At its expansive pole, the digital always refers to some outside, for it never determines its own meaning through automated algorithm, but awaits its encounter with difference. The outside steps in to keep the digital from collapsing into an empty formalism. Even the materiality of the digital is on its outside, a parastratum, as Deleuze and Guattari would have it, an associated milieu in which the ideal digital becomes actual material. The digital is material abstraction, an ideal made actual without foregoing its ideality. Rendering its materiality on its outside, constituted of abstraction, the digital exposes all of its inside at once, a random access at every scale. The digital employs numerous (if standardized) materials, but largely subordinates them to its equivocal abstraction, sidestepping material resistance to offer the untroubled flow of logic and its willing submission to any structure, any logical instruction. Topologically, the digital is made of sequences of bits, but instead of hiding in sequence, every bit is within reach, exposed to the outside, to constitute an organization one might call hyperlinear.
Both polarities, equivocation and increment, advance by processes of abstraction, which names the most general power of the digital, its technique. In the service of abstraction, the bit is the central technology of the digital. There are three vectors of abstraction that support each other to organize the digital, and each draws on a different aspect of the bit. A reductive abstraction makes of all difference a discrete, numerical difference, a sequence of 0s and 1s. To abstract is to set aside difference, to substitute an idea for something concrete. Stripped of generative difference, submitted to an ideal logic, the binary code returns to an equivocal condition, the Ecumenon, a plane flattened and without texture. With no productive difference of its own, the bit can lend itself to any information, all facets of the world capturable in posits, whatever can be true or false. Reductive abstraction powers the digital’s universality, rendering digital code maximally generic.
A second vector of abstraction, deductive abstraction, is the digital’s most familiar face. Deductive abstraction generates bits from bits by a formal logic. Deduction closes the gap between input and output, enforcing the inevitability of the axiomatic conclusion on the basis of the given premises; all results become predetermined and time is counted in steps rather than duration. Everything in the digital happens according to this deductive logic. Deduction names the flow of logic after reduction has done its work, an operation within a purely formal domain; whereas reduction begins from contentual elements and induction reaches back toward the actual world, deduction purchases its perfect and smooth operation only by confining itself to the plane of equivocation. It cannot accommodate content, for deduction works only outside of contingency and accident, seizes only the abstract part of its objects. This separation from the world of content allows the digital to operate independently and without resistance, but its distance from accident establishes this domain as one of pure possibility. All of the calculations have been laid out on the Ecumenon, every pathway already implicit in its practical availability, as deduction ensures that every conclusion is foregone. Potential, the term for a creative future, finds no purchase on this equivocal plane, as deduction moves inexorably and without hesitation from bit to bit. Deduction offers to the digital the power of automation, the ability to move in discrete steps within its positivist world of bits.
Running counter to the equivocation of 0 and 1, the inductive abstraction pushes toward the other pole, n+1, advancing by sectioning planes in discrete increments; n+1 adds a dimension, takes a step toward an outside, a view from above that takes in many discrete individuals together, organizing them in groups with structures. This abstraction is inductive because it brings different parts together into an abstract coherence, a gathering of cases performed from without, and thus having no internal reason, only an external determination, control from the next level up. Groups are thus induced on the plane of equivocation, outlined by a shadow from above. This view from above is the first meaning of plus-one, an invitation to bring the user to the party, an opening to the outside. Reuniting the pure, formal, equivocal logic of the Ecumenon with an outside that provides an expressed content to go with the digital’s form, inductive abstraction gives the digital its power of simulation.
Three vectors of abstraction, based in the bit, afford the digital a universal code, drained of meaning, operating autonomously, and reaching toward its outside by its power of simulation. These abstractions reach far enough to instantiate within the material world an ideal, the ideal form of a bit. The bit is an abstraction captured in a material substrate, an entity equal to its idea even as it operates in the real world. Engineering the bit to read and write 0 or 1 exactly, the digital drives a wedge between the bit’s material and its behavior, assigning all resistance and fuzziness to the material side so as to maintain the ideal side in its abstract perfection. The bit’s submission to logic offers no ambiguity, no resistance, as though ignoring the inertial drag typical of materiality.4
One might imagine that the Ecumenon, built out of bits, is anything but equivocal. After all, the difference between 0 and 1 could not be more stark; surely this is a difference that makes a difference. But in fact the two values of a bit—conventionally called 0 and 1 but largely unrelated to the numbers that go by those same names—are practically equivalent. As the names of bit values, 0 and 1 have no meanings of their own, for they signify only their formal distinction: 0-and-not-1 or 1-and-not-0. The abstraction of the bit, evacuated of all meaning except a formal distinction, renders the two values equivocal, each nothing but its difference from the other. But this extreme of abstraction also offers the digital its extraordinary reach and power, its function as a universal code language. The bit can assert its binarity universally only because it has been drained of its own difference: 0 and 1 mean nothing in themselves, nothing in particular. They are placeholders for a meaning still to be assigned.
