Infinite monkeys on infinite typewriters...

[Marquis de Carabas]

I use zero.

 

[maatorc]

I'm going to go out on a limb here, and guess that your understanding of "present quantum thinking" is non-orthgonal from asking the aforementioned monkeys to choose random buzz words from a textbook on quantum mechanics. But feel free to prove me wrong...

Tez -
Your angle is quite right.
maatorc.

 

[Dave1001]

Let's say you have finite monkeys. How many monkeys would one need to have functionally sure odds that one of them would type out Hamlet? With correct spacing and punctuation? I think we can simplify this a bit to a probability problem involving all the characters of Hamlet randomly being assembled in the correct order, with enough independent random agents that that odds that none of them would type out Hamlet would only be one in a million. So, how many monkeys would we need?

Technically the question is how many monkey hours would we need. We can then divvy that up among monkeys as we determine is realistic. (1 monkey working for X hours is the same as X monkeys working for 1 hour. But either way the monkey hours needed would be X.)

 

[Paul C. Anagnostopoulos]

Paul I think I know that you know what I think about this , but I'll say it for anyone else: Science is not about empericism, verifying predictions, following some sort of "method" or any of that nonsense. Its about a desire and a quest for deeper understanding. And in that sense Fermi is spot on.

Absolutely. I was not supporting Popper with my observation. I daresay Popper was a postmodernist.

~~ Paul

 

[chriswl]

That's easy. Yes. Here's my question, how long would it take to get them? If you can't cut and paste fragmented copies between monkeys (which I think would be cheating), then I think you'd get your infinite copies in the shortest possible amount of time it would take a monkey to physically type out a Hamlet-length document. I'm guesstimating a day or two.

You would never get your copy of Hamlet. Monkey's are quite large. If you can pack 10 monkeys into a cubic meter then you could fit "only" 10^49 monkeys into each cubic lightyear of space. A sphere of radius 70 light years would contain 10^55 monkeys. Imagine yourself at the centre of such a sphere. Assuming you live for 70 years then for any monkeys outside that sphere you would not live long enough for them to send you their copies of Hamlet, given that they can only send them to you at the speed of light.

I'm guessing here, but I think 10^55 monkeys isn't nearly enough to have any kind of reasonable chance of generating Hamlet within a human lifetime.

 

[The Atheist]

How come nobody's mentioned the Infinite Improbability Drive?

 

[Dave1001]

You would never get your copy of Hamlet. Monkey's are quite large. If you can pack 10 monkeys into a cubic meter then you could fit "only" 10^49 monkeys into each cubic lightyear of space. A sphere of radius 70 light years would contain 10^55 monkeys. Imagine yourself at the centre of such a sphere. Assuming you live for 70 years then for any monkeys outside that sphere you would not live long enough for them to send you their copies of Hamlet, given that they can only send them to you at the speed of light.

I'm guessing here, but I think 10^55 monkeys isn't nearly enough to have any kind of reasonable chance of generating Hamlet within a human lifetime.

Oh, you're introducing constraints that we didn't previously agree were relevant. Such as that I actually have to have my copy of hamlet in hand, rather than for it just to be generated. Let's start with the big question and then deal with whether or not it's realistic. How many random character sequence generator (RCSG) work minutes would it take to have only 1 in a million odds of not generating hamlet, if the RCSG produced 60 characters per minute?

 

[brodski]

I daresay Popper was a postmodernist.

~~ Paul

How did you come by that opinion? Popper argued that all interpretations of data (and reality) are not all equal, and provided a framework for discerning useful information from useless. You may disagree with that framework, but it's pretty far from postmodernism.

 

[Oleron]

The question is, given a long enough time, would the monkeys eventually reproduce every book ever written?

What about every book ever going to be written?

If so, can someone please build a quantum supercomputer and get me a pdf of the next Terry Pratchett novel?

 

[Didaktylos]

Apropos of nothing at all - anybody else here ever read "Been a Long Long Time" by R.A.Lafferty?

 

[Brainache]

The question is, given a long enough time, would the monkeys eventually reproduce every book ever written?

What about every book ever going to be written?

If so, can someone please build a quantum supercomputer and get me a pdf of the next Terry Pratchett novel?

I think you would need some kind of L space transport device. A good old-fashioned second hand bookstore that just appears out of nowhere is the usual method I believe...

 

[Dave1001]

The question is, given a long enough time, would the monkeys eventually reproduce every book ever written?

What about every book ever going to be written?

If so, can someone please build a quantum supercomputer and get me a pdf of the next Terry Pratchett novel?

I think that has answered already a few times in the thread, and the answer is yes. It's the nature of infinity, which is "a long enough time".

 

[JamesDillon]

The sad part of the whole thing is, think of all the achingly beautiful books that will never be written, because we just don't have enough monkeys.

 

[Dave1001]

Okay, I did my back-of-the envelope calculations. I think it would take a little less than 10^346,938 monkeys to be sure to type out Hamlet, giving them each the amount of time necessary to type out a Hamlet length document (about 48 monkey work hours). Overall, it would take a little less than 10^346,937 monkey work years to accomplish this, in any # of monkeys/amount of time combination that you'd like.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++
Calculations and reference links below:

Characters in Hamlet: 173,467*
Numbers of characters to choose from for typing monkeys: 97**

So, how do we calculate the number of ways to arrange 97 characters into a string 173,467 characters long? I think it's just 97^173,467 power.

