No More Learning

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
Algebra and Allegory 53
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
Algebra and Allegory 55
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
Algebra and Allegory 57
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
Algebra and Allegory 59
60 Arkady Plotnitsky
"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
Algebra and Allegory 61
62 Arkady Plotnitsky
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
Algebra and Allegory 63
64 Arkady Plotnitsky
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
Algebra and Allegory 65
66 Arkady Plotnitsky
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
Algebra and Allegory 67
68 Arkady Plotnitsky
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. These conse- quences emerged in the subsequent developments, specifically in yet another great paper by Heisenberg himself, introducing the uncertain- ty relations, and in Bohr's work. 22 Heisenberg's invention of quantum mechanics, however, appears to have been partly enabled by the de- configurative phenomenology just discussed.
From this viewpoint, the ultimate "aesthetics" or "poetic vision" of physics is not that of coherence, harmonious wholeness, and other icons of classical aesthetic ideology, although these may apply at other
Algebra and Allegory 69
70 Arkady Plotnitsky
levels of quantum theory. Instead it is the aesthetics of the radical de- coherence, of the formal without form--the quantum aesthetics, if not the quantum sublime, although "the formal without form" would fit the sublime as well. And yet, for all that, the quantum-mechanical for- malism, or radical formalism or formalization elsewhere, may remain only another form of aesthetic ideology projected into the radical and nonformally formal "configuration" (a term henceforth inadequate) of material marks, if any nonaesthetic or nonideological perception of them is possible. I shall return to this topic later. My main point here is that, once divested of all mathematization and, especially, geometriza- tion, such as that of optics, the formalism (mathematical or conceptu- al) of quantum mechanics, for example, of quantum optics, can only conform to radical formalization. It does not conform to a radical for- malism analogous to the radical formalism of the material sublime, which is parallel to the formalization of classical physics, that is, again, short of "linguistic terms" of understanding it. Linguistically under- stood, it might be seen as subsumed by radical formalization.
Then, reflecting back, the material vision of the sublime would be seen as only appearing (in either sense) to be a classical (and classically architectonic) vision of the mathematization or geometrization of pure optics. In fact, however, as the vision of the sublime qua the sublime, it will have involved radically deconfigurative aspects that are analogous to those found in "contemplating" the data of quantum physics, as just considered. Would this be the vision necessary in order to find the sub- lime, as poets do, if not the vision of the sublime itself? The sublime appears to correspond to a vision of that which always escapes archi- tectonics, geometrization, and so forth, while appearing to be available to them. (We recall that, in contrast to the beautiful, this vision cannot be seen as having an object, but rather as making such an object im- possible. ) By contrast, in the quantum-mechanical vision the material marks constituting quantum data should be "seen," should be made to be seen, as altogether devoid of any conceivable architectonics, with- out phenomenally suggesting this evacuation of the architectonic. Inso- far, however, as it may not in fact be possible to see anything in that last way, this vision comes closer to the sublime, although it may still be different from what either Kant or de Man had in mind. For, on the other hand, if we apply this more radical deconfiguration or disfigu- ration to the sublime itself, we may enact, as it were, the material desublimation of the sublime. The latter would undermine the already "deconstructive" visions and "ideologies" based on the sublime, which
now appear as merely more sophisticated forms of aesthetic ideology. Perhaps once made "more intelligible," "understanding [the materiali- ty of the sublime) in linguistic terms" reveals the un-architectonic un- sublime thus suggested, although, and because, Kleist's and Shelley's disfigurative visions appear to offer its best model.
