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Comment by WalterBright | Hacker News Reader

One physics exam question I remember was derive Maxwell's Equations from the starting point of presuming the existence of magnetic monopoles. This sounds like an intractable problem, but it turned out that if you really understood how they were derived, all you had to do was switch out the charge monopoles with the magnetic monopoles, and it was a piece of cake.

A similar exam problem in AMA95 was to derive the hyperbolic transforms. The trick there was to know how the Fourier transforms (based on sine/cosine) were derived, and just substitute in sinh/cosh.

If you were a formula plugger or just memorized facts, you'd be dead in the water.

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Both are beyond my math, but I have found several more elementary cases where calculus shows simple relationships between related formulas.

And I recall a sci-fi short story long ago, technological civilization on a single continent with a permanently clouded sky. They had not figured out they were living on a sphere, they were having trouble with train tracks mysteriously being the wrong distance and train passengers feeling light on the high speed trains. I didn't check the guy's math but it sure seemed right when the answers looked exactly like Einstein's equations even though the units were very different. (Limiting velocity = orbital velocity, the discontinuity being weightlessness.)

I do think that's one of the reasons it's easier to do in physics. You're taught to see math as a language and therefore need to interpret it. With that in mind who cares if you memorize formulas and can churn out some algorithmic computation. You'll memorize formulas "accidentally" as you use them frequently. But if you don't know how to interpret the math you're completely fucked and frankly probably won't do well as a physicist. Much of the job is translating back and forth.

I actually loved my classical mechanics class. The professor was really good and in the homeworks he'd come up with creative problems. The hardest part was always starting. Once you could get the right setup then you could churn away like any other (maybe needing to know a few tricks here and there).

Coming over to CS I was a bit surprised how test based things were. I'm still surprised how everyone thinks you can test your program to prove its correctness. Or that people gravely misinterpret the previous sentence as "don't write tests" rather than "tests only say so much"

It's normal for young engineers to believe they can write code that cannot fail, design parts that cannot fail, design bridges that cannot fall down, etc. Fortunately, it was beaten into me in my first job that the idea is not to create designs that cannot fail, but to create designs that can tolerate failure. It's a very different mindset.

Unfortunately I don't think this is being beaten out of people these days. I meet plenty of people that are seniors at quite reputable companies that believe that and it scares me...

What I hear sometimes is along the lines of "I know my program has crashed, but I know it can continue to run safely."

What was your first job?

Designing machinery parts for the 757 airplane.

Reminds me of this article - https://firstthings.com/math-is-erotic/ - strangely titled “Math is Erotic” but talking about the relationship between Maxwells Equation and water waves, and magneticism.

Funny enough, I was going to include those relationships in my original comment but pulled them out for brevity. Was going to be something like "I think it is really hard to get a physics degree and not stumble upon the similarities of Gravity and Electromagnetism where there's a striking similarity in forms. I think most people start by thinking there's some link to the unification (and imagine solving a TOE) but you end up finding incredible beauty in something seemingly simple like the inverse square law." I actually remember one of my favorite lectures (and expanded on as a homework question) was deriving why everything is in inverse square law and not some variation like r^1.9 or r^1.5. It just completely changed how I saw these equations and even the process of analysis. I was a pure experimentalist before that class and gained a lifelong appreciation for theory because of it. I'm in ML now, so definitely still in application/experimentalist mindset but when I stumbled upon this Knuth quote it resonated strongly

  If you find that you're spending almost all your time on theory, start turning some attention to practical things; it will improve your theories. If you find that you're spending almost all your time on practice, start turning some attention to theoretical things; it will improve your practice.

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