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Romanticism and Complexity

Chaosmic Orders: Nonclassical Physics, Allegory, and the Epistemology of Blake’s Minute Particulars

Arkady Plotnitsky, Purdue University

Chaos Umpire sits, And by decision more imbroils the fray By which he Reigns: next his high Arbiter Chance governs all. Into this wild Abyss, The Womb of Nature, and perhaps her Grave, Of neither Sea, nor Shore, not Air, nor Fire, But all of these in thir pregnant causes mixed Confus’dly, and which this must ever fight, Unless th’ Almighty Maker them ordain His dark materials to create more Worlds

Milton, Paradise Lost, Book II, 907-16


. . . in fury of Poetic Inspiration, To build the Universe stupendous, Mental forms Creating

Blake, Milton, Book the Second, 19-20

And the dim Chaos brightened beneath, above, around! Eyed as the Peacock

Blake, Jerusalem, Chapter 4, Plate 97

  1. 1. Nonclassical Physics and the Artists’ Book

  2. This essay proceeds along the following three lines of inquiry:

    1. an investigation of the epistemology of Blake’s poetic vision and practice;
    2. an exploration of the connections between Blake’s epistemology and key epistemological aspects of quantum physics and of chaos theory; and
    3. a discussion of Blake’s illuminated manuscripts as the artists’ books—the art form that combines the self-conscious investigation of the conceptual and material form of the book with the interplay of the literary and the visual within it, and indeed pursues the former through the latter.
  3. What brings these subjects together? First of all, as I shall argue here, the scientific theories in question and Blake’s vision and practice share certain key epistemological features. These epistemological considerations allow one to make a more rigorous conceptual argument, as opposed to looser connections between Blake’s work and these theories that are more commonly found in literature on Blake.[1] The nature of this commonality is complex. Quantum mechanics and chaos theory have fundamental epistemological differences. These differences split the relationships between them and Blake’s epistemology in relation to them, and reflect the ambivalence of Blake’s epistemology itself. The connections themselves in question are not accidental. The epistemology of these theories and those found in Blake’s work or Romanticism and related cultural phenomena, such as German Idealism, have a number of historical genealogies in common, which would require a separate discussion. But even if these connections between Blake and modern science were of a more contingent nature, both types of epistemological thematic could still, and here will, serve to illuminate each other.

  4. Extending and ultimately (epistemologically) radicalizing Blake’s vision of "minute particulars" and of (indeed always in) their organization, I shall specifically relate the shared epistemological features to a certain concept of organization, which I shall here term "radical organization." According to this concept, certain collectivities or multiplicities may, in certain circumstances, be subject to organization, while individual elements comprising such multiplicities are, in general,unorganizable or lawless. In the limit cases of radical organization, this dis-organization or lawlessness is more radical than that envisioned by Blake for minute particulars and their organization (although this may depend on one’s view of what is radical). Following Paul de Man’s view of allegory, such limits cases will here be seen as allegorical. Accordingly, throughout this essay I shall use the term allegory primarily in de Man’s sense. The latter entails a particular form of epistemology, correlative to the epistemology of quantum physics, specifically in Bohr’s interpretation, known as "complementarity," which I would argue to be the most radical among a host of available interpretations and which I shall follow here. I shall explain de Man’s view of allegory in detail later. Briefly, according to this view, allegorical representation ultimately (there may be more accessible intermediate represented strata) relates to that which cannot be represented or even accessed by means of this representation and, conceivably, by any means that are or will ever be available to us. The same epistemology defines Bohr’s complementarity, thus making it (epistemologically) an allegorical theory.

  5. It may be useful to introduce from the outset key pertinent elements of the scientific theories involved, especially as concerns their relationships to the ideas of chance and chaos, and the concepts of (physical) reality correlative to them, which are my main subject here (these theories have other aspects). I shall explain the application of the concept of "radical organization" to quantum mechanics later. I shall also postpone a discussion of fractals, which is a subfield of chaos theory (dealing with the repetition of the same pattern on different scales, indeed specifically on an ever-diminishing scale). I shall, first, outline the classical understanding of chance in physics and in general, which equally pertain to chaos theory (it differs from classical physics, including classical statistical physics, along other lines). Then, I shall explain the nonclassical concept of chance, such as that found in quantum physics. I here see a theory, such as classical physics, as, ontologically, causal when the state of the systems it considers (these systems may, again, be idealized) at any given point is assumed to determine its behavior at all other points. Classical physics is also, epistemologically, deterministic insofar as our knowledge of the state of a classical system at any point allows us to know, at least in principle and in ideal cases, its state at any other point. Not all causal theories are deterministic in this sense. Classical statistical physics or (differently) chaos theory (which is, in most of its forms, classical and is sometimes a direct extension of Newtonian mechanics) are causal or at least may be interpreted as such. They are, however, not deterministic even in ideal cases, in view of the great structural complexity of the systems they consider. This complexity blocks our ability to predict the behavior of such systems, either exactly or at all, even though we can write equations that describe them and assume their behavior to be causal.Quantum mechanics is irreducibly noncausal rather than only indeterministic.

  6. Classically, chance or, more accurately, the appearance of chance is seen as arising from our insufficient (and perhaps, in practice, unavailable) knowledge of the total configuration of forces involved and, hence, of the lawful necessity that is 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 practice), 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 by God. Most classical mathematical or scientific theories and the classical philosophical view of probability are based on this idea: in practice, we have only partially available, incomplete information about chance events, which are nonetheless determined by, in principle, a complete architecture of necessity behind them. This architecture itself may or may not be seen as ever accessible in full or even partial measure. The presupposition of its existence is, however, essential for and defines the classical view as causal and, by the definition given earlier, realist. On this point classical reality and classical causality come together; or rather this point (the assumption of the ultimate underlying causal architecture of reality) brings them together[2] For example, if we cannot fully (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 unavailable to us. These factors may extend from a particular movement of a human (or perhaps divine) hand to minute irregularities in the material make up 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 change the essence of the point in question). If we knew all such factors, we could predict and explain the outcome exactly by using these laws, which would describe both individual and collective behavior, and (law-fully) correlate them, in accordance with classical physical (or philosophical) laws.[3]

  7. Subtle and complex as they may be, all scientific theories of chance and probability prior to quantum theory, and many beyond it, such as chaos theory, and most philosophical theories of chance, from the earliest to the latest, are of the type just described. They are classical. Most of them are also, and, as was just pointed out, often interactively, realist. In particular, due to the complexity in the behavior of the systems involved, chaos theory prevents us from making deterministic predictions of this behavior, in other words, it is not a deterministic theory, as standard, Newtonian, (rather than statistical) classical physics is. That does not mean, however, that there is no underlying causal dynamics defining the behavior, quite the contrary, it depends on the latter. In other words, the latter type of theory is causal, according to the terminology adopted here. Causality and order underlie randomness and chaos. (As will be seen, in quantum physics these relationships are reversed and enriched: randomness and chaos underlie and constitute the efficacity of both manifest order and manifest chance.) Certain (complex) patterns of order, which we can sometimes partially access, as in the case of such fractal entities, such as the Mandelbrot set, are manifestations of this underlying causality and order. One can see these patterns in, by now famous, pictures and computer simulations. Indeed a better name for it would be the order theory, the theory of certain complex and unpredictable forms of order. In Roger Penrose’s summary:

    Chaotic systems are dynamically evolving physical systems, or mathematical simulations of such physical systems, or just mathematical models …, in which the future behavior of the system depends extremely critically upon the precise initial state of the system. Although ordinary chaotic systems are completely deterministic [causal, in present terminology] …, they can, in practice, behave as though they are not deterministic at all. This is because the accuracy according to which the initial state needs to be known, for a deterministic prediction of its future behavior, can be totally beyond anything that is conceivably measurable. (Penrose 21-22)
  8. An example that is often quoted in this connection is the detailed long-range prediction of the weather. The laws governing the motion of air molecules, and also the other physical quantities that might be relevant to computing weather, are all perfectly well known. However, the weather patterns that may actually emerge, only after a few days, depend so subtly on the precise initial conditions that there is no possibility of measuring these conditions accurately enough for reliable predictions. Of course the number of parameters that would enter into such a computation would be enormous, so it is perhaps not surprising that prediction, in this case, might prove to be virtually impossible in practice.

  9. Thus, in the case of the theories assembled under the rubric of chaos theory, indeterminism arises due to the sensitive dependence on the initial conditions. That is, a small change in such conditions can lead to a big change in the behavior of the system (sometimes also known as the butterfly effect). The equations themselves, however, are assumed to exactly map the behavior of these systems.[4] As Penrose observes, "chaotic behavior can occur also with very simple systems" (22), as Henri Poincaré, sometimes seen as the creator of chaos theory, discovered in his analysis of the behavior (proven by him to be chaotic) of three or more bodies in a gravitational field, say, the Sun, the Earth, and the Moon. Newtonian physics is both causal and deterministic, while classical statistical physics and chaos theory are causal but not deterministic.

  10. The latter two theories differ in other respects, specifically insofar as classical statistical physics enables good statistical predictions, which are impossible in chaos theory. In contrast to chaos theory, in classical statistical physics the origins of the statistical nature of our predictions is specifically the multiplicity of objects involved, such as molecules of a gas, each behaving according to the nonchaotic or not necessarily chaotic equations of Newtonian mechanics. Accordingly, the formulas of statistical physics, enabling our statistical predictions, do not describe the (causal) behavior of these objects as such, even as they generally presuppose such behavior, again, in contrast to standard Newtonian mechanics, even in idealized situations. Thus, in contrast to chaos theory, in this case we have in principle two sets of descriptions: one maps the actual behavior of the objects involved, the other does not, while it depends on this behavior in establishing the counting procedures that enable statistical predictions of the theory. The equations of chaos theory "predict" the unpredictability of the physical behavior of the systems in question (in spite of the underlying causality), while the formulas of classical statistical physics allow one to make good statistical predictions. Both of these theories, or the standard Newtonian mechanics, are also realist. Realist theories in physics (or elsewhere) may be described most generally by the presupposition that their objects in principle possess independently existing attributes (such as those conceived by analogy with classical physics) whether we can, in practice or in principle, ever describe or approximate them or not.

