Index-Null

Lillian Patch - 𝌽𝌱

There are two forms of singularity, one of which is based on a misunderstanding. These can be diagrammed through the affordances of numeracy. The common misunderstanding takes the form of a tally system used in denoting numbers in base one. This notational—not mathematical—error assumes that, in base one, the only numeral is 1. A number is represented as a series of added ones, summation being implied by juxtaposition, but impossible to actualize. This style of denoting is the basis and the betrayal of all positional numeracy to come. Conversions from unary into higher bases always take the form of a digital sum; if the numerals of a unary number undergo a digital sum in a given base, the number they represent is converted into that base. Yet the definitional feature of this unary system, on which the other bases are taken to be founded, is the complete impossibility of digital reduction. The tally marks of unary cannot be reduced at all—not to 1, not to 0—because addition in a tally system is constantly deferred through additional place values. This denotational inconsistency of unary is the defining feature of this singularity and the central presence of its system, the exception that is the rule.

The second singularity is consistent, at the cost of its complete inutility. Denotational consistency demands demands that 0, not 1, be unary’s exclusive numeral. But from the beginning, by the definition of 0, it cannot hold a count. A single 0 must, in this system, equate to 1, but its definition as a numeral equates it to the absence of 1. No addition of zeroes resolves the problem. Rather than the basic, exceptional numeral of all numeracy, base one becomes a painful mockery, forcing a pursuit of a quantum which can never be reached. Singularity is fully complicity with void, reducing all which aims to escape her to mere breath. It may even be plausibly claimed that one, in this system, has the most compelling claim to the heritage of the void. One, in equality with zero, inherits her; what is absent in zero is here radically absent in one. Singularity marks the absence of any realized unification.

Under this whip and this discipline which denies all gratification, by a radical cruelty which ego can only despise, we reach a numogram. The unary numogram is bare, awfully bare. It has no lemur, no syzygy, no current. Its only possible rite is 0, and without a second zone, there is nothing to follow it. What a meagre prize to earn for such austerity! But the zero, under the radix of one, has at least not betrayed its spirit as a numeral, as it does in the aforementioned distortion. From this consistency, at least, we can eke out a beginning—a start within in this syzygetic mirror, reflecting nothing.

In every numogram, the numeral zero possesses an abysmal gate. Like all gates, it counts all combinations it and its lower numerals can form, and finding none, it returns to itself. This road, which we are used to call the third hidden road but is, in all honesty, the first, is not in any respect attainable. To go from zero to zero accomplishes nothing, just as the appendage of a second zero to a number in this base does not resolve its paradox. It is from this recognition and this model that rites in all bases exclude repeating rites. But moreover, a gate is a gathering-in of combinations—lemurs—used to constitute their complete system, and here, there is nothing to gather in. It is said, correctly, of gate zero that “between its existence and its non-existence there is no difference.” Superior subtlety is void.

But it is this affordance from which our tradition may begin, in which it finds its grounds for action. In a queer way, superior subtlety is not an odd exigency of numogrammatics, but rather, its heart. For this internal road permits the beginning of elaboration, the first hint that one may stray otherwise: into the gate, even if it cannot be left. This is an elaboration which cannot be represented in that elaboration’s terms, because numogrammatics occurs not around, but within the gate whose terminus, because it was departed from, cannot be returned to. How right that so many numograms exclude gate zero from their depictions! The gate is the numogram itself.

It is in this sense that the numogram is a map, and a technics, of time. Gate zero coincides with, and captures, the pure intuition of time in becoming the precondition of any numogrammaticism. It serves as the inexpressable foundation, the ultimate position of all practice. Yet the higher order numograms do not add to this this gate; rather, they are of it. They serve to elaborate the radical numeracy through which that gate is implied, amounting to an elaboration of the productive mechanism behind it. The time of numogrammatics is heterogenous, ridged, and vibrating, a purring instrument, a deafening toad. Yet its basis and its product and its implication is a pond of the darkest water. It is the vibrant flail and flagrancy of a severe and merciful blank.

The elaborated numograms also serve as a place of contest and possession. Beyond base one, the notation of a zeroed and a misconceived numeracy converge. But it is the latter that has, for the most part, attained cultural dominance. While certain operations evoke a memory of the unstable, collapsing sequences of zeroes—tricks for the multiplications of threes and nines, cardioid functions, modular arithmetic, and digital roots—it is the predominant mode of reading to adhere strongly to place value and the number line. Our time amounts to much of the same, counting the uniform beats which a sequence of ones provides a model for. The matter is not to return to a form of time divided by humans in accordance to what exists in time, but to go further in rejecting it. Beyond the second as a moment of human thought, beyond labour time and lifetimes and the homogenous body of history. Into the vicissitudes of the number which we have summoned to number our days, into a reading which can do without us, in which the works of man dissolve and leave, in their abolished ruins, a standard.

And so, we begin with the numophoric name. The fundamental implication of the unary numogram is 1=0; in binary, this principle takes on an inarticulate sound. The division of zero into itself and one permits the possibility of one’s expression, yet it is a one which makes no difference, whose digital root is zero. In bringing the numeral in from the heavens and expressing its unidentical equality with one, the binary numogram names its foundation and integrates that name into its functioning. The mirror is split in two, each mirroring the other, the word and the name. The plex, which first emerges here, is the testament of that unspeakable name, and all the modes of the numogram proceed from that name as their attribute. The essential rallying of the numbers and the model of all the lemurs to come is 1=0. Whatever else there is, it encompasses.

We say, in decimal, that 9=0, leaving all the rest as commentary. Decimal is the body of that name, its bearer and glory.

Coda 0

Before any of the tricks of reflections and doubles, before fate and subtlety in all its grades, before activity, before patience, before the lemurs themselves, there is nothing. Some call her Tiamat or Dragon, some call it welter and waste, tohu wabohu. Nothingness has, to this day, its representatives, but here we conceptualize it in itself, the complete and undeferred abyss. Abomenon, Venomenon, seething void, blooming dream. Lo, she is here—unspeakable, unthinkable, unindexed. She cannot be conceptualized and never has been. There is nothing here to speak of, nothing to be gained or lost, and nothing of relevance. Not even the absence of meaning can be found here, not even a schism or a rift. The bloom unblooms and the seething simmers down. We must not get ahead of ourselves.

Nothing does not suffice. There must be, rather, a numbered nothing. It must be an ordinal number, the start of a count, but never for the sake of quanta. We are interested, now, in nothing as a zero, nothing as a nullity. For a void-oriented drive, the move to numeracy has nothing to do with quantities. The number emerges because the active function of void belongs to void as cipher, indexed void. As indices, it has always been nullity to which Tiamat or welter and waste refer, and they have always consequently been, in veiled and imperfect forms, a number. They intimate, vaguely but surely, the emergence of a more perfect name in full concord with the cipher beneath, a name which is bound by nothing but nothing, a name which is utterly null.

Coda 1

One questions whether the statement “God is one” has not been terribly misread. God’s breath hovering over the waters approximates that unreachable index under which zero acquires its frenzied activity. This is an annihilating, unreachable god, a God whose face we may not look upon and whose kiss is an exalted death by incompatibility. A great loss is suffered when God’s singularity is seen as a succession of ones, as in the doctrine of the trinity, which is perfectly consistent in a numeracy where three digits can all be one. We lose the God of Job, of Moses on Mount Nebo, of the Tower of Babel, of the cinder in Isaiah’s chest and the prophetic compulsion of Jeremiah. God is one, one is zero, all is breath and dust and an unfolding, terrific power. In doing away with the indulgent idols of man, a creative singularity lets zeroes multiply.