Friedman on Dialectics, Part 1: Of Formalist Denial

This is the first in what I hope is a series of fairly serious and personal posts I will write in the coming days, which will also address several issues that arose in my MA thesis, which I completed last spring. Part 1 deals with the intellectual background of a formative period of my life, roughly 2003-2008. Part 2 will deal with emotional and musical aspects of the same period.


 My music sometimes seems mysterious. Part of the mystery comes from the fact that I wait, receptively, then I welcome, I accept … Listen, there are two kinds of people: the type that is only interested in what they understand, and the type that wants at all costs the hermetic mystery, enigmas. The first gets bored when they don’t understand, the second is bored when they do understand. Me, I accept poetry, the inexplicable. Things are born in the waiting.

Morton Feldman, interviewed by Martine Cadieu in “Morton Feldman – Waiting, May 1971” in Morton Feldman Says: Selected Interviews and Lectures 1964-1987. Edited by Chris Villars. London: Hyphen Press, 2006, p. 40.

In grade 12, my school counsellor asked me why, when I was definitely going to be doing a degree in music, was I also studying calculus, chemistry and physics.  At some point a few years earlier, I had come across the 17th century polymath Athanasius Kircher’s exhortation that “there is nothing more beautiful than to know all” (where this quote came from I have no memory). This may have been possible at the time he was writing, but is clearly not now, something I obviously knew intuitively but did not really believe until after I started university. For my entire childhood and adolescence I intentionally read books that were far too difficult, culminating in Roger Penrose’s The Road to Reality, an attempt to explain the physical properties of the universe in 1100 pages. I vaguely remember understanding about the first 200, which deal with the math required to understand the rest of the book; I read the next 900 in a daze, trying to at least absorb the terminology. My reading was not limited to science: I also read books at random from my family’s shelves. My family owned somewhere in the area of 2000-3000 books at this point, skewing heavily towards CanLit and literary theory, thanks to my father. I read experimental novels like Death Kit by Susan Sontag and the highly obscure the telephone pole by Russell Marois (which I know I finished on Oct. 28, 2003 and Jan. 18, 2004, respectively, thanks to a Microsoft Access database [!] I kept of my reading at the time).

The book that most affected me during this period, however, was Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter. I read GEB in the fall of 2004, which was otherwise a very difficult part of my life (something I will address in my next post). In both his preface to the 20th anniversary edition of the book and in his later book I Am a Strange Loop, Hofstadter essentially complains that no one understood the underlying message of GEB, which is an examination of self-reference and its ramifications on the possibility of artificial intelligence. GEB very easily comes off as seeming to be about fanciful connections between its various subjects: not only the titular figures, but also Zen Buddhism, microbiology, computer science and the like. Its highly novel structure helps this misinterpretation: it alternates fairly normal chapters with dialogues between the characters Achilles and the Tortoise (drawn from a dialogue by Lewis Carroll [pdf], who himself got them from one of Zeno‘s paradoxical thought experiments) which are in the form of contrapuntal pieces by J. S. Bach. I do not pretend to have fully understood GEB, but I definitely gathered quite a bit from it, particularly the enormous paradoxes that loom under the surface of logic and therefore underpin nearly every aspect of thought. It’s possible that I took almost the exact opposite message from the average reader of GEB, namely that, while everything is connected, it is connected in such a way that nothing makes sense.

The most important paradox discussed in GEB is Kurt Gödel‘s so-called incompleteness theorem (of which there are actually two). I will attempt a simple explanation of it, which is probably ultimately fallacious, but will give the reader an idea of what it entails. A formal system is a logical construct where one can use certain axioms (statements which are assumed to be true beforehand) and rules (which transform axioms and other statements which are derived from axioms). Gödel leans heavily on the notion of compactness, which can be used to prove that, in a particular formal system, provability by the system is logically equivalent to truth. A compact formal system can have the property of completeness, whereby it can prove every true statement, as well as the property of consistency, whereby no false statement can be proven. Let us examine a statement in a formal system that can be translated as something like “this statement cannot be proven,” which is clearly a paradox: if it is true, then we have no way of proving it, so the formal system is incomplete (since we have found an unprovable truth); if it is false, then it can be proved, so the formal system is inconsistent (since we have found a provable falsehood). The result is that any system must be either incomplete or inconsistent, and that any attempt for a system to describe itself either fails because of incompleteness or yields dangerous results because of inconsistency. In the first case it means that in order to describe a system completely, we must create a meta-system, which must be described via a meta-meta-system, and so on. These statements hold true for even relatively simple systems, like those describing arithmetic. Interpretation of these theorems in other fields is often overblown (much like quantum physics), but it does essentially destroy the positivist perspective of Russell and Whitehead’s Principia Mathematica, which sought to derive all of mathematics from logic.

GEB was my first exposure to dialectical thinking, or at least unresolved dualities: Hofstadter dwells on several of them, particularly holism vs. reductionism. He attempts to resolve them via the Zen notion of mu, which “unasks” the question or at least points out its absurdity. In some questions the answer is both of “both and neither” of the choices, but also neither of those, and so on. The infinite regress of dialectics seemed to be isomorphic to the infinite meta-levels required to completely describe any formal system given Gödel’s incompleteness, while contradictory bare dualities seemed to map onto inconsistency. These notions led me to actively engage with the fundamental dichotomies I encountered in every subject I studied after this point, particularly in my undergraduate philosophy electives. But, in a sense, it was too late for my earlier interests: I believed that any formalist notion of truth was bound to end in an infinite tree of undecidability or a flat-out contradiction. I still tried to take a second major in math during my first year, but found the time demands of a music degree precluded much external commitment, and I realized it was basically impossible, at least at UVic, after two semesters. I was still helping some of my friends in sciences with their homework in second semester classes I would never take when I realized that I had to radically rein in my ambitions, however I did continue to take electives in philosophical logic until my fourth year, which were some of the most creatively stimulating classes I have taken, even if no longer directly relevant to my work.

What does all of this have to do with music? Though I am now unquestionably primarily a composer, I still have serious parallel interests in philosophy, math, science and literature, and these concepts provide some vital underpinning to the way I think about music. My interests have always straddled the art/science divide and I believe that I chose to pursue an academic career in music because, in my opinion, it is located at the nexus of the arts and sciences, and can be produced and interpreted using a plethora of different fields and techniques. Being a composer is my way of intellectually having my cake and eating it too. My next post will address the joint emotional aspects to the intellectual issues raised here, as well as their impact on the music I wrote until fairly recently.

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