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I heard Stephen Fry tell this on QI (Episode B08) and I just didn't get it. Thanks for the explanation.
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The word "sill" can be used to refer to manmade or natural structures that divert or impede the flow of some fluid, like as with a a window sill (which keeps water away from the bottom of the window), or a natural sill between two bodies of water. So a blood clot would be doing something similar, and so would sort of like a sill, or "silly."