Catastrophes, Kaleidoscopes, String Quartets:

Lucy in the sky with diamonds! Lucy in the sky with diamonds! Lucy in the sky with diamonds!

Picture yourself on a train in a station, with plasticine porters with looking glass ties,

Lucy in the sky with diamonds! Lucy in the sky with diamonds! Lucy in the sky with diamonds!

The concept of the album had already evolved: it would be as though the Beatles were another band, performing a concert. Paul and John said I should imagine that the band had just finished the concert, perhaps in a park. I then thought that we could have a crowd standing behind them, and this developed into the collage idea. I asked them to make lists of people they’d most like to have in the audience at this imaginary concert. . . . We then got all the photographs together and had life-size cut-outs made onto hardboard.

No one knows that this tale is a part of an immense poem: myths communicate with each other by means of men and without men knowing it. . . . The situation which Le Cru et le cuit describes is analogous to that of musicians performing a symphony while kept incommunicado and separated from each other in time and space: each one would play his fragment as if it were the complete work. No one among them would be able to hear the concert because in order to hear it one must be outside the circle, far from the orchestra. In the case of American mythology, that concert began millennia ago, and today some few scattered and moribund communities are running through the last chords.

The very end of the album typifies the advanced studio trickery applied throughout Sgt. Pepper. After the last droplets of the crashing piano chord of “A Day in the Life” have evaporated, come a few seconds of 15 kilocycle tone, put there – especially to annoy your dog – at the request of John Lennon. Then, as the coup de grâce, there is a few seconds of nonsense Beatle chatter, taped, cut into several pieces and stuck back together at random so that, as George Martin says, purchasers of the vinyl album who did not have an auto return on their record player would say “What the hell’s that?” and find the curious noise going on and on ad infinitum in the concentric run-out groove.

– Liner notes to Apple’s 1987 20^th anniversary CD release of Sgt. Pepper’s Lonely Hearts Club Band

Somebody calls you, you answer: “In theory, a twirl of kaleidoscopes” – why?[i]

If you were called to provide a summary of the first two installments preceding this, to someone who’s only just joined us, the perpetual revolution of Sir David Brewster’s famous tube should certainly be the very first image to pop from that jack-in-the-box you keep in your head. For Jacques Derrida, as we saw, lopped off this capstone of Lévi-Strauss’s extended metaphor of how the mythic mind operates: the workings of “bricolage” were like those of a kaleidoscope, as the anthropologist summed it up; but Derrida’s demolition job didn’t so much as footnote, much less explicitly point to, this motif.

Yet this “primal scene,” to use Freud’s term from one of his own myths, of postmodernism’s unfolding from that final patricidal conference presentation at Johns Hopkins in 1966, came a mere handful of months prior to the Beatles’ paean to “the girl with kaleidoscope eyes.” This veiled reference to Dr. Timothy Leary’s contemporary advocacy of psychedelic exploration with the aid of lysergic acid, best known by the 3-letter acronym it shared with Lucy’s apotheosis (“LSD,” of course), served like the shot of a starter-pistol, marking a revolutionary upheaval at least as epochal in general culture as deconstruction’s advent was among academics. Leary and Ralph Metzner meanwhile wrote about, and advocated, the use of low-tech kaleidoscopes, imported from the East, for inner exploration as well: I refer, of course, to mandalas. Mixing scientific and New Age styles, they managed to synthesize, in brief compass and without the “depth psychology,” the gist of what Jung’s approach toward such sacred objects (about which, more in the next installment) is taken to be by those who’d worn bell-bottoms and “love beads” while reading such things:

[The] mechanism of the mandala can also be understood in terms of the neurophysiology of the eye . . . [As] the mandala is a depiction of the structure of the eye, the center of the mandala corresponds to the foveal “blind spot.” Since the “blind spot” is the exit from the eye to the visual system of the brain, by going “out” through the center, you are going in to the brain. The Yogin finds the mandala in his own body. The mandala is an instrument for transcending the world of visually perceived phenomena by first centering them and turning them inward. [ii]

Note that Leary’s reading of the foveal blind spot is markedly at odds with Derrida’s – which is, if anything, to Leary’s credit. What we have, indeed, is one of many instances of the “inversion of significances” as one crosses the border between whatever one calls what Derrida does and science.[iii] The “blind spot” is his code for supplementarity and all its anomalies, initiated in his famous double-edged reading of Rousseau’s use of such terminology, also dating, like Leary and Metzner’s paper (and the Beatles’ psychedelic masterwork) from 1967. The gist of the notion is this: writing “supplements” (adds to, augments) speech, while creating a dependency on note-taking and reviewing (supplement now seen in opposite sense as “substitute” connoting and enhancing a lack) that erodes our capacity for remembering and thinking on our feet.

Rousseau cannot utilize [the concept of the supplement] at the same time in all the virtualities of its meaning. The way in which he determines the concept and, in so doing, lets himself be determined by that very thing that he excludes from it ... conveys neither a passivity nor an activity, neither an unconsciousness nor a lucidity on the part of the author…. [T]he law of this relationship to the concept of the supplement … is certainly a production, because I do not simply duplicate what Rousseau thought of this relationship. The concept of the supplement is a sort of blind spot in Rousseau’s text, the not-seen that opens and limits visibility…. And what we call production is necessarily a text, the system of a writing and of a reading which we know is ordered around its own blind spot. We know that a priori, but only now and with a knowledge that is not a knowledge at all.[iv]

For those who’ve read the last two installments, it should be obvious that this is just another instantiation of the application of the “différance” crowbar to someone else’s concepts – the “chiasmus” tactic, that is, wherein some binary opposition of themes basic to another thinker’s system is stood on its head to “deconstructive” effect. But it should also be obvious, from what’s just been said above, that this is not “just another instantiation” of the standard attack: for by “bouncing off” the blind spot at the level of the concept, instead of “going out through the center” it offers the meditator (or, for that matter, the mathematician attuned to the Kaleidoscope’s meta-significance), Derrida’s resistance to the pull of the Kaleidoscope/Mandala can show us, like Poe’s hero, how to escape from the (deconstructive) maelström itself![v]

In the final footnote to the last installment, we saw Derrida praise mathematics as the privileged tool to advance his own cause: “the resistance to logico-mathematical notation has always been the signature of logocentrism and phonologism in the event to which they have dominated metaphysics and the classical semiological and linguistic projects…. A grammatology that would break with this system of presuppositions, then, must in effect liberate the mathematization of language…. The effective progress of mathematical notation thus goes along with the deconstruction of metaphysics, with the profound renewal of mathematics itself, and the concept of science for which mathematics has always been the model.”[vi]

We’ll see many instances of the siren’s-song-like lure of the mathematical for Derrida, who, like Ulysses strapped to the mast while his minions have wax in their ears, can be maddened by the music which his crew steadfastly can’t hear. Indeed, as he writes with the ropes off, he stays deaf to it himself, albeit while paying it the obeisance of lip-service. Such “flirting,” however, needn’t be seen as a conscious deception, or unintended act of cowardice or ignorance. Rather, this contradictory attitude, to use Derrida’s own argot, demarcates the “blind spot” of his own systematic approach – one which the ongoing “Science Wars” begun in the late ‘90’s are serving, if anything, to exacerbate and caricature. Like the movie critic whose column you never miss because you count on disagreeing with him, Derrida’s deconstructions will provide a source of carefully wrought dissonances that will help keep our wheels greased. What Geoffrey Bennington says in his co-authored portion of Derrida’s autobiography should be read in just this light:

Every system excludes or expels something which does not let itself be thought within the terms of the system, and lets itself be fascinated, magnetized, and controlled by this excluded term, its transcendental’s transcendental…. The reading work carried out by Derrida consists in the location of these excluded terms or these remains that command the excluding discourse: the supplement in Rousseau; the index in Husserl; the parergon or vomit in Kant [; the goal of mathematicized philosophy in Derrida himself!][vii]

Returning to the crime scene, we’ve sensed a reverb connecting momentous events in the blue-jeaned and tweedy strains of recent culture; more, the secret history of the magician class – of the mathematical wizards, that is, whose enigmatic doings have as spin-offs all those technological marvels which have caused our general economies, our personal expectations, and our indices of detachment from our own inner natures to “grow,” as Lennon said, “so incredibly high”[viii] – also suffered overhaul in its gossamer world, which took, as we saw, the same form. Triggered by Catastrophe Theory (part of the same late-60’s shock wave on which Derrida and Sgt. Pepper surfed into awareness), Vladimir Arnol’d called it the “A, D, E Problem” just prior to the Watergate break-in. But this, as we’ve seen, was tantamount to rewriting Plato’s Timaeus and replacing all those references to regular polyhedra and primordial triangles with classes of “reflection groups” – a.k.a., types of kaleidoscopes. (The only salient difference is, we don’t know what sort of new “Age of Cathedrals” will erect itself upon this redacted text the way the last such Age articulated itself upon a previous edition[ix] – although the imagistic dyad of “Cathedral and Bazaar” has been a lightning rod for rethinkings of priorities, and focusings of visions, in Internet culture recently.[x])

And this, if we chose to open it now, could serve as yet another window on the workings of the “excluded term” commanding the “excluding discourse” in Derrida’s own work. In two celebrated studies of Plato, Derrida confirms our suspicions most concretely, by going out of his way to avoid discussing the mathematical creation myth contained in the Timaeus. The many paragraphs leading immediately into and away from the vision of Platonic solids and the trio of mysterious universe-creating triangles are referred to, even cited in bulk, in “Plato’s Pharmacy” and “Khora”; but the central, mathematical, core has a decidedly repulsive force on Derrida’s discourse.[xi] Yet these are the very verses which no less a physicist than Werner Heisenberg cited as providing him with his adolescent sense of vocation! In a sudden aha! experience inspired by the first great D minor chords of Bach’s Chaconne, “All at once, and with utter certainty, I had found my link with the center” – a link to the “central order” which had always been there in the languages of music, philosophy and religion, “today no less than in Plato’s day and in Bach’s. That I now knew from my own experience.” This revelation took shape during the next days’ hikes and talks with friends: in one such discussion, Heisenberg recalled speaking as follows:

Perhaps what we are arguing about is not so much our knowledge of atoms as the meaning of the words ‘actually’ or ‘real.’ You have mentioned the Timaeus and told us that Plato identifies the smallest particles of matter with mathematical forms, with regular bodies. Even if he was wrong in fact … he could have been right in principle. Would you call such mathematical forms ‘actual’ or ‘real’? If they express natural laws, that is the central order inherent in material processes, then you must also call them ‘actual,’ for they act, they produce tangible effects, but you cannot call them ‘real,’ because they cannot be described as res, as things. In short, we do not know what words we should use, and this is bound to happen once we leave the realm of direct experience, the realm in which our language was formed in prehistoric times.[xii]

Perhaps what Derrida is groping toward is a vocabulary that would allow the evocation of phenomena akin to these, “in which our language … formed in prehistoric times” is lost at sea. This is not so far-fetched as it might seem. For, while he and his followers give no signs of having a clue where things quantum mechanical are concerned, the epistemology of quantization is a far broader matter than its place of origin in the arcana of microphysics would suggest. Thresholds at which continuous processes are necessarily perceived as segmented occur in virtually all domains – including those of language, and hence of signification as thinkers from Saussure to Derrida would understand the term[xiii]; the only thing truly “special” about the domain of “Uncertainty” we associate with Heisenberg’s name is its “court of last resort” status: one can appeal to no deeper level of phenomena to overturn the “segmentation effect” found there.

Dennis Gabor, who won a Nobel for his invention of holography, based much of his analysis on an exact analogy to Heisenberg’s principle, applied to the general (and inverse) relationship between signal duration and effective spectral bandwidth: if signals are received through a channel of bandwidth ΔF, then the shortest impulse signal that channel can communicate is ΔT, where the product of ΔF and ΔT is a constant, of order unity, with an exact value “depending upon the arbitrary definition of ΔT and ΔF. No shorter signals can be communicated; such simple elements are the bricks out of which practical signals are built, whether they be speech, television, etc. We may then imagine that the time scale is graduated in intervals of ΔT; no briefer event than ΔT is measurable.”[xiv] In such a set-up, the so-called “continuous” signal is, while a very useful notion, a mathematical fiction nonetheless; Gabor called his discrete elements of uncertainty, ΔF· ΔT logons.

In 1950, D. M. MacKay referred to the generality of this logon concept, “pointing out that many instrumental measurements show an analogous uncertainty: for example, the aperture and resolving power of a microscope, or the sensitivity and response time of a galvanometer.” Three years later, Woodward showed “that the resolving power of radar, for moving targets, is uncertain with regard to discriminating target positions and velocities.”[xv] It would not seem so big a deal to imagine even philosophers getting the gist of this ubiquitous proliferation of “uncertainty” throughout all areas of communications theory thirty years after the fact – especially those focused on theories of language. (Out-of-work particle physicists hired by Wall Street, meanwhile, have already developed a mathematical analog of quantum electrodynamics to come up with innovative financial instruments: think of mundane frozen-orange-juice-concentrate futures contracts as logons, for instance, where a fixed time for delivery yields uncertainty in energy-level or price, allowing for contract pyramiding and all those other “virtual particle cascade” effects that make or break fortunes when the time-window closes and someone has to “take delivery” on real stuff.)

