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

## Recommended Posts

On ‎10‎/‎20‎/‎2017 at 0:16 PM, Lord Antares said:

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.

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?''.

Lord Antares,

Well there is a reason there could not be infinite tries.  We die somewhere before we get to infinity.

If the monkey is just a metaphor for randomness and the point is that we emerged from a random universe by accident, then the outside limit for how long it would take a monkey to type Hamlet would be 13.8 billion years.   If the odds are against the monkey typing Hamlet in 13.8 billion years, which earlier posts indicate is the case, then the odds against there being monkeys, typewriters, and  us by accident are not very good at all, and something in addition to randomness must have been in play over the last 13.8 billion years to get such certainty as it is that you will read this post and type an understandable response.

Regards, TAR

#### Share this post

##### Share on other sites
On 10/20/2017 at 6:16 PM, Lord Antares said:

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.

Because monkeys, or any other organisms with brains, are a bad metaphor for randomness seeing how they aren't random. If you're going to use a metaphor, use a good one.

#### Share this post

##### Share on other sites

It's a pretty good metaphor. Everyone understands Hamlet is quite long and everyone can imagine that a monkey could be taught to bash a typewriter but that it wouldn't know what it was doing so for practical purposes it would be random. Together with the revelation that the monkey would eventually produce the work gives a sense of the depth of infinity and the strangeness of some results in probability theory using infinity.

Giving a metaphor using a truly random process like the decay of some unstable atom would loose more than half the general population halfway through the first sentence. Or maybe we should just leave it to purely mathematical arguments - rigorous for sure, but hardly any lay people would even be thinking about it let alone discussing it.

#### Share this post

##### Share on other sites
7 hours ago, Thorham said:

Because monkeys, or any other organisms with brains, are a bad metaphor for randomness seeing how they aren't random. If you're going to use a metaphor, use a good one.

But if used an example which was purely random, then I wouldn't be using a metaphor at all, would I?

9 hours ago, tar said:

Lord Antares,

Well there is a reason there could not be infinite tries.  We die somewhere before we get to infinity.

If the monkey is just a metaphor for randomness and the point is that we emerged from a random universe by accident, then the outside limit for how long it would take a monkey to type Hamlet would be 13.8 billion years.   If the odds are against the monkey typing Hamlet in 13.8 billion years, which earlier posts indicate is the case, then the odds against there being monkeys, typewriters, and  us by accident are not very good at all, and something in addition to randomness must have been in play over the last 13.8 billion years to get such certainty as it is that you will read this post and type an understandable response.

Regards, TAR

Again, this is a mathematical problem, not a practical one.

If someone asked you what were the odds of a random person rolling a 3 on a die, you would answer ''1 in 6'' and not ''well why is the person doing that? You should consider what are the chances of him being willing to participate in this? What of the very small odds that he dies before he completes the throw'' etc. etc.

WTF already touched on what you are saying, but this is not what we are discussing. We were discussing mathematics.

#### Share this post

##### Share on other sites

Lord Antares,

Understood, but mathematically the monkey would take longer than the projected life of the universe to type out Hamlet, so the only recourse math has is to propose other universes or more monkeys.

So the literal mathematical answer to the question of how long it would take a monkey to type out Hamlet, is there is not enough time available to get the job done.   So the correct answer is, the monkey will not type out Hamlet.  There is no possible way he can do it.  There are a million ways he will not even type out the first sentence, and all these other ways are much more possible than him or her getting it right.   And there is also the problem of who is checking and recording the output, and what rules they are going by in the grading.  If the monkey jams the typewriter on the last stroke and hits the right key but it doesn't type, or the ribbon is out of ink and the impression is made but it is not readable by the naked eye, does it count?

So literally you need a human judge to say it is Hamlet, so you cannot take  a human's judgement out of the equation.   Hence you cannot achieve the goal in an imaginary fashion that does not take the realities of objective reality into account.

One of the problems with infinity is that no matter how big you make it, I can make it one more bigger, every time.  This works in our brains, as we have the ability to put ourselves in other peoples shoes, shift grain size, count and so on.  The real world has to fit together and make sense, work and operate, even without our equations that describe how it does it.

Regards, TAR

It is a similar question to "how many angels can fit on the head of a pin."

Whenever you mix imaginary stuff, with real stuff, the mathematical answer will vary according the variables allowed by imagination.

Back when I was first playing with a Commodore 64, I ran into the problem of trying to write a program that would have a random output.   Even the built in random number generator worked off a program that utilized the regular clock pulses of the crystal, so randomness was just simulated, and had beneath it a pattern that could repeat or become evident in artifacts, analogous to the moire patterns put out inadvertently by digital copiers.  Chaos theory and Mandelbrot fractals show us that the world is not random at all, but operates usually in patterns that repeat themselves and show up, up and down the line, like overtones and undertones in music.  The string vibrates at a certain frequency but that is not the only frequency it vibrates at.

It vibrates in halves and thirds and fifths and so on.