In fact this minimal definition of the bit needs already to be amended in light of the equivocation of bit values. For it is not just that a 0 is not a 1 and a 1 is not a 0; these values take their meanings in part because, wholly equivocal, they could have been their others. Instead of 0-and-not-1, the bit is 0-but-might-have-been-1. Which is to say that the bit asserts its empty formal meaning as a posit and a possibility. And this possibility at the foundation of the equivocal bit lends to the digital its distinctive modality, thrusting the digital into a realm of possibility. Bits eventually come to mean something only in relation to the idea that they might have meant the other thing, a Sausserian principle applied to a simple discrete distinction.
Because the bit—even as material actuality, say a tiny spot that induces a magnetic field around it—has no particular meaning, no prejudice, it remains abstract. It is not only the idea of a bit that is abstract or conceptual, but also the operative, materialized bit as it flows through machines and diffuses throughout the electromagnetic aura in which we live. Its wireless instantiation exemplifies the complementarity between the bit’s design and its power of abstraction. In the history of digital technologies, material has been stripped away, resistance ameliorated, to allow the smoothest, fastest, most consistent, most ubiquitous flow of bits. Progressive dematerialization, though never entire, allows the bit to exist as actual without abandoning its ideality. In the real world, in digital machines, the bit behaves as its own idea, a perfect simulacrum of itself, a pure form substantiated. Materially reduced to a nearly frictionless conveyor belt of logical values, the digital offers a world rarefied through abstraction, a domain stripped to an empty representation of nothing but structure, the austerity of 0s and 1s without character and without will. The digital is materialized abstraction.5
The discreteness of bits exhibits plainly the meaning of the digital as material abstraction. Every bit, not just in principle but in fact, is exactly one or the other value, and every bit is wholly distinct from every other; discretization institutes another dimension of ideality. To develop instrument
s sufficiently refined and durable to keep bits from blurring into each other is an essential contribution to digital substance.6 And to develop mechanisms that simulate the bit’s discrete values by treating a continuous interval as an exact determination, this too is a founding moment of digital technology.7 Thus when space and time, the bit’s materiality, cease to follow their controllable, predictable, normal course and blur these discrete distinctions at the core of digital actualization, this de-idealization typically produces not an interesting moment of creative unpredictability but simply a system-wide unraveling, for the whole system relies on discreteness. A digital computer that cannot distinguish consistently between 0 and 1 or between one bit and another is a computer that will not compute.
The bit pulls back from its material substrate, its logic working the same regardless of what material it occupies. The material arrives as though from outside the bit, which huddles around its formalism. The abstraction that produces bits, subtracting difference from the actual to render equivocal, constitutes the digital’s interiority as a domain of idealization. Indifferent to its material, its only allegiance to logic, the digital makes possible a treatment of its interior as a pure logic. The difference in the digital between form and substance is thus a matter of logic versus electricity, an ideal versus an invisible real. This is not idle philosophizing: the extreme abstraction of the digital founds its extraordinary abilities, its extensive reach, its unimaginable speed and scale, its agnostic availability for any simulation whatsoever. Stripped of any lingering meaning of its own and divorced from the material that would weigh it down or lend it a character, the digital is so effective because it is neuter and without resistance, the very form of instrumentalization.
As the engine of the digital, the bit expresses the digital’s divergent polarities. Its reductive abstraction drains it of all meaning and strips away material resistance, to allow an easy flow of logic across a plane of formal difference, the Ecumenon. At the other pole, the bit underpins the inductive abstraction, retaining in its distinction between 0 and 1 a sliver of asymmetry, a moment of difference that exceeds formal distinction.8 True, each value has no meaning but to refer to the other as its negative definition, in which sense the two values are the same. There is a remainder, however: the two values are the same in their symmetrical equivalence, but their difference is not the same difference. The binary operates not just by marking a discrete, formal distinction within a bit between 0 and 1 but also by maintaining this distinction across a vast plane of sequenced 0s and 1s. A 0 (for example) is equal to itself, but also equal to another 0, such that all 0s are similarly distinct from all 1s. Each bit therefore contains an internal distinction of value, but also an external distinction of place, an index that identifies and distinguishes it from other bits. This formal posit, a part of the bit that asserts its generic uniqueness, evinces not the indifference of the Ecumenon, but an increment, n+1, a step toward the outside. That it bears a relation to values outside of it, a perspective from which to recognize the same 0 in two different instances, this references another dimension, a beyond.9 Both differences in the bit, its internal distinction of value, and its external distinction of place, remain formal or abstract, pending a meaning that will only arrive from without.
