I wonder if our common expectation that true theories somehow had to be beautiful and elegant is going to survive the coming century. What if "real" nature phenomenon were actually best described by horrible mess of impossible equations, that only machines could actually manipulate and reason about ?

That would be really sad..

> our common expectation

I think you're going too far with this. Most people understand scientific theories to be an approximation. F=ma is approximately true, in the sense that it's only accurate within the newtonian regime and each of those terms includes so many asterisks that you will only ever measure it approximately.

The latter is the jokes about the physicists "assuming a perfectly spherical cow."

In fact that's kinda the whole point of the "unreasonable effectiveness of mathematics" essay. It is unreasonable that mathematical approximations are so good at describing our world.

Would it be sad? If it’s gnarly and it solves the problem, as an end user I don’t really care. The only people who lose are the mathematical purists

I often think this about medicine and the human body. We want to believe that our bodies are some miraculous well oiled machine. But it often seems that it’s a barely held together bag of mess.

This has been on my mind lately! Especially in light of the many incomprehensible but machine-checkable proofs we've been hearing about.

Occam's Razor is a useful heuristic, but it biases us towards simpler explanations.

The "common expectation" I think, misses the point. The idea isn't that fundamental theories are simple or elegant (quantum physics equations are pretty darn ugly), it's that, given the choice between a more complicated and a more simple theory, generally the simplest one is the most accurate choice.

That is very unlikely due to Solomonoff induction...

>I wonder if our common expectation that true theories somehow had to be beautiful and elegant is going to survive the coming century.

That's the layman's idea of physics theories. They are beautiful and elegant only on the surface, that's why they're technically models and approximations of the real world. The standard model renormalization techniques are a mess of patches and ad-hoc heuristics, pretty far from the "this lagrangian literally contains all physics". Generally you just _ignore_ higher order terms and just call it a day. The famous E=mc^2 it's just the first term of a Taylor expansion. The beautiful form of physics it's what you would call "good enough" and often just a pedagogical tool.

It would be really cool. We already know everything at the lowest levels is a probability cloud. There’s beauty and contentment in not really being able to nail anything down for eternity…

Does the nature look like a horrible mess to you?

How would nature be best described as a horrible mess of impossible equations? They would be best described as elegant and beautiful no?

I think your point is more that we might be able to initially describe complex phenomena as messy, horrible complex equations, that doesn’t mean we shouldn’t work to simplify them and make them more understandable to us.