In 1991, two mathematicians proved that you cannot always hear the shape of a drum. There are different shaped drums that make the same sound.
What about hearing numbers? For instance, can you hear pi? The answer is yes, you can. In fact you can listen to two renderings, though it took a recent court ruling to make this possible.
The story begins on Pi Day (March 14, or 3.14) 2011, when New Scientist posted a video by a musician called Michael John Blake, in which he played a piano rendering of the first 31 decimal places of pi, played at a tempo of 157 beats per minute (314 divided by two).
The video immediately went viral, but a few hours later, YouTube was contacted by a lawyer representing jazz musician Lars Erickson, who claimed that Blake's work sounded very similar to his 1992 composition "Pi Symphony", which he had registered with the US copyright office. With a claim of copyright infringement, YouTube removed the video. But Blake decided to lodge an appeal.
Both musicians had produced their works by converting decimal digits to notes on the musical scale and then adjusted tempo, phrasing, and harmonies to give the resulting composition recognizable musicality. The basis for Blake’s appeal was whether it was legally possible to copyright such a representation of pi. This is clearly an interesting question, since books and articles talking about pi and visual art based on pi clearly are copyrightable. Indeed, this very blog post automatically carries copyright.
One year later, on March 14 of this year, US district court judge Michael H. Simon, deliberately choosing to announce his decision on Pi Day, dismissed Erickson’s claim of copyright infringement. "Pi is a non-copyrightable fact, and the transcription of pi to music is a non-copyrightable idea," Simon wrote in his legal opinion. “The resulting pattern of notes is an expression that merges with the non-copyrightable idea of putting pi to music.” (Ideas are not copyrightable.) The only features of his work that Erickson’s registered copyright protected, the judge said, were the musical flourishes he added to give the result a pleasing sound, and on the face of it the flourishes the two composers added were different. Erickson disagrees with Judge Simon’s opinion on that point. Readers can make up their own mind.
In any event, the world now has access to two musical renderings of pi.
I’ve always been intrigued by artists who try to push the boundaries of their form, as indicated by an aside I made during my talk at Wonderfest 2010. As a mathematician, I’m particularly fascinated by attempts to interpret mathematics in different artistic media, novels, movies, TV shows, painting, sculpture, and of course music and dance.
Which brings me to the “Devlin’s Angle” column I posted back in January, when I mentioned the project I worked on with the choral group Zambra, where we set out to interpret some of my favorite mathematical equations in song. I ended my article by promising to say more about that project, but then other topics came up that seemed more pressing, and that promise was not fulfilled.
The equations/formulas we chose were Euler’s equation, Pythagoras’ equation, Area of a circle formula, Einstein’s energy equation, Leibniz’s series for pi, Newton’s second law of motion, and Euler’s polyhedron formula. You can find a description of the entire project on my website.
The stage performances of our show also involved dance, provided by math professor and dancer Karl Schaffer and members of his dance troupe MoveSpeakSpin, but unfortunately we did not have the funding for a video recording.
There is clearly considerable potential in the use of music and dance (and other artistic media) in school mathematics education. Someone else I am aware of, in addition to Schaffer, who is doing great things in this area is Malke Rosenberg with MathInYourFeet.
There is also a new TV series that includes some mathematics, Touch, on Fox TV. I commented on the portrayal of mathematics in that new series in a recent commentary in The Huffington Post. As I said there, I have positive and negative feelings about that particular portrayal, but surely anything that connects mathematics to an aspect of everyday life, particularly recreational activities and popular culture, provides an excellent opportunity for the mathematics educator faced with interesting students in a crucial subject whose many important applications are, to a large extent, hidden from public view.