Tag Archives: probability

In Praise of Stupid Questions

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Ask a silly question, get a silly answer. — Tom Lehrer, “New Math”

I ask too many questions. A case in point is the time I lost out on a place I wanted to rent when I asked my potential future landlord one question too many (“Does the pond have mosquitos in the summer?”). Another example is the time I ticked off a car salesman by asking him, after a long string of similar requests that he had gamely complied with, whether I could try changing the tires of a car I was considering buying from his dealership before I bought it. (I mean, shouldn’t every responsible consumer go through the entire owner’s manual when contemplating such a major purchase?) As a member of a local singing group, I developed such a reputation for asking the music director questions that when we went on a tour, one of my fellow singers got a laugh by interrupting the tour-guide with my signature line: “I have a question!”

But my topic today isn’t questions in general. I want to focus on the species of question that I often tell students doesn’t exist: the Stupid Question. And I want to talk about how one stupid question led me to an interesting and new (albeit a bit stupid) way to estimate the mathematical constant pi.

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Randomness Made to Order, part 1

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As a member of the Advisory Council for the National Museum of Mathematics (“MoMath”) over the past decade, I’ve had a number of unique opportunities, such as the thrilling chance to improve the Museum’s datebase via my smartphone and watch exhibit-content update in real-time, and the less thrilling opportunity to break an exhibit on the museum’s opening day (buy me a coffee and I’ll confess to you that shameful episode from my past). But the opportunity I’m writing about today is one that’s still playing out: the chance to play a role in creating a new kind of Math Thing, namely, a programmable quincunx.

If you look up the word “quincunx”, you’ll find that one definition is this arrangement of five dots:

A quincunx as seen on a standard die.

But I’m talking about the kind of quincunx that looks like this:

A quincunx as seen in some science museums. From p. 261 of “Lady Luck” by Warren Weaver (permission pending).

You’ll notice that the balls piled up at the bottom form a bell-shaped curve, reminiscent of the normal curve from statistics:

This isn’t a coincidence; the quincunx was designed to illustrate statistical principles in general and the Gaussian distribution in particular. Many science museums have a quincunx, but MoMath was unique in having an adjustable quincunx in which a lever allowed users the chance to introduce biases at the junctions, making it more likely for balls to go to the left or to the right, and correspondingly shifting the bell-shaped curve to the left or to the right.

I wrote “MoMath was unique …”, not “MoMath is unique …”, because when MoMath’s lease at its old location on 26th Street ran out, it moved to a temporary smaller location on Fifth Avenue, and the adjustable quincunx wasn’t included in the downsized museum. But in 2026 a bigger-than-ever MoMath on Sixth Avenue will feature something new under the sun: a customizable quincunx, in which each junction will have its own individual bias, and in which the distribution of the balls at the bottom won’t necessarily be a Gaussian at all, but a curve of your own devising.

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