Joining South America and Antarctica across Drake Passage to make Antarctica more habitable? (not taking costs into account)

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Is it theoretically possible to build a long sea wall to join South America and Antarctica across Drake Passage therefore blocking Antarctic Circumpolar Current, allowing warmer sea water to reach Antarctica, hence making Antarctica with a milder climate and somewhat more habitable like current Arctic region and Antarctica once was — when it was still connected to South America millions of years ago, ACC hadn’t formed and even had forests?

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Yes, not taking costs into account it would be possible to fill the 400 km wide and 5 km deep Drake Passage. It would mean hacking up a major mountain chain into boulders and then shipping these boulders to Drake Passage and dumping them there. I’d guess it could take a few decades, but it can theoretically be done. Melting all the Antarctic ice would raise the global sea level by about 60 meters though, so you’d better be busy relocating every coastal city further inland while you are at it.

Edit: Some back of the envelope calculations tell me that the total weight of this dam would be about a hundred trillion tons. The gross tonnage of the entire world’s merchant fleet is about a billion tons, so it would need to make a hundred thousand runs to do the job. If we choose a nearby mountain chain like the Andes, then maybe every ship could make fifty runs every year. So then it would take two thousand years to fill the Drake Passage using the extant merchant fleet. Of course we can make it faster by building many more ships first.

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