It seems that we're exact opposites! But if mathematics is your thing, it might be interesting for you to explore trying to learn things from a lagrangian perspective first?

Not sure if it'll help you with gaining an intuitive understanding, but at least it'll be interesting!

https://en.wikipedia.org/wiki/Lagrangian_mechanics

Lagrangian / Hamiltonian mechanics, the principle of least action, always seemed neat, in L&L and other places I encountered it, until I tried doing exactly what you're saying: gaining an intuitive understanding. At that point it just never made sense to me and seemed like a gratuitous deus ex machina that happens to work beautifully but for no apparent reason. You won't be surprised to learn I dropped out of my STEM program shortly after, though I keep a keen interest in the topic.

About the stationary action concept: Yeah, it looks impenetrable, but here's the thing: there is a way of looking at it from just the right angle, and then becomes transparent.

Part of the story is this: the actual criterion is: the true trajectory corresponds to a point in variation space where the derivative of the action (derivative wrt applied variation) is zero.

In the cases examined when the concept was first introduced I suppose that in those cases the derivative-is-zero point was seen to be a minimum. From there, I suppose, came a supposition that there was some form of minimization at play.

However, within the scope of classical mechanics there are also classes of cases such that at the point in variation space corresponding to the true trajectory the action is at a maximum.

The above, and other aspects, are discussed in a resource that I created.

https://cleonis.nl/physics/phys256/energy_position_equation....

In the resource the mathematics is illustrated with interactive diagrams. Move sliders to sweep out variation. The diagram shows how the kinetic energy and the potential energy respond.

About interpretation: As we know: motion along the true trajectory has the property that at every point in time the rate of change of kinetic energy matches the rate of change of potential energy. As we know: that property is known as the work-energy theorem.

The criterion derivative-wrt-variation-is-zero corresponds mathematically to the property: rate-of-change-of-kinetic-energy-matches-the-rate-of-change-of-potential-energy.

In the resource a two stage process is presented:

- Derivation of the work-energy theorem from F=ma

- Transformation from the work-energy theorem to classical mechanics stationary action

Of course: when you look at the work-energy theorem you wouldn't expect that it can be transformed to classical mechanics stationary action. The transformation consists of multiple steps. In the resource I present it step by step; for each step the logic and consistency is readily recognizable.

For me, having the breakdown into mathematical elements available changed my whole perspective on classical mechanics stationary action.

I hope I can persuade you to check out the resource

More than twenty years ago, I quit a program that taught math/cs/physics (the notorious French "classes préparatoires") ~almost precisely over this: I felt like I was being taught physics like it was an axiomatic system where the tricks should not be questioned, they just work so "shut up and calculate" (and you don't even need to be doing quantum mechanics for that).

I just felt like we never got to the heart of the matter of why the models work and how to approach developing them, it was all about learning a bag of tricks.

Meanwhile, math and CS being a lot more axiomatic by nature, they also made a lot more sense to me.

That being said, that specificity of physics, the unbridgeable gap between reality and the models we build to describe it, in retrospect, is what makes it more interesting to me today (it's not just a "closed" system in the sense that math is — of course the relationship between math and physics is itself fascinating but that's yet another topic), but I still feel like I haven't found the right pedagogical approach to make it fit my mindset.

Your issue with physics but not with math reminds me a little of Hume's law. The difference that has always made that difference "make sense" to me is that math rules, even the axiom we use, are entirely chosen by the people using them, but the rules of physics are only useful if they match/predict what happens in the real world. For math we get to pick the ones that happen to be useful at a given time for a given problem (my go-to example of "it's all made up and the points don't matter" is why 1 isn't considered prime). For physics we're constrained to pick what best describes the real world. It probably helped that nearly all the physics course I had in high school/university had lab components focused on experimentally validating those rules/using those rules to predict results.

