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somenameformetoday at 4:12 AM1 replyview on HN

I'd disagree and have done exactly that. I started with a reasonable basis in physics, but self studying through an entire course dramatically expanded my understanding. For an example of what I mean this [1] is Feynman's lecture on conservation of energy. It's something every schoolkid learns -- I'm fairly sure I saw my first pendulum from the nose demo in middle school, yet Feynman will take this and make you completely rethink your understanding.

So for instance, what is energy? Somebody who knows a little would probably tell you something like the capacity to do work, and so it feels quite abstract. But the interesting thing is that energy really "exists" so to speak. If you paused the universe somehow, and then resumed it - you'd need to know exactly how much energy was and where in order to keep things moving as they were. Yet there is no known 'thing' that is energy - just a wide array of mathematical abstractions.

And then this thing is also perfectly conserved such that the amount in play will never change. It's completely bizarre to think about, and this is something you initially "learned" in grade school, and probably never even really though twice about.

--

And more generally I think the point of learning should not be to do something, but to expand your own mind and understanding of the world (and beyond). Outside of this being arguable alone as a philosophical point of view, I also think there's even a practical reason for it - unknown unknowns. There are things you can't even imagine that you don't know, and the only way you can reconcile this is trying to dive into things across a wide breadth.

[1] - https://www.feynmanlectures.caltech.edu/I_04.html


Replies

gmueckltoday at 6:59 AM

Conservation of energy is simply the invariance of a system to translation in time: the system shows the same time evolution from a well defined starting state regardless of whether that state exists at a time t or a time t+t' with an arbitrary t'. This is one application of Noether's theorem.

This is an example of a topic that unstructured self study would likely skip. But it is included in every properly structured course because this theorem puts a fundamental explanation to all conserved quantities that occur in classical mechanics.