No More Learning

8. At least one other commentator on de Man has drawn a similar comparison between the Althusserian concept of ideology and de Man's account of tropes; see Andrzej Warminski's Introduction to Aesthetic Ideology, 9-12. Warminski takes up the relationship between de Man's extant texts and The German Ideology in his "Ending Up/Taking Back (with Two Postscripts on Paul de Man's Historical Materialism)," in Critical Encounters: Reference and Responsibility in Decon- structive Writing, ed. Cathy Caruth and Deborah Esch (New Brunswick, N. J. : Rutgers University Press, 1995), 11-41.
9. Cf. the following: "The point is that the neoclassical trust in the power of imi- tation to draw sharp and decisive borderlines between reality and imitation . . . depends in the last analysis, on an equally sharp ability to distinguish the work of art from reality. . . . The theoretical problem [of the aesthetic], however, has been dis- placed [between its original formulation by Schiller and its presentation in Kleist's apologue "U? ber das Marionettentheater"]: from the specular model of the text as imitation, we have moved on to the question of reading as the necessity to decide be- tween signified and referent, between violence on the stage and violence in the streets" (Paul de Man, "Aesthetic Formalization: Kleist's U? ber das Marionettentheater," in The Rhetoric of Romanticism [New York: Columbia University Press, 1984], 280).
10. Cf. de Man: "the political power of the aesthetic, the measure of its impact on reality, necessarily travels by way of its didactic manifestations. The politics of the state are the politics of education" (ibid. , 273)--a formulation that Plato would have heartily endorsed.
11. As de Man elsewhere observes: "Thus Kant would have forever ended the play of philosophy, let alone art, if the project of transcendental philosophy had succeeded in determining once and forever the limits of our faculties and of our freedom" (ibid. , 283). Notoriously, Kant's project was a failure, the principal evi- dence for which is the Critique of Judgment itself, the text to which de Man turns to disclose this other Kant.
12. In the discussion following her own presentation, Judith Butler contested this formulation, asserting that in this instance materialism for Kant (and presum- ably for de Man as well) was not a concept at all. That there could be something like a "materiality without materialism" (as Jacques Derrida perspicuously put it in his paper), I would not wish to deny. But to the extent that Kant is attempting in the passage cited to define a representational modality ("seeing as the poets do it") and thereby to make it available to the understanding, what he writes necessarily pos- sesses a conceptual dimension, or else it would not be readable at all. Materiality (that to which Kant refers or that which he posits) may not be conceptual, but a
theory (the mode of Kant's referring or positing) of the materiality of art, of seeing "as the poets do it," cannot do without concepts, empty or not. This is the same, ele- mentary, distinction insisted upon by Althusser between the "real-concrete" and the "concrete-in-thought"; see the latter's "On the Materialist Dialectic: On the Unevenness of Origins," in For Marx, trans. Ben Brewster (1969; rpt. London: NLB, 1977), 188-89.
13. Even famous limit cases like John Cage's performances of silence require the appearance of the composer/performer on stage sitting motionless for a certain number of minutes before the piano. The silence requires this minimal phenomenali- zation for the composition to be realized. The point is evident in the passage on the sublime from Kant's third Critique cited by de Man, but it is slightly obscured in de Man's translation. The standard English rendering discloses the necessity for even the most rigorously anti-aesthetic practice to exhibit itself in phenomenal form: "we must regard [the sublime], just as we see it [bloss wie man ihn sieht], as a dis- tant, all-embracing, vault. Only under such a representation can we ranage that sublimity which a pure aesthetical judgment ascribes to this object" (Immanuel Kant, Critique of Judgement, trans. J. H. Bernard [New York: Hafner, 1951], 110; quoted from Rodolphe Gasche? , The Wild Card of Reading: On Paul de Man [Cambridge: Harvard University Press, 1998], 101).
14. This is the burden of Gasche? 's exposition of de Man's theory of reading; see especially chapter 3, "Apathetic Formalism," in The Wild Card of Reading, 90-113. 15. Gasche? discusses de Man's anti-Hegelian, that is, anti-aesthetic, theory of reading in relation to the passage from Hegel's Aesthetics on silent reading in ibid. ,
115-16.
16. One of the anonymous referees who evaluated the present volume for the
University of Minnesota Press took my essay to task for "its old-fashioned com- paratist strategy," characterized by its "presentation of 'parallels' between the work of de Man and Louis Althusser," and for failing (in contrast to Ernesto Laclau's contribution) "to demonstrate how de Man can help us to read history and politics. " The reader also complained that my paper "lack[s a] conclusion" but "'concludes' with a discussion of Brecht that fully 'forgets' de Man. " I would have thought that the point of the pages that follow is clear: to contrast Althusser's ex- ploration of the political and ideological effects of artworks and to show how it cashes out de Man's provocative, but practically underdeveloped, assertions. That I have recourse to the example of Brecht to illustrate Althusserian theory is hardly fortuitous. I do not so much "forget" de Man as I suggest that his critique of aes- thetics culminates in a gesture toward art's politicality, rather than in any determi- nate politics of art. My aim is therefore quite different from that ascribed to Laclau's text: it is not "to demonstrate how de Man can help us to read history and politics," but rather, to examine the potential for and the limits of a political prac- tice of art. These are not, in my view, de Manian questions; hence, my turn away from de Man at the end.
17. Warminski, "Ending Up/Taking Back," 34.
18. Louis Althusser, Sur la philosophie (Paris: Gallimard, 1994), 45; my trans- lation. On the continuity between the early Althusserian concept of the overdeter- mined conjuncture and the later program to develop an "aleatory materialism," see Gregory Elliott, "Ghostlier Demarcations: On the Posthumous Edition of Althusser's
Art and Ideology 47
48 Michael Sprinker
Writings," Radical Philosophy 90 (July-August 1998): 27-28. That there may be a deeper theoretical affinity between Althusser and de Man connecting the former's "aleatory materialism" with what Gasche? identifies as de Man's object of defining the "absolutely singular," an affinity that would involve their respective commit- ments to nominalism (noted by Fredric Jameson in the case of de Man, and by Warren Montag in the case of Althusser), is a topic requiring detailed examination of the entire corpus of both thinkers. Such a project clearly exceeds the scope of the present occasion, which is devoted to a more restricted inquiry into the relation of aesthetics to ideology, and to the political effects of art.
