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 […]
German tanks and Doomsday
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 […]
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 […]
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 […]
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 […]
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.
Spontaneous Inequality
A fun problem making the mathematical rounds: if you give everybody some number of dollars (say you give 45 people $45 each), and at every tick of the clock everyone with money chooses one random person $1, how will the money eventually end up distributed? You might think it’ll stay approximately equal—”approximately” only because of […]
“Genie” Coefficient
Spice Blendoku
Since deciding to renew our lease for a second year, we’ve been trying to improve our apartment in several small ways: getting fabric for curtains, moving the recycling from a paper bag in the coat closet to a bin under the sink, re-gluing sections of doors that have warped apart, etc. One project we’ve had in mind […]
How to draw an impossible triangle
If you’re like me, you like to doodle fun patterns. One of my favorite things to doodle is an “impossible triangle” that looks like three straight bars meeting in right angles, which can’t exist in real life: But I had trouble drawing an impossible triangle from memory, until through trial and error I came up with this […]