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Infinite Grid of Resistors

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Re: Infinite Grid of Resistors

#21

Post by pixl97 »

QuadmasterXLII wrote: post #13
bravesoul2 wrote: post #4

Earlier quoted context omitted.

Given an infinite grid of resistors... would you expect planets to form?

I think it collapses into a black hole. black hole mass scales with radius, grid mass scales with radius squared

Thats what I'm not sure about here...

If we assume this is an infinite grid in its own universe then nothing can actually move. The gravitational pull should be the same from every direction. If we assume the grid is perfect then there is no nucleation sites to start a collapse. The grid would be in perfect balance.

The same is thought about our universe. If there hadn't been small quantum fluctuations during the inflationary stage it would have taken much longer for what we see in the modern universe to form.

Re: Infinite Grid of Resistors

#22

Post by jfengel »

bravesoul2 wrote: post #7
corysama wrote: post #6

Earlier quoted context omitted.

They say hydrogen is an odorless colorless gas which, in sufficient quantities, given enough time, turns into people. I’m sure the same could be true of resistors.

Resistors are made of heavier elements though. And I remember something like everything wants to become iron (fuse if lighter, decay if heavier) That said there might be enough energy (infinity!) for anything to be possible.

You get stable things heavier than iron, and they're more common than you'd expect. It's possible that they form in neutron star collisions, which are complete anarchy in atomic terms.

Re: Infinite Grid of Resistors

#23

Post by ordu »

petschge wrote: post #2

See also https://xkcd.com/356/

Why mathematicians are three points? I think it is easier to disable a mathematician. Look at this discussion, for example. EE engineers and physicists are dismissing the problem outright, while mathematicians have no issues thinking about it.

Re: Infinite Grid of Resistors

#24

Post by jfengel »

QuadmasterXLII wrote: post #13
bravesoul2 wrote: post #4

Earlier quoted context omitted.

Given an infinite grid of resistors... would you expect planets to form?

I think it collapses into a black hole. black hole mass scales with radius, grid mass scales with radius squared

It becomes a black hole, but it doesn't necessarily collapse, at least not at first. A supermassive black hole has very low density and a very gentle gravitational gradient.

All of the mass does end up in the singularity, in finite time (at least for any finite subset of the black hole), but it doesn't automatically become super dense just because it's a black hole. It can remain quite ordinary for a very long time.

Re: Infinite Grid of Resistors

#25

Post by choonway »

steamrolled wrote: post #18

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…

There are two parts to education. One is to impart knowledge, the other is to filter the students.

Re: Infinite Grid of Resistors

#26

Post by goochphd »

steamrolled wrote: post #18

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…

I was about to say "they still torture students this way" but stopped myself when I remembered I took Circuits 1 and 2 back in 2007. So maybe my knowledge is dated too...

It's a weird butterfly effect moment in my career though. I had an awesome professor for circuits 1, and ended up switching majors to EE after that. Then got two more degrees on top of the bachelor's

Re: Infinite Grid of Resistors

#27

Post by colechristensen »

choonway wrote: post #25
steamrolled wrote: post #18

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…

There are two parts to education. One is to impart knowledge, the other is to filter the students.

Not entirely wrong but it's a little too easy to use that argument for squashing any criticism for education content.

Re: Infinite Grid of Resistors

#28

Post by jesuslop »

steamrolled wrote: post #18

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…

If all you mind is the EE curriculum then ok. Or else there is an interesting work of Gerald Westendorp on the web [1] on how allowing other classical passive components (Ls & Cs) you can get discretizations (and hence alternative views) of a very wide class of iconic Physics partial differential equations (to the point that the question is more what cannot be fit to this technique). G. W. is alive and kicking in mathstodon.

[1] https://westy31.nl/Electric.html

Re: Infinite Grid of Resistors

#29

Post by staplung »

pixl97 wrote: post #21
QuadmasterXLII wrote: post #13

Earlier quoted context omitted.

I think it collapses into a black hole. black hole mass scales with radius, grid mass scales with radius squared

Thats what I'm not sure about here... If we assume this is an infinite grid in its own universe then nothing can actually move. The gravitational pull should be the same from every direction. If we assume the grid is perfect then there is no nucleation sites to start a collapse. The grid would be in perfect balance. The same is thought about our universe. If there hadn't been small quantum fluctuations during the inf…

In fact, we might have a different problem: dark energy should tear the grid up into (very large) bits. I guess the question is then would the bits then collapse into black holes or not. I assume so since the mass would not longer be perfectly balanced.
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