Wednesday, March 5, 2008

Zero

In the Tarot the card of the Fool is given over to 0, the numerical symbol for nothing; his errant liberty thus escapes the consecutive march of the Trumps. Our word for zero is derived ultimately from the Arab sifr, which means cipher.[i] In this light, 0 is a puzzle, a nonentity. How can the Fool’s individuality be identified as nothing? Zero has two simultaneous but incompatible tasks: it must act like a numeral when used a placeholder, but it also, in it denotation, negate the numeral and signify nothing. Mathematical logic, at least today, demands a zero, even if zero is where logic breaks down [1] In other words, how can the Fool, as zero, possibly inhabit the schizophrenic position of marking meaning and marking the void? It is the nothing that implies that what it names is something, is one. The Fool, like zero, is at once distinct and obscure- his only guarantee is a lack of sense. He is oblique, a number twisted out of vacuity, a lively zero, a signifier that cannot fully signify.

The logical coherence of the Fool’s zero hangs on a precarious balance, just as the Fool is poised at the threshold of a solid ground underfoot and the bare abyss ahead. Is the idea behind zero the absence of a number or a number for such an absence? The former keeps it estranged from the rest of the numbers, merely part of the landscape in which they move; the latter puts it on par with them. Another way to ask the question is whether the fool is a member of the Major Arcanum, or is he the surrounding wilderness threatens constantly their disappearance? The word sifir is translated from the Sanskrit sunya meaning “desert, empty place, naught.”[ii] The semantic paradox is even apparent in topology of the Tarot - the Fool is both the exterior desert, the extensive and empty landscape in which the numeric Trump cards assert their presence and the singular enclosure of an empty interior.

The most basic depiction of absence is a hole, the encircling of something that contains nothing, a circumference enclosing emptiness within, creating and inside and an outside. Hence the almost intuitive recognition of a closed loop O as a sign for zero. Like a pictogram it seems to hover across, if not bridge, the divide between the letter and the image. Yet we know that the zero has not always been written as an O. Babylonian tablets show us that around 400 BC that the Babylonians used two wedge symbols “ to bracket a place for zero, thereby establishing a difference between say, 101 and 11. [iii] We can see from this that the early use of zero to denote an empty place is not really the use of zero as a number at all, merely the use of some type of punctuation mark so that the numbers could communicate a correct interpretation. Zero was also often marked as a cross in early Mayan mathematics, a curious testament to zero’s chiasmic or cruciform activities.[iv] There is other evidence that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. The symbol became quite prevalent throughout the east.[2] Some ancient Indian mathematical documents sometimes also used a dot to denote an unknown, similarly we might use x in an algebraic equation.[v]

The mysterious metamorphosis of zero from a dot to a cross to a circle has much to tell about the complexity of the Fool. A dot or point, as a solid mark, functions as a symbol of fullness; it contains no empty spaces. But geometrically, the point is precariously present, visible but also a horizon of invisibility. Though it can perhaps be thought of as the mark of presence, of bare existence, its slightness in form recalls that the point is always, inevitably on the verge of disappearance. Somewhere in its travels westward, the symbol of zero underwent a crucial change to an oval, literally and figuratively embodying the emptiness that it embodies. My point is the replacement of a symbol (.) suggestive of a fullness just at the brink of fading into emptiness for the emblematic oblong (0) that circumscribes an absence is a testament to the epistemological paradox of the Fool’s very essence. The suggestive numerical genealogy of zero is a potent marker of its, and the Fool’s in-between-ness- bound neither to fullness nor emptiness, they are possibly, impossibly both.