All of which makes the hero of the “Science Wars,” Alan Sokal, he of the quantum gravity deconstruction spoof, seem a tad unfair when he pillories a rather shrill feminist postmodernist for a formulation of an anti-logic of signification that looks somewhat like the physicist’s key quantization principles, which he assumes said camp follower couldn’t possibly know, much less know what to do with them.[xvi] All of which is likely true enough, but moot: we can go to the horse’s mouthpiece to get the same thing straight, no chaser. Here is what Geoffrey Bennington interlineates in Derrida’s so-called autobiography (and note, this quote may sound like gobble-de-gook; I intend to show, though, in what immediately follows, that it’s nothing of the sort . . . well, sort of):

Our problem has been constantly to stand between or short of, in the milieu of differentiation, and this is what we must try to formalize further: so we will not say that Derrida answers to one rather than the other of these descriptions, nor that he answers to one and the other, nor that he answers to neither one nor the other. The fact that we have to double up the neither/nor here (the form of our proposition is “neither (either a or b) nor (a and b) nor (neither a nor b),” which we can formalize further as ~((a^b) v (~a~b)), or, to bring out in what way it would be a “contradiction,” ~((~(~a~b)) v (~a~b)) (read as “it is false that of the propositions ‘at least one of a and b’ and ‘neither a nor b,’ one is true”), would be, precisely, the mark, in a propositional logic, of the questioning of opposition and negation in their philosophical versions, and one index among others that one cannot formulate everything in a logic, but at most in a graphic.[xvii]

In Sokal’s BS-banishing masterwork, there is a collection of appendices offered as commentaries on the parody which started the whole thing. In the first of these, where he explicates some of the spoof’s at times outlandish footnotes brought to bear on quantum mechanics proper, he reserves rare words of praise for one text in particular: appearing in the “serious” footnote 8, a referenced book by David Z. Albert on Quantum Mechanics and Experience is touted as “an excellent introduction for non-specialists.”[xviii] I defer to Sokal’s judgment (and also share his taste); here, then, is a crucial swatch of Albert’s setup, concerning the superposition principle.

Here’s an unsettling story (the most unsettling story, perhaps, to have emerged from any of the physical sciences since the seventeenth century) about something that can happen to electrons. The story is true. The experiments I will describe have all actually been performed.

The story concerns two particular physical properties of electrons which it happens to be possible to measure (with currently available technology) with very great accuracy. The precise physical definitions of those two properties don’t matter. Let’s call one of them the “color” of the electron, and let’s call the other one its “hardness.”

It happens to be an empirical fact that the color property of electrons can assume one of only two possible values. Every electron which has thus far been encountered in the world has been either a black electron or a white electron. None has ever been found to be blue or green. The same goes for hardness. All electrons are either soft ones or hard ones. No one has ever seen an electron whose hardness value was anything other than one of those two.

It’s possible to build something called a “color box,” which is a device for measuring the color of an electron and which works like this: The box has three apertures. Electrons are fed into the box through the aperture on the left, and every black electron fed in through that aperture exits through the aperture marked b, and every white electron fed in through that aperture on the left exits through the aperture marked w; and so the color of any electron which is fed in through that aperture on the left can later be inferred from its final position. It’s possible to build “hardness boxes” too [with apertures marked h and s], and they work in just the same way.[xix]

Albert next spends some pages backgrounding the nature of the apparatus and testing procedures, which anyone who finds this new should read. There’s a sliding wall which, when “in” position, blocks a particular beam, or, when “out,” facilitates its bouncing off a mirror which can ricochet it to another such box, allowing us to channel differently colored electrons into hardness boxes, or the reverse. Assume we’re talking about a “hardness box” in all that follows. Here’s how Albert continues, nine pages later:

So what we’re faced with is this: Electrons passing through this apparatus, in so far as we are able to fathom the matter, do not take route h and do not take route s and do not take both of those routes and do not take neither of those routes; and the trouble is that those four possibilities are simply all of the logical possibilities that we have any notion whatever of how to entertain!

What can such electrons be doing? It seems they must be doing something which has simply never been dreamt of before (if our experiments are valid, and if our arguments are right). Electrons seem to have modes of being, or modes of moving, available to them which are quite unlike what we know how to think about.

The name of that new mode (which is just a name for something we don’t understand) is superposition. What we say about an initially white electron which is now passing through our apparatus with the wall out is that it’s not on h and not on s and not on both and not on neither, but, rather, it’s in a superposition of being on h and being on s. And what that means (other than “none of the above”) we don’t know.[xx]

It would, I think, be preposterous to assume that Bennington/Derrida had somehow rediscovered the foundations of quantum mechanics and applied them to the roots of language; it is my own opinion that they’ve no notion at all of the superposition principle – which doesn’t invalidate their stumbling upon it anyhow! There is a good reason for this, one of which physicists seem generally unaware – and the “supplemental [sic] bibliography” of the Bennington/Derrida tome can tell us where to look. For in Harold Coward’s book on Derrida and Indian Philosophy, we can find, indirectly, an extended discussion of the same construction. (I say “indirectly,” as Coward – like most deconstructionists, and like most humanists – does not think in ways a mathematician or physicist would feel comfortable with: an explicitly symbolic formulation like that provided by Bennington, then, is not forthcoming: one needs to know in advance what Nagarjuna’s “catuskoti or four-pronged negation,” which “shows the futility of attempting to take any sort of ultimate philosophical position,”[xxi] is, in order to see the “self-evidence” of the connection.)

The great mythologist Joseph Campbell tells us that the Buddhist philosopher Nagarjuna (c. 200 A.D.) offered “paradoxical teachings of the ‘full void’” which “represent perhaps the culmination of the history of metaphysical speculation”[xxii]; but the “full void” (out of and into which matter is continually created and destroyed, and which “emptiness” Casimir’s Nobel work showed even has a “force”[xxiii]) is the seminal paradox of quantum mechanics as well. The Madhyamika school of Buddhism saw Nagarjuna’s teachings as the starting point on the road to Enlightenment; the Copenhagen (and all later) interpretations of physics see the exactly analogous mystery of superposition as a similar launching pad. The big difference, of course, is that the mystery as pondered by physicists, and manipulated with mathematics, opens out on the most accurate and profoundly extensible physical theory ever built. Far from having attained to the exhaustion, so evident in Derrida’s excluded and excluding position in relation to it, of the Western philosophical tradition (the Nagarjuna-like formulation cited above comes from a section of text focused on the issue of Western philosophy’s “Closure”), a scientific “philosophy” attuned to quantum theory must draw upon the (meditative as well as philosophical) traditions of the East – New Age mushy-headed nonsense notwithstanding.[xxiv]

Upon completing the twelve-year ordeal of writing his magnum opus, The Masks of God (in four volumes), Joseph Campbell reflected on what for us will be a mission statement, but was, for him, at once his main result, and “a thought I have long and faithfully entertained: of the unity of the race of man, not only in its biology but also in its spiritual history, which has everywhere unfolded in the manner of a single symphony, with its themes announced, developed, amplified and turned about, distorted, reasserted, and, today, in a grand fortissimo of all sections sounding together, irresistibly advancing to some kind of mighty climax, out of which the next great movement will emerge. And I can see no reason why anyone should suppose that in the future the same motifs already heard will not be sounding still – in new relationships indeed, but ever the same motifs.”[xxv]

It is rather easy to segué from this overarching mission statement, to that specified before for this particular installment. The very first sentence of The Masks of God, after all, reads as follows: “The comparative study of the mythologies of the world compels us to view the cultural history of mankind as a unit; for we find that such themes as the fire-theft, deluge, land of the dead, virgin birth, and resurrected hero have a worldwide distribution – appearing everywhere in new combinations while remaining, like the elements of a kaleidoscope, only a few and always the same.” Sixty pages in, he reverts to the image again:

It has been the chief function of much of the mythological lore and ritual practice of our species to carry the mind, feelings, and powers of action of the individual across the critical thresholds from the two decades of infancy to adulthood, and from old age to death; to supply the sign stimuli adequate to release the life energies of the one who is no longer what he was for his new task, the new phase, in a manner appropriate to the well-being of the group. And so we find, on the one hand, as a constant factor in these “rites of passage,” the inevitable, and therefore universal, requirements of the human individual at the particular junctures, and on the other hand, as a cultural variable, the historically conditioned requirements and beliefs of the local group. This gives that interesting quality of seeming to be ever the same, though ever changing, to the kaleidoscope of world mythology, which may charm our poets and artists but is a nightmare for the mind that seeks to classify.[xxvi]

“And yet,” muses Campbell, with an almost audible sigh, “with a steady eye, even the phantasmagoria of a nightmare can be catalogued – to a degree.” And to such cataloguing he did proceed – he and Lévi-Strauss both, in four-volume works of similar length and comparable depth, each preaching the discovery of One Myth Only, written virtually simultaneously (publication dates for Mythologiques: 1964-71; for Masks of God: 1959-68), yet with never a reference of one to the other, so opposite-seeming were their methods and purposes.

For all their differences, however, there is one area where Campbell’s approach can make defending Lévi-Strauss’ from Derrida’s critique much easier. The route, while indirect, is easy to follow, and begins with the 1868 work of a German scholar who applied the then-nascent techniques of comparative biology and psychology to the eliciting of the “constants” and “variables” in the mythologies of mankind.

Jung’s idea of the “archetypes” is one of the leading theories, today, in the field of our subject. It is a development of the earlier theory of Adolf Bastian (1826-1905), who recognized, in the course of his extensive travels, the uniformity of what he termed the “elementary ideas” (Elementargedanke) of mankind. Remarking also, however, that in the various provinces of human culture these ideas are differently articulated and elaborated, he coined the term “ethnic ideas” (Völkergedanke) for the actual, local manifestations of the universal forms. Nowhere, he noted, are the “elementary ideas” to be found in a pure state, abstracted from the locally conditioned “ethnic ideas” through which they are substantialized; but rather, like the image of man himself, they are to be known only by way of the rich variety of their extremely interesting, frequently startling, yet always finally recognizable inflections in the panorama of human life. [xxvii]

If one switches terminology a bit, one could try to think of the elementary ideas as “ideal” objects in the phenomenologist’s sense, and say of their relations to their concrete manifestations much the same as Derrida has: put simply, they never appear “purely,” as they must be evinced through a “communal subjectivity,” hence historicity;[xxviii] corollarily, they adhere to an “idea of science [which] is the index of a pure culture in general” – the idea, that is, “of what, from the first moment of its production, must be true always and for everyone, beyond every given cultural area.”[xxix] But some ideal objects, in Husserl’s scheme, are “privileged”: those of mathematics.[xxx] And Derrida, beginning with his study of Husserl’s privileging of these, contemplated the “privileging” of certain others. Between these two cases – placed, like Max Ernst’s umbrella and sewing machine, on the “operating table” of Adolf Bastian’s “elementary ideas” – something like a critique of Derrida’s critique of bricolage begins to emerge, almost by itself.

Consider, first, the ideal objects of mathematics: Husserl, himself a gifted mathematician slated to take over the chair of the great Karl Weierstrass before he opted, instead, for a philosopher’s career, knew of what he spoke in their regard. And it is very clear that a signal difference between the modern practitioner of engineering and the jack-of-all-trades Mr. Fixit who is Lévi-Strauss’ bricoleur concerns their necessary relationship (or lack of same) to this field of ideal entities. Unlike a general humanist, and certainly unlike the typical deconstructionist, an engineer (with the exception of those, like “sanitation engineers,” who owe their title to euphemism) cannot attain certification in his or her area of expertise without demonstrating proficiency in a significant quantity of mathematics. The fact that the general “praxis” a bricoleur engages in would seem to involve some comparable sort of ideality only serves to heighten what Husserl called the “crisis of phenomenology” and, hence, the shortcomings of its purely introspective approach.[xxxi] For the skills of a particular bricoleur are, like the “assembler code” and “machine language” levels of computer programming, heavily context-dependent, and not, in general, “portable” to other cultural “machinery” (unlike the case, say, with mathematical training) in any straightforward way.

Part of the problem, as François Jacob noted, is this: “Unlike engineers, tinkerers [his English term, recall, for bricoleurs] who tackle the same problem are likely to end up with different solutions.”[xxxii] But the history of science and mathematics has shown time and again that many routes to the same solution may be taken (phenomena of “simultaneous discovery” are rampant[xxxiii]); solutions to the same problem may seem different for a fleeting historical instant (the radically opposite approaches of Schrödinger’s wave, and Heisenberg’s matrix, mechanics, were translated into a unified formalism by Paul Dirac within a few months[xxxiv]); yet science, almost tautologically, hits upon unique solutions.

And yet, this self-evident fact – the miracle of what E. P. Wigner called “the unreasonable effectiveness of mathematics”[xxxv] in describing the world; a miracle, moreover, contingent upon asking limited questions, instead of metaphysically universal ones, in order to garner ever more general answers – is dismissed as a “theological idea” by Derrida![xxxvi]

We have every reason to suspect that such a dismissal is pejorative, and can find even more blatant instances of ad hominem argument in the 1966 attack. For instance, Lévi-Strauss’ intentions of thinking “bricolage” mathematically (as he’d done with kinship structures already) were well-known, and predated his use of the term. In “The Structural Study of Myth,” he announced a “canonical law” of mythological transformations which he claimed guided his analyses constantly . . . and which he explicitly envisioned as attaining at some future date to a rigorous mathematical expression (which we saw, in the previous installment, one can argue it has). Yet this clear-cut agenda is never addressed in Derrida’s critical text on Lévi-Strauss, even though it was written in the same “moment” as his math-venerating Positions were put forth.

On the contrary, the least significant aspects (for us, at least) of Lévi-Strauss’ thought – his sentimental attachment to Rousseau’s positions on the topics of speech and writing – are highlighted instead, to the exclusion of everything a programmer or mathematical modeler would deem of interest. But I find this inexcusable by the same style of argument Derrida uses against his target here: “the praise of living speech, as it preoccupies Lévi-Strauss’ discourse, is faithful to only one particular motif in Rousseau,” we are told. But ditto for Derrida and his one-sided agenda when approaching Lévi-Strauss![xxxvii]

Adding further fuel to ad hominem suspicions, Lévi-Strauss carefully indicates that while mythological thought builds its structural sets by bricolage effected on the products of language, “it is not at the structural level that it makes use of it.”[xxxviii] (The debris in the object box is not at the same level as the patterns created by the kaleidoscope’s mirrors, in other words.) But Derrida indulges in petitio principii: he implicitly bundles his conclusions in his assumptions and then triumphantly deduces them.

