Roanoke Times
Copyright (c) 1995, Landmark Communications, Inc.
DATE: THURSDAY, January 13, 1994 TAG: 9401120074
SECTION: EXTRA PAGE: 6 EDITION: METRO
SOURCE: Joel Achenbach
DATELINE: LENGTH: Long
A: Seems to us this whole evolution business has been pretty much a waste of time - we've been mutating for millions of years and we still need glasses.
The way evolution is supposed to work is like this: Two hunter-gatherers go looking for some wild game. One guy has keen vision, and he's able to discern which critter is the slowest afoot. He dashes out of the bushes and gathers the animal in his customary fashion (if we're not mistaken the usual technique in prehistoric times was a swift, disabling bite to the throat).
But the other hunter-gatherer has lousy eyesight, and all he sees is a bunch of fuzzy shapes, and so he starves, and his genes aren't passed on, and good eyesight is thus "selected."
So why do so many people need corrective eye wear?
Three reasons:
1. Modern society is a strain. The hunter-gatherers didn't have to stare at computer terminals all day or scrutinize the agate listings in the sports section. Children who read books suffer worse vision problems than those who don't. But as optometrist Michael Jones of Athens, Tenn., points out, "I would much rather my child be nearsighted and be a good reader."
2. It doesn't really matter. Poor vision from birth, or blindness, certainly doesn't preclude survival, because other senses become keener. And there is also a peculiar correlation between myopia and certain kinds of intelligence, which is why smart, nerdy kids often have thick glasses.
3. Presbyopia. At about the age of 40, almost every human being starts to have trouble with near vision. This is because the unusual tissue that makes up the lens of your eye has never been sloughed off or replaced, like most tissue. It's been there since you were an embryo. The tissue gradually becomes less elastic, and by the age of 40 it's hardened up, and doesn't focus as well.
Natural selection didn't affect presbyopia because, during most of the time humans have been evolving, hardly anyone lived to the age of 40 anyway. As we always say, anyone over 40 is really just a technological marvel, i.e., a freak of nature.
Q: Why did it take 350 years to prove Fermat's Last Theorem?
A: Like most people you probably dabbled a little over the years with your own proof to Fermat's Last Theorem, jotting down a few sines and cosines and logarithms on the back of a napkin, running the odd polynomial equation through your mind during a shower, and so on. And what did you get? Nothing but frustration. Agony. In a fit of pique you Cuisinarted the calculator. Who hasn't done that at least once?
Thus you were fascinated this summer when Princeton mathematician Andrew Wiles announced that he had found a proof for Fermat's Last Theorem, more than three centuries after Fermat's demise. Pardon us for restating the obvious, but F.L.T. says that if "n" represents any positive whole number larger than 2, there is no solution to the equation "x to the nth power plus y to the nth power equals z to the nth power."
The reason that seemed so marvelous a theorem is that it is simple, by math standards, and yet not at all obviously true. For one thing, if "n" is 2, then there are lots of solutions to the equation. Do it yourself: 3 squared plus 4 squared equals 5 squared (9 plus 16 equals 25). But 3 cubed plus 4 cubed doesn't equal 5 cubed! Two cubes added together never equal a third cube.
Pierre de Fermat jotted a note to himself in a book margin saying that he had found "an admirable proof of this theorem, but the margin is too narrow to contain it." No one, until Wiles, had come up with a proof.
Here's why it took so long: There is no "admirable" proof. There's no single a-ha! solution. Wiles' proof runs 200 pages. More than marginalia, indeed! Whatever Fermat was thinking of when he said he had a proof, we know he wasn't thinking of what Wiles came up with.
Moreover, Wiles had to build on the incremental gains of others. The most important leap in recent times occurred eight years ago when a mathematician showed that something called "Taniyama's Conjecture" implied the truth of Fermat's Last Theorem. But no one had a proof to Taniyama's Conjecture either. So Wiles, wily guy that he is, managed to prove T.C., and thus proved F.L.T.
Five "referees" are now examining Wiles' work to see if it is completely sound. We understand that Wiles himself is busy, at this writing, trying to deal with a portion of his proof that might possibly be flawed.
"Whatever happens, he's made a fantastic advance," says Wiles' colleague at Princeton, John Conway.
Conway points out that a proof is not the same thing as a calculation. A calculation can be done with a computer, but a computer can't usually prove a theorem. For example, A times B is always the same as B times A. You can plug in some numbers and see that it does work out (3 times 5 is 15, and 5 times 3 is 15), but how do you prove that it's true for all numbers?
Conway suggests that perhaps you would argue that the equation represents dots shaped in a rectangle; by reversing the factors you are essentially turning the rectangle 90 degrees. Same number of dots, different orientation.
The point is, math is not just about number manipulation, it's also about ideas, concepts, visions of the universe. So the next time someone tells you that 2 plus 2 is 4, you should lift one eyebrow and say, "Yeah? Prove it."
Washington Post Writers Group
by CNB