alt Hacker News> "in 2x time you can access 8x as much memory"
is NOT what the article says.
The article says (in three ways!):
> if your memory is 8x bigger, it will take 2x longer to do a read or write to it.
> In a three-dimensional world, you can fit 8x as much memory within 2x the distance from you.
> Double the distance, eight times the memory.
the key worda there are a, which is a single access, and distance, which is a measure of time.
N is the amount of memory, and O() is the time to access an element of memory.
The operation GP is thinking of is a full scan, and that will always take n(n^(1/3)) lower bound time. Though if done right all of that latency will be occupied with computation and allow people to delude themselves into thinking it doesn’t matter.
But when something is constrained two or three ways, it drastically reduces the incentive to prioritize tackling any one of the problems with anything but small incremental improvements.