We could say that the digital is made of interfacial planes, surfaces each facing two directions without symmetry.15 Take the epistratum that hovers closest to the plane of bits. On its out-facing side it gathers sequenced bits from the Ecumenon below it into groups of eight, organizing bits into bytes that allow a ready treatment of eight sequenced bits as a provisional unit. These simple structures are established independently of the values of their particular bits; as a structure, the byte is indifferent to its value. Facing in, this plane reflects the value of each discrete bit, filling in the eight-bit byte, inscribed in outline on its flip side, with one of 256 possible values, every combination of 0s and 1s that can be made with eight bits in sequence. The digital is stretched across many such planes, related in a succession of homologies from plane to plane, from a stream of 0s and 1s, to a stream of bytes, to a datum or command, to a data structure or sub-subroutine, to a collection of data structures or an algorithm, to an object: at each junction an interface, each step instituting a further abstraction, which subsumes and partially hides the smaller units within it.16
The isomorphism that obtains from plane to plane is a power of organization, to induce, via rules of simple logic, groupings and orderings of the discrete objects from the plane below. Though objects are constructed using the discrete parts from lower planes of organization, the structure itself comes from without, the next higher plane, but at the same time it is already there on the Ecumenon. The logical determinations that establish a layer of digital organization are themselves encoded in the bits of the plane of equivocation. As a universal code, the digital does not distinguish between data and instruction; it is all 0s and 1s, all on the same plane. Form of form (structure) and form of content (value) become just form at this extreme of abstraction. The inductive abstraction that gathers discrete parts into larger objects relies on the deductive abstraction, the rule of the Ecumenon, that plays out the deterministic processes of logic, making time itself into a formality, a calculable number of microseconds between initial state and terminal state, or between input and output.
Divisible in the digital into chunks of arbitrarily small size, space and time can be readily manipulated, empowering the digital’s signal ability to simulate. As representations made of pure abstraction, space and time do not exert in the digital the sorts of inexorable constraints and directed possibilities that they do in the actual. Solar systems and molecules appear side-by-side on the screen, thousands of simulated years can be compressed into a second, or a complex process can be slowed down, stopped, reversed, or resequenced for observation and analysis. Simulated objects, untethered from a materiality that would give them particular characteristics, need not behave like the objects they appear to be: a mountain can be weightless, a ruler can oversee millennia of continuous history, a refrigerator can transform smoothly into a set of keys.
Guided by such examples as these, one observes in the two faces of each plane a strange divide, characteristic of the digital, that separates form from content, or structure from value. As with the bit, structure—its boundaries and its place in sequence—is determined from outside of it, whereas its value—0 or 1—is given on its inside. Place is assigned without regard for value. This divide persists in the bit’s material, which designates individual bits separately and by a different reason from their values. The two-faced character of each plane, modeled on the bit’s original two distinctions (of value and place), establishes a gap at the heart of digital operation, dividing form from content, structure from value. In the actual world, form and content are not just coincident but are tied together, they have the same reason, or at least deeply entangled reasons. Thought sound, to return to our chief example, is entangled in its world through strands of idea and material, a reason that brings together threads from disparate ontological registers to tell the sonic story. A sound sounds like its origin, and it speaks to what is to come, bringing time, space, matter, and motion into sympathetic resonance. (Or is it the resonance that brings about the sound?) Separating, in the digital, form of form from form of content severs sound from its reason and the spatial displacement at its start. On a digital epistratum, groups form with no reason in their parts, for they are induced as a shadow of a higher plane. And values are determined without any inherent relation to the structure they come to define.
Though the term is normally reserved in computer jargon for certain structures on relatively lofty planes of organization, we might call any grouping on a discrete digital surface a digital object. Objects are made of parts, each of which is given as a quality. Parts and qualities are not really distinct, but refer to two sides of the same plane. Parts are given by the structures outlined on a plane, while qualities are given by the values of the bits grouped into those structures. A part is an outline, a formal structure, while a quality is a formal value. (Form and content are both formalized in the digital, hence form of form and form of content.) They are determined separately but given together; parts are determined from the outside, structures imposed by a logic that casts shadows on the plane of equivocation. Qualities fill out those structures, determined from within by the bit values of the enshadowed bits. Parts organize qualities and qualities qualify parts but they do not share a genesis. Digital objects therefore have no reason in themselves but from without, as they are equivalent to the collection of their part-qualities. Digital objects could be described as groupings of qualified parts.17
Thus the digital offers two lines of determination, one of value and one of place, one of quality and one of parts. But they both remain formalisms, abstractions, such that they await their content and meaning in a contact with the outside. That is, a sequence of bits that represents a numeric value does not represent the intensity of color in a given color channel except according to a convention built in to the hardware interface of the machine, a convention that refers to perception. It is only in contact with a world of reasons that the digital finds its own reasons. Else it remains inert, indifferent, a formality of structure or a formality of number. So that the values that determine the length of a curved line on the screen or the brightness of a simulated lantern or how many items are in a given menu, these values, equivocal in themselves, become significant when given a reason, not just the actualization of possibilities but the idea of a future.