  11. Now, the nonclassical understanding of chance and reality (or the lack thereof), which defines quantum theory in particular, is fundamentally different. Nonclassically, chance is irreducible not only in practice (which, as I have explained, 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 eliminate chance and replace it with the picture of necessity behind it. Nor, however, can one postulate such a (causal/lawful) economy as unknowable (to any being, individual or collective, human or even divine), but existing, in and by itself, outside our engagement with it. This qualification (which entails, and in quantum mechanics results from, the suspension of realism at the ultimate level of description) is crucial. For, as I explained above, some forms of the classical understanding of chance allow for and are indeed defined by this type of (realist) assumption. By contrast, nonclassical chance, such as that which we encounter in quantum physics, is not only unexplainable in practice and in principle but is also irreducible in practice and in principle. It is irreducible to any necessity, knowable or unknowable. It is, in David Bohm’s words, irreducibly lawless (73).Anything, well almost anything, can happen in a given individual event, in which respect quantum mechanics is indeed very much like life. In other words, quantum physics and analogous theories elsewhere are neither causal, nor deterministic, nor, indeed correlatively, realist, in any of the senses described above.

  12. Quantum theory requires, and depends on, the concept of the individual physical event. The individuality of such events is essential, in the strict sense of being irreducible. It is in part this concept that defines quantum mechanics as quantum, even though it has, Bohr argues, to be given a complex (and in particular nonrealist) architecture. At the same time and by the same token, quantum mechanics and its mathematical formalism offer us no laws which would enable us to predict with certainty the outcome of such individual events, or when some of them might occur. Nor, in dealing with quantum statistical multiplicities, can particles be seen as individually distinguishable, as they can and must be in the case of classical statistical physics. The laws of quantum mechanics rigorously allow for the irreducible individuality, the irreducible "un-lawfulness" or "lawlessness" of individual quantum events. By contrast the behavior of quantum collectivities is ordered. The nature of this order, it follows, is more complex and enigmatic, and indeed the law of quantum mechanics makes it irreducibly inaccessible. Because of this order analogously to classical statistical physics and in contrast to chaos theory, excellent statistical predictions are possible. Quantum theory is, thus, a theory of (irreducibly) statistical predictions, correlations between macroscopically observed experimental events, and so forth, rather than a theory describing individual objects and their behavior in the way classical physics does. Accordingly, as Bohr says, "the recourse to probability laws under such circumstances is essentially different in aim from the familiar application of statistical considerations as practical means of accounting for the properties of mechanical systems of great structural complexity" (2: 34). Thus, chance and, correlatively, the suspension of realism appears to be in practice irreducible from any account of the physical world.

  13. The preceding discussion deals with considerations of a more general nature and is applicable to other Romantic figures or elsewhere, and in recent years these considerations have been applied, with a varying degree of success throughout the humanities, especially in the fashionable case of chaos theory. By contrast, Blake’s making his illuminated manuscripts into artists’ books may be seen as a uniquely Blakean contribution, most significantly for this essay insofar as they serve as both the practice and an allegorical model of the epistemology in question. This contribution is also crucial to a different, more aesthetic or cultural (rather than epistemological) tradition, that of the artists’ book.

  14. Blake is often seen as one of the inventors, if not the inventor, of the genre. [5] While this view is amply justified, Blake himself would not see it quite in this way. First of all, while he would see his own or any artistic work (book or not) as, by definition, an invention, any such invention, or the event of such an invention, would be seen by him as absolutely unique, singular, and thus unrepeatable. It could be, and for each of his illuminated manuscripts was, an invention of genre, but the genre, too, would be unique each time and hence in turn unrepeatable. This would have to be said already of each copy (each different) of his illuminated manuscripts, say, of the eight copies of The Book of Urizen—eight different (artists’) books, eight different genres of the (artists’) book.[6] This view is correlative to the concept of radical organization (in a Blakean version), which here applies at the level of more comprehensive entities, such as books.

  15. Secondly, Blake knew well that he was not the creator of the genre of the artists’ book (or what we now so call), any more than of the genre of the book itself. Of course—and this is important—in Blake’s view, anything that could, in truth, be a book or a genre of the book, could only be an artists’ book, a de facto illuminated manuscript, or something that is allegorizable as one. This is the case not merely because Blake was well aware of his predecessors in the genre of illuminated manuscripts (which are seen as major precursors of the present-day artists’ books). Rather, if there were a single inventor of the genre of the book, it would have to be God, the creator of the Book of Nature or (Blake, we recall, is suspicious of the very idea of Nature, as anything outside the shaping workings of Spirit) of the World. This Book would be for Blake a book in his sense, an illuminated manuscript. Indeed, to some degree reversing the preceding proposition (a customary move for Blake), this Book is created by God, each time the work of the Poetic Genius in man is activated, analogous to the way the Last Judgment occurs in Blake’s vision. In a way this is the structure of Blake’s phenomenology, which I shall explain in more detail below.

  16. It would not be possible to trace here the genealogy of the topos of the Book of Nature.[7] It is worth recalling, however, that for Galileo the book of nature is written in the language of mathematics, here specifically geometry: its characters are circles, triangles, and other geometrical figures. So conceived even the Book of Nature is, in a way, an artists’ book, although the epistemology of physical theories here mentioned would radically transform the topos, in (varied) proximity to Blake’s epistemology of the Book. The relationships between Galileo’s and to the Medieval allegories of the book of nature, and to Medieval books themselves, in particular illuminated books, are all pertinent here. Even more significant are the twentieth-century versions and dislocations of the topos, such as Mallarmé’s "Book"; Blanchot’s concept of the "absence of the book"; Derrida’s economy of différance, writing, dissemination, and so forth, which led him to proclaim "the end of the book and the beginning of writing"; and de Man’s framework of allegory and rhetoric. All of these are also positioned in relation to the joint critique of writing, poetry, and painting within Plato’s scheme in the Republic, while (this is sometimes forgotten) they also refigure "the book" within a richer and more complex dynamics of textuality, rather than only dislocating or suspending the topos. I can only acknowledge these connections without being able to discuss them. I shall, however, further comment on Plato. My point is that Blake’s vision and practice still offer some among the richest and most radical forms of de-figuring and refiguring of the topos of the book and of the artists’ book, as the illuminated manuscript. At the refigured limit, both the book and the artists’ book are indissociable for Blake. As such it also forms an allegorical model, perhaps the allegorical model, of all liberated, reformed (aesthetically, politically, or erotically) human perception and cognition. In this sense, my (more radical than usual) claim here is that rather than being only an inventor or, at least, a co-inventor, of the genre of the artists’ book, Blake conceives of "the artists’ book" (as illuminated manuscript) as the primary model of all human perception and knowledge. The moment—even as short as the blink of the eye—we see, or truly see (in Blake’s sense), the artists’ book emerges. This also means, however, that our extended or, in Blake’s terms, "infinite" perception (to the degree the latter term may still apply to this, in the deep sense, constructivist machinery) of the book must be seen as defined by Blake’s epistemology.[8]

  17. Thus, the two traditions in question—epistemological and cultural-aesthetic—become linked in turn. It would not be possible to consider their other intersections without extending this essay too far beyond its intended scope. I would argue, however, that they come together, and, again, illuminate each other in Blake not only for the first time but perhaps still most powerfully. Blake’s concept of the artists’ book may be still the most radical yet available or at least as radical as any yet available. As such this concept and Blake’s work itself establish a radical epistemological and conceptual agenda for the genre which is far from yet fulfilled.

    2. The Letter and the Book

  18. Although one can begin with Blake’s earlier works, my point of departure in considering this agenda is a specific textual juncture of The Marriage of Heaven and Hell, that links two, as Blake calls them, "memorable fancies."[9] The first (Plate 13) describes Blake’s "dining" with the Prophets Isaiah and Ezekiel, the authors of arguably the two greatest prophetic books of the Bible. The plate also (re)introduces Blake’s concept of "Poetic Genius"—the primary principle of human perception, found in every human being, but often dormant or inactive, or rather (since no perception would be possible without it) not properly put to work, as an active principle. It is especially disabled in contemporary man, who is enchained by organized religion and its extensions or equivalents, such as contemporary legal and political institutions, or post-Newtonian mathematics and science (as Blake sees them).

  19. The second "memorable fancy" (Plate 15), "A Printing House in Hell," offers an allegory of the liberated or awakened, activated (in the direct sense of the term), workings of Poetic Genius. It anticipates much vaster allegories of this process found in, among other works, Milton and Jerusalem, most directly the closing line of the latter (Plate 98), on which I shall comment presently. Indeed, each of the latter works as a whole should be seen as this type of allegory, as should in fact be The Marriage of Heaven and Hell. It is an allegory (even if not, for Blake, quite in de Man’s sense) of human perception, creation and transmission of knowledge—as the production, printing and dissemination of books, specifically (as) engraved, illuminated manuscripts or/as artists’ books, such as Blake’s. Making (also in the original sense of poesis and tekhné) or reading such a book is, interactively, both an actual form of liberated perception and knowledge, and an allegorical model for the workings of Poetic Genius.

  20. The two plates are bridged by Plate 14, which, preparing the Printing House plate, ends with a call for "cleansing the doors of perception." The process would make "every thing … appear to man as it is, infinite" (emphasis added). Blake’s "infinite" is a complex concept (but then no simple concept of infinity appears to be rigorously possible) and I shall delineate its structure or architecture, specifically, as the organization of minute particulars, below. For the moment, the expanded vision in question is contrasted to the un-reformed, closed or finite, vision "of all things thro’ narrow chinks of his cavern." The latter phrase is an allusion to Plato’s cave in Book VII of the Republic, via Locke’s passage on the darkened chamber of the mind, itself already alluding to Plato.

