Ice floating and cooling the upper part of a drink should start a natural convection type cycle which cools the whole drink. If the ice sank, you’d have a very warm surface layer. Never thought about this with focus before 😅
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It’s even more important than your drink! The fact that I’ve floats is what allows ice to act as an insulator on top of frozen lakes and oceans. If it sank, liquid water would take its place and freeze. After a while the whole body of water would be frozen.