[pqh]

Except "why does Snell's law over a continuous gradient effect the path of shortest time?" is equivalent to asking "why is the universe quantum?"

It's plenty bizarre that electricity follows the path of least resistance, light the shortest path, etc.

[gryfft]

Bizarre in comparison to what?

[pqh]

Let me put it this way: never have I heard an explanation in terms of classical mechanics. In my intuition, the billiard ball model of physics makes perfect sense. But a current taking the path of least resistance really seems like it "knows" the best way. And it's amazing.

[tannercollin]

That's a misconception. Electricity takes ALL paths in amounts proportional to each path's conductance.

If you have a 1000 Ω path and a 10 Ω path (in parallel), current will go through both paths. However, much more current will go through the 10 Ω path.

The current through each path ends up being the voltage applied across the path, divided by its resistance.

[planteen]

Yep. Came here to say exactly this (electricity takes all paths) and then saw your reply.