  21. It is this epistemologically charged allusion to Plato’s Republic at this particular juncture—which is also a juncture of the prophetic book and Blake’s illuminated manuscript (as the artists’ book)—that especially interests me. I am, however, primarily concerned with what the Republic has to say about poets and painters, with the cave allegory itself, although it remains important and must be kept in mind. For example, not unlike some of Duchamp’s works, Blake’s designs can be seen as shadow-like projections of higher-dimensional spaces (that is, spaces of dimension four and higher, ultimately perhaps infinite-dimensional spaces) of extended vision onto the two or three-dimensional spaces of his designs. Of even greater significance is a particular shape or structure of the spaces that his designs are aimed to convey. Although these (speaking broadly) non-Euclidean geometries are found throughout Blake’s illuminated manuscripts and are often suggested or even entailed by his texts, the texts and the spaces of the designs of Europe and, especially, of The Book of Urizen and Milton offer arguably the most spectacular examples. They become a kind of "finite" figuration of the Blakean "infinite." This figuration, as will be seen, occupies a complex space between allegory and symbol in de Man’s sense, and its epistemology is defined accordingly. The more general connections between mathematics and specifically geometry (their epistemology, phenomenality, and materiality) and technology, tekhné, specifically the technology of writing (also in Derrida’s sense), is an immense subject, which cannot be addressed here.

  22. Now, the poets are famously exiled. In a rough outline (which cannot do justice to either Plato or his critics), this exile takes place via their metaphorical or allegorical identification with painters, defined (again, exaggerating) as shameless and useless imitators, in contrast to the divine creator, or even to carpenters. Plato famously illustrates the situation by the order of the three beds—the first created by God (and there can only be one, since God only creates, never imitates), the second is built by a carpenter, and the third is imitated (from the carpenter’s bed) by a painter. (Throughout Plato, though, speech and writing are placed in a parallel and indeed related order, which, it may be shown, also makes the order of the three beds into the order of three books.) Carpenters are at least useful, if not as creative as God or (by implication), at the human limit, philosophers.[10] As will be seen, at a certain level, the fundamentally creative significance of philosophical thought (albeit now pursued by means of art) is retained by Blake’s view, which is, on this point, analogous to Shelley’s argument in A Defence of Poetry. This argument is applied by Shelley to Plato himself and making him a poet, along with (and prototypically or even archetypally) other philosophical creators, the creators of new philosophical concepts (in the above sense) or even, as Deleuze and Guattari would have, "the concepts that are forever new" (12). Nietzsche would call them "philosophers of the future," a concept analogous to Shelley’s idea of poets as creators of new forms of thought and/as life in any domain—literary, philosophical, religious, legal, political, or other, including mathematical and scientific. For the moment it is the negative conjunction of poetry and painting in Plato that is especially significant. From, as it were, the prophetic wilderness of poetic exile, it is their conjunction, now made into a positive force, activating or activated by Poetic Genius, that defines Blake’s vision and work, or his books. His books would be seen by him as the work of all three or all four—God or at least the divine portion of man, the carpenter (the engraver), the artist and, and as, the poet. The coming together of all four is what, according to Blake, enables Poetic Genius in man and the poetic "perception" of the infinite. Blake’s prophetic call from the wilderness is: change your perception so to make its workings akin to Blake’s production of illuminated manuscripts, artists’ books, and all that they imply or allegorize, materially, phenomenally, or epistemologically, by their texts and designs in all of their aspects.

  23. The book is, thus, conceptualized and materialized by Blake as a model or an allegory of all expanded human perception. From this perspective, reversing Derrida’s famous argument, we may speak of the end of writing and the beginning of the book.[11] This reversal, however, has the character of a double negative that does not return to the original positive, especially to the idea of the book that is "short of" writing in Derrida’s sense. In particular, each "minute particular" of writing (ultimately in the sense Derrida gives the term), say, a "letter," or in Blake’s own words in Jerusalem, "every Word & Every Character," is structured as a book and as an artists’ book—an illuminated manuscript. By the same token, each is a "Visionary form Dramatic," and indeed each is also "Human," and a human form, body and soul, "according to the Expansion and Contraction," and also the city, a kind of "Jerusalem" of its own (Jerusalem, Plate 98: 35, 27). I shall further comment on the conjunction or superimposition of the body, the book, and the city in Blake, at the micro (minute particulars) and the macro levels below.

  24. The (visually) allegorical conjunction of writing and drawing, and indeed their passing into each other, is pervasive in Blake, but this is a relatively minor point here. Specific elements involved may, of course, be crucial, for example, when one needs to read written characters as human bodies ("human forms"), cities, or books themselves, and vice versa. Or, again, each element of writing, say a letter, would have to acquire the character of the book (Blake could hardly be unaware of the pun, as the above quotation would indicate), often superimposing each such micro-book, almost a microchip-book, on the body and the city. We make take advantage of Lacan’s famous pun and use it literally—each letter of Blake’s writing is not only expandable into but is a letter——a long, perhaps infinite, epistle to his readers. (Blake could hardly be assumed not to have thought of this pun either.) This is of course not to say that such minute particulars become merely isolated macro-structures. This is true only insofar as they become divested, Blake would say "liberated," from conventional reading, before, or rather as, they are radically reorganized into a new order as expanded minute particulars, as they form a radical organization. The "alphabetization" (with the Hebrew alphabet) of Blake’s illustrations for The Book of Job could serve as the most immediate allegory of this process, an allegory of Blake’s writing and of reading Blake, along with, and even as, the Bible, the book, itself. The work allegorizes the letters (characters, epistles, literature, writing, and so forth) no less than the Hebrew alphabet itself does the Bible in Blake’s design. Indeed, both allegorizations must be seen as reciprocal as, at every level, from letters to the books, a "convers[ation] together in Visionary forms dramatic," each element being itself already such a form—a gigantic, "infinite," living fabric (textum) of organized minute particulars (Jerusalem, Plate 98:28).

  25. From this perspective, each individual "element," each minute particular, of Blake’s design (using this term in referring to the graphics of his texts as well) may in part also be conceived on the model of Leibniz’s monads. One may also view from this perspective Blake’s persistent quasi-fractal (I shall explain the term presently) use of the shape(s) of the human body from ever more minute (minute-particular) to ever increasing scale. This vision would culminate in the infinite body of Albion in Jerusalem, the city of Blake’s vision and the poem (Jerusalem, Plates 98-99), or, ultimately, the body of Christ, defining the cosmology or chaosmology of Blake’s Universe.

  26. This deployment of the human body may be seen as an ironic reversal of Leibniz, since, according to Leibniz, monads are souls, or proto-souls. On the other hand, Leibniz’s monads do possess bodies, materiality, and a complex material, as well as spiritual, architecture (and textuality), while Blake’s bodies-monads are also souls, spiritual forms. "Architecture" can be here used in either sense, as the body and the city, and indeed the book, come together in Leibniz’s Baroque (especially via Deleuze’s reading) via and in Blake’s Romanticism, again, most immediately and powerfully in Jerusalem.[12] Blake’s "Man has no Body distinct from his Soul for that calld Body is a portion of Soul discerned by the five senses, the chief inlets of Soul in this age" (The Marriage of Heaven and Hell, Plate 4) brings Blake closer to Leibniz (specifically monadology) than it may appear even to Blake himself, however radical the differences between them in other respects may be.

  27. The title page of The Marriage of Heaven and Hell is a spectacular early example of this body-monadology, with a characteristically Blakean erotic and enriching twist: the embracing couples populating the plate nearly dissolve into the foliage of trees (of knowledge?, of life?, of love?, of liberty?) and the foliage into the letters of the word "marriage" of the title. I would argue that, if there is a single ultimate "shape" (quasi-fractally) defining Blake’s world, from minute particulars to its ultimate scale, it would, rather than a single body, be an "embrace" of two bodies, also interfusing the body and the soul within each. This process can then be unmonotonously extended into infinity, in both directions, thus reinscribing or reembodying, or re-embracing, bodies from within and from without into complex multiplicities, from within which embraced bodies or, sometimes, single bodies (or what we see as such) emerge. This process is, I would argue, parallel to Leibniz’s monadological vision, again, especially in Deleuze’s reading. It adds the “embrace” structure to the latter (and thus also eroticizes and enriches it), but retains its fundamentally chaos-theory-like epistemology—realist and causal (but not deterministic)—rather than an epistemology that would be quantum-theory-like, allegorical (which ultimately suspend the possibility of vision). For, each monad constitutes a world of its own, each is the Book of Nature or of the Spirit, even as all monads jointly contribute to the material and spiritual constitution of the World, as the soul, the body, the city, and the book—the artists’ book.[13] Thus understood, "embrace" may be seen as the general structure of the Blakean superimposition, such as that of the body, the book, and the city, with Milton’s embrace of Angels in the cosmic dance in Paradise Lost as, arguably, the main literary prototype or archetype. Milton and Jerusalem appear to confirm this view and this archetype as well, both textually, specifically in the closing elaborations just mentioned, and structurally and conceptually as a whole. In general, later prophetic books take the overall (embrace) monadology just described to its limits at every scale—textually, conceptually, and pictorially. This is the order (in either sense) of Blake’s minute particulars and (and forming) the Blakean infinite. This order makes the world and our vision, and/in their interactions simultaneously both contract from one perspective and expand from another, more visionary, perspective, "expelling" chaos and replacing it with the order of minute particulars.

  28. Blake’s designs, or the world, may of course be contracted into classical arrangements of primitive elements or impoverished or empty (rather than rich, minute-particular) singularities, such as the point particles of Newtonian physics, by unregenerated perception or knowledge, which (re)assemble the world on the basis of this reductive (in either sense) vision. This process is allegorized in the "minute-particular" plates of Jerusalem (such as Plate 45 of Chapter 2 and Plate 55 of Chapter 3, Plate 45). Each "Minute Particular" of Albion is "hardened" by a Newtonian vision into a "grain of sand," from a superimposition-fusion—embrace—of the book, the body, and the city (each of these is clearly intimated in the plate) of the infinite vision.