Zero is not the same as nothing. Without substance itself, it nevertheless carries the power to make things happen in the subtlest and most brazen ways. It’s worth mentioning that it was only long after the symbolic logic of all the other numerals was “found,” did mathematicians fully realize the logical paradoxes inherent in such a peculiar numeral.[vi] At the chiasmus of the Cartesian plane, the zero becomes a fulcrum around which all numbers begin to turn.[3] So at one moment, the zero is punctualized into a very precise term, and all the other numerals it supposedly generates make use of it, call upon it, to act as a fellow number. But, residing at the crucial intersection of number lines and planes, it is also the zero which does the “calling,” acting as the necessary plane that creates the possibilities of all the other numbers. It should help to mention that mathematics refer to the point of intersection in a Cartesian grid, where the axes meet, as the origin normally labeled O. [4] The shape of the zero- an egg- is a rebus, representing not just an absence but a beginning as well. So while the history of zero shows that it could only be grasped as a concept after the other numerals, but after it is found, zero comes before all the other numbers. The Fool shares this aporia. The zero makes complete the number system, but it also as nothingness must reside as the originary basis of logic, a swansong which is elusively though permanently there. Always, zero is hiding in the interstices.

In the Tarot tradition, the Fool represents wandering, figured as frozen in a pose right before action. When the tarot cards are played like a game, the fool trumps all other cards because as a no-thing he upsets the established numbered order and ranks of the Tarot cards.[vii] Without the Fool, the tarot forms a closed system and a conclusive set of narratives. As zero, the fool opens up the system and grants the deck its infinity of potential interpretations. As for the fool’s symbolic importance in the tarot tradition, he represents ultimate potentiality and paradox.[viii] Like the circularity of zero, he expresses nothing and contains everything. In this sense, the generative capabilities of a nothing presupposes annihilation or cancellation- the logic of zero makes clear that if something can be, it necessarily must also be capable of not being. The figure of the Fool, the o-thing, represents the indeterminacy of this zero-state, throwing the whole seemingly closed system of the tarot into a realm of multiplicitous and unbounded potentiality.[5]I n this sense, the fool finds empathy with the argument of creation ex nihilo because his zero generates all the numbers in the mathematical universe.[6] For him, the absence of a number is the very plane that makes possible a set of possibilities.

The number zero specifically enacts the same double edged contradiction around which the Tarot turns. Zero is the blind spot of meaning and sense. Mathematically, geometrically, etymologically, it seems to say that nothing is the substratum of unity. The circularity and precision of the 0-operations makes a clearing in the sober opacity of the rest of the numerals and Trumps. The Fool leaves but a light mark on the world, a mere dot in space. But as he is himself a contradiction, a puncture into the void and a point marked on the universe. He thereby plunges the rest of his comrades into confusion, because it is impossible to grasp his doubleness as something really distinct. In his suspended changeability, the Fool is potentially capable of both creation and annihilation. [7] Appearing as if he might simply throw himself into groundless chasm before him, something suspends the Fool in mid-leap. Alone in a world of numerous more vivid and richer presences, the Fool is like no one else. We can imagine the silence of the abyss calling out all around him. What he summons in his pose is an offering, a giving over of possibility to airy nothing. If he were to call out to the void, he might say something like, “The world, alas, is real. I, alas, am Zero,” a Borgesian cry, one of composed neutrality, a resignation of the eternal contradiction of his very being, or non being.[8]

As a zero, the Fool makes space for us to consider the operations of such a cipher when it comes to reading the text of the Tarot. There are several tales that can be read in the nil. One is a history of a mark, a testament to the iconographical particularities by which a sign comes to concretize its own contrariness. Another is a story of reason and the metamorphosis of a sign, where zero is first an absence, then a symbolic unit, a crux, an origin, and finally a threshold; eventually it is zero, not reason, around which the other signs move. One more might be the zero of authorship, the space of silence from which the cards speak. Also there is the zero of reading itself, the blind spot where a text outfoxes itself and upturns as yet another object of knowledge. The zero point of a text is a non-position, a state of stalled hesitation, where there is nothing available to subsume contradiction or tame incoherence, only a potential for further paradox and ambiguity. The zero, as a vacuum, inverts things.