Although contextualized somewhat differently in relation to the vi- sion of poets ("the way the poets look at the oceans severed from their geographical place on earth"), something of this type is suggested by de Man's remark, via Montaigne. We must, de Man says, consider "our limbs," formally, "in themselves, severed from the organic unity of the body. " "We must, in other words, disarticulate, mutilate the body in a way that is much closer to Kleist than to Winckelman," or one might say deprive them of their geometry (AI 88). Within the ma- terial vision of the sublime thus understood, any, for example, linguis- tic, formalization of such "parts" is a form of "algebra. " Some of its aspects can serve to construct partial and ultimately inadequate alle- gories (some of them geometrical) of the materiality of the "body" in question, both that of the manifest effects (analogously to those of quantum-mechanical marks) or their efficacities. Indeed, the original "parts" or "limbs" are already such allegories, derived from the classi- cal view, and hence as supplementary as the body itself. Accordingly, a more radical disarticulation, mutilation, disfiguration of the (un)body is at stake, even at the level of manifest effects. Following the overall epistemology here discussed, the efficacity of these effects is, again, in- accessible in any way, no more by means of disarticulation, however radical, than by means of articulation. With respect to this efficacity, the dismemberment and disarticulation in question (at the level of the effects) itself reflects only this inaccessibility. This disarticulating dis- memberment of the body will be linked to the linguistic understanding of materiality and specifically to the disarticulation of tropes, as indeed the term (figure? trope? ) disarticulation suggests. 23
De Man's reference to Kleist here and in closing "Phenomenality and Materiality in Kleist" is crucial and confirms my overall point. The question, then, would be whether it is any more possible to experience such a vision or even assign it any geometry than to have any vision the (un)configurations of marks constituting the data of quantum me- chanics. What would such an experience, say, in a vision of a sea, be? Is it possible? Can it be shown to be rigorously impossible? For, to see something as the poets do, however, may correspond to the situation in question, if we can see "anything" here at all, even beyond the radically
Algebra and Allegory 71
72 Arkady Plotnitsky
inaccessible efficacity of all visible effects involved. The allegorical al- gebra enabled by this vision or un-vision would be quite enough in itself. We may call such a (nonvisualizable) sublime or unsublime the algebraic or the algebraic-allegorical sublime, as opposed to the geo- metrical or the geometrical-symbolic sublime. Indeed, the symbol may be argued to always remain geometrical, as is suggested by Coleridge's description of it in terms of translucent geometrical optics--a key starting point of de Man's investigation opened by "The Rhetoric of Temporality" (BI 192). This algebraic-allegorical sublime may corre- spond to the sense Kleist made of Kant's work, from The Critique of Pure Reason on. This sense also reflects subtle gradations of proximities and differences, between perhaps ultimately "algebraic" (and "quantum- mechanical") reason and the ultimately "geometrical" judgment of the sublime in Kant, even if in a Kleist-like reading.
Alternatively, the quantum-mechanical "vision" just outlined and the quantum-mechanical formalization overall may indicate the space of differences, infinitesimal and radical (and sometimes simultaneously both), between Kleist's aesthetic, literary formalization and Kant's philosophical formalization of the vision of the sublime, which self- deconstructs into Kleist's. Either way, here, too, in order to find this more radical formalization, we might want to do what poets do, now also as philosophers. The literary, now defined in accordance with, or indeed as, radical formalization, is part and parcel of this understanding, or reasoning, also in Kant's sense of "reason. " The scheme just out- lined must, again, be seen as fundamentally correlative to the irre- ducibility of techne ? --the technology of measuring instruments, the technology of writing, or of reading, or of painting, such as Ce? zanne's. I would argue that the interaction of materiality and phenomenality, individuality and collectivity, singularity and regularity, in late Ce? zanne, considered by T. J. Clark in this volume conforms and perhaps for the first time introduces this "quantum-mechanical" vision or un-vision in painting. This may indeed be "the [impossible] truth of painting" for Ce? zanne, the truth of painting as ultimately algebra, not geometry. 24 This--that is, always working with and through techne ? and the ir- reducibility of techne ? --is what poets and quantum theorists with a po- etic bent do, and how they ultimately find everything, for example, the sublime or quantum mechanics.
I would now like to discuss further features of radical formaliza- tion, first, the question of randomness and chance. It is famously in- voked at the end of "Shelley Disfigured," where de Man writes: "The
Triumph of Life warns us that nothing, whether deed, word, thought or text, ever happens in relation, positive or negative, to anything that preceded, follows, or exists elsewhere, but only as a random event whose power, like the power of death, is due to the randomness of its occurrence" (The Rhetoric of Romanticism 122; emphasis added). This formulation reflects the nonclassical concept of chance as correla- tive to the irreducible lawlessness--singularity--of individual entities, such as random and discontinuous ("quantum") events here invoked. This concept of chance links the thought of earlier figures, such as Kleist and Shelley, to the twentieth-century thinking, mathematical- scientific (specifically in quantum physics) or philosophical, to which de Man's and related nonclassical concepts of chance belong. It is worth, however, recalling the classical understanding of chance before defining the nonclassical understanding of it.
