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 changes based on how much charge is dumped into the system.
That was my initial thought, but on further reflection it feels wrong. The electron is also a wave, and that wave can spread across the entire grid.
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.
That only matters if you're measuring in the time domain and seeing the noise due to individual carriers. Often you just care about averages over some time and space (e.g. the macroscopic flow of water behaves quite different from the speeds of the individual molecules).
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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 changes based on how much charge is dumped into the system.
That was my initial thought, but on further reflection it feels wrong. The electron is also a wave, and that wave can spread across the entire grid.
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.
That only matters if you're measuring in the time domain and seeing the noise due to individual carriers. Often you just care about averages over some time and space (e.g. the macroscopic flow of water behaves quite different from the speeds of the individual molecules).
Funny to put "intuition" and "infinity" into the same sentence.
The only type of person for whom intuition about infinity to form is not entirely unlikely are mathematicians.