“Mathematics is the art of giving the same name to different things (as opposed to the quotation: Poetry is the art of giving different names to the same thing)."
“Logic and intuition each has its necessary role. Each is indispensable. Logic alone, which can give certainty, is the instruction of demonstration; intuition is the instrument of invention.”
“Mathematicians do not study objects, but relations between objects. Thus, they are free to replace some objects by others so long as the rations remain unchanged. Content to them is irrelevant: They are interested in form only.”
Much has been made about the connection between math and music, from the harmonic properties in ratios, to the notion that Mozart makes you do better on math tests. One can certainly use different elements from math to interpret works of music and similarly, composers make use of several mathematical ideas when writing songs or improvising. Use of these techniques of composition or analysis seems to at first take away the magic. The connection between math and music can become a prosaic set of tricks like inserting a significant modulation at some golden ratio point or carefully counting the number of notes needed to fit a harmonic progression. Such applications hardly allude to some massive secret about ourselves and our universe, as some would hope a deep understanding of the math-music connection would yield. But seen another way, it is in fact a miracle that such simple principles can be applied to organizing sound consistently induce emotional and spiritually satisfying results. Technical knowledge causes the magic to move from starry eyed mysticism into the real lived and shared experiences of people from all over the world.
I’d like to take it a step further. Suppose that there is a locus of creativity in the human spirit from which spring all things beautiful and inspired. That the experiences of creating art, performing music, playing a game, or solving a problem constitute a kind of spirit journey into a sublime space where all manner of these connections exist. Suppose we could access this space easily, and upon touching it, we would gain practical realizations and insights and knowledge that makes magic real. Suppose that we as a society learned how to do this systematically and actively taught and learned this 'meta-skill'.
This is a pet theory of mine that comes from being overwhelmed by a sense of beauty and wonderment in many aspects of life, and I first formed this theory while studying music. Often times, I’d listen to music I didn’t like. However, by forcing myself to discover at least one magical thing inside of it and allowing that magic to sweep me away, I would always gain something profound and applicable in some other area of life. The subjective headspace of passion induces a sensitivity to the lessons and latent connections available, and so the tricky discipline of discovering passion exposes you to deeper truth.
Jazz builds this skill through group improvisation. Given some pre-agreed structure, musicians perform using their skill and intuition about what to play. The best, most musical moments occur when everyone is listening to one another and playing in a conversational manner. It elevates the experience for the musicians, pushing them to discover new ideas, and to surprise themselves in the moment. Their enthusiasm then elevates the experience for the audience, who can somehow feel the music sync, groove, and breathe. This experience induces feelings of wonder, revelation, and magic.
Mathematics relates to all of this because, as Poincaré pointed out, it effectively names and makes exact the relationships between ideas. The logic reveals the structure of the beauty and the power to point out similarities and differences between disparate structures. This is what allows me to make use of the sublime as a learning tool. Studying math can help one develop a certain sensitivity to the similarity and dissimilarity of fields like music, martial arts, literature and others because math gives a rigorous “pure” sense of structure and relationship.
Thus it seems like improvisation and the study of music grant us access to the sublime through practice of intuition. Mathematical thinking gives us the logic of how to apply and relate these sublime moments. A proprietary, perhaps novel notion about the connection between math and music. All of this leads me to believe that we should play with these ideas!
Let's have a conversation around them. Let’s try this as a social experiment.
Let’s do it at the National Museum of Mathematics in New York City
Let’s play jazz music and talk about math and throw a party with a DJ and food and drink after to celebrate the sublime.
It’s called the Quadrivium series and you can get tickets here.