The core fallacy is easy to miss: “If,” he says, “one calls bricolage the necessity of borrowing one’s concepts from the text of a heritage which is more or less coherent or ruined, it must be said that every discourse is bricoleur.”[xxxix] The supposition hinges on a single “weasel word”: for the bricoleur does not ‘borrow’ concepts! Concepts are what the engineer manipulates and creates, which participate “at the structural level” (they expand the vocabulary, even the grammar, of the language). They are, in fact, what separate him from the bricoleur. Indeed, this one seeming nuance contains the whole difference. Once this is realized, Derrida’s argument is seen as so much wind. Here is what Lévi-Strauss actually says:

Both the scientist and ‘bricoleur’ might therefore be said to be constantly on the look out for ‘messages.’ Those which the ‘bricoleur’ collects are, however, ones which have to some extent been transmitted in advance – like the commercial codes which are summaries of the past experience of the trade and so allow any new situation to be met economically, provided that it belongs to the same class as some earlier one. The scientist, on the other hand, whether he is an engineer or a physicist, is always on the look out for that other message which might be wrested from an interlocutor in spite of his reticence in pronouncing on questions whose answers have not been rehearsed. Concepts thus appear like operators opening up the set being worked with and signification like the operators of its reorganization, which neither extends nor renews it and limits itself to obtaining the group of its transformations.[xl]

Likewise, if explicit separation of levels is ignored when it suits him, the explicitly stated interdependency of the notions of bricolage and engineering is conveniently overlooked: while “the relation of priority between structure and event is exactly the opposite in science and ‘bricolage,’” the scientist “too has to begin by making a catalogue of a previously determined set consisting of theoretical and practical knowledge, of technical means, which restrict the possible solutions,” so that their difference is “less absolute that it might appear.”[xli] And it is from this pre-given set that he creates new things which then get added to it – just as the kaleidoscope (which required a scientist to invent it) generates endlessly new patterns of predetermined symmetry, which stand in relation to the debris in the object box much as our evolving thoughts do to the ephemeral firings of synapses in our brains’ myriad cells.

Derrida clearly indulges in these surgeries so that he can frame the coupling of the bricoleur and engineer as a rigid “all or nothing” dichotomy, which he can then claim to demolish, thereby leaving us with a notion of objective scientific progress sufficiently relativized and deprived of its indispensable innovativeness as to no longer threaten the rape and pillage of his liberal-artsy audience’s turf. In fact, it is this notion of scientism (the “big stick” sensed carried by soft-walking structuralism) which would seem to be the real target here – which no doubt helps explain the undeserved acclaim won by Derrida’s shoddy argument among so many technophobic humanists.

Indeed, Derrida “plays to the house” with a bit too much gusto: he tells us, for instance, that “the engineer and the scientist are also species of bricoleurs”; in fact, that “the engineer is a myth produced by the bricoleur.” He even tells us when we’ll be persuaded of this: “As soon as we cease to believe in such an engineer and in a discourse which breaks with the received historical discourse.”[xlii] Intoning these words into a microphone wired into a state-of-the-art sound system as people are making their way by internal-combustion-engine-driven taxis to catch their computer-scheduled connections to waiting jet planes with choice of beverage and in-flight movies, it seems he expected he could make his audience cease in such beliefs by steady application of Hitler henchman Joseph Goebbels’ “Big Lie” technique. (And in this, not for the first time or the last, history has shown this sort of cynical assessment to be, alas, correct.)

In a caricature that serves almost as well as an honest argument (albeit unintentionally) to show how much the engineer is not a bricoleur, we are told “how the language of the social sciences criticizes itself”: by

conserving all these old concepts within the domain of empirical discovery while here and there denouncing their limits, treating them as tools which can still be used. No longer is any truth value attributed to them; there is a readiness to abandon them, if necessary, should other instruments appear more useful. In the meantime, their relative efficacy is exploited, and they are employed to destroy the old machinery to which they belong and of which they themselves are pieces.[xliii]

Yet no science, “social” or otherwise, could proceed in this manner and be a science at the same time. Consider applying this description to a physicist: the first sentence in the above is quite unobjectionable; but in the second, things begin to wobble a bit. The “tools” of the physicist, after all, are mathematical: it is not possible, then, to say “no longer is any truth value attributed to them”; quite the contrary, they wouldn’t be in the toolkit in the first place unless their mathematical truth were indisputable. There is certainly a “ readiness to abandon them” in a given context: this means they’re inappropriate for the job at hand, not false. The final two clauses give proof of the confusion of levels that has become ever more evident in its predecessors: if these concepts are “employed to destroy the old machinery,” then this latter must be the physical theory the objects were involved in constructing. But this is a theory to which they do not “belong,” even though “they themselves” fabricate (not “are”) “pieces of it.” (This is the same distinc-tion, recall, that young Heisenberg made between “actants” and “real things.”) Instead, they belong to, and are parts of, mathematics, whose creations are cumulative and proven, and from whose storehouse they can be loaned out to any theories, even bad or merely wrong ones.

Is bricolage, then, a “theological idea”? It is clear that the only “theology” we can point to in the texts we’ve just reviewed is perpetrated by Derrida himself – “if,” to paraphrase the wording of what I’ve called his “core fallacy,” “one calls” theology “the necessity of borrowing one’s concepts from the text of a heritage which is more or less coherent or ruined” – with the “heritage” here being, of course, not the set-in-stone revelations of Sacred Scripture, but the “one size fits all” imprecisions of endlessly recycled fragments of failed metaphysics, the Sargasso Sea where deconstructionists “bricolage” their argot.

All of which is just so many jabs to the body, meant to “soften up” our quarry for the knock-out uppercut to the head. But we can let Derrida punch out his own lights; for, as mentioned above, the insufficiency of Husserl’s notion of “ideality” was explicitly felt by him to be a real problem; but his approach, as we’re about to see next, can only serve to make things worse -- especially in the current context! Indeed, in his notoriously delayed thesis defense, one could even argue that “the jig is up” completely when he lets on what his intentions had been from the get-go.

As he makes clear in “Time of a Thesis,” Derrida’s hidden agenda predated, apparently, even his first published book, a work which focused on “those ideal objects par excellence, mathematical objects.”[xliv] What was this agenda, then? Nothing less than to promote to the first rank of philosophical consideration the “non-mathematical or non-mathematizable object”; in particular, the object which was both his “most constant interest”[xlv] and the most idiom-constrained of all human creations: the literary artefact[xlvi]-- and above all, as epitomized in his studies of Mallarmé[xlvii] and Ponge[xlviii], the poetical work.

Given such inclinations, it is rather incredible Derrida thought he could use his favored analytic instruments to cobble together an argument against Lévi-Strauss’ structural mythology in the first place – and even more amazing that it convinced so many for so long. One is reminded of Dr. Johnson’s description of a dog walking on its hind legs: “the wonder is not that it does it well, but that it does it at all.” For the materials of myth are especially resistant to any working up with such a toolkit:

Myth is the part of language where the formula traduttore, tradittore reaches its lowest truth value. From that point of view it should be placed in the gamut of linguistic expressions at the end opposite that of poetry, in spite of all the claims which have been made to prove the contrary. Poetry is a kind of speech which cannot be translated except at the cost of serious distortions; whereas the mythical value of the myth is preserved even through the worst translation. Whatever our ignorance of the language and the culture of the people where it originated, a myth is still felt as a myth by any reader anywhere in the world. Its substance does not lie in its style, its original music, or its syntax, but in the story which it tells. Myth is language, functioning on an especially high level where meaning succeeds practically at “taking off” from the linguistic ground on which it keeps rolling.[xlix]

Some fifteen years after writing the above, the fourth and final volume of the Mythologiques was complete; in its lush, six-dozen-page “Finale,” he reflected on the text just cited, and opined that “if, in spite of the decisive part played by philology in Professor Dumezil’s outstanding works, from which I have learned so much, I had made it a preliminary condition that I would study the myths only in the original languages, my project would have been unrealizable, not only by me, … but by anybody else.” And yet, reflecting upon the finished work, “undertaken in the face of limitations serious enough to make it theoretically unfeasible,” the outcome “proved most fruitful” – which “seems to constitute a mystery, which calls for explanation.” The key to its unraveling resides, he felt, in the myth creation process revealed in his work, “which it alone could demonstrate clearly by being carried through to its conclusion.”

If, as is shown by the comparative analysis of different versions of the same myth produced by one or several communities, conter (to tell a story) is always conte redire (to retell a story), which can also be written contredire (to contradict), it is immediately understandable why it was not absolutely essential ... to study the myths in the originals, instead of in a translation or a series of translations. Properly speaking, there is never any original: every myth is by its very nature a translation, and derives from another myth belonging to a neighbouring, but foreign, community, or from a previous myth belonging to the same community or from a contemporaneous one belonging to a different social sub-division – clan, sub-clan, descent group, family or brotherhood – that some listener tries to plagiarize by translating it in his fashion into his personal or tribal language, sometimes to appropriate it and sometimes to refute it, and therefore invariably distorting it. A particularly striking instance of this phenomenon is supplied by a Hupa myth about the origin of fire that the demiurge is said to have tried initially, and unsuccessfully, to produce by percussion, and then by inventing the first fire-drill. The person who recorded this story states specifically that it was produced with the intention of giving the lie to a myth belonging to a neighbouring tribe and which asserted that the first fire had been obtained by theft…. Therefore a myth never belongs to its language, but rather represents an angle of vision on to a different language, and the mythologist who is apprehending it through translation does not feel himself to be in an essentially different position from that of the native narrator or listener.[l]

There is a fantastic irony in all this: for it is Lévi-Strauss, who never discusses phenomenological theories, and certainly never Husserl’s, who would seem most true to the spirit of Husserl’s mathematical “privileging”; Derrida, on the other hand, in his search for some “other” sort of ideality, takes flight from what we saw him, in an earlier note, refer to as the aridity of “desertlike technoscientificity,” in order to embrace the Babel-like buzzing of the “universal hive of inviolable secrets.” On the other hand, though, it is just because such agendas don’t interest him that he is able to transcend their severe limitations and find a more general kind of “ideality” anyway – that based on universal human praxis, the ritualized and mythologized expressions of those “rites of passage” undergone by all acculturated humans. Yet this “ideality” is no longer introspective (hence Husserl’s “crisis” in failing to incorporate it); rather, the mathematical transformations to which the anthropologist subjects all such undergoings, the better thereby to “translate” them across cultural boundaries, are, we might say, “ontologically appropriable” – it is a question, at bottom, of “actants” again, and not of “things” – and hence not amenable to phenomenological registering at all.

The phrase “ontologically appropriable” is suggestive of some of Lévi-Strauss’ own words: in a famous passage in the Proustian “Overture” which begins the Mythologiques, he compares his method’s expansionary agenda to that of “an amoeba engulfing its prey” . . . and when he says, soon thereafter, that his own work could be called “the myth of mythology,” it is clear that this engulfing tactic is seen as integral to his quarry as well as his method. However, the phrase is clumsy, and smacks too much of modes of philosophizing which he seems to have scant use for. A far better term would be to speak, as the authors of The Embodied Mind do, of “emergent properties.”[li] These authors’ Madhyamika Buddhist stance is, after all, far closer to the blatant strain of Buddhism Lévi-Strauss reveals in his “Finale”; and both would strive to reintegrate the human and the natural, “while making it possible to disregard the subject – that unbearably spoilt child who has occupied the philosophical scene for too long now, and prevented serious research through demanding exclusive attention.”[lii]

It is this subjectivism which is the greatest impediment to serious progress in Derrida’s project, as his connoisseur’s discussion of the different flavors of Narcissism[liii], among many other symptoms, would tend to indicate. And it is also – also ironically, perhaps – the key to grasping the objective content of the kaleidoscope imagery that Derrida, knowingly or just instinctively, found it necessary to suppress. As its inventor well knew, “the fundamental principle of the kaleidoscope” is this: if its mirrors “be set in any position upon any object, however confused, or distorted, or irregular, they will create the most perfect and symmetrical designs.”[liv]

The mirrors, then, are “universal symbolizers,” creating order out of chaos wherever it is met – but only by acceding to severe constraints. Paramount among these? According to Brewster, the instrument’s inventor, its effects “cannot be produced by any combination of mirrors, in which the objects are placed within them.”[lv] Put another way, the kaleidoscope is a system of “speculation” – in the original sense of pure mirror play – engaging the tactile interplay of eye-hand coordination while excluding Narcissus: not only can no objects go between the mirrors, but no reflection of the viewer is returned by them.

The Surrealists and those who shared their orientation had a strong aversion to the ego cultism of our century, and cultivated, instead, the getting ego out of the way to let inspiration take its place. Lévi-Strauss himself is quite clearly of this camp, as his remarks about “that unbearably spoilt child” cited above make self-evident. Of his own personal self, moreover, he professes not to know how even to locate it:

I never had, and still do not have, the perception of feeling my personal identity. I appear to myself as the place where something is going on, but there is no “I,” no “me.” Each of us is a kind of crossroads where things happen. The crossroads is purely passive; something happens there. A different thing, equally valid, happens elsewhere. There is no choice, it is just a matter of chance.[lvi]

To fully appreciate the implications of such a rich technological allegory as that implied in Lévi-Strauss’ kaleidoscope, we need to contrast its “play of mirrors” with other sorts which are not “symbolic” in the senses required. Optical images of all varieties abound in the anthropologist’s writings, so it’s easy to find significant examples. One crucial to his fundamental method calls for singling out, which he first evoked in his famous 1955 essay, “The Structural Study of Myth.”

