The Infinite Monkey Theorem

[Wikipedia]

The Infinite Monkey Theorem states that having an infinite amount of monkeys randomly typing on a typewriter for an infinite amount of time will eventually produce one of Shakespeare's plays or any other pre-chosen literature.

My source for this information is;
http://en.wikipedia.org/wiki/Infinitely_many_monkeys_(probability_theory)

The math for it is actually very simple.

Direct proof
The infinite monkey theorem is straightforward to prove. If two events are statistically independent, meaning neither affects the outcome of the other, then the probability of both happening equals the product of the probabilities of each one happening on its own. For example, if the chance of rain in Sydney on a particular day is 0.3 and the chance of an earthquake in San Francisco on that day is 0.008, the chance of both happening on that same day is 0.3 × 0.008 = 0.0024.
Suppose the typewriter has 50 keys, and the word to be typed is "banana". Typing at random, the chance that the first letter typed is b is 1/50, as is the chance that the second letter typed is a, and so on. These events are independent, so the chance of the first six letters matching banana is
(1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50)6.
For the same reason, the chance that the next 6 letters match banana is also (1/50)6, and so on.
From the above, the chance of not typing banana in a given block of 6 letters is 1 ? (1/50)6. Because each block is typed independently, the chance Xn of not typing banana in any of the first n blocks of 6 letters is

As n grows, Xn gets smaller. For an n of a million, Xn is 99.99%, but for an n of 10 billion Xn is 53% and for an n of 100 billion it is 0.17%. As n approaches infinity, the probability Xn approaches zero; that is, by making n large enough, Xn can be made as small as one likes.[1]
The same argument shows why infinitely many monkeys will (almost surely) produce a text as quickly as it would be produced by a perfectly accurate human typist copying it from the original. In this case Xn = (1 ? (1/50)6)n where Xn represents the probability that none of the first n monkeys types banana correctly on their first try. When we consider 100 billion monkeys, the probability falls to 0.17%, and as the number of monkeys n increases to infinity the value of Xn — the probability of the monkeys failing to reproduce the given text — decreases to zero. This is equivalent to stating that the probability that one or more of an infinite number of monkeys will produce a given text on the first try is 100%, or that it is almost certain they will do so.

I don't know why but I thoroughly enjoy this theory, although not my favorite, it is still enjoyable to think about. My mind cannot simply comprehend a monkey typing out the complete text of Macbeth but the math is simple to support this event.

Discuss this and any other theorems. Please, avoid the absurdly controversial ones, we wouldn't want this getting ugly. I think you know what I'm talking about.

 

[Dodongo]

It would be better too because of all the smeared feces on the paper.

 

[commonyoshi]

"How big of a monkey?"

Simpsons did it.

Edit: I think you're really an adbot sent by Wiki or some other Organization for Learning to dupe us into learning over Spring Break. Shame on you.

 

[Mic_128]

More like hitchikers guide to the Galaxy did it. The monkeis tried giving Arthur the script when they got aboird the Heart of Gold.

 

[Wikipedia]

Although I cannot say I have read the Hitchiker's Guide to the Galaxy, I do know the The Infinite Monkey Theorem has been alluded to in a wide variety of literature.


Would an adbot do this?:

 

[Crimson King]

I knew I heard that before. Hitchhiker's Guide did it best.

I'm a bit suspicious of the name myself, but the IP check was clean. So no worries.

 

[Wikipedia]

Well that's a relief. Thanks, Crimson King.

Under the Yggdrasil, Eh? That was a good book.

 

[Jazzy Jinx]

It's a shame really. Though an infinte amount of monkeys can remake famous literature, an infinite amount of PRoomers would probably crap it up.

Edit: PM me, Wikipedia. I always wanted to challenge my wits against an anonymous source of information.

 

[Wikipedia]

I'd suggest reading books.

 

[Jazzy Jinx]

I'd suggest reading books.

Why read them when I can write them? Yes, I'm an aspiring writer.

But seriously, come down from your high horse, loosen up, and let's have a good ol' duel of wits. Nothing like solve the puzzle or whatever. It's more of an outsmart the other guy by making him look like a fool through brain power alone kind of thing.

Come on. It'll be fun.

Edit: You're only a year older. You are also a teenager.

This has nothing to do with pride or whatever. It's just for kicks. And besides, how do you benefit by registering to a message board? Money? Fame? I see none of this in your future should you stay here.

At least exercise your mind. I need some practice for my next DWYP round and I can't stand organized debates so I want to pick an excellent challenger for a one-on-one duel.

But if you truly believe yourself superior then forget about it. Challenging somebody cocky takes the fun out of the duel.

 

[Wikipedia]

And what would that accomplish? It's not like I'd recieve any feelings of pride or overwhelming happyness at the prospect of verbally destroying a teenager. The only other option is to be thoroughly defeated by a teenager in a battle of wits. It looks like I lose either way.