Classically, chance or, more accurately, the appearance of chance is seen as arising from our insufficient (and perhaps, in practice, unavail- able) knowledge of a total configuration of forces and, hence, of understanding a lawful necessity always postulated behind a lawless chance event. If this configuration becomes available, or if it could be made available in principle (it may, again, not ever be available in prac- tice), the chance character of the event would disappear. Chance would reveal itself to be a product of the play of forces that is, in principle, calculable by man, or at least God. In other words, in practice, we have only partially available, incomplete information about chance events, which are nonetheless determined, in principle, by a complete architec- ture of necessity behind them. This architecture itself may or may not be seen as ever accessible in full, or even partial, measure. The presup- position of its existence is, however, essential for and defines the classi- cal view as both causal and realist, for this assumption of the ultimate causal architecture underlying randomness and chance brings classical causality and classical reality together. For example, if we cannot exactly--rather than only in terms of probabilities--predict how the dice will fall, or fully explain why a particular outcome has occurred, it is because the sum total of all the factors responsible is in practice un- available to us (from a particular movement of a human, or perhaps divine, hand to minute irregularities in the material makeup of the dice themselves). In principle, however, a throw of dice obeys the laws of classical, Newtonian physics (or else chaos theory, which would not, however, change the essence of the point, since chaos theory is classical at bottom). If we knew all such factors, we could predict and explain
Algebra and Allegory 73
74 Arkady Plotnitsky
the outcome exactly by using these laws, which would describe both individual and collective behavior, and (lawfully) correlate them, in ac- cordance with the definition of classical law.
The nonclassical understanding of chance, correlative to radical for- malization, is fundamentally different. Nonclassical chance is irre- ducible and irreducibly lawless not only in practice (which may be the case classically as well), but also, and most fundamentally, in principle. There is no knowledge, in practice or in principle, that is or will ever be, or could in principle be, available to us and that would allow us to assume chance to be the product of the imperceptible workings of ne- cessity behind it. Nor, however, can one postulate such a causal/lawful structural necessity as unknowable (to any being, individual or collec- tive, human or even divine), but existing in and by itself outside our en- gagement with it. This qualification is crucial, since, as just explained, certain forms of the classical understanding of chance allow for or are even defined by the latter assumption. The nonclassical chance is not only unexplainable in practice and in principle, but is also irreducible in practice and in principle. It is irreducibly lawless.
We recall that nonclassical formalization or law does not account for individual events (again, understood as phenomenal effects) in the way classical formalization does, thereby also correlating individual and collective configurations they consider. As we have seen, classical formalization is defined by this concept of law. By contrast, it is a law of nonclassical formalization that individual events are, generally, not comprehended by its laws or by law in general, certainly not in the way they would be in classical physics. Nonclassical formalization allows for the concept of individuality or discontinuity at the level of the phe- nomenal effects. Indeed, taken to the limit of the irreducible singularity of the individual, this concept defines nonclassical formalization. At the same time, however, it offers no law that would enable us, in prin- ciple (rather than only in practice), to predict with certainty the out- come of individual events or when some of them may occur, or their ultimate nature and emergence (at least only certain, partial aspects of such events). Just about any outcome is possible, anything can happen in any given case, and each case is ultimately unique, singular. In this, the nonclassical world (even that of quantum mechanics) is very much like life, to which--or, one might say with Shelley, to the triumph of which--we must ultimately submit.
