On musical metaphors in string theory
This is the first draft of part of the last chapter of my current manuscript-in-process, The Sonic Episteme: acoustic resonance & post-identity biopolitics.
String theory is a subdiscipline within physics that blends general relativity (which focuses on macrocosmic spacetime) with quantum mechanics (which focuses on the workings of subatomic particles); related to the physics Karen Barad uses to ground new materialist philosophy, string theory holds that the fundamental unit of existence is a one-dimensional vibrating string. Popular science accounts of string theory often use musical metaphors to translate the mathematical relationships they derive from their equations into terms the general public can appreciate. As Pesic and Volmar put it, “for the public understanding of science, musical metaphors seemed to offer opportunities to provide the imagination of the lay public with affective experiences of abstract mathematical theories (emphasis mine).” In other words, these pop science accounts of string theory use a literary device–metaphor–to represent propositional abstractions as non-propositional, affective abstractions that we learn by listening to Western music
In this section I look at two representatives of this trend: the most well-known and foundational one, by Brian Greene, and a recent one by Stephon Alexander. Both accounts use acoustically resonant harmony as a metaphor for the probabilistic relationships string theorists derive from their mathematical analysis. This makes them constituents of the sonic episteme: they’re using acoustically resonant harmony and probabilistic statistics as interchangeable abstractions or methods of abstraction. Though both authors are explicit about their metaphorical and analogical methods, the thing that does most of the conceptual work is not a metaphor or an analogy, but a slippage between two kinds of mathematical abstraction: geometric ratios and probabilistic ratios. Even though “the unheard cosmic music is not conceptualized in terms of ratios between celestial objects…but as the result of the various vibrational modes (or resonant patterns) of the tiny but highly energetic strings” (Pesic & Volmar), Greene and Alexander (and others, as Pesic and Volmar detail in their article) insist on appealing to Pythagorean concepts of harmony (which are geometric ratios) to describe acoustically resonant vibrational patterns.
This slippage lets Greene and Alexander present what is actually a disanalogy as an analogy. Their main conceptual tool isn’t a metaphor or an analogy, but a sleight in Mader’s sense. As she explains, “sleights” are “conceptual collaborations that function as switches or ruses important to the continuing centrality and pertinence of the social category of” a political system like “sex” (SoR 3). Sleights, in other words, are conceptual slippages that render underlying hegemonic structures like cisheteropatriarchy coherent; they’re “cognitive dysfunctions that are socially functional” (Mills RC 18).
Sound is central to Mader’s explanation of a sleight. To flesh out its mechanics, Mader turns to a concrete example: sleights are, she argues, “conceptual jacquemarts” (SoR 5). Jacquemarts are effectively the Milli Vanilli of clocks: sounds appear to come from one overtly visible, aesthetically appealing source action (figures ringing a bell) but they actually come from a hidden, less aesthetically appealing source action (hammers hitting gongs). The clock is constructed in a way to “misdirect or misindicate” (SoR 8) both who is making the sound and how they are making it. A sound exists, but its source is misattributed. This is exactly what happens in Greene’s and Alexander’s use of Pythagorean concepts of musical harmony to explain what is actually acoustic resonance: their outward accounting of sound misindicates its precise internal mechanism.
Unlike Pessic and Volmar, who attribute string theorists’ slippage between geometric ratios and probabilistic ratios to a desire for the “scientific sublime,” I attribute the slippage to political, not aesthetic, motivations. I don’t think these motivations are conscious concerns for these authors–they’re not trying to pull a fast one on us–but embedded in background epistemic frameworks. As Mader explains, neoliberal biopolitics reframes classical liberalism’s “binary system of offense against the law” (SoR 48) with a “gradational social space” (SoR 48). String theory is a gradational theory of actual, cosmic space. Relying on the same basic epistemic framework as neoliberal biopolitics (i.e., probability ratios), string theory does for cosmology what social physics does for social science: it reconceives the universe and the relationships between its elementary particles in the same terms neoliberal biopolitics uses to analyze and manage society. Statistical normalization, the normal curve, and frequency ratios are neoliberal biopolitics’ distinctive socially functional cognitive dysfunction; there are thus strong social incentives to take this epistemic framework for granted, and that’s what these pop science accounts of string theory do. Though theoretical physicists may not think of themselves or their theories as having any politics, this epistemic framework is socially functional for a very specific kind of society: one whose social ontology, ethics, and aesthetics are modeled and managed as matters of statistical normalization. The epistemic framework facilitates a politics that the original string theory may have no necessary or direct connection to.
