Infinity

B

Bigtraine

Registered Member
I read an interesting question and i was wondering what you all thought about it.

Hypothetically, if a monkey were to type randomly on a typewriter for infinity, would at some point the complete, exact works of Shakespeare be typed?
 
Yes. Infinite time is a VERY long time. In this particular example, every conceivable text which could be produced on the typewriter <i>would</i> be produced eventually.
 
And who is going to feed the monkey during all this time? Better get a factory making paper, ribbons, typewriters and even trash baskets on the job, their going to need a lot of them.

Talk about a project for all time.

Oh, I forgot, welcome to sciforums, Bigtraine.
 
thanks for the welcome wet1

I agree with you James but I have heard people argue against it. I was hoping someone would offer a counter arguement that made some sense.
 
To me the odds would be extremely small that you would get such in any meaningful and reasonable time. Remember you are talking infinity here. So you basically come up with all things are possible however unlikely, as you can not rule out what chance will give you given enough time.
 
Here's an argument I just came up with:

Suppose your monkeys produced the complete text of <i>Hamlet</i> at some stage, somehow, except that they got one letter wrong somewhere (e.g. they typed "To be or not tx be..."). Given an infinite amount of time, having typed the whole thing at least once except for that one letter, what are the chances of typing the whole thing correctly? That one letter can only be replaced by about 100 other characters from your typewriter keyboard, and there would be an infinite time in which to repeat all the rest of the text and get that one letter right. Pretty high chance of doing it, given that they've done the whole thing before except for that letter, wouldn't you say?

Now suppose they had typed the whole thing except for two wrong letters. A similar argument shows that it is plausible that they could type the whole thing correctly given enough time. So, what if they typed the whole except for three letters? Four? Five? Ten? One thousand? Ten thousand?

Eventually, we ask the question: given that they haven't typed <i>any</i> of <i>Hamlet</i> yet, will they ever get it right? I'd say the answer is clearly "yes", since they have ample time to correct all their "mistakes".

How's that?
 
Butterfly collectors have been finding the alpabet on their wings for centuries.

My theory is that somewhere there is a butterfly with E=mc<sup>2</sup> on one wing and on the other wing is the formula to unite all four forces.

So I'd have to say yes.
 
Think about this:

If the universe is infinite there is another Earth with another you doing the exact same thing. In fact, there are an infinite number of you's!
 
Hmmm... I have heard his (and similar questions) before.
How about: if you were to write down the entire decimal code for the number pi (3,14159....) would there be a region in the code of exactly 245376328 executive times nuber 7, with a 2 in front and followed by a 9?
It's just too hard to imagine.
 
shrike:

That's not necessarily true. The processes which led to you being here now need not occur anywhere or anywhen else, even in an infinite universe.


Merlijn:

The answer to your question is no. It is quite possible that after a certain number of decimal places pi has a decimal pattern which looks like this:

...2456010010001000010000010000001....,

in which case a given pattern of the type you mentioned need never appear in pi, yet the decimal expansion would still never repeat.
 
I say no. How can an infinite amount of randomness produce a pattern? There can be no pattern, or it's not random.
 
Alpha,

The pattern in this case is one which <i>we</i> recognise after the event. It is in no way pre-destined or anything like that. To get to it, we'd have to wade through an infinite amount of text which had no discernable pattern.
 
Hmm, I think I see your point, but there is a flaw.
Since the sequence is infinite, there is an infinite number of combinations of characters that the monkey can type without ever typing anything meaningful to us. While it is possible it may type something that long that makes sense, it is (dare I say) infinitely unlikely.
 
Infinity, by definition, means that every possible permutation will occur - no matter how unlikely they are. Obviously, there is a possibility of the Monkey typing the works of Shakespeare by chance, even if the probabilty 1 in 1,000,000,000,000,000,000 (or whatever it is). So, given infinity, I dont see how the monkey could NOT type the works of Shakespeare.
 
Bigtraine ...

Aaaah ... maybe because someone ran out of bananas?

Welcome to Sciforums.

Take care ;)
 
<i>Since the sequence is infinite, there is an infinite number of combinations of characters that the monkey can type without ever typing anything meaningful to us.</i>

Yes, but for any finite section of that infinite sequence, such as one the length of <i>Hamlet</i>, there is only a finite number of possible texts the monkey could type. One of those is the text of <i>Hamlet</i>. The chances of typing that text by chance are very small, but since the monkey has an infinite number of "tries" at it, it is guaranteed to do it sooner or later, provided it is indeed typing completely randomly.
 
Infinity, by definition, means that every possible permutation will occur - no matter how unlikely they are.
Click to expand...
Wrong. Check the dictionary[/ul].
Yes, but for any finite section of that infinite sequence, such as one the length of Hamlet, there is only a finite number of possible texts the monkey could type.
Click to expand...
True.
One of those is the text of Hamlet.
Click to expand...
Not necessarily.
The chances of typing that text by chance are very small, but since the monkey has an infinite number of "tries" at it, it is guaranteed to do it sooner or later, provided it is indeed typing completely randomly.
Click to expand...
In an infinite sequence of random characters, there are an infinite number of finite sections you could check for Hamlet. Since the entire sequence is infinitely long, you could check an infinite number of finite sections and never find anything. If you try every possible section in order, you may never get to where the section is. If you try every section at random, you may never land on it, or you may land on part of it, but not all of it. The chance of it being typed out in full is infinitely small, and so is the chance of you finding it even if it is there.
 
alpha,

It must be there, somewhere. Finding it is a completely different issue.
 
Back to the original post, of course i think it is possible. Practically speaking, a monkey would not be typing for infinity et cetera, but how could it NOT be possible?
 
Hypothetically, if a monkey were to type randomly on a typewriter for infinity, would at some point the complete, exact works of Shakespeare be typed?


that was the question right? And it states, if A monkey. one. dearies. A monkey can't live forever.
Maybe if it were a whole bunch of monkies. but then wouldnt that screw up the probability.
 
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