[Dylan16807]

While you're factoring in real world constraints, you've gone back to theory rather than practice. In practice the RAM is not far enough away for the travel time to get past a rounding error. Also very high RAM installs use all three dimensions to pack more.

[gpm]

Yeah the justification I gave is pure theory until you're talking large distributed systems... and the theory amuses me here so I'm going to keep talking about it first.

But it's actually a place where practice happens, by coincidence, to match theory pretty well: https://www.ilikebigbits.com/2014_04_21_myth_of_ram_1.html

[Dylan16807]

That's an interesting correlation between the sizes and latencies for cache levels. Thanks for linking it.

Though once you're at the "distributed" tier, I wouldn't expect further increases to be sqrt. Distributed within a datacenter is probably going to have a log(n) topology of links, and distributed across datacenters is a fixed number of milliseconds based on the area you're serving with no real connection to amount of RAM.