The Infinite Monkey Principle

[Pete H]

I think it will take a million years to evolve a monkey that will sit at a typewriter and type long enough to type anything of significance. I am sort of evolved and I had a hard time in college finding the motivation to type my homework. Has anybody put any number of monkeys in a room with a typewriter and seen if they do anything with it except sniff it and use it to scratch their armpits? I think given an infinite amount of time, the monkeys will break the typewriters throwing them around the room - bored silly because they are in a room full of typewriters.

Yes but there was a monkey evolved enough to write the works of Shakespeare - he was called Shakespeare (or possibly Bacon ) so it has already happened.
It doesn't need an infinite number, just an unbounded number (ie if it hasn't happened yet there are more monkeys to keep going until it does.)

 

[Shangheye]

The problem with the Infinite Monkey theory is that it does not take into consideration the nature of the function being evaluated.

Take it like this: P = f(x)

Where P is the probability of (Hamlet, Ulysses, The Gioconda, etc) being created by monkeys, and f(x) the function linking the number of monkeys (x) with the probability P.

Now if f(x) were linear, as in f(x) = 2x, then an increasing number of monkey would mean an increasing probability. An infinite number of monkey would therefore be an infinite probability, which doesn't work since probabilities are calculated as fractions of 1.0

So let's put it this way then:

f(x) = (-1 / (x+1)) + 1

The limit of f(x) as x approaches infinity is now 1. Congratulations! for an infinite number of monkeys, we have a function that asymptotically approaches 1, the certain probability.

But wait a minute: we are looking at the problem backwards, trying to fit the data into the answer we want to have. If you're a bureaucrat, this may not strike you as odd, but by golly! this is not how science works!

How do we really know that this is the right function? What if the function linking the number of monkeys to probability was this instead:

f(x) = 1/x

As x approaches infinity, the probability becomes asymptotically zero!!

So, the next time someone comes up to you with the Infinite Monkey Principle, waxes philosophical on the utmost wisdom therein, ask the bugger "what is the probability function?" and watch the puzzlement on their face as they realize that their mind experiment was nothing more than wankery and hogwash.

I think you are trying to make a monkey out of me

 

[2F/2F]

Does this Infinite Monkey know how to load medium format film backs? If so, we may find a use for it yet.

 

[st23]

Yes but there was a monkey evolved enough to write the works of Shakespeare - he was called Shakespeare (or possibly Bacon ) so it has already happened.
It doesn't need an infinite number, just an unbounded number (ie if it hasn't happened yet there are more monkeys to keep going until it does.)

Shakespeare (or whoever) happened (lived, experienced ,felt, thought) in a time and place with experiences that will never happen again, and would not happen to a monkey. I think that is the wonder of a great work of art is that it could not happen by chance, and sometimes not even by another individual. It is unique to a person and era. The creative mind is a miracle.

 

[Steve Smith]

Do you think the monkeys will be able to answer this?

This monkey did.....

 

[st23]

With that said ... I don't know if monkeys could do it, but if anyone could type the entire works of Shakespeare at random it would be my three year old son. I sometimes let him type in notepad and he only stops when I get impatient and tell him its time to stop. I think notepad has a limit to the amount of gibberish he can type before it runs out of room and he has certainly pressed this limit. I call it "gibberish" but he can recite word for word what it says. Usually he reads four screens of text as two sentences, but I guess he uses big words.
Now that I think of it, he probably couldn't type out the complete works of Shakespeare even if he had infinite time at his current pace (who knows when he grows up!) For one reason, after a few minutes of typing nonsense, he sees how long he can hold down the ";" key till the text scrolls down several pages. I think a monkey typing at random would have a better chance than this. But the most important reason I will still have to go out and buy a copy of "As You Like It" rather than wait for him to type it, is that he backspaces out almost everything he types till he has a blank page, giggling the whole time.

 

[nick mulder]

I think a skill in any busy-body/smart fart philosophers tool belt should be to come up with thought experiments that aren't as easily subverted with triviality as this one :rolleyes:

 

[lxdude]

I don't care how many monkeys type on typewriters for how long, they will produce nothing of significance.
And this is why:

The typewriters will break, and there will be no one around anymore who knows how to fix them.

Or even before that, someone will walk in, see the typewriters, tell the monkeys NOBODY uses THOSE anymore. The monkeys will be too embarrassed to continue.

Or after just the first night, the monkey-keeper will yell at them to "Knock off that infernal racket!".


So, human beings will be the limiting factor, not the monkeys.