We’re told that while “it cannot be too strongly emphasized that all available variants should be taken into account” in myth analysis, we needn’t fret over lack of evidence if a small handful – four or five, perhaps – is all we can get. The point is brought home vividly through reference to an experience familiar to most people who’ve ever sat to have their hair cut in a barber shop:

If the furniture of a room and its arrangement were know to us only through its reflection in two mirrors placed on opposite walls, we should theoretically dispose of an almost infinite number of mirror images which would provide us with a complete knowledge. However, should the two mirrors be obliquely set, the number of mirror images would become very small; nevertheless, four or five such images would very likely give us, if not complete information, at least a sufficient coverage so that we would feel sure that no large piece of furniture is missing in our description.[lvii]

The mirrors here function as an inventory mechanism: they provide “sufficient coverage” for symbolic consolidation to be effected. The move from between the barber’s mirrors to behind the kaleidoscope’s eyepiece is akin to a shift from conducting an inventory to inventing. The latter always seems somehow paradoxical or problematic to Derrida (see his essay “Psyché: Inventions of the Other,” which focuses on the problem of invention via a reverie on the vertically flippable full-length mirror used by Beau Brummels and fashion models to dress themselves, and called, fortuitously, a “psyché” in French). [lviii] Attempts at systematic optical imagery by Derrida, moreover, have, like the interrelatedness of images in Joyce Kilmer’s “Trees,” the contorted incoherency of a 60’s partygoer who’s been playing Twister too long. (See the fun-to-read, hard-to-fathom “genoptics” of his Mandela homage, “Laws of Reflection.”[lix])

The celebrated remark from the “Overture” to the Mythologiques’ first volume, cited by Octavio Paz in the third lead-in quote at the top of this installment, can be seen to summarize as well as introduce this point of view: “myths communicate by means of men and without men knowing it.” Cultural objects, then, to use the term made famous in Richard Dawkins’ popular book on The Selfish Gene, are “memes,” and if we want to study their workings, we need to get our egos out of the way and consider their behaviors as parts of complicated systems. In this regard, the rather condemnatory results of Jean-Pierre Dupuy’s comparative study of Dumontian anthropology, Derridian deconstruction, and “the concept of a self-organizing (autopoietic, autonomous) system” (as studied, for instance, in the work cited often here, The Embodied Mind of Varela, Thompson, and Rosch) serve only to underscore everything said above.

In “Tangled hierarchies: self-reference in philosophy, anthropology, and critical theory,” Dupuy describes how Varela and company’s efforts at computer-simulated “Artificial Life” and the like require considering the meaning, and means of creation, of programs which write themselves. Such programs, from “neural nets” in heavily parallel ensembles of processors, to “genetic algorithms” run on Connection Machines or their successors, to proteins which themselves transcribe and translate DNA into proteins, paradoxically require the outputs of their execution in order to be executed. “Now, the amazing fact is the following: it is this very same paradox which has been taken by the theoreticians of autonomous systems as the distinctive characteristic of what they call autonomy. On the other hand, the same paradox is the Derridians’ main weapon for the deconstruction of any pretension to autonomy or self-sufficiency. As long as academic compartmentalization keeps these two groups in total ignorance of each other, the opposition of interpretations could continue for a long time to come.” My only complaint with Dupuy’s assessment is that he’s much too kind. [lx]

While Lévi-Strauss never deigns in his books to respond directly to attacks like Derrida’s, his “Finale” contains an indirect dismissal whose real target would be rather obvious to his contemporary readers:

I could have no tolerance for a form of deceit in which the left hand slips under the table to restore to the worst kind of philosophy what the right hand claims to have taken from it above board, and which, through simply replacing the Self by the Other and by sliding a metaphysics of desire under the logic of the concept, deprives this logic of its foundation.[lxi]

Speaking more generally about contemporary philosophizing at large, he offers these remarks:

Contemporary philosophy, being imbued with a mysticism that is rarely openly admitted and more often concealed under the appellation of humanism, and always hoping to discover a gnosis that would allow it to mark out for itself a private area inaccessible to scientific knowledge, has taken fright on seeing mythology, which it wanted to be full of hidden meaning, reduced to what some people take to be the vacuity of a series of translations without any original text. This is to fail to see that the same might be said about an area where, however, mystical aspirations and sentimental outpourings are given fairly free rein; I am referring to music. The truth is that the comparison between mythology and music, which was the leitmotif of the ‘overture’ to this work, and which was condemned as arbitrary by many critics, was based essentially on this common feature.[lxii]

What is fascinating about this link to music is that it provides the perfect place for earnest deconstructionists to insert their “crowbars”: for music indeed serves to organize Lévi-Strauss’ entire oeuvre, in precisely the manner an excluded controller of an excluding discourse is supposed to! For this idolizer of Wagner’s operas and great-grandson of the director of Napoleon III’s imperial orchestra had a lifelong ambition to become something quite other from that which he wound up:

To me, at any rate, it appears certain – since I embarked on this Introduction to the Science of Mythology in full consciousness of the fact that I was trying, in a different form and in an area accessible to me, to make up for my congenital inability to compose a musical work – that I have tried to construct with meanings a composition comparable to those that music creates with sounds: it is the negative of a symphony which, some day, some composer could well try to produce the positive image; I leave it to others to decide whether the demands that music has already made on my work can be said to prefigure such an image.[lxiii]

But an honest attempt at such a deconstruction would be bound to fail, for a number of reasons. The most obvious of these is suggested by an image which appears in one of Derrida’s too-numerous papers: two men on escalators heading in opposite directions recognize each other through the glass partition separating their stairwells; they can press their hands and faces against the glass in an attempt to convey messages in mime, but they cannot make out each other’s speech, and ultimately, pulled toward different destinations, they cannot communicate at all. For all their alleged radicalness of approach, deconstructionists are horribly, quaintly, crippled by an incapacity to cross disciplinary boundaries in any constructive manner: like viruses, like kudzu, or like the “obscurantist terrorists” Michel Foucault is alleged to have epitomized them as[lxiv], all they know how to do is to apply their ironic bag of tricks to whatever’s in their path and watch it corrode and collapse. But their “method” has no shape, no life-force, of its own. How is the problem of linguistic translation “like” that of musical transposition, variation, and so on, and how does this relate to the structure of myths? And how is this approach amenable to mathematical treatment? Such questions are never addressed, or even allowed (or even imagined) by deconstructionists – nor can they be, until they become something else.

The tables, though, can be turned the other way, as we’ll soon see. Before actually “seeing” this performance, though, its trajectory can be conveyed with succinctness in an abstract summary this way. A fourfold classification of high-level objects “open to structural study” is posited: “mathematical entities, the natural languages, musical works, and myths.”[lxv] This fourfold scheme is implicitly related to one of the simplest forms of symmetry in mathematics – the four-element Klein Group, “including a theme, the contrary of the theme and their opposites” – whose use in the prior volume of the Mythologiques is reviewed. But this utilization “gave sets of interlocking four-term structures, retaining a relationship of homology with each other.”[lxvi] Yet this fourfoldness is also quite clearly a cyclical instancing of the “canonical law of myths” we saw, last installment, to be epitomized mathematically by the “Double Cusp” Catastrophe.[lxvii] And “it so happens” that the Klein Group is, via “A, D, E” magic, uniquely associated with the “umbilic cycle”[lxviii] of elementary catastrophes, which are uniquely “made compact” by being embedded in the Double Cusp. This much states the basic theme of our abstract summary. But now, in true Klein Group style, I’ll state the contrary of the theme (which will imply quite opposite results from those the 1966 talk claimed!).

In a gushing, lushly self-indulgent 79-page preface to her translation of Of Grammatology, Gayatri Chakravorty Spivak says of her hero, “Derrida would not privilege a signifier into transcendence. The movement of ‘difference-itself,’ precariously saved by its resident ‘contradiction,’ has many nicknames: trace, différance, reserve, supplement, dissemination, hymen, greffe, pharmakon, parergon, and so on. They form a chain where each may be substituted for the other, but not exactly (of course, even two uses of the same word would not be exactly the same): ‘no concept overlaps with any other.’ Each substitution is also a displacement, and carries a different metaphoric charge, as Derrida reminds us often.” In other words, he provides us endless “flavor of the week” variants on the Lévi-Straussian “transformation of a metaphor into a metonymy,” conflating each such instantiation with a “new, improved” concept (implicitly in quotes, since “the concept of the concept” is something he’s been known to worry about). “He does not hold on to a single conceptual master-word for very long. ‘Arche-writing,’ ‘trace,’ ‘supplementarity,’ such important words in the Grammatology, do not remain consistently important conceptual master-words in subsequent texts. Derrida’s vocabulary is ever on the move.”[lxix]

Of course, juxtaposed with the Klein-Group concatenating of the Mythologiques, this could sound as if Derrida, to put it in Piagetian terms, is seriously stuck in pre-adolescent “concrete operator” thinking, with no “logical operators” in sight. But of course, for that to fly, we’d have to buy into the myriad instances of “new, improved” concepts with names that stay shiny for an essay or two being somehow reducible to the “3+1” structure of a Klein Group daisy-chain. I imagine Perseus swinging Medusa’s head like a mace, chasing the shape-shifting seagod Proteus through a hall of mirrors: will Proteus/Derrida finally have his conceptual apparatus forced into fixity, or will Perseus/Lévi-Strauss lose him in the conflation of real things with their images?[lxx] But, unfortunately for Proteus, the proliferation of “3+1 structures” with different names but playing the same game, essay after essay after essay, would suggest quite strongly that Perseus wins the day. And we can point to Spivak’s own essay to see how likely this should seem.

In a footnote concerning a book “relating this project – the desire that word be one with meaning – with Narcissus’s desire to be one with his image, and with the child’s narcissistic desire to be one with the mother,” we are told that in Dissemination, “Derrida presents the structure of the square with an open (yet presupposed) fourth side,” which a forthcoming review of the book being referenced shows can be related “to the forever active triangularity of the oedipal position , which intervenes to resolve the unfulfilled narcissistic desire for self-enclosure.”[lxxi] This sounds suspiciously like a lot of self-obsessed verbiage hiding the simplicity of Lévi-Strauss’ “nuclear triangle,” from the second presentation of his “canonical law of myths,” discussed in the notes of the last installment. One can be fairly certain, however, that such is not consciously the case. Why? Because all deconstructionists I’m aware of who’ve thought about this structure at all are too mathematically inept to handle even this incredibly simple sort of symmetry – indeed, they can’t even properly see, much less work with, it, as the discussion of Derrida’s “tetrapolarity” which Spivak refers the interested reader to, can’t tell 2 x 2 from 3 + 1.[lxxii]

The cataloguing of types of symmetry – and hence, as discussed last installment, of forces and particles in fundamental physics – is the basic subject of Group Theory. The simplest kind of group is the so-called “cyclic group,” eminently representable by circuitings of arbitrary polygons: traversing a pentagon entails one group element, call it “p,” which, repeated five times, takes us clockwise back to our starting point, so that we can write p⁵ = p⁰ = 1 (where “1” is the so-called “identity element”). A group needs an identity, closure (i.e., you can never say “you can’t get there from here”), and reversibility (there’s always some operator that can combine with a given one and take you back to the identity: p⁴ here would be the counterclockwise move that would cancel out p and leave you where you started).

Now, cyclical groups are pretty boring after the first few minutes of one’s first Group Theory 101 lecture. “Dividing” the cyclic structure of the calendar by the seven-element cyclic group leaves a residue that can be mapped one-to-one to the days of the week. The first time you hear this, it’s exceedingly interesting to realize you can think that way; the thrill is gone, though, by the second or third occasion you hear such an argument. So one can say that Group Theory – hence, the study of symmetry – only starts to be interesting once you begin to play with groups that aren’t simply cyclical: that involve, say, multiple independent cycles, like the joint manipulations of solar and lunar calendars required to figure out when Easter will come next.

And here’s the pathetic thing: the Klein Group is the simplest possible non-cyclic group. (That is, it’s not the same animal as the four-element cyclic group we use to keep track of the seasons.) It can be used to represent a wide variety of disparate-seeming things in mathematics. Make a tetrahedron’s faces switch places by 180^o flips along one of its three mutually perpendicular medians (the lines joining midpoints of opposite edges), instead of by 120^o rotations around a fixed vertex, and you’re in a Klein Group (itself a subgroup of the 24-element group defining the symmetry of this simplest Platonic solid). If you wonder what sort of symmetry is obeyed by spacetime (and by the “vector mechanics” of motion within it, which science and engineering students learn as freshmen), there are straightforward ways to relate space’s 3D to the Klein Group’s “even” terms, with the time-line providing the “identity.” What’s truly sad, however, to anyone with the most minimal exposure to mathematical thought, is that the cited piece on Derrida’s “tetrapolarity” can’t tell the two fourfold symmetry types apart! Only someone completely ignorant of mathematics (and totally complaisant in their postmodernist smugness) could not find this appalling.

But that is the state of things in the Derridian universe. Hence, nobody has made even a simple inventory of “3+1 structures” in the Master’s writings to make it clear just how ubiquitous these “excluded controllers” are from the “excluding discourse” of his scribblings. Indeed, there is hardly any work of his, of any significant length, which does not reveal instances (sometimes quite plural) of these wolves lurking within the sheep’s clothing of the Master’s “new, improved” thinking. A very curtailed laundry list of per-sonal favorites, culminating in one for which I’ve special fondness, goes like this:

“Qual Quelle: Valéry’s Sources” – the great French poet Paul Valéry quoted as follows: “I, You, Him, this triangle – Trinity! The three roles of the same in relation to the verb, Mouth, ear, thing,” about which Derrida says, “A very enigmatic sequence from 1910, in examining the ‘believer’ who ‘believes he believes,’ proposed what is doubtless the most efficacious formula for every deviation of the source: ‘Thereby, change 3 to 4 in the Trinity!’”[lxxiii]

“The Supplement of Copula: Philosophy before Linguistics” – concludes with a number of pages focused on the peculiar Indo-European tripartite structure of the verb “to be” as contemplated especially by Benveniste and Heidegger.[lxxiv] As pointed out by M.I.T. linguistics professor Steven Pinker in Words and Rules, this fusion of the meanings of three distinct roots (beon => be/being/been; esan => am/is/are; wesan => was/were) is the paramount instance of “suppletion” in English, the only other being the assimilation of the past particle of “wend” by the commonplace verb “to go.” (This is my favorite for-instance of a very common but typically invisible structure to introduce the dynamics of the Catastrophists’ umbilic cycle.)

“Passe Partout,” the 13-page introductory essay to The Truth In Painting – the phrase “passe partout” is a typical Derridian pun, since in French it means both “skeleton key” and the kind of rapid-fire change-the-image picture frame favored in art galleries, where one of the four sides is open for quick insertions and removals, while the other three are fixed.[lxxv] (Yes, he can talk for a dozen pages about this!)

At least four distinct clusters of instances with different names in The Post Card;[lxxvi] a comparable fistful in Glas (I’m running out of gas: find the instances yourself – it’s very easy, since all of these are really just attempts to outgrow Hegel’s trinitarian “thesis/antithesis/synthesis” logic anyhow!).