Finally, there is the desire couched in reading and the pleasures that the zero affords.[9] Since desire is always a desire for a ‘something else,’ a something else which is continuously shifting, reading around the zero entails that the reader undergo a ceaseless and cyclic re-writing of desire. Linguistically speaking, the lack of sense that desire continuously defers and substitutes with other selves, other stories, other signifiers. The effect that zero has on reading is a metonymic one: each sign refers to another history of signs in a perpetual deferment and dallying of meaning. The means of delaying sense in a reading- repetition, digression, deferral - are the invisible marks of the Fool, hints of zero’s persistent mischief. This is why the act of reading and the pleasures of the Fool’s zero never mean to wholly satisfy.

Where I once desired the text, I become the site of the text’s desire.[10] The hesitations that come from this ambiguous position also involve a kind of yielding to seduction, one where we let the text survey us, frighten us, tease our desire, tempt us. The Fool who might fling himself into the abyss at any moment is also the reader yielding to the temptation of a brief intertextual, intersubjective fling. As we inhabit the textual nexus of the tarot, we can never entirely surrender to nor have authority over the pangs of zero that crop up. Reading the zero disturbs, in the most wanton of ways, my sense of readerly decency, suggestively disrobing any fantasies that this encounter could be unstained.

The crossing of desire with meaning and sense is inevitably results in a transgression, the point zero who is contrariness incarnate. The thrill of the Fool’s disobedience comes from his intimate knowledge of junctures- he preserve the plane of possibilities from which everything changes. The chiasmus of this crossing denotes loss, as I’ve shown. But what the Fool offers us is ecstatic loss: a thrill at a lapse in self, a way to relent thought to the void in being, the empty circle at the center of our hunger. This private zero is teeming with life. It is our interior Fool who, standing on the brink of a precipice, can only see pure prospective in the abyss, the unrealized universe that lies dormant in nothingness. Here, on the seductive brink of oblivion, the immediate possibilities within the boundlessness tremble with anticipation.


Works

Agamben, Giorgio. "Bartleby, or on Contingency." Potentialities. Stanford: Stanford UP, 1999. 243- 271.

Barthes, Roland. The Pleasure of the Text. New York: Ferrar, Straus and Girous, 1973.

Borges, Jorge Luis. “A New Refutation of Time.” Other Inscriptions. Austin:University of Texas Press, 1964

"Cipher." Oxford English Dictionary. .

Melville, Herman. "Bartleby, the Scrivener." Norton Anthology of American Literature. Ed. Nina Baym and Francis Murphy. New York: W W Norton and Company, 1985. 2200-2230.

Menninger, Karl. Number Words and Number Symbols. New York: Dover Publications, 1969.

Nichols, Sallie. Jung and Tarot. 1st ed. York Beach: Samuel Weiser, Inc, 1980.

Pollack, Rachel. Complete Illustrated Guide to the Tarot. London: Element Books, 1999.

Scholem, Gershom. Kabbalah. New York: New American Library, 1975.

"Zero" Oxford English Dictionary. .

Notes


[1] The path of scientific thought led to the discovery of "0" only after the invention of the most abstract type of number system, which is called "positional" because the value of a character depends on its position. Our modern way of counting is positional (Menninger, 372). The figure "5" has a different value in 102 and in 1020, determined by its position. The Romans, Greeks, Hebrews (and Aztecs and pre-Islamic Arabs and a great many others) used an "additive" system, which is fundamentally a transcription of counting (305-6). As far as historians know, the positional concept emerged in only four places: c.2000 B.C.E., in Babylon; around the start of the Common Era, in China; between the 4th and 9th centuries C.E. among the Mayan astronomer-priests; and in India (37, 396-98). Positional systems have certain features in common. One is that each base number is denoted by a discrete symbol, purely conventional and not a graphic representation of the number itself (i.e., not "four slashes" for "four," as the Greeks and Romans had). Another feature of positional number systems is that they lack special symbols for numbers which are orders of magnitude of the base number. This was necessary in additive systems, for simplicity of notation and record-keeping, but is incompatible with a positional system. (372) Most importantly, in a positional system, mathematicians had to find a way to indicate the absence of "tens" and "hundreds." It became necessary to have a "zero," a character that signifies "empty." (401) The next step was to realize that that "symbol for nothing" is not just a place-holder, but an actual number: that "empty" and "nothing" are one (422). The null number is as real as "1" and "10" - that's when the door blows open and numbers become complicated. Without that, there's no modern mathematics, no algebra, no modern science.

