> In essence, as data size 'n' grows, the random access time grows as sqrt(n), because that's the radius of the growing circle with area 'n'.
I was about to write a comment suggesting that if we made better use of three dimensional space in constructing our computers and data storage devices, we could get this extra latency factor down to the cube root of n.
But then, I decided to imagine an absurdly large computer. For that, one has to take into account a curious fact in black hole physics: the radius of the event horizon is directly proportional to the mass, rather than, as one might expect, the cube root of the mass [1]. In other words, as your storage medium gets really _really_ big, you also have to spread it out thinner and thinner to keep it from collapsing. No fixed density is safe. So, in fact, I think the extra factor for latency in galactic data sets is neither the square root nor cube root, but n itself!
The main difficulty with growing computing devices in three dimensions is cooling. All that heat has to be somehow carried away. It's already difficult with 2D devices. One would have to incorporate channels for cooling liquids into the design, which takes a bite out of the gains from 3D.
If its stored far away enough re-doing the calculation is faster. Depending on how much accuracy you need you might as well load a 2022-07-22 07:26:34 earth and have that guy on HN evaluate his thoughts all over again.
I was about to write a comment suggesting that if we made better use of three dimensional space in constructing our computers and data storage devices, we could get this extra latency factor down to the cube root of n.
But then, I decided to imagine an absurdly large computer. For that, one has to take into account a curious fact in black hole physics: the radius of the event horizon is directly proportional to the mass, rather than, as one might expect, the cube root of the mass [1]. In other words, as your storage medium gets really _really_ big, you also have to spread it out thinner and thinner to keep it from collapsing. No fixed density is safe. So, in fact, I think the extra factor for latency in galactic data sets is neither the square root nor cube root, but n itself!
[1] https://en.wikipedia.org/wiki/Schwarzschild_radius