Part V:  Spelling the Tree, from Aleph to Tav

(While  Not Forgetting to Shin)

 

Click here for Part I - Part II - Part III- Part IV

 

 

But the fact that we now come full circle . . . can only mean that the world of mythology is spherical, in other words, forms a closed system.  However, from our present standpoint we are seeing all the major mythical themes on the reverse side.  This makes the task of interpreting them more arduous and complex, rather as if we were having to decipher the theme of a tapestry from the intricate tangle of threads at the back, and which blurs a picture that was much clearer when we were looking at it on the right side, as we did in The Raw and the Cooked [(Mythologiques I)].

 

Claude Lévi-Strauss, From Honey To Ashes (Mythologiques II)

 

 

“The heart has its reasons which the reason does not at all perceive.”  Among Anglo-Saxons, it is rather usual to think of the “reasons” of the heart or of the unconscious as the inchoate forces or pushes or heavings – what Freud called Trieben.  To Pascal, a Frenchman, the matter was rather different, and he no doubt thought of the reasons of the heart as a body of logic or computation as precise and complex as the reasons of consciousness.  (I have noticed that Anglo-Saxon anthro­po­logists sometimes misunderstand the writings of Claude Lévi-Strauss for precisely this reason.  They say he emphasizes too much the intellect and ignores the “feelings.”  The truth is that he assumes that the heart has precise algorithms.)

 

Gregory Bateson, Steps to an Ecology of Mind

 

 

If you are going to think about the problems of time within a civilized, literate, culture, there are basically two different ways to look at it.  One is through myth; the other is through history.  History, by definition, is a civilized, literate record of events; it is a conscious self-image of a society projected by an elite. . . .  Myth is the mirror-opposite of history.  Myth is not the story of the ego of a civilization but the story of the soul.  If you apply the terminology of C. G. Jung, you can say that myth is the story of the higher Self and that history is the story of the ego.

 

William Irwin Thompson, Darkness and Scattered Light

 

 

 

Robert de Marrais

 

 

 

 

Thoughts While Heading for the Refrigerator During the Half-Time Show

 

                Somewhere in Steps to an Ecology of Mind, Gregory Bateson suggests we’ll know com­puters have finally attained true intelligence only when, upon being given an exceedingly difficult question con­cern­ing that most difficult of topics, human behavior, the machine’s response begins more or less as fol­lows:  “That reminds me of a story…”

 

                The first half of this panoply of abstract arguments, interpretations of other people’s notions, and (one can only hope) occasional insights, began from a smallish-seeming problem with surprisingly largish implications.  The launching of deconstruction in America by the last-to-be-heard, lowest-status speaker at yet ano­ther lit-crit confer­ence in 1966, not merely served to steal the laurels for leading-edge thought from Claude Lévi-Strauss (the conference having been organized to celebrate the triumph of the latter’s structur­al­ist vi­sion among state-side humanists).  More than this, Jacques Derrida’s (highly flawed) argument hinged upon the sup­pression of a central metaphor – the “kaleidoscope”-like workings of the mythic mind, which was the capstone of Lévi-Strauss’s most famous argument, wherein he launched his most famous buzzword (“bricolage”).  This metaphor, moreover, hindsight shows to be the most palpable image for “the mysterious unity of all things” that would soon be revealed in the so-called “A, D, E Problem” in leading-edge mathema­tics.   This tiny-seeming repression of imagistic content was then tossed and turned upon, like the pea under all those mattresses the fairy-tale princess couldn’t sleep on, leading to a “deconstruc­tion” of decon­struc­tion itself – as seen, in particular, against the backdrop of the ongoing “Science Wars”:  a back­drop which serves, I argued, to make Lévi-Strauss’ original agenda look far fresher today than its repudi­ator’s.  (Which has all sorts of nifty implications, of course.)

 

The better to make the necessarily reified issues upon which this debate revolves go down with a maximum of ease, it was framed in a fairly ludic­rous manner (although this is, of course, as much an effect of the author’s own warped proclivities as it is inherent in the needs of his subject matter).  Moreover, the argument was unfolded with the sort of manic attentiveness the great physicist James Clerk Maxwell once derisively dismissed (and he was referring to Darwin’s polymath cousin Sir Francis Galton, one of my heroes and a central figure in my last installment, when he wrote this) as “riding other people’s hobby horses to death.”  But now that the steed that’s carried us through four installments is deceased, what will carry us through the four that I’ve projected (beginning with this one) for the argument’s second half?

 

                Poised between the rock of what’s written and the hard place of what isn’t yet, I have had much cause for reflection of late as to my own motivations in constructing this bowerbird’s nest.  And often, what comes to mind in these reflections of mine is a favorite story (and the only that’s truly funny) by William Faulkner, his tale of the incredibly vulgar family of yahoos called Snopes, and how Flem and Eula and the rest of their boorish tribe take over the once-grand pre-Civil War plantation lands of Frenchman’s Bend from the grasping hands of the local kingpin, Boss Varner.  Varner was often seen “sitting in a home-made chair on the jungle-choked lawn of the Old Frenchman’s homesite” where he would stare into space in the general direction of all that “fallen baronial splendor,” chewing tobacco or smoking a corn-cob pipe and not showing a willingness to com­mu­nicate much with the folks who occa­sion­ally passed by.  It was assumed by everyone that “he sat there planning his next mortgage foreclosure in private,” but one day, for no ap­par­­ent reason, he confided in a young itinerant sewing-machine salesman his real motiva­tion:  “I’m trying to find out what it must have felt like to be the fool that would need all this … just to eat and sleep in.”[1]

 

                The first half of this cross-disciplinary travelogue through the land of Theory was begun, with an ironic sense of the moment, in the midst of the heavily contested Presidential election of November, 2000 – the eve of the purist’s Mil­len­nium celebrations, and a moment still reverberating from a sequence of events that had only just transpired in Florida (the election being contested, of course, in that Cuban-refugee-filled state).  These events concerned the fate of a child whose mother fled with him from the pov­erty and lack of freedom of Castro’s regime on a flimsy raft and died, leaving little Elian’s fate in the hands of political forces beyond his comprehension, with implications reaching far beyond anyone else’s at the time.

 

                The doctoral dissertation based on the last four installments of this essay was all formatted, proof­ed and boxed, and ready for submission (save for the last pages of the pre­face), when another set of unanti­ci­pated historical events – even more monumental and horrific in scope – inter­rupted my (and doubtless your own) train of thought.  Two massive mansions of French conceptual archi­tecture (the struc­tu­ralist inter­weaving of two thousand American myths; the postmodern “conceptual kudzu” of the deconstruc­tion­ists) seemed to dilapidate in signifi­cance, and the outcome of the “Science Wars” epitomized by their oppo­si­tion, become irrelevant, when compared to the collapse of the Twin Towers in the heart of Manhat­tan’s financial district to kamikaze terrorists.  A new Snopes tribe had arrived – Bedouins, not hillbillies, hiding in mountainous terrain instead of leaving it behind.   A vision of historical unfolding modeled by Catastro­phe and Chaos mathematics had gained yet another, even more painful, unintended layer of irony.