[2] The common practice of using ellipses (…) to denote missing pieces of a text or verse originated in the Indian use of the dot. (Menninger, 403)

In mathematics, the Cartesian coordinate system is used to determine each the position and relations of a unique point in a plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate. To define the coordinates, two perpendicular lines (the x-axis, and the y-axis), are specified, as well as the unit length, which is marked off on the two axes. The zero point of the cross is the point where the x and y axes intersect- its coordinates are (0,0). Cartesian coordinate systems are also used in space (where three axes are used). There, the zero point would be (0,0,0).

[4] The graph of Cartesian coordinates. Zero is marked as o for origin

[5] The idea of the potentiality of mere existence, or bare life, was a major thread in the philosophy of Giorgio Agamben, an Italian intellectual who writes about aesthetics and political philosophy in the 21st century. In his reading of Melville’s story “Bartleby, the Scrivener,” Agamben makes a distinction between the significance of the copyist’s enigmatic response to his employer’s orders, “I would prefer not to” and Hamlet’s more famous and resonant refrain. For Agamben, the prince’s “to be or not to be” simply points to an opposition between being and non-being (Agamben, 259). Bartleby’s phrase points to a third term beyond mere nothingness and mere existence. For Agamben, this term is potentiality. Here, we can understand this term to mean the state of infinite suspended possibilities of what one can and can not do. Agamben identifies here a potentiality that can only be fully recognized in the potential not to. Bartleby lived so stolidly in the abyss of impotentiality/ potentiality without ever willing to leave it. He refuses to let his capabilities become actualized or concretized into a world of subjects and objects. So in terms of creation and the copyist fool who possesses such capability and withholds all willingness, “Bartleby is the extreme figure of the Nothing from which all creation derives; and at the same time, he constitutes the most implacable vindication of this Nothing as pure absolute potentiality” (253). To be willing is not the same being able, and it is in this disjunction that pure potentiality lies. For Agamben, Bartleby is simultaneous figured as the void of nothingness and the universe of potentiality, in a state of suspension. In this sense, Bartleby the scrivener has become the blank sheet on which he would prefer not to write, paradoxically suspended between what he is capable of actualizing, and that which he prefer to preserve as potentiality.

[6] Early Cabalistic mystics coined the term Ein-Sof (Infinity) to describe the unknowable-ness of the Divine Creator. The first step in the manifestation or actualization of God is called ayin, or nothingness. The Cabalists saw God as turning towards creation, so as Ein-Sof (or infinity) actualizes itself, it turns to face both ayin and creation at the same time (Scholem, 94). Speaking of the Cabalistic notion of a nothing from which everything proceeds, Agamben points out that the “obscure matter that creation presupposes is nothing other than divine potentiality. The art of creation is God’s descent into the abyss that is his own potentiality and impotentiality, his capacity to and not to” (Scholem, 253). But it is the will of God that turns towards creation. Bartleby’s potentiality differs in the sense that when a lawyer asks “You will not?” the scrivener corrects the statement in reply with “I prefer not.” Like Bartleby, the Fool dwells so stolidly in the abyss of impotentiality/potentiality without ever willing to leave it. His zero comes not from a will to nothingness, but an affirmation of what might become in the opening of this nothing. (Melville, 2200-30)

[7] The operations of zero as numeral are bizarre to say the least. If it is nothing, then it should be nothing, or at the very least merely a place-holding punctuation mark. But sometimes it is nothing and other times it is something: 1+0=1 and 1-0=1, so here the zero is nothing, it is not expressed, and when it is placed in front of a number, it does not change it: 01=1. But write a zero after a number, and suddenly it has a real function, multiplying the number times ten: 20=10x2. So now it is something- something incomprehensible but powerful, especially if a few “nothings” can raise a number to an immeasurably vast magnitude. And of course, multiplication with zero is utterly perilous- 999,999,999x0=0, and the zero reduces every factor it touches to nothing again, destroying even the largest of numerals. It has no value in itself, but has the power to radically transform all the other digits.