Surfaces of encounter reach from the plane of equivocation to the “graphical user interface,” but these many interfaces do not stop at the boundaries of the computer hardware. The digital extends beyond its hardware’s edges, meeting the world only by touching what is already digital in it. Thus, even outside of the machine, perception of the digital also shows two faces, one turned toward discrete elements related by deterministic logic and one turned toward the abyss of thought. “In short, both exterior and interior are interior to the stratum” (Deleuze and Guattari 1987: 49). The eye does not cease to see pixels, even when, as Apple claims of its retina displays, the individual pixels lie below the threshold of human visual perception. For one sees not only a version of the image represented by the data that produced that image, one sees also the possibilities of other images—filters, erasures, partitions, replacements, rearrangements—possibilities inherent to the digital milieu because inherent to the bit.
Thought sound, carrying its origins with it, does not share digital sound’s nostalgia for what could have or might have been. Indifferent to those many roads not taken, equally comfortable with any path, digital sound could always suddenly become something else, any available data, and the combinatoric character of the digital suggests the proximity of every possible next sound. Any sound might come next, any value might be the next value; bits, or their values, have no reason but the austere self-satisfaction of numbers, perfect unto themselves and so without reason. As possibility, all of the digital’s achievements are already inscribed in its equivocation. To encounter the digital is to choose among discrete possibilities, possibilities that inhere in the encounter with digital sound.
At some point—in some subsystem or at the end of some bus or in some computer peripheral—the data and code cede a measure of their ideality, mapping their abstract numeric values to a concrete, analog, continuous property, usually, as a first step, a flow of electricity. The continuous electrical flow results from a digital-to-analog conversion (decoding) that takes a sequence of discrete data as input and produces a continuous signal flow (electricity) as output. (Even on the digital side of this conversion, the discrete data to be decoded are materially instantiated in bits as continuous electrical flows; but those continuous flows are engineered to simulate a perfect binary logic, to behave like discrete bits with discrete values.) For example, through a D-to-A conversion, a number encoded in bits might regulate an electric potential that determines how brightly the blue component of a given pixel should shine for the next sixtieth of a second (until the next datum comes down the pipeline).
In the terms of Deleuze and Guattari, the digital-to-analog conversion is both a decoding and a reterritorialization. It decodes a stream of bits, according to established conventions built into the hardware of the machine, to generate a phenomenon whose codes are not those of a discrete machine but of human culture and embodied perception. As it decodes it also reterritorializes, moving from an ideal stream of numbers essentially unrelated to their material substrate to an actual, perceptible phenomenon, concretized in time, space, and a material context essential its meaning.
How does this visible datum make any more difference than it did when it was a sequence of 0s and 1s? But that is precisely the distinction selected by adding thought to sound. To make a difference, that blue-ishness or that pixel require a further destination, a destiny beyond the digital; is it enough that someone sees it? The human is a bulwark against the collapse of difference back into the binary. Grouping is real, parts and qualities are real, but all continue to refer to an outside, a beyond in which the digital’s equivocal abstraction does not hold sway. It would be mistaken to conflate this connection from the digital to its outside with the well trodden notion of interactivity. Interaction typically comes late, as the last gesture of contact between digital and actual. Interaction could never happen, would be purely accidental, were it not for the countless conventions that contribute to the history of digital technologies; the outside determines the meaning of the digital in terms of an accretion of habits, indexed to vision, hearing, and the action of touching as the privileged senses of rationality. These conventions that have grown alongside digital technologies as their final and formal causes give sense to the equivocal structures that cover the digital’s planes of organization. Conventions associate designated bits in indexed computer memory with particular pixels on the monitor, for example, giving those bits meaning as image, color, shape, etc. Other conventions determine formulas and mechanisms to turn bits into sound. Coding is entirely an adherence to conventions, syntactic regulation and rules of order that map codes onto logical processes and simple operations on bits; these rules restrict the meaning of those codes, enforcing a logical transparency in place of the polysemy of language.
Like all digital conventions, code looks in two directions, facing outward toward a world of sense, and inward toward an ideal domain of perfect logic. Designed to allow easy reference to the part-qualities of complex data structures and methods for manipulating them, code assails digital objects as worldly, investing meaning in the conventional determinations that draw outlines on the outward-facing surfaces of the digital’s many layers. Restricting expression with formal definitions and a rigid syntax that govern every term, code insists on a digital mode of address, where every statement refers to well defined, logical operations on discrete groups of bits, and every command is directed at some specifiable end.