  29. The infinite vision would, conversely, expand a grain of sand into this type of infinity. A Blakean vision (of Blake himself or of his true readers) is attended by, and requires, a very different form of individuality and singularity of certain elements or "events"—minute particulars—of Blake’s texts. In order to reach this vision it is necessary, first, to divest the text (verbal or visual) of or, again, liberate it from a reductive reading and, then, to reassemble, reorganize, it into a different text. It is in this process that each textual element becomes enveloped in, and indeed becomes, a kind of enriched monad, or conglomerate of monads (with qualifications offered above). Blake’s infinite vision, or the vision of the infinite, is defined by this type of process of reorganization of minute particulars, divested of Newtonian vision (in the broad sense) that contracts them into dead point-like elements, subject to strict mathematical law, "Single vision & Newtons sleep."[14]


    3. Radical Organization

  30. The same general type of the (re)assembling of an ordered organization of the world from unique elements that are themselves not subject to a classical, or at the limit any conceivable, order or law, or, as I call it here, "radical organization," is found elsewhere in Romanticism and beyond. One can specifically think of Hölderlin, Kleist, Wordsworth, Shelley, and Keats or, more recently, in Bataille, Blanchot, Levinas, Deleuze, Lacan, Derrida, and de Man, or in Niels Bohr’s epistemology of quantum mechanics. Such figures as Leibniz, Kant, Hegel, Nietzsche, and Heidegger, whose ideas link those of these figures, may be considered from this perspective as well. The situation, however, takes on a different conceptual character and epistemology in different cases. This difference is especially determined by the plenitude or, conversely, scarcity (and ultimately the irreducible loss) in representation and meaning, which I shall now sketch in a preliminary fashion, before proceeding to a more rigorous discussion.

  31. When, as in many cases just mentioned, the balance of these relationships is shifted away from plenitude, the ultimate constituents of a given vision may appear to participate in the plenitude of meaning, but in fact they do not. They are irreducibly meaningless, and the overall configuration is properly allegorical in de Man’s sense and, as such, is also correlative to the epistemology of the irreducibly unrepresentable. The formulation from "Pascal’s Allegory of Persuasion" is especially 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."[15] Indeed this clarity may be said to stand in the service of that which cannot be represented by any means, which epistemology also defines quantum mechanics and makes it allegorical. What appears or even is ordered is ultimately constituted by, is an effect of, what is irreducibly singular and disordered. Disorder ultimately underlies order, although "disorder," in this case, is closer to the Greek arreton or alogon, as that which is incomprehensible or is incommensurable with understanding, rather than (only) relating to a (say, spatial) chaotic configuration.
  32. When the balance is, conversely, ultimately shifted towards plenitude as, I would argue, in Blake’s work, or in that of Leibniz, Hegel, and Deleuze (although the last two cases are more ambivalent), what appears to be singular is always a part of a new, more radical form of organization. Order ultimately underlies disorder.

  33. The difference, thus, is in the structure of the unknowable, defined by its relation to the loss and the plenitude of meaning or order (and to the degree of each in either vision). Or, indeed, the difference is between assigning (and perhaps envisioning) and the impossibility of assigning (and hence ultimately suspending the possibility of vision), a structure to the unknowable that is behind and is approachable (or unapproachable) by the knowable and the known. It is the difference between the unknowable in practice and the unknowable in principle, the unknowable that is ultimately unknowable even as the unknowable. This difference may be subtle and may emerge only at the limit of the oscillations between both types of knowledge and the unknowable, as is the case in Blake (or most other figures just mentioned). That, however, does not make it, or the difference in balance of both types of epistemology, insignificant.

  34. On the other hand, in both cases we deal with the search for order and the means to cope with chaos, even if approaching the border of chaos is our goal. We may not be able to do more than to reach this border (rather than enter chaos itself), unless perhaps in madness, which may (or may not) itself be chaos, but of which we can only think (as madness) through order and reason, however perhaps mad (but in a different sense). The latter, paradoxically, appears to require the highest and most complex forms of order, just as the unknowable appears to demand, and emerges at the limit of, the best possible knowledge, as quantum mechanics taught us. It might just be mad enough to be true, as Bohr liked to point out.

  35. Analogous epistemological situations are found in mathematical and physical theories that epistemologically intersect with and shape, or are shaped by, Romantic and, specifically, Blake’s epistemology. While both visions just described may be juxtaposed to classical physics (including classical statistical physics, the classical understanding of chance), the first, allegorical, vision corresponds roughly to that of quantum physics, especially in Bohr’s interpretation (there are more classical-like, realist and causal interpretation and versions of quantum mechanics); the second to that of chaos theory.[16] Blake’s vision, I argue, occupies a complex position in between, although epistemologically it is ultimately closer to chaos theory. (Fractals is yet another question, which I shall discuss below). Quantum epistemology disallows one to speak of any properties of quantum objects and their behavior as such, but only of the effects of their interaction with measuring instruments (described in terms of classical physics). Accordingly, any physical description of quantum objects or their behavior based on conventional physical attributes can only be "allegorical" in the sense just defined. Classical physics can offer us only incomplete and partial—and specifically complementary—allegories of the quantum world, both in general conceptual terms and as specifically applied to the measuring instruments involved in a particular (and in fact always unique) situation of quantum measurement. While the relevant behavior of these instruments is described fully classically, the sum total of the effects of their interaction with quantum objects is rigorously unaccountable by means of classical physics. Only, at most, half of such effects is accountable in any given case, say, only their positions or only their momenta, but never both together, as we could do in classical physics. (This fact is correlative to and is a rigorous physical interpretation of Heisenberg’s uncertainty relations, as well as, under different circumstances, the wave-like or the particle-like observable effects.) Nothing appears to be able to offer us more than, in this sense, partial or, in Bohr’s terms, complementary allegories of the quantum world, which cannot even be assumed to add up to a classical whole, even if an unrepresentable one.

  36. The concept of "radical organization" is designed with this epistemology in mind, and I shall now introduce it in more rigorous terms, and position Blake’s epistemology more carefully in relation to it. Paradoxically, or so it may appear, radical organization, and its orders or laws, are defined by the fact that they allow for and indeed entail that which is not subject to organization, order, or law. They entail that which is irreducibly unorganizable, irreducibly lawless, and is indeed ultimately inaccessible or inconceivable otherwise, including as (absolutely) inaccessible or inconceivable, both of which are of course merely conceptions, as Hegel realized. At the same time, however, it is not something that is excluded from the domain or system governed by organization, is not an absolute other of the organization, but is instead irreducibly linked to it.[17] Hence, Joyce’s coinage chaosmos—chasm/cosmos or chasm/chaos/cosmos—found in my title, may be more suitable here.

  37. The particular version of radical organization that I shall now introduce appears to be epistemologically the most radical yet available. But then it may also be the only available (or even the only possible) model of the configuration of the organizable and unformalizable just defined. Accordingly, from this point on, by "radical organization" (an alternative locution, to be explained presently, will be "nonclassical organization"), I refer to this version. The complexities and implications of the concept are many and far-reaching. The configuration itself defining it, or constituting the point of departure for it, is, however, simple to formulate: the representation of the multiple or collective may, in certain circumstances, be subject to organization, formalization, law, and so forth; that of the "individual" is irreducibly nonorganizable, nonformalizable, lawless. In other words, a radical organization is an organization of individual entities, which are the constituents of the order or orders arising in multiplicities governed by radical organization, while each such constituent, considered in isolation, cannot itself be subject to this or any order, law, organization, comprehension, and so forth. Thus, under these conditions, order and law apply only to (I am not saying fully describe) collectivities, but, in general, not to individuals, which are the ultimate constituents of such collectivities. It follows (in accordance with the general definition of radical organization given above) that such elements cannot be excluded from or placed outside the domain governed by radical organization. But it also follows that the constitutive elements of such organizational structures can no longer be seen as part of a whole, (with)in which both are comprehended by the same law or a correlated set of laws. The latter identity or correlation of two laws (for the whole and its parts) defines classical systems and classical organization, including those of chaos theory, and I here use the term "classical" in accordance with this feature. We may also call such systems Newtonian systems, which would include those in physics itself and those (a very large class of classical systems) that are modeled on them elsewhere, or on which Newtonian physical systems are modeled.

  38. Such systems would be in conflict with Blake’s vision as well. In full measure, however, the above formulations only apply to allegorical epistemology. Thus, as I have indicated, in quantum physics, individual quantum events are, in general, not comprehended by law; for example, individual particles cannot be assigned mathematically describable individual trajectories in the way they can in classical physics. Yet, such events are the constituents of all knowable orders, for example and in particular (indeed there is no other order in quantum theory), specific statistical correlations between quantum events. These correlations, and only they, are described by the mathematical formalism of quantum theory, while remaining outside the reach of any classical explanation. Analogous situations are found in the case of certain Romantic allegories, again, in de Man’s sense, for example, those of Shelley and Kleist. By contrast, in Blake’s epistemology, at the limit of Blake’s infinity, such individual elements, minute particulars, are seen as elements of a new non-classical, and specifically non-Newtonian (in the broader sense defined above), order. In other words, (properly) allegorical epistemology is a necessary but intermediate stage in Blake’s scheme (the stage ultimately transcendent by the infinite vision), while it is irreducible in the epistemological regime of (de-Manian) allegory, to which quantum mechanics belongs as well, in contrast to chaos theory.

