations of pronounceable sounds that aren't in the sample... a fair number of combinations of pronounceable sounds that aren't actually used in 'proper' english are because they kinduv got reserved for profanity.

The big problem, as I see it, is that to get a really decent shot at something interesting, like a novel better than any produced before, or the transcript of rudolph's hiring interview with santa claus (filed in Esperanto of course,) you need to be able to model something that simple letter sequence frequency charts won't give you. For one thing, you would kind of need a sense of when a string of 20-30 characters are 'meaningful', and which combinations remain meaningful when added together and which ones cancel each other out.

receipt for my two cents please. :)

CalMeacham

10-10-2005, 07:21 AM

Here's the reference:

W.R. Bennett, Jr., "How Artificial is Intelligence", American Scientist , 65(1977),694- 702.

To my utter surprise, this article is cited as a reference for several (apparently related) U.S. Patents:

http://www.ffldusoe.edu/Faculty/Denenberg/Patents/4620286details.htm
http://www.ffldusoe.edu/faculty/Denenberg/Patents/4599693details.htm
http://www.freepatentsonline.com/4593367.html

Malacandra

10-10-2005, 07:56 AM

I heard of some zoo where they stuck a typewriter in a monkey cage to see what the inhabitants would make of it, and one of the keepers thought it would be really funny to sneak in one night and tap outto be or not to bebut thought better of it. :D

msmith537

10-10-2005, 09:13 AM

It should also be pointed out that the monkeys could just as easily type a sequence of random giberish for eternity, never producing a single work of fiction.

"It was the best of times, it was the BLURST OF TIMES!??!!!!"

Small Clanger

10-10-2005, 09:42 AM

It should also be pointed out that the monkeys could just as easily type a sequence of random giberish for eternity, never producing a single work of fiction. Not even Simpsons scripts?

I have wondered about this. There must be an infinite number of ways of getting (say) Hamlet wrong (like the aforementioned Elvis version) so even given infite time the monkey won't necessarily ever give you any of Shakespeare, or e e cummings, or Matt Groening.

But I'm not sure about this, that's the problem thinking about infinity*. Could a math type show that given infinite time (or monkeys) that it is a certainty that all texts must (eventually) be generated?

* for me anyway.

Q.E.D.

10-10-2005, 09:54 AM

e e cummings
Cut that out, it's wrong. (http://www.gvsu.edu/english/cummings/caps.htm)

Small Clanger

10-10-2005, 10:10 AM

Cut that out, it's wrong. Stupid monkey!

I tried to ask a serious question about infinity there, any maths wizz got an answer?

Lemur866

10-10-2005, 10:49 AM

It has recently been confirmed, however, that it took a single Ring-tailed Lemur only a day-and-a-half to produce the script for Deuce Bigelow: European Gigolo.
Anti-Lemurist!

KlondikeGeoff

10-10-2005, 10:51 AM

For years I've considered the fact that if they could reproduce the works of Shakespeare, then they would likely come up with a lot of excellent new novels.

I always wanted to start the Simian Publishing Company. All that would needed in addition to the monkeys and typewriters would be a bunch of editors to sort the wheat from the chaff, and as soon as the Great American Novel had been produced, it could be rushed to print.

Oh, yeah, of course, truckloads of bananas would be required, but as the monkeys and editors work for next to nothing, it could be quite profitable. ;)

Revtim

10-10-2005, 10:52 AM

It got me thinking: why haven't scientists gotten together like these guys did and run a program like theirs, but w/ a supercomputer, to figure out the age old question (actually, not a question, but a scientific answer to a bewildering claim!): if you put enough monkeys in a room w/ typewriters and let them type long enough, they will eventually produce the entire works of Shakespeare.It would be a waste of supercomputer resources, because nothing new would be learned. It's a trivial exercise to find out what the probability of a particular sequence of letters coming up is, once you know how long the sequence is and how often a new random sequence is generated.