This contact with the outside, an accumulation of convention built in to the logic of the machine, repercusses all the way back to the plane of bits, satisfying the structures and numbers, the 0s and 1s of the Ecumenon, and giving them a reason. An individual bit becomes meaningful as 0 or 1 as determined by this encounter with difference, the staged connection of formal quality to actual quality.18 But the bit remains formal in itself, even as it admits this donation of meaning from without. Bits retain their equivocal stance, even as they carry that stance into the actual. One symptom of this equivocation is the glib, cynical, or ironic character of much digital culture: the digital is impoverished, a “mere” simulation, and the lack of precarity in the digital may present an intractable limit.19 In another sense but according to the same logic, the digital is thoroughly precarious, as its might-have-been destabilizes its values into a combinatoric haze of possibilities. That is, one encounters in the digital not only the simulation of objects but also a determinate set of determinate possibilities of what those objects could be or could become. But the possibilities for an object are aimed at that object taken as a group of part-qualities, any of which can be individually altered independently of the others. Digital possibility respects the separation of the two sides of each plane, the split into parts and qualities, the division between form and substance, between ideal and actual, the ubiquitous increment that induces always another layer, a new reterritorialization on a new inside and outside. Digital objects are equivalent to the collection of their parts, and those parts are ever at our service. What is a computer program but a possibility access interface?20
Digital code is possibilistic in still another sense. For the most part, code does not execute but stands by in fast-access memory banks. Most subroutines await their turn at the Central Processing Unit, when they will be invoked by some already running process. Process algebras—mathematical models of the way computer code works—capture very well this uncommitted modality of “standing by,” pure possibility without actualization; in general, this is a hallmark of mathematics, to offer assertions of indefinite mode, symbolic abstractions that make no claim on the actual, but rest on grounds internal to mathematical discourse.21 These statements hover in an indeterminate modality. They are at the ready, but as statements of pure logic, they are, for the moment, outside of time.
One of the simplest digital operations, often associated with a single command in a computer processor’s machine language, is copying of data from one memory location to another. Indeed, the possibilistic character of the digital implies the triviality of digital reproduction. Copying a bit value from one indexed location to another is a basic function of bitwise operation, and iterative repetition of this operation over a set of data large or small is almost as trivial. There is a minimal material cost of making a copy, and the simplicity of this bit-for-bit reproduction means that there is almost no time cost, either. Thus does the digital reproduce itself perfectly and without effort. Not time nor space but logic becomes the dominant organizing force of the digital, which, unburdened by the massive and enduring forms of space and time, exposes its entire inside at once, a condition prosaically referred to as “random access.” The digital is made of logic and made by logic. Compared even to language, whose linear sequentialism is tied to time (as speech) and space (as writing), the digital gains an even higher degree of abstraction. One might imagine every point on the Ecumenon connected to every other, by virtue of the numerical indexing scheme that allows bits to act on other bits.
This abstract dimensionality of the digital stays faithful to the plodding sequentialism of the processor; notwithstanding current popular advances in parallel processing, digital processors still treat digital codes in strict sequence, admitting and acting on commands one at a time. Linear but randomly accessible, the digital exhibits a hyperlinearity. In Deleuze and Guattari’s study of strata, the mode of reproduction in each case reveals a stratum’s dimensionality. The crystal, on the geological stratum, reproduces by expanding outward along its borders, absorbing layers of material (epistrata) into its crystalline form. It moves outward in three dimensions at once, but only at its surfaces, which form a complex stack of layers between inner material already cryst
allized and outer material still to be incorporated (or not). A significantly different organization characterizes the organic stratum, where reproduction refers to coded strands of formed substance, which decode to produce proteins. The double helix unwinds in reproduction, exposing the code’s spatial linearity, so that its elements may be read in sequence. “The essential thing is the linearity of the nucleic sequence” (Deleuze and Guattari 1987, 59). The third stratum, the cerebro-neural stratum, exhibits a superlinearity, a temporal linearity untied from spatial constraint—the prime example is language—that gives language enough abstraction to reach all of the other strata. The digital steps over a further threshold, abstracting even time and space to achieve a logical linearity, hyperlinearity.
Digital sound, thought
Another description of hyperlinearity: the digital stratum organizes organization per se. It refers only to itself, and it does so unimpeded by the contingencies of materiality. Given its logical ideality, the digital includes no motion, only the representation of motion. It consigns the continuous traverse from one discrete state to another to its materiality, and then disregards or minimizes that materiality by design. (A material bit changing its value from 0 to 1 undergoes a change of magnetic field strength, which passes through a continuum of intervening values as a matter of physical necessity. But the logic that determines the structural significance of a bit switches its value from 0 to 1 without anything in between.)
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