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I've heard the following expression from people all over the country and on television. It makes absolutely no sense: "That's the exception that proves the rule." Is this a bastardization of some other phrase? If not, what does it mean? --Lorraine Nicotera, East Weymouth, Massachusetts

Lorraine, kid, don't you get it? The whole point of this saying is that it doesn't make sense. It's what you say to confound your enemies when your argument has been shot out from under you by some pesky counterexample. From the point of view of advancing the debate it's about one jump ahead of "yo mama," but it beats standing there with your mouth open.

To be sure, a few scholarly types have tried to make excuses for "The exception proves the rule," as the quotation books usually phrase it. They say it comes from the medieval Latin aphorism Exceptio probat regulam. Probat means "prove" in the sense of "test," as in "proving ground" or "The proof is in the pudding." So "the exception proves the rule" means a close look at exceptions helps us determine a rule's validity.

If Latinists understand it that way, however, they're pretty much alone. I've looked up citations of this saying dating back to 1664, and in every case it was used in the brain-dead manner we're accustomed to today--that is, to suggest that nonconforming cases, by the mere fact of their existence, somehow confirm or support a generalization. Obviously they do nothing of the kind. We like to think proverbs become proverbial because they're true; this one is an exception. It certainly doesn't prove the damn rule.

What is the opposite of absolute zero? I can accept the idea that there's a coldest possible temperature, but I like my limits in pairs. Is there a limit to how hot things can get? If so, what is it and why is it? --Mark Stewart, Chicago

There is a limit, but it's so inconceivably large that nobody but high energy physicists talk about it (although as I think about it, absolute zero doesn't exactly qualify as breakfast table conversation either). The highest possible temperature, called the Planck temperature, is equal to 10 32 degrees Kelvin. For comparison, the center of the sun bubbles along at 15 million degrees K (15 x 10 6); silicon can be created by fusion at 1 billion K (10 9). In short, the Planck temperature is very toasty indeed.

Some scientists believe that we, or at least our universe, have already experienced the Planck temperature, although it went by so quickly you may have missed it. It occurred at 10 -43 of a second after the Big Bang, the great cataclysm in which the universe was born. (10 -43 of a second, in case you're not hip to the notation, is an incredibly tiny fraction of time. Time enough to create the universe, but not, as a University of Chicago physicist was once at pains to explain, time enough to get off a disputed last-tenth-of-a-second shot against the Chicago Bulls.)

Absolute zero is easier to understand than the Planck temperature. What we perceive as heat is a function of motion. The colder something gets, the less internal motion or vibration its molecules exhibit. At absolute zero--that is, zero degrees Kelvin or -460 degrees Fahrenheit--molecular motion virtually stops. At that point the molecules are as cold as they're going to get.

There's a lot more latitude in the opposite direction. The faster molecules move, the hotter they get. At 10 10 K electrons approach the speed of light, but they also become more massive, so their temperature can continue to rise. At 10 32 K such staggering densities are attained that greater temperature would cause each particle of matter to become its own black hole, and the usual understanding of space and time would collapse. Ergo, the Planck temperature is as hot as things can get. Or at least it's the highest temp conceivable in present theory. There's a chance when a quantum theory of gravity is worked out we may find even higher temperatures are possible. I personally don't view the prospect with enthusiasm, but when you're a scientist you learn to take it as it comes.

Art accompanying story in printed newspaper (not available in this archive): illustration/Slug Signorino.

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