Orbital datacenters suffer from the same problem: limited surface area. You think cooling is a problem now? Try not having conduction or convection. Radiation is all you get. A huge proportion of the mass and size of the ISS is radiators, and that only has to deal with the heat of low-power electronics and a few measly human beings.
Using an entire Mars only nets us about a 2x multiplier for our energy expenditure budget. Then we need four planets to double it again. Exponential growth is a bitch.
Thermodynamics and the tyranny of exponential growth are going to win this battle every time, regardless of the unobtanium technology you try to invent.
Not quite the same problem, because only a small portion of that energy radiated from space will make it back to the environment on Earth. For convection that is 100%.
> Using an entire Mars only nets us about a 2x multiplier for our energy expenditure budget.
That is not the problem being discussed. Radiators can be scaled up, but the thermal mass of Earth is finite. GPUs can survive at temperatures the organisms of Earth cannot.
I am quite certain that you are drastically underestimating the scope of the problem of "getting rid of heat" when you're dealing with the discussed levels of power production.
Maybe, but that's a "simple" resource problem. The Earth radiates 20x more heat than that today, and it has not been optimized for purpose. Remember that the initial assumptions were that AI has already designed and manufactured tens of thousands of these plants.
The problem at hand is not just getting rid of heat however, it's getting rid of heat without cooking the Earth. I still fail to see how generating the heat off planet fails to solve that.
Using an entire Mars only nets us about a 2x multiplier for our energy expenditure budget. Then we need four planets to double it again. Exponential growth is a bitch.
Thermodynamics and the tyranny of exponential growth are going to win this battle every time, regardless of the unobtanium technology you try to invent.