19. Althusser explicitly rejects the Enlightenment concept of ideology in the ISAs; see LP 163-64.
20. The claim is argued more fully by Fredric Jameson in Brecht and Method (London and New York: Verso, 1998). See also, inter alia, Michael Patterson, "Brecht's Legacy," in The Cambridge Companion to Brecht, ed. Peter Thompson and Glendyr Sacks (Cambridge: Cambridge University Press, 1994), 273-87; and the essays by John Willett (on Brecht's reception in Britain), Bernard Dort (on Brecht in France), Karen Laughlin (on Brecht's assimilation by American feminist playwrights), Renate Mo? hrmann (on Brecht's influence on women's cinema in West Germany), and Thomas Elsaesser (on Brecht's incorporation by film theory and practice in France, Britain, and Germany), collected in Re-interpreting Brecht: His Influence on Contemporary Drama and Film, ed. Pia Kleber and Colin Visser (Cambridge: Cambridge University Press, 1990). A more specialized but highly in- formative study is George Lellis, Bertolt Brecht, Cahiers du Cine? ma, and Contem- porary Film Theory (Ann Arbor: UMI Research Press, 1982).
21. See Jameson, Brecht and Method, especially the two concluding sections, titled "Actuality" and "Historicity. "
22. See the concluding pages of Thomas Elsaesser's essay on Brecht and con- temporary film, cited in n. 20 above.
23. The Loach-Leigh connection is commonplace in accounts of contemporary British cinema; see, for example, Michael Coveney, The World according to Mike Leigh (London: HarperCollins, 1996), 13-14; and the introduction to Leigh's inter- view with Cineaste 20:3 (1994): 10-17. But just as quickly as the connection is as- serted, it is disavowed, or heavily qualified (not least by Leigh himself). Despite no- table differences in political affiliation, their shared commitment to realism as an aesthetic mode is of the utmost importance, as are each director's methods of preparing cast and narrative for production. Both practice that form which Fredric Jameson argues was Brecht's preferred vehicle for dramatic realization: the work- shop or master's class (see Brecht and Method).
Algebra and Allegory: Nonclassical Epistemology, Quantum Theory, and the Work of Paul de Man
Arkady Plotnitsky
The "nonclassical epistemology" of my title refers to the epistemology defined by a particular configuration, to be assembled in this essay, of the concepts of materiality, phenomenality, formalization, and singu- larity. These concepts would be naturally associated with de Man's work by his readers, as would be the concept of allegory, which is, I shall argue, correlative to the epistemology and the conceptual configu- ration in question. 1 The appeal to "algebra" is somewhat more eso- teric. It is, however, far from out of place, especially in the context of the question of formalization and given the relationships among de Man's work, nonclassical epistemology and quantum theory, which I shall also discuss here.
It would indeed be difficult to circumvent de Man's work in consid- ering these subjects or such figures as Kant, Kleist, and Shelley, to whom a significant portion of this essay will be devoted. 2 In particular, nonclassical epistemology has fundamental connections to aesthetic theory, beginning (at least) with Kant and Schiller, and to the practice of literature and art, such as of Kleist, Shelley, and other Romantic au- thors, or, as T. J. Clark's "Phenomenality and Materiality in Ce? zanne" (in this volume) suggests, that of Ce? zanne. These connections are cen- tral to de Man's later works, specifically Aesthetic Ideology, where Kant's third Critique, The Critique of Judgment, and aesthetics and (the critique of) aesthetic ideology, are given a special place. 3 The history of the particular aesthetic-ideological (mis)reading of the third Critique in question in his work is seen by de Man as beginning with and still gov- erned by Schiller's encounter with Kant. By contrast, the work of, espe- cially, Kleist and of some among his Romantic contemporaries appears
49
50 Arkady Plotnitsky
to mark for de Man the opening of a different aesthetic theory. This opening also leads to a very different type of reading of the third Critique (which may be closer to the spirit, or indeed the letter, of the work) by de Man and such authors as Jacques Derrida, Jean-Franc? ois Lyotard, Jean-Luc Nancy, and several others. This difference is, I argue, defined by the set of, in terms of this essay, nonclassical concepts-- in particular, "formalization," "materiality," "phenomenality," and "singularity"--to which I now turn. I begin with formalization and what I call radical or nonclassical formalization.
Paradoxically, or so it may appear, the radical character of radical formalization, and of its formal laws, is defined by the fact that they allow for, and indeed entail, that which is irreducibly unformalizable, irreducibly lawless; that is, whereas the "algebra" of any formalization may be seen as defined by a set of (specified or implicit) laws, here the configuration or ensemble of configurations of elements governed by these laws entails that which cannot be comprehended by these laws or by law in general, and furthermore, that which cannot be conceived by any means that are or even will ever be available to us. Accordingly, the irreducibly lawless in question is not something that is excluded from the domain or system governed by formalization, is not an ab- solute other of the system, but is instead irreducibly linked to it. 4 This is in part why radical formalization may appear paradoxical, and it does lead to an epistemology that, while technically free of contradic- tion, is complex and difficult (and, for some, impossible) to accept.
The particular version of radical formalization that I shall now in- troduce appears to be epistemologically the most radical yet available. But then it may also be the only available (or even possible) model of the configuration of the formalizable and unformalizable just defined. Accordingly, from this point on, by either radical or nonclassical for- malization I refer to this version. The complexities and implications of the concept are many and far-reaching. The configuration itself defin- ing it, or constituting the point of departure for it, is, however, simple to formulate: the representation of the "collective" may, in certain circumstances, be subject to formalization and law; that of the "in- dividual" is irreducibly nonformalizable and lawless; and the overall efficacity of both types of effects, formalizable and nonformalizable, is inaccessible by any conceivable means. 5
This formulation does not merely mean that formalization or law in this case does not apply in certain exceptional situations. Instead, every individual entity (element, case, event, and so forth) that belongs
to the law-governed ("organized") collectivities in question is in itself not subject to the law involved, or to law in general. More accurately, one should speak of what is "seen" (is phenomenal) or represented as such an entity or such a collectivity. The qualification is important to the relationships between "materiality" and "phenomenality" in non- classical epistemology. I shall consider these relationships in detail later. It may, however, be useful to offer a preliminary sketch here, be- ginning with this qualification.