Suppose you had enough computing power and/or time to actually run it, and it happens after a thousand years. Then you can say "Oh, it happened after thousand years, which we previously calculated had a 37 percent chance of happening by this time." Nothing new was learned, and you just wasted a thousand years of supercomputer time that could have been used to generate realistic fake porn of your favorite celebrities.

msmith537

10-10-2005, 11:00 AM

There must be an infinite number of ways of getting (say) Hamlet wrong

Actually there isn't. Hamlet is a finite number of characters long. There are a finite number of keys on the typewriter. Don't confuse"infinite" with "incredibly large" number. Also do not assume "infinite" means "every possible combination".

Lemur866

10-10-2005, 11:13 AM

Look, the calculation is simple. Assume random character distribution, 26 lower case, 26 upper case, 10 numbers, space, carriage return, period, comma, (, ), !, :, ?, and ;.

That makes 72 characters. How many characters long are the entire works of Shakespeare? Let's call that number S. The odds of getting the works of Shakespeare--or any other specified output--from a random run of a 72 character set is 72^S.

However, for every exact copy of the works of Shakespeare, expect S copies that are off by one character, S^2 that are off by two characters, etc. You'd have to do a lot of proofreading when you get a close copy to ensure that you don't have a copy that's off by only a few characters.

Another exploration of this idea was the library of Borges. This library has a copy of every possible book , arranged in order. So the first book in the library is blank, the next book is blank except for one A, the next has AA, the next has AAA, and so on. If you limit books to 500 pages, works longer than that can just take up two volumes.

Of course, if you were dropped into this library and started opening books at random, the likelyhood is that you would never find more than a few coherent sentences even if you searched for a lifetime. Every book you ever read is there, including every book ever written or ever will be...but how can you find them?

Small Clanger

10-10-2005, 11:22 AM

That makes 72 characters. How many characters long are the entire works of Shakespeare?But the monkey isn't restricted to writing a text which matches the length.

And what if he decides to type out Pi or e first? He'll never get to start on Hamlet.

saoirse

10-10-2005, 11:34 AM

Quarto or Folio?
Because any primate could come up with "this too too sullied flesh"
Especially one who demonstrates agression by throwing his own feces.

But seriously, a minor nitpick:

were it done completely randomly without retaining correct letters, it would take 2613 trials to hit the correct text, which is more seconds than have elapsed since the solar system was formed.

You can expect it to take 2613 seconds. It could happen on the first try.

vetbridge

10-10-2005, 12:32 PM

Given infinite time, you don't need any more monkeys than one.

Infinite time???? Christ, I aint got all day!

Chronos

10-10-2005, 12:57 PM

My favorite musing on the Library of Borges: What do you title the books? If you want each to have a unique title, the titles would have to be as long as the books themselves.

And there are an infinite number of ways to mangle Hamlet, but only a finite (though very large) number of ways to mangle it within the same length as the original. The result is that as time approaches infinity, the probability approaches 1 that you will get Hamlet (this is often stated as, given an infinite amount of time, you're guaranteed to get it). One can debate whether this means that you cannot fail to get Hamlet, or if failing simply has zero probability. Personally, I would assert that if you go infinitely and fail to get Hamlet, that's evidence that your selection method was not truly random.

Kozmik

10-10-2005, 01:47 PM

If you have an infinite number of monkeys typing for an infinite number of years then there must be an infinite set of monkeys typing the complete works of Shakespeare AND there must be an infinite set of monkeys typing everything else.

Let's say that you walk up and check what one of the monkeys has typed so far. Do you find a masterpiece or complete jibberish? How can you explain the laws of probability in cases involving infinity?

Logically, there should be a 50/50 chance but - an infinite number of checkers could check an infinite number of monkeys and only find them typing jibberish! They would never find the infinite set of monkeys typing Shakespeare and would conclude the hypothesis to be a failure.

CalMeacham

10-10-2005, 01:52 PM

My problem is that the damned Monkeys get halfway through "Hamlet", but then they start typing a Clive Cussler novel or some other gibberish and I have to toss it out!

Omphaloskeptic

10-10-2005, 02:21 PM

Per the same source, were it done completely randomly without retaining correct letters, it would take 2613 trials to hit the correct text, which is more seconds than have elapsed since the solar system was formed.That's only true for the Reader's Digest ultra-condensed version, 13 uppercase alphabetic characters long: "THEY MOSTLY DIE." (Spacing and punctuation added by editor.) The full text is more like 130000 characters long, giving a somewhat larger (immense understatement here) expected number of trials.

