# So, how long would it take the monkey to type out Hamlet?

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2. Dude. We can't assume the money will write this out in it's first try. That's ludicrous.

If you roll a dice, you have 1/6 chance of rolling a 1. If it's a perfectly fair dice, you can assume that within 6 rolls a 1 would have showed up at least once. Now it's not guaranteed, but it's probable. So you'd have to multiply the 1/6 chance by 6 to get a fair idea of how many times it would take before the monkey should have done it by that point. The monkey has 26^130,000 of typing hamlet.

There is a 33% of not getting a 1 on 6 rolls of a fair dice, which i don't think is close enough for this method to work.

I think what you guys need to figure out the expectation: what is the expected number of types until Hamlet is produced. I'm not sure how easy that would be though: i don't have time to look into it.

I just tried to do it and I realized I can't, which is a shame. I'm not sure how you factor time into the equation and get the expected time of the monkey's success.

It is the same as asking ''What is the expected amount of time it would take you to flip 5 heads in a row?'' only with higher figures. It seems simple, but I realize that I don't know how to solve it. Note that time refers to physical time and not the number of coin flips.

But factoring in time is the easy part. You just make assumptions as did Raider. Just estimate how long it would take a monkey to push a button (and whether you want to give them breaks etc).

I have run into this 95% certainty thing before in statistics. I have read that a 95% certainty in statistics is considered to be statistically sound and likewise, a 5% certainty unsound.

What is the significance of these numbers? Surely, this is just an arbitrary, generally agreed upon limit. There is no other significance of the number, right?

Right.

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It occurred to me that, because 10^184000 is so insanely large, my probability of 63% is somewhat misleading. For a 10% probability, it would also take 10^184000 seconds. Likewise for a 99.9% probability, is would take 10^184000 seconds. It would also take 10^184000 years, since there is no appreciable difference between 10^184000 seconds and 10^184000 years.

We lost all these distinctions when I rounded to 184000, or in fact when someone rounded to 130000 characters.

Some more fun with insanely big numbers: you could freely change the typing rate without changing the result significantly. If instead of a rate of one character per second, you only type once during the entire life expectancy of our universe, it would still take 10^184000 years (or microseconds, or universes, or whatever). On the other hand, if instead of monkeys, you use the fastest computer in existence and let it generate random characters as fast as it can, it would still take 10^184000 years.

10^184000 is so large that you could change it by a factor of one googol, and you wouldn't even notice.

Regardless of how stupid large this number is, infinity is still in another league. In an infinite amount of time, Hamlet would show up an infinite amount of times.

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10^184000 is so large .....

If you think that's large, try working out the time it would take for somebody to read all the stuff typed and confirm that one of them is indeed Hamlet.

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10^184000 is so large that you could change it by a factor of one googol, and you wouldn't even notice.

True.

Basically, it will happen. But it will take a long time.

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If you think that's large, try working out the time it would take for somebody to read all the stuff typed and confirm that one of them is indeed Hamlet.

Easy. It will take 10^184000 years.

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Easy. It will take 10^184000 years.

Brilliant lol

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This makes me think that you don't understand probability. The monkey, given an infinite amount of time will certainly (or almost certainly, as was correctly noted in another thread) produce every literary work ever made. We are trying to calculate the expected amount of time it would take.

Please do not post if you have nothing of value to contribute.

Sorry, crosspost. I will check your calculation, Raider.

Just because you disagree with my opinion you say I have nothing of value to contribute. And since I dismissed the Infinite Monkey problem as not being viable I have no grasp of Probability?

You sound like an arrogant ass. Are you?

It's like an apologist for astrology saying I don't understand astronomy or Cosmology if I don't think astrology is a valid science.

I don't think monkeys randomly typing can ever produce all the works of literature. You're forgetting, or maybe just don't know, the infinite thus prohibitive possible number of combinations they could talk out. And the fact that all of them but one would be wrong! After all, we are talking about monkeys typing, say, Hamlet in it's exact entirety, in it's exact verbatim order, right? Not just all the individual words used?

If we are, then I maintain the notion is an absurd one. Not science in any aspect. Nor is it mathematical. Why must I explain this here on a site like this? You need to educate yourself on past mini tests regarding the IM problem. Where hundreds of monkeys over weeks got nothing at all. Hardly a real words here and there. The difference between what they got and, say, even comprising a ten page children's story was skin to the difference between a two by four leaning on a walk and a newly constructed two story house.