                The irony, though, for me, was even more thoroughgoing:  for the long-anticipated plan of this work required the next installment (the one you are now reading) to focus on the common terrain of meta­physical speculation shared by the medieval Jewish Kabbalists – the compilers of  the massive edifice of the Zo­har, erected while their Christian Neoplatonist neighbors built the first Gothic cathedrals in France –  and their Islamic contemporaries, the Ismai’li Tayyibites of Yemen.  (Both were expelled, perhaps not ironically, from their homelands at about the same time – the late fifteenth century.  The leading lights of the Spanish exodus of 1492[2] collected in Sfad in Palestine around Yitzhak Luria, “the Ari” or “Lion” who, without actually writing anything himself, revolutionized Kabbalistic speculation through the sheer force of his presence.  The Tayyibites, meanwhile, whose spiritual leader or “Dā´i” was appointed by the last, so-called “hidden” imam of the Fatimite Egyptian line, were forced by sectarian warfare in the time of the 23^rd Dā´i  to flee to Bombay, India, where the 52^nd Dā´i of the so-called Dawoodi Bohra[3] lives today.)

 

                It is, of course, not intuitively obvious that the search for commonality in the deepest speculative systems of Jewish and Islamic thinkers follows in any natural way from the arguments made in the four prior installments of this ongoing work.  Indeed, the events of September 11 could make this shift in focus seem opportunistic, if not outright ghoulish.  And while this would be completely incorrect, events beyond my control or anticipation necessitate this apparently radical shift be at least rationalized, and at best made self-evident, before glibly embarking in the directions it might indicate. 

 

Let me rationalize first:  the primary structure contemplated in the first half of this disquisition – one whose capacity for manipulation by the “control panel” of the Catastrophists’ Double Cusp was a seminal conclusion – devolved upon the workings of collage.  In fact we saw how this instancing of the “canonical law of myths” was seen to be epitomized (by Lévi-Strauss itself) in Max Ernst’s famous mise en scène of the sewing machine and umbrella on the operating-room table.  In our pre-half-time thoughts, the dissecting table was the largely unexamined stable backdrop against which the correla­tions and contrasts between Lévi-Strauss’s “sewing machine” and Derrida’s “umbrella” were highlighted; but in the argu­ments to come, our attention will be turned to the “table” of their common ground.  And from this vantage, what could be more striking than the fact of their shared “outsider” status as assimilated Jews who were witness to the Holocaust (and, in Derrida’s case, was not even raised in France, but in France’s last Islamic colony, now the rabidly funda­mentalist tyranny of Algeria)? 

 

Let the Age of Exploration inaugurated by Columbus be taken as the start of  the Modern West (and in the last installment, we demarcated its onset in the cluster of events contemporary with this mo­ment: the fall of Constantinople; Gutenberg’s printing press; Alberti’s treatise on perspective; the expulsion of Arabs, then Jews, from Spain).  If the first half sketched a history lead­ing up to the Science Wars (and the new War of Religions now upon us), is it not sensible that the second half map the return trip?  Provide, that is, a counter-history of the soon-to-be-excluded thought-world whose culmina­tion (in the Zohar, in the Tayyibite doctrines) was the immedi­ate harbinger of the explosion of the Medi­eval hegemony the Age of Explo­ration inaugurated?  A counter-history whose own “primary struc­ture” – the Tree of the Kabbalists – might also prove manipulable by the very same “control panel” of the Double Cusp’s unfolding?

 

Indeed, if this suggestion can be justified convincingly, the unity of the total argument will be rea­di­ly demonstrated.  The overall task, then, is not unlike that of the ancient Greek engin­eer commis­sioned by the tyrant of Syracuse to put a tunnel through a mountain:  we must dig from both sides, and try to make the two lines of our excavating meet somehow in the middle.  And the climax of this “mid­dle”?  The string quar­tet intruded at the first half’s end of play, marking  a transition begun with “the invention of the fugue,” when, due to “the new scientific knowledge,” music “took over the structures of mythic thought.”[4]

 

Now to make this seem self-evident:  the first headquote, from Lévi-Strauss himself, points the way; allow me, then, to follow up its lead.  The first volume of the Mythologi­ques articulates a series of systems of mythic interrelationships.  These devolve upon attempts to under­stand the origins and utility of that most profound of all technological innovations:  man’s harnessing of fire.  As its primary purpose is to transform the most primary felt need of humans (and, indeed, all animal life) every­where – consuming food, which, thanks to it, now can be cooked –  its most profound and unin­tend­ed con­sequence is to create a palpable divide between Nature and Culture (the exact definitions of which are, of course, highly fluid and subject to endless demarcations by a never-ending supply of further myths).  

In the sequel study, this primordial contrast between “the constitu­ent elements of the meal” – or, as the volume’s title expresses it, The Raw and the Cooked – is embedded in a more extensive system of mythical themes, clustering around “a second pair of opposites – honey and to­bac­co”:  as we’re told in the introductory chapter of From Honey to Ashes, “I shall be able to follow up the previous investigation into the mythic origin of cooking, with an examination of what might be called the peripheral adjuncts of the meal.”[5]

 

                My argument about Lévi-Strauss’s argument (and Derrida’s argument against it) can have its two parts viewed in a manner rather analogous to this – but in reverse.  For while the anthropologist’s second tome builds out from a pair of myths concerning the origins of honey festivals, the first half of this rant un­wound itself from the implications of events at an academic gabfest . . . one held at the onset of an era that saw (thanks to the Pill) what the myths euphemistically designate as “jungle women wild about honey” in crash pads, be-ins, and open-air concerts everywhere – plus lots and lots of “fragrant smoke” (and they have some pretty good weed, if William Bur­roughs’ Yage Letters to Allen Ginsberg are to be believed, in the Amazon as well).   Moreover, the central theme of deconstructionists has always been, not the “main course” of philosophical discourse, but the mere “peripheral adjuncts” to any real cognitive “meal” (a.k.a. Derrida’s “supplements,” also known by an ever-shifting array of short-shelf-life names, as we have seen).

 

                The core myth upon which The Raw and the Cooked is organized, however, is of quite a different nature:  it concerns a culture hero who is a bird-nester – that is, someone who climbs high trees to capture winged things and their eggs.  But in the myth, the hero is marooned in the treetop as the result of a quarrel, and, depending upon the tale, “punishes his persecutor by sending down rain which puts out domestic fires” or else “brings back to his parents the burning log of which the jaguar was the master, thereby procur­ing cook­ing fire for the human race, instead of taking it from them.”[6]

 

                Now, the climbing of high trees by mythic heroes – if one is reading Joseph Campbell, Ananda Coomaraswamy, or Mircea Eliade, say – has a universal, quite clear connotation:  such myths persist for millennia, and become the basis for elaboration by many others (and not just in the Americas), for a reason.  For they encode the mysteries of the shaman’s ascent, and hence the penetration of the realm of spirit (where the high-flying birds whose nests he seeks live).   And this ascent (to give away the plot a bit) re­quires the perilous navigation of what mathematician James Callahan has called the “trance tunnel,” whose point of access lies hidden in the higher-dimensional reaches of the Double Cusp’s geometry.[7]

 

And this is where the “myth of reference” for this argument’s return trip, corresponding to the 1966 conference presentation of the first half’s joyride, can finally be derived.  Specifically, we will be in­ves­tigating the Tree of Life – that hardy survivor of distant shamanic trance-inducing practices, preserved for many centuries in the medita­tive flights of shtetl-dwelling rabbis and whirling Sufi dervishes.  What remains to be explained, of course, is just what such a thematic motif can possibly have in common with the arguments already put forth.  And the answer, in essence, is profoundly simple. 