10-10-2005, 02:23 PM

saoirse

10-10-2005, 02:47 PM

Personally, I would assert that if you go infinitely and fail to get Hamlet, that's evidence that your selection method was not truly random.

That only gives rise to the question: can you start over with a corrected method?

CalMeacham

10-10-2005, 03:04 PM

voice from the past

--------------------------------------------------------------------------------

People my age may remember what were quaintly referred to as "comedy records," which recorded for posterity the comedy routines of many performers. On one of these, Bob Newhart portrayed a technician in one of those labs of monkeys at typewriters. He said, as I remember, " Uh, I think we might have something over here on number 456. It...it says...'To be or not to be. That is the gazornenbladt'." It tickled me then. Tickles me no

Read the end of post #5

10-10-2005, 03:12 PM

:smack: never was real good at speed reading.

CalMeacham

10-10-2005, 03:16 PM

Hey, no need to slaop your forehead. It was just an allusion. I wanted to see if anyone caught it. You named the comedian.

andrewdt85

10-10-2005, 04:41 PM

I think we should restrict this conversation to what a finite amount of monkeys could do w/ infinite time- b/c if both variables are infinite, I think most of us are in agreement that, as the website linked to above says,

http://brunching.com/randommonkeys.html
Obviously enough, an infinite number of monkeys will instantly come up with Hamlet, along with every other piece of literature from the past, present, and future.

But if the number of monkeys is just ginormous, and the time is infinite, would they produce everything at some point? I am fascinated by the idea small clanger came up with- what if the monkeys simply started typing numbers for all infinity? Or ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ? (I guess if he fell asleep at the typewriter ;)). Or as someone else said, just typing gibberish into eternity?

But w/ that size a number of monkeys, not all of them will type numbers or other marks non-Hamlet for eternity, or a single letter for eternity, and the odds of just getting gibberish- well, is Hamlet (or anything readable) a certainty over eternity?

Colibri

10-10-2005, 04:54 PM

Yes, if time is infinite even one monkey will eventually produce Hamlet and every other work ever written. And as you mention, if the number of monkeys is infinite one of them will inevitably produce Hamlet in the amount of time it takes to type the number of characters in that work. (More precisely, as Chronos says, as either time or the number of monkeys approaches infinity, the probability of Hamlet being produced approaches 1.)

I am fascinated by the idea small clanger came up with- what if the monkeys simply started typing numbers for all infinity? Or ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ? (I guess if he fell asleep at the typewriter ). Or as someone else said, just typing gibberish into eternity?

If this is the case, then they are not typing randomly, which is one of the assumptions.

andrewdt85

10-10-2005, 04:56 PM

People my age may remember what were quaintly referred to as "comedy records," which recorded for posterity the comedy routines of many performers. On one of these, Bob Newhart portrayed a technician in one of those labs of monkeys at typewriters. He said, as I remember, " Uh, I think we might have something over here on number 456. It...it says...'To be or not to be. That is the gazornenbladt'." It tickled me then. Tickles me now

Just for fun, here's what my Monkey Shakespeare program window (http://user.tninet.se/~ecf599g/aardasnails/java/Monkey/webpages/index.html) has produced so far!:

The best five at this point are 30 letters from Coriolanus, and 30 more from Coriolanus, 30 from Pericles, 30 from the Second Part of King Henry IV, and 30 from Julius Caesar. The first one, for instance, happened 2.76004e+55 years into the session, when there were 1.23986e+53 monkeys that had typed 4.35501e+59 pages of gibberish. Here's that example:

1. Citizen. Before we proceed W zKrSjrjJXF(x)vdBrdFyhvuvC8zKf

which matches

1. Citizen. Before we proceed any further, heare me speake

from Coriolanus. Can you believe a monkey typed that? :D

And in terms of 'to be or not to be,' once a monkey even typed the beginning of King Henry VIII:

Prologue. I come no more

which matches

Prologue.

I come no more to make you laugh; things now
That bear a weighty and a serious brow,

Colibri

10-10-2005, 05:05 PM

Of course, remember in all this we a dealing with ideal monkeys, not real monkeys. An experimental test of the idea (http://www.wired.com/news/culture/0,1284,58790,00.html) did not turn out too well:

Give an infinite number of monkeys an infinite number of typewriters, the theory goes, and they will eventually produce prose the likes of Shakespeare.

