This series is devoted to some of the underappreciated and misunderstood limits of human reason. Interspersed throughout are more Wikipedia articles than any normal person has time to read in a day—consider them an optional and often superior companion to my presentation of the ideas herein.
Infinity is the trump card of childhood argument—an unstoppable arithmetical power play in encounters of escalating scale. Only when your friend Suzie had the gall to quip, “Nuh uh, I have infinity-plus-one dollars!” did you falter.
“That’s against the rules” you stutter.
But it’s too late. Suzie is already running down the hall with your lunch money and calculator, having unquestionably Won the exchange (to any onlooker), and Quashed your pride (and that of your House).
Much like Star Wars, I don’t actually remember when I first heard about the idea of Infinity. Upon first learning about numbers, the specter of some always bigger thing suggested itself, just out of reach. I remember distinct pride in mentally counting to one thousand on a plane flight to Disney World when I was younger (in hindsight, I may have skipped the entirety of the 700s (I was a strange child)). But the infinite, as many a Math teacher will remind, isn’t really a number. At least, it isn’t the sort of number you’re used to. (As an aside, it’s worth pointing out that, should you find yourself in a properly refereed duel of Large Numbered wits with Suzie in the future, Scott Aaronson offers an excellent strategy). Even among educated scientists, Infinity is little more than that thing which makes integrals either a lot easier or lot harder to evaluate.
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