There’s a false dichotomy which supposedly stands between aesthetics and analysis. But art and emotion do not stand in opposition to logic and reason. This nonsense is, in many ways, the bastard offspring of the “two cultures” story we’ve inherited since before C. P. Snow gave it a name, and which we’ve variously integrated into our teaching programs for almost all levels of education. Back in the “good old days” of classical education (by which I mean the ancient Greeks) mathematics and music were treated as much the same thing. Even today, we have not quite lost all sight of those connections, and if one takes the time to listen to mathematicians, one will notice that the issues of whether a proof or a theorem is beautiful or not takes on primary importance.

http://www.youtube.com/watch?v=1XWlK-cL504

Careful, meticulous reasoning is not cold; quite the contrary, it is a fire that will consume you without mercy. I’ve touched on the idea of mathematics and the beautiful before, but wish to revisit the idea again because it can bear the company, even in this Thanksgiving season. This time around, however, I wish to approach matters from a more “musical” perspective that specifically highlights some ideas around “rhythm.” I mean to tackle these ideas from what I take to be a very Whiteheadian point of view. Whitehead was, of course, an accomplished mathematician and educator, and well attuned to the subtleties of mathematical aesthetics. But as he began to worry about the philosophical underpinnings of our physical sciences, his inquiries began to lead him from issues of organization (of thought) to organism itself. Rhythm became one of Whitehead’s central concepts.

A little backstory might be appropriate here. Whitehead, as a mathematician, was always concerned with matters of algebraic order and the abstract structure of space. But after his son Eric died in the Great War, Whitehead’s writings changed subtly but noticeably. While Whitehead always had a soft, even poetic, gift for language (as evidenced in his essays on education and his biographical sketches of his boyhood), with the Great War over, he permitted his grief to speak momentarily in his 1919 Enquiry into the Principles of Natural Knowledge (“PNK”) The book itself is dedicated to Eric, and the final chapter – something of a comet in comparison to the rest of the book – is on rhythm.

Rhythm is not the same thing as mechanical repetition. Much of Whitehead’s mathematical work was invested in the study of a kind of mechanical repetition, because that was where a great deal of all mathematical work was invested. Whitehead came up through Cambridge at the time when Clerk Maxwell‘s work on electromagnetism (mechanically repeating waves of energy) was redefining our concepts of spatial relatedness. It was Maxwell’s work – far, far more than any of the numerous experiments that might have been cited – which motivated Einstein’s developments of special, and then general, relativity.

But mechanical repetition is not organic, and it is not rhythm. An example here might help illuminate theis. It is traditional for orchestras to tune to the oboe, playing a concert “A”. To whom or what does the oboist tune? (It is said that an oboe is an ill wind that nobody blows good.ⁱ) Inevitably, all questions of measurement come back to matters of human judgment, but that is a discussion for another time. For now, the interesting fact is that the oboe comes closest to a “pure” concert A, 440 hertz in the auditory realm.

Closest, but not identical.

It is a matter of utmost triviality to construct an electronic device that produces a genuinely pure – which is to say, purely mechanical – tone of 440 hertz. Yet no one tunes to such a device because, evidently, no one can. I have no citeable evidence to justify this claim, only the assurances of a few musicians I know, whose authority on the subject of music I am inclined to accept. (You, of course, must make your own decision on this matter, but I invite you to find a counter-example.) What differentiates the oboe from the electronic device is that the oboe is not really “pure,” it is not simply mechanical. Its tone, when it plays a concert A, is statistically stabilized around 440 hertz, but not simply identical with it. There is an organic variation in the tone; the waveforms exhibit rhythm.

The sheer aliveness of rhythm comes as no surprise to anyone who has seriously touched on music in any form, but it manifests itself with the most absorbing intensity in drumming itself. If I may be permitted a personal anecdote, I am a “Rennie” (renaissance faire enthusiast). At my home faire of Bristol, one of the closing events has, for many years, been a “drum jam.” This is all about rhythm, and it can be a very intense, liberating, and primal experience for the participants. (The preceding link is of a publicly shared video of a public event in a public space, so I do not believe I am violating anyone’s privacy in sharing the link here. For the record, I recognize a great many of the persons in this video.) Along these lines, Mickey Hart, the drummer for The Grateful Dead, has given voice to such experiences, about this connection between rhythm and spirit as a central reality of organic being, in both his books and his drumming performances.

Intense! Liberating! Primal! Magical! Beautiful! Mathematical!

That last one may jar anyone not actually acquainted with mathematics. I’m fairly sure it would not at all be that jarring to Whitehead, however. Proper Victorian gentleman that he was, I cannot imagine him doing more than staring in bemused astonishment at the spectacle of a Bristol drum jam. But I am satisfied that a very strong case can be made that Whitehead understood – better than most anyone before or since – about the connection between intensity, mathematics, rhythm, and human development. There is something indescribably intense, liberating, primal, and magical, about a mind unleashed through mathematical education. It is a kind of beauty of which the poets speak, a beauty of untapped and unimagined possibilities. The pulsing rhythms of life reach in both directions, to the muddy rootedness of the earth, and the dazzling expanses of abstract thought. As a boy, Whitehead spent days and days wandering about the ancient countryside of Kent, near his home of Ramsgate; as a man, he probed the abstract relational structures of time and space. It is a mistake, born of intransigence and unfamiliarity, to imagine these two are really all that different. What binds them together is the intensity of aesthetic experience.

People often wrongly imagine that mathematics is just and only about “truth,” or, at least, some kind of “truth.” But as far as that goes, so are painting, or dance, or music, or poetry, about some kind of “truth.” The “kind” varies, but the ultimate connection of truth to the world is through the aesthetic structure of experience.

Stated as baldly as this, the first reaction might be to reject this claim outright. Fully defending the claim would take more space than this blog. But an outline can be presented very briefly. First off, any claim to reject the idea of “truth” is self-contradictory nonsense (what claim to being “true” could such an anti-truth position justify for itself?) But what connects truth to the world? Any attempt to go beyond human experience is automatically reduced to nonsense by the fact that human experience is the only thing we have access to, and hence the only thing that can connect truth and the world.

So what, then, is experience? It is primal, it is magical, it is mathematical. Experience shines forth in different kinds of aesthetic expressions. Each kind answers to its own rhythms, but those rhythms are all innately organic in character. The connection of truth to the world is alive and multifaceted; it is both rhythm and logic.