Give six monkeys one computer for a month, and they will make a mess.

Researchers at Plymouth University in England reported this week that primates left alone with a computer attacked the machine and failed to produce a single word.

"They pressed a lot of S's," researcher Mike Phillips said Friday. "Obviously, English isn't their first language."

. . .

At first, said Phillips, "the lead male got a stone and started bashing the hell out of it.

"Another thing they were interested in was in defecating and urinating all over the keyboard," added Phillips, who runs the university's Institute of Digital Arts and Technologies.

Eventually, monkeys Elmo, Gum, Heather, Holly, Mistletoe and Rowan produced five pages of text, composed primarily of the letter S. Later, the letters A, J, L and M crept in.

Enderw24

10-10-2005, 05:36 PM

Given an infinite number of monkeys typing at an infinite number of keyboards, will we reproduce Shakespeare?

The World Wide Web has been around since 1993 and ARPAnet predating even this. In that time we seen the advent had instant messaging, message boards, chat rooms, profiles, dating sites, and personal blogs. We've all read through most of these.

So yeah...my vote is no.

alterego

10-10-2005, 07:43 PM

The text of Hamlet, except that Horatio is named "Elvis." :D

Randomness and infinity are very tricky concepts, and computers can't really do either.

Randomness can be accomplished by a peripheral most of us likely don't have at home - a hardware random number generator (http://en.wikipedia.org/wiki/Hardware_random_number_generator).

ccwaterback

10-10-2005, 10:20 PM

Mr. Jibby Jabbish

10-11-2005, 10:37 AM

I'm concerned about all of these monkeys in a corporate or academic setting. Will they be using the employee or student washrooms?

Small Clanger

10-11-2005, 11:02 AM

. . . hardware random number generator I was aware of these, every now and then ERNIE sends me £50 (I've not won any more than that, yet) National Savings (who run ERNIE) make the point that ERNIE is not a computer.

. . . as either time or the number of monkeys approaches infinity, the probability of Hamlet being produced approaches 1.OK. But if your resources are limited to a single Universe full of monkeys typing for the entire age of the Universe I'm guessing (I don't know where to start on the sums) that you'll still have a few typos in the sonnets.

alterego

10-11-2005, 11:31 AM

I was aware of these, every now and then ERNIE sends me £50 (I've not won any more than that, yet) National Savings (who run ERNIE) make the point that ERNIE is not a computer.

OK. But if your resources are limited to a single Universe full of monkeys typing for the entire age of the Universe I'm guessing (I don't know where to start on the sums) that you'll still have a few typos in the sonnets.

I don't know what ERNIE is but I said that it was a peripheral. Some of them, however, do preprocessing byte conversions - which is a computation. Aside from that, you wouldn't call your mouse a computer, but it is part of your computer (as it is known in the common sense - not sure where your point came from). But if you demand a hardware RNG be on a cpu, then I should point out that some intel chipsents have them onboard (http://www.intel.com/design/chipsets/manuals/298029.htm), so in your sense they can be computers. (Although they are perhaps not truly random, they could be).

Q.E.D.

10-11-2005, 11:42 AM

I don't know what ERNIE is but I said that it was a peripheral.
It's not a peripheral. It's a standalone unit which generates random numbers using the thermal noise which exists in semiconductor devices. It's not a cimputer in the sense that it's a nondeterministic device (the outcome of its output is not decided in advance by an algorithm), and it is not capable of being programmed to do anything else. It's as much a computer or a peripheral as a vacuum cleaner is.

Small Clanger

10-11-2005, 11:43 AM

alterego ERNIE (http://en.wikipedia.org/wiki/ERNIE) gets a mention in your link. It's the device that generates the winning premium-bond numbers. I was dimly aware that some chips did (or would soon have) hardware random number generators, so maybe computers can do random. They still can't do infinity.

Colibri

10-11-2005, 11:48 AM

OK. But if your resources are limited to a single Universe full of monkeys typing for the entire age of the Universe I'm guessing (I don't know where to start on the sums) that you'll still have a few typos in the sonnets.