Edited by tar

#### Share this post

##### Share on other sites

Do you know what mathematics is? Because you seem to struggle with what a hypothetical mathematical problem is. Do you think I don't understand that a monkey doesn't have infinite time at its disposal? You seem to be mistaking me for a complete idiot.

A monkey is a metaphor for true, unbiased mathematical randomness, something both you and I agree doesn't exist.

50 minutes ago, tar said:

Back when I was first playing with a Commodore 64, I ran into the problem of trying to write a program that would have a random output.   Even the built in random number generator worked off a program that utilized the regular clock pulses of the crystal, so randomness was just simulated, and had beneath it a pattern that could repeat or become evident in artifacts, analogous to the moire patterns put out inadvertently by digital copiers.  Chaos theory and Mandelbrot fractals show us that the world is not random at all, but operates usually in patterns that repeat themselves and show up, up and down the line, like overtones and undertones in music.  The string vibrates at a certain frequency but that is not the only frequency it vibrates at.

Obviously. Randomness is a misunderstood term. It doesn't exist in its true form. It's only a measure of our ignorance. So we would give 50/50 odds of a coin landing either way, even though it has nothing to do with chance. We've even talked about this particular issue before and I've opened threads on it.

#### Share this post

##### Share on other sites
On 20/10/2017 at 5:16 PM, Lord Antares said:

Why do people here have trouble understanding that monkeys are a metaphor for randomness?

12 hours ago, tar said:

Well there is a reason there could not be infinite tries.  We die somewhere before we get to infinity.

Aaaarrrrrgggghhhhh!

Talk about "missing the point".

Lord Antares, it isn't just you (or monkeys). I have had many frustrating discussions about physics with tar where he thinks that what someone had for lunch, or what colour shirt they were wearing, might be relevant to tests of the theory of relativity. (And, before tar asks me to point to the exact thread where we had that exact conversation: it's a caricature. But not an unrealistic one. As this thread shows.)

#### Share this post

##### Share on other sites
2 minutes ago, Strange said:

Aaaarrrrrgggghhhhh!

Talk about "missing the point".

Lord Antares, it isn't just you (or monkeys). I have had many frustrating discussions about physics with tar where he thinks that what someone had for lunch, or what colour shirt they were wearing, might be relevant to tests of the theory of relativity. (And, before tar asks me to point to the exact thread where we had that exact conversation: it's a caricature. But not an unrealistic one. As this thread shows.)

The confusing part is, it's not just him. A couple of people have made similar comments. It's baffling. I was actually wondering if he was just fucking with me. I don't think he quite understand what the purpose of a hypothetical mathematical problem is.

A case of this?

#### Share this post

##### Share on other sites

Thread,

Raider5678 said 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.

Then went on to calculate the time it would take to randomly arrive at the correct order of the characters.  The time was silly large, so to have the question at all, would be to prove a point about randomness or infinity, so I went there.

If it was just a hypothetical mathematical question, then Raider should not have divided 130,000 by 200 and gotten 650,000.

Are we making a literal mathematical calculation or are we talking hypothetically about infinity and randomness?

If we are talking basic math lets start with being able to type 130,000 letters, at 200 characters a minute in 650 minutes, which is 10.833 hours which is about a workday with lunch and 3 hours overtime.

Regards, TAR

#### Share this post

##### Share on other sites

Yes, we were doing a literal mathematical calculation. But since you bring up the philosophy of probability:

15 hours ago, tar said:

If the monkey is just a metaphor for randomness and the point is that we emerged from a random universe by accident, then the outside limit for how long it would take a monkey to type Hamlet would be 13.8 billion years.   If the odds are against the monkey typing Hamlet in 13.8 billion years, which earlier posts indicate is the case, then the odds against there being monkeys, typewriters, and  us by accident are not very good at all, and something in addition to randomness must have been in play over the last 13.8 billion years to get such certainty as it is that you will read this post and type an understandable response.

I've heard this type of argument before and it is 100% nonsensical to me.

It is exactly like this:

If you had a quintillion balls each numbered from 1 to quintillion, you picked one and commented ''Wow! What a coincidence that you picked that one since the odds of picking this exact one were 1 in quintillion. How remarkable!''

It is simply because every possibility has incredibly small odds of happening in scenarios such as these. Any possible way the earth and life or the universe might have turned up would have yielded unbelievably small odds of happening. The problem is you're considering the scenario which DID happen as special.

What are the odds of there being a bird in this specific town in the world which was chased by humans and blown away by the wind which blew at this exact force and the bird ultimately got hit by a yellow Toyota truck with the exact X license plates at 2:36 PM on a Sunday of October, 2017.? The odds are practically impossibly small, yet it happened today. So how is that possible? Do you see the problem with this kind of logic?

#### Share this post

##### Share on other sites

The problem is you're considering the scenario which DID happen as special.

Why, yes I am.  This is the only universe we've got.

The logic of the situation is clear to me. I understand that things are the way they are because they evolved that way.  But the idea at issue is whether the place happened accidently or on purpose. At least that is why the argument is usually had.  Did it happen by accident, or did god do it.

I propose it has to be neither, and am looking for the organizing principles and the natural patterns from which an explanation can be formulated.

