As Peter already hinted at in his contribution last week, it was at a conference on music and technology at Berkeley in May 2014 that the first stones were laid for what was to become this online reading group. There, I presented a paper on a process called ‘dithering,’ called “A Soft Landing into a Bed of Noise. Dithering: Hiding Noise with Noise in Digital Sound” (see the slides for that presentation here). In two paragraphs of that paper I talked about Leibniz, noise and Siegert’s ‘Riß’ (which I translated with “rupture,” but which could of course also be ‘crack,’ or ‘tear’ or something similar). Peter suggested I’d put these two paragraphs on the blog at some point and because of their connections to the issues at hand in the current and previous chapter, here they are…:
6. Leibniz’s Evil Infinity
Leibniz believes the world must be perfectly rational and completely continuous. To illustrate this, he writes in the ‘Preface To The New Essays,’ he “usually make[s] use of the example of the roar or noise of the sea that strikes us when we are at the shore” (Leibniz, 1989: 295-296). This noise is made up of an endless amount of individual noises: one for each wave. Humans can only hear these infinitely many individual ‘small’ sounds “in the confused assemblage of all the others.” But in fact, they are, Leibniz argues, an infinite sum of ‘minute perceptions,’ perceivable as such only by God. Consequently, the roar of the sea is not truly noisy at all; it’s just so in human perception.
Notably, Deleuze describes Leibniz’ monadic logic as a fold that “is always folded within a fold” (Deleuze, 2006: 6). Although this idea of an infinite integration of small perceptions helped tackle the problem of the mathematical analysis of the entangled and confused, it ultimately, argues Serres, does not support Leibniz’s model of a completely integrable world. On the contrary: with this idea of infinite folding, Leibniz opened the floodgates for the introduction of the profound irrationality of contingencies and infinities into mathematics and physics (Serres, 1995: 20).
This lead to what Daniel Heller-Roazen in The Fifth Hammer: Pythagoras and the Disharmony of the World describes as “the disappearance, from philosophically and scientifically valid concepts, of the conception of the world as a finite, closed, and hierarchically ordered whole” (Heller-Roazen, 2011: 125). In Passage des Digitalen, media scholar Bernhard Siegert therefore argues that in such a world, in which continuity is not given but always only inclined by a reduction of complexity, noise is not merely a result of man’s limited perceptual capabilities, but rather a central trope.
7. A Rupture
Because, Siegert writes, “the order of which Leibniz dreams, is [in fact] a noise order,” Leibniz’s rational, continuous world broke in many pieces (Siegert, 2003: 187 ). He calls this fracture a ‘rupture’ in the representational order of classical analysis (Siegert, 2003: 416). It constitutes a growing crisis of representation, as everything that Leibniz’s Law of Continuity conceptually tried to hold together, such as “the connection between mathematics and physics, writing and nature, office and world,” slowly fell apart (Siegert, 2003: 253).
From Leibniz’s infinitesimal calculus in the late seventeenth century, Siegert’s extensive book traces this rupture along Leonhard Euler’s discontinuous functions in the eighteenth century, and toward Joseph Fourier’s influential ‘Fourier-series’ in the nineteenth century. After Fourier, the complexity of sound and noise became mathematically calculable. But, as irrational numbers proved fundamental to this analysis, it also turned out to be fundamentally non-representable (Siegert, 2003: 235).
However, instead of representation, it did open the road for something else. Although Leibniz’s “evil infinity” and the mathematical analysis that sprung from it did not make signals representable, it did make them manipulable and, crucially, by means of technical media like sound recording, reproducible. Hence, as they are borne from the analysis of the entangled, the inextricable, the confused and the infinite, noise is a crucial part in the history of technical media.
Deleuze, Gilles. The Fold. Leibniz and the Baroque. Trans. Tom Conley New York: Continuum, 2006.
Heller-Roazen, Daniel. The Fifth Hammer: Pythagoras and the Disharmony of the World. New York: Zone Books, 2011.
Leibniz, Gottfried Wilhelm. Philosophical Essays. Trans. Roger Ariew and Daniel Garber. Ed. Roger Ariew and Daniel Garber. Indianapolis: Hackett Publishing Company, 1989.
Serres, Michel. Genesis. Trans. Geneviève James and James Nielson. Ann Arvor: University of Michigan Press, 1995.