Why the infinite monkeys with the infinite typewriters wouldnt end up writing a Shakespeare play.
In: Mathematics
* The idea is that because they have infinite time, they will eventually type every possible combination of every symbol on the type writer.
* One such combination of symbols is a Shakespeare play.
* Another such combination of symbols is a Shakespeare play but everyone is a frog.
They would, given infinite time.
Each monkey has a probability to write something, lets say each letter has a ~4% probability to be written at a given moment.
That means a combination of letters has a lower probability (think of 4% for the first letter and 4% for the second etc) that means for example an 0.16% probability for the combination ‘aa’ or any 2 letter comb.
With more complex combinations the probability approached 0, but never fully reaches it.
Infinite time and tries means that even an event that is highly unlikely is bound to happen sometime, because it has infinitely many chances.
The chance that they write Shakespear in 1000000 keystrokes is not zero. Statistically, repeating an experiment that has nonzero probability inifinitely often will essentially guarantee that it succeeds eventually, regardless of how small that probability is.
Because of probabilities. There is 44 keys on a typewriter, so there is 1 chance out of 44 that a monkey will press the first letter of Shakespeare. Then there is another 1 chance out of 44 that the monkey will press the second letter of Shakespeare and this keep going making the probability of the monkey pressing all the right keys in the right order. Of course, the probability of that happening rapidly become ridiculously low to the point of impossibility.
But it doesn’t matter that in reality the probability is so low that it would be practically impossible for that to happen, because if you have an infinite amount of monkey typing it’s gonna happen at some point. That’s what infinity is, if there is a probability of something happening, even if that probability is low, if you have infinite try, it’s gonna happen eventually.
Of course in reality we don’t have an infinity of monkey, so that just a funny little story to show you how probability and infinity work.
it’s a thought experiment, it’s not describing anything real people would do.
given infinite time, all things that are possible will eventually happen.
there’s actually a site to demonstrate, [library of babel.](https://libraryofbabel.info) it uses a single seed to pseudo-randomly generate books (that is, while the books it generates are essentially random, everyone will get the same set of books because they use the same seed.
you type in a phrase you want to look for, and it runs the generator until it finds that phrase. it will find that phrase. pages are 3200 characters long and every possible combination of up to 3200 characters exists inside that infinitely long random string. for example, [see here](https://libraryofbabel.info/bookmark.cgi?l_pndf243). look in the middle
In fact, you don’t even need an infinite amount of monkeys, just a sufficiently large amount. Based on numbers that others have given, (44 keys on the keyboard, 30,000 words in Hamlet), you would only need around 10^296,000 monkeys.
**Math!**
30,000 words -> 180,000 characters (say, an average of 5 letters per word + a space. Occasional punctuation doesn’t increase this number very much)
Since each monkey has 1/44 odds of hitting the right key per stroke, (1/44)^(180,000) equals about 1 : 10^296,000 odds for a monkey to actually do it. Thus 10^296,000 monkeys make a pretty good chance of one randomly doing it after 180,000 keystrokes.
You can fiddle with the numbers to get a more accurate number (or allow more keystrokes to use fewer monkeys), but it’s already so spectacularly huge that it’s probably not going to move it much.
Okay, people have answered this question already, but I just wanted to use this to illustrate a cool example of the law of large numbers, which suggests that the more trials you run and the more data you accumulate, the closer you get to the average.
The average number of letters in an English word is 4.5 letters.
Hamlet has 132,680 letters, split into 29,551 words
132680/29551=4.489 letters per word. That’s a deviation of about 0.25% from the average.
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