Better than binary: four kinds of false dichotomy

I’ve been helping put together some materials for a new class we’re tentatively calling “Math and Public Life”, organized around ten or so concepts from higher mathematics and how they relate to the way we think about life and each other. One of the themes I’m hoping to show is that often as our understanding … More Better than binary: four kinds of false dichotomy

New Math vs Old Math

A frequent reader of this blog sent me a link to this video on Facebook, of a side-by-side comparison between a traditional method for doing multidigit multiplication (which is over very quickly) and a new “grid” method (which takes a long time to explain): She wanted to know why anyone would use the long, drawn-out … More New Math vs Old Math

More information doesn’t have to make you more certain

FiveThirtyEight recently posted a piece called “The Impeachment Hearings Just Confirmed Voters’ Preexisting Opinions”: the same wave of new information has just made everybody more convinced of what they already thought: One explanation of this phenomenon is “motivated reasoning”: a person finding data more reliable and arguments more convincing if they fit with what the … More More information doesn’t have to make you more certain

10 percent liable

Last month, this New York Times headline caught my eye for three reasons: Netherlands Was 10 Percent Liable in Srebrenica Deaths, Top Dutch Court Finds Reason #1: Having lived in the Netherlands, headlines about Dutch affairs usually stick out to me. Reason #2: I’d just been reading The Themis Files, a fiction series in which … More 10 percent liable

You’ll never believe what weird trick fixes p-values

Okay, I’m taking a quick break from my regular posts because I can’t stop geeking out about this recent XKCD comic: If you already know about clickbait (likely) and p-values (less likely), you may not need the joke explained to you. But there’s something deep going on here too, tying into the themes of probability … More You’ll never believe what weird trick fixes p-values

If you have a question, someone else probably has it too…

I often tell my students, “When you have a question, ask, because you’re probably not the only one who’s wondering.” I heard the same thing when I was a student, but I still felt embarrassed to ask. What if I really was the only one? Wouldn’t I be slowing down class to ask? If no … More If you have a question, someone else probably has it too…

Cantor’s Arch

Triumphal Arch: Arch of Titus, Rome Arc de Triomphe, Paris Washington Square Arch, New York Triple Arch: Arch of Constantine, Rome Arc du Carrousel, Paris Marble Arch, London Septuple Arch: ??? Cantor’s Arch: It seems to me that no arch is more triumphant than one that rests on a set of measure zero.