[8] The Argentinean writer Jorge Luis Borges argued in a 1944 essay called “A New Refutation of Time” that the negations of idealism, which declare that objects in the world are ideas which only exist in the mind of God or people who see them, may also apply to time. Just as George Berkeley denies that there is an object existing independently of our perception of it, and David Hume denies that there is a subject apart from a mere recollection of sensations, Borges tries to demonstrate that there is no time. He proceeds with the idealist assumption that each of us can reduced to a collection of sensations, then a single repeated perception—either in one life or in the experience of two different lives—suffices to prove that time is a fallacy, since this repetition will destroy its linear sequence. In the spirit of the fool, Borges concludes his refutation with a cancellation, another refutation, a paradox: “Time is the substance I am made of. Time is a river that carries me away, but I am the river; it is a tiger that mangles me, but I am the tiger; it is a fire that consumes me, but I am the fire. The world, alas, is real; I, alas, am Borges.” (171-187)

[9] In The Pleasure of the Text, the French semiotician Roland Barthes distinguishes between two kinds of textual delight. One he refers to as a text of pleasure; this kind of text simply fulfills the reader’s wishes and expectation. This is a text that merely comforts. Contrary to this kind of textual satisfaction, the text of bliss disrupts these desires for contentment, fulfillment, or meaning:

Text of bliss: the text that imposes a state of loss, the text that discomforts (perhaps to the point of a certain boredom), unsettles the reader’s historical, cultural, psychological assumptions, the consistency of his tastes, values, memories, brings to crisis his relation with language…he enjoys the consistency of his selfhood (that is his pleasure) and seeks it’s loss (which is his bliss). (14)

The text of the Tarot is precisely of this sort. There is a “seam” to every text- where the edge of culture meets the edge of transgression. Its emphasis on loss undermines our faith in the cogito which authors itself and in the integrity of signs and their meanings; it forces us to recognize that, instead of a tool which we use, language speaks us. For Barthes, a text of bliss is a text that undoes the reader, unravels the assumed consistency or narrative coherence of human life. Whereas a text of pleasure "milks" us, a text of bliss weans us and, therefore, repeats that original moment of loss by which we find ourselves and our desire. Similarly, this kind of text that undoes its reader is not only relational to the potential transformations and distortions that that readers might perform, but is also relational to all the other texts that engulf and surround it.

[10] One of the devices displayed in The Pleasure of the Text is Barthes' use of shifting personal pronouns to riddle the speaker's status as both a univocal and unified "author" and a multiply located, libidinally dynamic, and linguistically ambiguous “reader.” To Barthes, this subject is dissenting and duplicitous, conventional and iconoclastic. This subject emerges and re-creates his/herself in the seam of the Tarot text- he/she is both the subject that the text addresses and the very corresponding “subtext” which itself addresses the cards and is “read” by them. Barthes is clear that text of bliss always imposes this duplicity as cut, by which:

Two edges are created: an obedient, conformist, plagiarizing edge , and another edge, mobile, blank (ready to assume any contours), which is never anything but the site of its loss…Neither culture nor the destruction of culture is erotic; it is the seam between them , the fault, the flaw that becomes so. (6-7)

The zero is this cut, “which is never anything but the site of its loss.” Obedience to and transgression of the logic of signification are both necessary practices within the text of bliss. It is this threshold, this border, this zero this cut, this absence-as-presence that is erotic for Barthes; it demarcates the desires that have drawn individuals into this space. After all, what is the point of desire without the threat of the forbidden?


[i] Menninger, 400

[ii] "Cipher." Oxford English Dictionary.

[iii] Menninger, 171

[iv] Ibid., 404

[v] Ibid, 40

[vi] Ibid, 401

[vii] Pollock, 43

[viii] Nichols, 42.

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