The Infinite Monkey Principle

Hang on - 'the first ooops' and what exactly is over ?

 

Actually, I think you regressed, not digressed.

 

The chances of an infinate number of monkeys typing and finally one of them by chance types out "Hamlet" to me seem more remote then an infinate number of monkeys printing out a picture. However both situations are minuscule by chance. I believe there is no chance at all but that is not the theory. But then I buy a lottery ticket every week. There is about the same chance of winning it as an infinate number of monkeys making a print or typing a play. But then I buy one anyway so go figure. I guess I do not understand the context actually. Has somebody said that photography is so easy a Monkey can do it. Or how about it's so easy a Cave Man can do it.

 

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.

 

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

 

Posted wirelessly..

Wow.

 

I don't understand why it's all over after the first oops, either. Won't one of the monkeys eventually mix some more chemicals and use them in the right order?

 

They're trying.

 

Googling for 'infinite number of monkeys' brings forth an infinite number of references to same:

http://en.wikipedia.org/wiki/Infinite_monkey_theorem

Interestingly, the number string representing the number pi passes all tests for being truly random. Therefore there is a finite probability that it contains at least a few of the opening words of Hamlet. But pi can be calculated from a simple formula and the digits of pi are fixed - does this mean that Hamlet is deterministic? Is the genius of Hamlet the ability to spot the right 120,000 characters from an infinite stream?

Hamlet = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 ....

 

What if an infinite number of monkeys were using digital P&S cameras with instant wireless printing -- would one of them ever photograph a burning blimp?

 

If you stuff them into the hole, sure.

(What?!)

 

Posted wirelessly..

Are any of these monkeys wearing cute little vests? Did we ever give consideration for random use of apparell?

So now the equation should be P = f(Tommy Hilfigger)

 

Sniffing fixer for too long is not good. Get some fresh air.

 

Have you ever heard of a place called Flicker.com? It may be a finite number of people with a finite number of cameras, but there are those gems shot by first time photographers using disposable cameras. Point proven in photography.

In writing we have Margret Mitchel, Mary Shelly, and Brahms Stoker all of whom only wrote one book, I bet you can name all three books.

In Chemistry we have the man that figured out how to refine Aluminum by tossing jumper cables attached to a car battery into a boxite solution.

The man who discovered Pluto was the observatory handy man, not an astronomer.

So yes, an infinite number of monkeys would eventually process a perfect photo, but you would need a lot of chemical and should expect a lot of disasters and plenty of dead monkeys, and don't ask them to do it again.

 

Margret Mitchell wrote more than just that one book.
Mary Shelly wrote many books.
And yes, so did Bram Stoker (Brahms?).

Yet not accidentally.

No, he wasn't.
He was hired because his astronomical work impressed Lowell, who was fed up with looking for what was to be named Pluto later himself.

In short: none of the example above are of a one-of, first-try successes.

Though it is of course true that it didn't take an infinite number of attempts.

Infinity does not exist. Nor do infinite amounts of monkeys.
So the old 'ex falso sequitur quodlibet' applies. In an infinite way.

 

I wouldn't call it a "finite probability"; it either does or it doesn't, although at the moment (as far as I can tell) we don't know which.

I think most people in a position to have a good guess believe that every finite sequence probably does appear in the decimal expansion of pi somewhere---a million zeros in a row, the ASCII codes for a transcription of _Hamlet_ followed by an essay attributing it to Francis Bacon, a high-resolution bitmap representing that nice portrait I took of my grandma last year. The last I knew it had not actually been proven.

Someone---I think the author David James Duncan---made the trenchant observation that not only will the hypothetical monkeys produce _Hamlet_, but they'll also come very very close and then screw it up; if you accept that a monkey at a typewriter is a random letter generator (which probably isn't true of real monkeys, but never mind), your roomful of monkeys will occasionally get all the way down to the end of the play, and then have Fortinbras say "Go, bid the soldiers shoo$!*&bqlkaddf."

See Jorge Luis Borges's _The Library Of Babel_ (text, probably in violation of copyright, at http://jubal.westnet.com/hyperdiscordia/library_of_babel.html) for a really thorough treatment of this question.

To get back on topic, this is a very digital discussion; text is intrinsically a digital-like medium, in the sense that it uses a finite alphabet in well-defined sequences and so makes it really easy to answer the question "when are two texts the same?" (You can argue about specific criteria like case and spacing, but whatever decision you take on those criteria, you'll get a clear definition of "the same".)

Analog photos are different; in any sense we can recognise, there is no good way to decide that two prints (resp. negatives, slides) are "exactly the same". Is the spacing of the grains on the medium the same? (I mean, *really* the same? To within the diameter of an atom? What about the electron clouds in the constituent silver atoms---are they the same? What does that question even mean?) If you have an infinite crew of monkeys scattering photons over light-sensitive media, or directly scattering activated and deactivated silver grains on a substrate, it's not at all clear that you'll eventually get an "exact" duplicate of _Pepper No. 30_. But you will get a lot of very, very, *very* close approximations.

In _Hamlet_, it's pretty clear that those close approximations are wrong: "Go, bid the soldiers sh*t." isn't *that* far from "Go, bid the soldiers shoot.", but it has a drastic effect on the tone in which the play ends! By contrast, you could move quite a lot of grains around at random in Weston's print without making an appreciable visual difference, and it's almost impossible to find specific areas where a little localised change would really affect the semantics of the image. At the most, it would end up looking like a technical problem in printing---until you start talking about clusters that are *really* large in grain terms, large enough to represent their own identifiable images within the picture.

What I'm saying, I guess, is that the distance between the "randomisable" level of individual photons or grains, and the "semantic" level of the overall work of art, is a lot larger for a photo than it is for text. This much is true for d*g*t*l too---it's a long way from individual pixels to artistic semantics---but analog has the extra complication that the randomisable level itself is still quite complex, rather than being based on a simple discrete model like letters or pixels.

Is this line of thinking artistically important? Maybe so; a lot of us seem to have a general feeling that the complexity and "slipperiness" of the underlying mechanics create part of the appeal of analog. On the other hand, considering how far below the threshold of visual perception those complex mechanics are, maybe this discussion is just a theoretical exercise with no real applicability to the photographic image.

I don't think it's possible to make an airtight argument for either perspective on scientific grounds; certainly not by expanding pi or training monkeys. But both of those have their own rewards, not least in allowing us to burn time on speculative discussion threads like this one!

-NT

 

Do you mean the "Hall-Héroult" process from 1886?

Benz built his first car in 1885 - perhaps he had invented the jumper cable by the following year, but I'd be surprise, as who else had a car to give him a jump start?

 

Yes, we do.
It doesn't.

 

I think it is very interesting that Perry first began formulating these thoughts about photography and infinity on May 25, which is universal Towel Day, in honor of Douglas Adams, author of the Hitchhiker's Guide to the Galaxy. Adams's characters traveled around the Universe in the Heart of Gold, a spaceship powered by the infinite improbability drive. Read the Guide, and you'll become a believer in what an infinite number of monkeys can do. Anyway, assuming Perry is not aware of Towel Day, what were the chances that he'd come up with this infinity question on that very day?

 

(on whether pi contains all finite substrings)

Cool. Do you know where I can find a sketch of the proof?

We *do* know that as n increases, the probability of finding a given substring in the first n digits approaches 1, right?---which I think means that the finite substrings of pi are dense in the space of all finite strings of digits.

-NT

 

Have you read Shakespeare?