  39. Otherwise the concept of organization in which the un-organized and un-organizable (lawless) would be defined as constitutive of organization rather than placed outside of it may appear paradoxical (in the end, it is not), rather than only entailing an epistemology that is complex and difficult, and indeed for many impossible to accept.  Einstein, who encountered it in quantum physics, was among them.  In particular, how lawless individual elements "conspire" to sum up into law-ful collectivities is indeed enigmatic and may in turn be inconceivable.  It may be impossible to conceive how this "conspiracy" is ultimately possible at any and all levels. This is why such an organization and laws may only be said to apply to collectivities but not fully describe (the ultimate structure of) those collectivities. This is also why the overall configuration is so radical epistemologically, or, as the case may be, anti-epistemologically, as well as anti-ontologically, since it may ultimately disallow ontology, or disallow any ultimate ontology, along with any ultimate epistemology—any possibility of knowing or conceiving how that which is stake here is ultimately possible.  It is, however, technically free of contradiction (in part by virtue of the latter impossibility).  Einstein acknowledged this in the case of quantum mechanics, without, however, changing his overall critical attitude, since he still found quantum epistemology "so very contrary to [his] scientific instinct," which could perhaps be called more properly an epistemological instinct, quite common indeed. He hoped that an epistemologically different, classical-like, theory of quantum data would eventually be found.  His desiderata were similar to Blake’s, a vision of an underlying order, except that the underlying order he searched for was mathematical, at least as a good approximation—an anathema (in either sense), a Newtonian anathema, for Blake. All true Blakean orders, true visions of the infinite, are irreducibly nonmathematical, or otherwise formalizable.  At its ultimate limit, an infinite vision, according to Blake, would tolerate neither chaos, nor emptiness (Blake’s "Ulro"), nor formalization, but would instead be a vision of order, cosmos, whose richness can never be contained by any formalizations, mathematical or other.  This (ordered) nonformalizability distances him, indeed in a significant way, from chaos theory and brings him closer to quantum theory, which contains an apparently irreducible nonformalizable and, hence, on mathematical component.That is, unless one assumes, as some do, especially in the wake of Gödel’s incompleteness theorems and related findings, that the richness of mathematics cannot be contained by any formalization.This would be a kind of Blakean view of mathematics.  In contrast to Blake’s epistemology, however, the nonformalizable of quantum mechanics, including as the efficacity of order found in the theory, cannot be assigned order.Indeed, it may be shown that the possibility of so doing would lead to a conflict with the available experimental data of quantum physics.[18] Were it possible in practice, the (infinite) mathematical vision of the Blakean type would enable us to see the order (for example, a fractal-like order) and causality ultimately underlying manifest disorder and chance of chaos-theoretical objects.  In quantum mechanics (at least in Bohr’s interpretation, which I follow here) such an underlying order and, ultimately, any conceivable "bottom" configuration cannot be assumed in principle, which impossibility, however, enables the consistently configured possibility of radical organization at the manifest level. Admittedly, these considerations further contribute to a rather labyrinthine picture of the relationships between Blake’s vision and modern (including classical) mathematics and science (or between different aspects of the latter, to begin with) here presented. I would argue, however, that this type of picture does more justice to the complexity of these relationships than any determinate identification or parallel, say, between Blake and chaos theory, or between Blake and quantum mechanics (itself subject to a variety of interpretations, intensely debated).  Indeed such determinate relationships do not appear to be rigorously possible.  The qualification just considered concerning Blake’s proximity to chaos theory in view of his critical attitude to mathematization of thought is particularly crucial.

  40. An important qualification or emphasis is in order, before I proceed further. I do not mean that under the conditions of radical organization, order, organization, and law do not apply only in certain (by classical standards) exceptional, extraordinary individual situations, although such situations are abundant in and are central to Blake’s work or elsewhere in Romanticism. Such a view would, again, place the unique and the singular outside a given order, rather than allow us see them as giving rise to this order. Instead, more radically, every individual situation (cases, event, and so forth) within an ordered or law-governed overall configuration is not subject to the order and law defining this configuration, or order and law in general. It is irreducibly dis-ordered (which not the same as disordered or chaotic) and, in David Bohm’s terms, "irreducibly lawless." Or, more accurately, every situation, no matter how ordered or (we may take advantage of their common etymology) ordinary, is "decomposable" into and is an effect of the organization of individual entities, each of which is singular or unique and, as such, is outside any conceivable order or law. This also explains why extraordinary situations are so ordinary, so common, in Blake, or (allowing for the differences indicated above) other Romantic literature; they are in fact the minute particulars constituting what we reductively see as ordinary situations. Ultimately, everything is extraordinary, or one might say, extra-extraordinary, insofar as (classically) extraordinary entities are neither excluded from chaosmic orders nor are composites of anything less extraordinary. Something more extraordinary is possible; hence my perhaps extravagant terminology. Or, still more accurately, underneath or alongside the perceived order of the ordinary, which we may call classical, there subsists a different organization, which I here call radical or nonclassical.

  41. In Blake’s world each such entity, each minute particular at a given moment of vision, is infinitely expandable or, as it were, re-expandable so that the same process may and must be infinitely reenacted, in each case possibly giving rise to a different (sub)universe of its own where an analogous organizational dynamics would apply. I say "analogous" because new minute particulars themselves may be quite different, thus making this dynamics fundamentally nonfractal—that is, the pattern may change with the change of scale—although more fractal-like sequences are found as well in this process, or elsewhere in Blake’s poetry and design. The process itself, however, is, according to Blake, interminable or infinite, just as the iteration of fractals is. Blake would appear to find the latter conceptually and aesthetically interesting and productive up to a point, but boring in infinity, however intricate fractality may be, such as that of the famous Mandelbrot set. Accordingly, Blake’s equally famous description of the ultimate poetic vision in "Auguries of Innocence,"

    To see a World in a Grain of Sand And a heaven in a Wild Flower Hold Infinity in the palm of your hand And Eternity in an hour        ("Auguries of Innocence," 1-4; emphasis added)

    would entail an ultimately nonfractal expansion rather than fractal iteration (although it may involve fractal strains), an ultimately non-fractal iteration, rather than to fractals, and specifically to the Mandelbrot set, to which it has been often compared in recent years. The "Newtonian" order, which contracts and "harden[s]" minute particulars, "the jewels of Albion," "into the [same] grains of sand" and in which minute particulars and their assemblages are governed by the same law, or properly correlated set of laws (I shall explain this in more detail below), subject to (mathematical) "Demonstration," would never apply (Jerusalem, Chapter 2, Plate 45:17, 20, 44).

  42. Thus, rather than ultimately suspending order, the Blakean universe is conceived so as to have more order than any Newtonian universe can possibly have. (With due qualifications, especially insofar as this richer order borders on the irreducible chaos and the invisible, the unknowable, and so forth, this proposition applies to quantum physics.) It is just that this order is, by definition, assembled out of elements—minute particulars—that cannot obey any Newtonian-like law, and hence the overall order is not Newtonian either, in any reasonable sense of the term "Newtonian." It should also be qualified that, at each stage, once all or some minute particulars are expanded into richer structures, the dynamic of radical organization would apply to the whole new assembly of new minute particulars arising from each previous minute particular. The Blakean universe is the infinite limit of this process, which "limit," however, remains unlimited—interminably expandable. This, I would argue, also makes Blake's vision of the infinite the deliberate opposite of differential calculus, which would be for Blake, the calculus (in either sense) of the finite limit of the infinite, which is both, as Blake perhaps realized, its power and (ultimately Satanic) limitation.[19]

  43. What is the actual character or structure of the minute particulars that emerges once this vision becomes open on to infinity remains, short of possessing such a vision, mysterious. One might argue that the ultimate shape of Blake’s minute particulars is a human (and even specifically male) body, thus reinstating a fractal or quasi-fractal character to Blake’s vision. There are significant reasons for this argument, and more generally one cannot disregard fractal aspects of Blake’s vision and work. They may, however, and I would argue, must be differently taken into account. First of all, however (suspending for the moment the question of the constitution and unconstitution of the human body, in Blake and elsewhere), it would hardly be possible to think of the human body in Blake in terms of a single or fractally iterable shape. Rather, on the (visual) model of Michelangelo’s "Last Judgement," on the one hand, and, on the other, the dance of the angels in Paradise Lost, one should think in terms of the infinite dynamic transformation of the "shape" (there is no longer a single one) of the body.  Secondly, as was suggested earlier (and with the same qualifications), Blake’s ultimate shape is an embrace of two bodies, male and female, with the same dynamism of transformations and multiplicities extending within and without (in the sense discussed above) applied.  Finally, the body is, again, always superimposed with the book and the city in Blake, which superposition would further enrich or be enriched by the "embrace" structure. Thus conceived, "embrace" may be seen as the structure of Blakean superimposition, although here, again, the relationships between all components are continuously reshuffled in the process. The economy just outlined would define both Blake’s local and global structures, such as those designated by various figures (in either sense) and their permutations or, again, embrace-superimpositions—from various minute particulars to Albion and Jerusalem, and ultimately the body of Christ. One may say, that unlike the radical fragmentation and dismemberment of the body found, according to de Man, in a properly allegorical vision, Blake’s body is never fragmented, but instead is always multiply superimposed and hence irreducibly multishaped and multistructured wholeness. This "wholeness" (rather than fragments) would define his minute particulars as well. It is worth qualifying that the Blakean "superimposition" just described is not here intended to invoke and be related to the so-called (linear) "superposition" of quantum mechanics. Roughly, the latter concepts allows one to think of a quantum system as, if left to itself, being simultaneously in a (linear) combination of different states, “collapsed” into a single outcome by a measurement.  This concept and its metaphorical implications would require a separate analysis.One can, in principle, consider linking it to Blake’s vision, especially if one follows more realistic interpretations of quantum mechanics.  In the Bohrian interpretation, followed here, this concept does not correspond to any physical reality, to any process occurring in space and time. One can also attempt (and some have) to link Blake’s vision to David Bohm’s "hidden variables" version of quantum mechanics, which is mathematically different from the standard version here discussed. Bohm’s theory is both realist and causal, and, hence, epistemologically similar to chaos theory, to which, I would argue, Blake’s vision is ultimately closer in any event.  Accordingly, I shall bypass these connections here.

