Not true, because then in theory you could build just L1 - L2 - L3 Cache with 64GB RAM instead of 1 - 2 MB: For SRAM in L1/L2/L3 for example you need to manufacture 6 transistors for 1 bit, while for DRAM you need 1 transistor and 1 capacitor. Thus, would men your chips at that high speed would become very big, and the speed of information through the wires would make a difference: On semiconductor level its a difference if you need to travel 1inch or 10inch billion times per second, creating an "efficient border" of how big your SRAM could max be in dependence of chip-size (and other factors like thermal effects)

Source: "What every Programmer should know about memory" https://people.freebsd.org/~lstewart/articles/cpumemory.pdf

You’re cheating and I don’t think you realize it.

Why didn’t computers have 128 terabytes of memory ten years ago? Because the access time would have been shit. You’re watching generation after generation of memory architectures compromise between access time and max capacity and drawing the wrong conclusions. If memory size were free we wouldn’t have to wait five years to get twice as much of it.

Memory access times have not significantly improved in many years.

Memory bandwidth has improved, but it hasn't kept up with memory size or with CPU speeds. When I was a kid you could get a speedup by using lookup tables for trig functions - you'd never do that today, it's faster to recalculate.

2D vs 3D is legit, I have seen this law written down as O(sqrt N) for that reason. However, there's a lot of layer stacking going on on memory chips these days (especially flash memory or HBM for GPUs) so it's partially 3D.

While in absolute terms memory access has gotten faster, in relative terms it is MUCH slower today, compared to CPU speeds.

A modern CPU can perform hundreds or even thousands of computations while waiting for a single word to be read from main memory - and you get another order of magnitude slowdown if we're going to access data from an SSD. This used to be much closer to 1:1 with old machines, say in the Pentium 1-3 era or so.

And regardless of any speedup, the point remains as true today as it has always been: the more memory you want to access, the slower accessing it will be. Retrieving a word from a pool of 50PB will be much slower than retrieving a word from a pool of 1MB, for various fundamental reasons (even address resolution has an impact, even if we want to ignore physics).

You are correct in that the OP used the wrong metric. He should have written a big omega, not a big O.

> PCBs and integrated circuits are basically two-dimensional.

Yes, what pushes the complexity into Ω(n^1/2), that fits the original claim.

> Access times are limited by things like trace lengths

Again, Ω(n^1/2)

> and parasitics

And those are Ω(n)

So, as you found, on practice it's much worse, but the limit on the article is also there.