 

[Marc Leest]

Ook. Ook ! Ook !

The Librarian of the Unseen University

 

[Pete H]

Shakespeare (or whoever) happened (lived, experienced ,felt, thought) in a time and place with experiences that will never happen again, and would not happen to a monkey. I think that is the wonder of a great work of art is that it could not happen by chance, and sometimes not even by another individual. It is unique to a person and era. The creative mind is a miracle.

I would agree that a great work of art is unique to a person and era, and it is influenced by the local cultural and historical context. That doesn't mean it's not by chance. Have you read the amazing 17th century works by Flurzell? No? Neither have I, as I just invented him, but it is only chance through a long line of evolution that Shakespeare existed and Flurzell didn't. Maybe as this line of monkeys evolves further, Flurzell's works will be written - the infinite experiment is (by definition) never finished. There is also no need to invoke miracles. If you generate enough samples (of evolved monkeys, in this case) some of them will be far away from the average, so Shakespeare, Einstein, Hitler, and Ansell Adams (just for a few examples) all did things that were in some way far from average. They were all products of their time, culture, and so on, but if they hadn't existed then we would still be talking about Flurzell and other exceptional people instead.

 

[kossi008]

No infinity needed.

I don't know why you all get so hung up on infinity. You don't need it.

Jorge Luis Borges wrote that nice short story about "The Library of Babel", which contains all books ever written and all which ever WILL be written as well.

You can look it up on Wikipedia. Note however that they make the faulty reference to infinity again: the number of printable books with a fixed number of pages and fixed number of characters per page drawn from a fixed supply of characters is clearly finite. Although it is a mind-staggeringly huge number, of course.

The catch is of course that you never find the useful books in the overwhelming mass of gibberish. This applies also (though somewhat less hopelessly) to flickr and such...

 

[lxdude]

Ook. Ook ! Ook !

My thoughts exactly!

 

[eclarke]

the heck with printing a photograph
can the million monkeys fix an oil leak ??

They are attempting to..EC

 

[st23]

I would agree that a great work of art is unique to a person and era, and it is influenced by the local cultural and historical context. That doesn't mean it's not by chance. Have you read the amazing 17th century works by Flurzell? No? Neither have I, as I just invented him, but it is only chance through a long line of evolution that Shakespeare existed and Flurzell didn't. Maybe as this line of monkeys evolves further, Flurzell's works will be written - the infinite experiment is (by definition) never finished. There is also no need to invoke miracles. If you generate enough samples (of evolved monkeys, in this case) some of them will be far away from the average, so Shakespeare, Einstein, Hitler, and Ansell Adams (just for a few examples) all did things that were in some way far from average. They were all products of their time, culture, and so on, but if they hadn't existed then we would still be talking about Flurzell and other exceptional people instead.

I think my point was, though Shakespeare may have been formed by chance, there are too many factors involved to create another exact Shakespeare and Shakespeare's time unless we erase the past somehow.

Also, if I may be allowed to disagree with myself a bit, some of my best work has at least had an element of chance, if not entirely by chance except that I pointed the camera and pressed the shutter, etc.
Most photography is "found" in some way. But the great one's reflect the artist or that moment in some way.

 

[Q.G.]

I don't know why you all get so hung up on infinity. You don't need it.

Jorge Luis Borges wrote that nice short story about "The Library of Babel", which contains all books ever written and all which ever WILL be written as well.

You can look it up on Wikipedia. Note however that they make the faulty reference to infinity again: the number of printable books with a fixed number of pages and fixed number of characters per page drawn from a fixed supply of characters is clearly finite. Although it is a mind-staggeringly huge number, of course.

If it is finite, i could take all of those books (starting with one - my capabilities certainly are finite), and add another page of meaningless text to it and create more books.
More books will be written that way, that were not contained in that library that contains all books that will be written.

Faulty the reference to infinity is not.
Infinity however is.

 

[Michel Hardy-Vallée]

I think you are trying to make a monkey out of me

Take your stinking typewriter off me, you damn dirty ape!

 

[Pete H]

So does the library contain a catalogue listing all catalogues which do not list themselves? Can all these monkeys type it?

Russell's paradox awaits ...

 

[Q.G.]

So does the library contain a catalogue listing all catalogues which do not list themselves? Can all these monkeys type it?

Russell's paradox awaits ...

Also to be demasqued, and shown to be a trivial bit of nonsense?

 

[Pete H]

Also to be demasqued, and shown to be a trivial bit of nonsense?