There is a point via the method of extrapolation that even a limited text will discern whether or not something I'd possible, even if given eons of time and participants. To think monkeys only need time and numbers to recreate thousands of crafted literary works, verbatim, is magical thinking. Any way you slice it, and regardless of how you try to spin the aspects of probability.

Also. And to close...I'll post whenever and wherever I please. You'd do well to remember that and not try to tell to tell me what to do. Last I checked you were not a moderator.

Capisce?

Great.

Edited by Velocity_Boy

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Where hundreds of monkeys over weeks got nothing at all.

This is where you show that you don't understand it.

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You sound like an arrogant ass. Are you?

!

Moderator Note

You sound like you're tired of having an account here. Are you?

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Another reason this entire premise is flawed is that it does not accurately depict primate behavior. The Infinite Monkey Theorem just assumes that monkeys would sit behave and diligently type out random letters. Conveniently....Ignorantly?...Forgetting or not knowing that it is very likely they do nothing of the sort.

Rather, they would likely engage in money behavior. Breaking the typewriters, urinating on them, simply not cooperating and leaving their chair. Eating, playing with each other. They are also not random. They get more likely to be very deliberate and repetitive in their actions. Probably hitting no more than half the keys, ever.

And if you apologists for the validity of the IMT accuse me of being overly technical and literal and not understanding this whole thing is a metaphor for not monkeys but a random letter generator, than this must be stated at the outset of the thread. Either we are speaking of real monkeys or not. It has been assumed we are, from the posts I've read. So I am thus taking this real scenario a few steps further in its realistic probabilities.

After all, this whole thing allegedly deals with probability, right? And since we are on a science forum and this thread is not in the speculation section...Where it should be, imho...Then we need to apply all scientifically pertinent factors. Or, as the case may be here, all zoological factors.

Monkeys don't cooperate, amigos. How many of you have worked with them? Ever. I have. Trust me on this.

The IMT advocates cannot have it both ways. The thought experiment either is comprised of real monkeys if it is not. If the case is the former, my above claims from experience on their performance is a major factor in this whole case that merits consideration.

http://news.bbc.co.uk/2/hi/3013959.stm

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Another reason this entire premise is flawed is that it does not accurately depict primate behavior. The Infinite Monkey Theorem just assumes that monkeys would sit behave and diligently type out random letters. Conveniently....Ignorantly?...Forgetting or not knowing that it is very likely they do nothing of the sort.

Rather, they would likely engage in money behavior. Breaking the typewriters, urinating on them, simply not cooperating and leaving their chair. Eating, playing with each other. They are also not random. They get more likely to be very deliberate and repetitive in their actions. Probably hitting no more than half the keys, ever.

This misses the point very, very hard. Obviously, the monkeys are a metaphor for randomness.

And if you apologists for the validity of the IMT accuse me of being overly technical and literal and not understanding this whole thing is a metaphor for not monkeys but a random letter generator, than this must be stated at the outset of the thread.

This was immediately obvious to everyone else. I cannot fathom how you though I was describing a realistic scenario. If I was describing a realistic scenario, the monkey would not have infinite time at his disposal.

After all, this whole thing allegedly deals with probability, right? And since we are on a science forum and this thread is not in the speculation section...Where it should be, imho...Then we need to apply all scientifically pertinent factors. Or, as the case may be here, all zoological factors.

Allegedly? This IS probability and it belongs in mathematics as it is both universally accepted and shown to be correct. Your further comments or this are, to be polite, senseless.

If you feel like I am making a speculation in the mainstream forum or otherwise breaching the rules, please report it to the most. Do not taint the thread with ignorant comments. You have contributed absolutely nothing to the discussion.

Your comments about the monkeys not getting a result after weeks (!) of trying shows a tremendous lack of understanding of probability.

I do not appreciate your comments on me being an ass, especially because you are wrong.

And by the way, even if we were talking about real monkeys, this would hold true (if you can get past their infinite lives). Even an actual monkey would, after an unfathomably long time, reproduce Hamlet through the rules of randomness and infinite time. To say this is not a speculation, it is fact. You should not make further comments if you don't understand this.

