Kunze: Sculpture on Stage 1

Sculpture on Stage PART II: Obversion, Chance, and the Unconscious of Optics

Donald Kunze1

The first part of this essay revisited Rosalind Krauss’s landmark essay, ‘Sculpture in the Expanded Field’, published in the journal October (1979). As with other of Krauss’s works, she employed what is known as the Klein four-group, related to Griemas’s square, a Structuralist device for expanding, internally and externally, meaning according to relations of opposition, negation, contradiction, and implication. Although many, including Krauss, who employ the Klein four-group metaphorically, ignore its mathematical basis (it involves symmetries and number theory), the square is the basis of the idea of the ‘expanded field’ — a critical construct allowing writers to ‘anticipate’ and account for the emergence of new art forms.2 In a sense, the logical category is constructed out of the necessity of the square’s expansion from four vertices to eight; the new vertices, once ‘calibrated’ by a fixed category that is shown to have a hybrid form (and thus reside on the outer-most square), other ‘new’ forms, first identified by ‘?’ can be filled in as artists innovate independently. Their art form has ‘always-already’ been waiting for them to act, created in advance by the (mostly unnoticed) hybrid nature of the original art form.

Fredric Jameson employed a version of Griemas’s square, which he described as ‘a virtual map of conceptual closure, or better still, of the closure of ideology itself, that is, as a mechanism, which, while seeming to generate a rich variety of possible concepts and positions, remains in fact locked into some initial aporia or double bind that it cannot transform from the inside by its own means’.3

Jameson’s operational version has Aristotelian roots:

‘A ninth century manuscript of Apuleius' commentary on Aristotle's Perihermaneias, probably one of the oldest surviving pictures of the square’ (Edward Buckner, The Logic Museum, thelogicmuseum.com).

The question we must ask in the deployment of such squares is: what is negation? The square also focuses on the important sub-theme in the question of negation, what is double negation: both a negation of predicates as well as subjects (i.e. not just the relationship between them) and the case of the negation of a negation. Languages everywhere have their own special means of dealing with negations of negations, indicating that the matter is quite unstable and must be decided by convention. Eastern

1 Don Kunze is Professor Emeritus of Architecture and Integrative Arts at Penn State University. He writes about critical theory and is the author of a book on Giambattista Vico.

2 George Baker, “Photography’s Expanded Field,” October 114 (Fall 2005): 120-140.

3 Fredric Jameson, “Forward,” in Algirdas Greimas, On Meaning: Selected Writings in Semiotic Theory, trans. Paul J. Perron and Frank H. Collins (Minneapolis: University of Minnesota, 1976), xv.

Kunze: Sculpture on Stage 2

European languages thus tend to specify a larger number of tolerated multiple negations. Not only is ‘I didn’t do nothing’ acceptable, it is required. Triple forms in some languages are required: ‘I never didn’t do nothing’.

The missing case is the ‘obverse’, where both subject and predicate are negated. ‘All S is P’ would become ‘No S is not P’. In The Optical Unconscious, Krauss allows for this possibility by ‘misreading’ the square of oppositions. Unlike the case where ‘Every S is P’ has as its contradictory ‘Some S is not P’, a true obverse would be ‘No S is P’. This is what Krauss does in her version:

This, Krauss and Jameson agree, return the square of oppositions to the Klein group and to the semiotic square of Griemas. However this corresponds to the mathematical particularities of the Klein group or the seeming differences of Griemas’s square (Krauss reverse the bottom pair of negations, so that below ‘Life’ is ‘Not-Life’), it accommodates Ernst Jentsch’s definition of the uncanny through its two ‘pure cases’: (1) the deceased who refuses to die or does not know he is dead and (2) the living subject who carries a kernel of death at his center, a kind of magnet drawing him to an appointment with death. The criss-cross paradigms of the uncanny appear in an extensive literature and populate folklore and religious ritual as well.

I would argue that Jentsch’s criss-cross uncanny is logical in its way, but not in the Boolean sense that is the basis of the (Aristotelian) square of oppositions. Krauss’s ‘error’ is interesting. It modifies the alliance between life and not-death and the symmetrical alliance between death and not-life. Not-death is the Jentschian vampire who refuses to die; not-life is

Kunze: Sculpture on Stage 3

the fate-driven servant who will go to meet death in Samarrah. We understand these human models through a logic of ‘inscription’: human experience and being are hollow at the center, and from this inner void an alien program is written that will convert our apparent experiences into anamorphic ciphers that lead us to the antipode of where we think we are going. Double inscription, shown by the square of oppositions, is another word for Lacan’s model of the unconscious, as an inscription of the unconscious as an ‘automatic/automaton’ function within the seemingly random choices we make for whatever reasons seem to make sense. This double inscription process seems to involve Aristotle’s two forms of chance, added to his classic four types of cause. ‘Automaton’ is the kind of accident that comes from nature. A meteor falls from the sky and destroys our roof. We cannot assign it to any kind of cause that relates to finality or efficient cause, except through the folklore concerning the will of the gods. It simply ‘falls out of the sky’. Tuchē is based on the contingencies of human choice and chance encounters; opportunities taken or missed; good or bad fortune.