Picture of “Cover of the first of the notebooks preparatory to a book on circumcision, ‘The book of Elijah,’” projected from 1976, featuring a central logo surrounded by – yes! – an “open square” of text, all three sides of which feature a variant of the word “schizo,” included, along with family photos and favorite paintings, in the autobiographical text co-authored with Bennington. [lxxvii] (If only you’d learn some real mathematics, Jacques! Time to consult Dr. Jung about that “inferior function” of yours?)

And now, the best for last: in the 1993 Specters of Marx, we are back to where it all started, with Husserl’s so-called “noematic/noetic correlate” – a kind of “four-elements analysis,” but with a twist. This “correlate” is the fundamental frame for Husserl’s introspective reporting, and Derrida wishes to relate it to a phenomenology of the non-image, or the virtual or “ghost” image, which he refers to broadly by the rubric of “hauntology.” And what he accomplishes in this fascinating text is a clearly delineated preparation of Husserl’s key structure for those whose obsessions are Catastrophe Theoretic; for what he gives us is a blatant Klein Group, via which I will be able to obtrude with a most surprising dynamic reading.

The radical possibility of all spectrality should be sought in the direction that Husserl identifies, in such a surprising but forceful way, as an intentional but non-real [non-réelle] component of the phenomenological lived experience, namely, the noeme. Unlike the three other terms of the two correlations (noese-noeme, morphē-hulē), this non-reality [non-réellité], this intentional but non-real inclusion of the noematic correlate is neither “in” the world nor “in” consciousness. But it is precisely the condition of any experience, any objectivity, any phenomenality, namely, of any noetico-noematic correlation, whether originary or modified. It is no longer regional. Without the non-real inclusion of this intentional component (therefore inclusive and non-inclusive inclusion: the noeme is included without being a part), one could not speak of any manifestation, of any phenomenality in general (that being-for-a-consciousness, that appearing appearance which is neither consciousness nor the being that appears to it). Is not such an “irreality” [irréellité], its independence both in relation to the world and in relation to the real stuff of egological subjectivity, the very place of apparition, the essential, general, non-regional possibility of the specter? Is it not also what inscribes the possibility of the other and of mourning right onto the phenomenality of the phenomenon?[lxxviii]

And the answer? Yes and no. The problem? A lifetime of buzzwords rolled into one ball notwithstanding, this Husserlian box-kite won’t fly high enough. The same mathematician, Jean Petitot, who “translated” the “canonical law of myths” into the Double Cusp’s context recently co-edited a collection with Francisco Varela, among others, on Naturalizing Phenomenology: Issues in Contemporary Phenomenology and Cognitive Science. Petitot, like many mathematicians (especially those with European educations) has a deep admiration for the groundbreaking work of Husserl. In a piece he wrote himself in the collection, “Morphological Eidetics for a Phenomenology of Perception,” he gives a profound analysis of Husserl’s theories “by example”: specifically, as they apply to the relation of dependence between spatial extension and sensible qualities (as per the third Logical Investigation); the links between geometry, vision, and kinesthetic control (Ding und Raum); and, the discussion in Ideen I of adumbrative perception. Geometric models are worked out, which build up to catastrophe-theoretic structures “from the ground up” (i.e., what’s a smooth manifold? fibrations and their sections? what are germs?) in a thoroughgoing manner. [lxxix]

As the analysis progresses, and ever richer degrees of algorithmic applicability to real cognitive data are solicited by Petitot, one gains an ever-deeper appreciation for the prescience of many of Husserl’s formulations, and the subtlety of the program he architected. (And, for his obstinacy: he was of the rather pronounced opinion that morphological geometric appropriations of his synthetic a priori laws were not possible: intuitive data were too “vague” to be treated by “exact and ideal concepts.” But modern theories like that of Catastrophes have gone a long way toward formalizing the vague!) But buried in the midst of other arguments, a restriction implicit in Husserl’s scheme is offhandedly cited which, for our purposes, is tantamount to raising a red flag. For reasons well grounded in the theory of mental representations, the geometric schematization must be a “smooth” or differentiable one. Kinky, merely “topological” patterns like fractals (hence chaos) would not be allowed within the Husserlian scheme. And this means the full unfolding of the Double Cusp cannot be built in, since its “parameter” (sorry, next installment!) makes it a “non-elementary” dynamical object, i.e., one with a “backdoor” which can open on Chaos. (Its kaleidoscope also has three mirrors, arrayed in a prism whose section must be one of the Timaeus triangles, and an infinite number of centers of symmetry, not one . . . but for more on these themes, you’ll have to wait.)

But this means the “umbilic cycle” buildable on a Klein Group scheme, like “the curious noise going on and on ad infinitum in the concentric run-out groove” at Sgt. Pepper’s end, cannot be subjected to “closure” in a full-blown Husserlian treatment. Which means, as long as one is a Husserlian purist, the chaining of noematic/noetic correlates will remain open-ended – will not, as a topologist would put it, be “compact.” What does this mean? In a nutshell, the meta-concept which links all the daisy-chaining of Klein Group cyclings into one “aha! experience” of a structure – like the “canonical law of myths” does, and “emergent” approaches generally allow for – cannot happen. One is forced, at a certain formal level, to repeat oneself over and over like some semiotic Sisyphus – or like Derrida and his epigones. This is put abstractly, granted, for reasons of space: but given the amount of space taken up by deconstructionist blather, the amount of space potentially saved (on one’s bookshelves, at least) could be considerable. It’s a case of “close, but no cigar”: Lévi-Strauss takes the prize after all. (Thirty-five years too late, but…)

We can complete the Klein Group if we bring in one last (and rather amazing) facet of Lévi-Strauss’ analysis. If the contrasting themes we’ve just exhaustively banged up against each other be seen as “metaphorically” related, there’s also a “metonymic” (i.e., cause and effect) relation to complete the picture: this is the ultimate conclusion Lévi-Strauss comes to, as to why musical structures are so applicable to the analysis of mythic modes of thought in the first place. For it is not just any music’s structures that can perform this service . . . and this leads him to make the following startling pronouncement:

It would seem that the point at which music and mythology began to appear as reversed images of each other coincided with the invention of the fugue, that is, a form of composition which, as I have shown on several occasions, exists in a fully developed form in the myths, from which music might at any time have borrowed it. If we ask what was peculiar about the period when music discovered the fugue, the answer is that it corresponded to the beginning of the modern age, when the forms of mythic thought were losing ground in the face of the new scientific knowledge, and were giving way to fresh modes of literary expression. With the invention of the fugue and other subsequent forms of composition, music took over the structures of mythic thought at a time when the literary narrative, in changing from myth to the novel, was ridding itself of these structures. It was necessary, then, for myth as such to die for its form to escape from it, like the soul leaving the body, and to seek a means of reincarnation in music.[lxxx]

The true science of cross-disciplinary thought must begin here. The vision for this discipline already has a name. In fact, the Nobel-winning novel that elaborated it had a number of short stories and poems appended to it alleging to be studies by the protagonist, Joseph Knecht, of his real or imagined reincarnations. How myth becomes music, how this transformation is catalyzed by the advent of modern science – how all the above are interrelated with all aspects of our culture, our souls, where we’ve come from, and what we might become: Hermann Hesse called it “The Glass Bead Game.”

Glass-bead game A fictional game described by Hermann Hesse’s novel Das Glasperlenspiel (1943), translated in English as Magister Ludi (the game master). Discussions of V[irtual] R[eality] often evoke references to the glass-bead game because the game’s players combine all the symbols of world cultures so as to devise surprising configurations that convey novel insights. Each player organizes the cultural symbols somewhat like a musician improvising on an organ that can mimic any instrument. The glass-bead game’s synthetic, non-linear information play is a forerunner of hypertext and of virtual worlds. Hesse’s fiction also touches on some of the human problems underlying the advent of cyberspace and virtual reality, such as the role of the body and of disciplines for deepening the human spirit.[lxxxi]

[i] This is how the song begins: “Picture yourself in a boat on a river, With tangerine trees and marmalade skies. Somebody calls you, you answer quite slowly, A girl with kaleidoscope eyes.” Intone the first line of the opening text in rhythm with the italicized phrase. Be sure to inhale, and don’t bogart that joint. (And please – no plastic cups: just pass the jug!) [This acid flashback provided free of charge by the author.]

[ii] Ralph Metzner and Timothy Leary, “On Programming Psychedelic Experiences,” Psychedelic Review, No. 9, 1967, pp. 4-19. Citation from José and Miriam Arguëlles, Mandala (Berkeley: Shambhala, 1972), p. 24. It’s worth noting that many kaleidoscope artists (an art-form which took off, no surprise, with the advent of the New Age movement) see their work as explicitly meditative and entailing mandala construction. See, for instance, leading kaleidoscope artist Sherry Moser’s comments on p. 53 of Thom Boswell, editor, The Kaleidoscope Book (New York: Sterling Publishing, 1992). Moreover, as we shall see in the next installment, Jung’s own focus on mandalas evolved quite naturally from kaleidoscope imagery – the latter making some half a dozen appearances in the landmark work marking his separation from Freud (which work, alone among all his writings, he felt compelled to return to and overhaul decades later): I refer to the 1912 Transformations and Symbols of the Libido, written when he was 37, and completely revised in 1952 as Symbols of Transformation, R. F. C. Hull, transl. (Princeton NJ: Princeton University Press, 2^nd edition, 1967), available as Volume 5 of the Bollingen Series translation of the Collected Works.

[iii] As we’re now about to see in some detail, when Derrida’s own theoretical tactics and chosen problems can be demonstrated to bear more or less exact analogy to those in some other, scientific, domains, there is good money to be made betting that he and the scientists will invariably interpret things in diametrically opposite ways. At the very least, this is an instance of Lévi-Strauss’ own “canonical law” applied to the inversion of significances as one crosses linguistic domains: as he says of certain masks found among the natives of the Pacific Northwest, “When, from one group to another, the plastic form is preserved, the semantic function is inverted,” and vice versa. [The Way of the Masks, Sylvia Modelski, transl. (Seattle: University of Washington Press, 1982; first French publication, 1979), p. 93.] But at its worst, this “Doppelgänger effect” can promulgate a sort of Gresham’s Law of conceptual exchange, where the “good” theories are hoarded by specialists, and the more sensation-mongering postmodernists get the press clippings.

[iv] Jacques Derrida, Of Grammatology , transl. Gayatri Chakravorty Spivak (Baltimore and London: Johns Hopkins University Press, 1976; first French edition, 1967), pp. 163-4.

[v] In Poe’s classic “Descent into the Maelström,” the hero noted that as his craft whirled ever closer to destruction in the funnel of the enormous whirlpool’s vortex, certain objects – cylindrical barrels, per Archimedes’ De Incidentibus in Fluido, lib. 2, as Poe’s footnote tells us – “had descended so slowly after entering, that they did not reach the bottom before the turn of the flood came, or of the ebb, as the case might be. I conceived it possible, in either instance, that they might thus be whirled up again to the level of the ocean, without undergoing the fate of those which had been drawn in more early and absorbed more rapidly.” The hero “resolved to lash myself securely to the water-cask upon which I now held, to cut it loose from the counter, and to throw myself with it into the water” – and thereby lived to tell his tale. And so – by lashing ourselves not to cylindrical ballast, but to the meta-level of mathematical “ejectables” – shall we.

[vi] Jacques Derrida, Positions (Chicago: U. of Chicago Press, 1981, Alan Bass, trans.; first French publication, 1972, based on interviews published separately in December 1967, June 1968, and Fall/Winter 1971 with Henri Ronse, Julia Kristeva, and Jean-Louis Houdebine and Guy Scarpetta respectively), pp. 34-5.

[vii] Geoffrey Bennington, in the “Derridabase” text that runs across the tops of the pages, while Jacques Derrida’s “Circonfession” runs below, together comprising their Jacques Derrida (Chicago: University of Chicago Press, 1993; first French publication, 1991), pp. 283-4. Obviously, the clause inserted between square brackets at the end of the citation is mine!

[viii] The classic Firesign Theater album cover of the same period showed a mock Soviet rally in a great hall with posters of Marx (Groucho, not Karl) and Lennon (John, not Vladimir) hanging above all. The lyric of Lennon’s acid classic bridging the gap between the first invocation of “Lucy in the sky with diamonds” and the appearance of “Newspaper taxis” onshore is as follows: “Follow her down to a bridge by a fountain where rocking horse people eat marshmallow pies, everyone smiles as you drift past the flowers, that grow so incredibly high.”

[ix] William Anderson, The Rise of the Gothic (Salem NH: Salem House, 1985; photos by Clive Hicks): “The sudden appearance in the years 1135-1150 of a group of men capable of transforming the artistic landscape of Europe was not fortuitous. It happened because these men had as an ideal a new conception of Man to make manifest, a new understanding of their own natures, and a new insight into the springs of art and of science. What I am suggesting comes closer to an ancient theory of the origins of art: Longinus’ statement that great literature comes from greatness of soul. The splendour of Gothic art and architecture derives from the magnanimity of soul of its makers. That was the source of their imaginative grasp of the possibilities of the new technology and of the quality of life revitalized that shines from their work.” (Pp. 82-3) But their new conception of man was tightly linked to their embracing newly available texts from the ancient world, and ladling them into the mix of the newly awakened speculativeness: “The rise of the Gothic coincided with the birth of scholastic philosophy and the beginnings of an independent western science. As men discovered the latent powers of their own minds and speculated on the nature and form of the universe, so their interest grew in the nature of the intellect of the angels and the role they played in a Christian cosmos. If, behind the surge of devotion to the Virgin Mary in the twelfth century, there was a profound drive to redress the balance of the Church and society against its masculine domination, so behind the Gothic portrayal of the angel there was the equally strong drive for men to learn how to think.” But this new western cosmology developed, as Anderson reminds us, “first through study of the Timaeus and of Aristotle and then of Ptolemy,” and of the Neoplatonic eschatology devolving from these contained in the angelic hierarchies of the pseudo-Dionysus, wherein – as Dante later expressed it – “the spheres of the heavens and the planets were moved as an effect of the contemplation of the angels.” (Pp. 132-3)

[x] Eric S. Raymond, The Cathedral and the Bazaar: Musings on Linux and Open Source by an Accidental Revolutionary (Cambridge MA: O’Reilly, 2001, 2^nd edition) grew out of Raymond’s 1997 address to the Linux Kongress, and has quickly provided a rallying cry for advocates of open software initiatives. (Raymond is now president, in fact, of the Open Source Initiative.) The juxtaposition of the “open source” of the medieval bazaar which grew up in the shadow of the monolithic, IBM- or Microsoft- like cathedral is interesting in its reversal of the semantic charges the Cathedral was meant to evoke in the prior footnote: in medieval times, the Cathedral was a “memory palace” serving to coordinate communal efforts and thought processes, crossing class and category boundaries in astonishingly rich ways; our own age, even in these days of Internet cross-disciplinary thinking, still finds the polymorphous symbol-hostings of the Cathedral Age too threatening in their scope to embrace as an ideal of any sort. I consider this a sort of litmus test for how much further we have to go in embracing the possibilities of the World Wide Web: in the early days of plastics, Plastic Man was an evil character in the comic-book world, but evolved – with the ubiquity of plastic in our environment – into a comic figure, and finally a hero. I expect a resurgence of “Cathedral” thinking within the next generation of internet technology and human beings employing it.