  44. There are fractal aspects to Blake’s work and the recent appeal in Blake studies (as fashionable there as elsewhere) to fractals (sometimes as part of chaos theory) is not unjustified. The key differences are crucial, however. First of all, Blake’s vision is non-fractal insofar as "fractals" refer to the interminable repetition of the pattern of the whole in the parts. This is, arguably, the most common use of the idea of fractals in Blake and elsewhere, albeit a somewhat thin basis for an appeal to the mathematics of chaos and fractals. The interminable nature of the process is often forgotten and the appeal itself to fractals, by and large, becomes that to the mirroring of the structure of the whole in the structure of its parts.[20] The latter is indeed found in Blake, both in the organization of his text and in his designs. Thus one finds it in certain plates of Jerusalem (Plate 23), where one finds a fractal-like descending scale repetition of human figures and their curvatures, perceptively pointed out by Paul Yoder in his "Self-Similarity and Blake’s Jerusalem," which also makes a compelling general case for fractal aspects of Blake’s work but which is, I would argue, by and large consistent with the present argument. The lines strictly demarcating (and hence, in contrast to fractals, terminating) the process or non-fractal changes in the shapes of the bodies themselves may give one pause, but, I admit, this is a matter of interpretation, since such figures may be read as indicating potential fractality of the type one finds in the Mandelbrot set. The design may indicate an infinite fractal extension, symbolizing the expansion—zooming up—of the order of human vision and/as the order, organization, of the Blakean infinite.[21] Accordingly, to the degree it is fractal-like and up to a point, Blake’s world would be akin to the zoom representation of such fractal entities as the Mandelbrot set, rather than to more monotonous fractal objects, such as, say, the Koch curve. Ultimately, however, in Blake’s vision, the constitutive parts of any pattern are uniquely singular in their patterns, as they organize into the order, or possibly multiple orders, of the whole. It is analogous to a fractal picture in that there is no punctual termination of the process. But, in contrast to fractals, there is no (interminable) repetition of pattern, nor, again, diminishing scales.

  45. The ultimately infinite (unlimited and unending) interplay of such minute particulars, would, thus, entail immense (dynamic) order and organization, that Blake claims to be open to the expanded (infinite) human perception, which, at this limit, inevitably becomes a vision and/as creation, rather than merely perception. In order to illustrate Blake’s conception, it is worth considering Milton’s conception of chaos in Paradise Lost, which is my epigraph. The passage, I would argue, has a momentous significance for Blake, perhaps especially in Milton, but, I would also argue, throughout his work, including in relation to the epistemological problematics here in question.

    Before thir [Satan’s, Sin’s and Death’s] eyes in sudden view appear The secrets of the hoary deep, a dark Illimitable Ocean without bound, Without dimension, where lengths, breadth, and highth, And time and place are lost; where eldest Night And Chaos, ancestors of Nature, hold Eternal Anarchy, amidst the noise Of endless worth, and by confusion stand. For hot, cold, moist, and dry, for Champions fierce Strive here for Maistry, and to Battle bring The embryon Atoms; they around the flag Of each his Faction, in thir several Clans, Light-arm’s or heavy, sharp, smooth, swift or slow, Swarm populous, unnumber’d as the Sands Of Barca and Cerene’s torrid soil, Levied to side with warring Winds, and poise Thir lighter wings. To whom these most adhere, He rules the moment; Chaos Umpire sits, And by decision more imbroils the fray By which he Reigns: next his high Arbiter Chance governs all. Into this wild Abyss, The Womb of Nature, and perhaps her Grave, Of neither Sea, nor Shore, not Air, nor Fire, But all of these in thir pregnant causes mixed Confus’dly, and which this must ever fight, Unless th’s Almighty Maker them ordain His dark materials to create more Worlds, Into this wild Abyss the wary fiend Stood on the brink of Hell and look’d a while Pondering his Voyage: for no narrow frith He had to cross (890-920)
  46. This passage would require an interminable analysis, in particular in the context of Blake or Romanticism. One would be hard pressed to find a major Romantic poem that would not engage it in one way or another. My main point here is that Blake’s vision just described may be seen and was seen by him as equivalent to the total organization of all materials, all of its "minute particulars" (I shall explain the quotation marks presently) of Chaos, as here described, into new Worlds, thereby eliminating or expelling Chaos altogether. It is this process that gives meaning to Blake’s famous maxim, "The Eye altering alters all" (The Mental Traveller, 62). In chaos theory, it is worth noting, the order of its object is assumed given at the underlying level, there is no need to create it.  In quantum mechanics "chaos" (again, in the sense of arreton, the incomprehensible) is ineliminable, even in principle: there is no "god" which could, at least in principle, create, reform it (in either sense) into cosmos. 

  47. Blake was, of course, far from endorsing the concept of creation from Chaos; quite the contrary, as can be shown by ample textual evidence. His vision is quite different from Milton’s, which is closer to that of quantum theory (except for its theological or, in Heidegger’s and Derrida’s terms, ontotheological aspects). But, in a way, this is the point, and as Milton might suggest, Blake may well have read Milton, "a true Poet and of the Devils party without knowing it" (The Marriage of Heaven and Hell, Plate 5), here in his own way as well. (Some caution is due in reading this statement, though.) Chaos, or indeed Nature itself (materiality), would be merely an aspect of unregenerated vision.[22] The process of creation here suggested by Milton would be read by Blake as an allegory of the transformation into the vision of the Poetic Genius, akin to that of the Printing House in Hell in The Marriage of Heaven and Hell. (I leave for the moment aside de Man’s sense of allegory, which would have thrown this reading into a new ocean or yet another abyss.) Accordingly, the designation "minute particulars" can only apply to this world and vision of organization. Ironically, almost perversely, Blake reconceives the whole Voyage of Satan, albeit, necessarily, superimposed with Christ’s descent into Hell, as in fact an allegory of this creation of new worlds and total transformation of vision into organization. This organization gives light, illuminates, but thus also eliminates chaos—"in a trail of light as of a comet/That travels into Chaos: So Milton went guarded within" (Milton, Book the First, Plate 15, 19-20)—and replaces it instead with the organized infinity (Plate 15, 21-35). Jerusalem renders this process, too: "And the dim Chaos brightened beneath, above, around! Eyed as the Peacock" (Jerusalem, Chapter 4, Plate 97).

  48. It would not be possible to consider the immense allegory of the link between Milton, Milton’s Satan, and Blake in Milton. It may be worth mentioning, briefly, that the image of a comet in the above passages must also be an allusion to Newton’s mathematical predictions concerning Halley’s Comet and the controversy surrounding it. Nor can I discuss specific concepts and stages of chaos and organization pertinent here (in particular the way "Chaos" functions in the first book of Milton), especially organized innocence, or Beulah, the quasi-pastoral "place where Contrarieties are equally True" (Milton, "Book the Second," 1).[23] The latter is a crucial, but intermediate stage of Blakean order, in contrast, say, to the architectural order of Jerusalem. It may be observed that mirroring and merging (superimposing) with Milton’s journey in the poem, Beulah emerges in the first line of the second book, after, as it were, Blake/Milton’s traversal of poetic chaosmos of the first book. But, it is not the end of the organizing, building, process. The City is, thus, preparing the way (in either sense) to Jerusalem. This (radical) organization is what "justifies the ways of God to Man" for Blake or, according to Blake, for Milton, as his epigraph to the poem indeed says. These conceptions both complicate and elucidate my point here, but their analysis would require a nearly interminable traversal of Blake’s works, let alone the secondary sources. This cannot be done here. My main point is the order, organization, of minute particulars ultimately suspending or indeed organizing—ordering—chaos into an immense order, "in fury of Poetic Inspiration/ … build[ing] the Universe stupendous: Mental forms Creating" (Milton, "Book the Second," 19-20). Or perhaps one should speak of removing (through this work of organization) the veil, the illusion of chaos and even Nature, since the latter—that is, the Newtonian vision of the world as Nature or as divided into Nature and Spirit, the Soul and the Body, and so forth—is complicit with Chaos. This complicity is clearly found in Milton, including in the passage cited here, but read very differently by Blake.

  49. The interplay of minute particulars is what Blake calls the vision of the infinite, which, accordingly, presupposes a particular concept of infinity rather than refers to any common meaning of it (if such a common meaning exists to begin with). Insofar as the object of this vision is not formalizable, this concept is different from all mathematical concepts of the infinite, especially those involved in Newtonian physics or what Blake sees as the Newtonian vision of the world. From this perspective alone, one would apply chaos-theoretical considerations to Blake’s vision with the greatest caution, even though both share the concept of underlying order. On the other hand, as I have indicated, it may not be as unmathematical as it may appear, and perhaps had appeared to Blake. For the ultimate structure of infinite mathematical objects, such as those of chaos theory, but also many (perhaps all) others as well, may not be mathematically formalizable either. It may ultimately not be mathematical in any given sense, that is assuming that it is ordered or could be available to a vision, to begin with, which would make the situation epistemologically analogous to that of quantum mechanics and hence properly allegorical. In Blake, this organization would become available to the infinite vision, activated by the working of the Poetic Genius, which is, again, the central difference between the Blakean and allegorical epistemology.

  50. In the latter case, as in quantum mechanics or certain Romantic allegories other than Blake’s, defined by "radical organization," the vision (in either sense or indeed in any sense conceivable) is always terminated. In quantum theory (in Bohr’s interpretation), this termination takes place at the level of the ultimate constituents of matter, usually identified with elementary "particles." To the latter no properties (including those which would define them as particles) can be assigned and this must, thus, be seen as ultimately unknowable, ultimately unknowable even as unknowable. No expansion of vision can remedy this situation, and hence, no Blakean "vision" is possible. At this level knowledge, any knowledge, even that of the impossibility of knowledge, would be rigorously impossible, but—this is crucial—only at this level. Otherwise this unknowable is not only compatible with knowledge but is the efficacity of knowledge, perhaps of all possible knowledge, assuming the world is like this (as opposed to the Blakean world). In this sense this vision is, on the one hand, irreducibly finite as concerns the limit of the "visible" (knowable), and, on the other, neither infinite nor finite (or anything), as concerns that which is beyond its limit (assuming, again, that such terms can still apply at this limit). As Bohr stressed on many occasions we are here far, indeed irreducibly, beyond the limit of pictorial visualization. We are beyond any visualization and vision, conception, possibility of representation and so forth, whether of order or of chaos, except insofar as the latter is used to designate the irreducibly inaccessible and thus, as I said, is in accordance with the Greek alogon (outside logos) and arreton (incomprehensible). (Milton’s Chaos may be read so as to include certain aspects of this conception as well, rather than merely or only designating a vision of disorder and chance, even though one may assume that it may in principle be controlled or ordered without limit by God.) The scale of termination may be differently conceived and may be more variable in other nonclassical or allegorical epistemologies, but would, by definition, be irreducibly ruptured at a certain point or set of points without, in any event, allowing for an infinite extension. Under the conditions of (de Manian) allegory, in quantum mechanics or elsewhere, there may be (if one wants to retain Blake’s terms, perhaps no longer quite applicable under these no-longer quite Blakean conditions) minute particulars. But there is no infinity, except insofar as it is deployed allegorically, as infinite mathematical objects, in particular, mathematical spaces of infinite dimensions (the so-called Hilbert spaces) may be deployed by the mathematical formalism of quantum mechanics.We may call this limit of the irreducible termination of vision—this radical discontinuity of allegory—materiality, a term analogously deployed by de Man throughout (whether one speak of the body,language, or history) and shunned by Blake.

