Most of the standar model complexity comes from the variety of particles, forces, and aggregations thereof that need to be contended with.

GR likewise becomes a brutal computational mess with these many body problems.

What will be interesting in these new experimental results is whether we’re reaching the limits where determining the correctness of our approximations becomes impractical.

Nature doesn't care how complicated it is. A bias towards beauty is a trap that any serious scientist will not fall for.

https://www.youtube.com/watch?v=xFKgIOX8IRE

A bias towards "beauty" or simplicity of some form is inevitable and part of good science.

For every theory, you can generate a more complicated theory with more moving parts that generates the exact same predictions. For instance, my theory of gravity is the same as general relativity, except that at 3 PM April 9th, 2021, all gravity will be reversed.

You have to appeal to some principle to sort out such theories from good descriptions of how the world works.

> A bias towards "beauty" or simplicity of some form is inevitable and part of good science.

> For every theory, you can generate a more complicated theory with more moving parts that generates the exact same predictions.

I agree with the second point, but disagree with the first.

Yes, by Occam's razor, a simpler theory with fewer moving parts should be preferred over a complex theory, if both produce correct answers. But the most accurate theory might not be "beautiful".

What matters most is if the theory correctly predicts reality. If it has a weird arbitrary format, but correctly predicts everything, it's better than a theory that's beautiful but incorrect.

Most of science has been using "beauty" as a way to help guide it to the correct answers. For example, there's been a lot of work on string theory because it has a kind of mathematical beauty. But it may turn out that a search for "beauty" in this sense was misguided. Beauty is not the goal, truth is.

"the most accurate theory might not be 'beautiful' "

Welcome to Biology! :-)

(Except DNA -> RNA -> Protein, but it's still sloppy along the way)

> You have to appeal to some principle to sort out such theories from good descriptions of how the world works.

Yes: testable predictions followed by experimental evidence.

Beyond that I don't see how what you're talking about is anything other than an appeal to aesthetics.

> Yes: testable predictions followed by experimental evidence.

But there are an infinite number of theories matching the current evidence. Some predictions of the theories might not be testable, what do you do then?

Simple: you label them as fiction rather than science. The scientific method has experimental feedback built into the loop.

Well then you have to label everything as fiction rather than science because if you don't single out the simplest theory you can't say that general relativity is science and general relativity plus sun turns into cake tomorrow isn't science. And if someone tells you the sun will turn into cake tomorrow and claims that your theory where the sun doesn't turn into a cake tomorrow is fiction and unscientific cause it doesn't make predictions to distinguish it from their theory, you don't have any principled philosophical ground to disagree whith them .

And that's not so clearly bad there because they are obiously wrong, but then you get to complicated topics where everyone has hard to resolve disagreements about which theory should be the default from a big pool of theories that seem to agree whith the evidence.

Doing something clearly outside of empiricism then saying “why doesn’t empiricism cover this” is complete nonsense. What is the ontological explanation for your hypothesis that the sun will turn into cake? Misunderstanding the scientific method is not an issue with the scientific method.

If its turtles all the way down, and physics goes on forever like a fractal, you'll find domains where you can approximate with relatively simple mathematics ("beautiful") and domains that require much more mathematical machinery to describe

On this point, you might enjoy "A Fortunate Universe (Life in a Finely Tuned Cosmos)" by Lewis and Barnes. It discusses this "fine-tuning" problem in a detailed and up-to-date way, and avoids the theological speculation found in some other treatments. (That is, fine-tuning is sometimes presented as evidence for God.)

It doesn't seem obvious that the fundamental models of reality would just happen to match up with the mathematical constructs that we humans have come up with.

On the flip side, it wouldn't be entirely surprising if mathematical constructs that we have thought of are in fact very good models of fundamental reality. We should remember that, after all, nothing exists outside of fundamental reality, and if certain basic patterns can be encoded such that the encoding is both high-fidelity and simple, that won't be shocking. It might be awe-inspiring, but not really surprising.

>nothing exists outside of fundamental reality

A bold assertion.

This is a deep philosophical debate: Is mathematics invented or discovered?

https://www.pbs.org/wgbh/nova/article/great-math-mystery/

I think it's a bit less deep than that. It's more, "is the language we use to describe mathematics invented or discovered", which I would put myself (and most people) firmly in the invented camp.

Despite its complexity, the model has been remarkably successful during the last decades.