For the analysis in the article, it is enough to assume an unlimited amount of space into which you can put your memory as well as an unlimited amount of time. For your own analysis, you can of course make any assumptions you wish, but the author argues (and I agree with him there) that the spatial scaling O(sqrt(N)) for random access is both relevant in practice (as seen by the caching graph) and cannot be improved on when considering the laws of physics.

> The limits of the real world are good to remember but that does not invalidate Big O analysis.

No, it just means that you failed to take one specific bit into account and that your analysis may hence be less relevant to the real world. Much the same way we can say that integer addition is O(1), because usually we deal with fixed-size integers, we can say that memory access is O(1), because usually we deal with a fixed maximal memory size. Of course, integer addition is O(log(N)) and, according to the arguments made in the article, memory access is O(sqrt(N)).