Nitpick: a 60 million digit number divided by 1 billion is not 51 million digits, instead, it would be ≈ (60 million - 9) digits ≈ 59,999,991 digits long.
That would be true if the monkey’s keypresses were statistically random, in that each key would have the same probability of being pressed as any other key, but my personal hunch is that a monkey banging away on a keyboard is not statistically random and thus they would never achieve this goal.
Heck, I’d bet that if a human pounded “randomly” on a keyboard, and the resulting characters were converted into their ASCII binary equivalents and then run through the Diehard statistical test suite, they’d fail those tests miserably.
Good catch, thanks. My math had erroneously slashed my gigantic number by about 1/6, but your correction shows how big the number really is; dividing by a billion is barely noticeable.
As long as there is some nonzero probability of hitting every key, the monkey would eventually produce Hamlet. It might just take longer than if the probability of each key were the same. In fact, there must be some nonuniform probability distribution that would produce Hamlet faster than if the keys were uniformly likely.
I’d also (and maybe more controversially) add I’m a fan of the Trolley Problem thought experiment, despite now being meme-fied to the point of being somewhat meaningless. I do think its actually a good thought experiment that highlights real complications in ethical systems.
I like Galileo’s thought experiment where he proved that heavy objects do not fall faster than light objects. Usually people think he dropped two stones from the tower of Pisa, a heavy one and a light one, and both dropped simultaneously. He probably never did that, and if he did, he did knowing the result. And he knew from thinking about it like this:
Start postulating that heavy objects fall faster than light ones. Take two objects, one heavy, one light, and bind them together with a slack rope. A rope transmits force by pulling but not by pushing. Let them fall. The heavy object falls faster, the light one lags behind. Until the rope is tight, when the total mass of both bodies falling increases, so they suddenly accelerate. Which is absurd, so heavy objects do not fall faster than light ones. QED.
I find this brilliantly visualized.
Yeah, after considering it some more, you’re absolutely right.
I must’ve been thinking along the lines of the monkey pressing multiple keys simultaneously with their palms, of which the probability distribution of consecutive keys would correspond to the monkey’s hand shape mapped onto the keyboard, implying certain keys would never follow each other because the other keys covered by that hand shape would interpose first.
On the other hand, if the monkey was pressing keys one at a time, then like you said as long as each key has a nonzero chance of being pressed, then Hamlet is inevitable.
A quantum physics thought experiment that I only half understand but it still seems fascinating: what happens when an observer is themselves in a superposition of states according to another observer? Wigner's friend - Wikipedia