 

The deconstructionist irruption signified a “hidden agenda” which only came into the open in the last decade – by which I mean, the “Science Wars” and the conflicted stance against mathematical thinking taken by misguided postmodernists.  The nonlinear mathematics portended by “Claude’s kaleidoscope” gives promise of an “art of modeling” which is already being wielded in ef­forts to translate the archetypal psychology of Carl Jung, for instance, into the language of chaotic attrac­tors . . . which means a sea-change of tsunami proportions in how we think about the relations between technology and humanities, science and psyche.[8] 

 

But if we run the movie of the history of West­ern science in reverse, we find, at the far end, yet another bout of  “Science Wars” (fought in tandem with the ferocious religious wars that strafed the European world of that era).  These largely articulated themselves against the radically un-Cartesian, non-empi­ri­cist ways of thinking which leading lights on both sides of the divide associated with the attempts of folks like Giordano Bruno and Pico della Mirandola to assimi­late Kabbalah to the new agenda – one whose greatest architect (and the era’s last great alchemist), Sir Isaac Newton,  simply called “natural philosophy.”

 

                Interestingly enough, an enormous revival of interest in such arcana as Medieval and Renaissance “memory palaces” like Bruno’s was contemporary with the first mad rush to embrace deconstruction.  The epochal study of The Art of Memory by Dame Frances Yates dates, in fact, from the very same year as Der­rida’s Johns Hopkins lecture.  While he would undermine speech by overvalorizing writing (and, by exten­sion, print-based literacy), Yates diverted her attentions to the mnemonic arts of the pre-printing press age of manuscript scarcity and ela­bo­rate ora­tory.  Her work plumbed the long-suppressed cultural memory of the Memory Art itself – its AI-like navi­ga­tion of vast imagistic architectures[9], and their utilization in the Renaissance as transducers of occult ener­gies . . . a usage which led to a violent reaction in the seventeenth century among the first scien­tific philoso­phers. 

 

No less a figure than René Descartes devoted himself to a wholesale reform of the memory art.  He streamlined the vast complexities of image deployments and their scanning sequences (typically “put in storage” through long bouts of pacing the corridors of  the iconically rich “UI’s” cathedrals provided), with an extremist’s urge to simplify – an urge exemplified, in our own time, by the reduction of musical devel­op­ment by post-Sgt. Pep­per, Moody-Blues-orchestration-loathing punk rockers (Johnny Rotten’s Sex Pis­tols come readily to mind) to a meager raised-fistful of roughly chunked, nose-bleed-loud chords.  Attack­ing one of the more popular mnemonic systems then extant, he wrote this anticipation of his Discourse on Method in his Cogitationes privatae:

 

On reading through Schenkel’s profitable trifles (in the book De arte memoria) I thought of an easy way of making myself master of all I discovered through the imagination.  This would be done through the reduction of things to their causes.  Since all can be reduced to one it is obviously not necessary to remember all the sciences.  When one understands the causes all vanished images can easily be found again in the brain through the impression of the cause.  This is the true art of memory and it is plain contrary to his (Schenkel’s) nebulous notions.  Not that his (art) is without effect, but it occupies the whole space with too many things and not in the right order.  The right order is that the images should be formed in dependence on one another.  He (Schenkel) omits this which is the key to the whole mystery.[10]

 

                It is the “memory art” aspect of the Kabbalah (the seminal concern of Yates’ last work, her 1979 study of The Occult Philosophy in the Elizabethan Age) which obsessed its Christian adapters.  This is still the case in modern times, as writings of the circle of Golden Dawn members collected around another Yates (but spelled differently:  Irish poet, playwright and visionary William Butler Yeats)      give evidence.  In her book on The Mystical Qabalah (and note the leading “Q”:  the telltale code for magickal orientation!), Dion Fortune wrote an appreciation of the symbol-gathering potency of the Tree which a Renaissance mage would find little to quibble with:

 

It is amazing what ramifications of association-chains can be followed when the attribution is correct.  It seems as if it were only the extent of our knowledge which limits the length of the chain that can be linked logically together; it will extend through science, art, mathematics, and the epochs of history; through ethics, psychology, and physiology.  It was this peculiar method of using the mind which in all probability gave the ancients their premature knowledge of natural science, knowledge which has had to await the invention of instruments of precision for its confirmation.  We get clues to this method in the dream-analysis of analytical psychology.  We might describe it as the symbol-using power of the subconscious mind.  It is an instructive experiment to toss a mass of irrelevant symbolism into the mind and watch it sort itself out in meditation upon the Tree, rising into consciousness in long association-chains like dream analysis.[11]

 

                The blatant Paganism of much of the Memory Art (for vast quantities of classical images formed its iconic mainstay), aided and abetted by the profoundly irrational character of the psychic forces it tapped, made it the target of virulent attacks by the new rationalists.  Paramount among these enemies of the ani­mis­tic, personified view of nature was Descartes’ cohort, the Minimist friar Marin Mersenne.  The “per-sonification of that figure both in our Western collective history and in each of us who upholds reason at the cost of imagination,” Mersenne’s significance has been limned by Jungian James Hillman this way:

Between 1619 and 1648 with feverish activity and personal torment Mersenne carried on a thirty-years’ war of his own against the threatening recrudescence of the hosts of paganism.  Robed in black to his ankles and ensconced in his monkish Parisian cell near the Place Royale, but traveling too for talks and meetings, he became the arachnoid center of the European learned world, always attacking the “magical” early Renaissance – especially alchemy – in order to further the “mechanical” later Renaissance.  His writings, except in the areas of music and mathematics, did not contribute much that was new; his great value lay rather in the keenness with which he sensed the intellectual danger of animism for Christianity and the ardor with which he supported all scientific work that could meet that danger rationally.[12]

 

                For present purposes, there is one act of rationalistic extremism that stands out among the many this Joe McCarthy of the “animist menace” perpetrated; it will provide the pea which will keep the prin­cess of this argument tossing and turning atop her abstract mattresses for many more pages to come.  (For this and the remaining installments, in fact.)  Hillman, once again, can give us the lowdown:

 

It is precisely the literal mode of his mind that makes Mersenne crucial to both religion and science.  He stands unyieldingly for concrete knowledge of facts.  Like Bacon, he preferred contemporary empirical experience to the opinions of the ancients.  Since he believed that facts alone could dispel both skepticism in religion and magic in science, he took metaphorical statements at their literal level, asking “scientific­ally,” for instance, “How high is Jacob’s ladder?”  He also transposed the mystical question of the Unity and Trinity of God into a scientific problem to be worked out by means of a parabolic mirror that could  reduce multiple visible images to a single point…. Soul was confined to the persons of Christ and those baptized in his name, all else burnt out of Being or moved mechanically around a clockwork orbit.  Animals were bereft of psyche, and children, even when baptized, did not have the full reality of souls.  Both modern science as it was then being formed and modern Christianity as it was then being reformed, required that subjectivities be purged from everywhere and everything except the authorized place of persons:  the rational Christian adult.  To experience otherwise was heresy and witchcraft.[13]

 

                As Hillman remarks in a footnote to this text, “The reduction of ‘Jacob’s Ladder’ to a matter for measurement epitomizes the destruction of a traditionally central image of mythical mysticism by asking the wrong sort of question.”  Ditto for the “divinization of mathematical science” implicit in “using geo­metry to resolve the theological mystery of the Trinity (in which, of course, as Mersenne knew, remain traces of prior polytheism)”.[14]

 

                But what, for us here, are the right sorts of questions to ask?  In Callahan’s mathematical treat­ment of anorexia, the “trance tunnel” emerges as a sort of deus ex machina, offering a way out of an insolu­ble dilemma – choosing between the Scylla and Charybdis of binge and purge behavior.  Here we have a similar situation:  do we look at Kabbalistic symbols with the allegedly objective distance (and likely re­duc­tionist bias) of the “neutral” scientist who, true to his heritage, dreads anything tainted with psychic con­tent?   Or, do we approach them with the all-embracing (and likely indis­criminate) openness of New Age “all is one” enthusiasts – and thereby lose our mental moorings in direct proportion to how good this makes us feel? [15]

 

Even those few scholars who have managed to walk this tightrope successfully – Dame Frances Yates, for instance – still manage to make some striking blunders that show how merely “bookish” their grasps of their subjects could be.  In the midst of sumptuous plates from classic old texts, Yates’s Occult Philosophy provides one drawing of its own, showing the Kabbalistic Tree – and mucks it up considerably.  While more than one representation of the Tree can be found, all major variants show 22 paths (one for each Hebrew letter) connecting the 10 circles representing the Sefirot (singular:  Sefirah) arrayed in 3 col­umns of 4 down the middle and 3 on each side, comprising a sort of “bucket brigade” for the pass-along of Divine Effulgence to Planet Earth.   Yet Yates’s diagram is missing the two key paths from bottoms of the sides to the next-to-bottom-most central Sefirah, Yesod or “Foundation,” the seat of Ego and sexual energy.