  51. In Blake, human poetic vision, which the Poetic Genius takes over, does not encounter such limits. It remains (epistemologically) radical, however, insofar as Blake’s world is not governed by a single law or set of laws, even though the constitutive minute particulars of this world interact and are connected. Any meaningful reading of Blake (or, again, of other Romantics) must take this organization of minute particulars—words or smaller linguistics units or signifiers, images, concepts, and so forth—into account. Indeed, more radically, it must be a reading of this organization, and hence a reading of the multiplicity of orders of Blake’s poetic universe. Each such image is a Leibniz-like monad, itself structured as a world (rather than merely a mirror of the World, as in Leibniz), as all monads together are organized into the non-fractal and non-whole World, which is the Blakean infinite.[24] Our reading, itself monadological in this sense, enters, with Blake, into the infinite opening of the finite: "it finitely represents infinity," as Leibniz once said. It also gives the world itself the possibility of beginning over and again in each monad (again, keeping in mind the non-fractal character of the Blakean world). Complex, and it seems nearly interminably or infinitely "zoom-able" (i.e. always amplifiable into a complex picture), elements of Blake’s design, which continuously restructure the whole, allegorize this process. This zooming and de-zooming process extends in the other direction as well, insofar as each book relates to and is a different "whole" universe. Whether this difference is only perspectival or whether we deal with an interactive many-worlds "world" even at the global level may remain undecidable, too. In any event, as each monad forms a book and/as the artists’ book, their (radical) organization continuously undermines the possibility of the classical wholeness and, thus, we may say with de Man, all aesthetic ideology as well. Blake’s illuminated books are, thus, also allegories of aesthetic de-ideologizing and, hence, de-aestheticizing. In a certain way, they have nothing to do with art, at the very least insofar as art serves any aesthetic or otherwise uncriticial ideology. Indeed, this, ultimately, may be the most crucial contribution of the genre of the illuminated manuscript or the artists’ book to modern aesthetics and politics alike.

  52. Let me, in closing, return from the perspective here sketched to the order of the three beds, which, as I said, may have been the order of three books, in Plato. Plato’s classical account is not out of order here, since for all or most practical purposes, an ordinary bed or its image, either at the level of its prototype or archetype, or at the level of its constitutive elements would obey some form of Plato’s scheme or another, even if considered in this somewhat simplified way. Ultimately, a greater pay-off might come from rereading Plato (or, as was suggested above, Leibniz) in terms Blake, as here considered, which is of course not say that one should disregards the differences between them.  An extraordinary bed, say, one painted by Van Gogh, would be outside, or partly outside and partly within this order.  Now, in the Blakean universe, every bed would be more like Van Gogh’s.  Once Poetic Genius becomes truly active, one simply cannot create or (and this are the same) perceive any other, which is in fact rigorously true, as Plato knew well. In Blake, however, it would be an organization and, in relation to the classical order, a reorganization—and emergence—of singular, unique "minute particulars" as here described, rather than, as (or so it would appear) in Plato, "derivable" (however complex the mediation of this derivation) from an underlying quasi-mathematical divine order (however remote).  (Naturally, the latter scheme has richness and significance of its own, including in mathematics and science.  We deal with the simultaneous workings of both schemes in most cases, even though the balance of their relationships may be different.) Indeed the very concept (it would in turn not be one) of "bed" acquires the same structure. That is, Van Gogh’s bed or, hence, any other bed, would not be comprehended by a general concept, as in Plato’s scheme, but would give rise each time to a new concept of bed. One of the effects of this organization of minute particulars and/as this reorganization of Plato’s scheme would be the interfusion of God’s, the carpenter’s, and the painter’s bed making, or book making.  This interfusion is allegorized by Blake’s process of production and dissemination, "from generation to generation," of his illuminated manuscripts, itself allegorized throughout his books, as in A Printing House in Hell. This allegory is clearly, albeit not uniquely, an allegory of continuous decomposition and reorganization of textual and visual minute particulars, and of the resulting interplay of the classical aesthetic order or ideology and radical, nonclassical organization in the present sense. In truth, however, any plate of Blake’s illuminated works is designed (in either sense) in accordance with the same principle.  It is the "principle" (Blake’s word) of Poetic Genius.


    5. Conclusion: Flyers

  53. It would appear that the difference and even opposition between art and philosophy would be established thereby. This is not the case, however. Or, at least it depends upon how one sees the vision and practice of philosophy itself, including, Shelley and Deleuze would argue, Plato (whose thought would be thus juxtaposed to the Platonism of the scheme of the three beds). Indeed the concept of concept underlying the preceding discussion corresponds to that of Deleuze and Guattari in What Is Philosophy? Rather than in any common sense of it, such as that of an entity established by a generalization from particulars, or indeed "any general or abstract idea," as Deleuze and Guattari argue, a true philosophical concept is an irreducibly complex, multi-layered structure—a multi-component conglomerate of concepts (in their conventional sense), figures, metaphors, particular (ungeneralized) elements, and so forth (What is Philosophy?, 11-12, 24). The practice of philosophy is defined, accordingly, as the creation, fabrication, architectural construction (out of minute particulars, or minute generals). Blake’s art would be conceptual art precisely in this sense, and as such, would be, along with and as the art of the artists’ book, a precursor of the modernist and then postmodernist conceptual art from Duchamp on, including that of the artists’ book. It is precisely at this level that the radically creative character of philosophy, defining Plato’s scheme, is (re)established. According to Deleuze and Guattari, a philosophical concept (always a singular concept) of, say (this is the example they use), the "bird" would not be defined merely by generalization from particulars (although this may play a role), but rather by an organization of the general or generalizable and of the particular or singular: a bird in flight, its posture, the composition of its colors, its trajectory, its relation to space around it, and so forth (What Is Philosophy?, 20-21). As such this concept is much closer to Shelley’s Skylark or Keats’s Nightingale, or any number of birds—indeed all the birds—one finds in Blake, in particular the one in The Marriage of Heaven and Hell, which could have been Deleuze and Guattari’s model.

    How do you know but ev’ry Bird that cuts the airy way Is an immense world of delight, clos’d by your senses five? (Plate 5)

    Indeed, the whole work is itself a bird-like manifesto of that type, literally a flyer. (It can hardly be doubted that Blake had the concept, if not the word, in mind, too.) Of course, a radical restructuring of all our perception, "our senses five," is necessary. It needs to be re-tuned or re-attuned so as to see the organization at the level of things and concepts alike as the organization of minute particulars. Its new model or at least allegory is the artists’ book as conceptual art. This is what Blake’s "Printing House in Hell" allegorizes. The key aspects of this allegorization are suggested, or indeed inscribed, in the inscription, itself already allegorizing the materiality of inscription and the material carpentry of inscription of the couplet just cited in Plate 6. Blake, first, describes himself as "walking among the fires of hell. Delighted with enjoyment of [Poetic] Genius" and collecting "proverbs of Hell," minute particulars of wisdom, and hence of philosophy in Deleuze and Guttari’s sense. (The "radical organization" now takes place at the level of concepts themselves, treated as "minute particulars," rather than generalizations; and given this sense of concepts it could not be otherwise.) Then, Blake says: "When I came home, on the abyss of five senses, where a flat sided steep frowns over the present world, I saw a mighty Devil folded in black clouds, hovering on the sides of the rock, with corroding fires he wrote the following sentence [that is the couplet under discussion] now perceived by the minds of man, & read by them on earth" (The Marriage of Heaven and Hell, Plate 5). It would take another essay to follow the minute particulars of this passage and their organization. My simple point at the moment is the allegory of Blake’s process of etching, in which corrosive acid is used to burn away the surface of a metal plate. The allegory itself, ultimately that of (and itself defined as) radical organization here considered, is of course hardly simple, whether you read along more Blakean or more strictly allegorical, quantum-mechanical, lines in the present sense. It is as complex an allegory of this process as any hitherto available, or perhaps as there can be. Nature, or, since quantum physics makes us pause here, at least mind, can no further go.

Works Cited

Ault, Donald. Visionary Physics: Blake’s Response to Newton. Chicago: University of Chicago Press, 1974.

Blake, William. Complete Poetry and Prose. Newly Revised Edition. Edited by David V. Erdman. Berkeley and Los Angeles: U of California P, 1981.

Bohm, David. Wholeness and the Implicate Order. London: Routledge, 1995.

Bohr, Niels. The Philosophical Writings of Niels Bohr. 3 vols. Woodbridge, Conn.: Ox Bow, 1987.

Deleuze, Gilles and Felix Guattari. What is Philosophy?. Trans. Hugh Tomplinson and Graham Burchell. New York: Columbia UP, 1993.

Grabo, Karl H. A Newton among Poets: Shelley’s Use of Science in Prometheus Unbound Chapel Hill, NC.: University of North Carolina Press, 1930.