Experience is not neatly ordered, and any schema based on logical distinctions is seemingly defeated whenever levels and contexts shift, as they often do in real life. The Boolean conditions of the rotated square-within-a-square needs a non-Boolean, more ‘operational’ field model. In Lewis Carroll’s development of the logical form known as ‘sorites’ we have a possible option. Sorites were based on the following conundrum. Imagine a pile of grains of sand. Remove one grain. At some point, we no longer have a pile of sand, but what is that point? The conundrum sounds idiotic but it relates to conditions where change of the ‘figure’ of experience also alters the ‘ground’. The complexities resulting from the coupling of non-figures with non-grounds interests Krauss. How might they be seen by expanding the Kruassian field?

The University discourse, according to Lacan, involves the secret operation of master signifiers. When art criticism moved from the urban and urbane private circles of intellectuals and connoisseurs to the comparatively more public private universities (Columbia, Princeton, Yale, Harvard) this signifier was passed on but not transformed. It was no longer the discourse of the master(s) but the university, where masters, following Pythagoris’s famous example, stay behind curtains. The curtain (compare the images of curtains, such as the ‘double blind’, the standard of reviewing for academic journals) became significant. The base of the work of sculpture could be compared to the campus itself: a zone to set off and protect the university as a special kind of place. Krauss’s ‘racization’ of the question of what is sculpture took place through regional metaphors. ‘New sculpture’ had slipped passed the borders. Krauss wants to naturalize these immigrants, not expel them. Her ‘expanded field’ is a means of finding place for the illegals, a kind of interstitial but previously unnoticed space that opens up with the ‘rotation’ of the logical square. Out of negation, new places as well as new opportunities appear. They were already-always there but we had forgotten to rotate our logic to see them and make them available. The artists are thus mnemonicists, who do not create novelties but ‘remind’ us what was always-already available as a ‘logical’ category. In other words, ‘Enjoy!’

I recommend turning away from Boolean conceptions to non-Boolean ones not just to justify Krauss’s semiotic use of the square of oppositions but to make room for a discussion of Aristotle’s ‘stray causes’, automaton and tuchē. Lacan has given advice on this. If one works backward from his algebraic metaphor for the Real, and his associations of the Real with tuchē and automaton, one gets a clear indicator.

The algebraic metaphor is an expression that equates two forms of negation: -x and 1/x.4 The first, -x, is simple absence; in algebra this is created by moving across the ‘line’ of equation. X=1 is the same as 0=1-X. The motion is virtual. In fact one subtracts X from both sides of the equation. X=1 is the same as 1=1/X performs the same ‘virtual’ movement, this time by

4 According to Lucien Scubla, ‘Hesiod, the Three Functions, and the Canonical Formula of Myth’, trans. Françoise Dondin-Bunelle and Marc R. Anspach, in Pierre Maranda, ed., The Double Twist: From Ethnography to Morphodynamics (Toronto and Buffalo: University of Toronto Press, 2001) 150, Lévi-Strauss thought he realized, in looking at Barbut’s explanation of structures in mathematics, particularly the Kein four-group, the quadripartite system he needed to ‘formalize his theoretical intuition’. He abandoned the canonical form he had formally used and adopted a system of x, -x, 1/x, -1/x to ‘designate the same morphogenetic process’, which he described as the same as used by myth.

Kunze: Sculpture on Stage 4

dividing both sides of the equation by X. The common action of negation of the two forms is the virtual movement across the ‘line’ of the equal sign. The two forms, when equated, give an equation, -X=1/X, or X2=-1, or X=√-1, the imaginary number i, which Lacan thought to be a perfect analogy for the way in which the master signifier (and the master) were both members and not members of the chain of signifiers. -1, a kind of presence/absence version of the negative, seems to relate best to Lacan’s notion of separation; 1/x relates to anxiety, in that the ‘x’ is subordinated to the ‘1’, for which it becomes the denominator or basis. Together, the close the cycle specified by $◊a, Lacan’s matheme for fantasy — what the subject concocts in the face of the impossibility of the Real, the Real’s ‘obscene demands’.