- The appeal to harmony.
Science writers use musical harmony as a metaphor to translate the mathematics that grounds string theory into terms non-specialists can understand. ‘Harmony’ is used to explain mathematical relationships in sensory terms, not numerical terms, to transform the ontology of numbers to the ontology of ‘normal’ human perception. Both Alexander and Green explicitly state that they’re using music to translate mathematical abstractions into terms a lay audience, especially those with no training in mathematics or physics” (TEU 7), can understand. For example, Alexander argues that “mathematics is like a new sense, beyond our physical senses” that can be used “…to extend our perceptions” (JoP 34), music is the sense that’s best suited to translate things that “are naturally communicated with the language of mathematics” (JoP 2) into terms naturally communicated by one of the five senses. Arguing that “it is hard to embrace quantum mechanics viscerally” (TEU 82) and that “sound” is a “tangible manifestation” (JoP 89) of the behavior of quantum strings, Greene and Alexander also rely on ideas of naturalness and immediacy: music mediates mathematical abstractions so they are (apparently) perceptually immediate for regular people. (This, of course, obscures the fact that listening also relies on abstractions to help us separate out signal from noise.) In fact, like the new materialists in chapter 3, Alexander implies that “putting into words subjects like general relativity and quantum mechanics” (JoP 2) is less precise a translation of the math than analogies (JoP 3) to music, that words mediate and distance us from the ‘naturalness’ of mathematical representations of elementary particles and forces. This is because words perform representational abstractions, whereas music and the math behind string theory perform abstractions that result in “similar patterns” (JoP 40).
If music is the best analogy to translate math into qualitative terms, what do Alexander and Green mean by “music”? As you can probably infer from the fact of their inclusion in this book, they understand “music”–also referred to as “harmony and resonance” (JoP 6) or “symphonies”–as acoustic resonance. As I’m defining it in this book, acoustic resonance is “rhythmic” patterns of intensity (e.g., condensation and rarefaction) and/or chance occurrences, patterns which can be represented as frequency ratios and which interact in (ir)rational phase relationships. When explaining what they mean by “harmony,” both Anderson and Green define it as some sort of acoustic resonance. Green argues that string theory “unit[es] all of creation into vibrational patterns” (TEU 254) that “rhythmically bea[t] out the laws of the cosmos” (TEU 21), and Alexander’s claim that “the structure of the universe is a result of a pattern of vibration” (JoP 115) is more or less identical to Greene’s. The precise nature of this vibratory pattern is both crucial for the analogy to work and an opening for a sleight (which I’ll explain more fully below) in both Greene’s and Alexander’s argument: three-dimensional strings, like the strings on an instrument, vibrate in a back-and-forth motion, but acoustically resonant sound waves vibrate in patterns of increasing and decreasing intensity (i.e., condensation and rarefaction). These are two different kinds of motion. Explaining that “sound is a vibration that pushes a medium, such as air or something solid, to create traveling waves of pressure” (JoP 89), Alexander clarifies that the analogy between quantum physicists’ math and music holds only if we understand sound’s vibratory patterns as “a series of compressions and rarefactions that propagate the wave through the medium” (JoP 147), not back-and-forth motion. Thus, even though the “string” in string theory might lead us to think about a string’s back-and-forth vibration, the math in string theory describes “the cosmic dance of the expansion and contraction of a cyclic universe” (JoP 209).