Lyotard, Jean-François. The Postmodern Condition: A Report on Knowledge. Trans. Geoffrey Bennington and Brian Massumi. Minneapolis, Minn.: Minnesota University Press, 1984.

Lakatos, Imre. Mathematics, Science and Epistemology: Philosophical Papers, Volume 2, Eds. John Worrall and Gregory Currie. Cambridge: Cambridge University Press, 1983.

Latour, Bruno. We Have Never Been Modern. Trans. Catherine Porter. Cambridge, Mass.: Harvard University Press, 1993.

Penrose, Roger. Shadows of the Mind: A Search for the Missing Science of Consciousness Oxford: Oxford UP, 1994.


1 I shall, by and large, bypass here the literature of Blake and science, or indeed scholarly literature on Blake in general. This literature is immense, and I am indebted to a great many works on Blake and Romanticism (the list would be too long to cite here). On the other hand, the present approach appear to me rather different from the treatments I have encountered, even though a number of works deal with quantum theory, and specifically complementarity, and chaos theory. In my view, while it would by now require substantial updating, Donald Ault’s earlier Visionary Physics: Blake against Newton (Chicago: U of Chicago P, 1974) remains the best full-length study of the subject. Ault’s more recent work on the relationships between Blake’s work and mathematics and science has been presented at several conferences, but remains unpublished. I am also indebted to R. Paul Yoder for helpful discussion. His article, "Unlocking Language: Self-Similarity in Blake’s Jerusalem," on the present issue is among the more balanced and fair-minded treatments of fractal-like aspects of Blake’s work. I have considered the quantum-mechanical epistemology in a number of previous works, and the present essay is a continuation of this, by now long, project, to which and to the literature cited there I permit myself to refer the reader for further details of the present argument. These works include Complementarity: Anti-epistemology After Bohr and Derrida (Durham, NC.: Duke UP, 1994), "Complementarity, Idealization, and the Limits of Classical Conceptions of Reality," Mathematics, Science, and Postclassical Theory, ed. Barbara H. Smith and Arkady Plotnitsky (Durham, NC.: Duke UP, 1997), and "Techno-Atoms: The Ultimate Constituents of Matter and the Technological Constitution of Phenomena in Quantum Physics," Tekhnema: Journal of Philosophy and Technology 5 (1999): 36-95, and, in the context of Romanticism, "All Shapes of Light: The Quantum Mechanical Shelley," in Shelley: Poet and Legislator of the World, eds. Stuart Curran and Betty Bennett (Baltimore: Johns Hopkins UP, 1995); "A Dancing Arch: Formalism and Singularity in Kleist, Shelley, and de Man," International Romantic Review (Winter 1998), and "Algebra and Allegory: Nonclassical Epistemology, Quantum Theory, and the Work of Paul de Man" in Material Events, ed. Thomas Cohen, J. Hillis Miller, and Andrzej Warminski (Minneapolis, Minn.: U of Minnesota P, 2000).

2 The point was well realized by Schrödinger in his famous "cat paradox" paper, "The Present Situation in Quantum Mechanics," in Quantum Theory and Measurement (hereafter QTM), eds. John Archibald Wheeler and Wojciech Hubert Zurek (Princeton, NJ: Princeton UP, 1983). In particular, he observes "If a classical state does not exist at any moment, it can hardly change causally" (154). Discussions of the cat-paradox are found in many accounts of quantum physics. I have considered it in Complementarity (284-85, Note 20).

3 The situation is more complex in classical statistical physics as well. The classical view even of classical statistical physics (i.e. physics disregarding quantum effects) has been challenged more recently, in particular in the wake of quantum mechanics. In general, it is no longer altogether clear how classical physics is or can be.

4 Actual systems are often chaotic. The point of chaos theory is that deterministic predictions are not possible even in idealized situations.

5 I shall be able here to give it only a restricted attention, concentrating, in accordance with my main subject, on the key concepts involved. The subject of artists’ books is by now a filed of its own. For comprehensive thematic and historical introductions to it, see, for example, Artists’ Books: A Critical Anthology and Source Book, ed. Joan Lyons (Rochester, NY.: Visual Studies Workshop P, 1985), Joanna Drucker, The Century of Artists’ Books (New York: Granary Books, 1995), and for a more general context of the question of the book, Roger Chartier, The Order of the Book, trans. Lydia G. Cochrane (Stanford: Stanford UP, 1994).

6 The subject has been approached from the perspective of the connections to both mathematics of complex variables (originating in Bernhard Riemann’s work) and chaos theory in recent investigations (yet unpublished) by Donald Ault and coworkers.

7 This topos has been a subject of well known investigations from Ernst R. Curtius, European Literature and the Latin Middle Ages (Princeton 1967), 319-326, to Jacques Derrida, Of Grammatology, 6-26, and beyond, although surprisingly not in the scholarship on the artists’ books.

8 The latter would be much closer to "writing" in Derrida’s sense than to the classical conception of the book. Accordingly, the beginning of Blake’s book may also be seen as the beginning of writing.

9 All the reference to Blake are (by plate numbers) to The CompletePoetry and Prose of William Blake, ed. David V. Erdman (New York: Doubleday, 1982).

10 Derrida’s well-known investigation of the subject in his earlier works remain an unavoidable reference here.

11 See especially Jacques Derrida, Of Grammatology, trans. Gayatri C. Spivak (Baltimore; Johns Hopkins UP, 1975), 6-26.

12 The latter may in turn be shown as conceived by Leibniz in terms of the superimposition of the body, the book, and the (Baroque) city or, at least, architecture. On these questions see, Gilles Deleuze, The Fold: Leibniz and the Baroque, trans. Tom Conley (Minneapolis: U of Minnesota P, 1993).

13 The topology and epistemology of Leibniz’s monads has been a major subject of recent investigations, relevant here, by both Michel Serres and Gilles Deleuze, most especially in Gilles Deleuze, The Fold: Leibniz and the Baroque.

14 "Letter to Thomas Butts, 22 November 1802" (The Complete Poetry and Prose of William Blake, 693).

15 Paul de Man, Aesthetic Ideology (Minneapolis, Minn.: U of Minnesota P, 1996). This statement cannot be seen as strictly defining allegory, which, as de Man says on the same occasion, is difficult to do (Aesthetic Ideology, 51). If, however, there could be one (or any) such definition, the formulation just cited appears to come as close to it as possible. The feature itself indeed appears to characterize the practice of allegory, at least from Dante on. Galileo’s project of the mathematical sciences of nature can be seen from this allegorical viewpoint, and connected to Dante, along these lines. I permit myself to refer to a forthcoming article by David Reed and the present author, "Discourse, Mathematics, Demonstration and Science in Galileo's Discourses Concerning Two New Sciences."

16 Conceptual parallels with other ideas from twentieth-century mathematics may be invoked as well.

17 The epistemology becomes classical once such exclusion takes place. This point is crucial to Derrida's reading of Kant in "Economimesis" (Diacritics 11, no. 3 [1981]:3-25).

18 This is a consequence of the so-called Bell’s theorem, at least insofar as one maintains Bohr’s interpretation of quantum mechanics. See David Mermin’s essays on the subject of quantum mechanics in Boojums All the Way Through (Cambridge: Cambridge UP, 1990).

19 The differences between Newton’s and Leibniz’s conceptions of differential calculus are of some interest here.

20 In actuality the key feature that mathematically defines fractals qua fractals (and gives them their name) and that is often ignored by the humanists addressing the subject, is their fractional, rather than whole, dimensionality, most often, a fractional number between 1 and 2. It is also worth noting that not all (mathematically) chaotic systems are fractal.

21 I here refer to the difference between symbol and allegory, as considered by de Man, in particular as concerns any possibility of deriving representations from an original or primordial unity, which define "symbol" and is prohibited by "allegory," or "irony." See, especially, his "Rhetoric of Temporality," Blindness and Insight (Minneapolis, Minn.: U of Minnesota P, 1981).

22 At the level of practice, materiality remains crucial in Blake, whether one speaks of the materiality of the book, the materiality of the signifier, or the materiality of engraving, or, to return to Plato’s allegory, the materiality of carpentry or of painting. One can also give the concept of materiality has a complex architecture, in part defined, and reciprocally defining, a concept of concept itself, which I shall consider below; and I can only briefly indicate a few key aspects of this architecture. According to this concept materiality and materialism are not seen as something only associated with matter, but refers to a certain field of concepts, theoretical and political strategies and interventions, events, and so forth. These may not in turn be subsumed by any single concept, strategy, event and rubric, or even by a single configuration of concepts, strategies, events, or rubrics. A much greater degree and a more radical form of heterogeneity are here at work. The rubric of materiality itself becomes ultimately provisional. In particular an analysis of "materiality" of this radical type entails a deployment of an equally radical form(s) of ideality, conceptuality, and phenomenality. (Still other rubrics and conceptualizations become necessary as well.) This radical critique redefines both concepts materiality and ideality, or phenomenality. Indeed it redefines all concepts that it considers and engages in this irreducibly multiple and multiply interactive field. However, the "elements" (which, it follows, cannot be seen as strictly or "absolutely" elementary either) that constitute this field work so as undermine all idealist ideologies, including those of metaphysical materialism philosophical, aesthetic, political or other and, to return to Althusser’s phrase, ideological state apparatuses. The case in point is aesthetic ideology, according to de Man’s analysis. In this sense, Blake’s conceptuality is materiality, and his conceptual art a form of materialism as such, rather than only by virtue of its irreducible association with matter. From this perspective, Blake’s suspicion concerning, and his ultimate suspension of, nature or matter, in particular if conceived according to a Newtonian view, is, contrary to appearances, ultimately a "materialist" strategy.

23 The latter concept is often compared to Bohr’s complementarity, but rarely, if ever, with due caution as concerns the specificity of both concept in Blake or, especially, Bohr. At the very least, the differences (specifically epistemological ones) are just as significance as similarities.

24 See, however, Note 22 above.

25 On these issues see, again, Deleuze’s analysis of monads throughout The Fold.

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March 2001