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
For a future blog post, I’ve been thinking about how sometimes, when we have two alternatives, one is really a special or “limiting” case of the other, the way a square is just a special case of rectangle. I’m still working on that post, but meanwhile I’ve been distracted by thinking about other shapes that … More A Quadrilateral Venn Diagram
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
A recent Washington Post article has the title “When a danger is growing exponentially, everything looks fine until it doesn’t.” The article talks about how suddenly exponential growth seems to go from vanishingly tiny to passing a major threshold. This made me wonder if there is some natural moment in time at which we can … More Does an exponential curve have a corner?
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
In World War II, allied forces faced an unusual statistical puzzle: to make good strategic decisions, they needed to know roughly how many tanks Germany was building every month, but they had very limited evidence whether that number was small or large. One clue was that captured tanks had serial numbers on some of their … More German tanks and Doomsday
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
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
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…
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.