Today, paradoxes. The University of Houston's College of Engineering presents this series about the machines that make our civilization run and about the people whose ingenuity created them.
I want to talk about paradoxes, even though I know how hard they can be to follow on the fly. Paradoxes are mental traps that can take time to sink in. Example:
Pinocchio says, "My nose will grow now." Since his nose grows only when he lies, that statement is never true. Or a simpler paradoxical sentence: "This statement is false." That one incurs the error of self-reference. Statements about themselves lead to logical loops. But we need a moment to think through any paradox.
Ok, what makes a paradox? It's from two Greek words that mean contrary to opinion - something that outwardly contradicts itself. Most paradoxes can be diagnosed. When Yogi Berra said, "I never said most of the things I said," it had the look and feel of a paradox; but it was pretty easy to see through. The ones that're really fun leave us struggling years after we first heard them.
In this paradoxical picture, a real boy runs into a Trompe L'Oeil town in Old Quebec City. (Photo by John Lienhard)
Physics is full of things that, at first, look paradoxical. And a few still leave us scratching our heads. Take Schroedinger's cat. A box holds a live cat, a flask of poison, and a mechanism that'll break the flask with the right quantum-level disturbance. The event that will or will not kill the cat occurs on the level of quantum uncertainty. It's beyond physical predictability. That means the cat is both alive and dead until an observer looks in the box and determines its fate. Schroedinger meant to illustrate a flaw in the current quantum mechanics. But now some argue that it dramatizes the existence of parallel universes.
Physicist Eugene Wigner went further. He said, "Suppose I have a friend who opened the box. The cat is still both alive and dead until I see sadness or happiness on my friend's face."
Of course physical paradoxes all stop being paradoxical, once we know what's going on. Take the tea leaf paradox. Why, when we stir tea, do the tea leaves (which are heavier than the brew) end up near the middle instead of the edge? It all makes perfect sense once we know that a torus-shaped vortex forms as tea drags on the cup wall. That vortex swooshes the leaves back toward the middle. When we know that, the paradox evaporates.
So the paradox about paradoxes: They cease being paradoxes once we understand. Engines commentator Richard Armstrong pointed out that Pompeii presents us with a paradox in the more literal sense of the word. It's a town preserved by the very disaster that destroyed it. Nothing there we don't understand! Yet it certainly is para doxa - against our thinking.
So it was with the original Catch 22: A combat pilot, Orr, was deemed crazy if he flew more missions, and insanity meant he should be grounded. But as soon as Orr asked to be grounded, he proved he was sane. So he kept flying, which was clear evidence of insanity.
Well, I'd really like to finish with a nice generality about all these paradoxes. But I'm afraid I'll just have to remind you that: All Generalities are False.
I'm John Lienhard at the University of Houston, where we're interested in the way inventive minds work.
See Wikipedia entries on Paradox, List of paradoxes, Schroedinger's cat, Tea leaf paradox, Catch 22 (logic).
See also Episode 2818, The Pompeian Paradox
The artist M. C. Escher specialized in creating visual paradoxes such as this one. It portrays a perpetual motion machine waterwheel configuration. (Image courtesy of Wikimedia commons)
This episode was first aired on August 1, 2014