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Comment by mr_overalls | Hacker News Reader

I did an undergrad in physics decades ago, and it pleases me to no end to see that someone else has made this observation. Especially when dealing with quantum weirdness, the advice of professors to focus "follow the math" always seem to gloss over the extensive interpretation (Copenhagen and otherwise) that gave context and meaning to the math & experimental results.

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In my experience, the reason to “follow the math” is that it is the best and perhaps only way to truly understand a physical theory, especially one as strange as quantum mechanics. One can understand the math first, and then develop an understanding of the context and meaning. But this abstract understanding is anchored in math. This is important because when the meaning gets too obscure, one can return to the math to resolve any confusion. The other way around does not work.

Scientific understanding (defined by the ability to make accurate predictions) can be (must be?) anchored in both the math and physical intuitions/observations, and it's very difficult to bridge the two without resorting to natural language (even if it's just you talking to yourself in your head while you look at the equations).

The whole problem with the Navier-Stokes equations is that the math seems to work extremely well, but we have no way to be sure it actually captures every aspect of reality (given suitably accurate initial inputs). You can use the equations to generate pretty convincing simulations, but they certainly do not always predict the fine-grained behavior of real-world turbulent systems.

Feynman's lectures repeatedly stress that physical laws (and the math that formalizes them) are, at best, idealized approximations of reality. Here's one, but you can google "feynman approximation laws" for more: https://www.feynmanlectures.caltech.edu/I_01.html

> Scientific understanding (defined by the ability to make accurate predictions) can be (must be?) anchored in both the math and physical intuitions/observations

I wouldn't conflate intuitions and observations like that. Observations in many physical realms are best described by math, which is used to build up a natural-language approximation for communicating of unintuitive findings.

you're right, I should have replaced "intuitions" with "observations" instead of waffling

"This is important because when the meaning gets too obscure, one can return to the math to resolve any confusion. The other way around does not work."

Note: my math is not very advanced, at least not good enough to understand quantum mechanics

But why does it not work the other way? When the math tells me something very wrong, can't the conctext and meaning show where the math modell is wrong?

As far as I understood, every physical modell is only a limited model of reality, so they all have flaws. Meaning the math can be wrong when applied to reality, which one could spot, with the understanding of reality?

> When the math tells me something very wrong, can't the context and meaning show where the math model is wrong?

The point is that when learning a new part of physics, it is far more likely that your intuition was wrong as the math was right, even if it's surprising.

Sure, the mathematical model is not a perfect model, but it can still be _very_ good, so if you disagree with it, you're very likely to be wrong.

GP is indeed wrong. We do use fundamental principles and philosophical positions to figure out what's wrong with our math when the results are wrong or nonsensical. These are in fact part of even an undergraduate physicist's training to be able to tell if some model is violating energy conservation or the second law of thermodynamics or the speed of light etc.

However, if you count the number of times a physicist uses math to resolve conceptual confusion and count when they use physical principles to fix the math, you will find the former many times larger than the latter.

Doubt anyone can understand the reality outside of the mathematics. Tho I will say that I've had math classes taught by physicists and they talk about how the math works/what it means a lot better than the math people, that know the theorems and the logical connections well butn't always develop the conceptual framework implied.

The mathematical formalism of quantum mechanics is (believed to be) central in the network of facts about quantum mechanics, if we draw an edge between two facts when one helps you understand another. Therefore, it makes more sense to learn the formalism first and use it to help you understand the data, predictions and interpretations, rather than the reverse.

The point of follow the math is that on this specific case, the only valid interpretation is the trivial ones that map your numbers into your observations.

The possible explanations for the weirdness are all speculation about how to solve a very important problem. But they neither valid interpretations (because they don't explain anything anybody can see) nor about Quantum Mechanics (they are about an open problem of physics, not about the theory the teacher is explaining).

It is important to speculate on how one can solve problems. That's where solutions come from. But this is not the same thing as interpreting results.

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