These rhythmic patterns of expansion and contraction relate via phase relationships. For example, Alexander argues that order appears in the universe once cosmic inflation “synchronizes these phases” (JoP 192), creating signal where there was once only noise. Greene’s claim that “the universe–being composed of an enormous number of these vibrating strings–is akin to a cosmic symphony” (TEU 102) similarly relies on notions of musical consonance. These descriptions of a “symphonic orchestra” of “harmonious vibrations” (JoP 120) that “resonat[e] with, or vibrat[e] in synch with” (JoP 71) one another use notions of musical harmony as rational phase relationships to translate the mathematical function known as the Fourier Transform into non-mathematical terms. The Fourier Transform is an operation for combining different frequencies or waveforms to create a new waveform. Because audio engineers apply the Fourier Transform to actual, not metaphorical, soundwaves, it makes sense for Alexander to use sonic harmony as a metaphor for this mathematical function (JoP 111-113). Understanding “music” as rhythmically patterned intensities that interact in phase relationships, Greene and Alexander’s accounts of string theory model sound on acoustic resonance and are thus constituents of the sonic episteme.
Now that I’ve established that string theorists’ appeals to music and harmony are actually appeals to acoustic resonance, I can focus more specifically on what those things are metaphors for: quantum strings. This will get us closer to seeing the sleight Greene and Alexander pull. String theory argues that the elementary unit of existence is a one-dimensional looped string. This string can vibrate at a number of different frequencies, and the frequency determines the physical properties of the string (which particle or force it is). As Greene explains, “according to string theory, the properties of an elementary ‘particle’–its mass and various force charges–are determined by the precise resonant pattern of vibration that its internal string executes…What appear to be different elementary particles are actually different ‘notes’ on a fundamental string.” (TEU 101-2). As I mentioned earlier, three-dimensional strings vibrate in a back-and-forth motion. This is not the same motion as “resonant” one-dimensional strings. However, the whole metaphor rests on using three-dimensional strings as representations of and analogies for one-dimensional strings. Greene repeatedly appeals to “more familiar strings, such as those on a violin” (TEU 101) or “the strings on a violin or on a piano” (TEU 20). One-dimensional strings, however, behave less like a three-dimensional string and more like a sound wave: “the strings in string theory…are resonant vibrational patterns that the string can support by virtue of their evenly spaced peaks and troughs exactly fitting along its spatial extent” (TEU 101). These peaks and troughs represent areas of high and low intensity (condensation and rarefaction)–acoustic resonance, resonance understood and represented mathematically as a frequency ratio, not a geometric proportion.
Green, Alexander, and others who use music to explain string theory perform a sleight, a sleight that is related to the one Mader attributes to biopolitics, but different in the details of its execution. This sleight is particularly clear in Alexander’s book, which argues both that “in quantum mechanics, the Pythagorean theory of the harmony of the spheres was finally realized but on a microscopic, not macroscopic, level” (JoP 166) and that “if the universe is musical then it is fundamentally wave-like and can be represented as a temporal evolution of sound waveforms” (JoP 208). Recall that Pythagoras and Plato used geometric ratios to measure vibrating strings, not soundwaves. String theory, on the other hand, treats one-dimensional ‘strings’ like soundwaves, not a three-dimensional string divided in a hierarchical series of ratios. Pythagoras and string theorists are observing different phenomena, and describe those phenomena with different mathematical relationships: hierarchically ordered geometric ratios, on the one hand, and statistical probabilities, on the other. Where biopolitics slides from mathematical relations to social relations, these pop science accounts of string theory slide from one type of mathematical relation–Pythagorean proportionality–to a different type of mathematical relation–probabilistic statistics. As I have explained earlier in this book, ancient Greek notions of musical harmony were grounded in then-contemporary math. Pythagoras developed a hierarchically-ordered series of geometric ratios by observing the behavior of a three-dimensional string. The ratios didn’t describe the soundwaves the string produced, but the proportions into which the string