The core aspect of information theory is how much information fits in a sphere. Getting from there to memory access latency in a real computer is several abstractions away and a lot of those abstractions might not hold.
It says that for a sufficiently large storage system, the information within will ultimately be limited by the surface area and not the volume. That you can indeed judge a book by its cover. For the sake of asymptotic analysis of galactic algorithms, one need only consider schemes for reading and writing information on the surface of a sphere. Where it comes to "real hardware," this sort of analysis is inapplicable.
It's obviously about latency. How do you not see the latency aspect of it?
Latency is directly bound by the speed of light. A computer the size of the earth's orbit will be bound by latency of 8 minutes. A computer the size of 2x of earth's orbit will be bound by a latency of 16 minutes, but have 4x the maximum information storage capacity.
The size of the book is directly proportional to the speed of light. Ever heard of ping? Does the universe you live in have infinite speed of light, and therefore you don't see how R contributes to latency?
Off the top of my head: Assuming there's a specific point the data needs to get to. Assuming the size of the data sphere doesn't impact the speeds of anything inside it. Assuming we're using a classical computer. Assuming the support scaffolding of the computer stays a fixed percentage of the mass and doesn't eat into the data budget.
And I know some of those still fit into "at least" but if one of those would make it notably worse than sqrt(n) then I stand by my claim that it's a bad speed rating.
Time dilation for one. As you get closer to a black hole, an observer far away sees it as if time is slowing down for you. Not really sure how this changes the Big O analysis.
