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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.

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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.

We don't need to care about cooking Mars.

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Compute doesn't need to happen here, but it can, so it will. Building datacenters on Mars or Jupiter doesn't reduce our ability to build datacenters here, so naturally, they will still be built, everywhere that they can be. It's an orthogonal capability.
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Maybe, but there are counterexamples today. The processing of raw materials can be done all over the world, but it's not. Modern nations actually disassemble their blast furnaces and ship them out at a certain point.
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