Math, Music and Polyphonic States

The following exchange between M.P. Schutzenberger and A. Connes is lifted from the book Triangle of Thoughts:

M. P. S. — …language begins with poetry
rather than with grammar; euphony
plays a big role here.

A. C. — Your point of view coincides
with my own, since I sincerely believe
that music is at its very beginnings, like
language when it was at the stage of euphony.
I think we might succeed in this
way to educate the human mind to deal
with polyphonic situations in which several
voices coexist, in which several
states coexist, whereas our ordinary logic allows room for only one.

These words led me to wonder again about music, language and mathematics, but with an eye to music.  Schutzenberger and Connes seem to be pointing to the way sound moves thought before grammar (or logic), but they caused me to wonder more generally about the overlap between music and language, and even whether mathematical intuition participates in this.

Many questions about music are yet unanswered:  How is it in our nature to make music?  To what extent do we share this facility with other creatures?  What is melody or harmony? Does music precede language? How is it that music plays with sensations of movement, or of space, even when the body is still?  While it may be said that poetry does this as well, our usual language does not.  Our musical and linguistic sides are related, but they are not the same.  An online article about the evolution of music and language refers to work at the Harvard Medical School where they found that:

patients who have suffered severe lesions on the left side of their brain showed that while they could not speak – no language skill as we might define it – they were able to sing phrases like “I am thirsty”, sometimes within two minutes of having the phrase mapped to a melody.

The argument was made that the persistence of some musical literacy supported the idea that it predated language.  Here’s another article on language before music.

L.E.J. Brouwer, founder of the doctrine of mathematical intuitionism, writes in 1951 that the first act of intuitionism is:

Completely separating mathematics from mathematical language and hence from the phenomena of language described by theoretical logic, recognising that intuitionistic mathematics is an essentially languageless activity of the mind having its origin in the perception of a move of time. This perception of a move of time may be described as the falling apart of a life moment into two distinct things, one of which gives way to the other, but is retained by memory. If the twoity thus born is divested of all quality, it passes into the empty form of the common substratum of all twoities. And it is this common substratum, this empty form, which is the basic intuition of mathematics.

A move of time…….There isn’t time or space to explore all of the questions that come to mind when I think about the relationships between music, time, language and mathematics.  But the ones I am drawn to today have primarily to do with the failure of Hilbert’s program to make logic the foundation of mathematics in the first part of the twentieth century, and the Connes quote I started with.  It seems to me that logic guides mathematical perceptions, brings great clarity to them, extends their descriptive power, and is indispensable in this regard.  But the music, the more fundamental experience, comes first.  And Connes’ interest in “polyphonic situations”   in which “several voices coexist” made me think again of modern physics, where, while doing so with precision and care, mathematics required that clear cut, this or that, expectations of physical states be abandoned in favor of the coexistence of more than one quantum mechanical state.

Mathematics and science always open doors to new experience, new sensation, new vision.   But, equally revealing is to look back at ourselves, at where the vision may have come from.

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