> 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 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.