/cut

I will read and reply to this tomorrow, as good quality posts should be replied and given attention to when completely sober.

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If the OP is about the odds of randomly writing Hamlet, is it reasonable to constrain the amount of possible writing space to that of Hamlet?

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...rant. ..

This the mathematics section. As I've shown, it perfectly possible to calculate the result in mathematics, even if the probability is inconceivably small.

It can be amusing to take such a premise litterally as a joke, but there is no point to keep ranting about it, even after it has redundantly been pointed out to you that the OP is not interested in being taken litterally.

Now, if the universe is infinitely large (or manyworlds interpretation is true, or there are an infinite number of universes), it contains an infinite amount of intelligent life forms who can conduct a similar experiment. If they can make it sufficiently random, in some of them, Hamlet will be produced on the first attempt. And by "some" I really mean an infinite amount of them.

Edited by Bender

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I have run into this 95% certainty thing before in statistics. I have read that a 95% certainty in statistics is considered to be statistically sound and likewise, a 5% certainty unsound.

What is the significance of these numbers? Surely, this is just an arbitrary, generally agreed upon limit. There is no other significance of the number, right?

I should add that with reason 95% is often chosen is that in a normal distribution it means that 95% of observations are within approximately 2 standard deviations of the mean. Still an arbitrary choice, but nice round(ish) numbers i guess.

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seems the answer to the OP question  of how long it would take is "a stupid large number of years

And being that we don't have a stupidly large number of years to play with, it seems the literal answer is "they won't"

Infinity is a device, not a number, so it can not be considered in the calculation.   Neither can infinite universes or the consideration of an infinite amount of attempts or an infinite amount of monkeys.   I think as soon as you put infinity in the equation your answer is by definition undefined.  Like dividing by zero.   Infinity is not a number, and can not take part in the literal calculation.

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On 4/24/2017 at 7:54 AM, Raider5678 said:

Oh. Math. Alright. Let's take a try at this.

Hamlet has approximately 130,000 letters in it. Not counting spaces. The average typing speed is 200 characters per minute. So if the money typed it perfectly, it would take about 650,000 minutes. Or 10,833.3 hours. Or 451.4 days. Or 64.5 weeks.

Now, the money has a 1/26 chance of typing the first letter of hamlet. For the second letter, it's 676. For the third, 17,576. All in consecutive order. So there's a 1/17,576 chance the monkey will type the first 3 words in order. 26^130,000 would be the probability of it typing out the whole hamlet story. Without spaces. That, is a really really large number.

Really large.

Now what ever chance that is, we have to multiply it until it's equal to 100%. Which would be by a factor, at minimum, of 1 octillion.

1 octillion is 1,000,000,000,000,000,000,000,000,000.

That's 27 zeros. The number we're looking for has 130,000. Either way, let's say its a really fast typing monkey, and could type all of hamlet in a year. If it's odds were 1/1,000,000,000,000000000,000,000,000, it would take 1 octillion years.

The universe is 13.772 billion years old.

You would need to take at least 72,000,000,000,000,000,000(72 quintillion) times as long as the age of the universe for the monkey to have a good probability of typing out hamlet.

NOW REMEMBER.

That is if it's odds are only 26^27

The real odds are 26^130,000.

It's impossible to calculate how long it would take.

The idea that a money will do that is deceiving.

It makes some really really large numbers seem a lot sooner then they really are.

+1 if this was helpful. It took a while.

wtf

*sarcastic clap*

Lets see.

How long would it take you to do the math required?

Thank god there's always a mathematician around when you need one...

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On 4/23/2017 at 10:42 PM, wtf said:

How long did Shakespeare take to write his plays? Is he a primate or not?

Yes, he's a primate but since he's not a  monkey (he's one of the great apes), your suggestion doesn't work.

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Technically, hamlet is a modern ape, so i guess the answer is however long hamlet took to write it

Humans are modern apes...

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On 4/23/2017 at 2:04 PM, wtf said:

4.5 billion years, the time it took evolution to produce Shakespeare.

No, that's how long it took single celled bacteria to produce Shakespere.

