As we all know, if you try to place a live frog directly in boiling water, he’ll hop out, and you’ll be left with an unboiled frog. The thing to do instead is to place the frog in lukewarm water and slowly turn the heat up. He’ll be dead and boiled before he knows what hit him.
But why do we know this? I can’t imagine that too many people need to boil live frogs, and that very few people ever have. How did this come to be an instructive metaphor?
(This came up during a discussion on the use of homotopy methods in convex optimization, and it struck me as a curious topic for a math class. Hence the question.)