No More Learning

"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. As it makes the allegory irreducible in any representation, phenome- nalization, knowledge, and so forth, death, or life-death, becomes a model or, better, allegory, perhaps the allegory, for the structure of every event of life. We may indeed define Romanticism in terms of this disassembling magnification or, more accurately (it is, again, not a question of magnifying the small), radicalization of any configuration, classically individual or classically collective, into the irreducibly sin- gular, unique constituents--minute particulars--and the nonclassical reconstitution or reassemblage of such minute particulars (from a nec- essarily different perspective or set of perspectives) into richly ordered multiplicities. We may, accordingly, also speak of radical organization along with radical lawlessness and singularity. We must, however, keep in mind the very different epistemological status of the nonclassical patterns and laws, the "algebra" and "allegory" of their functioning, as opposed to, one might say, the symbolic "geometries" of classical thought.
This is, then, what such literary texts as Kleist's and Shelley's, or such philosophical texts as Kant's and Hegel's, or Ce? zanne's paintings, do. They offer us new--efficaciously nonclassical--patterns, orders, or laws, and un-patterning, unordering, and unlawfulness, and new ways in which these relate to each other. Of course, we need to read and understand these texts in great detail in order to study how all this takes place in them. Such texts and such readings also question the philosophical, aesthetic, historical, and other roles and limits of the nonclassical. For, as I said, the latter may ultimately prove to be yet an- other case of aesthetic (or counteraesthetic) ideology. These complexi- ties are, I think, the main reason why de Man does not close "Shelley Disfigured" with the randomness of death as the final warning of Shelley's poem. Instead he adds the following:
[The poem] also warns us why and how these events [that is, all events as singularities] then have to be reintegrated in a historical and aesthetic system of recuperation that repeats itself regardless of the exposure of its fallacy. This process differs entirely from the recuperative and nihilis- tic allegories of historicism [or aestheticism]. If it is true and unavoid- able that any reading is a monumentalization of sorts, the way in which Rousseau is read and disfigured in The Triumph of Life puts Shelley
Algebra and Allegory 77
78 Arkady Plotnitsky
among the few readers who "guessed whose statue those fragments had composed. " Reading as disfiguration, to the very extent that it resists historicism [or aestheticism] turns out to be historically more reliable than the products of historical archeology [or aesthetic ideology]. To monumentalize this observation into a method of reading would be to regress from the rigor exhibited by Shelley which is exemplary because it refuses to be generalized into a system. (The Rhetoric of Romanticism 122-23; emphasis added)
The last clause must, I think, be read as indicating that Shelley's rigor refuses to be generalized into a system that would not allow for the nongeneralizable. Shelley's poem possesses a great power of gener- alization and offers us very general aesthetic, historical, and political laws, a whole constitution even. So does Kleist's aesthetic formaliza- tion in U? ber das Marionettentheater. In question in both cases, how- ever, are nonclassical organizations of "fragments" and (when pos- sible) the "algebra" and "allegory" of their nonclassical formalization. The latter relates to no underlying pattern ("geometry") of wholeness, and yet (similarly to quantum mechanics) it offers us a better guess as concerns the history or aesthetic (or otherwise cognitive) structure of the configuration in question. In question, again, is only the impossibili- ty of the ultimate knowledge, the knowledge of the ultimate efficacity of the events in question and at bottom of all events. By putting this impossibly into play, however, both a greater richness and a greater re- liability of a "guess" become possible as well. But then (which may be the main point of de Man's last sentence) each nonclassical reading may itself remain unique, singular. The lessons of such texts or of their reading or of their grouping together (which apply to de Man's own texts, such as those assembled, in either sense, in Aesthetic Ideology) are complicated accordingly. Thus, de Man's essay (via Shelley's poem) and his work in general teach us a lesson of great caution, or indeed issue a stern warning (the word that occurs twice in this passage). The success (or a failure) of any strategy, general (such as methodological) or singular, classical or nonclassical, is never guaranteed, except per- haps that, as the saying goes, "in the long run we are all dead. " In other words, ultimately nothing survives, even though in the shorter run (which may be long, even indefinitely long, but is always finite) certain strategies, such as that of Shelley's disfiguration, may be more effective, but even this cannot be certain. These are inevitable conse- quences, "effects," of the nonclassical efficacity here considered.
