Cat's cradle“There are several ways,” Dr. Breed said to me, “in which certain liquids can crystallize – can freeze – several ways in which their atoms can stack and lock in an orderly, rigid way.”

That old man with spotted hands invited me to think of the several ways in which cannonballs might be stacked on a courthouse lawn, of the several ways in which oranges might be packed into a crate.

“So it is with atoms in crystals, too; and two different crystals of the same substance can have quite different physical properties.”

He told me about a factory that had been growing big crystals of ethylene diamine tartrate. The crystals were useful in certain manufacturing operations, he said. But one day the factory discovered that the crystals it was growing no longer had the properties desired. The atoms had begun to stack and lock – to freeze – in different fashions. The liquid that was crystallizing hadn’t changed, but the crystals it was forming were, as far as industrial applications went, pure junk.

How this had come about was a mystery. The theoretical villain, however, was what Dr. Breed called “a seed.” He meant by that a tiny grain of the undesired crystal pattern. The seed, which had come from God-only-knows-where, taught the atoms the novel way in which to stack and lock, to crystallize, to freeze.

“Now think about cannonballs on a courthouse lawn or about oranges in a crate again,” he suggested. And he helped me to see that the pattern of the bottom layers of cannonballs or of oranges determined how each subsequent layer would stack and lock. “The bottom layer is the seed of how every cannonball or every orange that comes after is going to behave, even to an infinite number of cannonballs or oranges.”

“Now suppose,” chortled Dr. Breed, enjoying himself, “that there were many possible ways in which water could crystallize, could freeze. Suppose that the sort of ice we skate upon and put into highballs – what we might call ice-one – is only one of several types of ice. Suppose water always froze as ice-one on Earth because it had never had a seed to teach it how to form ice-two, ice-three, ice-four…? And suppose,” he rapped on his desk with his old hand again, “that there were one form, which we will call ice-nine – a crystal as hard as this desk – with a melting point of, let us say, one-hundred degrees Fahrenheit, or, better still, a melting point of one-hundred-and-thirty degrees.”

Kurt Vonnegut in Cat’s Cradle, 1963


Incredulity doesn’t kill curiosity; it encourages it


Incredulity doesn’t kill curiosity; it encourages it. Though distrustful of logical chains of ideas, I loved the polyphony of ideas. As long as you don’t believe in them, the collision of two ideas — both false — can create a pleasing interval, a kind of diabolus in musica. I had no respect for some ideas people were willing to stake their lives on, but two or three ideas that I did not respect might still make a nice melody.

Umberto Eco in Foucault’s Pendulum, 1988