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In school I would have tried to solve this… now if I want to know I just get out my multimeter and measure. Faster, simpler, and more practical.
Where are you going to find an infinite grid of resistors in real life to measure?
I'm a bit mathematician and a bit electrical engineer. The electrical engineer suggests it's not measurable unless you apply current and also asks "when" after the current is applied referring to the distributed inductive and capacitive element and the speed of field propagation. The mathematician goes to a bar and has a stiff drink after hearing that.
Eventually you need to pullin a physicist too who will point out that at an appropriate distance quantum effects will dominate - because eventually at a far enough distance the number of electrons moving per second (ie current flow) will be either 0 or 1 at some nodes
But that's fine because knowing which path the electron took is not part of the problem. Both paths contributed to the resistance even if one was not taken.
We only have to worry about quantum effects if the probabilities are not a decent proxy for the partial-particles that we suspect don't exist. In this case, the Physicist can probably proceed directly to the bar and have a drink with the Mathematician.
See also https://xkcd.com/356/
I'm a bit mathematician and a bit electrical engineer. The electrical engineer suggests it's not measurable unless you apply current and also asks "when" after the current is applied referring to the distributed inductive and capacitive element and the speed of field propagation. The mathematician goes to a bar and has a stiff drink after hearing that.
Eventually you need to pullin a physicist too who will point out that at an appropriate distance quantum effects will dominate - because eventually at a far enough distance the number of electrons moving per second (ie current flow) will be either 0 or 1 at some nodes
Why are the currents in the two node solution (not symmetric) a simple sum of the currents of two single node solutions (symmetric)?
Obviously the 2 node solution still has some symmetries but not the original ones that let us infer same current in every direction.
My math isn't strong enough to follow the whole article, but my intuition as someone who works in electronics is that when a quantized system interacts with an infinity, the infinity is restricted based on the magnitude of the quantized factor. Electric charge is quantized. Less than one electron cannot pass through a node, therefore an infinite grid of resistors is effectively a finite grid of resistors whose size c…
Another interesting aspect is that in an infinite grid, a spontaneous high voltage is going to exist somewhere at all times. It is probably very far away from you, but it's still weird.
I don't get why EE education emphasizes problems of this sort. The infinite grid is an extreme example, but solving weirdly complicated problems involving Kirchoff's laws and Thevenin's theorem was a common way to torture students back in my day... Here, I don't think it's even useful to look at this problem in electronic terms. It's a pure math puzzle centered around an "infinite grid of linear A=B/C equations". Not…
Earlier quoted context omitted.
Eventually you need to pullin a physicist too who will point out that at an appropriate distance quantum effects will dominate - because eventually at a far enough distance the number of electrons moving per second (ie current flow) will be either 0 or 1 at some nodes
Intuitively I knew this class of problem was theoretical only BS when it came up in college... I hadn't considered that sort of strange effect though! Makes me feel not so bad for 'never really getting it' because I just couldn't wrap my mind around the problem description's obvious inanity and the infinite edges.
It's simply an evaluation of your mathematical ability to manipulate the equations and overall understanding of them, wrapped up in a cute little thought experiment. This evaluation IS relevant to more realistic scenarios and therefore your grade and engineering ability.
My math isn't strong enough to follow the whole article, but my intuition as someone who works in electronics is that when a quantized system interacts with an infinity, the infinity is restricted based on the magnitude of the quantized factor. Electric charge is quantized. Less than one electron cannot pass through a node, therefore an infinite grid of resistors is effectively a finite grid of resistors whose size c…
The only type of person for whom intuition about infinity to form is not entirely unlikely are mathematicians.