On 9/25/2017 at 11:39 AM, tar said:

seems the answer to the OP question  of how long it would take is "a stupid large number of years

And being that we don't have a stupidly large number of years to play with, it seems the literal answer is "they won't"

Infinity is a device, not a number, so it can not be considered in the calculation.   Neither can infinite universes or the consideration of an infinite amount of attempts or an infinite amount of monkeys.   I think as soon as you put infinity in the equation your answer is by definition undefined.  Like dividing by zero.   Infinity is not a number, and can not take part in the literal calculation.

Not a fan of the Many Worlds Interpretation to Quantum Mechanics I take it?

BTW, MW would involve a finite number of universes, Im pretty sure. There are a finite number of possible superposition states. for example, you cant use the gamma function to create a smooth curve in combinatorics solutions that could imply infinite outcomes. It would have to be a weighted average of distinct possible solutions for each fundamental particle.

BTW, seems like a brute force problem for a really long password to me, which would be a really sick factorial problem that could never be solved.

so a good question might be which would be the dominating number?

That factorial of characters in the numerator or the number of possible Universes in the denominator?

Edited by TakenItSeriously

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The monkey would run out of paper.

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I've been thinking about this post many times since it first popped up. It's become an obsession.

I find myself waiting for the bus and imagining a immortal scientist looking at an immortal scribe monkey typing, waiting for her to write hamlet and after 10^184000 years it's almost done.

And on the last word of the last sentence  the monkey types: And they all lived happily ever after, the enb. The scientists then flips and chases the monkey.

That's what you guys and your post did to me! People think about problems and solutions, I think about poet chimps.

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On 4/23/2017 at 5:07 PM, Lord Antares said:

This makes me think that you don't understand probability.

That's funny, because It should make you think he does't understand monkeys.

No one here does. At least not enough to make any kind of meaningful predictions.

First of all, it was never a scientific claim about monkeys. I'm sure it was just a dramatization of the absurdity of infinity. But popularized claims takes on an assumption of fact because its been repeated so many times.

The fact is there is no real data on monkeys typing ability AFAIK.

But even if you assume truely random key punches by the moneky that's still not enough to make it a reasonable problem. Languages have inherrant biases as well that changes the problem. That's what makes codebreaking possible. But no one knows that kind of information for old english.

So now we have to assume random vs random, which amounts to just calculating the number of permutations for a long string of characters. But that's probably no linger within the spirit of the OP..

There is a massive difference when saying anything about infinity which should have no bearing to reality in finite time.

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For any possible character combination of a specific length to occur, you need unbiased randomness, otherwise it's possible that certain character sequences will simply never occur. Monkey brains, like human brains, are probably not good generators of randomness, and as such it's possible that a monkey will never type out Hamlet, or any other complete text.

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5 hours ago, TakenItSeriously said:

That's funny, because It should make you think he does't understand monkeys.

/cut

2 hours ago, Thorham said:

Monkey brains, like human brains, are probably not good generators of randomness, and as such it's possible that a monkey will never type out Hamlet, or any other complete text.

Why do people here have trouble understanding that monkeys are a metaphor for randomness? Substitute monkeys with random.org or God's unbiased mathematically random machine or whatever you feel is more fitting to the scenario.

19 hours ago, thoughtfuhk said:

Technically, hamlet is a modern ape, so i guess the answer is however long hamlet took to write it

Humans are modern apes...

You mean ''Shakespeare'', not ''Hamlet'', right?

On 25. 09. 2017. at 8:39 PM, tar said:

seems the answer to the OP question  of how long it would take is "a stupid large number of years

And being that we don't have a stupidly large number of years to play with, it seems the literal answer is "they won't"

Infinity is a device, not a number, so it can not be considered in the calculation.   Neither can infinite universes or the consideration of an infinite amount of attempts or an infinite amount of monkeys.   I think as soon as you put infinity in the equation your answer is by definition undefined.  Like dividing by zero.   Infinity is not a number, and can not take part in the literal calculation.

This is simple mathematics. There is no reason why there couldn't be infinite tries. It is the same as saying ''given infinite time, when would you be expected to roll 10 threes on a die in a row''. It doesn't imply that infinity will ever come into play and it won't. It is simply a different problem than saying ''what are the odds that you will roll 10 threes in a row on the first try?''.

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4 hours ago, Lord Antares said:

You mean ''Shakespeare'', not ''Hamlet'', right?

Yes, I definitely meant Shakespeare

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