I'm not sure that infinity is a trivial bit of nonsense. It does not exist in the same way that 2 does not exist. Both are convenient abstract concepts which can simplify thinking if used in the right way, and they can be misused too. It is very easy to misuse infinity, which leads to some of the confusion one hears.

I would suggest the the "infinite monkeys" principle is one of those confusions. All it needs is a finite number of monkeys typing for a long time. The time is unbounded - if a monkey dies of old age, you can add in another one in the thought experiment. Then, eventually, one/some of them may have typed the works of Shakespeare.

The same holds (as you said) for the library. If the number of pages in a book is unbounded (but still finite) you can always add an extra page and produce a new book, so the number of possible books is unbounded too.

 

[ntenny]

Jorge Luis Borges wrote that nice short story about "The Library of Babel", which contains all books ever written and all which ever WILL be written as well.

...of a certain fixed size, which makes the range of contents vast but not infinite. Borges was all over this aspect (and had a more than passing familiarity with Russell's paradox too, though I don't remember if this particular story riffs on it).

Of course any book of finite size can be constructed by concatenating a finite number of smaller books, so in some sense even a finite but exhaustive library "contains" all possible (finite) books implicitly---but only in the same rather loose way that you could say "the alphabet contains all possible books".

It's a great story, in spite of (or perhaps because of) being a pretty elementary piece of mathematical philosophy. A bright grade-school kid can grasp the ideas in the story, but they'll probably never be quite right afterwards.

-NT

 

[st23]

...There is also no need to invoke miracles. ...

Perhaps the word "miracle" had connotations that I did not intend. I think that atheist, zealot and all those in between can all agree that the universe is amazing and complex. It was not my intent to start a religious discussion.

 

[ntenny]

I'm not sure that infinity is a trivial bit of nonsense.

I'm sure that it's not. So is anyone who's done any amount of science.

It does not exist in the same way that 2 does not exist. Both are convenient abstract concepts which can simplify thinking if used in the right way, and they can be misused too. It is very easy to misuse infinity, which leads to some of the confusion one hears.

Well said. Actually, you can fiddle around with definitions of "exist" and come up with ideas that would cover 2 but not infinity (e.g., "a collection of that many objects could exist"), but they all run into other problems (especially with negative numbers, irrational numbers, transcendental numbers, imaginary numbers, quaternions...)

This is old, well-worked territory in the philosophy of mathematics, but having been there professionally in an earlier part of my life, I came away convinced that it doesn't make much sense to talk about the meaning of "existence" of mathematical objects one way or another unless you *are* a philosopher of mathematics. They either do what you need them to or they don't, and various concepts of infinity are so replete with useful characteristics that if they didn't exist we would have to invent them anyway.

-NT

 

[brianmquinn]

The typewriters will break, and there will be no one around anymore who knows how to fix them.

Blue Moon camera can fix them!

http://bluemooncamera.com/Typewriter_Repair_Services.php

 

[st23]

As said before, infinity would not be needed to generate the entire works of Shakespeare at random, just a really, really long time. Once the books were typed we could just sit back and relax for the rest of eternity? Unless we wanted to start the monkeys on "The Little House on the Prairie" series.

Please help me understand it - wouldn't it be the same as calculating the amount of time it would take to roll a 12 on a pair of dice? Or flip a coin and get heads for that matter. You calculate the odds, see how long it takes to roll or flip as the case may be. The works of Shakespeare would just be on a grand scale?

I would think a monkey is not a good random character generator, though. If they type the way my 3 year old currently does, they may not type a "t" for millions of years, then they have to start over. I think a computer would stand a chance in a few billion years though, maybe less.

 

[Q.G.]

I'm not sure that infinity is a trivial bit of nonsense. It does not exist in the same way that 2 does not exist. Both are convenient abstract concepts which can simplify thinking if used in the right way, and they can be misused too. It is very easy to misuse infinity, which leads to some of the confusion one hears.

No. Infinity most certainly does not exist, in a different way that 2 does not exist.

I agree that it (infinity) gives rise to a lot of confusion.

The infinite monkey thing is an expression of a very human yet completely unfounded optimism, the believe that given an infinite chance (there's another concept that is more confusion than anything else) that something might happen, it must. It's an expression that given (albeit ludicrous) the right circumstances, nothing is impossible. And that makes us feel just great.
Arguing whether a finite yet unbounded number of monkeys, or even a simple finite number of monkeys, would do as well fails to recognise that, misses (though not by far) the point.