Archimedes's Fables #3: The Experimentalist
Written 21 March 1999
There was a man who read a corrupted version of Zeno's arrow paradox and was confused by it.
"Let's see...if I want to go from point A to point B, I have to pass through an infinite number of points, which means it should take an infinite amount of time...but that doesn't seem right."
In an attempt to disprove Zeno, he decided to try an experiment. He went to a long, featureless beach, marked out one meters, and then walked half a meter from A towards B. He made a note in his notebook. Then he walked a third of a meter in the same direction and made another note. Then a quarter of a meter.
At this point he became very excited; he had already passed the point B. Having thus invalidated (as he thought) Zeno, he decided to continue in this fashion. After only seven more journeys, he had gone an additional meter. He became increasingly excited and continued on.
His new goal was to complete a hundred meters. He made good progress early on, completing ten meters after the first day or so and the next ten after only two years. But the years wore on, and finally only his skeleton could be found a mere twenty-five feet away from point A, next to a notebook with page after page of checkmarks.
Moral: The harmonic series diverges, but does so very very slowly.