It seems like barely yesterday I was giving people a tip about this podcast. In Our Time, a BBC panel-discussion programme about topics of general interest, this week repeated an episode about Zeno’s Paradoxes. It originally ran in 2016.

The panel this time is two philosophers and a mathematician, which is probably about the correct blend to get the topic down. The mathematician here is Marcus du Sautoy, with the University of Oxford, who’s a renowned mathematics popularizer in his own right. That said I think he falls into a trap that we STEM types often have in talking about Zeno, that of thinking the problem is merely “how can we talk about an infinity of something”. Or “how can we talk about an infinitesimal of something”. Mathematicians have got what seem to be a pretty good hold on how to do these calculations. But that we can provide a logically coherent way to talk about, say, how a line can be composed of points with no length does not tell us where the length of a line comes from. Still, du Sautoy knows rather a few things that I don’t. (The philosophers are Barbara Sattler, with the University of St Andrews, and James Warren, with the University of Cambridge. I know nothing further of either of them.)

The episode also discusses the Quantum Zeno Effect. This is physics, not mathematics, but it’s unsettling nonetheless. The time-evolution of certain systems can be stopped, or accelerated, by frequent measurements of the system. This is not something Zeno would have been pondering. But it is a challenge to our intuition about how change ought to work.

I’ve written some of my own thoughts about some of Zeno’s paradoxes, as well as on the Sorites paradox, which is discussed along the way in this episode. And the episode has prompted new thoughts in me, particularly about what it might mean to do infinitely many things. And what a “thing” might be. This is probably a topic Zeno was hoping listeners would ponder.

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