Although law here does apply only at the level of certain collective, rather than individual, effects, both types of effects, lawful and law- less, are manifest, materially or phenomenally. Accordingly, when in- volved, material strata of such effects may, at least, be treated as avail- able to phenomenalization, representation, conceptualization, and so forth, for example, for the purposes of formalization. By contrast, the ultimate efficacity of these effects cannot, in principle, be so treated (even though, as will be seen, this efficacity may, at a certain level, be considered as material). In other words, this efficacity is irreducibly inaccessible not only to formalization and law--to "algebra"--but to any representation, phenomenalization, and so forth. Nor, ultimately, can we think of it in terms of any properties or qualities that, while in- accessible, would define it. It is irreducibly inaccessible by any means that are or, conceivably, will ever be available to us; any conception of it is, and may always be, impossible, ultimately even that of the impos- sibility of conceiving it. As will be seen, it would not be possible to ac- count for the coexistence of both types of effects (collectively lawful and individually lawless) in question otherwise. The presence of both types of effects is logically possible if and only if we cannot conceive of their efficacity at all: the peculiar character of the effects makes one infer the even more peculiar character of the efficacity. It follows that all conceivable terms are provisional, suspect, and ultimately inade- quate in describing this efficacity, including efficacity or ultimate, both quite prominent here. It is worth, however, registering more specifically some of the terms that need to be suspended.
First, although this efficacity manifests itself through the effects of both types, it cannot be thought of in terms of an underlying (hidden) governing wholeness, either indivisible or "atomic," so as to be corre- lated with manifest (lawless) effects, while subject to an underlying coherent architecture that is not manifest itself. Either type of under- standing would (classically) reduce the (nonclassical) "counterposition" of the manifest effects of collective lawfulness, on the one hand, and of
Algebra and Allegory 51
52 Arkady Plotnitsky
individual lawlessness, on the other. This efficacity is neither single in governing all of its effects (individual and collective), nor multiple so as to allow one to assign an unambiguously separate efficacity to each lawless individual effect.
Second, an efficacity of that type cannot be seen in terms of inde- pendent properties, relations, or laws, which, while unavailable, would define a certain material entity that would exist in itself and by itself, while, in certain circumstances, giving rise to the (available) effects in question. Instead, it must be seen as reciprocal with and indeed indi- visible from its effects: it can never be, in practice and in principle, con- ceived as isolated, separate from them. Nor, however, can it be seen as fully "continuous" with these effects either. All individuality or, con- versely, collectivity in question appears (in either sense) only within the manifest strata of such indivisible configurations. These configura- tions, however, also contain the inaccessible strata that cannot be iso- lated and hence cannot appear, either as accessible or even as "inacces- sible. " It is irreducibly inaccessible and yet, indeed as a corollary, equally irreducibly indissociable from that (part of the overall configu- ration) which is accessible--is subject to phenomenal representation, conception, knowledge, and so forth. One might say that, while the in- accessible in question is indeed inaccessible absolutely, it cannot be seen as something that is the absolutely inaccessible. It follows that nonclassical epistemology does not imply that nothing exists that, in certain circumstances, gives rise to the effects in question. Instead the point is that this efficacity or the corresponding "materiality" (which also designates something that exists when we are not there to observe it) is inconceivable in any terms that are or perhaps will ever be avail- able to us. Naturally, "existence" or "nonexistence" are among these terms, along with the possibility or impossibility to "conceive" of it, or "possibility" or "impossibility," or "it" and "is," to begin with.
As will be seen, these conditions are the conditions of both quan- tum epistemology and allegory in de Man. It is true that de Man often associated allegory (or irony) with discontinuity (in earlier work in juxtaposition to the continuity of symbol). We may, however, more properly think of this relation as neither continuous nor discontinuous, or in terms of any conceivable combination of both concepts, or, again, in any given terms, as just outlined. De Man's emphasis on disconti- nuity of allegory appears strategically to point in this direction, away from the continuity of the symbol or of classical thought in general, for example, aesthetic ideology. Both continuity and discontinuity are re-
tained at the level of "effects," and the effects of discontinuity are in- deed more crucial to allegory (or irony).
In the circumstances in question, then, formalization and laws apply only to certain collectivities, but in general not to individual ele- ments composing such collectivities. (I am not saying that they fully describe the latter, since, as follows from the preceding discussion, how the "workings" of the efficacity just considered make lawless individu- al elements "conspire" to assemble into lawful collectivities is ulti- mately inconceivable. ) Accordingly, the (lawless) individual effects in question can no longer be seen as a part of a whole, so both are com- prehended by the same law, or by a correlated set of laws. This possi- bility defines classical systems and classical formalization, and I use the term classical accordingly. A classical formalization may and often must apply within nonclassical formalization. Within classical limits, however, nothing is, in principle, lawless, even though, in practice, laws may be difficult or, as concerns the ultimate laws, impossible to apply. In the latter case, an underlying lawfulness, however unknown or even unknowable, would be presupposed. By contrast, nonclassical, radical formalization not only figures as lawless the manifest individu- ality of certain effects involved, but rigorously suspends even the possi- bility of ascribing any structure, law-governed or not, or properties to the efficacity of all manifest effects, lawful or lawless.
Under these conditions, individuality becomes not only uniqueness but also singularity. Indeed, "singularity" may be defined by this prop- erty of manifest lawlessness in relation to a given law, or to law in general, perhaps especially when this property arises in a point-like, "singular," fashion--spatial or geometrical; algebraic or analytical (a "singular" point of a function or a "singular" solution of an equation in mathematics); temporal or historical; and so forth. To some degree, one might see the inaccessible efficacity of the singular (or indeed all) effects in question as itself "singular," as Rodolphe Gasche? appears to do in his reading of de Man in The Wild Card of Reading. 6 Historically, however, the term singularity has been associated with the (manifest) point-like configurations or with a relation to the inaccessible, and it is, I would argue, in de Man as well. In addition, the efficacity of such singular events in de Man is indivisible from its effects (in accordance with the analysis just given). Accordingly, it cannot be conceived of as an independent entity severed from them and, hence, as isolated from them either materially or phenomenologically, as the appeal to "singu- larity" in describing it might suggest. By contrast the singular effects in
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54 Arkady Plotnitsky
question can be isolated phenomenologically, although, in view of the same reciprocity, ultimately not materially or efficaciously. Indeed, they are phenomenologically defined by this "isolation" from their (ul- timate) history and (both materially and phenomenologically) from each other. 7
Given the features just outlined, however, nonclassical formaliza- tion and nonclassical epistemology are indeed singularly radical episte- mologically or, as the case may be, antiepistemologically, as well as anti- ontologically. The view just outlined equally disallows any ultimate ontology and any ultimate epistemology--any possibility of knowing or conceiving how that which is at stake in it is ultimately structured, or is ultimately possible. For example, it would not be possible to pre- dict which information will become available at a later point. Hence, unknowability is not certain either, any more than knowability, except, again, at the ultimate (efficacious) level, where the unknowable be- comes irreducible. At this ultimate level, we may adopt Gasche? 's for- mulation, "any [ultimate] knowledge, even that of the impossibility of knowledge, is . . . [indeed] strictly prohibited" (The Wild Card of Reading 182)--but only at this level, hence I insert "ultimate" here. One would be reluctant to say, especially in the context of de Man's work, that nonclassical epistemology disallows materiality, although at the ultimate level no given concept of matter can apply any more than any other concept. One might say instead that one needs the kind of conceptual architecture here discussed in order to argue for the ne- cessity of a certain form of "materiality," in particular as "materiality" without an ultimate epistemology and an ultimate ontology. 8 De Man specifically associates this radical materiality with both Nietzsche and Derrida (161-62), and earlier Kant and Hegel, although such thinkers as Bataille, Blanchot, and Lacan are pertinent here. De Man also as- sociates this materiality with the "textuality" of Kant's and, by im- plication, other radical texts. He speaks of "the simultaneous [with idealism] activity, in his [Kant's] text, of a materialism much more radical than what can be conveyed by such terms as 'realism' or 'em- piricism'" (AI 121). I shall return to de Man's understanding of textu- ality later.
