The Book of Infinity
Throughout Spring 2023 I shall be serializing here the chapters of my book, The Book of Infinity, a series of vignettes on infinity. I aim to cover a huge collection of topics—Zeno’s paradox, the coastline paradox, fractal dimension, supertasks, the paradox of the largest number contest, Galileo’s Salviati, Hilbert’s Grand Hotel, Cantor’s uncountable cardinals, Goodstein and the Hydra, counting in the ordinals, the infinitary Liar paradoxes, the continuum hypothesis, the axiom of choice, orders of infinity, infinitary utilitarianism, infinitary computability, indescribability, the sand reckoner, paradoxes of high dimension, the outer limits of reason via incompleteness, and much more.
I’ve decided to experiment with this serializing style of publishing my book, rather than publishing in the conventional manner, since I see several benefits. One of them is the stronger connection with all of you, my readers. Please participate in the comment sections on the posts. I try to read everything there and I shall often respond to posts.
Chapters will be released, about one or two a week, all through the Spring. I am using this book as the main text for a new undergraduate course I have designed on infinity, which I am teaching this semester at the University of Notre Dame.
Here are the currently-released chapters, in the book order. Please enjoy!