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It's a pretty straightforward geometric argument, from your own analogy
I'm sure there's a coherent rebuttal but "That is plainly rubbish" isn't the reply I'd expect in good-faith discussion
It's well in the realm of obvious, but possibly outside the realm of personal experience on your part.
I think pointing at Greenland for a start and asking you to think about the problem for a bit will lead to the same coherent view on the matter.
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