 Also, the “non-Sefirah” called “Da’at” or “Knowledge,” from which the “Voice of Prophecy” emanates from higher reaches (being literally “disseminated” from the phallic Yesod of the Tree for the next higher World on the Ladder:  recall the double meaning of the Hebrew, as in “Adam ‘knew’ Eve”!) is notably absent as well.  Hence, the “impulse function” nature (as opposed to the stability of the Sefirotic struc­tures) of this node – the basis of the whole dynamics of Creation at all levels – is just not present:  one might fairly say that Yates’s Tree has been “castrated.”  All of which indicates that she really had no true understanding of the workings of Kabbalistic thinking in the sense a practitioner would consider significant or adequate.[16]

 

But at least she tried valiantly.  The same cannot be said generally.  One of the rare scholars of the Kabbalah who not only reads the texts with an academic’s distance but has some respect and feel for the prac­tice whose mere shell they are, Moshe Idel, has expressed himself on this matter in rather strong terms: 

 

Strangely enough, despite the close proximity of Kabbalistic circles in Jerusalem and Be­nai Barak to the academic centers for the study of Kabbalah, such contacts are not regard­ed by the academic establishment as productive, all research in Kabbalah instead being focused exclusively on written texts.  For this reason, no up-to-date picture is avail­able on current Kabbalistic thought.  More than one hundred years after ethno­logists came to re­gard the collection of data and contact with remote tribes as essential for their descriptive work, and two decades after the introduction of the psychophysiological study of mysti­cal experiences, researchers in Jewish mysticism work exclusively in relation to texts, with­out even an awareness of the necessity of making the acquaintance of their close neigh­bors, the Kabbalists…. The historicist bias of the academic perspective, if not coup­led with the sensibility that grows out of the phenomenological effort to understand a mystical phenomenon as an entity in itself, may cut the dialogue short at the beginning.[17]

 

                We would expect the worst offenders to be those cranium-up-buttocks deconstructionist scholars, who – following their leader’s famous slogan – would tell us that “il n’y a rien dehors le texte”:  nothing exists outside the text.  In fact, this is not the case:  such scholars, as a rule, won’t touch sacred texts at all.  Philip Beitchman, one of the rare deconstruction-savvy investigators to tackle such things – and a most ad­mi­­rab­ly balanced and insightful one on top of it – has covered some ground we’ve traversed in the last in­stallment from a most interesting angle. 

 

You might recall a quote from Jung comparing our individual consciousness to the “fruit of a sea­son, sprung from the perennial rhizome beneath the earth”:  the gist of Jung’s remark was that the Uncons­ci­ous, like the hidden underground vastness of the root system that typically underlies and unites in its life the surface network of seemingly disparate plants, resides at a deeper level of reality than our conscious existences.  It is therefore interesting to contemplate the radically different interpretation of “rhizome” ima­gery given by typical postmodernists like Deleuze, who ironically miss the organic unity Jung focuses on entirely, misconstruing the biological nature of the rhizome so as to make it an image of decentralized net­working.  What is suggested thereby is not a higher unity, but the anarchic opposi­tion to that very possibi­li­ty, e.g.,  “guerilla warfare.” 

 

The earlier discussion of Dupuy’s depiction of Derrida’s “upside-down” readings vis à vis scienti­fic thinking (see Part III, between Notes 59 and 60) could easily be resumed and expanded here to consider things depth-psychological and spiri­tual.  Such a discussion could not do better than to begin with a look at those Deleuze-inspired pages in Beitch­­man’s Alchemy of the Word:  Cabala of the Renaissance  which fo­cus on the theme of “Cabala as Rhizome.”  Here, he warns against the “defiant resistance to extending [de­con­struction’s] parameters to include religious or sac­red writings, as if a fis­suring of authority might be ac­cep­table for the literary text but must not be pur­sued into the inner sanc­tum of faith.”[18]  But this question of “critical vocabu­lary” for discussing such themes is one crucial for the history of science as well – in parti­cu­lar, for understanding science’s origins in the rab­id­ly anti-Occult­ist sensibility of Descartes’ fellow tra­vel­ers (and especially, Marin Mersenne, who made a spe­cial target of the Cabalistic “Tree” and “Ladder” symbolism, as we’ve seen already); but also, for prognosticating science’s future.

 

*              *              *              *              *

                One of the definitive features of the second half – almost totally in absence in the first – will be a necessary reliance upon pictures.  Here’s three to get things started:  these are straightforward line diagrams of the Tree.  The leftmost is from Rebbe Aryeh Kaplan’s introduction to, translation of , and commentaries on, the medieval classic Kabbalistic text The Bahir[19], which I had the pleasure and great good fortune to stu­dy with him in his living room, in the traditional small-group setting which has been the basis of trans­mit­ting this mode of knowing since time out of mind.  In the middle is the botched diagram described above, from Yates’ otherwise estimable book.  The third is from An Introduction to the Cabala[20] by Z’ev ben Shi­mon Halevi:  but for his giving the last public lecture at the Lindisfarne Association’s former loca­tion in a landmark church on Manhattan’s lower West Side, I might never have taken the step beyond Yates’s sort of “bookishness” into actual immersion in Kabbalistic praxis . . . and the second half of this argu­ment never would have been contemplated, much less written.  (And thanks to an “accident” of the sort such immersion tends to abound in, I had been engaged in finally “translating” Lévi-Strauss’s “canon­ical law” into the geometry of Zeeman’s “umbilic bracelet” treatment of the Double Cusp just an hour or so before Halevi’s lecture – making me especially receptive to the diagrams of Trees and Ladders he kept ref­erencing in his talk . . . and derailing my plans for dissertation completion by a more than a few years!)

 

               

      

 

 

                For all three Trees, the layouts of the Sefirot are identical:  the “Crown” or “Keter” is at the top, with “Tiferet” or “Beauty” beneath (separated , at least implicitly, by “Da’at,”and shown as a dotted circle in the rightmost drawing).   Continuing down the cen­tral “Pillar of Clemency,” the phallic, egoic “Yesod” (“Foundation”) comes next, with “Malkhut” (vari­ous­ly styled “The Bride” or “Kingdom”) hanging as a pendant from either the center only, or all three columns collectively.  On the right are the three Sefirot of the “Pillar of Mercy” or Force.   “Chakh­mah” or “Wis­dom” at the top receives directly from the Crown, then either dispenses horizontally to the top of the “Pillar of Severity” or Form, “Binah” or “Understand­ing,” or else acts as a circuit-breaker or “step-down function” to pass the current along to the next-lower “con­trol” in the Force column, “Chesed” or “Loving­kind­ness.”  This is horizontally linked to its polar opposite, the seat of fear, “Gevurah” or “Din,” whose primary attri­butes are judgment and severity.  The bottom-most dyad, “Netzach” (“Victory”) and “Hod” (“Glory”), are the most volatile manifestations of the forcing and formative behavioral controls respectively.  Where “Chakh­mah” is viewed as pure potentiality – the un­man­i­fest seed-form of an idea, say – “Netzach” embodies its putting into practice through endless repetition (whence its frequent rendering as “Eternity”).  “Binah,” the ultimate matrix or primordial mother, stands at a similar distance from the “Reverberation” of “Hod.” 

