Space and Time, Harmony and Melody
I've mentioned before that in the course of writing my book, I had to race through so many other books that there are many I hardly remember reading. Actually, I remember reading them. I just don't remember much of what's in them. If they weren't useful for the purpose of mapping out the cosmic adventure, it was necessary to flush them down the forgettery, at risk of hopelessly cluttering my mind. Unlike a proper scholar, I only remember the things I need, and forget the rest.
A case in point is the book before me, Emblems of Mind: The Inner Life of Music and Mathematics. For Music Saturday, no particular topic popped into my melon, so I snatched this book from the shelf in the hope that perhaps it might cough up a worthy thought or two. I notice that the book is in my bibliography, but when you look up the author in the index (Rothstein), the name is there, but there are no page numbers afterwards. However, I used a quote of his on page 45.
All I remember is that the book, for some reason, did not address my immediate needs, which had more to do with the spiritual nature of music, and how the existence of music is sufficient to undermine any form of materialism for those with ears to see.
Hmm. Perhaps this is the problem: "Rothstein, who is both a mathematician and a musician, is currently the chief music critic for the New York Times." That's a pretty tough hurdle to get over.
As for the book's purpose, "In moving back and forth between the worlds of music and mathematics, he has frequently encountered the generally accepted notion that there are many connections between the two. This book attempts to explain why these connections are far from accidental or incidental and why they reveal something profound about the nature of each activity."
However, "for all his clarity, Rothstein does not ever really succeed in drawing them together." D'oh!
Let's see what some of the amazon reviewers say. You never know. Perhaps there's a Raccoon among them. This is helpful: "In all honestly, I have not read this book HOWEVER, let me tell you why I just purchased my copy!"
What kind of person.... never mind.
Here's another: "One way of defining music is that it's a... language for a lot of different things that people do with patterns of sound and silence. And one way of defining mathematics is that it's [a language] for a lot of different things that people do with pattern. By exploring the ways in which music and mathematics handle pattern, one is naturally pointed in other directions (weaving, art, science) that demonstrate how valuable it is to recognize and explore the inter-connectedness of apparently 'different' fields."
I don't like that way of putting it, because it's far too simplistic, even a kind of meaningless horizontal tautology: language = pattern recognition. So what? This pseudo-explanation must ignore the most shocking property of music, which is its ability to convey spiritual content through the medium of vibrating air molecules. In what kind of cosmos is such a thing even possible?
"It might be poorly written, but what can one expect from a mathematician?" Ouch. Important point, however, for there is no way one can write about the spiritual content of music unless one's prose is also able to directly convey a bit of that musicality and spirituality. In writing about such lofty matters, one's prose must literally "rise to the occasion," or else be "about" something much less than it purports to be.
Let's look at some of the passages I highlighted in the book. Here is a quote from the mathematician Marston Morse: "Mathematics are the result of mysterious powers which no one understands, and in which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth."
One could say the same of jazz improvisation, in which a there is a range of virtually infinite choice before one, and one must choose which path to follow, not just once, but on a moment to moment basis. Thus, it is more like "math in motion."
But to say that the process is "guided by beauty" is to take one well outside any realm reducible to mathematical mapping. Beauty is either spirit or it is illusion, just as the cosmos is either ultimately meaningful or it is absolutely meaningless. For the intellectually honest, there is no in between.
Music conveys things that mathematics never could. No one can use numbers to provoke a subtle spiritual state in another, or even a purely emotional state. There are no "sad mathematics," although I suppose one could argue that my tax returns qualify.
So right away the analogy between math and music is strained, because music uses math for the purpose of communicating things that are not math. No one is interested in purely mathematical music.
The materialized mind can touch the world of spirit, but cannot penetrate its own thick layer of ice. Of Beethoven, Rothstein observes that "in his late years, like a Newton," he was "voyaging in strange seas of thought, alone." Quite true, but what can this mean? What is this "strange sea of thought," and how is it possible for human beings to set sail for uncharted lands on it, to colonize new and unmapped areas which lesser humans can later inhabit?
No, that was not a rhetorical question, for the Raccoon takes it quite literally: the worlds of truth, beauty, and virtue are real worlds. They are discovered, not invented. Or, to be precise, they are simultaneously created and discovered, much in the paradoxical manner that God creates.
Here's a useful passage. In reading music, it is not a "purely linear" exercise; rather, "it involves the vertical dimension along with the horizontal, the first presenting a form of musical space, the second the progression of musical time."
The author doesn't pursue this where it leads, but it is actually quite useful to think of the vertical in terms of harmony and of space, and the horizontal in terms of melody and of time. Our lives necessarily partake of both; that is, our life is the warp and weft of horizontal and vertical influences (which is why one's "area rug of life" comes apart at the seams -- or never pulls things together -- without both).
Note that the vertical is pure harmony, thus, situated outside time. It is "static," like a single chord, but with an infinite number of instruments with different timbres and tones. Time is the drawing out of the implications of the chord in time, again, very similar to jazz improvisation.
It is not at all straining this metaphor to say that this complex horizontal chord consists of the archetypes, angelic powers, transcendentals, and other perennial realities which guide man, and toward which he is drawn. In other words, they are both origin and destiny.
But each person is a unique melody played with this timeless chord (a spacetime harmelody). We revere artists who are most successful at combining the two, say, Shakespeare, who "uniquely" expresses truths that are anything but unique. In other words, like all great artists, he expresses timeless truth, only in a uniquely creative manner.
Out of timelessness.