In short, the texts in question offer us allegories of nonclassical knowledge, which may also be seen as "reading," and hence the texts in question as "allegories of reading" in this sense as well. By a quali- fied analogy (considered earlier) with quantum mechanics, such texts may be seen as material signifying "surfaces" in which certain peculiar material effects manifest themselves and make possible certain mani- fest phenomenological effects. As manifest, these effects may be pro- cessed (and the corresponding linguistic clusters read) classically. Some of these effects, however, and, especially, their overall configuration are meaningless, and some of them (certain, to borrow Gasche? 's phrase, "linguistic atoms") are meaningless otherwise, and remain, or some- times are made, meaningless nonclassically. In a nonclassical reading, all of these effects will be convertible into a nonclassical configuration of singular marks or, again, "linguistic atoms," although in practice this program is difficult to follow through. This is why such texts defy classical reading and resist any reading. This resistance even to read- ing is ineliminable and defines nonclassical reading or knowledge. 26 Such texts also enact both nonclassical epistemological configurations and their, inevitably allegorical, analytical explorations. They non- classically and multiallegorically read themselves. Kleist's essay, by its very structure, also enacts the nonclassical grouping of particular texts and is read by de Man as such. It introduces textual particulars/ singularities at all levels, from the "linguistic atoms" of the signifiers to large textual and narrative units, which allegorize each other. In other words, the texts in question allegorize their own reading, which can it- self only be allegorical. In the process they offer us allegories of non- classical reading and, hence, teach us the latter and/as nonclassical knowledge.
De Man, in a nonclassical ensemble of his own individual texts, reads these texts as such "allegories of reading," partly classical and partly (and most fundamentally) nonclassical, partly general and partly unique, and so forth. For de Man, nonclassical configurations can only emerge by way of reading, each such reading being, again, unique, rather than in terms of a (independent) conceptual architecture. These readings do contain and enable the latter as well and make it nonclassical. De Man opens his reading of Kleist with a quotation from Schiller:
I know of no better image of a beautiful society than a well executed English dance, composed of many complicated figures and turns. A
Algebra and Allegory 79
80 Arkady Plotnitsky
spectator located on the balcony observes an infinite variety of criss- crossing motions which keep decisively but arbitrarily changing direc- tions without ever colliding with each other. Everything has been arranged in such a manner that each dancer has already vacated his po- sition by the time the other arrives. Everything fits so skillfully, yet so spontaneously, that everyone seems to be following his own lead, with- out ever getting in anyone's way. Such a dance is the perfect symbol of one's own individually asserted freedom as well as of one's respect for freedom of the other. (Friedrich Schiller, Aesthetic Education 300; The Rhetoric of Romanticism 263; emphasis added)27
This is, in present terms, a classical and classically "geometrical" description, or at least a description that allows for a classical reading. As such it can be, and is by de Man, contrasted to Kleist's nonclassical "algebraic" allegories (which may also be juxtaposed to Schiller's "symbol" here), which disallow classical readings. Schiller's passage and his related elaborations are considered by de Man both in terms of the aesthetic formalization they offer and as Schiller's points apply to the formal structure of Schiller's text itself. The same strategy will be applied to Kleist's U? ber das Marionettentheater, with an exposure of the nonclassical character of the text and of its self-reading as an out- come. After a complex analysis, de Man arrives at a dance that is very different from the "strictly ballroom" dance of Schiller:
We have traveled some way from the original Schiller quotation to the mechanical dance, which is also a dance of death and mutilation. The violence which existed as a latent background in the story of the ephebe and of the bear now moves into full sight. One must already have felt some resistance to the unproblematic reintegration of the puppet's limbs and articulations, suspended in dead passivity, into the continuity of the dance: "all its members (are) what they should be, dead, mere pendula, and they follow the law of pure gravity. " (The Rhetoric of Romanticism 288)