The qualifier "ultimate," which recurs throughout this essay, is cru- cial. For it is not that no account or knowledge is possible, which is not an uncommon misunderstanding of nonclassical theories, specifically de Man's or certain interpretations (such as that here considered) of quantum mechanics. On the contrary, rigorous and comprehensive ac-
counts of the situations in question only become possible once the epis- temological circumstances in question are themselves taken into ac- count. Specifically, at the level of "effects," classical ontology, episte- mology, and phenomenology become possible and necessary. Indeed, these are the effects that make us conclude that their emergence entails something that is ultimately inaccessible to us in that it may not toler- ate an attribution of any properties, terms, conceptions, and so forth, including, ultimately, any conception of the ultimate. For, at the very least, the sum of these effects is unaccountable for classically, even when they are subject to classical knowledge, as at a certain level they must be, since they would not appear to us otherwise. Nonclassical knowledge does not offer us a better knowledge of the irreducibly in- accessible in question in it than classical knowledge does. But it does allow us to infer this inaccessible from its effects and to account for these effects themselves, retaining the irreducibly inaccessible as part of this account.
The overall epistemological situation may, again, appear paradoxi- cal and (ideologically? ) unacceptable to some, in the case of quantum physics, Einstein, among them. It is, however, consistently defined and free of any logical contradiction, as Einstein indeed admitted in the case of quantum mechanics in his debate with Bohr. Do such configu- rations actually exist, or need to be constructed in certain situations? Do we need radical formalization to account for anything, even if it is conceivable and technically free of contradiction? Yes, such configura- tions do exist, or need to be constructed, both in literature (where they may be more expected as "inventions" of poets) and life (where one may expect them less). They appear to be necessary in facing the "dead nature" as well, at the level of its ultimate constituents, as we under- stand these constituents now, that is, in terms of quantum physics.
Indeed, in order to make "phenomenality" more rigorously appli- cable in nonclassical circumstances, we may, following Bohr, define "phenomenon" in terms of the reciprocal or indivisible relationships between the effects in question and their nonclassical efficacity, and, accordingly, recast these relationships in phenomenological terms. A "phenomenon" is a representation of a specific (material or already phenomenal) configuration where such relationships are found.
In quantum mechanics, such configurations are defined by the physi- cal interaction between quantum objects and measuring instruments, while manifesting, in a trace-like manner, the effects of this interaction only in the latter. In contrast with classical physics, the role of measuring
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56 Arkady Plotnitsky
instruments is irreducible in quantum physics. 9 The behavior of mea- suring instruments is described by means of classical physics and in terms of classical epistemology, since classical physics may be treated as epistemologically classical, in particular causal and realist. In these arrangements there "appear" traces (say, on silver bromide photo- graphic plates) of quantum objects, such as elementary particles (or what is so called by convention)--photons, electrons, and so forth.
Such traces emerge as the effects of the interaction (itself quantum) between the latter and the measuring instruments. Both the physics of measuring instruments and of the traces in question are available to us, while quantum objects themselves cannot be ascribed physical (or perhaps any) properties, for example, such conventional "quantum" properties as discontinuity, or of being "objects" in any given sense.
The mathematical formalism ("algebra") of quantum mechanics applies to some of these effects, specifically to certain collective effects, found within one type of phenomena, and does not apply to other such effects, specifically certain individual effects, found within the other type of phenomena. Both types of phenomena can never be combined, or be seen as derived from a single efficacious situation, however hid- den. Nor can we have both types of effects within a single phenome- non. If we are to "see" each effect of a formalized (lawful) collectivity as lawless, this collectivity has to be (re)phenomenalized so as to be di- vested of both collectivity and law--either through a single phenome- nal collectivity of lawless individual (singular) effects or through a col- lectivity of singular individual phenomena. In other words, the lawful collectivity and lawless individuality in quantum mechanics, or in any radical formalization, require different phenomenalizations, even when dealing with the "same" set of effects. Accordingly, both the sets of ef- fects and the efficacity of such phenomena will be different by virtue of the different material or mental agencies of phenomenalization in- volved. This is in part why this efficacity can never be seen as an entity isolated from its effects but instead as that which is irreducibly recipro- cal with and indivisible from its effects. It may of course be stratified as to the "location" of some of its strata, while retaining the radically in- accessible character of each such stratum.
These circumstances manifest themselves most famously in the ap- pearance of either the ordered or patterned wavelike effects (which pertain only to collectivities of such traces) in some circumstances and the particle-like effects (in general not subject to law in quantum me- chanics) in other circumstances. The presence of both types of effects is
essential to and defining for quantum physics, even though (and be- cause) it is impossible to ever combine the two types of phenomena together or derive them from a single common configuration. The cir- cumstances of their emergence and hence the phenomena that corre- spond to them are always mutually exclusive or, in Bohr's terms, com- plementary. The latter fact is primarily responsible for Bohr's choice of the term complementarity for his overall interpretation of quantum mechanics.