It does not work for me, if the explanation requires multiple universes or multiple chances to work out this way.

It does not work for me to consider infinity because it is not a real thing.  It does not work for me to consider other universes because they are not real things that we have any access to.

And it does not work for me to consider god did it, because an anthropomorphic lonely creator makes no sense to me, and we have zero evidence that such a creature exists and it is just as logical to think the cosmos always was, as to consider that this imaginary creature always was.

I am perfectly able to conceive of infinity as all I have to do is consider that any quantity you name, I can mentally add one two, and still have a quantity I can name back to you.  But that all happens within our respective brains.  I love mental challenges and matching wits and figuring stuff out and understand the "point" of infinity. But neither you nor I can actually conceive of a number of that size, nor mentally catalog each of the members of an infinite set.

So I think you misunderstand why I make the comments I make.  Not to prove anybody wrong, or settle the argument one way or the other, but to request that we look at the place as special, in that it is the only one we have, and not consider it inconsequential, as if we have any alternative reality to inhabit.

Regards, TAR

#### Share this post

##### Share on other sites

Gosh, that puddle thinks its' pothole is really special. It's just the right shape.

#### Share this post

##### Share on other sites

By the time this thread runs out of steam the monkeys will have evolved into some species  that writes its own literature.

#### Share this post

##### Share on other sites
Posted (edited)

Sorry but information cannot come out of randomness. Claude Shannon’ established that in his entropy theorem. The monkey can type his fingers away. No Hamlet will come out.

Edited by agcala
typo

#### Share this post

##### Share on other sites
21 minutes ago, agcala said:

Sorry but information cannot come out of randomness. Claude Shannon’ established that in his entropy theorem. The monkey can type his fingers away. No Hamlet will come out.

When I was a kid we were taught to program computers. Some of the stuff we did was not on the syllabus.

It didn't take us long to work out that you could get a computer to assemble random four letter words and print them on the screen.

We were, of course, delighted when it came up with rude words.

The monkeys, given time, would randomly type Hamlet in the same way that the computer typed "fork".

#### Share this post

##### Share on other sites

I avoided this thead until now but have just read through it.

Lord Antares,

You have worked hard to keep your thread on  topic and made some good points and explanations of your position, despite the noise level so +1 for all that.

However you have made one mathematical mistake wtf tried to draw your attention to.

You are trying to use prior probabilities to predict certainty.
That is impossible (+inconsistent with mathematical statistics).

You ask how long... before something will (certainty) happen.

Prior probability can only ever offer an estimate, which is couched in terms of a cumulative of overall probability.

You have then two approaches.

If you allow the mokey-writer to start and slice the output into 130000 characters (I think that was the right number) of episodes and call each one a trial or experiment,

1) You can try to calculate the overall probability of success which should gradually increase as the number of trials increases.
But it will never reach 1.

2) You can try to calculate the overall probability of failure which should gradually decrease but never reach zero, as the number of trials increases.

2 hours ago, agcala said:

Sorry but information cannot come out of randomness. Claude Shannon’ established that in his entropy theorem. The monkey can type his fingers away. No Hamlet will come out.

.

Rubbish, you get information every time you select a random number. (Kolmogorov).

#### Share this post

##### Share on other sites

What a coincidence. I had been off the forum for months now, probably a good year since I was active and I came right back the day someone replied to something of mine.

10 hours ago, studiot said:

However you have made one mathematical mistake wtf tried to draw your attention to.

You are trying to use prior probabilities to predict certainty.
That is impossible (+inconsistent with mathematical statistics).

You ask how long... before something will (certainty) happen.

No, you're right. It was a phrasing error, though and not a mathematical one. I understand that certainty and probability cannot be combined like that. I meant ''how long before something is expected to happen'' but then I would have to define ''expected''. Over 50% chance would work.

#### Share this post

##### Share on other sites

Well, i think no one can guess this. Because in this world any thing can happen.

#### Share this post

##### Share on other sites
1 hour ago, RjMaan said:

Well, i think no one can guess this. Because in this world any thing can happen.

Every single person alive can guess this (even if a guess must be correct, every person is capable of guessing correctly).

And no, some things are impossible. Try to use a 3D printer to make me a fork like this:

#### Share this post

##### Share on other sites
10 minutes ago, Phi for All said:

Every single person alive can guess this (even if a guess must be correct, every person is capable of guessing correctly).

And no, some things are impossible. Try to use a 3D printer to make me a fork like this:

Is that an Escher fork?

#### Share this post

##### Share on other sites
9 minutes ago, StringJunky said:

Is that an Escher fork?

Yes, for eating delicacies like ewe testicles, hippo wings, and vegan sashimi. It works on perpetual motion.

#### Share this post

##### Share on other sites
1 minute ago, Phi for All said:

Yes, for eating delicacies like ewe testicles, hippo wings, and vegan sashimi. It works on perpetual motion.

LOL!

## Create an account or sign in to comment

You need to be a member in order to leave a comment

## Create an account

Sign up for a new account in our community. It's easy!

Register a new account

## Sign in

Already have an account? Sign in here.

Sign In Now