Comment by MaxBarraclough
8 years ago
> even if you don't buy that it clearly can't be less than O(N^1/3)
Maybe I'm missing something, but why's that?
To the rest of your comment: all good points.
8 years ago
> even if you don't buy that it clearly can't be less than O(N^1/3)
Maybe I'm missing something, but why's that?
To the rest of your comment: all good points.
Well, if with your best technology you can pack B bits of information in 1 m^3 of space, and you need to store N bits of information, you are going to need (N/B) m^3 of space to store it. And then the speed of light limits you to around (N/B)^(1/3)/c seconds of latency to get to the farthest bits.
(This ultimately violates the Bekenstein bound - as your server cube grows it will eventually collapse into a black hole - but this is not really a concern with forseeable technology! More practically, though, Earth's gravity makes it hard to build very high in the air, which limits you to O(N^1/2), and things like cooling and maintenance access probably impose a limit somewhere in between.)
Makes sense, thanks.
Imagine your bits stored in a sphere around your CPU. Take into account the time light needs to reach the bit you want to touch.