"Quantum objects" or, more accurately, that which makes us speak of such entities can be assigned an independent existence as something that may be assumed as existing when we are not there to observe it. That "something," however, cannot be assigned any conceivable inde- pendent physical (or other) properties, for example, those defining (classical) particles or waves. Nor can it be isolated from their inter- action (itself quantum) with measuring instruments so as to establish their independent impact and hence ascertain their independent prop- erties on the basis of the effects of this interaction. Classical physics fails to describe the sum total of these effects and can be shown to be rigorously incapable of doing so: the possibility of a classical-like de- scription would be in conflict with the experimental data of quantum physics. Quantum theory is able to account for both types of effects and for their complementarity. It does so, however, in a nonrealist and noncausal way. As I said, quantum theory (at least in Bohr's interpreta- tion) does not describe the properties and behavior of quantum objects themselves but only (in a statistical fashion) certain phenomenal effects of their (again, quantum) interaction with measuring instruments. This is why, in contrast to classical physics, in quantum theory this inter- action can never be neglected or compensated for, while entailing the irreducibly inaccessible efficacity of the effects constituting the data of quantum physics. "Quantum objects," detected in any given experi- ment, are part of this efficacity. In general, however, the latter involves other agencies, such as measuring instruments, perhaps in turn ulti- mately quantum (in view of the ultimate quantum constitution of all material objects).
Bohr's interpretation of quantum mechanics, as just outlined, is, I argue, generalizable to all nonclassical epistemology, and the nonclas- sical phenomenology it entails, in particular those found in de Man's work. We must, of course, rigorously adhere to the specificity of the workings of the general scheme here presented in different situations, even when we can leave aside technical aspects of modern mathematics
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58 Arkady Plotnitsky
and science, including in their connections to each other, such as, in the case of quantum mechanics, making experimentally well-confirmable statistical numerical predictions, or sometimes even exact numerical predictions concerning certain information, say, the position or the momentum of a particle, but never both together. (Hence, from the classical viewpoint, such information is always partial. The laws of quantum mechanics disallow us to assume a wholeness, however un- knowable, behind this information, hence making it complete, as com- plete as any information than can, in principle, be obtained in any experiment performed on quantum objects, or, again, what we infer as such from this information. ) In nonscientific nonclassical situations, the nonclassical effects would emerge through such entities as (materi- al) signifying structures of the text (de Man's "materiality of the signi- fier"); material texture (in either sense), such as that of Ce? zanne's paintings; the materiality of historical occurrences or events; or certain "mental" configurations of the same joint (classical-nonclassical) type. (At bottom, [material] materiality may be irreducible even in the last case, even though, given the epistemology in question, there is no ulti- mate bottom line here, and the concept itself of materiality is affected accordingly. ) Also, we now deal (or so it appears) with "macroscopic" human subjects (in either sense) rather than the ultimate (microscopic) constituents of matter (seen as material) of quantum physics. The epis- temology of quantum mechanics and nonscientific epistemology here considered do, however, (re)converge at certain points, including, from both sides, on the latter point. In particular, they share the supplemen- tary (Derrida) or allegorical (de Man) production of phenomenaliza- tion and indeed, as Bohr stressed, idealization from "technomaterial" marks. This term may be applied to such marks with "writing" in Derrida's sense in mind. In quantum mechanics, or already relativity, this application would involve certain parts of the (material) technology of measuring instruments, where the scientific data in question in these theories appear in the form of certain material marks or traces. The situation may be rigorously shown to correspond to Derrida's "econo- my" of trace, supplement, writing, and so forth. 10
More generally, in all situations here in question, the key nonclassical features are brought about by the irreducible role of "technology" (in the broad sense of techne ? ) in them. From this perspective, we may de- fine as "nonclassical" situations those in which the role of technology is irreducible. The technology of measurement in quantum physics, or of techne ? of "writing" in Derrida's sense, and the techne ? of "linguistic
materiality" in de Man's sense (which I shall discuss later), make the situations in question nonclassical. By contrast, in "classical" situa- tions techne ? is, at least in principle, reducible, as, for example, in the case of measurement in classical physics, since measuring instruments play only an auxiliary role there so as to allow us to speak of the inde- pendent properties and behavior of classical objects. One can view analogously certain forms of reading or textual processing and produc- tion in general, insofar as the role of "writing" may be neglected there. Thus, classical textuality is not only possible but is necessary within certain limits. By definition, we depend on it even in nonclassical situa- tions insofar as (as in the case of measuring instruments in quantum physics) nonclassical effects appear through classical textual processing.
These connections are not coincidental. Although physics played the most decisive role, the ideas of Bohr and other key figures in the history of quantum physics may be traced to nonclassical aspects of the nineteenth-century philosophy, literature and the arts, and then to modernism. Conversely, the relevance of, among other mathematical and scientific fields, quantum mechanics to de Man's work is hardly in doubt. Nor is it surprising in view of the significance of new science for modern intellectual history, even leaving aside that de Man was edu- cated in science and engineering. Relevant elaborations are found throughout de Man's works, if often reconceptualized or allegorized so as to function independently of their scientific frames of reference. "Pascal's Allegory of Persuasion" offers more direct connections to mathematics and science. In particular, de Man's analysis there may be linked both to mathematical formalization and to its role in physics. As will be seen, both subjects are significant for Aesthetic Ideology and related work. The connections to physics, from optics to quantum me- chanics, could be traced throughout de Man's work. The interplay of optical tropes of "reflection" (admittedly a customary trope in such discussions), "translucence," "transparence," and so forth in de Man's essay "The Rhetoric of Temporality" may be read as metaphorically shuttling between geometrical (linear), wave, and quantum theories of light. "Quantum-mechanical" themes emerge in most of de Man's "optical" tropology and in his epistemological arguments. The connec- tions between both is a more complex question, since nonclassical epistemology does not always govern the architecture of optical tropes, although de Man's essay "Shelley Disfigured" suggests more direct connections of that type. It may, however, be argued that most radical and most significant forms of "blindness" and "insight" in de Man are
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"quantum-mechanical," even when they relate to the blindness and insight of reading. The latter is not surprising, given the technological and material character of textuality as considered by de Man, and the fact that for de Man epistemology is indissociable from reading. A massive deployment of "optics" is found in "Shelley Disfigured," where it is also especially justified, given Shelley's own deployment of optical theories in The Triumph of Life and elsewhere. 11 The essay also con- tains a number of formulations of a general epistemological, rather than specifically "optical," nature (although in this case they can be brought together) that are parallel and perhaps indebted to quantum epistemology. Thus, de Man writes at the outset, virtually defining his analysis: "The status of all these where's and what's and how's and why's is at stake, as well as the system that links these interrogative pronouns, on the one hand, to questions of definition and of temporal situation and, on the other, to questions of shape and figure. "12 This is strikingly reminiscent of and is epistemologically parallel to Bohr's in- augural definition of complementarity (1927): "The very nature of quantum theory thus forces us to regard the space-time coordination and the claim of causality, the union of which characterizes the classi- cal theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and definition respectively" (PWNB 2:54-55).
