The Shape of This Summer

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Jordan Ellenberg is the author of the new book Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else. I just received it as a Father’s Day present.

Today we convey some short musings on some ideas in the book.

Ellenberg is both a biological father and a Doktorvater. Indeed, if we make a correct inference from his Mathematics Genealogy count of “12 students and 13 descendants,” he must be a doctor-grandfather. His own advisor was Barry Mazur. Ellenberg holds the John D. MacArthur professorship in Mathematics at UW-Madison and a distinguished professorship named for former Wisconsin senator William Vilas. (We’ve had UW-Madison on our minds for over a month about something else, but various events including new kinds of chess-cheating cases have delayed the work needed to do it justice. While writing this paragraph, I have had a seconding role in a disqualification by an online chess platform of a player in a tournament played today.)

I made my inference in the last paragraph by counting—I did not take time to click on his twelve students to verify which one has a graduated student. What strikes us about the new book is the aspect of making inferences not by counting.

Pandemic Phasing

Our picture above was tweeted by Ellenberg on Christmas Day, 2019, a half-hour before the start of the Milwaukee Bucks playing at the Philadelphia 76ers. Notice that the seats behind him have not yet filled, as of course they did for a pre-pandemic holiday game. Last night, I had on the terrific Game 7 between the Bucks and the Brooklyn Nets while processing chess data. The stands at the Brooklyn Barclays Center were within 1,000 of full capacity, but there seemed to be some spaced-out sections nearest the court that would have been teeming usually.

My wife and I ventured out two weeks ago to see the Toronto Blue Jays play in Buffalo’s Sahlen Field, their home until the border with Canada reopens. Our stadium has increased the allowed capacity from 35% that day to 80% now, but our paper noted today that by month’s end it may be the only venue not allowing 100%. Will the return to large close-packed crowds be safe—will there be sufficient “herd immunity”—involves questions raised in two chapters of Ellenberg’s book. Here is a main idea—in my words, because I haven’t had time to actually read the book yet (and while writing this section, it seems I am having a primary role in another impending ban from the same overseas chess event).

Often the most immediately valuable inferences are made from judging the shapes of curves rather than calculating numerical projections.

Here is an example composed from today’s new-cases charts of Florida and the UK from the Worldometer coronavirus pages:

The recent uptick in the UK is said to be caused by the new “delta” strain of the virus. I’ve chosen Florida rather than the whole US for similarity of scale and because Florida began a June upsurge this time a year ago. The US on the whole and most states show a similar fully-downward trend. Of course we hope it stays that way everywhere as the reopening phase continues.

The point we are making is that if you just go by the numbers—and if you give highest weight to recent trends in those numbers—then your numerical projections can vary wildly. The logic of shape rather than number may be a more stable basis for judgment. This aligns with what we said about Ayanna Howard’s giving primacy to human rules of judgment in designs for robots in our post a month ago.

A Caveat

There is, however, a caveat that falls in with the opening example of Ellenberg’s chapter 11, “The Terrible Law of Increase”:

An early judgment based on a seemingly best-fitting shape has maximum potential to go wrong.

The example is an over-optimistic projection of Covid-19 cases and fatalities based on an initial expectation of a cubic curve fit. We neither wish to be academically impassive or blaming over the terrible toll which we have all had to endure, but to promote depth and wisdom in spatial thinking in line with the book’s purpose.

Open Problems

How can we best get quick and accurate judgments of what is in store this summer and fall?