In other words, the first time a monkey typed out a 173,467 long document, it would have a 1/(97^173,467) chance of being Hamlet. To make it so that there's only 1 in a million chance the monkeys won't type out hamlet (a functional sure thing*** that that they will type out hamlet) I think I would need (97^173,467)x999,999 monkeys to make it a functionally sure thing that one of them would type out Hamlet in the length of time it takes each of them to type out a Hamlet length document.

If I round 97 up to 100 and 999,999 to 1,000,000, that means I would need less than (100^173,467)x1,000,000 = ((10^2)^173,467)x(10^6) = (10^346,932)x(10^6)=10^346,938.

So I'd need something less than 10^346,938 monkeys to each type a hamlet length document to have functionally sure odds that one would type Hamlet.

Now if a monkey on average types one characters per second, it would take a monkey 173,467 seconds, or 48.1853, or a little less than 10^1.7 monkey work hours to type out one hamlet length document. Overall, the number of monkey work hours necessary to have functionally sure odds of typing out Hamlet are (10^346,938)x(10^1.7) or 10^346,939.7, or less than 10^346,940. There are more than 10^3 hours in a year, so it would take less than 10^346,937 monkey work years to have functionally sure odds of typing out Hamlet.



*as calculated by MS Word 2003, copied from this website: http://www-tech.mit.edu/Shakespeare/hamlet/full.html)
**I counted any character alterable by the shift key as 2 characters, and tab, spacebar, and return as one character
*** 1 in a million odds of adverse outcome is considered negligible risk according to website such as this one: http://www.hc-sc.gc.ca/ewh-semt/pubs/radiation/98ehd-dhm216/management-gestion_e.html
An illustrative quote from it:
"the concept of negligible lifetime risk at one in a million (10-6) was often applied, predominantly in the U.S. [Kelly and Cardon 1994]."

 

[Tricky]

Who the hell uses typewriters any more? This raises a question as to whether this old canard needs to be updated. After all, modern word processing programs have all sorts of spell checks and things that would greatly reduce the number of attempts that it would require to get "Hamlet". I mean, if it was all correct except "Alas poor Yorick, I kenw him Horatio", then the word processors would fix that. So we would only need ∞/2 or maybe even ∞/10 monkeys with computers. I regard this as a legitimate scientific breakthrough.

 

[Dave1001]

Who the hell uses typewriters any more? This raises a question as to whether this old canard needs to be updated. After all, modern word processing programs have all sorts of spell checks and things that would greatly reduce the number of attempts that it would require to get "Hamlet". I mean, if it was all correct except "Alas poor Yorick, I kenw him Horatio", then the word processors would fix that. So we would only need ∞/2 or maybe even ∞/10 monkeys with computers. I regard this as a legitimate scientific breakthrough.

eh, first of all you don't need infinite monkeys to write hamlet using monkeys.

 

[andyandy]

eh, first of all you don't need infinite monkeys to write hamlet using monkeys.

i think it was a joke

 

[Dave1001]

i think it was a joke

Well, as currently written, I can't say that it's funny because it's true.

 

[AmateurScientist]

You would never get your copy of Hamlet.

Well, using real monkeys, as opposed to theoretical monkeys as in the thought experiment, I suspect you may be right, but for a different reason from the one you gave.

Although the thought experiment is intended to illustrate how anything is possible given enough time and opportunity to experiment, and also the incomprehensibility of infinity, someone once pointed out a practical problem here. I may be mistaken, but I have a recollection of seeing some researcher with animals on television who took several laboratory chimps (I think that's what the thought experiment usually actually contemplates anyway) and placed them in a room full of typewriters, and showed them how to hit the keys by simply doing it himself for a while (monkey see, monkey do).

After so many trials, he examined the papers from the typewriters used by the chimps. One key observation he made is that rather than striking the keys at random, as the thought experiment suggests would happen, the chimps showed strong biases/preferences towards hitting certain keys and/or combinations of keys in succession. There were several keys they simply never struck in the experiment (I suspect those keys were on the periphery, as the chimps seemed to favor heavily the keys in the middle of the keyboard, such as "f," "g," "h," and "j").

The point here is that the chimps are not randomized machines. They're living, breathing creatures of habit and preference, as we humans are. If that is in fact true, then a computer running a program to randomly select letters and punctuation found on keyboards and string them together randomly might actually fare better than chimps in eventually producing Shakespeare's works -- that is, unless you could successfully explain to the chimps that they are to strike all the keys with roughly the same frequency, and they would actually comply.

AS

 

[Dave1001]

Well, using real monkeys, as opposed to theoretical monkeys as in the thought experiment, I suspect you may be right, but for a different reason from the one you gave.

Although the thought experiment is intended to illustrate how anything is possible given enough time and opportunity to experiment, and also the incomprehensibility of infinity, someone once pointed out a practical problem here. I may be mistaken, but I have a recollection of seeing some researcher with animals on television who took several laboratory chimps (I think that's what the thought experiment usually actually contemplates anyway) and placed them in a room full of typewriters, and showed them how to hit the keys by simply doing it himself for a while (monkey see, monkey do).

After so many trials, he examined the papers from the typewriters used by the chimps. One key observation he made is that rather than striking the keys at random, as the thought experiment suggests would happen, the chimps showed strong biases/preferences towards hitting certain keys and/or combinations of keys in succession. There were several keys they simply never struck in the experiment (I suspect those keys were on the periphery, as the chimps seemed to favor heavily the keys in the middle of the keyboard, such as "f," "g," "h," and "j").

AS

That wouldn't make it impossible, it would just mean that that many more monkey work hours would be needed. Although if there are some typing keys that monkeys will never, ever hit (something I doubt) and those keys produced necessary characters for hamlet, then yup, that would make it impossible.