“The Bride,” meanwhile, is the pliant receptacle, whose fructifying is the whole purpose of all the dis­pensings from the higher reaches – and ultimately, from the ineffable pure potential of the “En Soph Aur,” or “Limitless Light,” the veil cloaking the realms of  “negative existence” from all that is mani­fest.  In the modern language of mathematical dynamics, we will contemplate the Bride as the “user interface”:  the place where results or “behavior dimensions” are on display.  As Kaplan tells us in his Bahir commen­tary, “It is an im­por­tant Kabbalistic teaching that Malkhut-Kingship is the Sefirah through which all others are revealed.”[21]  This view is further reinforced by the standard view (which we’ll look into in more detail shortly) that the bottom seven Sefirot correspond to the seven days of Creation – with the Bride being the Sabbath, or day on which God rested.

 

The Sefirah called “Beauty” or “Tiferet” is also known as the “Seat of the Soul,” and it is easy to see it is the “action central” in all the drawings, with paths leading out from it to all other Sefirot save for the Bride.  In Halevi’s many Tree renderings of basic processes, the “thing itself” being modeled always has its label placed here:  for this is clearly, to the mathematically inclined at least, the place-holding “zero” of the coor­dinate grid.  This is what suggests the most basic tactic for appropriating the Tree to Double Cusp model­ing:  take the rhombus of the latter’s monomials derived by “Siersma’s Trick” and depicted in a simple graphic last installment; then, attach “marionette strings” from each (save the topologically uninter­esting “1” at the top) to the  “control panel” (or “Zero point”) held in the hands by the puppeteer. 

 

Comparing Kaplan and Halevi’s Trees, the differences in pathing are quite obvious; yet the simi­larities beneath the differences are more subtle.  The kite-shaped pattern of paths leading to the Bride in Halevi’s version in fact recapitulates the “kite” made by those leading around and through Da’at in Kap­lan’s.  (In fact, among the most extremely orthodox of Hasidic communities, as epitomized by the Luba­vitchers,  Keter is considered too remote to talk about directly, and one speaks instead of Chakhmah, Binah and Da’at as the “trinity” behind the Creation of the seven lower Sefirot . . . leading to the acronym of “ChaBaD” as the term referring to the ultimate roots and structure of the soul.[22])  This is especially evi­dent if one suppresses the extensions of the two paths crossing through Da’at beyond it to Gevurah and Chesed in Kaplan’s rendering; for then one sees the un-indicated locus of Da’at as a “higher octave” of Yesod.  It is these so-called “Upper and Lower Faces” which are associated when the Trees of relatively Lower and Upper Worlds, respectively, are overlayed in the extended “Jacob’s Ladder” representation.

 

Note, too, that different letters are put in quite different places.  While the count of 22 paths is basically invariant for most applications, the designations of letters placed upon them can vary consider­ably, to suit quite different purposes.  Halevi, for instance, has devoted a whole book[23] to exploring the systems of triads (16 in all) formed by the letters on the Tree at the right:  in Hebrew, letter triads form the fundamental roots of the language from the semanticist’s vantage, so the scheme of letters bounding each such triad is given great significance in the pre-1492 tradition Halevi is presenting.   And when one starts contemplating the schemes dreamed up by the post-1492 Kabbalists around the Ari in Sfad, complexities abound to a degree it would be senseless to even imagine tackling here.

 

Complementary to the need to eschew obvious complications, there is an urge to hallucinate great simplicities that may prove illusory or overly distracting.  Consider the 16 triads:  we’ve seen prior to this installment how the three “Timaeus triangles” can be related to the three 3-mirrored prismatic kaleido­scopes, one of which (the isosceles right) gives us the Double Cusp.  But in fact all three of these closely allied forms contain the same strata (up to and including the “trance tunnel”) which will interest us in our Tree modeling.  Moreover, while these three are the simplest members of an infinite series of higher-di­men­­sional forms, there exist 14 exceptional forms – “exceptional” in the same manner as the Platonic sol­ids, meaning they instantiate “A, D, E” classes that don’t generalize to higher reaches – which also include the “up-through-tunnel” strata.  Their surprising dis­covery by the Russian I. V. Dolgachev came from con­tem­plat­ing the hyperbolic plane so familiar to devotees of M. C. Escher’s prints:  for they corres­pond to the 14 distinctive hyperbolic triangles with which one can tessellate or “tile” it. [24] As 14 + 3 = Tree + 16 triads, it is natural to ask whether, in fact, one can treat each “triad” on the Tree as the potentially recursive con­tain­­er of ano­ther, “flavored” by its placement on the original “Tree of reference”?  I find the idea very in­trigu­ing – and also feel pursu­ing it would guarantee “losing it”:  until a lot more can be demonstrated, such pos­si­bi­lities must be “put on hold.”  This is the fundamental modesty of the scientific method[25] – something easy to lose sight of when dealing with such psychically charged contemplative objects as the Tree. 

 

Considerably more will-o’-the-wispy would be pursuing things like the intriguingly prime number (613) of rules in the Torah:  these split into 248 positive commands “rooted in love,” plus 365 “prohibitive com­mands” based in fear (and hence associated with the right- and left- hand columns of the Tree, respec­tively).  These are related in the literature to many other things:  the 248 “members” plus 365 “blood ves­sels” that comprise the “organs” of the human body, made in God’s likeness, and so forth.[26]  And here the problem is of a different nature:  for while the overactive imagination of the algebraist would see in 248 the 240 + 8 primary representations of the physicist’s “E8” (whose product with itself is so critical to super­string theorists), the 365, one’s commonsense would argue, is the number of days in the year.  Barring other evidence, then, one’s working hypothesis would have to be that we are dealing, in this case, with elaborate mnemonics of the sort still in use by medical students, and not patterns amenable to abstract derivation in their own right!

 

With these caveats in mind, my aim will be to start at the most fundamental – yet simply convey­able – level.  I’ve dropped two hints already about its nature:  the first concerned the days of Creation.  If the lower seven Sefirot cor­respond to them, what are the top three doing?  This is readily clarified when one puts another system of attributions on the Tree’s template:  when the Ten Commandments are tradi­tion­ally placed on the Tree, the “Supernal Triad” of Sefirot at the top are mapped to the first three com­mand­ments – those which concern not the nature of right behavior in the world, but the right way to per­ceive God’s nature:  “no other gods,” “no graven images,” “no blaspheming” in Keter-Chakhmah-Binah order.  (Just to keep things interesting, however, the mapping Halevi gives assigns “keeping the Sabbath”  to the sphere of Chesed’s Loving­kind­ness, while the Bride admonishes, “Thou shalt not covet.”)[27]

 

The second hint concerned the suppression of extensions on the paths through Da’at’s locus in Kaplan’s drawing.  Criss-cross paths from the uppermost dyad to the next are absent entirely in Halevi’s.  In fact, there is another pattern, called the “Lightning Flash,” which moves from Keter to the Bride in a zigzag route to Chakhmah, then Binah, through Da’at to Chesed, then over to Gevurah and through Tiferet and so on.  And there is also a “Return of the Lightning Flash,” when man’s will can return “divine sparks” to their source.  Taken together, the full pathing through Da’at in Kaplan’s Tree becomes motivated.

