You can have same software running on multiple machines. There’s still intermediate steps where you go from 1 to 2.
I think the question is fundamentally misguided with regards to the meaning of the word “probability” , and the phenomenalist position is the only correct one. I.e the question is meaningless. The “probability” is not a property of the world of sleeping beauty problem, it’s just an intermediate value in the calculations, correctness of which is only defined by it’s end use, e.g. in bets. Where the best value depends on which instances of the program we prefer to end up betting wrong.
I have a lot of sympathy for the idea that probability is just a helper for betting (i.e. decision theory), but what do you make of all the talk about limits of subjective frequencies, etc.? Do you think it’s all meaningless, and the laws of physics that we observe to be “statistically true” (e.g. the second law of thermodynamics or the Born rule in QM) somehow come from betting as well?
Thermodynamics works fine under fully deterministic laws of physics. And with QM we don’t have satisfactory quantum gravity so I wouldn’t put much weight on implications of that.
Let’s consider the sleeping beauty thing without abstracting out randomness. A coin is tossed, it bounces several times, making it final orientation highly sensitive to the original orientation. It comes to rest, heads up, or tails up (we don’t know such things, ultimately because our head is a region of the universe smaller than the universe itself). For the given conditions it was physically impossible for it to have ended up the other side up. The betting is quite straightforward (dependent on whenever there’s 2 bets vs 1 bet).
edit: and the probabilities of the cylinder landing on either side or the edge, they are properties of real world all right—they’re the fraction of the hyper volume of possible initial phase space mapping to either final orientation, derivable without having to do statistical averaging.
You can have same software running on multiple machines. There’s still intermediate steps where you go from 1 to 2.
I think the question is fundamentally misguided with regards to the meaning of the word “probability” , and the phenomenalist position is the only correct one. I.e the question is meaningless. The “probability” is not a property of the world of sleeping beauty problem, it’s just an intermediate value in the calculations, correctness of which is only defined by it’s end use, e.g. in bets. Where the best value depends on which instances of the program we prefer to end up betting wrong.
See Cox’s theorem for what kind of objects I’m talking about when I refer to a non-betting “probability.”
I have a lot of sympathy for the idea that probability is just a helper for betting (i.e. decision theory), but what do you make of all the talk about limits of subjective frequencies, etc.? Do you think it’s all meaningless, and the laws of physics that we observe to be “statistically true” (e.g. the second law of thermodynamics or the Born rule in QM) somehow come from betting as well?
Thermodynamics works fine under fully deterministic laws of physics. And with QM we don’t have satisfactory quantum gravity so I wouldn’t put much weight on implications of that.
Let’s consider the sleeping beauty thing without abstracting out randomness. A coin is tossed, it bounces several times, making it final orientation highly sensitive to the original orientation. It comes to rest, heads up, or tails up (we don’t know such things, ultimately because our head is a region of the universe smaller than the universe itself). For the given conditions it was physically impossible for it to have ended up the other side up. The betting is quite straightforward (dependent on whenever there’s 2 bets vs 1 bet).
edit: and the probabilities of the cylinder landing on either side or the edge, they are properties of real world all right—they’re the fraction of the hyper volume of possible initial phase space mapping to either final orientation, derivable without having to do statistical averaging.