The invocation of Newton's law of gravity, the paradigmatic classi- cal physical law, is of much interest and significance in the context of the present essay and in general. Both the question of the classical laws of physics and, hence, the formalization of nature, and how classical such formalization can in fact be are at stake. I cannot pursue these subjects here. I shall, however, return to the question of "falling," physically the defining phenomenon of gravity. In Einstein's general
relativity, his theory of gravitation, the fall is merely an aspect of the geometry of a space curved by gravitation. The analysis of this space, however, involves a very complex "algebra" (of the so-called tensor calculus) and the technology of rulers and clocks, which would open yet another chapter in the history of the book of nature, the role of al- legory in physics, and the reading of de Man. 28 De Man continues:
The passage is all the harder to assimilate since it has been preceded by the briskly told story of an English technician able to build such perfect mechanical legs that a mutilated man will be able to dance with them in Schiller-like perfection. "The circle of his motion may be restricted, but as for those available to them, he accomplishes them with an ease, ele- gance and gracefulness which fills any thinking mind with amazement. " One is reminded of the protests of the eyeless philosopher Saunderson in Diderot's Lettre sur les aveugles when, to the deistic optimism of the Reverend Holmes, disciple of Newton, Leibniz and Clark, he opposes the sheer monstrosity of his own being, made all the more intolerable by the mathematical perfection of his highly formalized intellect: "Look at me well, Mr. Holmes, I have no eyes. . . . The order (of the universe) is not so perfect that it does not allow, from time to time, for the produc- tion of monsters. " The dancing invalid of Kleist's story is one more vic- tim in a long series of mutilated bodies that attend on the progress of enlightened self-knowledge, a series that includes Wordsworth's mute country-dwellers and blind city-beggars. The point is not that the dance fails and that Schiller's idyllic description of a graceful but confined free- dom is aberrant. Aesthetic education by no means fails; it succeeds all too well, to the point of hiding the violence that makes it possible. (The Rhetoric of Romanticism 288-89)
At stake, then, is the possibility of formalization, aesthetic or other, under the condition of the radical, lawless, singularity and deformity-- monstrosity--that is quite manifest, materially and phenomenally. Both singularity and law--formalization--and their relationships and conflicts take a very radical form, parallel to the radical disfigurations of Shelley's The Triumph of Life. There is also a revealing textual par- allel. Here de Man invokes "a long series of mutilated bodies that at- tend on the progress of enlightened self-knowledge. " The essay on Shelley asks about our (according to the present analysis un-Romantic) aesthetic, historical, and other formalization of Romanticism: "For what we have done with the dead Shelley, and with all other dead bodies that appear in Romantic literature--one thinks, among many others,
Algebra and Allegory 81
82 Arkady Plotnitsky
of the 'dead man' that ' 'mid that beauteous scene / Of trees, and hills and waters, bold upright / Rose with his ghastly face . . . ' in Words- worth's Prelude (V. 470-72)--is simply to bury them, to bury them in their own texts made into epitaphs and monumental graves" (The Rhetoric of Romanticism 121). Thus, the Empedoclean algebra-allegory of the dismemberment of the body, (re)thought or (re)allegorized in "quantum-mechanical" terms, now applies within very broad limits. It can be further correlated with the quantum-mechanical allegories in- volved in the optics of Shelley's poem: the wave and particle imagery there; the manifest quantum-like discontinuity of events and textual atoms; the divestiture of marks and traces from all architectonics so as also to reveal their inaccessible (material efficacity); the radical materi- al aesthetics; the collapse of realism and causality; the "algebraic" and "allegorical" nature of whatever patterns or forms of order are left to us; and so forth. In other words, the nonclassical features of quan- tum physics and Shelley's poetic epistemology can be assembled and brought together in reciprocal allegories. 29 De Man's reading does not do this but is in part made possible by these reciprocities, as considered earlier in relation to quantum physics and its nonclassical formalization.