[xi] “Khora” has been translated in Jacques Derrida, On the Name, Thomas Dutoit, ed.; David Wood, John P. Leavey, Jr., and Ian McLeod, transl. (Stanford CA: Stanford University Press, 1995; first published in French as three separate booklets, 1993), pp. 89-127. The creation by Triangles is contained in verses 53-7, and “Khora” reaches into the first stirrings of Chaos and element formation on pages 89, 90, 105, 111, 124, 125 (where the verses touched range from 50a-52e). Coming from the other side and moving backwards, pages 112-3 brush up against 59c-d and 57d. “Plato’s Pharmacy” is contained, meanwhile, in Jacques Derrida, Dissemination , Barbara Johnson, transl. (Chicago: The University of Chicago Press, 1981; French original, 1972), p. 63-172. While more concerned with Plato’s Phaedrus and its myth of the origin of writing, it likewise touches down on the Timaeus at several points: on pp. 100-1 and 103-4, but far from our target; but also p. 157, upon paragraphs 59c-d, just after the “Triangles” discussion is done; and then, a sustained focus from pp. 159-162. Large passages are lifted just shy of the target (48e-52b, 52b-c), and a brief discussion of some interest ensues about the relation of the khora or “receptacle” to the “mathematical play of proportions based on a logos that can do without voice, God’s calculation being able to express itself in the silence of numbers.” In ancient times, numbers and letters were signified by the same marks, a detail which does not catch Derrida’s attention – even though his master-phrase of “différance” depends upon a dual reading as written and sounded markings! He does say, however, just prior to the line just cited, that “in all these comparisons with writing, we are not supposed to take the letters literally. The stoikheia tou pantos, the elements (or letters) of the whole are not assembled like syllables (48c). ‘They cannot reasonably be compared by a man of any sense even to syllables.’ And yet…” The interchangeability of number and letter, at this primordial level, is fundamental to the “Creation Myths” of early literate cultures – the techniques of Gematria in the Hebrew Kabbalah, where the number values of the constituent letters of a word are added together to test equivalences with other words, for instance, have their analogues in Arabic and Hellenistic mysticism as well, as Derrida, in other contexts, shows himself to be aware.

[xii] Werner Heisenberg, Physics and Beyond: Encounters and Conversations, trans. Arnold J. Pomerans (New York: Harper & Row, 1971), pp. 11, 13-14.

[xiii] “Quantization is a logical necessity of describing any physical phenomenon, for example, the process of communication…. All spoken languages are tied to the time continuum, streams of sound, but must be segmented for the purpose of description; the segments may be chosen to be of different lengths, and given names such as phrases, words, phonemes. As an example relevant to our present theme, the words in an English dictionary may be regarded as types of segment or quantal elements with which we transmit their various syntactical forms, et cetera – the various messages may be constructed. (This is very far indeed from saying that these listed words “are the English language.”) Equally well, though with less popular use, dictionaries of phrases, or of syllables, might be compiled which could be regarded as quantal elements. The important point is that all such quantization is entirely arbitrary – a form is chosen on some occasion which suits the particular purpose of that occasion. The linguist breaks down the raw material of his subject – language – into elements, units, or segments. He speaks of phonemes, morphemes, words. Such elements are conceived for the purpose of talking about language. The language used for talking about language is called a meta-language.” Colin Cherry, On Human Communication (Cambridge MA: M.I.T. Press, 1966; 2^nd edition), pp. 81-2. As we’ll see, Derrida’s attempt to “deconstruct” Lévi-Strauss’ “bricolage” hinges upon (and fails because of) a blatant suppression of the necessity of recognizing the meta-linguistic level built into the anthropologist’s argument.

[xiv]Ibid., p. 142.

[xv]Ibid., p. 143.

[xvi] Alan D. Sokal and Jean Bricmont, Impostures intellectuelles (Paris: Editions Odile Jacob, 1997), Chapter 4 on the hopelessly clueless feminist headshrinker, Luce Irigaray, who keeps finding more sexist plots in the foundations of mathematical objects she doesn’t grasp than Sen. Joe McCarthy ever found Communists under his bed. Sokal’s book made her idiotic “anti-sexist” analysis of the history of fluid mechanics justly infamous; but the follow-up pages (109-113) on her attempts at revealing the sexism lurking in the foundations of logic are so hard to not laugh at as to merit a wider audience.

[xvii] Bennington and Derrida, op. cit., pp. 286-7. It looks silly, but I take it seriously: this is, as we’ll see, one way to deal with the unavoidable distinction, residing in the foundations of the matter we think about as well as the thinking that matters, which the youthful Heisenberg made between “actants” and “things.” Unfortunately for Bennington and deconstruction, though, a (rather graphical) logic based upon this distinction is quite possible: “quantum logic” is a thriving business, and quantum mechanics starts, as we’ll see next, where deconstruction quits.

[xviii] Sokal and Bricmont, op. cit., p. 255. The next appendix, on the next two pages, focusing on his spoof’s citations concerning the “hermeneutics of classical general relativity,” singles out a particularly ridiculous passage from Derrida himself, and refers the bemused reader further to a 1997 reinterpretation of the passage, by a postmodernist who actually knew his physics, Arkady Plotnitsky, “pour une tentative amusante.” This work, “’But it is above all not true’: Derrida, relativity, and the ‘science wars,” Postmodern Culture 7, no. 2, can also be found online at http://jefferson.village.virginia.edu/pmc/issue.197/plotnitsky.197.html.

[xix] David Z. Albert, Quantum Mechanics and Experience (Cambridge MA: Harvard University Press, 1992), pp. 1-2.

[xx] Ibid., p. 11. I love the sense of mystery conveyed, quite properly, by Albert here; but his “we just don’t know” is not quite so: the operator language he begins introducing in the next chapter “passes the baton” in the magical relay race to imaginary numbers and matrices. It is interesting that Albert doesn’t place superposition in its historical context, as the notion did not originate with quantum mechanics, but rather derives from the century-older wave mechanics of Joseph Fourier . . . who, it “just so happened,” was running things in Egypt for his friend Napoleon when the Rosetta Stone was discovered. (The Stone was first seen by its decipherer, Champollion, while seated on Fourier’s knee as a small boy!) The significance of this, for Derrida’s project, is great: as one of his most interesting disciples, Gregory Ullmer, has noted in Applied Grammatology (Baltimore and London: Johns Hopkins University Press, 1985), “Theoretical grammatology is an allegory (a narrative investigation of a threshold text) of the history of the decipherment of the Rosetta stone.” (P. 319) This allegorization is enhanced when we realize that Derrida’s key deconstructive notion of “iterability” – which my notes in the last installment indicated could be seen as the indirect object of much of my commentary – finds a necessary and sufficient purely mathematical embodiment in the “fiction” of the indefinitely repeatable cycle which is, “in reality,” but a once-only hodgepodge, which underwrites Fourier’s famous “series.” Meanwhile, the “Tower of Babel” thematic that runs throughout Derrida bears obvious analogy to the Rosetta Stone on one level . . . but both aspects of the “Fourier connection” can be exploited via reference to a wonderful book, Who Is Fourier? A Mathematical Adventure , Alan Gleason, transl. (Belmont MA: Language Research Foundation, 1995), put together by the students of the “Transnational College of LEX” – a worldwide movement, originating in Japan, which touts learning foreign languages by immersing oneself in as many as eight of them simultaneously! These folks decided to treat Fourier’s mathematics – so crucial to communications theory and quantum mechanics – as just another language and teach themselves how to “speak” and “think” it. The result is a marvel of clarity, simplicity, extensibility and enthusiasm which is absolutely unique – and offers up an apparatus-free experience of polyvalent semantics far more interesting than anything Derrida or his minions have offered up in theory to date. I will develop these threads into a coherent skein much later on in this series: indeed, after the current series of eight installments concludes Part One of the overall argument. As the eighth installment will outline, this thematic will be given room to trot in Part Two, where our focus will be only incidentally on Derrida or Lévi-Strauss as such, but rather on building historical “architectures” spanning the time from the Age of Cathedrals, through the new “Scriptural Time” of the Age of Science, and reaching across to the Internet-indicated “Virtual Cathedral” to come. (End of inscrutable “coming attractions.” Stay tuned . . . )

[xxi] Harold Coward, Derrida and Indian Philosophy (Albany: SUNY Press, 1990), p. 134. The entirety of Chapter Six (pp. 125-146) is devoted to the joint consideration of “Derrida and Nagarjuna,” and has many references to other work in this vein, the first, by Maglioli, dating back as far as 1984. See, too, Harold Coward and Toby Foshay, editors, Derrida and Negative Theology (Albany: SUNY Press, 1992), which was not available at the time of Coward’s book. This contains two long (exclusively Western-oriented) essays, plus a conclusion, by Derrida himself, as well as an insightful essay on “The Deconstruction of Buddhism” by David Loy. Two snippets from Derrida’s “Post-Scriptum,” with which the book ends, are worth juxtaposing, if only to indicate the persistence, for better or worse, of his biases: “The movement toward the universal tongue oscillates between formalism, or the poorest, most arid, in effect the most desertlike technoscientificity, and a sort of universal hive of inviolable secrets, of idioms that are never translated except as untranslatable seals. In this oscillation, ‘negative theology’ is caught, comprised and comprehensive at once.” (P. 318) And: “Negative theology, we have said this enough, is also the most economical and most powerful formalization, the greatest reserve of language possible in so few words.” (P. 321) Yet such economy and power of expression are the well-known, oft-touted hallmarks of mathematics – the “language” in which “desertlike technoscientificity” is, of necessity, thought!

[xxii] Joseph Campbell, The Masks of God, Vol. I: Primitive Mythology (New York: Arkana, 1991; first published 1959, revised edition, 1969), p. 439.

[xxiii] The literature on the “zero-point energy” and Casimir force is vast: for the uninitiated, Charles Seife’s popular text on Zero: The Biography of a Dangerous Idea (New York: Penguin, 2000), and in particular the discussion on “The Quantum Zero: Infinite Energy” (pp. 165-174) is a good start. The section begins with a citation from physicist Sir Martin Rees, to this effect: “To physicists, vacuum has all particles and forces latent in it. It’s a far richer substance than the philosopher’s nothing” – unless that philosopher is an Eastern thinker like Nagarjuna!

[xxiv] A critical text for this enterprise is The Embodied Mind of Francisco J. Varela, Evan Thompson, and Eleanor Rosch (Cambridge MA: M.I.T. Press, 1991), which explicitly posits its post-AI vision of “emergent order” in the Madhyamika Buddhist tradition. This work, already cited in the last installment for other reasons, provides an excellent introduction to the thought of Nagarjuna, especially in its tenth chapter on “The Middle Way,” with the extra bonus of putting such “philosophizing” to scientific use. Anyone sick of the soullessness of Marvin Minsky and/or deconstruction should put this profound and clearly written book on their “must read” short-list. Varela, by the way, is, with Humberto Maturana, one of the founders of “autopoeisis” and, more recently, the “artificial life” approach to “emergent software” experimentalism. (Evan Thompson, meanwhile, is the phenomenologist son of New Age heavy-hitting cultural historian and visionary founder of the Lindisfarne Association, William Irwin Thompson.)

[xxv] “On Completion of The Masks of God” is included as a one-page frontispiece to all four volumes of the Arkana paperback edition.

[xxvi] Campbell, op. cit., p. 3 and pp. 60-61 respectively; my italics, however. Another elaborate evocation of “the mythological kaleidoscope” can be found later on in the same volume, on p. 367. Here, a fourfold symmetry is imposed on the imagery – a symmetry which, as we’ll see later on, can simultaneously accommodate a “reading” of Lévi-Strauss’ image as an instantiation of the Double Cusp invoked to cover his “canonical law of myths,” while privileging the “mirror system” of a specific kaleidoscope’s construction. Campbell’s fourfoldness is that of “the wisdom of the elders; the tact, grace, and competence of socially oriented individuals; and the interior depth-experiences of the ‘tender minded.’ Add the inevitable ‘child’s concept of the world,’ represented in such a society by the considerable fraction of its population under seven years of age, and you will have an elementary diagram of the structuring force centers from which the constellations of the mythological kaleidoscope have everywhere been constituted – showing shifts of emphasis, indeed, according to circumstance; showing, also, greatly differing ranges and powers of amplification; but always playing out of these four inevitable, ever-present centers of creative force.”

[xxvii] Campbell, op. cit., p. 32. (Campbell also refers to these interchangeably by Sanskrit names: “mārga” – or universal path or way, and “deśī” – pronounced “day-shee,” and meaning “of the region, local, ethnic.”) In a later discussion of shamanism, he says: “The elementary idea is never rendered or experienced except through the medium of the ethnic, and so it looks as though mythology and religion could be studied and discussed on the historical plane. Actually, however, there is a formative force spontaneously working, like a magnetic field, to precipitate and organize the ethnic structures from behind, or within, so that they cannot finally be interpreted economically, sociologically, politically, or historically. Psychology lurks beneath and within the entire historical composition, as an invisible controller. But, on the other hand, all mythological imagery and ritual forms, both in their bearing on philosophy and in their impact on society, can and must be studied historically.” What we have, then, is two modes for contemplating the mythical, complementary to each other and incomplete alone: in studying shamanism and the techniques of ecstasy independently of history, the same symbols work for “disengagement” as serve to interpret the way men and women are linked to each other and their world when historically/ethnically “engaged.”