was divided when fretted to make that specific interval above the string’s fundamental frequency. Just as string theory’s one-dimensional strings behave more like the sound waves made by a vibrating 3D string than the 3D string itself, the math behind string theory isn’t calculating geometric proportions but statistical probabilities, what Greene calls “probability waves” (TEU 79). As he explains, string theory asserts that “matter itself must be described fundamentally in a probabilistic manner” (TEU 78). String theorists don’t use math to find the determinate state of a quantum string, but the likelihood of it behaving in a particular fashion. For example, “an electron wave must be interpreted from the standpoint of probability”–the wave’s relative magnitude represents where it is “more likely to be found” and “less likely to be found” (TEU 78; emphasis mine). Alexander uses the idea of jazz improvisation to represent the probabilistic character of string theory. “Improvisation” he argues “provid[es] us with a tool for understanding” the “inherent uncertainties” of quantum matter (JoP 7). While the analogy itself is rather weak, Alexander’s exortion to “replace…improvisation with probability” (JoP 176) shows that string theory makes a particular kind of mathematical abstraction: a probabilistic one not a geometric proportion. Like Attali’s argument that both mid-20th century avant-garde art music and neoliberal models of the market are distinctive because they systematize chance, Greene says that string theory imagines “a universe whose precise form involves an element of chance” (TEU 79). These probabilities are, to call on Du Bois’s definition from chapter 2, rhythmically patterned chance–i.e., acoustic resonance.
But as I have been arguing throughout this book, acoustic resonance is a fundamentally different kind of abstraction than Pythagorean-Platonic geometric ratios. Though they are both conceptually understood as kinds of “harmony,” they represent two different kinds of relationships: acoustic resonance frames harmonious relationship in terms of normalized distributions, whereas Pythagoras and Plato frame harmonious relationship in terms of a hierarchically ordered series of geometric ratios. Alexander and Greene think their appeals to Pythagoras (e.g., JoP 166) work because, like him, string theory thinks “the harmony of the cosmos was, simply, a manifestation of the relationships between numbers” (JoP 71). I’m arguing that Pythagoras and contemporary string theory describe two different relationships between numbers, and that conflating the two is a sleight of reason in Mader’s sense. Though string theorists understand themselves as providing objective, factual, apolitical accounts of pre-political reality, this sleight functions to obscure the fact that string theory reconceives the fundamental nature of reality in the same terms that neoliberal biopolitics uses to conceive and control more obviously social phenomena like markets, subjectivity, and identity politics. Throughout this book, I have shown why neoliberal biopolitics’ acoustically resonant social ontology is politically worrisome and dangerous. Taking acoustic resonance as the foundation of cosomology, the ontology of the universe itself, has the potential to naturalize the kinds of abstractions that neoliberal biopolitics use to organize society (what Mader calls “the ontological dimension of the social technology of the norm and of social statistical measure” (SoR 43)) in harmful and unjust ways. Who can object to statistical normalization as a political tool when it’s just the way the physics of the universe works?
Framing social relations as natural givens is an old trick that Westerners have used since at least modernity. Social contract theorists, for example, separated out civil inequalities, which were bad, from natural inequalities (specifically, race and gender), which were inevitable. The danger I see in string theorists’ use of acoustic resonance as a metaphor for the fundamental structure of matter is that it makes a new variation on this same old move: it takes a socially contingent, historically specific and biased and motivated tool, a kind of mathematical relation that produces and maintains systematic relations of subordination and domination, and treats it as a neutral feature of reality itself. The acoustic metaphor can become its own sleight of reason, a sleight that naturalizes the kind of abstraction (i.e., the mathematical relation) that, when applied to people and social relations, produces post-identity biopolitics. As a constituent of the sonic episteme, string theory hides the conceptual tools that produce post-identity biopolitics behind apparently neutral mathematical abstractions that are easily translated into non-mathematical terms by musical metaphors.