On
Chimpanzees, Typewriters, Shakespeare, and Stuff It seems to be generally accepted that
applying infinite resources to a random process is guaranteed to
produce a particular outcome for which those resources are
necessary. So an infinite number of chimpanzees typing randomly
at an infinite number of typewriters for an infinite length of time
will inevitably produce the complete works of Shakespeare, right?
I don't think so. There is a difference between infinite and unbounded. I once knew someone who bragged about confusing his math teacher in high school because whenever she would refer to an "infinite container" in a math problem, he would insist that such a container would necessarily contain the entire universe, since it is infinite. That is utter nonsense. He's confusing infinite with unbounded, and they are not at all the same thing. An infinitely tall soup can, for instance, can contain an infinite amount of soup without ensnaring the entire universe. The boundaries of the can limit the infinitely tall container so that it takes up an insignificant fraction of our universe while still being able to hold an infinite amount of soup.
It is also the case that necessary is not the same as sufficient. Though it is necessary for something to type randomly on at least one typewriter to produce the complete works of Shakespeare, it does not follow that more -- even infinitely more -- would be sufficient.
Random is just that: random. And even an infinite amount of randomness is not guaranteed to produce any particular outcome, much less every conceivable outcome. Claiming that an infinite number of chimpanzees typing on an infinite number of typewriters for an infinite length of time will inevitably produce the works of Shakespeare (or, by inference, every conceivable literary work) is like saying that an infinitely tall soup can absolutely must contain a dog (or, by inference, every conceivable thing) simply because it is infinite.
If you're not convinced, then consider this: Flip a coin a hundred times, and count the number of times it comes up heads. Did it come up heads every single time? Probably not. But is it possible that it could come up heads every single time? Though it's not likely to happen, it is, of course, a possibility. Now flip it a thousand times. Is it still possible for it to come up heads every time? Yes, it is, though it is much less likely. Now flip the coin an infinite number of times. Is it possible that every coin flip throughout eternity will come up heads? Yes, it is a potential outcome, though the probability of such an outcome is vanishingly small. But the point is, it is a statistically valid outcome, even with an infinite number of coin flips.
Similarly, it is a statistically valid, though very unlikely, outcome for an infinite number of chimpanzees typing randomly at an infinite number of typewriters for an infinite amount of time to produce absolutely nothing but pages and pages of the letter "A". Such an outcome, which, I repeat, is statistically valid, would absolutely preclude anything like the entire works of Shakespeare from ever being produced. Therefore, since there exists a statistically valid outcome that precludes the production of the entire works of Shakespeare, then production of the entire works of Shakespeare is not at all guaranteed, even with infinite resources. And if that's still not enough for you, then consider the fact that an infinity of pages filled with the letter "A" is not the only statistically valid outcome that absolutely precludes the entire works of Shakespeare from being produced. For example, one valid outcome would be for no page among all the infinite pages to have more than one instance of the letter "E", which, as I recall, Shakespeare used quite a lot. There are, indeed, an infinite number of statistically valid outcomes -- many far more likely than the examples I've cited here -- that would absolutely preclude the entire works of Shakespeare from being produced.
So if it's a particular result you want, and your process is random, don't be fooled into thinking that more process -- even infinitely more process -- will necessarily guarantee the result you want. It is this fallacious thinking that makes our bosses think that adding more people to a project that is impossible to complete will make the project not only possible, but will even shave at least a week or two off the infinite schedule.
I don't think so. There is a difference between infinite and unbounded. I once knew someone who bragged about confusing his math teacher in high school because whenever she would refer to an "infinite container" in a math problem, he would insist that such a container would necessarily contain the entire universe, since it is infinite. That is utter nonsense. He's confusing infinite with unbounded, and they are not at all the same thing. An infinitely tall soup can, for instance, can contain an infinite amount of soup without ensnaring the entire universe. The boundaries of the can limit the infinitely tall container so that it takes up an insignificant fraction of our universe while still being able to hold an infinite amount of soup.
It is also the case that necessary is not the same as sufficient. Though it is necessary for something to type randomly on at least one typewriter to produce the complete works of Shakespeare, it does not follow that more -- even infinitely more -- would be sufficient.
Random is just that: random. And even an infinite amount of randomness is not guaranteed to produce any particular outcome, much less every conceivable outcome. Claiming that an infinite number of chimpanzees typing on an infinite number of typewriters for an infinite length of time will inevitably produce the works of Shakespeare (or, by inference, every conceivable literary work) is like saying that an infinitely tall soup can absolutely must contain a dog (or, by inference, every conceivable thing) simply because it is infinite.
If you're not convinced, then consider this: Flip a coin a hundred times, and count the number of times it comes up heads. Did it come up heads every single time? Probably not. But is it possible that it could come up heads every single time? Though it's not likely to happen, it is, of course, a possibility. Now flip it a thousand times. Is it still possible for it to come up heads every time? Yes, it is, though it is much less likely. Now flip the coin an infinite number of times. Is it possible that every coin flip throughout eternity will come up heads? Yes, it is a potential outcome, though the probability of such an outcome is vanishingly small. But the point is, it is a statistically valid outcome, even with an infinite number of coin flips.
Similarly, it is a statistically valid, though very unlikely, outcome for an infinite number of chimpanzees typing randomly at an infinite number of typewriters for an infinite amount of time to produce absolutely nothing but pages and pages of the letter "A". Such an outcome, which, I repeat, is statistically valid, would absolutely preclude anything like the entire works of Shakespeare from ever being produced. Therefore, since there exists a statistically valid outcome that precludes the production of the entire works of Shakespeare, then production of the entire works of Shakespeare is not at all guaranteed, even with infinite resources. And if that's still not enough for you, then consider the fact that an infinity of pages filled with the letter "A" is not the only statistically valid outcome that absolutely precludes the entire works of Shakespeare from being produced. For example, one valid outcome would be for no page among all the infinite pages to have more than one instance of the letter "E", which, as I recall, Shakespeare used quite a lot. There are, indeed, an infinite number of statistically valid outcomes -- many far more likely than the examples I've cited here -- that would absolutely preclude the entire works of Shakespeare from being produced.
So if it's a particular result you want, and your process is random, don't be fooled into thinking that more process -- even infinitely more process -- will necessarily guarantee the result you want. It is this fallacious thinking that makes our bosses think that adding more people to a project that is impossible to complete will make the project not only possible, but will even shave at least a week or two off the infinite schedule.
Copyright (c) by BSW, 2007. All Rights Reserved.