De Man explores the "algebra" of "the mutilated body" at some length in his late essays. The deepest and most significant instance may well be his analysis, considered earlier, of the Kantian architectonics in the third Critique. Accordingly, I shall only offer a few supplementary points. In a parallel gesture to his Kleist essay (cited by de Man), de Man invokes Diderot's Lettre sur les sourds and les muets in consider- ing the allegorization of the faculties of reason and imagination in terms of both the anthropomorphized dramatic conflict and the sacrifi- cially mutilated body. The invocation has Dionysian overtones and an invocation of the figures of Antigone and Iphigenia (AI 86-87). Then, he proceeds, via Kleist and Kant's first Critique, to a reading of Kant's architectonics and its self-de-architectonization in the Empedoclean terms of a mutilated body. The conclusion offers extraordinary elabo- rations on the allegorical algebra of Kant's text. De Man writes: "to the dismemberment of the body corresponds a dismemberment of lan- guage, as meaning-producing tropes are replaced by the fragmentation of sentences and propositions into discrete words, or the fragmenta- tion of words into syllables or finally letters" (AI 89; emphasis added).
One thus encounters the workings of radical materiality, or/as sin- gularity, both in the world and in the text. It would, however, be a mis- take to see both as merely (if at all) mirroring or mapping each other,
as de Man's usage of corresponds here might suggest, but should not. (It is difficult to be certain given the complexities of the concept and the very signifier of "correspondence" in de Man. )30 Instead, insofar as one wants to or can approach the world by way of a text (or a text by way of reading), the dismemberment or "decoherence" of language-- the divergence, ultimately irreducible and uncontrollable, of the mean- ing of figures, tropes, signifiers, and so forth, indeed of whatever carries meaning in a given text--manifests the irreducible inaccessibili- ty of the world or life through peculiar configurations of material and phenomenological effects. Accordingly, analogously to quantum- mechanical epistemology, the dismembered, decohered language or representation (i. e. , the configuration of the corresponding phenome- nal effects) does not map or otherwise represent them any more than "coherent" language and representations do, or reading represents a text. However, decoherent representations or allegories appear to be better suited to relate, via the algebra of allegory, to the world and life, or to read the kind of texts in question here. One might say that the radical (material) singularity of individual events of life and the radical inaccessibility of their efficacity find their proper expression or allegory in this circumstance of the dismemberment or decoherence of language and tropes.
Aesthetic formalization as radical formalization and the overall epistemological machinery in question also become, in an antithetical parallel with Schiller's classical text, enacted in Kleist's essay, at the level of figures or tropes. On the one hand, there is a certain "collec- tive" semantic field within which these figures and tropes function and which--that is, a more or less shared meaning or more or less coherent set of meanings--they obey. On the other hand, once rigorously con- sidered individually, or, again, in a certain ultimate decomposition, these figures and tropes can no longer be fully subsumed by such a meaning or a coherent configuration of meanings. Or, in the terms in- troduced earlier, they begin to decohere. Accordingly, one speaks of (an enactment of) a decoherence of figures and tropes, or of all lan- guage, in a nonclassical text, such as Kleist's, or Shelley's, or Kant's, if in the latter case, to some degree, against other forces, conceptual and tropological, of Kant's text. 31 This decoherence or dissemination (in Derrida's correlative sense) defines the functioning of virtually all fig- ures and tropes in these texts. They give the materiality of the signi- fiers, "linguistic atoms," a formal aesthetic structure or un-structure we encounter in the case of quantum mechanical marks, as considered
Algebra and Allegory 83
84 Arkady Plotnitsky
earlier. Or rather, the materiality of the signifier in de Man's sense is this un-structure, which then requires a very different "algebra" of for- malization. De Man writes:
[W]hen, by the end of the tale, the word Fall has been overdetermined in a manner that stretches it from the theological to the dead pendulum of the puppet's limbs to the grammatical declension of nouns and pro- nouns (what we call, in English, the grammatical case), then any com- posite word that includes Fall (Beifall, Su? ndenfall, Ru? ckfall (#46) or Einfall) acquires a disjunctive plurality of meaning.
