Connections between music and higher math were explored and celebrated the week of May 16-20 with a residency by composer Tristan Perich and American Contemporary Music Ensemble, culminating in ACME’s performance of a Hop-commissioned work by Perich that was inspired by mathematical concepts. The project was funded in part by the Andrew W. Mellon Foundation, the National Endowment for the Arts’ Art Works, and the Frank L. Harrington 1924 Fund No. 3, as part of ongoing Hop explorations into the connections between STEM fields–science, technology, engineering and mathematics–and music.
The week was built around dynamic encounters between Perich and ACME and students and faculty, both in and out of the Math Department, along with time to rehearse the complex and exacting musical work. Perich and ACME members spent time with students from the Math Society and Association for Women in Mathematics, the student society Casque & Gauntlet and the East Wheelock Residence Hall cluster. They also visited two sections of Prof. Andrea Kremer’s “Hazardous Data” course, a freshman seminar exploring how to be skeptical consumers of quantitative information; and Prof. Peter Winkler’s “Math Beyond Calculus.” Watch a five-minute video about the residency and commission.
During the residency, Hop Advisor on Student Relations Kate Adams sat down with Perich and Winkler to further explore the connections between math and music. Below is an edited transcript of their conversation.
Kate Adams: What does the intersection of math and science mean to you?
Peter Winkler: Students seemed to really enjoy the idea of a bit of a break from the subject we were doing. It’s very easy for students and professors to forget that their overall purpose is to communicate ideas and get people thinking and get people reasoning . . . and not just in the particular subject of that course, but in mathematics and general and even in life, music, and other topics in general.
KA: What are the parallels between math and music?
PW: I’ve never really pursued the connection between mathematics and music and have learned a lot from Tristan, about how just thinking about these connections can be quite fruitful. Music is something much older than mathematics and much more developed than mathematics. There is a language of music although it varies from culture to culture. Music is highly developed not from first [basic] principles; but from cultural needs and imagination and artistry and good taste.
Mathematics started a couple of centuries ago and for a while it was mostly an applied area with a lot of artistry in its development, but it is because of the nature of the subject that people started to think about the elementary pieces that hold mathematics together. Then when computer science began its reign a half a century or so ago, people began to ask questions regarding the basic things in computer science like wires and logic gates with which you could build up any circuit. This prompted Tristan to think about maybe doing some of these same things with music.
In his wonderful One Bit Symphony; he is saying “Let’s not forget that even pitch is not the elementary thing here, the elementary thing is a pulse. You can put together just the ordinary output of an electrical circuit, and that makes music in the most direct way possible. We play these pulses with a little program mounted on a CD and a CD jewel box and with your headset you listen to pulses which are music. It is amazing. If you think about it you know that this direct connection exists, but here you can really experience this direct connection.”
KA: What was it about meeting with a composer that spoke to you? Was it something you thought could bring to light what you were teaching in the classroom?
PW: I like music, I like composing, I like ideas, so it might seem like Tristan’s work would be more interesting to me than to a random mathematician. The truth, is however, I do think that it truly is interesting to a random mathematician and Tristan has proven that it is interesting to a random math student. It is just a group of great, simple ideas that you can understand and you can then hear and see. You don’t get to see that so much in a math class.
Tristan Perich: I think that one of the reasons these ideas might be interesting to a wide range of people–not just peoplewho come from a music background–is that we are in this cultural moment right now where music is becoming more ephemeral, we are listening to a lot of our music in the cloud, we are getting detached from the physical object, across the board. Cloud computing means our music isn’t even really coming from the technology we are holding but from somewhere else. I think that we as a culture are uneasy about losing the directness of a lot of things and this is something that I think about in my work. By presenting this circuit as transparent, as something that people can understand and actually trace the path of electricity through, I am trying to connect to some kind of reaction that we all have to the opacity of our phones and the fact that a phone is just this black box that we don’t really understand. Especially at a time where we are thinking about the subtle effects that technology can have on our behavior, when most of our interactions are mediated by social media websites, and especially during and election year, I think that the meaning of technology is dancing around a lot of issues. Through music and visual art I am trying to think about these things which I think are universal, cultural questions at a time when I think it is really important for us to have agency because we are losing it in the way we interact with each other, in the way we are influenced by business and politics.
PW: Nowadays it seems as though music just comes out of the cloud. Certainly some people are making music, good music, but it seems that we are now more so music consumers than music makers. [To Tristan] It seems that by doing your own programming as well as by making your own music, you are connecting to the fundamentals in both of these things at the same time.
TP: I teach a workshop in assembly language programming, not expecting people to go out and start writing assembly programs, but more so they grasp that there is a lowest level that is quite basic and understandable. Even if we have to take for granted a lot of the technology around us, there is this idea that it is built on something that is understandable, that isn’t just magic at the basic layer. If we stop questioning these things, we could almost imagine in the future we will come up with new mythologies for how the technology we built and no longer understand works, like not understanding lightening led to the invention of gods.
PW: It seems to me that what you are doing is actually allowing us to experience technology. By writing a specific program and listening to bits in it, you are not just saying, “This is how it works,” you are saying, “Let’s look at this directly and experience it.” This can cause people to look at more complex, less elemental music and art in a slightly different way.
TP: During my time here I focused mostly on some foundations of math ideas that revolve around proof theory, reverse math, computability, the difference between computability and definability and provability. I feel that I gained a slight advantage because this is tough stuff that people who have been doing this full time for many years are working very hard at and I am coming at it from essentially a laymen’s perspective. I was particularly inspired by the idea of reverse mathematics, which plays with the idea that mathematics is built from some basic axioms that are used in combination with certain proof operations to prove a theorem. The question is whether all those axioms are actually necessary for individual theorem. Sometimes you can prove a given theorem without all of those axioms, and the idea or “reverse math” is to see what axioms are actually necessary to prove a particular theorem.
PW: I think the idea of reverse mathematics is very close to the idea of minimalism in art. We have very powerful tools in mathematics and most of us spend our time using whatever tools we can get our hands on, but a few of us are interested in the idea of what we could get by with if we had to, what is the very least we need in terms of axioms to prove these theorems? Similarly, what are the very least elemental things that we need to produce a piece of music or to produce a piece of art? We have much more sophisticated ways to do it, we could take out the oils and so forth. However, if we understand what we can do with just the minimum maybe that will help us gain more when we go back to the whole tool box.