No, that’s not guaranteed. The set of possible outcomes is the set of all countably-long strings on the alphabet of typewriter symbols. @@@@@@… is one of those, and there’s no Shakespeare anywhere in there.
Note that the number of monkeys makes no difference in this case.
[Letterman]
I think we can all agree, that if an infinite number of monkeys were to type for an infinite length of time, the smell would be unbearable.
[/Letterman]
Thank you Mr Ekers, you are a gentleman and a scholar
Bob Newhart, on his live-performance-recording album The Button-Down Mind Strikes Back, tells a joke story about what would happen if you really did try to conduct an experiment with an infinite number of monkeys and in infinite number of typewriters. To actually check to see if they’d produced the works of Shakespeare yet, there’d have to be an infinite number of people hired to proofread the monkeys’ work:
“Harry, hold on, post fifteen here has something. I think this is famous or something. Uh … ‘To be or not to be, that is thegzornenplat.’”
I always thought it was 7000 monkeys for 7000 years, but now I have no idea why I thought that.
When considering infinite monkeys and/or infinite time, doesn’t the maxim of “all things that can happen must happen” come into play?
Yes, you’re right. The infinite number of sequences of non-Shakespeare (like the @@@…) can fill out the infinite amount of time. Damn, those monkeys can be wasting an awful lot of energy for nothing!
So… should I strap the monkeys in… and force them to sit at the typewriter?
what if they had predictive text style word processors…
also, does the world produce an infinite amount of Banana’s?
I can see this is going to be an expensive undertaking…
One question… has anyone thought maybe this experiment has been done already - - the evidence is there before us…
when reading Shakespeare - - most of it is gibberish - -
I just realized the Amazing Stories I was thinking of was actually a houseplant grown by the light of a TV that began to type up successful TV comedy scripts.
Monkeys…what was I thinking.
That article is incorrect because it makes the assumption that an event with probability 0 can’t happen (or more formally, that a set of measure 0 is necessarily empty).
For what it’s worth, it’s Asimov, but I don’t remember the title.
The Monkey’s Fingers.
Paraphrasing a Usenet .sig file…
“Come to think of it, we already do have a million monkeys at a million typewriters, and Usenet is nothing like Shakespeare.”
I hope no one considers me adding to noise rather than the signal. I recall a short story featured in one of those Dozois edited “Year’s Best” anthologies. A man writes a program that he names after the concept of a million monkeys at a million typewriters. As the story progresses he starts getting interesting results as he improves the program. He realizes with regular computers he can not achieve true randomness, just an illusion of randomness no matter how well he seeds it so he starts using data acquired from supercolliders and radio telescopes, using their background noise for true randomness. Towards the end he discovers old conversations he had while he was a child, things said and yet to be said or written. Sadly I do not recall the title or the author.
Given an Infinite amout of time, in our Universe, an infinite number of “Things” can happen.
I think.
Well, at least I happened!
Not so. This reminds me of a conversation I once had with a friend of mine when we were in fourth grade, while waiting for the bus one day.*
Roland: Let’s play a game. You pick a number, then I’ll pick a number, and we’ll see whose is higher.
Friend: Okay. Apple.
R: …what?
F: Apple.
R: “Apple” isn’t a number.
F: Yes it is. If there’s infinite numbers, then eventually there’s got to be one called “apple”.
R: (thinks about this for a minute) No, I think that’s still wrong.
F: Well, what’s a thousand times a million?
R: A billion.
F: What’s a thousand times that?
R: A trillion.
F: What’s a thousand times that?
R: …I dunno, I think it has a name though…
F: See, you run out of names after a while, and if there’s infinite numbers, you have to go through every name.
R: (thinks about this for a minute) No…that’s still wrong. Ok, what if we call a million times a million a “megamillion”. [I didn’t know what a trillion was, but I knew what the metric prefix ‘mega-’ meant. I was a weird kid.]
F: Okay.
R: Now, what if we called a million times that a “mega-megamillion”. And a million times that is a “mega-mega-megamillion”.
F: Okay.
R: So, from there you can go as long as you want, and just keep adding “megas” to it. You’ll still have infinite numbers, but you’ll never get anything called “apple”.
F: (thinks about this for a minute) Yeah, I guess…
(We stand in silence until the bus comes)
It’s the same thing with the monkeys and the typewriters. Even if the keypresses are completely random – and we have not-insignificant reason to believe that they wouldn’t be – it’s possible that you could still end up with a series of infinite 'K’s (with a nod to kevsnyde). Not bloody likely; indeed, exponentially less likely even than the works of Shakespeare, but possible nonetheless. It is possible to have an infinite string of random characters and not wind up with Hamlet, just as it is possible to have an infinite number of named entities (e.g. numbers) and never end up with one named “apple”.
*Yes, this conversation actually happened, and yes, we were in fourth grade. I promise. We were, and are, complete and utter dorks.
Er, a quadrillion, that is. Meaning that I couldn’t answer my friends question of “what’s a thousand times a trillion”. Just wanted to avoid confusion.
Surely a series of "k"s is just as likely as Shakespeare, assuming that each letter struck is independent of the one struck before it (in the same way that a series of coin tosses HHHHHHHHHH is just as likely as HTHTHTHT and HTHHHTHTTT)
For a string of "k"s containing the same number of characters as the relevant portion of Shakespeare, certainly. I was referring to the likelihood of a “k” series of indeterminate length, presumably greater than the length of Shakespeare’s texts, that would at any point of reference seem to continue indefinitely.
This gets around to the age old argument whether an infinite number of possibilities will guarantee all possibilities (it doesn’t). Lay folk who aren’t that familiar with probability and infinity find it counterintuitive.
Here’s a way to explain it:
Imagine the set of all counting numbers, {1, 2, 3, 4, 5…}
It’s a set with an infinite amount of members. Now take out the number ‘3,’ {1, 2, 4, 5…}. It still has an infinite amount of members, but it doesn’t have all possible members of the counting numbers set.
If an infinite amount of monkeys are forced to create random numbers, it’s a possibility that none of them will ever choose ‘3,’ even though you have an infinite amount of numbers created by those monkeys – just like the counting number set minus the number 3. Infinite, but not containing every possibility.
Now, it becomes more likely, that as the number of monkeys or their time spent hitting random keys approaches infinity that 3 will be pop up in their number set. Though, it will never be guaranteed.
If 3 isn’t guaranteed to pop up in an infinite list of number, consider how much more likely that Hamlet will not pop up in an infinite number of random-keystroke manuscripts.
Peace.