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Eliezer_Yudkowsky comments on One possible issue with radically increased lifespan - Less Wrong Discussion
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You're picturing the far-future civilization as a ball, whose boundary is expanding at a constant rate. But I think a more plausible picture is a spherical shell. The resources at the center of the ball will be used up, and it will only be cost-effective to transport resources from the boundary inwards to a certain distance. If the dead inner boundary expands at the same rate as the live outer boundary, we'll be experiencing quadratic, not cubic growth.
You know, you're right. I will change my reply accordingly henceforth - linear population growth, linear increase in energy usage / computing power, and quadratic increase in (nonenergetically stored) memories.
Don't you get some pretty nasty latency on accessing those memories?
You get a linear increase in low-latency memory and a quadratic increase in high-latency memory.
And a linear increase in the latency of the high latency memory.