Oh, dear. Would you look at the time, time to get back on topic. I also happen to like the String Theory, which is some overly embellished theory that I wish not to go into any further.

 

[shadenexus18]

Shakespearean monkeys? Wow, that's news to me!

All I have to say is that primates rule and I'll leave it at that......for now. It's way to late for me to get in a debate.

Don't let any of that stop you though.

@Wikipedia, you really are somethin else! Moreover, it looks like you're takin your frustrations out on Kenny. C'mon, let mi casa be su casa. Be friendly rivals.

 

[Blackshadow]

You're not very nice Wikipedia >: (

 

[Scav]

Check it out, guys. I like Wikipedia.

 

[Crimson King]

Under the Yggdrasil, Eh? That was a good book.

WHAT was a good book?

 

[Dodongo]

House of Leaves maybe?

Spoiler

trees are cool

 

[Mic_128]

I always find it funny when people talk about CK's location, because asside from what it means, I always think of the Hero Overlord in Starcraft. In which case you really DON'T want to be under Yggdrasil.

 

[commonyoshi]

I think I've had Yggdrasil at a Jewish man's house before.

 

[Xsyven]

Yggdrasil is like, a giant tree in Norse mythology, and it represents the world or something.

Everyone lives under the Yggdrasil. I think. I just remember that it's a tree.

 

[Venom Dream]

So, the other day, I was reading Wikipedia's article on Angular Measure, and it told me that "The degree unit of angle uses k = 360/2π, making the angle of a full circle = 360 hitler hitler aids." Could you explain this concept to me, please?

 

[pikachun00b7]

This is only by chance. Couldn't the letters a-d-j-h(an example ) be typed by an infinite amount of monkeys an infinite amount of times(so its adjhadjhadjh and so on) though improbable.

 

[Eor]

Yggdrasil is like, a giant tree in Norse mythology, and it represents the world or something.

Everyone lives under the Yggdrasil. I think. I just remember that it's a tree.

Nah, Norse Mythology says we live in the middle of it, I believe. I remember that because supposedly, during Ragnarök, the only two humans to survive do so by climbing down the branches and drinking the dew that fell off the leafs.

 

[Xsyven]

Nah, Norse Mythology says we live in the middle of it, I believe. I remember that because supposedly, during Ragnarök, the only two humans to survive do so by climbing down the branches and drinking the dew that fell off the leafs.

Yeah, like I said, I just remembered that it was a tree. Nice use of an ö, though.

 

[Red Exodus]

I understand it, it's pretty simple. The probablity is 100% because 1 of those infinity monkeys can type out Shakespeare. Very interesting.

 

[cF=)]

What happen when you put an infinite number of typewritting machines on an infinite number of monkeys ? Do you get, bananas ?

 

[Ensee]

This theory is a bit strange, I want to see some proof that this can actually happen. =)
That would be an amazing feat for a monkey, no doubt.

 

[Eor]

This theory is a bit strange, I want to see some proof that this can actually happen. =)
That would be an amazing feat for a monkey, no doubt.

The proof is in the link.

The monkey part is only for humor. In reality, all that the theory states that if letters are chosen at random for infinity, one of those results would be exactly the same as a Shakespearian work.

 

[Virgilijus]

And so is the world of probability; crazy stuff could potentially happen all the time. For example, there is an almost infinitely small chance (so says the probability equations of quantum mechanics) that you could fall through the floor or have your hair instantly disappear.

 

[pikachun00b7]

The monkeys will just look at porn all day.

 

[Matt]

I knew I heard that before. Hitchhiker's Guide did it best.

I'm a bit suspicious of the name myself, but the IP check was clean. So no worries.

# Rhea 67.189.37.127
# Wikipedia 67.189.37.127

THAT'S clean?

 

[Xsyven]

# Rhea 67.189.37.127
# Wikipedia 67.189.37.127

THAT'S clean?

It's DUKE?! CRAZY MORMONS EVERYWHERE!



...Duke was Rhea, right?

 

[Dodongo]

# Gonorrhea 67.189.37.127
# Stickypenia 67.189.37.127

THAT'S clean?

Fi x'd

 

[Wikipedia]

This is weird.

 

[Dibs]

I always find it funny when people talk about CK's location, because asside from what it means, I always think of the Hero Overlord in Starcraft. In which case you really DON'T want to be under Yggdrasil.

I really thought it was talking about the hero overlord.

 

[Crimson King]

# Rhea 67.189.37.127
# Wikipedia 67.189.37.127

THAT'S clean?

In my defense, there was only one IP when I posted that and it was JUST for Wikipedia. I retract that now.

 

[#HBC | FrozeηFlame]

As awesome as Starcraft is, CK's location actually makes me think of Tales of Symphonia. Mithos Yggdrasil anyone?