Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
The point is that there isn't enough time in the universe for all the random stuff to happen that scientists pin on random chance. The theorem was memorable, but a cop out.
> Yes, but the theorem is meant to explain what can happen in the universe over long time scales.
I never understood it that way. I always interpreted it as a fun way to explain the mathematical truth that no matter how low a probability is, as long as it is technically above 0, the event it describes WILL eventually occur given enough time/trials/etc.
I can't see anybody ever interpreting it as a statement about the real, actual, universe. Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side. Surely people can separate the mathematical ideal/concept from constraints of physical reality.
> Just like I don't think anybody truly believes that flipping a real coin with non-identical sides (such as every currency coin I've ever used) must have EXACTLY 50% probability of landing on either side.
That's a nice thought, but that's giving the average person too much credit when it comes to probability. In my experience, most people's understanding of probability is very poor. For example, few people truly understand the concept of independent events.
Most people believe that after flipping 10 heads in a row, the probability of tails on the next flip is much higher.
I'm sure you could convince a rational individual that the assymetry of the coin makes 50/50 impossible. But I doubt that the average person has ever really considered it.
> the event it describes WILL eventually occur given enough time/trials/etc.
What's the meaning of writing WILL with capitals, and then saying "nobody is talking about the real, actual universe"? What is the value of certainty about what WILL happen in hypothetical universes?
> What is the value of certainty about what WILL happen in hypothetical universes?
Talking about something that would take greater than 1 googol years in our universe has about as much value as talking about something that would take 1 googol years in our universe.
In other words, the fact that something might probably occur right before the heat death of the universe, rather than after, isn't particularly useful either. For that matter, there's about an equal value in talking about something probably "only" a trillion years out, either.
I don't think I've ever heard anyone use the infinite monkey example outside of theoretical mathematics; I'm sure someone has, but when I've heard it, it was to describe regular distribution of random.
I think it's a very bizarre thing for these mathematicians to act like they discovered something that I don't think anyone really disputed.
Perhaps not in our observable universe, but in the space of all possible physics that could take place and / or beyond the observable universe if it actually is infinitely big there, perhaps it can? (as in, anything can happen, there will be copies of the Earth with subtle differences somewhere there, Boltzmann brains appearing purely out of quantum fluctuations, etc...)
The point is that there isn't enough time in the universe for all the random stuff to happen that scientists pin on random chance. The theorem was memorable, but a cop out.