Certainly the time available for the monkeys to type in the real Universe is not infinite, due to the build up of entropy.

chrisk

10-11-2005, 11:56 AM

Just checking in because I've found that textbook I referred to earlier in the thread. It talks about 'claude shannon' doing work on computerizing the monkeys and trying to make random output more english-like without specifically copying huge swaths of input text 'in the late 1940s'

The name given to the problem, which was what I was really looking for, is 'travesty' :)

Jonathan Chance

10-11-2005, 12:01 PM

I would think the supercomputers of the world are busy enough trying to predict the weather, and other more useful problems.

Besides, if they did prove or disprove the monkey-shakespeare conjecture, what good would it do? About all they could garner from the study is, "Hmm, that's cool".

But, really, isn't that a primary motivator of science?

And, just for laughs, here's my favorite statement on the issue. From Steve Goodman:

"The law of averages says anything will happen that can.
But the last time the Cubs won the National League pennant
Was the year we dropped the bomb on Japan."

Chronos

10-11-2005, 12:33 PM

They still can't do infinity.Sure they can, if they're programmed for it. Computer algebra systems like Maple will quite happily process computations involving infinity. I can take an integral from 0 to infinity, for example, or a limit as x goes to infinity, and I can even get infinity as a result of some of these calculations. Anything that humans can do according to a set of logical rules, computers can be programmed to do using those same logical rules. And humans can logically work with infinity, and so can computers.

alterego

10-11-2005, 04:43 PM

It's as much of a peripheral as your keyboard, your mouse, or an external hard drive. Let's check the common wisdom:

A peripheral is a type of computer hardware that is added to a host computer in order to expand its abilities.

Yep, that's a fit.

What about some of the definitions from a google search for define peripheral (http://www.google.com/search?q=define%3APeripheral)?

Any of the devices which connect to the CPU and exchange information under the CPU's control. Peripherals include all of the computer's input and output devices.
Fit.
Any accessory device attached to the computer[...]
Fit.
A peripheral (truncation of “peripheral device”) is any computer device that is not part of the essential computer (the processor, memory, and data paths) but is situated relatively close by.
Fit.
Any number of devices connected to a computer to provide input, output, or other functions.
Fit.
An electronic device that sends or receives data from a CPU.
Fit.
Any machinery connected to the computer[...]
Fit.
A device connected to a computer to provide communication (as input and output) or auxiliary functions (as additional storage)
Fit.
A device connected to a computer system
Fit.
Any device or piece of equipment that is attached to and used by a computer[...]
Fit.
Pertaining to an outer region
Fit.
Any device that connects to a computer through an input/output port.
Fit.
electronic equipment connected by cable to the CPU of a computer;
Fit.

Q.E.D.

10-11-2005, 04:51 PM

Yes, that's nice. And, you'd be absulutely right if ERNIE were connected to a computer. It is not.

alterego

10-11-2005, 06:49 PM

Yes, that's nice. And, you'd be absulutely right if ERNIE were connected to a computer. It is not.
If ERNIE is not connected to a computer, how do you suppose they get numbers out of it. Hmm.

Q.E.D.

10-11-2005, 07:04 PM

If ERNIE is not connected to a computer, how do you suppose they get numbers out of it. Hmm.
Yes, there's absolutely no way to get data out of a device without attaching it to a computer. It's a real pain in the ass when I want to program my VCR, since I have to lug my desktop PC and monitor over to the entertainment center. Too bad it can't display menus and stored programs, I dunno, right on the TV screen or something.

Oh, wait...

alterego

10-11-2005, 09:43 PM

You are putting your foot in your mouth.

when I want to program my VCR

Let's see if your VCR is a computer (google define:computer)

An electronic device for the storage and processing of information.

Yep.

a programmable machine that inputs, processes and outputs data

Most definitely.

an electronic device that stores, retrieves, and processes data, and can be programmed with instructions

Yuppers.

An "electronic device that accepts information in digital or similar form and manipulates it for a result based on a sequence of instructions."

Yop.

Q.E.D.

10-11-2005, 09:44 PM

Now you're just being silly.

Nanoda

10-11-2005, 10:32 PM

Now you're just being silly.
In that case, lets all retire to our mp3 players, and listen about what can be done with a large, but finite number of monkeys (http://www.ampcast.com/music/22488/artist.php) (~1/2 way down).

