find the shortest algorithm that outputs the same predictions.
Prediction making is not a fundamental attribute that hypotheses have. What distinguishes hypotheses is what they are saying is really going on. We use that to make predictions.
The waters get muddy when dealing with fundamental theories of the universe. In a more general case: If we have two theories which lead to identical predictions of the behavior of an impenetrable black box, but say different things about the interior, then we should choose the simpler one. If at some point in the future we figure out how to open the black box, then the things you had labeled implementation details might be leading to predictions.
I don’t think we should abandon that just because we hit a black box that appears fundamentally impenetrable.
Why do you use the adjective ‘simpler’? I understand that this isn’t just you, but the common term for this context. But we really mean ‘more probable’, correct? In which case, why don’t we just say, ‘more probable’?
I’m not sure what ‘simpler’ means but I don’t think the relationship between ‘simple’ and ‘probable’ is straight-forward—except when the more complex thing is a subset of the more simple thing. That is, in the usual provided example that A∩B is more probable than A∩B∩C.
Simpler is not always more probable, it’s just something with which to build your priors.
If you have two theories that make different but similar predictions of noisy data, the one that fits the data better might be the more probable, even if it’s vastly more complex.
Prediction making is not a fundamental attribute that hypotheses have. What distinguishes hypotheses is what they are saying is really going on. We use that to make predictions.
The waters get muddy when dealing with fundamental theories of the universe. In a more general case: If we have two theories which lead to identical predictions of the behavior of an impenetrable black box, but say different things about the interior, then we should choose the simpler one. If at some point in the future we figure out how to open the black box, then the things you had labeled implementation details might be leading to predictions.
I don’t think we should abandon that just because we hit a black box that appears fundamentally impenetrable.
Why do you use the adjective ‘simpler’? I understand that this isn’t just you, but the common term for this context. But we really mean ‘more probable’, correct? In which case, why don’t we just say, ‘more probable’?
I’m not sure what ‘simpler’ means but I don’t think the relationship between ‘simple’ and ‘probable’ is straight-forward—except when the more complex thing is a subset of the more simple thing. That is, in the usual provided example that A∩B is more probable than A∩B∩C.
Simpler is not always more probable, it’s just something with which to build your priors.
If you have two theories that make different but similar predictions of noisy data, the one that fits the data better might be the more probable, even if it’s vastly more complex.