I think what it boils down to is that in my experience physics education lacks a clear historical component about how the current state of the art is a gradual process of proposing new models and rejecting old ones and figuring out the gaps between reality and the model. Instead, it feels like a God-given set of equations (that lots of people consider "the truth" for some reason), that you apply to cookie-cutter problems you must learn by rote. Though I understand the practical concerns (but then let's call it "physics for engineering"), as far as I'm concerned, you couldn't treat physics in a worse way.

that (edit: the way you were taught) sounds like an altogether awful way to learn any hard science

The world just is, regardless of what we think about it. Physics is our best attempt so far to understand and predict it at a low level, but it will always be incomplete.

Maths (and especially compsci!) are constructions by and for humans.

Is it any wonder it is as you describe? It would be odd if it was any other way.

My point is precisely that I was often taught physics as if it was mathematics, where there is in fact a profound ontological difference between the two.

Also, physics (the discipline) is also a construction by and for humans.

To find tools applicable to reality. Not to construct reality.

Same for me. I wanted to major in physics and I quickly realized that I have no intuition for physics. Math made sense to me and I went to graduate school in math and still don’t understand anything in physics. Differential geometry, no problem. Electromagnetism makes no sense to me.

Weird, I always loved physics because I felt like I didn't have to straight up memorize everything. In a pinch (years ago) I felt like I was able to pretty much derive everything I needed if I couldn't remember the exact formulas. It's all just forces and vectors.

I identify with this perfectly. (I mean, was able to get by in physics but it never crystallized into intuition for me the way math and CS do.)

Physics? Yes. Feynman Lectures On Physics and Computation. Landau & Lifshitz. If you like SICP you might like SICM. Nielsen & Chuang's Quantum Computation and Quantum Information then Faulkner's Modern Quantum Mechanics and Quantum Information

General advice take a look at the references in works you've recently read and look for lower level topics that interest you, after repeating a few times you'll find your way to physics or chemistry and you can use the above as reference works. The best resource is the one you actually use. If https://www.youtube.com/learning works better for you then use it.

What's the problem exactly? Could you not follow the example in the text?

The standard text to build understanding in physics is University Physics by Sears & Zemansky.

It's worth remembering you're quite far from the ground in physics, and it's mostly taught with "neat" cases that give insight into physics. I.e. the thought experiment to show why kinetic energy must scale quadratically with velocity is carefully designed to show that conclusion. You shouldn't expect to have come up with it off the cuff.

> I find math and compsci reasonably understandable, can read research papers in both fields ( and have published papers) etc. There’s something specific about physics I don’t get but I’ve never been able to figure out what. The main symptom is that most cause -> consequence in such demonstrations , which are seemingly obvious to everyone, make no sense to me.

Math and CS are mostly human-made, so most of the theorems/proofs/axioms are either straightforward or elegant—there are infinitely many possible axioms with no objective way to choose between them, so people generally choose to work with the ones that are the easiest for humans to reason about. You certainly could define a complicated set of axioms with dozens of special exceptions, but unless there are some external reasons why these axioms are important, nobody will want to work with them.

Conversely, physics exists to model the real world, so unlike math and CS, physics doesn't have the privilege of being able to choose the most convenient/elegant/simplest axioms to work with. Given the constraints of the real-world data, physicists will still choose the most elegant possible model, but sometimes a wacky model is the only way to accurately model the universe.

Nobody is really happy about this though, so physics textbook authors love to make their equations/derivations look simple/obvious/elegant, but this is often completely misleading, since often the rules of the universe are so weird that nobody would ever guess them without having ran the experiments first. But textbooks tend to downplay actual experiments in favour of post-hoc explanations, which tend to make the readers think that they're missing something.

> Physics is an endless source of frustration to me. It feels like a mix of random tricks, most of which I don’t understand.

Your feelings are correct, since physics really is mostly a set of random rules that nobody truly understands. But the important thing is that these random rules correctly model nearly everything in the universe to within a few hundredths of a percent, so they're not completely arbitrary.

> Are there good resources to learn it?

The annoying/inconvenient answer is to do lots of lab work. This is actually fairly accessible though, since a measuring tape, a scale, and a slow motion camera (present on any modern phone) is all that you need for most kinematics/mechanics experiments, and a multimeter, a 9V battery, some resistors, and some magnets are enough for most electromagnetics experiments.