Last night the Royce Gallery hosted the first of three performances of Pascal’s Triangle, the second concert in the 2017 season of Pamela Z’s ROOM Series. Both the music and the concept were the joint effort of Z and Donald Swearingen; and the result was a continuous composition lasting somewhat more than an hour conceived to celebrate the beauty, ubiquity, and indispensability of mathematics. That last sentence actually testifies to that indispensability, since the definition of “continuous” will be familiar to anyone acquainted with undergraduate mathematics after (if not during) the freshman year of college.
Z and Swearingen both worked with their own arrays of electronic gear, Swearingen supplementing his with a keyboard and Z adding her voice to the mix. She also designed the videos projected over the course of the performance, and the two of them both used some variant of a Smart Board as both a whiteboard and a screen for the display of some of those videos. They were joined by violinist Kate Stenberg and cellist Hannah Addario-Berry, both playing without electronic enhancement.
The title of the show refers to a triangular pattern of integers based on a very simple rule: Start with 1 at the top. Image that this integer is surrounded on both sides by an infinite row of zeros. The second row is shifted slightly to the side and each entry is the number that is the sum of the upper-left and upper-right numbers from the previous row. That means there will now be a 1 to the lower-left and lower-right of the first 1. Then, as the saying goes, “rinse and repeat.” In the next row there will now be a 2 directly under the top 1, and there will be a 1 to either side of that 2. The first six rows unfold as follows:
Image of Pascal's Triangle constructed by Conrad Irwin for Wikimedia Commons (licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license)
This array of numbers has a prodigious number of fascinating properties and even crosses the bridge from discrete mathematics to the continuum with an integer approximation to the normal distribution (or, as non-mathematicians call it, the “bell curve”). However, Z and Swearingen were less interested in this specific construct than they were in the broader scope of mathematics. For example, Z delivered a delightful riff on Georg Cantor’s discovery of an “infinity of infinities” (the idea that there were infinite numbers of different sizes … an infinite number of them). She also delivered an excerpt of a text by Albert Einstein in the original German.
However, the “spinal cord” of the evening involved the pursuit of the droll observation that you cannot count to one billion. In other words, if you start counting from 1 and the usual pace, even if you try to rush it as much as you can, it is unlikely that you will make it as far as half a billion over the course of your lifetime. Z prepared a series of videos to illustrate this, show subjects counting off numbers whose ages ranged from infancy to advanced old age. These video clips served as spacers between the other episodes of the evening. Their recurrence amounted to a running gag that kept getting funnier as the ages of the counters grew more advanced. (The oldest of those counters was sitting in the front row last night.) Much of the humor came from the fact that, as the numbers got larger, it took more time to recite each one of them.
If there was any shortcoming to this entertainment, it was that the subject matter tended to overwhelm the music. In fairness this may have just been the result of my holding both undergraduate and graduate degrees in mathematics. Nevertheless, the full breadth of Z’s vocal skills were on display last night; and, for me at least, there was something joyous about how she could engage her expressiveness in the service of higher (and sometimes not-so-high) mathematics. Beyond that, however, the most memorable musical effect was probably Kate Stenberg’s violin punctuations of a riff on why mathematicians prefer chalkboards to whiteboards. Anyone familiar with the former can probably guess the sorts of sounds Stenberg eked out of her instrument.
The remaining two performances will both be at 8 p.m., tonight (Saturday, May 6) and tomorrow night (Sunday, May 7). The Royce Gallery is located in the North East Mission Industrial Zone at 2091 Mariposa Street. General admission will be $13. Tickets may be purchased in advance online through a Brown Paper Tickets event page. That page also includes the Generous option of $20, which better represents the actual cost of producing this concert. However, there is also a Pick a Number! sliding scale for both those concerned about limited income and those whose support may be called more than generous. The only constraint is that the lower bound (another mathematical construct) for admission is $7.