why do solutions to 2nd order differential equations have to be so disgusting...

I finally remember why I quit studying physics:

In IT, when a solution is disgusting, it because of human imperfection. It ciuld always be better.

In physics, when a solution is disgustng, lt's because that's how nature behaves and that disgusting equation will never go away.

@wolf480pl Just define it as a macro called theta_one or something, it'll be fine

@wolf480pl or, you haven’t found a way to abstract them in a good way yet

It took decades for Maxwells equations to go from the form tgey were published in to the form we know them today

@ignaloidas I guess I'm just not interested in maths enough to try and find better ways to formulate things...

Nature, is not explainable with calculus.
@wolf480pl

@p is nature explainable?

Currently, I would say no, as all we have are approximations.
Fundamentally, not sure
@wolf480pl

@p is there some proof that differential calculus cannot explain nature - some sort of physics equivalent of Goedel's Incompleteness Theorem?

Keep in mind that these equations are approximations of experimental results, so another equation might be found which approximates the result better, and that equation will fall by the wayside.

@cjd yeah

and the better approximation will be more awful

@cjd which of the Bessel functions is your favourite?

Difference between theory and results. Theory supposes the equation is nature as opposed to being one possible description thereof.

@8384e79741c1f30ac31d35890740c244d2180160e20e3c85f246320e02bdde15 does anyone hope that we will discover better descriptions of reality that are both simpler and more accurate at the same time?