The Dichotomy Paradox and Marathon Training

The great philosopher Zeno
(Courtesy Stifts- och landsbiblioteket
i Skara's photostream @ Flickr)

There's something about the ancient Greeks - their culture, their language, and their brilliance - that I've always been enthralled with. Well, at least since those days when I took two years of classical Greek in high school. Remarkably, I still remember a few phrases in Greek from Homer's Odyssey, with all it's great imagery (e.g., ῥοδοδάκτυλος Ἠώς, which translates to rosy-fingered dawn). Still, my knowledge of Greek philosophy can be written in large print on the face of a small postage stamp. Many of us have heard the names but most of us - including me - haven't read their books. There are those we all know (e.g., Aristotle and Plato) and those we don't know much about. One of those lesser known philosophers was Zeno of Elea. Zeno was famous for his several paradoxes, one of which is known as the Dichotomy Paradox.


Zeno's Dichotomy Paradox can be explained as follows:

Suppose LSU's running back Michael Ford fields an opposing team's kickoff at his own goal line. His intention is to run the 100 yards from his starting spot to the opposing team's goal line and thereby score a touchdown. Zeno's Dichotomy Paradox suggests that Michael will not really be able to accomplish that but not because of an imminent tackle by an onrushing special teams player. You see, to reach that mark 100 yards away, Ford must first reach the halfway mark at the 50 yard line. However, before reaching that halfway point, he must first reach the quarter-way mark. Alas, before reaching even the quarter-way mark, he must first reach 1/8th the distance to midfield. And so on, and so forth - suggesting that there is no way in fact to reach the goal, or even midfield for that matter. Of course, this particular Zeno hypothesis is bogus; but it does take a bit of careful wording to disprove with logic, nonetheless. Oh, and intriguing as it may seem to consider, I don't believe LSU's problems on the football field are attributable to this paradox.

So, what does the Dichotomy Paradox have to do with the timelapserunner's marathon training? As it turns out, completion of the long run this week - Week 14 - will mark the halfway point in his training for the Louisiana Marathon. Fourteen weeks under the belt - fourteen more to go. The question, therefore, is this: will the timelapserunner EVER complete his training, or will he be doomed to the fate Zeno proposed of never quite getting the job done? Perhaps worse yet, will he start out on January 20th and never actually complete the race?

For your sake and mine, the timelapserunner sure hopes Zeno is wrong here or that his paradox has at least been misapplied. An infinite number of weeks of marathon training is not a prospect that I wish to consider, regardless of how rewarding the process might be. And never finishing the race, once started, would be a fate worse than ... well, trying to run back a kickoff in Tiger Stadium.