It is important to understand the limitations of logic and maths. They are fundamentally tautological systems - they can’t give you genuinely new knowledge abou

It is important to understand the limitations of logic and maths. They are fundamentally tautological systems - they can’t give you genuinely new knowledge about the world. Logic can’t tell you if purple swans exist or whether planetary orbits are circular or elliptical. You need empirical evidence for that. So information theory might give you a measure of the complexity of a theory, but can’t (on its own) say anyting about whether it is true or not. But hypothetically there could (as you suggest) be a correlation between the complexity of competing scientific theories and which theory turns out to best match evidence. But is there any empirical evidence for this to be the case? Just because it would be nice does not make it true, and it is not something you can prove mathematically.