More interesting at this point, however, is not the influence of mod- ern mathematics and science on de Man's and related work, but the conceptual reciprocity between both domains and the deployment of that work in our approaches to, at least, epistemological, conceptual, and aesthetic aspects of mathematics and science. I shall here consider two such examples--the allegorical character of quantum mechanics, and the relationships between formalization in science and the radical (materialist) formalism that de Man finds in the Kantian sublime.
Complementary phenomena are common in and peculiar to quan- tum physics. Those related to "wave" and "particle" effects and their complementarity are the most famous. Arguably the most significant, however, are those related to the measurement of physical variables, such as position and momentum, or time and energy, correlative to the complementarity of "the space-time coordination and the claim of causality," mentioned earlier. According to Bohr, such variables and the overall quantum-theoretical description can only be applied to quantum objects themselves provisionally or, in his terms, symbolically. For, as we have seen, even though we often (by convention) speak of
such variables in relation to quantum objects, in actuality we can only measure the corresponding physical quantities (either position or mo- mentum, or time and energy, but never both together) pertaining to the classically described measuring arrangements; that is, we measure clas- sical physical variables pertaining to certain parts of such arrange- ments, rather than to the quantum objects themselves, but describe the relationships between the mathematical variables corresponding to these physical variables in terms of quantum-mechanical, rather than classical, formalism. Classical physics can only describe each such physical variable in a corresponding experimental arrangement, but never both together, since there is no experimental arrangement that would make it possible. This situation can be numerically represented by Heisenberg's uncertainty relations, which, thus, become mathemati- cal correlatives of this situation. 13 The rigorous impossibility of ac- counting for this situation in terms of classical physics makes it neces- sary (a) to infer the existence of quantum objects and (b) to introduce a different, quantum, theory, including a different mathematical formal- ism or "algebra," which provides such an account. It does so, however, in a physically and epistemologically nonclassical way.
Now, I would argue that the situation is rigorously allegorical in de Man's sense, thus linking "algebra" and "allegory" within physics itself. The formulation from "Pascal's Allegory of Persuasion" is espe- cially fitting here: "the difficulty of allegory is rather that this emphatic clarity of representation does not stand in the service of something that can be represented" (AI 51). 14 Indeed, this clarity may be said to stand in the service of that which cannot be represented by any means. Thus, classical physics can offer us only incomplete and partial--and spe- cifically complementary--allegories of the quantum world. Nothing appears to be able to offer us more. Accordingly, Bohr's "symbolic" means "allegorical" in de Man's sense, for this "symbolism" in fact rigorously prohibits the classical epistemological features of "symbol" (as analyzed by de Man), in particular any possibility of deriving "alle- gorical" representations from any original or primordial unity. The formalization of collectivities in quantum mechanics does not offer a classical (or classical-physics-like) description of quantum behavior or, again, allow one to claim any primordial unity behind it. It only statis- tically predicts the emergence of certain collective patterns, but never of individual events or effects. If the mathematical formalism, algebra (no quotation marks are necessary), of quantum theory represents any- thing at all it represents this nonclassical and (with respect to using
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conventional concepts of classical physics) allegorical situation. 15 Inso- far as one can apply this formalism to quantum objects themselves, ei- ther by correlating it in some ways with classical physics and its mathe- matical formalism or otherwise, it can only be done allegorically.
We can have a further and deeper sense of these connections be- tween quantum mechanics and de Man's work, and the reciprocal theoretical possibilities they offer, by considering the question of the mathematical formalization of physics. Even beyond "Pascal's Allegory of Persuasion" (which would require a separate treatment), the subject of mathematical formalization is significant in Man's work, specifically in his analysis of Kant's sublime. It has, of course, a major significance for Kant's own analysis of the sublime (or of the beautiful) and in his work in general. In de Man's reading it acquires a special prominence not in Kant's treatment of the mathematical sublime, but as Kant's analysis enters the question of what Andrzej Warminski, in "As the Poets Do It: On the Material Sublime," aptly terms "the material sub- lime. " In this case we (must) "find" the sublime, if we regard, for ex- ample, the ocean, "as poets do, merely by what the appearance to the eye shows [or points] [was der Augenschein zeigt]. " (I modify de Man's translation [AI 80]; a stable, or any, translation may not be possible, only a reading, as Warminski's essay suggests as well. ) According to de Man, "Kant's [phenomenal? ] architectonic world is not a metamor- phosis of a fluid [material? ] world into the solidity of stone, nor is his building a trope or a symbol that substitutes for the actual entities" (AI 82; emphasis added). "Flat" and "the third person" as it is, this archi- tectonic world may be seen as a certain configuration of phenomenal "effects" produced by a reciprocal and yet inaccessible efficacity. "The only word that comes to mind," de Man says, "is that of a material vision" (AI 82).
