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.
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.
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.)
Do you think the monkeys will be able to answer this?
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.
the heck with printing a photograph
can the million monkeys fix an oil leak ??
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 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.
I think you are trying to make a monkey out of me
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?
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.
...There is also no need to invoke miracles. ...
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.
The typewriters will break, and there will be no one around anymore who knows how to fix them.
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.
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