Abstract mathematics is as removed from grubby politics as you can get, but a fascinating summer course organized by a research mathematician at Tufts University is trying to bridge the gap.
The five-day course set for August is titled “Geometry of Redistricting“. I discuss it briefly in my Monitor column this week, which you can read elsewhere in this newsletter, but didn’t have much room for detail. So I thought I’d use the newsletter to discuss more of what I learned from my conversation with with the organizer, Prof. Moon Duchin, whose specialty is metric geometry.
Duchin said the idea for the course came about like this: “Tufts has a long-standing course called The Math of Social Choice. I was teaching it last year during the primaries and I got really into thinking about gerrymandering and the shapes of (political) districts. My specialty is metric geometry, analyzing the qualitative features of different shapes using numerical scores, which is exactly what gerrymandering analysis calls for.”
“I was thinking of coming up with a model to take into account all the different legal requirements of districts and to project good districts for legislators or commissions. But I became convinced by the election this is not the moment for elite opinion – a group of math professors telling legislators how to draw their boundaries is never going to work.”
“My ideas shifted to the legal process. Working with the Lawyers Committee for Civil Rights Under Law, they told me there’s a major shortage of expert witnesses for a huge flood of redistricting cases” that followed a 2013 U.S. Supreme Court ruling that struck down “federal preclearance,” an important part of the Voting Rights Act.
“In legal history, courts and judges have said there’s no principled way to decide whether a shape is good or bad, and that’s wrong,” Duchin said, the mathematician in her bristling a bit. “One judge said something along the lines of districts ‘should not be subjected to endless beauty contests’ – to them there’s nothing to do other than have a beauty contest to say which shape looks lovelier than another shape.”
Part of the problem, she said, is a lack of people with technical expertise in shapes being called as witnesses. “Traditionally, experts (in redistricting cases) are statisticians. I was distressed to hear that geometers, like me, aren’t doing that yet.”
Hence the course, which will discuss such things as the Polsby-Popper method of quantifying compactness – roughly, how similar a shape is to a circlem in terms of the ratio of perimeter to area. Even this straightforward measure is more complicated than it sounds because of the “coastline problem,” which adds an element of subjectivity to something as simple as measuring borders. (I have discussed that delightfully geeky paradox previously.)
Initially, she said, the course was designed to teach about 30 research mathematicians, but that has changed.
“Once word got out, I got 360 messages in one day asking about applying. About one-third were from Ph.D. mathematicians – which is a lot. There’s aren’t that many of them!” she said.
The plan now is to open up two days of the course to the general public, streaming it online to meet requests from overseas, and have the other three days more technical for mathematicians – although Tufts and Duchin are still working out details in face of the unexpected popularity.
Reaching out to the non-technical world is vital is this approach is going to accomplish anything. “I have been giving public lectures on this topic and now I understand” why the typical mathematicians’ approach falls short, Duchin said. “It activates people’s math anxiety and doesn’t communicate to a non-mathematician. What we need is a rhetorically accessible but mathematically robust idea on how to judge shapes.”
For us fans of math, a really interesting aspect of this story is the way it is dragging an abstract field into the least abstract of human activities. “I think that’s what has touched a nerve,” said Duchin. “Pure math has, in its history, (rejoiced) in its inapplicability. People who are in the progressive community were excited to find ways to make the stuff work.”
Indeed. Consider it the opposite of G.H. Hardy bragging in “A Mathematician’s Apology” that “I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.”
I guess the purity of pure mathematics begins to seem less desirable when the world is in turmoil.