Things happen in nature. Cells socialize and build structure, organisms grow, and move, and interact, and then more things grow – like music, language, and mathematics. Generally, talk about evolution is very pragmatic. Cell organization, the shaping of roots, leaves, nourishment mechanisms, reproductive drives, are all usually understood as fairly specific purposeful processes. Perhaps by sheer habit we extend this to our study of language and culture, even mathematics and music. But there is growing evidence that it would be worth our while to shake this habit. It may be causing us to overlook the significance of structure that continuously emerges from the very flow of life.
In a nice post at National Geographic Virginia Hughes discusses a recent study on the mechanisms that underlie music as was reported by the National Academy of Sciences. The study, by researchers at the University of Singapore’s Graduate Medical School, focuses on the relationship between music, movement, and emotion. It was motivated by psychology professor Thalia Wheatley’s earlier work, where she did neuroimaging studies which showed that brain regions involved in perceiving motion were some of the very same regions activated during music perception. This suggested that the two skills were linked. The University of Singapore researchers found a clever way to demonstrate that music and movement share a common structure that will produce equivalent expressions (both in animation and in sound).
The National Geographic post referenced an earlier piece written by Carl Zimmer that describes the work of Aniruddh Patel, an expert on music and the brain at the Neurosciences Institute in La Jolla, California. Patel investigated the relationship between music and communication.
It looks as if music is riding the coattails of other parts of the brain that evolved for other functions.
In a chapter of the recent book Emerging Disciplines, Patel describes how that borrowing process might work. Listening to the tones in instrumental music, for example, activates language regions of the brain that also process words and syntax. Those regions may make sense of tones by parsing melodies almost as if they were sentences. To keep a beat, Patel’s research suggests, we co-opt the brain network that links our hearing and the control of our muscles. This network’s main job is to allow us to learn new words.
Looking further I found a piece in The Guardian by mathematician Marcus du Sautoy about music and mathematics in which he makes the argument that what binds music and mathematics
is that composers and mathematicians are often drawn to the same structures for their compositions. Bach’s Goldberg Variations depend on games of symmetry to create the progression from theme to variation. Messiaen is drawn to prime numbers to create a sense of unease and timelessness in his famous Quartet for the End of Time. Schoenberg’s 12-tone system, which influenced so many of the major composers of the 20th century, including Webern, Berg and Stravinsky, is underpinned by mathematical structure. The organic sense of growth found in the Fibonacci sequence of numbers 1,2,3,5,8,13 . . . has been an appealing framework for many composers, from Bartók to Debussy.
And we all know that the Fibonacci sequence is expressed in a multitude of living forms like tree branches and shell spirals. Together these thoughts reinforced my sense that a pragmatic view of life is a weak and stingy view of things. I wrote about music, movement and mathematics in an early post. There I quoted from Fritjof Capra’s The Science of Leonardo.
Since Leonardo’s science was a science of qualities, or organic forms and their movements and transformations, the mathematical “necessity” he saw in nature was not one expressed in quantities and numerical relationships, but one of geometric shapes continually transforming themselves according to rigorous laws and principles. “Mathematical” for Leonardo referred above all to the logic, rigor, and coherence according to which nature has shaped, and is continually reshaping, her organic forms.
Mathematics is not just a way to describe the world around us. It must be, itself, another living expression of it.
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