This world, however, also contains more order and richer orders than the classical one. Statistical or other (collective) patterns do emerge
within it--at the level of phenomenological effects (which is perhaps as much as one can hope for, even classically). Indeed, this emergence of patterns, or that which allows for patterns, is what is truly strange about life, or, again, quantum physics--in view of the irreducible uniqueness of all (rather than only certain) individual events. It also follows that in these circumstances the individual effects involved are in turn reciprocally, if equally enigmatically, affected by this "con- spiracy" and, hence, by the collective, even though--this is what is most mysterious and enigmatic--each remains singular and lawless even in these circumstances. Or rather, they would so remain, if one could, in these circumstances, trace them as individual effects. In other words, such lawful collectivities and lawless individualities appear al- ways to be mutually exclusive or, in Bohr's terms, complementary. In the nonclassical world, the irreducibly unknowable coexists with a greater and more multiple knowledge, orders, and so forth. All our ac- counts, or indeed conceptions, of what gives rise to these orders or these dis-orders or non-orders (they cannot be considered as disorders either) can only be ultimately inadequate allegories, correlative to the formal deformalization of material effects. But then, as de Man argues, this ultimately "algebraic" quality has defined the practice of allegory all along, in part as the practice of reading, reading books or nature, or both, and as each other. In this sense, all allegories may well be the al- legories of (epistemologically nonclassical) reading.
And yet, not only possible but very real events--such as, say, those described in Kleist's Penthesilea or Shelley's The Triumph of Life-- leave us no choice, any more than quantum physics leaves physicists a choice here. These events occur and their underlying, or indeed un- underlying, unreality--the lack of any conceivable reality underlying them--does not make them any less real, indeed makes them more real, than any (classical) reality we can conceive of. In de Man's terms, any such event manifests (the singularity of) radical material occurrence-- "an occurrence, which has the materiality of something that actually happens, that actually occurs" ("Kant and Schiller," AI 132). I would argue that at stake here is the radical materiality and/as singularity of events, corresponding to nonclassical epistemology. The latter, accord- ingly, would also disallow one to strictly locate when and where such events actually occur. What actually occurs does occur, but the point or moment itself of this occurrence is indeterminable. It always takes place, in Lucretius's remarkable and remarkably precise phrase, "incer- to tempore--incertisque loci" (at an uncertain time and at an uncertain
Algebra and Allegory 75
76 Arkady Plotnitsky
place), and, we may add, at an indeterminate juncture of the efficacious processes of occurrence. 25
It is, as I have stressed from the outset, crucial that, nonclassically, irreducible lawlessness defines and makes singular all constitutive indi- vidual events, including those composing (what is perceived as) ordi- nary events, rather than only certain absolutely extraordinary events-- such as, say, Penthesilea's final encounter with Achilles, the encounter that dismembers his body and Penthesilea's mind and language; Rousseau's encounter with "the shape all light"; or Shelley's dreamlike encounter with Rousseau, in The Triumph of Life. Ultimately, every event, specific configuration, or historical trajectory will prove to be unique--irreducibly singular and lawless. Or else each can always be nonclassically reconfigured as composed of certain singular, lawless in- dividual elements, on the one hand, and of certain lawful collectivities on the other; that is, in some situations, lawful individual elements of the classical type may, once refigured nonclassically, always be decom- posed into lawless individual constituents. Viewed from this perspec- tive, such elements will no longer be subject to classical law as such but instead will belong to a nonclassical lawful collectivity composed by lawless individual elements. It is worth noting that this decomposition need not be unique, even in quantum physics. From the perspectives centered on lawful collectivities, this lawlessness of the individual may not matter or be perceived at all, since certain patterns, statistical or other, allow us to disregard or make us miss this singularity and law- lessness in the classical, or classical-like fashion. To avoid this, we must, "quantum-mechanically," deconstitute this pattern as classical and complementarily engage both the perspectives--that of lawful col- lectivities and that of lawless, singular individuality. The classical view, as Blake understood so well, erases particulars as particulars (i. e. , ulti- mate individual constituents of such configurations), either by way of general concepts or by means of ethical, political, and aesthetic prac- tices. Indeed, the present argument as a whole may also be seen as a disfigurative reading or at least an extension of Blake's idea of "minute particulars. "
We can now give a more radical and more rigorous meaning to de Man's conclusion in "Shelley Disfigured. " "The Triumph of Life warns us that, [ultimately], nothing [and not only certain things], whether deed, word, thought or text, ever [and not only sometimes] happens in relation, positive or negative, to anything that preceded, follows, or exists elsewhere, but only as a random event whose power, like the
power of death, is due to the randomness of its occurrence," and hence to the radical, irreducible singularity and discontinuity of this event, and ultimately any individual event or particular historical trajectory.