To simplify it a lot, it’s like one person saying “multiplying by 10 is really simple, you just add a zero to the end” and another person says “the laws of multiplication are the same for all numbers, 10 is not a separate magisterium”. Both of them are right. It is very useful to be able to multiply by 10 quickly.
But it’s worse than that. There’s a difference between being able use shortcuts, and having to. And there’s a difference between the shortcut resulting in the same answer, and the shortcut being an approximation.
Since Bayes is uncomputable in the general case, cognitively limited agents have to use heuristic replacements instead. That means Bayes isn’t important in practice, unless you forget about the maths and focus on non-
fquantitative maxims, as has happened.
Cognitively limited agents include AIs. At one time, lesswrong believed that Bayes underpinned decision theory, decision theory underpinned rationality,
and some combination of decision theory and Bayes could be used to predict the behaviour of ASIs.
Edit:
(Which to is to say that they disbelieved in the simple argument that agents cannot predict more complex agents, in general). But if an agent is using heuristics to overcome it’s computational limitations, you can’t predict it using pure Bayes, even assuming you somehow don’t have computation limitations, because heuristics give different and worse answers. That is, you can’t predict it as a black box and would need to know it’s code.
So Bayes isn’t useful for the two things it was believed to be useful for, so whats left is basically a philosophical claim ,that Bayes subsumes frequentism, so that frequentism is not really rivalrous. But Bayes itself is subsumed by radical probabilism, which is more general still!
But it’s worse than that. There’s a difference between being able use shortcuts, and having to. And there’s a difference between the shortcut resulting in the same answer, and the shortcut being an approximation.
Since Bayes is uncomputable in the general case, cognitively limited agents have to use heuristic replacements instead. That means Bayes isn’t important in practice, unless you forget about the maths and focus on non- fquantitative maxims, as has happened.
Cognitively limited agents include AIs. At one time, lesswrong believed that Bayes underpinned decision theory, decision theory underpinned rationality, and some combination of decision theory and Bayes could be used to predict the behaviour of ASIs.
Edit:
(Which to is to say that they disbelieved in the simple argument that agents cannot predict more complex agents, in general). But if an agent is using heuristics to overcome it’s computational limitations, you can’t predict it using pure Bayes, even assuming you somehow don’t have computation limitations, because heuristics give different and worse answers. That is, you can’t predict it as a black box and would need to know it’s code.
So Bayes isn’t useful for the two things it was believed to be useful for, so whats left is basically a philosophical claim ,that Bayes subsumes frequentism, so that frequentism is not really rivalrous. But Bayes itself is subsumed by radical probabilism, which is more general still!