The nature of this materiality and of the formalism that, de Man ar- gues, accompanies it is complex. Indeed, de Man immediately adds: "but how this materiality is then to be understood in linguistic terms is not, as yet, clearly intelligible. " This understanding will bring with it further complications of the concepts of the sublime, materiality, and formalism (or formalization), and a more radical dislocation of aes- thetic ideology than those entailed by the material vision, qua vision, as here described by Kant and de Man--or at least as this vision has been described so far. This vision may entail more radical limits in this respect, which become more apparent through an understanding of its materiality "in linguistic [or/as textual] terms. " The analytical and tex-
tual pressure put upon Kant's text both by Kant himself and by de Man becomes extraordinary indeed, since we have already come quite far. For, as de Man writes:
The critique of the aesthetic ends up, in Kant, in a formal materialism that runs counter to all values and characteristics associated with aes- thetic experience, including the aesthetic experience of the beautiful and of the sublime as described by Kant and Hegel themselves. The tradition of their interpretation, as it appears from near contemporaries such as Schiller on, has seen only this one, figural, and, if you will, "romantic" aspect of their theories of imagination, and has entirely overlooked what we call the material aspect. Neither has it understood the place and the function of formalization in this intricate process. (AI 83; emphasis added)
It is not altogether clear whether the term formalization here refers only to the radical formalism in question at the moment; or whether it is seen more generally so as to encompass other forms of formaliza- tion, specifically those analogous to radical formalization; or whether, especially once understood in linguistic terms, the radical formalism of the material vision, qua vision, of the sublime entails something like radical formalization. It is also not altogether clear whether "ends up" refers to this particular moment of Kant's and de Man's analysis or anticipates de Man's final elaborations in the essay. The question, then, is whether this linguistic understanding of the materiality involved is "deconstructive" or even (in Kant's text) "self-deconstructive" in some sense (i. e. , whether Kant's text inscribes this understanding against its own grain); or whether this understanding is an actual outcome of Kant's analytical rigor; or whether a yet more complex space of read- ing is at stake. It would be difficult and perhaps impossible to give a fully determined answer. For one thing, what poets "see" or "do" in finding the (material) sublime, how we understand this materiality in linguistic terms or how poets do so (possibly at the moment of this vision), and the movements of Kant's argument appear to be already ir- reducibly entangled in Kant's text. Both the material vision in question and its understanding in linguistic terms (and by implication radical formalization) may be brought together by the kind of reading of Kant and de Man offered by Warminski in "As the Poets Do It. " According to Warminski's reading, what "poets" in fact find in finding the sublime is the radical linguistic materiality that we find in Kleist and, via Kleist, in the end of de Man's essay. Even so, certain differences between the
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materiality (and phenomenality) of the sublime and those involved in radical formalization may remain, especially as concerns what does and does not appear to the eye. The radically inaccessible in question in radical formalization cannot be "seen" in any conceivable sense. It would also be difficult to disregard the fact that Kant parallels, if not identifies, "[to find the sublime] as the poets do it" and "what the ap- pearance to the eye shows. " These complexities do not diminish the radical implications of de Man's analysis, and may be a virtue insofar as it offers new epistemological and aesthetic possibilities, even "insur- mountable possibilities. "
It appears that, in all circumstances, in order to reach the limits of materiality here at stake we need Kleist's aesthetic formalization, as radical formalization, through which de Man develops the linguistic understanding in question, rather than only Kant's radical formalism, as it emerges prior to this understanding. In particular, the latter corre- sponds to and, in a certain sense, is the mathematical formalism of classical physics, specifically, "the mathematization or geometrization of pure optics" (AI 83), rather than to the radical formalization of quantum physics, as is the aesthetic formalization of Kleist or de Man's linguistic understanding. 16 We recall that de Man closes "Kant's Mate- rialism" by suggesting that Kant's radical formalism (formalism, in question at the moment, rather than radical formalization) may not ul- timately be "formalistic enough" (AI 128). He may well have had Kleist's aesthetic formalization in mind, which, along with de Man's essay of Kleist itself, is invoked at the end of "Phenomenality and Materiality in Kant," and something similar is intimated in the end of "Kant's Materialism" (AI 89-90; 128).
The question of the mathematization of science, here specifically optics, enters at the point when the (purely) formal character of the (purely) material vision is ascertained. De Man writes:
The sea [of the material sublime] is called [by Kant] a mirror, not because it is supposed to reflect anything, but to stress a flatness devoid of any suggestion of depth. In the same way and to the same extent that this vi- sion is purely material, devoid of any reflexive or intellectual complica- tion, it is also purely formal, devoid of any semantic depth and reducible to the formal mathematization or geometrization of pure optics. (AI 83)
Beyond the more immediate reference to vision--here, moreover, a vi- sion of the sea as "mirror"--the role of optics has, as I said, a special place in de Man's thought, extending to the connections to quantum
physics, the ultimate optics, at least for now. The latter, however, al- lows for no mathematization and particularly geometrization of its ul- timate "objects. " Instead it entails radical formalization and, with it, both a materiality that is available to phenomenalization and (limited) formalization, and a materiality that is unavailable to any formaliza- tion, representation, phenomenalization, and so forth, and hence to any vision. The latter could still be seen as "material," insofar as any conceivable term could apply. It cannot, however, any longer be seen as formal, mathematically or otherwise. It may only form an (irreducibly invisible) part of a formal vision.
By contrast, the mathematization or geometrization of pure classi- cal optics (whether linear or wave optics, or classical particle optics) conforms to the formalization of classical physics. It is an obvious ex- ample of what Galileo called and was first to develop as, in his terms, the mathematical (and specifically geometrical) sciences of nature. One might argue that the latter are made possible (I am not saying fully constituted or governed) by a kind of material and formal vision analo- gous to the one de Man invokes at this juncture of his reading. This vi- sion enables one to treat the properties of material bodies (or of space and time) as experimentally measurable and theoretically mathematiz- able quantities, which are abstracted from or divested of the other properties that material bodies possess (the procedure sometimes known as the Galilean "reduction"). 17 It is crucial, of course, that, al- though this vision enables such a treatment, it is not identical to this (technical) treatment. With this qualification in mind, one might say that the vision of the sublime (or of the beautiful) in Kant is fundamen- tally mathematical-scientific, for the moment in the sense of classical science--at least short of understanding this vision in linguistic terms.
One might also reverse the point and argue that the formal and specifically mathematical character of the mathematical sciences of na- ture is fundamentally aesthetic in de Man's radical sense. It is true that most of the disciplinary ("technical") practice of physics, or mathe- matics, bypasses the experience in question. It cannot be seen as aes- thetic in Kant's sense, to begin with, because, to put it in Kant's terms, it involves the concept of understanding. Indeed, one of Kant's deep in- sights was that understanding can never be purely formal, including any conventionally "formalized," such as mathematical, understanding. The (pure) formalness can only be achieved in aesthetic judgment and perhaps, ultimately, only in the purely material and formal vision of the material sublime. The latter we can only find, as poets (or, at certain
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points, some physicists and mathematicians) do, by regarding certain objects by "merely [purely geometrically? ] what the appearance to the eye [sight] shows," even if it is the mind's eye. If one is a poet like Kleist, Ho? lderlin, or Shelley, the linguistic understanding of, and now within, this vision can become even more epistemologically radical or nonclassical in the present sense. For the moment, within classical lim- its, whatever may primarily define the technical practice of mathemat- ics or mathematized science, such as modern physics, they (or perhaps any understanding) would not be possible without this "founding" aesthetic moment or vision. This vision creates the formal "objects" of mathematics, or the mathematized objects of physics, or at a cer- tain level of all theoretical thinking, or even of all understanding, as Kant appears to intimate as well. 18 This "mathematical" or "quasi- mathematical" vision "precedes" (logically rather than ontologically) all mathematical or mathematized physics and even mathematics itself, as we understand them now. Neither would be possible without this "vision," even if the "contemplation" involved may no longer play much, if any, of a role once such objects are put into disciplinary circu- lation and are subjected to a technical treatment. Although this mo- ment or vision does not occur all the time, it need not have occurred only once either--as a single, absolutely founding moment (a problem- atic and ultimately untenable conception) of mathematization either in mathematics itself or in the mathematical sciences. It is, I would argue, this aspect or moment (prior to understanding) of "mathematization or geometrization of pure optics," given that de Man sees it as devoid of "any . . . intellectual complication. "
It is true that this purely formal and material "vision" in mathemat- ics or specifically geometry (where mathematical objects can be "con- templated" more visually) is not always sublime. It may be with re- spect to some mathematical, or mathematized, physical "objects," or presumed objects, such as mathematical infinities (now seen in terms of the material rather than mathematical sublime, as Kant defines it). Even when failing the sublime, however, the classical mathematical vi- sion in question is aesthetic, if perhaps not quite a vision of poets, and, specifically, purely formal. Indeed, as de Man observes in the passage in question, the same aspects define "the aesthetic experience of the beautiful" as well. It is, thus, not altogether certain whether de Man, or Kant, associates the vision of poets with any material and formal vi- sion of the type here described, as would appear more immediately, or more strictly the vision of the (material) sublime. The linguistic under-
standing of this vision brings further complications into this question and into the question of the relationships between this vision and for- malization in mathematics and science.
