As alluded to by the name of the website, part of Solomonoff/MDL is that there doesn’t necessarily have to be a unique “correct” explanation: theories are better to the extent that their predictions pay for their complexity. It’s not that compact generators are necessarily “true”; it’s that if a compact generator is yielding OK predictions, then more complex theories need to be making better predictions to single themselves out. You shouldn’t say that looking for compact generators of a complex phenomenon is asking to be wrong unless you have a way to be less wrong.
IME in this domain, in epistemology-for-humans terms that may or may not translate easily into Solomonoff/MDL, taking a compact generator of a complex phenomenon too seriously — like, concentrating probability too strongly on its predictions, not taking anomalies seriously enough or looking hard enough for them, insufficiently expecting there to be more to say that sounds different in kind — is asking to be wrong, and not doing that is a way to be less wrong.
(Looking for compact generators but not taking them too seriously is good, but empirically seems to require more skill or experience.)
You don’t need to single out a specific complex theory to say “this simple theory is concentrating probability too strongly”, or to expect there to be some complex theory that pays for itself.
As alluded to by the name of the website, part of Solomonoff/MDL is that there doesn’t necessarily have to be a unique “correct” explanation: theories are better to the extent that their predictions pay for their complexity. It’s not that compact generators are necessarily “true”; it’s that if a compact generator is yielding OK predictions, then more complex theories need to be making better predictions to single themselves out. You shouldn’t say that looking for compact generators of a complex phenomenon is asking to be wrong unless you have a way to be less wrong.
IME in this domain, in epistemology-for-humans terms that may or may not translate easily into Solomonoff/MDL, taking a compact generator of a complex phenomenon too seriously — like, concentrating probability too strongly on its predictions, not taking anomalies seriously enough or looking hard enough for them, insufficiently expecting there to be more to say that sounds different in kind — is asking to be wrong, and not doing that is a way to be less wrong.
(Looking for compact generators but not taking them too seriously is good, but empirically seems to require more skill or experience.)
You don’t need to single out a specific complex theory to say “this simple theory is concentrating probability too strongly”, or to expect there to be some complex theory that pays for itself.