this post was submitted on 25 Sep 2023
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Consider math, it doesn’t make any empirical predictions on its own, as it is just a set of abstract symbols and rules. Do you consider mathematical facts to be a form of knowledge?
Maths and reality are different. Very different. Reality can be explored empirically while maths is logic not empirical. We can never say we are 100% sure about the rules/laws we have discovered about our reality, but we can say for sure that a maths theorem is true or false.
Maths is a set of self-consistent tools that can be used to predict what happens in reality. The mathematical description of reality is an estimate, contains countless assumptions and inaccuracies about where things are and what properties they have. In fact in quantum physics, we literally can't know momentum and location at the same time.
Maths can describe (or I should say, approximate) realities that don't exist.
Because maths and reality are different domains, we can know different things about them using different approaches.
I mean, we can know a precise wavefunction, though. That's a bit like saying we can't give a single point where a tsunami is. It seems highly likely to me personally that physics is mathematical and we've just kind of absorbed it in the process of evolving intelligence.
Arguably "it's impossible to violate energy conservation given time-invariant action" is an empirical prediction, and that's a specific case of Noether's theorem.