The empirical argument actually states that memory access is O(n^1/2)
https://www.ilikebigbits.com/2014_04_21_myth_of_ram_1/3_fit.... "The blue line is O(√N)."
This has been rehashed many times before, and the best blog post on this topic is here: https://www.ilikebigbits.com/2014_04_21_myth_of_ram_1.html
Empirical arguments do not apply to asymptotics anyway.
Thanks for the good links. I think we generally have become so accustomed to the scaled up von Neumann strategy that we don´t see how much efficiency and performance we leave on the table by not building much smaller memory hierarchies.
Shameless plug here, where I explore possible gains in efficiency, performance and security by scaling out rather than up; (no subscription) https://anderscj.substack.com/p/liberal-democracies-needs-a-...