Even short of these complications, however, mathematics and sci- ence appear to involve features that make them more aesthetic, and differently aesthetic, than we usually think. The features just discussed are more deeply and radically aesthetic than what is offered to us by usual aesthetic ideologies, the appeal to and reliance on which, by mathematicians and scientists, philosophers, or laypeople we continue to encounter. This appeal is often based on the same ideologizing mis- reading (it need not entail actual textual encounters) of Kant and oth- ers, which, as de Man argues, may indeed be unavoidable. Conversely, the formal materialism in question makes a dislocation of these ideolo- gies possible.
And yet, this materialism or formalism does not go far enough, is not yet "formalistic enough," at least not so far. Both "Kant's Materialism" and, especially, "Phenomenality and Materiality in Kant" take the Kantian sublime further--to the point where a yet more radical stage of reading Kant's text, and of formalization and materiality, is reached. This stage is reached when how "[the] materiality in question is under- stood in linguistic terms" becomes more "clearly intelligible," whereby the situation acquires the key features of radical formalization in the present sense and, correspondingly, of quantum epistemology.
In particular, the application of the mathematical formalism of quantum mechanics may be seen as arising from, or at least as linked to, an extraordinary form of "vision" of the material constitution and, with respect to the viewpoint of classical physics, de-constitution of the quantum-mechanical data. I am now speaking specifically of the vi- sion ("phenomenality") relating to the marks/traces constituting the quantum data, rather than of the theoretical conceptualization of the quantum-mechanical situation as a whole. As the vision of poets in Kant, which helps us to find the sublime, this vision, which helps us to find quantum mechanics, may be seen as material in the same sense. It may, however, no longer be seen as formal, unless in terms of (if one may use such an expression) a radically de-formalized form--that is, if we can, phenomenally, and especially geometrically, "see" anything in this way at all. It may not be humanly possible to do so, even though, in contrast to the ultimate constituents of matter or the ultimate effi- cacity of the data in question, the elements constituting these data are available to phenomenological apprehension. We do, however, now
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treat these marks, even their collectivities, purely "formally" (without "form") rather than in any way configuratively. In particular, we divest them of their classical and hence configurable appearance (in either sense), even though they do form configurations, or what can be so seen in certain circumstances--say, wavelike patterns, or a trace of a particle in a cloud chamber. Even within a single phenomenon, where these marks appear, they must be divested of the possibility of being explained in classical terms and hence of their manifest classical con- figurativity. For example, they should not be seen either as points re- sulting from classically conceived collisions between "particles" and the screen or as forming a classically conceived wave pattern. Neither "picture" corresponds to what in fact occurs. At this stage, even the radical (Derridean) trace-like character of these marks is suspended, although this character will have to be given to these data in order to explain them in quantum-theoretical terms.
This suspension is necessary, and the vision that results is possible, for the following reasons. As we have seen, the mathematical formal- ism of quantum mechanics does not formalize or otherwise describe the configurations, individual or collective, of these traces as such, or for that matter any material physical process in the way classical physics would. Instead, it enables statistical (and statistically very precise) predictions concerning certain collective, even if not individu- al, configurations of material marks in certain circumstances. 19 Inso- far as one can interpret the situation and specifically the quantum- mechanical mathematical formalism as applicable to quantum objects themselves or their interactions with measuring instruments in terms of conventional physical (or indeed any) concepts, such an interpretation can only be allegorical in de Man's sense. First, this "allegory" does not at this level describe any physical configuration or process. Second, it does not (in contrast to a symbol, for example) relate the partial (complementary) descriptions involved to, or allow one to presuppose even in principle, any classical wholeness that would reduce their com- plementary character. Thus, in order for a theoretical formalization and interpretation of quantum physics to take place, these marks, while "visible," have to be divested of any form of mathematical and specifically geometrical representation. Classical physics is largely defined by the possibility of such representation or, more broadly, phenomenalization. 20 In quantum mechanics, neither is possible any longer. This impossibility is reflected in the trace-like or written (in Derrida's sense) character of the marks in question and the allegorical
(in de Man's sense) nature of the interpretation of these traces or of the mathematical formalism of quantum mechanics. All such classical rep- resentations may be seen (with caution) as forms of (aesthetic) ideolo- gy, even when they are divested of everything (tropology, figuration, reflexivity, semantic depth, and so forth) except for mathematical for- malization, including of the kind invoked by de Man in the context of the material sublime. At this point mathematization itself (such as that of the Galilean or Newtonian, or indeed Euclidean, program) may be seen as ideological, even if we see it as purely "formal" or purely "aes- thetic" and as devoid of technical, or standard ideological, dimensions of the practice of mathematics and science. The efficacious processes themselves will, again, be, in Bohr's terms, far beyond the reach of any pictorial visualization, phenomenalization, representation, conception, and so forth. Now, however, the manifest effects, the visible marks, in- volved, too, must be seen (in either sense) as divested of any geometri- cal structure consistent with classical physics. Either individually or collectively, these traces must be seen as allowing for no classical physi- cal description, as would be the case of the "radical formalism," at least in the mathematization and geometrization of science, if not of the Kantian sublime itself.
I cannot consider the subject here, but it may be argued that Heisen- berg's great paper introducing quantum mechanics appears to reflect the process just described. 21 First, it suspends the application of classi- cal physics to quantum data and the very possibility of configuring these data accordingly. Instead it treats them formally (but, again, without giving them form) as material and phenomenal effects, di- vorced from all classical configurativity. His introductory elaborations in the paper itself would suggest nearly as much. Heisenberg does not explore the epistemological consequences of the situation, of which he was only vaguely aware at the time. His main concern was to offer a mathematical formalism that would enable theoretical predictions in the situations where all previous attempts had failed.