C's story of the puppets, for instance, is said to be more than a ran- dom improvisation: "die A? usserung schien mir durch die Art, wie er sie vorbrachte, mehr als ein blosser Einfall. " As we know from another narrative text of Kleist ["U? ber die allma? hliche Verfertigung der Gedanken beim Reden"], the memorable tropes that have most success (Beifall) occur as mere random improvisation (Einfall) at the moment when the author has completely relinquished any control over his meaning and has relapsed (Zuru? ckfall) into the extreme formalization [emphasis added], the mechanical predictability of grammatical declension (Fa? lle).
But Fa? lle, of course, also means in German "trap," the trap which is the ultimate textual model of this and of all texts, the trap of an aesthetic education which inevitably confuses dismemberment of language by the power of the letter with the gracefulness of dance. This dance, re- gardless of whether it occurs as mirror, as imitation, as history, as the fencing match of interpretation, or in the anamorphic transformations of tropes, is the ultimate trap, as unavoidable as it is deadly. (The Rhetoric of Romanticism 289-90)
In introducing "the dismemberment of the body" toward the end of "Phenomenality and Materiality in Kant," de Man speaks of the word Glieder in Kant as "meaning members in all the senses of the word, as well as, in the compound Gliedermann, the puppet of Kleist's Marionettentheater" (AI 88). In the same paragraph de Man adds a playful reference to Montaigne's "cheerful" invocation of "Monsieur ma partie," further extending the multilingual decoherence--or again, coherence-decoherence--of tropes by dismembering all members in- volved in their constitution. "Fall" is a decisive figure and concept in Kleist, including in defining any stability, formal--linguistic or mathe- matical--or physical, for example, monumental. It is equally decisive for Shelley or Keats (whom de Man discusses in this context in "The Resistance to Theory"), or de Man, who brings all three together, al-
though, interestingly, he does not consider "fall" (or, again, dance), as he could, in Shelley, in the way he does in Kleist or Keats. It would not be possible to consider here the relevant physics, for example, the way gravity bends even light itself (which would bring all three figures and texts together in yet another way). These connections must be relevant to de Man's reading, even if only because from Newton to Einstein and beyond they changed our sense of fall or (they are perhaps ultimately the same) the world. Kleist once said of the arch, another great figural model or allegory: "the arch stands because all the stones want to plunge at the same time," and, I would add, with the preceding analy- sis in mind, each following its own trajectory. We know, of course, that a random, lawless event, such as an earthquake in Chile, can bring the arch down in any event. What Kleist tells us here, however, is that even the standing arch is a kind of dance in a gravitational field. We all know or assume, naively, that, in dancing, a fall is the least graceful event, or the least graceful--and the least formalizable--form of dance. It is more difficult to realize, as Kleist did looking at dancing mari- onettes, that dance is perhaps only a graceful form of falling (always commanded by many a gravitational field of our life, or death) and that grace itself is, in each case, a very singular, and very difficult, com- bination of fall and dance, just as is the grace of Kleist's or Shelley's writing--their dancing pens, without ever falling, except as a form of dance, albeit on thin ice. As Nietzsche tells us, however: "Thin ice is paradise for those who skate with expertise. "
NOTES
1. The use of the term concept requires caution here, especially in applying it to Paul de Man's work.