Hypnagogic Jerk

10-11-2005, 11:16 PM

Kozmik

10-12-2005, 12:55 AM

Besides, if they did prove or disprove the monkey-shakespeare conjecture, what good would it do? About all they could garner from the study is, "Hmm, that's cool". Think about it. Shakespeare wrote many of the greatest plays of all time. What does it say that those same plays could independently be created by an unintelligent agent?

If the complete works of Shakespeare can be randomly generated after that famous author died, then a book could be randomly generated before an author is born.

Supposing that the existence of mankind is infinite, then we ought to invest all our computer resources in randomly generating text so that future man will never ever have to write another book again.

Enderw24

10-12-2005, 11:29 AM

Here's Wikipedia on the Infinite Monkey Theorem (http://en.wikipedia.org/wiki/Infinite_monkey_theorem). Do note, though, that what it actually says is that every infinite string of characters with each character chosen uniformly at random will almost surely contain every possible substring, including the integrality of Shakespeare's works. An event that happens almost surely (the probability theoretic equivalent of measure theory's almost everywhere) will happen with probability 1, but you cannot say for sure that it is what happens. For example, if I do the monkey and hit on my keyboard at random an infinite number of times, I could only hit the letter 'a'. The probability of me doing this is 0, but it could happen.

Well here's an interesting thought. If you have an infinite string of characters created entirely at random it must, as you say, contain within it every possible configuration or substring.
One possible substring is the letter A strung together an infinite number of times. The liklihood of having a large number of As all in a row approaches zero the more we tack on to the string, but since no matter how small the probability is it is not equal to zero, then it must occur at some point as the entire string continues on towards infinity.

Given that, where on the string is there room for other characters if there's already an infinite number of As?
I understand that there can actually be different levels of infinity. I just said it was an interesting thought.

Hypnagogic Jerk

10-12-2005, 01:32 PM

Well here's an interesting thought. If you have an infinite string of characters created entirely at random it must, as you say, contain within it every possible configuration or substring.
No it must not. If I have an infinite string of characters, each of them chosen through an uniform distribution, and then choose a finite string of characters, I will find that it will appear as a substring in my infinite string with probability 1. But this doesn't mean that it will actually appear. We are used to believe that an event that happens with probability 1 certainly occurs, but it isn't true when dealing with infinite probability spaces.

One possible substring is the letter A strung together an infinite number of times. The liklihood of having a large number of As all in a row approaches zero the more we tack on to the string, but since no matter how small the probability is it is not equal to zero, then it must occur at some point as the entire string continues on towards infinity.
You're on the right track, but that's not exactly it. If you take a finite string of characters (say of length n, and suppose for the sake of simplicity that the only possible characters are the lowercase letters), with each one chosen uniformly, the probability that your string will consist only of the letter 'a' is 1/26^n. But if you now take an infinite string of characters, the probability that it will consist of only the letter 'a' will be exactly 0. Again, that doesn't mean that it is impossible, it only means that it will almost surely not occur.

alterego

10-12-2005, 02:16 PM

No it must not. If I have an infinite string of characters, each of them chosen through an uniform distribution, and then choose a finite string of characters, I will find that it will appear as a substring in my infinite string with probability 1. But this doesn't mean that it will actually appear. We are used to believe that an event that happens with probability 1 certainly occurs, but it isn't true when dealing with infinite probability spaces.

You're on the right track, but that's not exactly it. If you take a finite string of characters (say of length n, and suppose for the sake of simplicity that the only possible characters are the lowercase letters), with each one chosen uniformly, the probability that your string will consist only of the letter 'a' is 1/26^n. But if you now take an infinite string of characters, the probability that it will consist of only the letter 'a' will be exactly 0. Again, that doesn't mean that it is impossible, it only means that it will almost surely not occur.
I'm not a math guy, but isn't it true that infinity is not a number, it is a concept? If so, then would it be accurate to simply say that as n increases it approches 0?