In The Optical Unconscious, it is clear that Krauss’s use of the four-group and the square of oppositions is thoroughly Lacanian, but also extremely personal and somewhat arbitrary. She is aware of the L-scheme and its central relation to the Mirror Stage. Krauss slides back and forth between Lacan — sometimes using metaphors close to Lacan’s actual comparisons but being apparently unaware of this, as in her mention of the card-game analogy — and structuralism’s most reductionistic terms (‘deictic’ and ‘deixis’). It’s a mix-and-match methodology that end in an ‘anything goes’ justificationism. Altough Krauss was one of the three translators of Lacan’s Television, she borrows from Lacan arbitrarily, ignoring some of the key seminars and fitting together parts intuitively.

I am not in the position to judge any of these moves or note the incompleteness of Krauss’s ‘proofs’ (actually no proofs are offered). Rather, I would point to the missed opportunities to connect to some central Lacanian ideas that, being in sympathy with Krauss’s aims, would have promoted her project more efficiently and opened up a much more ‘expanded field’. The problem is that the ‘expanded field’ was not fully expanded to the point that its inner symmetries were apparent. The system keeps going, multiplying the possibilities far beyond anything that could be brought back within a system of coherent critical discourse. Occam’s principle is left in the dust as Krauss goes on an unlimited shopping spree within French Structuralism and psychoanalysis.

Take for example her first look, at Surrealism, through the lens of Adorno. Wouldn’t this have been a time to consolidate the wild extensions of the Klein four-group and L-scheme? The Surrealist object of desire is Ernst ‘Hundred Headless Woman” (La femme 100 têtes). The English translation captures the ambiguity of ‘100’, which is both ‘cent’ and ‘sans’. Both must be present to establish the base level absurd that Ernst requires, but Krauss does not use this translation or mention the cent/sans contrast. This involves the double negation that would have made a clear case for a use of a ‘-x = 1/x’ logic of the Real. Absence and anxiety then couple to establish the matheme of $◊a, fantasy. The description of the ‘jeu de quadre coins’, the French version of musical chairs, Krauss forgets about Lacan’s use of the dummy (le mort, dead man) in the game of bridge. It would have fit perfectly in her former analogy of the card game. In the connection of two fragments, she forgets both the x and 1/x analogy but also Raymond Roussel’s method of le procéde, the splitting of a single sentence into two punned parts and placement at the beginning and end of a story connecting the two pied meanings.

The Wrong Unconscious

Like some others who have used Jameson’s analogy of the ‘unconscious’, Krauss has gotten the meaning of ‘of’ backwards. The worst case of this is W. J. T. Mitchell’s What Do Pictures Want? Responding to a critical review of a previous book in Rolling Stone, Mitchell imputed an unconscious to pictures, animating them in the way ‘primitives’ are held to animate nature. The Lacanian idea, the source of the critical remarks, is actually the reverse. Picture, having no ‘mind’ of their own, become the perfect way of ‘automating’ the human unconscious.5 Lacan is not animism or demonology, although both of these can be understood quite clearly in terms of the Freudian-Lacanian field. Only the human has an unconscious because only

5 An even more idiotic example is Michael Tausig’s What Do Drawings Want?, which compounds the mistaken interpretation of ‘of’ into a fully right-swerve towards Joseph Campell’s sympathetic magic. Had Tausig gone to Cassirer and the origins of the distinction of magic into sympathy and contagion (Mauss), he would have realized that magic in fact follows the Lacanian, not the Jungian/Campbellian script.

Kunze: Sculpture on Stage 5

humans have language which gives the unconscious its particularly human structure and function. The unconscious belongs to the human, the subject. But, the unconscious must necessarily manifest itself in an ‘extimate’ way: i.e. in the ‘subjective objects’ that are modeled along the lines of, and in fact examples of, the object-cause of desire, a. The objective basis of the unconscious is the hallmark of the Freudian-Lacanian field. ‘The extimate’ is a means for understanding how subject and object ‘criss-cross’ (cf. the square of oppositions and the involvement of double negation). To repeat: it is not the object that has an unconscious; it is the object that ‘thinks on behalf of’ the subject. The subject’s unconscious is the object. The object automates the unconscious, and this is the radical materialist basis of the Freudian-Lacanian field and the reason why non-materialist bases (Deleuze, Foucault, etc.) ‘swerve to the right’ of the clinical-popular culture method; and why Jung and most Phenomenologists apart from Heidegger and Merleau-Ponty ‘swerve to the right’ by imputing consciousness (i.e. a system of value) to the object in a ‘non-automatic’ way.

