On Thu, Feb 21, 2013 at 2:43 AM, Eric Walker <eric.wal...@gmail.com> wrote: > I suspect there is an invalid assumption about randomness that we are making > when we go along with the old thought experiment of a corps of eternally > typing monkeys eventually producing Shakespeare's folio or imagining that the > folio can be found at some point transcoded in the decimals of Pi. I wonder > if there is already a mathematical proof out there to the effect that the > latter is an impossibility.
I suspect you are not fully appreciating what endless and non-repetitive means. If it never can end and does so without repeating then eventually in the fullness of infinity every long shot must occur. (actually, only if it is random. So the monkeys might win out) And with less frequency, every really really long shot must occur. What Monkeys or Pi writing Shakespeare actually implies however makes lite of just how long the search will go in each case before success, which is so inconceivably long, the scale of volume of the universe to Plank length falls impossibly short of conveying the immenseness of the time it would take in either case compared to say the believed age of the universe. And only after every other book that has or could be written pops up first, and of course almost but not quite perfect versions would pop up also. Every extra character required will multiply the task of how far you will need to go through Pi. Of course you are right about one thing, in theory it is possible that it might never occur. I do not know, does 86 show up in the first 20 digits of Pi? the first 100 digits? For that matter does it show up at all? There is nothing meaning it must, ever. But then again that becomes an increasingly improbably longshot the further you search. 3.141592653589793238462643383279502884197169399375105820974944592307816406286 Ah, didn't take long. Actually it is possible that I am all wrong since Pi is not random. http://www.youtube.com/watch?v=uXoh6vi6J5U Fun video. > > I have not seen the video, You should. But it is worth mentioning that non-zoomed in and slowed down versions do not reveal the activity as far as I can make out. Which might mean that we the were to be zoomed and slowed we could check the validity of what the other version shows.
