The infinite monkey theorem says that if you sit an infinite number of monkeys at an infinite number of typewriters, eventually one of them will type out Shakespeare’s play “Hamlet”.
Now a small scale experiment – 6 Monkeys at 6 keyboards – conducted by Plymouth University, showed there were some practical difficulties involved, such as monkey urine getting in the keyboards and them breaking the kit with rocks, but eventually one of them did press the letter “S” three times.
Such silliness aside, is there any mathematical flaw in the theory. Well, whilst math may be wholly abstract and notional in the mundane pure math way this statistical theory is expressed, and so as far as it goes the theory is flawless, it is only flawless in the abstract.
As far as applying the theory as an argument for a real outcome in the non-abstract universe is concerned there is a huge flaw. For a real concrete outcome in the real universe you need infinity to be a real possibility, not an abstract concept.
Now the real universe is a closed curved spacetime that ends up back where it began. In space you go round and round the hypersphere (let’s say arbitrarily at light speed C and discount time dilation effects simply to avoid complication) as many times as you like so you have at least pseudo infinite distance, but your journey does take some time – time passes as you journey along. Clearly to go an infinite distance round and round, will take an infinite time.
Now this is the real universe. Do you have an infinte amount of time in the real universe? Remember you want to apply the thory in the real universe to get a concrete real outcome, so you have to accept the limitaions of the real universe. if you go “along” (round) the time aspect – time passing as you go along – then you end up crossing where you started – its a circle (spacetime hypersphere). Now if time started at the big bang and you cross that point on completing your first circumnavigation of the spacetime hyperphere, then you have travelled back to where you started. You have pseudo-infinite time, not truly infinite time, as you have looped back on yourself and reset the clock, and presumably the “throws of the dice” to zero. You are destined to repeat the same journey again, and all things being equal the outcome on the next loop will be the same as on the last one. Ah, but the dice are truly random you say.
Hmm. Truly random.
Exactly and precisely conforming to randomness which is carefully defined as being…? Hmm. Need I do deep philosophy here or is the obviously oxymornic character of this notion enough to say that it’s hardly surpising that in the real world we have never achieved true randomness and logic has failed to even validate it as an abstract concept due to the hopeless paradox that it poses.
So at best you have repetitious pseudo infinity and no randomness at all. Not good ingredients for translating the abstract infinite monkey theory into applied math to achieve a concrete outcome in the real universe.
No, the infinite monkey theory isn’t even valid as a statistical theory in the abstract, as one of its underpinning concepts has not even abstract validity – namely randomness, let alone its other applied shortcoming, namely the lack of infinity in the real universe. It is a non-theory that even if it was a theory could not be applied. Darwinists please note.
Just as a nice little pun for the math geeks, whilst there is an “N” in “universe”, there is no N in The Universe.