MacGougan at Large
Notes on Paradoxes - 1 - Zeno's Paradox
Zeno’s Paradox
This is an old one that no self-respecting three year-old will find persuasive.
Zeno, confronted by an archer who means him harm, explains that an arrow shot in his direction can never reach him. Why? Because first, it would have to make it halfway to him, and before that it would have to make it halfway to the halfway point, and so on back to an infinite number of halfways.
At least, we think that was his reasoning. About five seconds into this explanation, he was killed by an arrow. (On hearing Zeno’s theory of infinite halfways making any sort of action impossible, the jury returned a verdict of Justifiable Homicide.)
I’m not sure, actually, that this is a paradox. It might just be Zeno’s Confusion About Infinity. He doesn’t seem to understand that anything can be infinitely subdivided. There is room for the infinite within the finite - so maybe there is hope for us all.
I have a variation on Zeno’s Paradox that I think makes more sense than the arrow. Our refrigerator usually contains several containers with leftovers of various kinds. My rule of thumb when raiding the refrigerator is to never take more than half of what is in a container. That way, I can’t be accused of finishing anything off and can’t be expected to clean out the empty container.
While we can all agree that an arrow won’t take an infinite amount of time to be shot a few yards, a Tupperware bowl that is repeatedly emptied by halves will at least seem to be in your refrigerator forever.
I was unfamiliar with Zeno. In my defense, I went to a Catholic college and learned important stuff like how many angels can dance on the head of a pin. I did, however, admire Zeno’s chutzpah (there’s probably a better word in Greek) in the face of the arrow. And by extension, I admired yours in the face of your wife’s irritation upon finding that fuzzy green stuff in the fridge.
However as I was reading about you and Zeno I realized that my partner and I had a corollary to his Paradox in our own lives - “Jackie’s Rule of One.”
Jackie, one of our three daughters, was famous for leaving just one of anything (her mother is a sensational cook!) on its platter. So we’d end up with one of everything at the end of a meal. Even now, years later, when there’s one morsel of anything left anywhere someone will ask, “Are we saving that for Jackie?”
Just to come full circle, the outcome of our Rule is the same. Something green and fuzzy ends up in the fridge.