Comment by selecsosi

Comment by selecsosi 3 days ago

Having studied undergraduate physics, I think this viewpoint is inverted from the realities of the matter. It is less that the math is complicated and more so these are the relevant tools invented for us to model the experimental results we obtain post discovery/formalization of SR/GR/Quantum experiences. There are computers that can run these simulations but they are infeasible to model large scale processes. That is the reason people are looking for more than numerical solutions to problems, but laws and tools that can simplify modeling large scale emergent behavior that it would be infeasible or unnecessarily complicated to do with numerical simulation. These tools are the more straightforward approach

xigency 3 days ago

It's evident and obvious in any of these explanations that the equations and properties of math are taken as true a priori, not grounded on observation (in their invocation).

If I write a partial differential equation that I came up with randomly and ask you to find all the potential solutions that really doesn't tell you anything about the natural world.

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selecsosi 2 days ago

I think that's more your interpretation/experience rather than the intention of the tools. Those constants and coefficients are there because the math is describing the shape of the solution based on logic, mathematical object rules, and symmetry/conservation laws and needs to be "grounded" to make them physical.
The Lagrangian is just "conservation of energy" (L = T[kinetic] - V[potential]). There isn't some magic, it's a statement that the energy needs to go somewhere.
Your straw-man belies the underlying issue you are experiencing, you don't just come up with a PDE, you see nature and then you describe ways to conserve counts of things, "energy", "population", whatever. The PDEs describe the exchange between these counts. The accuracy and additional terms are about more accurately representing the counts and conservation of things.

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