High dimensional world: to find something as useful as e.g. Fourier methods by brute-force guess-and-check would require an exponentially massive amount of search, and is unlikely to have ever happened at all. Therefore we should expect that it was produced by a method which systematically produces true/useful things more often than random chance, not just by guess-and-check with random guessing.
If you suppose that physics tries to deal with the whole of reality in one gulp, then its ability to come up with simple general rules would be remarkable. But actually , physics deals with extremely simplified and idealised situations … frictionless planes, free fall in a vacuum, and so on. Even experiments strive to simplify the natural messiness of reality into something where only one parameter changes at a time
(This is partly a response to the comment above, but I got kind of carried away.)
The Standard Model of particle physics accounts for everyday life (except gravity) in ridiculous detail, including all the “natural messiness” you have in mind (except gravity). It consists of some simple and unique (but mathematically tricky) assumptions called “quantum field theory” and “relativity”, plus the following details, which completely specify the theory: * the gauge group is SU(3) x SU(2) x U(1) (or “the product of the three simplest things you could write down”) * the matter particles break parity symmetry, using the simplest set of charges that works * there are three copies of each matter particle * there is also a scalar doublet * the 20ish real-valued parameters implied by the above list have values which you can find by doing 20ish experiments.
I dare anybody to give a specification of, say, all of known organic chemistry or geology with a list that short. You don’t need to spell out any mathematical details, so long as a mathematician could plausibly have invented it without being inspired by physical reality (which are the rules I’m playing by in this comment—I think QFT, relativity, and concepts like “gauge group” and “parity symmetry” that I assume knowledge of are all things math could/would have produced eventually).
In some sense I’m handwaving past the hard part, but I think the remarkable thing about physics is that the hard part is entirely math; if you did enough math in a cave without observing anything about the physical world, you would emerge with the kind of perspective from which the known laws of physics (except gravity) seem extremely parsimonious. (Gravity is also parsimonious but sort of stands alone for now.) On the other hand, if you go do a lot of experiments instead, the laws of physics will seem bizarre and complicated. Which I admit is kind of a strange fact! It’s not clear that “math parsimony” is the same concept as, say, Turing-machine-based Kolmogorov complexity, and it definitely isn’t anybody’s intuitive notion of “simplicity”.
And of course, quite a lot of the “natural messiness” of the world is captured by even simpler Newtonian-mechanics models, although chemistry becomes a kind of nasty black box from a Newtonian perspective.
You are responding as though I said something like “physics doesn’t work at all”, when I actually said it works via idealisations and approximations. To talk of Effective Field Theories concedes my point, since EFTs are by definition approximations .
You said “extremely simplified and idealised situations … frictionless planes, free fall in a vacuum, and so on”. That’s a pretty different ballpark than, say, every phenomenon any human before the 1990s had any knowledge of, in more detail than you can see under any microscope (except gravity).
Do you consider everything you’ve experienced in your entire life to have happened in “extremely simplified and idealised situations”?
This is true of the physics most people learn in secondary school, before calculus is introduced. But I don’t think it’s true of anyone you might call a physicist. I’m confused by the chip you seem to have on your shoulder re physics.
Calculus isn’t a magic trick that allows you to dispense with idealisations and approximations. You can start dealing with friction and air resistance, but you don’t get one equation that is completely precise and applicable to anything.
I don’t have a chip on my shoulder about physics: everyone else has a halo effect
If you suppose that physics tries to deal with the whole of reality in one gulp, then its ability to come up with simple general rules would be remarkable. But actually , physics deals with extremely simplified and idealised situations … frictionless planes, free fall in a vacuum, and so on. Even experiments strive to simplify the natural messiness of reality into something where only one parameter changes at a time
(This is partly a response to the comment above, but I got kind of carried away.)
The Standard Model of particle physics accounts for everyday life (except gravity) in ridiculous detail, including all the “natural messiness” you have in mind (except gravity). It consists of some simple and unique (but mathematically tricky) assumptions called “quantum field theory” and “relativity”, plus the following details, which completely specify the theory:
* the gauge group is SU(3) x SU(2) x U(1) (or “the product of the three simplest things you could write down”)
* the matter particles break parity symmetry, using the simplest set of charges that works
* there are three copies of each matter particle
* there is also a scalar doublet
* the 20ish real-valued parameters implied by the above list have values which you can find by doing 20ish experiments.
I dare anybody to give a specification of, say, all of known organic chemistry or geology with a list that short. You don’t need to spell out any mathematical details, so long as a mathematician could plausibly have invented it without being inspired by physical reality (which are the rules I’m playing by in this comment—I think QFT, relativity, and concepts like “gauge group” and “parity symmetry” that I assume knowledge of are all things math could/would have produced eventually).
In some sense I’m handwaving past the hard part, but I think the remarkable thing about physics is that the hard part is entirely math; if you did enough math in a cave without observing anything about the physical world, you would emerge with the kind of perspective from which the known laws of physics (except gravity) seem extremely parsimonious. (Gravity is also parsimonious but sort of stands alone for now.) On the other hand, if you go do a lot of experiments instead, the laws of physics will seem bizarre and complicated. Which I admit is kind of a strange fact! It’s not clear that “math parsimony” is the same concept as, say, Turing-machine-based Kolmogorov complexity, and it definitely isn’t anybody’s intuitive notion of “simplicity”.
And of course, quite a lot of the “natural messiness” of the world is captured by even simpler Newtonian-mechanics models, although chemistry becomes a kind of nasty black box from a Newtonian perspective.
The SM is itself a kludge. It’s not a satisfactory TOE for a bunch of reasons besides gravity.
It is definitely not a TOE, but it is a successful EFT that accounts for everything except gravity/cosmology.
You are responding as though I said something like “physics doesn’t work at all”, when I actually said it works via idealisations and approximations. To talk of Effective Field Theories concedes my point, since EFTs are by definition approximations .
You said “extremely simplified and idealised situations … frictionless planes, free fall in a vacuum, and so on”. That’s a pretty different ballpark than, say, every phenomenon any human before the 1990s had any knowledge of, in more detail than you can see under any microscope (except gravity).
Do you consider everything you’ve experienced in your entire life to have happened in “extremely simplified and idealised situations”?
This is true of the physics most people learn in secondary school, before calculus is introduced. But I don’t think it’s true of anyone you might call a physicist. I’m confused by the chip you seem to have on your shoulder re physics.
Calculus isn’t a magic trick that allows you to dispense with idealisations and approximations. You can start dealing with friction and air resistance, but you don’t get one equation that is completely precise and applicable to anything.
I don’t have a chip on my shoulder about physics: everyone else has a halo effect