The “infinite monkey theorem” states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost certainly write the complete works of William Shakespeare.
What utter rubbish. Let’s put aside for one moment the facts that the monkey won’t be able to insert the paper, remember to hit carriage return, sit still, not crap on the keyboard, etc, etc. Let’s assume the monkey is well behaved, let’s further assume someone takes care of adding paper when needed, feeding the monkey … let’s assume all the flaws in this ill thought out theorem are taken care of and let’s assume we have a perfectly behaved monkey who lives forever, who constantly types keys at random to a perfectly maintained typewriter, who never needs a poo … and this theorem is still rubbish. Even if someone hit carriage return at the end of each line (which is simplifying the problem for the monkey immensely).
If there are 50 keys on a typewriter, the probability of a monkey typing a Shakespearean word like “Forsooth” is 1.024E-17 = 0.000000000000000001024 which is really, really tiny. Don’t forget they need spaces either side of the word too. You can imagine the probability of a monkey writing a full sentence of say 150 characters and the probability plummets to 1.4272E-255 which is:
0.0000 … (insert 247 more zeros)… 00014272
To write a page of 20 such sentences and the probability becomes, well, zero. And so to write a complete novel, and then write several more books and poems and plays is so ridiculous it doesn’t bear analysing.
Mathematician: “But wait a minute – over an infinite period of time it might happen”
Me: “No it won’t.”
Assume Hamlet is 400 pages long and imagine if a monkey actually wrote the first 399 pages, and then got to the last paragraph of page 400, finally reaching the last sentence, and then the last 7 letter word and there would still be a 99.99999999999999999998976% probability of screwing the whole thing up. In other words it will inevitably fail, even then. Of course it won’t ever get that close.
It’s lazy science, it’s a cop out. By adding “over an infinite amount of time” you can suggest anything and hide behind the word infinite, when in fact infinity doesn’t exist, it’s just a concept that’s been introduced to put bounds on something we don’t really understand.
“Tomorrow, 17 cheerleaders from Boise, Idaho will knock at my door and take me out dancing”.
It’s not very likely, in fact it almost certainly won’t happen. No, it won’t ever happen, never mind tomorrow. But hang on a minute …
Idiot Mathematician: “Over an infinite period of time 17 cheerleaders from Boise, Idaho will knock on your door and take you out dancing”
I bet 16 cheerleaders won’t even turn up. Not tomorrow. Not ever.