The monkeys are irrelevant.

The point being that randomness plus infinity means any pattern of things that has happened could happen again.

The plays are an arrangement of symbols in a certain order. They are possible, because there they are. We've seen them.

If there is a situation where these symbols are being randomly placed one after the other (like a monkey hitting the keyboard) then the pattern that someone has arranged on purpose can also arise by accident.

If I type the letter "A" with intention and a chimp hits the letter "A" by accident both produce the same result. Supposing a keyboard with only 30 keys, then the monkey would have a 1/30 chance of hitting the "A" key first. If I type "AB" the chimp has a 1/900 chance of doing the same. The longer the sentence the longer the odds (in true randomness). As long as it's possible it will happen. the chimps and typewriter sets up a situation that makes something that is naturally impossible (due to time scales) possible, by removing the time scale limitation.

With intention I can form sentences and meaning like you see here on the first try. But these sentences too are just a string of effects that are possible. The longer the string the less likely for a random set of key slaps to produce the same effect. But as it IS possible to produce this string of symbols by intent, it is also possible to produce them by accident through random generation. The chances just grow longer with the length of the writing.

The thing to realize here is that ANY string of symbols is exactly as unlikely as any other (if we are talking true randomness). These two strings of symbols exactly as unlikely to occur if generated by a random symbol generator.

The quick brown fox jumped over the lazy dog.
lilililililililililililililililililililililil

They are the same length, but one is arranged in a meaningful pattern and the other is not. This is how entropy works. Every pile of sand is a unique arrangement of particles. They all look the same to us, but each is unique and dumping the same pile of sand over and over again a zillion times produces the same likelihoods as "a chimp writing the works of Shakespeare". That is, one particular pile of sand is unlikely. But A pile of sand is certain.

We pay attention to the pile of symbols that mean something to us, but they are no less likely than any other pile of symbols that are generated randomly.

If you were looking for the complete works of "oops I sat on my keyboard for half an hour" you would have to wait as long for that to surface as you would for Shakespeare if it was the same length.

Murmur wrote: I just watched the video. I find it very unconvincing, but I'll just take their word for it.

Yes that's the video. Notice he calculates by subtracting a number series from the series we're interested in, twiddles a bit more, then states "which implies S = -1/12." Implies? That sure does not sound like a proof. Plus when he's asked what if you summed up all the integers up to a Googleplex (10 to the google power), he answers "You'd get a huge number."

How 'bout this conversation.
Me: I will pay you an infinite number of dollars for your car, waddya say?
You: Cool, let's do it now!
Me: Give me 9 cents.
You: What? OK, here you are, 9 cents.
Me: Great, now we're even, give me the car keys.
You: WTF?
Me: Yes indeed it has been implied that an infinite number of dollars = $- 1/12. 1/12 of a dollar = 8.3 cents. The negative part means you pay 8.3 cents to me, which you did. Done deal, now gimme the keys.
You: WTF? Get outta here before I call the cops!

BTW, I've seen other "proofs" showing infinity = 0, infinity = pi, and infinity = 5.

Murmur wrote:It's a thought experiment. It takes place in a make-believe universe that mirrors our own in very minor ways that we care about. I don't understand why it's necessary for me to explain this.

After rather enjoying the goofy discussion leading up to this, the final sentence above earned some kind of prize in my mind. Those who have actually had to think about infinity (which pretty much makes anyone's head hurt) have trouble grasping the process by which less-ripped minds bounce off it.

There are 10 kinds of people in the world: those who understand binary numbers and those who don't.

geo wrote:"Infinity" is a conceptual tool for thinking about the abstract. I don't think there's anything in the real world represented by infinity, unlike, say, "12" which we can see represented by a carton of eggs. That means the monkeys-on-typewriters thought experiment must be seen as an abstract idea only. Given enough time, really improbable things can happen. That's as far as it goes.

For every number we know, there's the instance of the number, then the abstraction of the number. Our abstract set of numbers includes many that we've never seen instances of.

Sometimes we can manipulate abstractions and say something about the world. But it's not a given. It still requires evidence. Einstein's manipulation of numbers related to the speed of light and quantifications of energy still required experiments and testing.

You can't simply manipulate numbers and take the result as proof of something novel about the world. I can manipulate numbers and confirm that a certain sized beam will support a certain amount of weight, but that is nothing novel. The manipulations have been tested and retested countless times.

I don't understand the fascination with -1/12, it's just playing with abstractions divorced from instance. Show me something real.

You people are making this far more complicated than necessary. Where the hell is Occam's Razor?

I think of this problem in far simpler terms (possibly because I'm simp... nevermind)

You have a machine that punches typewriter keys randomly. The machine needs to produce The Complete Works of William Shakespeare. The machine has an infinite amount of time in which to accomplish this. Therefore, they way I think, it's impossible for the machine not to accomplish this because the machine need never stop punching keys. If you have infinity to work with, all things that are possible, no matter how improbable, will occur. No?

P.S. I'm having a great time digging through these old threads.

My mind is perhaps too small to wrap around this hypothetical. I need to know whether the claim is that,at some point millions or billions of years from the present, we would see before us one of more volumes containing all of his works, every line and word in the correct place (and what about stage directions?), the sonnets appearing in the order that has come down to us, and so forth. Because only if these criteria are fulfilled would we have the works of Shakespeare.

Also, just as important, there could be no extraneous words.