Zeno's Paradox and Infinite Sums—Lectures on Infinity (lecture 1)

An ancient puzzle leads ultimately to a remarkable observation on the malleable nature of infinite sums.

Welcome to the Lectures on Infinity, a series of lectures exploring all my favorite paradoxes and conundrums.

In this first lecture, we introduce the ancient puzzle of Zeno’s paradox and follow the thread where it leads—to the very meaning of our number expressions, to infinite summations, to convergent and divergent series. We will discuss what I call the most contested equation in middle school, and by the end we shall reach the remarkable Riemann rearrangement theorem, concerning the malleable nature of infinite sums.

• A transcript of the lecture is available.

• Find the lectures here on Infinitely More in the lectures-on-infinity tag.

• The lectures will appear on YouTube.

• The whole lecture course is hosted at Ergo: Lectures on Infinity.

• Find other philosophy lecture courses at Ergo.org.

• This lecture is based on my essay Zeno’s Paradox.

• The essay also appears in my new book, The Book of Infinity.