Bits flatten and bits increment, which capacities establish the planar topology, stacked planes related through homology. This nested hierarchy of layers by which the digital reaches toward its outside begins in the split or cracked binarity of the bit, which at the heart of its equivocation holds the seed of generative difference. The difference between 0 and 1 remains an internal, indifferent difference. But the consistent identification of 0s and 1s across an equivocal plane, this is a difference that refers to an outside of the bit, a difference among bits, that identifies a bit as occupying one place in a sequence and not another.10 A distinction of value and a distinction of place, these two differences constitute the operational bit.
This is to say that the digital’s means of treating a group as a unit, of regarding something as a whole, is via its power of dimensional incrementing, n+1. The digital takes a group of bits as a whole by viewing them from above, as it were, or by simulating a view from above. The view from above, the collection of bits, is already there on the plane of equivocation, built into the logic that governs the on-and-off blinking of bits as they retain or reassign their values according to logical demands inscribed in the structures of electrical circuitry on the surface of a chip or circuit board. The Ecumenon already outlines in its flows of binary logic the shadows of higher planes that float above it, reaching toward its outside,11 as if Edwin Abbott’s geometrical characters in Flatland could describe themselves as seen from above.
Basing its operation on the moment of generative difference within the bit, n+1 is a model of dimensional augmentation evident throughout the digital milieu. It stamps the digital’s relationship to time, describing the halting progress of the computer as a discrete state machine, in which instructions are processed one tick of the clock at a time; each discrete state already implies the subsequent one, such that the digital consists of a present state and a next state, n+1. On a grander scale, n+1 describes the digital’s relation to futurity, its association, dating to the earliest computers, with images of what is to come, its promise always to offer something more, something even better, a new version, an update, the echo of our age that answers digital at every announcement of the future. From the perspective of a working coder, n+1 further marks the discrete steps by which source code is tokenized, precompiled, compiled, assembled, and linked to become machine code, the layers or stages that seem to be the rule of digital construction. Describing the protocols that normalize and regulate internet communication, Alexander Galloway invokes numerous layerings, structures within structures within structures, seemingly endless zooms out.
Bits find their meanings, reach toward the world in discrete intervals, producing layers that define a space between digital and actual. The bit, as dematerialized ideal, offers no difference, and so lies in a plane of bits without texture, a hyperlinear sequence of random access bits.12 Reaching toward its outside, the digital accumulates its forms on another plane, hovering over the Ecumenon. Still made of bits, this epistratum groups bits together, casting shadows, abstract forms on the plane of equivocation.13 Bytes, words, variables, numbers, symbols—perhaps each of these terms defines its own plane, closely stacked sheets that make a sheaf of formal planes—discrete groupings of bits on one epistratum become grouped elements on still higher ones, data structures, algorithms, code libraries, applications, menus, icons, objects. In discrete steps, the digital moves away from the plane of equivocation toward its outside, each higher plane organizing the structures that lie below it. High-level programming languages are so called because they allow the specification of many bits in nested structures, a perspective farther from the bit plane and closer to the actual world.
The digital’s means of reaching beyond the plane of bits do not violate its ecumenical constraint. For the digital meets its outside not immediately but by a power of induction that produces the digital as simulation. The digital does not, for instance, treat at once a grouping or collection of bits, but always proceeds one bit at a time according to a relentlessly sequential logic. Because bits are equivocal, a group of bits does not find its reason in those bits, but always answers to an external determination that performs a grouping operation; groups are made using a cookie-cutter logic. The digital simulates its reach toward the outside using iterative techniques, which process a group of bits in succession to cover a whole field, and it abbreviates such ramified actions in its code. Digital encoding is itself a dimensional Aufhebung, a way of encapsulating a logic of multiple steps into a single lexical or logical unit. To take a particularly concrete example, the letter k might be described (from the computer’s perspective) as a table of bits, in which each bit in the table is either on or off. This description still takes the table as a whole entity, a
s though it could be surveyed at once by the computer, but to work with this table the digital processes its individual cells (bits) one by one, iterating over a sequence. (Think, for instance, of algorithms, repeating sequentially in nested loops.)
At the threshold dividing inside from outside, the digital relaxes its rule of discrete abstraction to meet what is not (or not altogether) digital: the user and her world of accident and affect. But even before any key is pressed or button clicked, the machine has already assigned content to the forms of digital abstraction. The parastratum that hosts this encounter of form and content, the interface, makes shapes, sounds, and colors, menus, windows, and icons out of the (equivocal) values and structures defining the tiered planes of digital abstraction.14 Being an interface, the interface faces two directions, a surface of encounter with one side turned to the Ecumenon and one turned to the outside. It is a privileged plane of encounter, a notable divide between inside and out. But according to the rule of the increment, the well remarked human-machine interface is not singular but is foremost among many; the digital generates multiple discrete surfaces, each of which establishes inside and outside according to its particular faces, to make steps in a logical traverse, a halting journey between the machine and the user.
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