Curiosity corner: A pair of paradoxical points to ponder

I am proud to announce that Curiosity Corner has found a home away from home in the blogsophere right here on Rob’s Megaphone.

by Dr. Jerry D. Wilson,

Emeritus Professor of Physics, Lander University

Question: Somebody recently mentioned “Zeno’s paradox.” Would you please explain this?  Thanks. (Asked by a curious and bashful column reader.)

Reply: First let’s define paradox. (We’re big on defining things in science so we know what we’re talking about.) Paradox comes from the Greek word meaning “contrary to expectation,” and more generally, a paradox is something that is seemingly contradictory to common sense and yet perhaps true.

          Zeno was a Greek philosopher who lived in the 5th century B.C. He dealt with paradoxes, and perhaps his most famous, in one form, goes something like this. Suppose you’re traveling in a straight line from point A to point B. In doing so, you first travel half the distance between the two locations, say to point C. Once at the midpoint C, you must then travel half the remaining distance (C to B). But once you arrive at the midpoint (D) of this remaining distance, you still have to travel half of the remaining distance (D to B). So, there’s always half the remaining distance to travel, and this goes on ad infinitum (even though we would run out of letters in the alphabet).

          Since it takes time to travel half of any given distance (no matter how small), and any remaining distance in our travel from A to B can always be divided in half, it will therefore take an infinite amount of time to travel from A to B. That is, you’d never reach B!

          Of course, Zeno knew that in reality the trip could be made. He was into philosophizing that common sense and the laws of motion couldn’t both be true at once, or more generally, that reality is unreal. I’m not going to get into that (take a philosophy course at Lander), but basically, in taking an infinite number of time and distance intervals, mathematically, you are dividing infinity by infinity, which is not defined or allowed. (But I’ve counted to infinity twice.)

          So, let’s get back to the real world and let me give you an old one to think about. Suppose you are half another person’s age. To make things easy, let’s say you are 10 and the other person is 20 years old. Then you are 10/20 = 1/2 = 0.50, or half the other person’s age.

          Let a decade (10 years) go by. The ages are then 20 and 30, so you are 20/30 = 2/3 = 0.67, and you are two-thirds the person’s age. Then another ten years goes by, and at the ages of 30 and 40, you are 30/40 = 3/4 = 0.75, or three quarters the person’s age. In another 10 years, we have 40/50 = 4/5 = 0.80, and you are four-fifths the person’s age. Notice how you are closing the gap and getting fractionally closer to the age of the other person. Question: How long will it take for you to catch up and be the same age as the other person?

(You should live so long.)

C.P.S. (Curious Postscript): So they [the Government] go on in strange paradox, decided only to be undecided, resolved to be irresolute, adamant for drift, solid for fluidity, all-powerful for impotence.  -Winston Churchill

 Check out last week’s Curiosity Corner here.

Curious about something? Send your questions to Dr. Jerry D. Wilson, Science Division, Lander University, Greenwood, SC, 29649, or for e-mail, jerry@curiosity-corner.net. Selected questions will appear in the Curiosity Corner. © JDW