We don't have enough time to go over things like this over and over again. Somebody already analyzed/tried all this and wrote in a book and they teach you in school from that book how it works and why. Yeah if you want to know more or understand better you can always dig it out yourself. At least today you can learn tons of stuff.
Oh you put this nicely.
> How does electricity know which path has the least resistance? It doesn't, it starts flowing down all paths equally at a significant fraction of the speed of light, then quickly settles in a steady state described by Ohm's law.
> because all of science and engineering are approximations with limited applicability
Something I heard but haven't dig into, because my use case (DIY, home) doesn't care. In some other applications approximation at this level may not work and more detailed understanding may be needed :)
And yeah, some theory and telling of things others discovered for sure needs to be done. That is just the entry point for digging. And understanding how something was derived is just a tool for me to more easily remember/use the knowledge.
Are you being serious or is this satire? What an odd perspective to share on Hacker News. We're a bunch of nerds that take pleasure in understanding how things work when you take them apart, whether that's a physics concept or a washing machine. Or am I projecting an ethos?
We don't have enough time to derive everything from first principles, but we do have the time to go over how something was derived, or how something works.
A common issue when trying this is trying to teach all layers at the same level of detail. But this really isn't necessary. You need to know the equation for Ohms law, but you can give very handwavy explanations for the underlying causes. For example: why do thicker wires have less resistance? Electricity is the movement of electrons, more cross section means more electrons can move, like having more lanes on a highway. Why does copper have less resistance than aluminum? Copper has an electron that isn't bound as tightly to the atom. How does electricity know which path has the least resistance? It doesn't, it starts flowing down all paths equally at a significant fraction of the speed of light, then quickly settles in a steady state described by Ohm's law. Reserve the equations and numbers for the layers that matter, but having a rough understanding of what's happening on the layer below makes it easier to understand the layer you care about, and makes it easier to know when that understanding will break down (because all of science and engineering are approximations with limited applicability)