 

The image of the “Lightning Flash” – with the Bride as the “grounding wire” of the process – is far richer than one might think at first.  It has a rich history, certainly – Vico saw the first societies arising in reaction to a primordial flash and thunder clap, and this inspired James Joyce’s “thunderword” in Finne­gan’s Wake – but it also has a surprisingly rich physics.  This physics is not something one could claim the ancient Kabbalists “knew” in any literal sense; nevertheless, it serves to encapsulate many of the key fea­tures of the Tree’s dynamics that we’ve just scanned in so summary a fashion.  Consider the account that follows, then, as a “just-so story” that we can take as a “myth for our times” about Kabbalah’s workings:

 

During World War I while Heinrich Barkhausen was eavesdropping on Allied field-tele­phone conversations at a distance, he occasionally heard curious whistling sounds which swamped the military messages.  Unable to eliminate the whistles from his appara­tus, he con­cluded that they must come from the atmosphere.

 

In the 1920s and 1930s investigators at Bell Laboratories and at Marconi Wireless Telegraph noted that a whistler often appeared about a second or so after a loud atmo­spheric click.  They developed the explanation that when lightning occurs, the very low-frequency components of the discharge are propagated along lines of the Earth’s magnetic field to the antipodes.  The click is a rectangular wave-form composed of many different wavelengths, for the same click can be detected all over the broadcasting band.  Now suppose that as a click moves through the ionosphere, its component frequencies will spread out, the highest frequency traveling faster and faster and the lower ones strung out behind.  If the click travels far enough before the magnetic lines guide it to a receiver, the frequencies will be well separated.  The observer will receive a drawn-out signal – a whistling tone of steadily falling pitch.  Whistlers are an interesting example of nonlinear propagation leading to dispersion.[28]

 

If we combine the progression of the Lightning Flash with the splitting of the Sefirot into two groups of three and seven, we obtain a primordial narrative of Design, Creation, Fall, and Rectification – a narrative which is ongoing:  for the rectification or Tikkun of the “288 Divine Sparks,” scattered by the “Bursting of Vessels” that marked the Edenic Fall in the higher Worlds, will occupy the devout until the “Return of the Lightning Flash” has progressed sufficiently to summon the “Return of the Messiah,” who will then complete the job.   (The reason why there are precisely 288 Sparks will emerge as a side-effect of the conclusions we’ll have attain­ed to by the end of the next installment.  Unlike the 613 of Torah com­mands, in other words, this number can be derived from abstract mathematical “first principles”!)

 

This “never-ending story” does not unfold, however, by the Double Cusp machinery I’ve envi­sioned; on the contrary, the latter derives its ultimate ground from it.  (Not, in fact, until the Lightning Flash has passed through Da’at will we be able to elicit its structures, although the “germ” of its idea will already be inchoate in the Flash’s first passage into Chakhmah.)  Jean Piaget suggested some while ago that the more advanced the progress­ion of mathematical thinking, the more primitive the level of cognitive develop­ment in which we find it mir­rored.[29]  In a somewhat analogous fashion, this ancient tale of First Beginnings is best apprehended keep­ing the most advanced results of modern logic in mind.  For the structures that guide its telling give surpris­ing evidence of what Lévi-Strauss, in one of his more striking phrases, termed the wish of the  “logic of the concrete . . .  to remind us of its logical nature by modeling a confused outline of Gödel’s theorem in the clay of ‘becoming’.”[30]

 

                Perhaps the clearest exposition of the extralogical significance of Gödel’s (and Post, Church and Turing’s) results was written by a renowned mathematical logician who was also a concert pian­ist and com­­poser.  John Myhill’s 1952 essay spelled out with great clarity the necessary existence of three classes of ideas.  These classes, moreover, are not in any way arbitrary philosophical constructs, but the immediate and inevitable outcomes of the logical laws he is contemplating – laws which, he avers, are “the only known psycholog­i­cal laws comparable in exactitude with the laws of physics.”[31]  Myhill dubbed these classes “effective,” “con­structive” and “prospective.”  The distinction between the first two is the essence of Church’s theorem; that between the second and third, of Gödel’s.

 

When we can reduce our knowledge-gathering in some domain to “cookie-cutter” methods which can be learned by rote, such methods are “effective.”  The dream of David Hilbert and other great mathe­ma­ticians was that, by the axiomatic method, all mathematics could eventually be rendered “effective,” its progress automated, its scope for ingenuity and invention eventually diminishing and even dis­appearing.  What Church showed was that there were classes of problems which, as a class, could not be solved by any generic method – even if all instances of the class were solvable on a case-by-case basis.  Myhill gives this simple-seeming example of an obviously true statement:  “All horses are animals, therefore all heads of horses are heads of animals”; the point, though, is that “there is no set of techniques which will enable us to decide of any given argument resembling the above whether or not it is valid.”[32]

 

The property inhering in the above class of problems is called “constructive,” because we can put together an assembly-line-like procedure which will eventually crank out all possible objects which have some property to whose presence or absence some organisms can be trained to respond differentially.  “But we cannot in general tell in advance of the production of such a thing whether or not it has that property.”[33]  “Constructive” results, though generated by a clear principle, are nevertheless unpre­dictable.

 

What Gödel showed, however, is that it is quite possible to entertain an idea which is neither ef­fec­tive nor constructive in these senses:  that for a given rule-based system, there would always be truths whose appearance could not only not be predicted in advance (“constructive”), but which could not be for­mulated as theorems within it (hence, as projections of any system-based “what-if” scenario spinning) in the first place – even though they may be shown, by other means, to be true.

 

Myhill’s “other life” as a musician and composer provided, not surprisingly, his most distinctive running imagery for the three categories’ differences.   The following paragraphs provide the penultimate remarks of his essay.

 

The character of being a consonance in the classical sense of the word is an effective character.  The character of being a chord which will, under suitable provo­cation, be used in a composition, by a certain composer, is from the point of view of the composer, a constructive character, since he will assuredly recognize that provocation when it arises, but cannot in general be expected to realize ahead of time whether such a provocation will or will not arise.

 

The character of beauty itself . . . may reasonably, at least as a hypothesis, be regarded as a prospective character.  This means that not only can we not guarantee to recognize it when we encounter it, but also that there exists no formula or attitude, such as that in which for example the romantics believed, which can be counted upon, even in a hypothetical infinitely protracted lifetime, to create all the beauty that there is.

