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Daniel_Burfoot comments on Crazy Ideas Thread - Less Wrong Discussion
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Not much lives 1000m under the surface. Also, the amount of heat that we would send is actually quite small compared to the heat capacity of the oceans. Water has 4000x higher heat capacity than air by volume.
Transferring heat from a hot place to a cold place is really easy. In principle you can just connect them with a highly conductive material like copper. In practice even copper might not have enough heat conductance, so it might be better to pump either water or air from one place to another.
Under the surface (for example, below the European continent) or in the deep seas? I'm not sure about the former but I'm quite confident that the following applies to the latter:
My layman impression is that investigating lower altitudes becomes increasingly (perhaps exponentially) difficult the lower you go. Wikipedia also says that "Humans have explored less than 2% of the ocean floor" so I would disagree with your assessment of "not much lives 1000m under the surface".
I'm honestly interested in how you came to that conclusion though - If you have an interesting and reputable text that refutes me, please share. I came to mine based on reading Wikipedia too much.
I should have said "not much lives below 1000m until you get to the ocean floor". Not much can happen in the deep ocean because light doesn't penetrate that deeply. The creatures that do live there have to rely on organic material falling slowly from the surface.
From this article
https://en.wikipedia.org/wiki/Geothermal_heating is already a thing.