Quote:
Quote by: GSM:Xtreme  While watching an episode of Nova a couple of months ago, I heard this thought about in a different way.
Let's say that the odds of a monkey randomly hitting keys on a keyboard and typing a perfect version of Hamlet can be demonstrated by the equation below:
10^x; where, lim x--> -()()
and yes for goodness' sake I'm using ()() as the sign for infinity...
That is effectively saying the odds are just about zero. But let's use the analogy 100% odds represents all matter in the universe and 0% is absolute nothingness.... that equation would represent less than one sub-atomic particle. (Is that clear? I tried...  )
Well, with infinantly many monkeys hitting keyboards for eternity, I think that the x value would be brought back to the realm of real numbers, and thus it may be possible for a version of Hamlet, as well as perhaps Galileo's Principia, and even every Dr. Seuss book to be typed quite perfectly.
What do you think? I'm a little new with calculus and limitations, but I think I hit the nail in the wall here; though, I did mention infinite monkeys instead of millions, as stated in the quote, but the concept is the same. |
There really is no point in making the statement since the concept of infinite monkeys is impossible. If one of the prerequisite conditions is impossible then the statement is also impossible even if it is theoretically possible.
Infinite monkeys would also require infinite computers with infinite drive space and infinite power consumption.
Also, how exactly would the work of the individual monkeys correlate with each other? Is the implication that a single monkey in the infinite scenario would compose the exact works of Shakespeare or is it that somehow the collaborative work of infinite monkeys over infinite time would have chunks that would exacly match the works of Shakespeare?
Also, if the amount of time is truly infinite, what is the difference between a single monkey with infinite time and infinite monkeys with infinite time? A single monkey would theoretically get the job done at some point as well.