[xxviii] Jacques Derrida, Edmund Husserl’s “Origin of Geometry”: An Introduction, John P. Leavey, Jr., transl. (Lincoln NB: University of Nebraska Press, 1989; first French publication, 1962): “Only a communal subjectivity can produce the historical system of truth and be wholly responsible for it. However, this total subjectivity, whose unity must be absolute and a priori (otherwise even the slightest truth would be unimaginable) is but the common place of all egological subjectivities, whether actually present or possible, whether past, present, or future, whether known or unknown.” (P. 60) Here, the problem eventually indicated is that mathematical truth inhabits a timeless Present, yet phenomenology can not lay claim to its experience, due to the paradoxical necessity of experiencing and liberating this truth through language – the theme of “delay” and “displacement” which will soon take shape in the famous neologism of “différance.” Again, this does not put mathematics’ absolute status in doubt; rather, it places “Absolution” out of reach of Husserl’s philosophy!

[xxix] Ibid., p. 58. The theme of Husserl’s “index” in relation to “expression” will be deconstructed in a manner akin to Rousseau’s “supplement"”in Speech and Phenomena and Other Essays on Husserl’s Theory of Signs, David B. Allison, transl. (Evanston IL: Northwestern University Press, 1973; first French publication, 1967). See especially Chapters 2-3 (pp. 27-47). Consideration of this theme herein, however, would be too much of a sidetrack, and will not be pursued. Of more interest is the relation of the “ideal” to “iterability,” as developed most intriguingly in a collection of Derrida’s essays entitled Limited Inc. (Evanston IL: Northwestern University Press, 1988), especially pp. 68-79 and 118-130. However, this theme would also take us too far afield, and so will not be pursued in this installment.

[xxx] “The ideal Objectivity of geometry is absolute and without any kind of limit. Its ideality … is that of the object itself. All adherence to any real contingency is removed. The possibility of translation, which is identical to that of tradition, is opened ad infinitum…” Ibid., p. 72. The theme of translation, “transparent” in mathematics, is irremediably problematic in a philosophy which cannot attain to its truth: this is perhaps the one most critical theme throughout all Derrida’s later writings. This theme is addressed most directly and concisely in Derrida’s response to Christie V. McDonald’s question about “The passage into Philosophy,” in Derrida’s The Ear of the Other: Otobiography, Transference, Translation, Christie V. McDonald, ed., Peggy Kamuf, transl. (Lincoln NB: University of Nebraska Press, 1985), pp. 119-126.

[xxxi] Varela, Thompson and Rosch, op. cit.: Husserl “took the first step of the reflective scientist: he claimed that to understand cognition, we cannot take the world naively but must see it instead as having the mark of our own structure. He also took the second step, at least partially, in realizing that that structure (the first step) was something that he was cognizing with his own mind. In the philosophical fashion of his Western tradition, however, he did not take the further steps…. He began with a solitary individual consciousness, took the structure he was seeking to be entirely mental and accessible to consciousness in an act of abstract philosophical introspection, and from there had great difficulty in generating the consensual, intersubjective world of human experience. And having no method other than his own philosophical introspection, he certainly could not take the final move which would return him to his experience, back to the beginning of the process. The irony of Husserl’s procedure, then, is that although he claimed to be turning philosophy toward a direct facing of experience, he was actually ignoring both the consensual aspect and the direct embodied aspect of experience. (In this Husserl followed Descartes: he called his phenomenology a twentieth-century Cartesianism.) It is not surprising, therefore, that younger European philosophers turned increasingly away from pure phenomenology to embrace existentialism.” (Pp. 16-7)

[xxxii] François Jacob, “Evolution and Tinkering,” Science 196 (1977), p. 1164. This is piece, as discussed last installment, from which most evolutionary theorists and computer scientists seem to have gained their notion of “bricolage” – even though Jacob only uses the term “tinkerer” while discussing it!

[xxxiii] The classic study is still Thomas S. Kuhn, “Conservation of Energy as an Example of Simultaneous Discovery,” in Marshall Clagett, ed., Critical Problems in the History of Science: Proceedings of the Institute for the History of Science at the University of Wisconsin, September 1-11, 1957 (Madison WI: University of Wisconsin Press, 1959), pp. 321-56.

[xxxiv] One of the more embarrassingly stupid incidents in the ongoing “Science Wars” focused on just this example. One tenured, self-important “science critic” pointed to the Heisenberg/Schrödinger split and jumped to amusingly ridiculous conclusions, only to have an actual scientist inform him about Dirac’s work. The sad thing is that the “critic” was feebly groping toward a point worth making – that there is, in fact, an “alternative tradition” within modern physics that would read the same evidence as, and come to quite opposite philosophical conclusions than, the mainstream would. This is the “hidden variables” approach of David Bohm, which has a fascinating history of its own, and seems to have become fairly main-stream in some quarters (e.g., in Japanese physics, thanks to Umezawa’s influence: see Mari Jibu and Kunio Yasue, Quantum Brain Dynamics and Consciousness: An Introduction (Philadelphia: John Benjamins, 1995)). The point the “science critics” and, apparently, Derrida and his cohorts, just don’t get is this: whenever scientific theory “looks like” bricolage, you know it won’t stay that way for long. Witness the “patchwork atom” of Niels Bohr, which “odd hack” of mathematical collagework catapulted the development of quantum theory at least as much as any “crisis.”

[xxxv] Eugene P. Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in Symmetries and Reflections: Scientific Essays (Cambridge MA: M.I.T. Press, 1980), pp. 222-237. The most famous passage in this wonderful essay bears repeating: “The first point is that mathematical concepts turn up in entirely unexpected connections. Moreover, they often permit an unexpectedly close and accurate description of the phenomena in these connections. Secondly, just because of this circumstance, and because we do not understand the reasons of their usefulness, we cannot know whether a theory formulated in terms of mathematical concepts is uniquely appropriate. We are in a position similar to that of a man who was provided with a bunch of keys and who, having to open several doors in succession, always hit on the right key on the first or second trial. He became skeptical concerning the uniqueness of the coordination between keys and doors.” (P. 223)

[xxxvi] Jacques Derrida, “Structure, Sign, and Play in the Discourse of the Human Sciences,” collected as Chapter 10 in Writing and Difference, Alan Bass, transl., (Chicago: University of Chicago Press, 1978; first French publication, 1967), p. 285. The full text couching this obscenely stupid argument is this: “The engineer, whom Lévi-Strauss opposed to the bricoleur, should be the one to construct the totality of his language, syntax, and the absolute origin of his own discourse and supposedly would construct it “out of nothing,” “out of whole cloth,” would be the creator of the verb, the verb itself. The notion of the engineer who supposedly breaks with all forms of bricolage is therefore a theological idea.” The first sentence is not only preposterous, and not only shows Derrida hasn’t read the text he’s criticizing (in the snippet I’ll lift three footnotes hence, Lévi-Strauss says not just the bricoleur, but the scientist as well, “has to begin by making a catalogue of a previously determined set”); worse yet, it shows he hasn’t read himself! (See the passages just cited from his study of Husserl’s “Origin of Geometry” – a text he never repudiates, and whose themes he reverts to frequently throughout his later work – and see if I’m making this up!)

[xxxvii] Jacques Derrida, Of Grammatology, p. 141. For completeness’ sake, here is the follow-up line to that cited: “This motif comes to terms with and is organized by its contrary: a perpetually reanimated mistrust with regard to the so-called full speech.” I do not include it in the main text above, as the analogous “mistrust”is not harbored within Lévi-Strauss’ thought, but in that of his attacker: by which I mean, Derrida’s mistrust of the “ideal” structures, and – judging by his actions, not his words – mathematics above all.

[xxxviii] Claude Lévi-Strauss, The Savage Mind (Chicago: U. of Chicago Press, 1966; in French by Librarie Plon, Paris, 1962), note at bottom of p. 21.

[xxxix] Jacques Derrida, “Structure, Sign, and Play in the Discourse of the Human Sciences,” collected as Chapter 10 in Writing and Difference, Alan Bass, transl., (Chicago: University of Chicago Press, 1978; first French publication, 1967), p. 285. The same argument, and much of the same phrasing, is incorporated in an expanded form in Part II, Chapter 1, “The Violence of the Letter: From Lévi-Strauss to Rousseau,” of his Of Grammatology.

[xl] Claude Lévi-Strauss, The Savage Mind, p. 20.

[xli] Ibid., pp. 25, 19. While Derridians seem to think that their hero’s analysis leads to an unresolvable paradox – is Lévi-Strauss’ own work that of an engineer or a bricoleur? – in fact, the very lack of their capacity for insulation from each other (and in this, their polarity is like that of the sexes, rather than, say, rain and drought) is something Lévi-Strauss is quite clear about. Just as mythic oppositions always engender a third term as their mediator, “it is clear that art has an intermediate position” between science and bricolage. (P. 25) The structural subtleties of this mediatory role, moreover, consume fully eight pages of the twenty devoted to the bricolage theme. To pretend, then, that bricolage and engineering are related by what logicians call an “exclusive or” relation is to either be incompetent at reading or dishonest (or both!). But as Derrida himself confesses in “Telepathy” [transl. Nicholas Royle, Oxford Literary Review, 10, 1-2 (1988), p. 23], “discourses in which lying is impossible have never interested me. The great liars are imperturbable, they never mention it. Nietzsche, for example, who unmasks them all, he can’t have been much of a liar, he can’t really have known how, poor chap…”

[xlii] Derrida, “Structure, Sign, and Play” (see Note 36), p. 285.

[xliii] Ibid., p. 284.

[xliv] Jacques Derrida, “Time of a Thesis: Punctuations,” in Alan Montefiore, ed., Philosophy in France Today, Kathleen McLaughlin, transl. (Cambridge UK: Cambridge University Press, 1983), p. 39.

[xlv] Ibid., p. 37. “It was then for me a matter of bending, more or less violently, the techniques of transcendental phenomenology to the needs of elaborating a new theory of literature, of that very peculiar type of ideal object that is the literary object, a bound ideality Husserl would have said, bound to so-called ‘natural’ language, a non-mathematical or non-mathematizable object, and yet one that differs from the objects of plastic or musical art, that is to say from all of the examples privileged by Husserl in his analyses of ideal objectivity. For I have to remind you, somewhat bluntly and simply, that my most constant interest, coming even before my philosophical interest I should say, if this is possible, has been directed towards literature, towards that writing which is called literary.”

[xlvi] Ibid., p. 36: “Around 1957, then, I had registered, as one says, my first thesis topic. I had entitled it ‘The ideality of the literary object.’”

[xlvii] Jacques Derrida, “The Double Session” in Dissemination (see Note 11) , and “Mallarmé” in Acts of Literature, Derek Attridge, ed. (New York: Routledge, 1992).

[xlviii] Jacques Derrida, Signéponge/Signsponge, Richard Rand, transl. (bilingual edition) (New York: Columbia University Press, 1984).

[xlix] Claude Lévi-Strauss, “The Structural Study of Myth,” in Structural Anthropology, Claire Jacobson and Brooke Grundfest Schoepf, transl. (Garden City NY: Anchor Books, 1967; first French publication, 1958), p. 206. This passage serves to justify my inclination, mentioned above, to find Derrida’s languagey critiques of Lévi-Strauss’ Rousseauian leaning irrelevant to a proper grasping and understanding of his structural mythology.

[l] Claude Lévi-Strauss, The Naked Man: Introduction to a Science of Mythology/Volume 4 , John and Doreen Weightman, transl. (New York: Harper & Row, 1981; French original, 1971), pp. 644-5.

[li] As the authors state, “The basic point we are illustrating here is that the emergence of global patterns or configurations in systems of interacting elements is neither an oddity of isolated cases nor unique to neural systems. In fact, it seems difficult for any densely connected aggregate to escape emergent properties; thus theories of such properties are a natural link for different levels of descriptions in natural and cognitive phenomena.” Varela, Thompson, and Rosch, op. cit., p. 90.

[lii] Claude Lévi-Strauss, The Naked Man, p. 687.

[liii] See, for instance, the April 1989 interview, ‘“This Strange Institution Called Literature’” in Jacques Derrida, Acts of Literature, Derek Attridge, ed. (New York: Routledge, 1992), or his identification with St. Augustine’s confessional mode in his co-authored and eponymous autobiography.

[liv] Sir David Brewster, The Kaleidoscope: Its History, Theory, and Construction (Holyoke MA: Van Cort Publications, 1987; facsimile of the 1819 original), p. 180.

[lv] Ibid., p. 48.

[lvi] Claude Lévi-Strauss, Myth and Meaning (New York: Schocken Books, 1995; first published, 1978), pp. 3-4.

[lvii] Claude Lévi-Strauss, “The Structural Study of Myth” (see Note 49), pp. 214-5.

[lviii] Jacques Derrida, “Psyché: Inventions of the Other,” Catherine Porter, transl., in Lindsay Waters and Wlad Godzich, eds., Reading de Man Reading (Minneapolis: University of Minnesota Press, 1989); originally given as two lectures at Cornell University in 1984, and appearing in French as the first text in Derrida’s collection of almost the same name: Psyché: Inventions de l’autre (Paris: Galilée, 1987).

[lix] “The Laws of Reflection: Nelson Mandela, in Admiration”, Mary Ann Caws and Isabelle Lorenz, transl., in Jacques Derrida and Mustapha Tlili, eds., For Nelson Mandela (New York: Seaver Books, 1987; French original, 1986).

