Top 10 Logical Paradoxeson October 15th, 2010
If you’re going to put together an arsenal of paradoxes which may or may not help you against a rogue A.I., there are a few things you should know.
Paradoxes are more than just unexplained phenomena. Some people call it a “paradox” that we have some evidence suggesting certain stars are the same age and other evidence suggesting they’re different ages, but that’s not any kind of seeming logical impossibility… it’s like noticing that one fraternal twin has crow’s feet, probably because he works harder than the other one.
And not all paradoxes are created equal. Some are way too specific, some show shallow thinking, some are restatements of basic ideas found in other paradoxes, and some appear to have been created with the aid of psychotropic drugs (“Dude. Why do we park in the driveway… AND DRIVE IN THE PARKWAY?” “Dude. What’s a ‘parkway?'”). Here, then, are the ones we’ve found most beguiling over the years.
10. Schrodinger’s Cat. The cool cat Schroeder has been put in a closed box by the jealous Lucy. Or something like that. You can’t see or hear the cat. Because of the observer effect, the cat is literally both alive and dead at the same time. Seen in many, many books, TV shows, movies, video games. Dresden Codak‘s treatment is a personal favorite.
9. The Tree in the Forest. If it falls, does it make a sound? How, exactly, do you define “sound?” This, and many paraphrases, figure into lots and lots of arguments, often as a synonym for the observer effect. The idea sometimes translates into fantasy as gods, fairies or entire worlds in danger of fading from existence if their “audiences” no longer hear them. For some fantasy/sci-fi writers, that may be a little too autobiographical to be healthy.
8. Achilles and the Tortoise. The tortoise had a head start in the race. Achilles is catching up. He keeps halving the distance between himself and the tortoise… but will never quite reach it, because adding 1/2, then 1/4, then 1/8 and so on ad infinitum will get you closer and closer to the number 1, but never quite there. The answer to this one will give you a firmer understanding of math in the real world, especially factorials. Seen in: informal calculus, the terrible romcom I.Q.
7. The Barber Paradox and the Set of All Sets. “The male barber shaves every man in town who does not shave himself. Who shaves the barber?” Assuming that every man in town has to get shaven, there is no escape from this dilemma. Bertrand Russell used this exercise to show that certain kinds of classification were impossible. Seen in: the excellent Bertrand Russell comics biopic, Logicomix.
6. The Paradox of the Stone. Can God create one so heavy He can’t lift it? If his power is infinite, what happens when infinity is turned against itself? It’s generally assumed that whether He can or can’t, He doesn’t… except in a few works of fiction and a few mythologies like the Greek, wherein the god/God who created the world finds himself running scared from his own creations like a divine Frankenstein. Seen in: Preacher.
5. The Nihilist’s Challenge. Not its official name, but, fittingly, it doesn’t really have one. Nihilists do not believe anything exists– and defy you to prove otherwise, which is insanely difficult since their thesis challenges any axiom you might use to begin your reasoning. It’s such a challenge that led Rene Descartes to “Cogito ergo sum…” which nihilists didn’t take long to start arguing against. A softer form of nihilism declares the world to be real, but meaningless, or to have no meaning save that which we impose (which is basically Sartre’s Existentialism). Seen in: Rorschach’s origin story and implied in the pitch for Seinfeld, “the show about nothing.”
4. Escher Stairs. We could have picked one of a half-dozen Escher artworks to represent his distinctive, logically challenging artwork, a form of visual paradox. But people always seem most taken with those stairs, perhaps because they’re so immersive. Seen in the movies Harry Potter and the Sorceror’s Stone and Inception, among others.
3. The Problem of Evil. Longtime readers know this is a favorite issue of mine. Time Magazine once put it very succinctly: “God is all-powerful. God is good. Bad things happen.” Some, like Rorschach, simply use the problem of evil as an argument for God’s nonexistence. Others grapple with it all their lives: it is, at the least, a severe challenge to a conventional Christian faith. Addressed very directly in: Penny and Aggie: “What You Can’t Teach.”
2. The Liar Paradox. “This sentence is a lie.” This statement is neither true nor false, merely dickish. The classic A.I.-destroyer, elegant in its simplicity. Seen in: one unforgettable Star Trek sequence.
1. Time Travel. What happens if you go back in time and try to kill your own grandfather? If all time fits together like a jigsaw, as in The Time Traveler’s Wife, then everything is predetermined, including your journey, and you’ll be prevented by some narratively frustrating coincidence. This seems pretty tough to believe, but arguably even harder to swallow is the idea that doing this would spark a wildfire through the fabric of the universe, destroying everything, as claimed in the Back To The Future series. The best-sounding theory (branching parallel universes) still conjures up images of another Earth being created every time a time traveler draws a breath. It may be that our heads are not currently equipped to deal with the true principles of time travel, just as the rules of quantum mechanics mock our intuition. But we’re learning those…