Infinite monkeys on infinite typewriters...

[Brainache]

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]."

Back to work monkey boy!

 

[Dave1001]

Back to work monkey boy!

If ever a post deserved it.
Thanks, friend.

 

[fuelair]

I hypothesise that 2 monkeys working for 15 minutes could recreate the works of lifegazer if one of them was on break.

and the other was tripping.

 

[fuelair]

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.

Minor cavil: infinity divided by anything is still infinity so you have not changed the number of monkeys involved.

 

[Tricky]

Minor cavil: infinity divided by anything is still infinity so you have not changed the number of monkeys involved.

I know. That was the joke. The mathematical definition of infinity is a limit, not a number, and so cannot correctly be used in any algebraic expression.

I guess I need to use more smilies.

 

[Dave1001]

I know. That was the joke. The mathematical definition of infinity is a limit, not a number, and so cannot correctly be used in any algebraic expression.

I guess I need to use more smilies.

General joke aesthetics require some grounding in shared reality though. That's why using infinity to joke about a finite thing killed the joke for me.

 

[c4ts]

I think Stephen Colbert had the funniest and last word on this. Suprised he hasn't been quoted yet. His punchline was that it only takes a few monkeys working over a 3 day weekend -drunk- to hammer out a Dan Brown novel.

He gives Brown too much credit. A blind monkey on mescaline could do it in half the time.

 

[andyandy]

General joke aesthetics require some grounding in shared reality though. That's why using infinity to joke about a finite thing killed the joke for me.

Got to keep those jokes rigorous Tricky

 

[Beerina]

so, can the human mind ever hope to understand infinity? What role does infinity play in philosopy and theology?

And that's just the countably infinite monkeys.

The uncountably infinite ones, higher-aleph transfinite sets of 'em, gosh, what couldn't they accomplish?

 

[Dave1001]

Got to keep those jokes rigorous Tricky

 

[drkitten]

Isn't it true that if we actually had infinite monkeys working for an infinite amount of time, one of them would in fact be likely to produce Shakespeare? In fact, just my speculation, but if we had infinite monkeys working for just one day, wouldn't one of them be almost statistically certain to produce as much of Hamlet as their little monkey hands could type in that period of time?

Yes, and yes. In fact, if we had an infinite number of monkeys working for just one day, we would expect to see an infinite number of copies of "as much of Hamlet as their little monkey hands could type," along with every other work of English literature, even written or in potentia.

 

[Beerina]

Yes, and yes. In fact, if we had an infinite number of monkeys working for just one day, we would expect to see an infinite number of copies of "as much of Hamlet as their little monkey hands could type," along with every other work of English literature, even written or in potentia.

Well the problem then becomes how would you separate out the good stuff from the crap? For every Shakespeare-quality play that is unknown, there are countless googolplex ones that, halfway through, suddenly turn into gibberish, and far more than that that are gibberish end-to-end.

For every formula for the cure to cancer, endless formulae that are almost correct, except for that one little spot. For every AI program that works, a neverending stream of AI programs that seem they should work, but for that little addition sign that should be subtraction, or that constant which should be 37 higher than it is.

 

[drkitten]

Well the problem then becomes how would you separate out the good stuff from the crap?

Traditionally, that's the job of the slush pile reader at any large publishing house.

As Avenue Q put it, "What do you do with a B.A. in English?"

 

[robinson]

"...the Infinite-Monkey Theorem cannot be true — otherwise Usenet would have reproduced the entire canon of great literature by now."

lot of monkey stuff is here

 

[HeavyAaron]

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.

Calculational error. Let's simplify the problem to flipping a coin and getting heads at least once. How many times would you have to flip it to be at least 90% sure you'll get a head?

Your answer is 9. That's not true.

The odds of getting heads at least once for one flip is 1/2. For 2 flips is 3/4. For 3 flips is 7/8. For 4 flips is 15/16, which is at least 90%. So we'd need 4 flips.

Now just modify that reasoning for your problem.

Aaron

 

[Dave1001]

Calculational error. Let's simplify the problem to flipping a coin and getting heads at least once. How many times would you have to flip it to be at least 90% sure you'll get a head?

Your answer is 9. That's not true.

The odds of getting heads at least once for one flip is 1/2. For 2 flips is 3/4. For 3 flips is 7/8. For 4 flips is 15/16, which is at least 90%. So we'd need 4 flips.

Now just modify that reasoning for your problem.

Aaron

oh crap.