Hypnagogic Jerk

10-12-2005, 03:27 PM

I'm not a math guy, but isn't it true that infinity is not a number, it is a concept? If so, then would it be accurate to simply say that as n increases it approches 0?
Infinity is indeed not a number (at least when working with standard definitions of the numbers). On the other hand, it is completely valid mathematically to work with an infinite string of characters. Such an object doesn't exist in the real world, but in the mathematical world, there's nothing contradictory about it. Yes, the probability that a finite string of length n will consist only of the letter 'a' (given the assumptions in my previous posts) will converge to 0 as n increases. But when working with an actual infinite string, the probability is exactly 0.

Mr2001

10-12-2005, 09:07 PM

Why bother with all this randomness? Just program the computer to produce every possible byte, then every possible 2-byte stream, then every possible 3-byte stream, and so on.

If you leave it running long enough, it will eventually produce:

The text of every book or article that has ever been written, or ever will be written, which of course includes Shakespeare's plays, every compilation of Shakespeare that was ever made, and every written work that quotes or refers to Shakespeare.
Every movie that has ever been made, or ever will be made, in MPEG 1 and 2, DivX, QuickTime, and every other digital video format that ever has or will be invented.
Every song that has ever been recorded, or ever will be recorded, in MP3, Ogg Vorbis, WMA, AAC (both with and without encryption for every person who ever has or ever will sign up for the iTunes Music Store), FLAC, WAV, and any other music format that ever has been or will be invented.
A perfect image of every CD or DVD that has ever been made, in ISO, BIN/CUE, and NRG formats, along with cover art in JPEG, PNG, and any other image format that ever has been or will be invented.
Every computer program, console game, and firmware that has ever been or will be made for every computer, game console, or embedded system.

Incidentally, this should make us carefully consider what it means when we talk about creating an intellectual work like a song or a program. Every track on a CD is just a very long number, and feeding that number into a CD player would produce the same sound whether or not a human being was ever around to work on it. All humans can do is speed up the process of finding the "right" numbers.

Otanx

10-12-2005, 10:30 PM

I think I saw it mentioned once, but if you have an infinite number of monkeys how do you monitor what they are producing? Well we have an answer for you.

The Infinite Monkey Protocol Suite (IMPS) (http://www.faqs.org/rfcs/rfc2795.html)

Yep someone took the time to come up with a scaleable protocol suite to manage the problem.

-Otanx

alterego

10-12-2005, 10:40 PM

Infinity is indeed not a number (at least when working with standard definitions of the numbers). On the other hand, it is completely valid mathematically to work with an infinite string of characters. Such an object doesn't exist in the real world, but in the mathematical world, there's nothing contradictory about it. Yes, the probability that a finite string of length n will consist only of the letter 'a' (given the assumptions in my previous posts) will converge to 0 as n increases. But when working with an actual infinite string, the probability is exactly 0.

Is there any propositional logic behind this?

alterego

10-12-2005, 10:43 PM

To clarify, I mean specifically the statement that, "when working with an actual infinite string, the probability is exactly 0".

Hypnagogic Jerk

10-13-2005, 12:11 AM

Here is a proof that if you have a uniform distribution over the set of all infinite strings of lowercase letters (or any set of characters), then the probability of choosing any one of them is exactly 0. It does require some basic knowledge of measure theory.

Note the set of all infinite strings of lowercase letters by S. S is an infinite set, indeed an uncountable set (easily proven with Cantor's diagonal argument, see here (http://en.wikipedia.org/wiki/Cantor's_diagonal_argument) or here (http://planetmath.org/encyclopedia/CantorsDiagonalArgument.html)). Consider a uniform distribution on S (that is, consider the act of choosing an element of S completely at random with each element having the same probability of appearing than any other one). Assume that the probability of an element of S appearing is not 0. Say it is equal to e > 0. Probabilities are countably additive, that is, if I take the union of a finite or countably infinite number of disjoint events, then its probability will be the sum of the probabilities of each event. Take any countably infinite subset of S, say T. The probability that we pick a string found in T will be equal to the sum over all elements of T of the probability that this particular element appears, that is, it will be equal to sum(e, n=1..infinity). But this equals infinity, which is a contradiction since the probability of choosing any string in S must be 1 and therefore the probability of choosing any string in T must be less than or equal to 1. Therefore, our assumption is incorrect: the probability of an element of S appearing must be equal to 0.