 

The analogue of Godel’s theorem for aesthetics would therefore be:  there is no school of art which permits the production of all beauty and excludes the production of all ugliness.  And the analogue of Church’s theorem, a weaker statement of course, would run:  there is no token (as pleasure or the like) by which you shall know the beautiful when you see it.[34]

 

Immediately after these remarks, he refers to the possibility of a similar analysis of the theory of ethics, alludes to the “effective” character of the Mosaic law, the “constructive” character of its role as a program which “has more the romantic character of a view of one’s life as a mission,” and the “prospec­tive” character of “the idea of the good as a lure, as something whose majesty is too vast to permit of its being incorporated into a body of laws or into even a Weltanschauung of unforeseeable outcome,” and having thereby “an almost mystical quality.”  His concluding sentences will lead us naturally into our first considerations of the Kabbalist’s “Supernal Triad” – or the Tayyibite’s “First Three Intelligences”:

 

The only importance of the role of mathematical logic in this line of thought is the crystal clarity which the abstract nature of its subject matter imposes.  It was here that we first had conclusive evidence of an essential rather than an accidental limitation of knowledge, and of the fact that this ignorance is but the obverse of creativity.  The next step does not lie in facile comparisons of ethics and esthetics with logic, but, I think, in a very precise development, on the basis begun above, of epistemology and the phenomenology of ideas.[35]

 

Two points for orienting ourselves before we begin.  Firstly, the Kabbalah attributes “Beauty” to the center of the Tree’s spider web, the eight-pathed Tiferet; yet the implication of what I’ve just said about Myhill’s analysis and the Supernal Triad would imply the Beautiful, as such, resides in Keter.  This is not a contradiction or indication of idle metaphors at work.  In the Jacob’s Ladder framework, there are four Worlds, hence four Trees, interconnected in a standard vertical arrangement.  These Worlds correspond, among other things, to the classical levels of textual exegesis – a commonplace, as well, in Christian her­me­neutics until quite recently, and revived over half a century ago among literary critics like Kenneth Burke and Northrup Frye, and metahistorians like Hayden White.  These are summarized in the acronym “Pardes,” or “orchard,” a Hebrew word comprised of the initial letters of the words meaning plain sense, intima­tion, homiletic exposition and esoteric meaning. 

 

In the Ladder’s scheme, as mentioned above, the Upper Face of a Lower World is associated with the Lower Face of the next World up.  But then, the Keter of the lower world is put in correspondence with the Tiferet of the higher (and the Malkhut of the next higher still).  The central pillar of the Ladder, then, knows multiple levels of interpretation of but two distinct entities:  the sexually charged “Knowledge” of Yesod/Da’at, and the “Beauty” of Keter/Tiferet/Malkhut.  The side columns, meanwhile, obey a different twofold logic.  Like the Catastrophist’s Cuspoids with which we will model them, they have a primordial “odd/even” nature, the first and third of one World resonating with the third and first of adjacent Worlds, while the second tier of “Gevurah” and “Chesed” form a triad with Tiferet which is the only triad straddling all columns which is not subjected to Ladder overlap (hence its designation as “Seat of the Soul”; and hence, as well, the notion of different levels or kinds of soul, evidenced in different Worlds).

Second point:  at the onset of everything, in the act called the “Tzimtzum”, God contracted his essence, to “make room” for His Creation.[36]   This is followed by the catastrophe called the “Bursting of Vessels,” an esoteric Fall, during which the Primordial Man, Adam Kadmon, radically shrinks in order to be trapped in physical embo­di­ment.  Yet in the modern cosmological picture of things, the universe we know is the result of an initial explosion or “Big Bang” associated with (per Alan Guth) an ensuing “cosmic inflation.”  These two accounts are not contradictory, but rather provide complementary depictions of the same “con­span­sive” process, as Chris Langan[37] has termed it.  The potential for confusion inherent in this duality of viewpoints mandates my strategy:  provide, as far as possible, parallel renderings of all notions discuss­ed, counterbalancing “introspective” metaphysics with “extroverted” physics.

 

And at the very onset, let’s first dispense with the assumption that physics need be strictly “extro­verted” in the first place.   Foundations of Physics is the only peer-reviewed journal dedicated to exploring the interface of physics and philosophy at the most basic levels, with Nobel laureates frequently appearing among the list of contributors.  Its first volume, in 1971, contained a paper based on the dissertation of quantum chemist Andrew Cochran, concerning the “Relationships Between Quantum Physics and Biolo­gy.”  Consolidating earlier work of Schrödinger, de Broglie, Margenau and others (including Einstein, who created the first quantum theory of heat capacities in 1907), he made a compelling empirical case, based on Kopp’s tables of specific heats, for viewing the feature dis­tinctive to life as its minimization of quantum heat capacity.  Not just the building blocks chosen – carbon and other standard “organic com­pound” ingre­dients – but, even more, the composites built from them – amino acids, and (to an even greater extent) pro­teins.   Indeed, “the heat ca­pa­­cities of proteins are amazingly low – so low that it is very difficult to imagine any substance as complex as proteins that could have lower heat capacities.”[38]  So low, in fact, that even were they nearly thrice as high, quantum mechanical effects would still have to be invoked to explain why.

 

The heat capacity of the handle of an iron cooking pot is obvi­ous­ly quite different from the zarf in which you insulate your coffee cup.  In substances where most of the atoms don’t partici­pate in energy ex­changes with their surroundings, much less heat is needed to raise their temperature by a degree:  they have low heat capacity. [39]  The low heat capacity of organic materials tells us that almost all atoms of living sub­stances are in the same energy state they would be in at the absolute zero of temperature.  “Because of their low heat capacities, proteins are largely unaffected by the pelting hail of quanta and thermal disorder that constantly bombard them, and this is one reason that they are able to main­tain their high degree of order and organization over long periods of time.”[40]  Put another way, “wave” (as opposed to “particle”) “pre­pon­derance” typifies living things.  This leads Cochran to imagine quite novel forms of life based on bizarre “supercon­duct­ing” substances like Helium II (residing, perhaps, in the Oort Belt past Pluto?), whose natural state is only observed near abso­lute zero.  And this also leads him to see consciousness as a built-in feature of matter, exhibited to maximum extent when matter is in its lowest quantum states:

 

When thermal disorder is not present to batter matter about, matter should exhibit its intrinsic properties to the greatest extent.  Since classical physicists believed that atoms and the fundamental particles of matter had no degree of consciousness, they believed that all atomic motions would cease near absolute zero, when thermal disorder was absent, and atoms would be like billiard balls at rest.  Instead, when matter is cooled nearly to absolute zero, it not only still has energy, but it exhibits unusual proper­ties that are completely alien to the axioms of classical physics…. As a particle with a degree of conscious­ness would have causal factors arising from within, it is apparent that the new hypotheses are consistent with the modern concept of causality.   It is also apparent that the classical concept of atoms and particles with no degree of consciousness is not consistent [with] the modern concept of causality.[41]

 

The experience of such a primordial, unadorned condition of consciousness, prior to any concep­tual mediation or external interference of any sort, is about as close as ordinary language can come to ap­prox­imating what the Tayyibites would call the “First Intelligence,” or the Kabbalists would designate as “Crown” or “Keter.”   The route toward attaining such experience – at its most basic, entailing meditation on the idea of light in the heart, say  -- implicitly directs one toward the realm of quantum-level perception (since only our visionary sense’s retinal registration is capable of discriminating events that are truly quan­tum level).  But as a theory of this experience (as opposed to its preconditions), this is woefully inadequate.

 

All mystical traditions tell us as much about this realm that Myhill called “prospective,” and all attempt to direct one toward such experience rather than describe it, by engaging in what’s called “negative theology”:   the neti neti (“Not this, not that”) of the Hindus reduces this to a minimal formula.  It is the porch light to the aspirant’s moth:  those who attain to it, no longer live.  Piaget, referring specifically to Gödel’s result, describes this “ground floor” of knowledge in his own paradoxical manner:  “the pyramid of knowledge no longer rests on foundations but hangs by its vertex, an ideal point never reached and, more curious, constantly rising!”[42]

 

The two greatest difficulties with the specific picture just put forth are entanglement, in the quantum sense, and symmetry (which, quantum mechanically, means “conserva­tion laws”) – and seeing our way to grasping the “barrier nature” of these will take us to the Second and Third Intelligences (Chakhmah and Binah) respectively. 