[lx] Jean-Pierre Dupuy, “Tangled hierarchies: self-reference in philosophy, anthropology, and critical theory,” Mark Anspach, transl., Comparative Criticism, 1990, pp. 105-124. The comparison to Dumontian anthropology can also be extended quite nicely, as its key construct for Dupuy would also be key in any comparison of Dumont’s work with Levi-Strauss’: Dumont’s hierarchy “is not a linear relation of mere superiority, but instead a relation of ‘hierarchical opposition’ between the encompassing (the whole) and the encompassed (the element). Dumont dubs this relation ‘the encompassing of the contrary’ and shows that in holistic societies, like India, there is always a reversal of the hierarchy within the hierarchy. Take the Brahmin and the king, for instance: the Brahmin represents the sacred, the encompassing level, and is hierarchically superior to the king. But in certain domains to which the social hierarchy assigns an inferior rank, the hierarchy is reversed and the king stands above the Brahmin…. Exactly the same abstract form and the same terms ‘reversal of a hierarchical opposition’ serve to describe the logic of the supplement in Derrida. That is an amazing fact because, if in Dumont this form characterized the pre-eminence of a social totality always already there, for deconstruction it bears witness to the destruction of every totality, it seals the impossibility of conceiving or achieving any autonomous totality at all.” (P. 107) The “rites of reversal” so commonplace in Brazilian or Medieval carnival, for instance, “within a space and time that are carefully marked off and circumscribed” (p. 113), and which serve, through their temporary dissolution of social barriers and obligations, to paradoxically preserve the social order, come readily to mind. But phenomena structurally akin to these are also fundamental to Levi-Strauss’ analysis, and in fact underwrite the “torque” or “twist” of his “canonical law” itself. A paper written shortly before introducing it, in fact, points to a “replacing of a term by its opposite” in just such a Dumontian manner – and at a time before Dumont’s key works were written: in “Social Structure” [collected in Structural Anthropology: see Note 49], he writes that “in human societies the actual forms of social order are practically always of a transitive and non-cyclical type: If A is above B and B above C, then A is above C; and C cannot be above A. But most of the human “potential” or “ideological” forms of social order, as illustrated in politics, myth, and religion, are conceived as intransitive and cyclical; for instance, in tales about kings marrying lasses and in Stendhal’s indictment of American democracy as a system where a gentleman takes his orders from his grocer.” (P. 305)

[lxi] Claude Lévi-Strauss, The Naked Man, p. 630.

[lxii] Ibid., p. 646.

[lxiii] Ibid., p. 649.

[lxiv] Derrida’s own hurt at this remark is documented in footnote 12 on p. 158 of Limited Inc. (See Note 29.) The image of the glass partition between the escalators derives from one of five or six papers among the hundreds of Derrida’s I force-fed myself, but I no longer can recall which. It’s a big haystack and a small needle, but I would appreciate anybody finding it and telling me about it, so I can add to the pontification index of this jeremiad by including an officious reference.

[lxv] Claude Lévi-Strauss, The Naked Man, p. 647. The implicit Klein Group devolved upon the fourfold distinctions being the possible flavors of sense vs. sound: “Mathematical entities consist of structures in a pure state, free from any embodiment. In this respect, they are in a correlational and oppositional relationship to linguistic phenomena which, as Saussure showed, exist only through their double embodiment in sound and sense, and arise in fact from the intersection of these two phenomena. This axis having been established, with mathematical entities and linguistic phenomena at the two poles, it is immediately obvious that the other families, in relation to it, occupy positions on a different axis, transversal to the first. In the case of music, the structure which is, so to speak, detached from the sense, adheres to the sound; in the case of mythology, the structure is detached from the sound and adheres to the sense. As far as mythology is concerned, this is precisely what I have tried to demonstrate in the preceding pages in connection with the problem of translation.”

[lxvi] Ibid., p. 649. On the next page, he elaborates: “the ordered series of the variants does not return to the initial term after running through the first cycle of four: as through an effect of slippage, or more accurately through an action comparable to that of the gear-change of a bicycle, the logical chain is jolted loose and engages with the initial term of the immediately following interlocking group, and the process is repeated right through to the end. The variant-producing cycle thus takes on the appearance of a spiral, whose progressive narrowing disregards the objective discontinuity of the interlocking levels. This is tantamount to saying that, in the case of myth, the periodic distribution of the group structures becomes inseparable from the semantic levels that the analysis brings to light… Transformations of the kind constitute the basis of all semiology” – and, as he suggests, may be structurally analogous to the 4-codon “read/write” of DNA!

[lxvii] In The Origin of Table Manners: Introduction to a Science of Mythology/Volume 3 , John and Doreen Weightman, transl. (New York: Harper & Row, 1978; French original, 1968), Lévi-Strauss makes this perfectly clear: referring to one of these instantiations (scalp, dandruff, liver, menstrual blood) of the Klein Group, he says this: “If the relations between a man’s scalp and woman’s dandruff is metaphorical in character, it follows that the relations between liver and menstrual blood is metonymical…. The possession of a scalp ensures success in war, while the ingestion of female scurf leads to lack of success in hunting. According to [one key myth], the non-ingestion of the liver is the pre-condition of the husband’s success in hunting…. Lastly, menstrual blood causes lack of success in fighting: the Plains Indians would remove the sacred bundles used for military rites from a tent where there was a menstruant woman. We thus arrive at a kind of Klein group, if we give the values x, – x,1/ x, and – 1/x to the scalp, the dandruff, the liver and the menstrual blood respectively.” (P. 403) The key buzzwords in this quote are “metaphorical” and “metonymic,” here signified respectively by the minus-sign’s operator, and the inversion operator. Recall the discussion last installment of the equivalence, as a rhetorical formulation, of the descriptor “transformation of a metaphor into a metonymy or the reverse” to the mathematical preconditions for invoking the Double Cusp Catastrophe. To make the point perfectly obvious (assuming you know the concrete context, that is!), the discussion of this Klein Group instance ends as follows: “Like the moon, the porcupine is a periodic creature. And its quills are used for embroidery, which – one might almost say in anticipation – occupied an intermediary place between the scalp, which is congruous with the sun, and the fringe of pubic hair. Obviously, the pubic hair is not congruous with the stone, the antithesis of the sun, in the same way as the scalp and the sun are congruous with each other. We know, however … that the stone is a transformation of the moon by virtue of the same operation which made the quills a transformation of pubic hair. This phenomenon of torsion should cause no surprise, since it constitutes a particular instance of a law I have enunciated in other contexts [references to prior statements of the canonical law then follow].” (P. 405) By the way, if these passages were symbolically self-evident, but made you feel like throwing up because of the gross references to bodily functions, you could be a mathematician; if they made you want to heave because they forced you to keep focused on Klein Groups while you tried to enjoy the images of pubic hair, dandruff, and bleeding scalps, you are, no doubt, a deconstructionist.

[lxviii] The “3+1 structure” of the Klein Group – that is, three terms which square to unity, plus unity itself, with all the latter’s powers, even or odd, being equal – manifests in the 3-cusp unfolding of the “elliptic umbilic,” and the 1-cusp unfolding of its “hyperbolic umbilic” partner, both of whose 3-dimensional control spaces are subsumed in the 4-dimensional control space of the “parabolic umbilic” container. These forms all involve two behaviors, unlike the Cuspoids we considered briefly at the end of the previous installment. Their two-behavior nature is indicated in their naming, since they all derive from conic sections, which are figures with two foci. The sequence of these forms in fact is related quite literally to the standard conic sections which provide the first part of their names: sweep a flashlight across a wall, and the beam will, in each instant, be cut in a conic-sectional shape, with an infinitesimal time-slice showing a parabola, with all hyperbolae on one side, and all ellipses on the other, of this time-lined sequence of sections. (To see where 3 cusps come from where the elliptic umbilic is concerned, consider the view of one planet’s elliptical orbit as seen from another’s in the same solar system: this is the geometric basis of what astrologers term the “triple return” of transiting planets. For a less New-Age-motivated way to envision it, the discussion of closest packing patterns in ensembles of small spherical pellets, and what happens when the catastrophe of a hole is induced into their containers, should be read in D’Arcy Wentworth Thompson’s classic On Growth and Form. In the readily accessible J. T. Bonner abridged edition (Cambridge UK: Cambridge University Press, 1966; originally published in 1917), focus on the footnote at the end of the “Hexagonal Symmetry” subheading on p. 102, and envisage the cartoon that would represent what’s happening dynamically. Hint: think hypocycloid of three cusps!) To motivate you to actually do this, I’ll do as Madison Avenue does, and throw in some (not quite gratuitous) sex: yonic and phallic symbolism is very graphically in evidence as we cycle through the control space of the Parabolic Umbilic; Catastrophe Theory’s creator, René Thom, went famously out on a limb on this theme in his landmark book, Structural Stability and Morphogenesis (Reading MA: W. A. Benjamin, 1975; D. H. Fowler, transl.; first French edition, 1972): “We have seen in the preceding interpretation that elliptic states can be interpreted as states of tension, and hyperbolic states, of release; this explains why a state of tension, although necessary for life, must always be limited and followed by release. This perpetual elliptic-hyperbolic dialectic recalls the yin-yang opposition of Taoism, or the excitation-inhibition opposition of neurophysiology. Because of the very nature of the spatial transport of the male sexual act, the masculine sex has a more elliptic nature than the feminine sex; perhaps this can explain (a generalization, already to be found in Empedocles and roughly verified from Escherichia coli to man) why males are more hairy (in a generalized sense) than their mates and are biologically more fragile.” Then he continues with a passage that is very close in spirit to Freudian dynamics as they’ve been abstracted by Lévi-Strauss (on which, see the final chapter on “A Jivaro Version of ‘Totem and Taboo’” in The Jealous Potter [Chicago: University of Chicago Press, 1988; Benedicte Chorier, transl.; first French edition, 1985]): “The important role that Freud attributes to sexual symbolism, particularly in dreams, is well known; it can be argued that the geometric-dynamic forms representing the sexual processes occur in so many objects of live and inert nature because they are the only structurally stable forms in our space-time realizing their fundamental function as the union of gametes after spatial transport. We might say that these forms existed before sexuality, which itself is only their genetically stabilized manifestation.” (P. 99)

[lxix] Gayatri Chakravorty Spivak, Translator’s Preface to Of Grammatology (See Note 4), pp. lxx, lxxi.

[lxx] The mythic images are in fact suggested by Derrida himself: see the interview collected in Derek Attridge’s book, Acts of Literature, in Note 53 for Derrida’s self-identification with Proteus, who was taken in the Renaissance to be the God of translation; for the form-fixing “writing” perpetrated by Perseus, on the other hand, see Derrida’s book on one of his favorite things to indulge in, self-portraiture: Memoirs of the Blind: The Self-Portrait and Other Ruins (Chicago: University of Chicago Press, 1993; Pascale-Anne Brault and Michael Naas, transl.; first French edition, 1990). Here, he speaks of the “Medusa effect”: “the mask shows the eyes in a carved faced that one cannot look in the face without coming face to face with a petrified objectivity, with death or blindness…. Perseus could become the patron of all portraitists. He signs every mask.” (P. 73) Indeed, if we wanted, we could make a Klein Group out of mythological figures to portray the workings of Derrida’s thought: pair up Narcissus with Proteus, and Mozart’s Il Commendatore, whose statue “unfreezes” so as to haul Don Juan off to Hell (he shows up playing a big role in Specters of Marx, in the neighborhood of the passage we’ll be citing below), and you’ve got it.

[lxxi] Spivak, op. cit., footnote 79 to her preface, on p. 322.

[lxxii] Robert Greer Cohn, “Nodes,” I, Diacritics 4, I (Spring, 1974).

[lxxiii] Jacques Derrida, Margins of Philosophy, Alan Bass, transl. (Chicago: University of Chicago Press, 1982; first French edition, 1972), p. 288.

[lxxiv] Ibid., pp. 198-205.

[lxxv] Jacques Derrida, The Truth in Painting, Geoff Bennington and Ian McLeod, transl. (Chicago: University of Chicago Press, 1987; first French edition, 1978), pp. 1-13.

[lxxvi] Jacques Derrida, The Post Card: From Socrates to Freud and Beyond, Alan Bass, transl. (Chicago: University of Chicago Press, 1987; first French edition, 1980). “3+1” emerges in discussion of the so-called “postal principle” (p. 54); on the structure of the pleasure and death principles (pp. 284-5) and on their forming a triplicity with the reality principle (pp. 286-7), all leading to a discussion of “the laws of this structure with one or three-in-one terms (the same in différance) [which] could be exposed without having to call upon a specific agency whose name would be Repression” (p. 287), but whose “structure of the 1, 2, 3 in one” is “inseparable from Repression” anyhow (p. 289). A handful of different discussion threads elicit the same sort of business pretending to be novel, my favorite being the 3-card monte “bonto trick” discussed on pp. 36 and 151. (The most interesting aspects of the book, though, are probably the author’s embarrassing enjoyment in embuggery imagery inspired by the post card of the title from the Bodleian Museum, which shows Plato standing behind Socrates in a suggestive posture; but then, the author’s embarrassing self-revelations concerning the joy he takes in dressing up in his wife’s clothes and putting on her makeup comes in a close second.) As the translator sums up in a footnote to yet another for-instance in the book: “The passage from three to four via irreducible doubleness is a constant theme in Derrida’s work. Throughout this essay, I have given se trouver in brackets whenever this wordplay [based on French reflexive verbs, which provide Derrida endless shorthand vehicles for punning to the same effect as these 3+1 “concepts”] occurs.” (P. 413)

[lxxvii] Bennington and Derrida, op. cit., p. 89.

[lxxviii] Jacques Derrida, Specters of Marx: The State of the Debt, the Work of Mourning, & the New International, Peggy Kamuf, transl. (New York: Routledge, 1994; first French edition, 1993), p. 189.

[lxxix] Jean Petitot, Francisco Varela, Bernard Pachoud, Jean-Michel Roy, Naturalizing Phenomenology: Issues In Contemporary Phenomenology and Cognitive Science (Stanford CA: Stanford University Press, 1999), Chapter 11: “Morphological Eidetic for a Phenomenology of Perception,” pp. 330-371.

[lxxx] Claude Lévi-Strauss, The Naked Man, p. 652. Bold italics provided by me, not Lévi-Strauss.

[lxxxi] Michael Heim, The Metaphysics of Virtual Reality (New York, Oxford: Oxford University Press, 1993), pp. 152-3.