Yesterday, I asked a gentleman at the gym we attend how he was doing with his workout. He told me he was half way there to which I answered, “if you keep doing that you’ll never get finished”. He looked at me as though I just ruined his day and then, after a small laugh, I then told him I was just expounding on one of Zeno’s paradoxes which is; (Paraphrased) If a man is traveling from point A to point B and for each step he steps half the distance of the one prior to it, he will never reach his destination. Of course, the gentleman I was speaking to laughed about it and told me that he was going to look the Greek up and read more about him and his paradoxes the very minute he got home. I told him that there are actually quite a few and the most studied ones even today are, “The Arrow” and “Achilles and the Tortoise”. Zeno published his paradoxes some 2500 years ago and is one of my absolute favorite philosophers / mathematicians of the ancient world. If one looks up the name, one will find philosophers and physics people still trying to disprove his amazing brain teasers. Perhaps we can look over some of his work and maybe even build a better liking for the old gent. Edit: It just occurred to me that there was more than one Zeno. This one is Zeno of Alea and not a Roman Emperor. Also, the example of one of Zeno’s paradoxes that I gave is called “The Dichotomy”.

Did that gentleman get back to you on the difference in his half way & your in put of “if you keep doing that you’ll never get finished”. Depending on what he was doing at the time & his intention to complete his goal time vs motion would be whether or not he finishes. Say for example he was on a tread mill expecting to complete 6000 strides and he did as you point out he would have to have measured his half way point then began the reduction you describe in his stride. But suppose time was his goal on the treadmill speed/distance/strides not a factor. He would finish. Achilles gave up because there was no goal, no set time or distance. The turtle talked Achilles into believing he would fail. That then becomes mind over physical ability.

@Bobby Cole If a man is traveling from point A to point B and for each step he steps half the distance of the one prior to it, he will never reach his destination. Sometimes, I feel like this when trying to pay my bills.

Whether distance or time and whatever the point might be, a half of a half of a half is still a half. It’s a given that on the macro level, the majority of the proposal is indeed absurd for no one’s footsteps can split a 32nd or a 64th of an inch. Finishing on that level is inevitable. Mathematically though, the physics demand that it goes throughout the quantum level for which there is no determination as of yet whether or not infinity truly exists. A half of a half throughout infinity, whatever that may be. Note: Zeno was one of the first if not THE first philosopher to delve further into the concept of infinity hence his concepts being laid down in a mathematical paradox or construct as it were.

I think you have your philosophers mixed. I believe Socrates had more to do with marital problems than Zeno.

"If a man is traveling from point A to point B and for each step he steps half the distance of the one prior to it, he will never reach his destination." If his steps are twelve inches apart, by the 5th reduced step, he’s at 3/8”. If he increased his steps by half as much as the last step, it would be more fun to watch, especially by the 3rd Step..