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:

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

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.

As a user of the exhibit, you won’t control the biases of the junctions directly; instead, you’ll draw your own not-necessarily-bell-shaped curve and a computer will adjust the biases in such a fashion that, when the balls fall randomly, the distribution that the balls form in their bins will closely match the curve you’ve drawn. Hence the exhibit’s name, Draw Your Own Conclusions (“DYOC” for short).

With the DYOC, you’ll be able to enter even a perverse shape like an upside-down bell-shaped curve and the algorithm will adjust the biases to produce the distribution you specified.

My role in the project was figuring out how the biases at the pins should be adjusted to achieve the desired distribution at the bottom. In the process of designing an algorithm for this, I discovered that in a way, what’s needed is a curious kind of sequential compression of one-dimensional images.

I gave a 20-minute talk about DYOC earlier this month at the MOVES conference on recreational mathematics (“MOVES” stands for “the Mathematics Of Various Entertaining Subjects”) hosted by MoMath. In some ways that talk was an expanded version of a talk that I gave back in 2014 at the 11th Gathering for Gardner conference. Here’s a link to the video of that talk:

https://www.youtube.com/watch?v=LDr8c2NmDDA

If that talk leaves you hungry for more details, here’s a link to the video of my MOVES talk, as well as a link to my slides:

https://faculty.uml.edu/jpropp/moves25a.mp4

https://faculty.uml.edu/jpropp/moves25a.pdf

Unfortunately the price-tag for an actual programmable quincunx is still too high, so the 2026 version of the exhibit will be a virtual mock-up preserving much of the user experience of the original DYOC concept. The math will be the same, but the balls will be simulated. Hopefully some people with good mathematical taste and flush bank accounts will come to the Museum in its new Sixth Avenue home and be so inspired by the virtual exhibit that they’ll fund the construction of a physical one!

I’ll report on later stages of the project as things evolve. Stay tuned.