As you move up levels starting from physics (eg. physics-> chemistry-> biochemistry-> biology), each layer has several "laws" which are generally pretty established, but a causal connection between the layers is hard to provide satisfactorily. And that is how I think it'll always be, else we'll be expecting to explain Shakespeare's plays using physics.
Also, this is where Rutherford's "all science is either physics or stamp collecting" holds a lot of water. As you move up the science layers, the laws themselves become less mathematically rigid until by the time you get to the social sciences, explanations are all hand-waving, and all "laws" are statistical at best and empirical.
Fundamental physics is also empirical. It's that as you move up to more 'fuzzy' sciences, the 'laws' become less strict, less formal defined, and (most importantly) less reliable.
Edit: and less universal. Physics underlies biology, chemistry, nuclear tech & more. Biology (so far) only applies to carbon-based life as we know it on Earth.
Yes, this is key in my mind. It's not really that the laws and definitions become less strict of themselves, it's that the subjects under study become less uniform. It's fine to study a few atoms in isolation and describe their features, but if you put a lot of them together they'd better be in a uniform lattice or your calculations will take more than a lifetime to complete. If you want to describe the interaction in a drop of water, you don't use the Standard Model to integrate over 3e22 baryon fields.
Yes, physics underlies all other fields. But fundamental physics is also completely untractable to solve problems in those other fields, even if Heisenberg would allow it.
> else we'll be expecting to explain Shakespeare's plays using physics.
This is just a data problem though. From the perspective of a deterministic universe, creative works theoretically can be explained as a physics outcome (ignoring the impact of potential quantum randomness).
Yeah, but that’s like saying predicting next week’s lottery numbers, or the precise weather exactly one year from now, is a data problem. There’s no simulation that could answer those questions even in principle even if the universe were fully classical.
> From the perspective of a deterministic universe, creative works theoretically can be explained as a physics outcome
In other words, physics can explain Shakespeare's plays when you hand-wave away the biggest reason it cannot.
> theoretically
... meaning not in reality, but in an abstraction of reality that conveniently leaves out the hard part.
> This is just a data problem though.
The word "just" makes it sound like that data problem is a minor inconvenience, and not a fundamental obstacle.
Becoming a billionaire is simple, after all it's just a money problem.
I mean, you're right in that (leaving out quantum randomness), you could predict macroscopic outcomes based on a physics simulation that includes all elementary particles explicitly, if you assume that such a simulation can be scaled from <10 particles to macroscopic numbers. But there is no evidence that this assumption is true, so it remains an interesting thought experiment that gets confused with reality because people like to slap the "in theory" label on it.
Yes, we've all seen the xkcd[1] but you've misunderstood it. Physics applies mathematics but mathematics cannot derive physics in the way that a complete physics (and a lot of compute) could derive chemistry and biochemistry.
Math isn't attempting to describe a physical universe. It provides the substrate upon which such a description can be expressed and validated - found to be consistent with itself - but many valid descriptions do not describe our universe. Physics is the empirical search for the correct mathematical description of our universe.
thats just at the current state of the art...doesnt mean a complete maths cannot...its arguably debatable why physics follow some maths and why the specific constrains
I don't think that's true. Mathematics can model every conceivable universe; you cannot derive the values of c or G in our universe from a purely mathematical model. Even if there were a proof that the current values for cosmological constants are the only possible values, that proof would necessarily have to rely on lemmas from physics.
It could be that once we truly understand math in a complete way it would lead inexorably to the definition of one and only one possible universe with only one possible set of rules and c and G would simply fall out naturally. I'd agree it seems unlikely given our current understanding of math and physics (and their relationship to each other). But given both are incomplete it remains a possibility. The one theme that seems to hold true as we dig deeper and deeper into how the world works is that the fundamental rules seem to get more and more unified.
Please tell us more about this. I’m not familiar with any definition of mathematics that would support the idea that it can prove statements about our universe without access to observed facts.
Are there any papers where this possibility is explored? What does it mean to have a complete understanding of mathematics?
Downvoters are probably misunderstanding this. Mathematical theory is based on axioms and inference. The axioms do not have to be true in any cosmic sense for the math to be correct or even useful.
Also, this is where Rutherford's "all science is either physics or stamp collecting" holds a lot of water. As you move up the science layers, the laws themselves become less mathematically rigid until by the time you get to the social sciences, explanations are all hand-waving, and all "laws" are statistical at best and empirical.