Per Vognsen
My favorite weird physical scaling limit in computing is that you can't tile a 3D networked grid of computers indefinitely because you eventually create a black hole: https://en.wikipedia.org/wiki/Schwarzschild_radius#Calculating_the_maximum_volume_and_radius_possible_given_a_density_before_a_black_hole_forms. Whereas you can in theory tile the computers in a 2D network indefinitely (edit: nevermind, you have this problem in 2D too, so you need 1D tiling).
Schwarzschild radius - Wikipedia

Mar 21 at 3:28amPhanpy
Show threadWolf480pl4d ago

@pervognsen
why's that not a problem in 2D?

Consider a flat disk of computers with height H and radius r, and density ρ.

V = H * πr²
M = ρ H π r²
to be a black hole, it needs
rc² <= 2GM

r c² <= 2G ρ H π r²
c² <= 2π * G ρ H r
r >= c² / ( 2πGρH )

Show threadPer Vognsen4d ago
@wolf480pl Thanks, I should have worked through that example. So 1D tiling would still work since with V ~ r, M ~ r you can select the tile mass low enough to satisfy the inequality for all r. I think what I was misremembering related to r^2 scaling limits in computing was something about black hole surface area. That'd somehow gotten compressed in my brain to "2D tiling still works" which, as you pointed out, it doesn't.
Show threadPer Vognsen4d ago
@wolf480pl So, with the 1D tiling still working at arbitrary scale, the Turing machine is even more physically realistic than I'd appreciated. :) Or I guess a more useful analogy than a Turing machine is a one-dimensional cellular automaton if we're talking about arbitrarily large-scale parallel computers or networks.
Show threadPer Vognsen3d ago
@wolf480pl I found the original thesis I read 20 years ago and half-remembered. He even mentions the planar disk example. The problem being studied also isn't exactly the same as a grid of computing elements.
Show threadzwarich3d ago
@pervognsen I'm honestly surprised I haven't seen this mentioned in the recent orbital datacenter discourse.
Show threadJohn Kaniarz3d ago
@pervognsen I misread the Compton Limit as Computation Limit and thought that they somehow linked information theory with general relativity.
Show threadFabian Giesen3d ago
@pervognsen so you're saying there's a golden lining