If Krauss is to correct her reversal of the ‘of’, she must see how the ‘optical unconscious’ is the unconscious’s use of the optical — but hasn’t this project already been completed, by the transect that Lacan and others constructed between the Mirror Stage and the gaze, the ultimate ‘partial object’, the ‘organ without a body’, the punctum sæcum of the visible scene that looks back at the observer. Here, the idea not of Adorno but Louis Altusser applies: interpellation. Just as interpellation specifies the physics peculiar to the ‘anxiety’ component of fantasy, it is ‘interpolation’ — the location of ‘missing pieces’ through a process of dialectical triangulation — specifies the physics of separation. Interpellation + interpolation = fantasy, or the subject’s response to the Real.

This is the logical side of the unconscious and it is from the evidence of the clinic that we get our clearest picture. The complementary side comes from popular culture, and here we have Slavoj Žižek’s program of seeing film, television, consumerism, politics, sexual trends, advertising, jokes, and history through a Lacanian lens.

What Happens to the Base?

Krauss uses the base as a metaphorical marker of historical periods of the ‘reception’ of sculpture. In the ‘traditional’ period, the base is a literal frame of the sculptural work, a means of separating it from the quotidian space around it. With modernism, the base is omitted or perverted. The boundary between ‘life’ and ‘art’ is, metaphorically, blurred. At the same time, the re-assignment of what constitutes a base allows the field of sculpture to expand. It does this through a ‘rotation’ akin to the Structuralists’ adaptation of the Kleinian four-group (with no little violence to the mathematical idea), which Krauss compares to Lacan’s L-schema, again, with no little violence to the original idea).

At every opportunity, Krauss misses the opportunity to connect to (1) the uncanny, (2) the extimate, or (3) the ‘subjective object’, the partial object, and the Lacanian gaze. This makes her vulnerable to a ‘Foucaulization’ of Lacan, a swerve to the left, as well as a ‘swerve to the right’, an investiture of objects with ‘unconsciousness’ that ‘demand’ that we Enjoy! them without knowing how. Krauss applies this logic retroactively but does not look at retroaction as such. She does not see the base as a frame that comes in a fundamentally theatrical/temporal form, which initiates a logic of retroaction. Those who object to Krauss’s ‘Lacanification’ are more likely to restore a more truly Lacanian account, just as those who objected to Christian Metz et alia’s presumptively Lacanian film theory.

The base of sculpture should, as a theatrical construct, be taken back to the idea of the Mirror Stage as both a temporal event and a physical space, the theatrical stage. There are many variations on this coupling: the double frame — iconicity, in the words of Max Nänny — where we see clear identification of the boundary of uncertain status between the official representation and the ‘representation of representation’ that mimics our own POV issues.

Our new base looks like this:

Kunze: Sculpture on Stage 6

The ‘logical’ categorical oppositions of Life, Death, Non-Life, and Non-Death are ‘rotated’ to their hybrid forms, found in the ‘nature’ of popular culture. The vertical axis constitutes a ‘cardus’ connecting the north and south poles of the narratives of fate (‘appointment in Samarrah’) to the narratives of the katabasis or descent theme, where the subject ‘does not know it is yet dead’. The decumanus connects Ad with Da, the living being with death inscribed as a kernel, in its geometric center and temporal origin/end, where a logic of return inscribes the final antipode at the heart and origin. This is like the logic of the ‘anacoluthon’, the sentence whose meaning is reversed by its final elements. Rhetoric supplies us other terms for this operation: metalepsis and analepses, the ‘metonymy of a metonym’ and ‘recovery’ of lost/suppressed elements that return us to the starting point, as in James Joyce’s Finnegans Wake.

Where Ad/Da constitute a diurnal kind of temporality, a +x/–x of day and night; the north-south cardus axis specifies the variety of narratives and metaphors that invert and obvert the themes of double inscription. Together, the constitute the cross that has missed, the central pivot or templum that is the sacrificial center of all criticism, its self-consuming nature. The center and periphery, following Borges’ citation of Pascal’s phrase about God as an infinite sphere whose circumference is nowhere and center everywhere, are interchangeable.

The x, -x, 1/x, -1/x square is not only closer to the Jentschian formula for the uncanny, as a criss-cross of polar conditions permuted by their own criss-cross; and also closer to Lacan’s L-scheme; it is the original form of the square that Claude Lévi-Strauss constructed to talk about myth and its applications to geneology, social relations, village space, and initiation rites.

Given the zig-zag, criss-cross, and entirely temporalized flow of the Structuralists’ real use of the Klein four-group, it seems that the historical evidence favors dynamic over static sets of oppositions. If there is an ‘unconscious of optics’ rather than an ‘optical unconscious’ — that is to say, if we are talking not about the optical nature of the unconscious but rather about how the optical is employed as a thinking machine, then this ‘automaton’ ordering device must indeed retrieve its mythic past from the imperatives of the subject’s fantasies in the face of the Real.