You know that kind of drifty dreamy state you get sometimes in the middle of the night? Anyway, I do, and last night I had a drifty dreamy thought that now that I'm awake, I'm not sure of the answer to.
So:
Ignore reality here, it's a thought experiment. Also assume the earth doesn't have a molten core and all that stuff.
I'm in my back garden. Assume that on the direct opposite side of the globe is the sea, and it's a thousand feet deep.
If I were to dig a hole straight down, all the way through the earth, and finally breach the bottom of that sea, would my house flood?
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