zlacker

That example would be two dimensions still in the limit computation, since you can keep building outwards (add buildings) but not scale upwards (add floors)

>>manwe1+(OP)
You can add floors though. Some datacenters are 8 stories with cross-floor network fabrics.

>>frollo+y7
When you get to, say, 100000 stories, you can't build more stories. At this point your computer costs more than the Earth's GDP for a century, so talking about theoretical scaling laws is irrelevant. Eventually you run out of the sun's power output so you build a Dyson sphere and eventually use all of that power, anyway.

>>immibi+Yx
Oh right, so the height is practically a constant. Square root for sure then.

>>frollo+Th1
All algorithms are O(1) in this case

>>LPisGo+hb2
You pick what things are constant and what's variable. If you're scaling a supercomputer to fit a problem, the height is going to max out quickly and can be treated as constant, while the other dimensions are variable.