Solved by walking (Part 1)

How do you solve Zeno’s paradoxes of motion? If you’re Diogenes the Cynic, you walk it off. [1 of 2]

Painting of Diogenes the Cynic
Jean-Léon Gérôme, Public domain, via Wikimedia Commons

No writing by Socrates survives. We know of him only through descriptions and texts from his students and others. A while ago I was reading Plato’s dialogues, in which Socrates is a key character, and I came to one important conclusion: Socrates was a bit of a jerk. He proclaims ignorance and then asks the most awkward questions possible, breaking down understandings and definitions until everyone else feels as ignorant as he claims to be. This is of course key to the Socratic method, Greek philosophy’s fine intellectual scalpel. But in the dialogues it also comes across as quite mean.

Despite all this, Socrates was not the biggest jerk in the ancient Greek philosophy scene. That title has to go to Diogenes the Cynic.

I could go on and on about the idiosyncrasies of Diogenes. His philosophy was one of simplicity, of rejecting the bounds and boundaries of society, and he really practiced what he preached. Among his (reported) behaviours: living in an overturned clay jar, begging in the marketplace, peeing on those who annoyed him, taking a dump in the theatre, flipping people off, heckling Plato, and insulting Alexander the Great.

(That’s a funny story – apparently Alexander sought out Diogenes. Star-struck, Alexander asked the famous philosopher if there was anything he could do for him, any boon he could grant. Diogenes replied: “yes, get out of my sunlight.” Alexander, of course, was delighted.)

Diogenes was famous for puncturing the self-importance of other philosophers. And one of his signature moves was a response to Zeno’s paradoxes of motion.

Zeno’s paradoxes have a simple premise and a bizarre conclusion: motion is an illusion. Take the dichotomy problem, for example. Say an athlete needs to run a race. In order to get to the end, they will have to run halfway there, and then run the rest of the way. But! In order to get halfway to the end, they would first have to run half of that half… a quarter of the way to the end. And in order to run a quarter of the way to the end, they would first have to run half of that: one eighth of the way. And in order to run that first eighth, they would have to first run one sixteenth of the way there.

You can keep dividing this task further and further, in fact an infinite number of times. And it’s impossible for anyone to complete an infinite number of tasks – because you can always divide it further. Therefore, paradoxically, you can never begin; the athlete can never move; motion is an illusion.

Now, whether Zeno actually believed that or was just making a point about the nature of argumentation (logical premises can lead us down illogical pathways) is not important. What is important here is Diogenes’ reaction to Zeno’s paradoxes.

Diogenes silently got to his feet and walked off. Motion must exist, because Diogenes is in motion. The paradox was solvitur ambulando – solved by walking.

[Part 2 on Monday.]

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