The Eureka Principle Isaac Asimov once wrote an essay about the "Eureka Principle" which he applied when he was stuck on a problem with his plots or his characters. He'd put the problem out of his mind and go to the movies and the answer would come to him (or not).

It was the Greek philosopher Archimedes who first proclaimed "Eureka!" ("I have found it!") He was working on a complicated geometric problem and took time out for a nice warm bath. Never a bad idea in my opinion.

The problem was rather complicated. The king of Syracuse was having a very splendid gold crown made, and he wanted to be sure that the makers were not cheating him. He wanted to be sure that all the gold he gave them ended up in the crown.

Now gold is so heavy, compared to the base metals that might be substituted, that you can tell how much gold is in the crown -- if you know its volume. The problem was figuring out the volume of an irregular shape -- in this case very irregular with lots of little fancy artistic motifs.

Archimedes thought it over and couldn't think of an answer. So he took his famous bath, and he noticed that he was displacing a bit more water when he got in. Maybe putting on a little weight. When it dawned on him...

He needed to go to the gymnasium! Well yes, that, but also how to get an exact measurement of the volume of an irregular solid. Immerse it in water and see how much water it displaces. Simple, precise, brilliant.

Of course I never think of "Eureka" without thinking of the Three Stooges rejoinder: "You don't smell so good, yourself."  ¶ 7:03 PM