Comment by frollogaston
19 days ago
If you have rows of racks of machines, isn't that 3 dimensions? A machine can be on top of, behind, or next to another that it's directly connected to. And the components inside have their own non-uniform memory access.
Or if you're saying heat dissipation scales with surface area and is 2D, I don't know. Would think that water cooling makes it more about volume, but I'm not an expert on that.
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)
You can add floors though. Some datacenters are 8 stories with cross-floor network fabrics.
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.
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Spatial position has nothing (ok only a little) to do with topology of connections.