 

If the universe be understood as emerging from (and, through the wonders of requantization, still being contained within) one single quantum of action, then all matter everywhere is interconnected, or “en­tangled,” at the quantum level.  Phenomena like those associated with Bell’s Theorem are associated with this, and the strange new world of quantum computing attempts to exploit such effects.  But what is indis­put­able is that there is nothing more difficult to think about than systems where everything is con­nected to everything else.  Such a theory does exist in mathematics, and is known as the study of Ramsey Graphs.  This is also the first place where Gödel’s theorem reared its head (as shown  in 1977 by Paris and Harring­ton) [43] in an easily defined arena of concrete problems.  These problems, moreover, emerge from contem­plat­ing children’s connect-the-dot games, played with crayons.  The ease with which such problems can be stated, combined with their near-impossibility of solution, brought them to the attention of the great puzzle-meister of Scientific American, Martin Gardner, who devoted a “Mathematical Games” column to them in the immediate wake of the Paris-Harrington shockwave.

 

Problem E 1321 of the June-July, 1958 issue of The American Mathematical Monthly asked its readers the following:  “Prove that at a gathering of any six people, some three of them are either mutual acquaintances or complete strangers to one another.”  This is considerably trickier than it looks, and does not scale up to larger-sized gatherings at all well.  Its solution entails reducing its premises to the proper­ties of a network of points, each connectable to each like entries listed in a phone book.  The trick is to see that the question is asking what amounts to a coloring problem:  you have two crayons with which you can “dial up” the connection between two “phones.”  If the parties are acquainted, use blue; if not, use red.  Play a game where turns are taken avoiding completion of a complete subgraph (i.e., subset of points with their own smaller phone book).  You are asked to prove that, no matter how well play’s conducted, one is forced to create a three-point “phone book” in either red or blue. 

 

There is a name for this 6-point game – it’s called “Sim” --  and Gardner discussed it in his Janu­ary, 1973 column.  To consider generalizations of this problem, a compact notation is called for.  Sim’s setup is shorthanded like this:  R(3,3) = 6.  “This means that R, the Ramsey number for the smallest com­plete graph that forces a ‘monochromatic’ (all red or all blue) triangle when the graph is two-colored, is 6.  Thus if two players alternately color the K₆ [for “complete graph of 6 points”] red and blue, one player is certain to lose by completing a triangle of his color.  The corresponding and easy puzzle is to two-color the critical graph, K₅ [the “complete graph” of 5 points, just small enough to avoid forcing], so that no mono­chromatic triangle appears.”[44]  Other examples of Nim-like crayon games are these:  R(3,4) = 9; R(3,5) = 14; R(4,4) = 18.  Of this one, Gardner says “This is not a bad Ramsey game, although the difficulty of identifying tetrahedrons makes it hard to play.  The graph and its coloring correspond to the fact that at a party of 18 people there is either a set of four acquaintances or four total strangers.” 

 

Three more examples, and then I’ll get to the punch line:  R(3,6) = 18 is the first instance of an ambivalent Ramsey number (two different games can be played on it, this one involving triangular and 6-point subgraphs:  “How these two sets are related to the two tetrahedral sets in the preceding example is an interesting question that no one seems to have investigated.”)  R(3,3,3) = 17 is a three-color game . . . and the only one known for more than two crayons!  Finally, there’s R(3,7) = 23 . . . and this should suggest something.  Especially when we consider the following:

 

Note that the above list does not include R(5,5).  That is because no one yet knows the Ramsey number for a complete graph that, if it is two-colored, forced a monochromatic K5.  Stefan A. Burr of the long-lines department of the American Telephone and Tele­graph Company, a leading expert on Ramsey graph theory, thinks it is possible that R(5,5) will never be known, so great is the jump in complexity.  Even R(4,5), he believes, is so difficult that it is conceivable it too may never be found.  In both cases, however, there are known bounds.  R(5,5) is between 38 and 67 inclusive; R(4,5) is between 35 and 29 inclusive.[45]

 

I recall reading that the R(4,5) problem was attacked by some supercomputer pit bulls, and even­tually was cracked a couple years ago.  The point, though, is that R(3,7) = 23 is the largest such problem that the human mind can hope to actually cope with unaided – and this is also a very concise definition of the intuitive picture of the Kabbalistic Tree:  if one’s crayons are labeled “Unmanifest” and “Created,” we have the minimal way of defining the Supernal Triad and the collectivity of the remaining Sefirot[46] – with the 22 line segments with which the points of K₂₃ can be minimally traced giving us the prototyope for those minimally distinctive acts of writing, the Letters.  (Considering such a minimal “scan­ning sequence” is, in fact, one of the standard ways to short­hand one’s thinking in Ramsey theory.)  One can, in other words, elicit an intuition of the Tree at this level – it is clearly a “constructive” result – but the impossibility of resolving even small-number problems in this domain makes it clear that no “effective” approaches exist – even in theory.

 

It is interesting that another “constructive” result can be obtained for the Letters if we think about “writing” in another sense – and indeed, the entities of interest are called “letters” by the mathematicians who study them!  A bizarre-seeming anomaly, due to renowned physicist and puzzle hobbyist Roger Pen­rose, concerns the problem of tiling the plane aperiodically.  It is well-known that periodic tilings or “wall­paperings” of the plane are completely exhausted by a very small set of symmetry groups (17, in fact).  The hexagonal tiles of bathroom floors, or the far more intricate patterns on the walls of the Alhambra, are in­stan­ces with which we’re likely all familiar.  As often happens in mathematics, a very simple result was adumbrated by some very wacky theoretic proof:  a few years before Pen­rose hit upon his two-tile “dart” and “kite” solution, it was shown that one could, with a set of basic “tiles” num­bering somewhere in five figures, create a tiling process that would never re­peat, yet could always be ex­tended.  The celebrated “Pen­rose tiles” simplified this theoretical result enor­mously, and showed a surpris­ing way around the fundamen­tal exclusion of five-fold-symmetry from the realm of crystallographic possi­bility.   Soon thereafter, actual “icosahedral quasicrystals” were discovered.  As crystals are 3-D, it was only natural that someone would ask if there were space-tiling equivalents of Penrose’s 2-D darts and kites. 

 

While numerous weird results have been found in the last few years, the first (and most natural) solution was hit upon by the Israeli mathematician André Katz, who may or may not have had his native alphabet in mind when he came up with it.  A meditation on the projections into 3-D of the 6-D unit hyper­cube, and their interactions with the full icosahedral symmetries displayed by the rhombic triaconta­hedron, let to the creation of a set of two tile-shapes, which he called “thick” and “thin” rhombohedra, each existing in variously “decorated” varieties.  The matching rules for differently decorat­ed “thick” and “thin” tiles required that there be 14 of the former, and 8 of the latter – 22 “letters” in all![47]

 

As if this weren’t crazy enough, the great Russian dynamicist Vladimir Arnol’d – the discoverer of the “A, D, E Problem” himself – showed that the aperiodic projection into 3-D from the six-dimensional lattice that Katz contemplated could be understood in terms of Catastrophe Theory.  Specifically, the set of tiles Katz generated could be obtained as a side-effect of the unfolding of the next-higher member of the “umbilic cycle” or “D series” which I’m arguing can generate the Tree.  This “D6” is the same-dimen­sion­ed sibling of the “E6” which is the minimal container of the “trance tunnel”:  from this vantage, the Letters and the Sefirot can be seen as complementary representations of the same higher-dimensional workings – making it all the more “natural” that intuition would want to combine them in the same diagrammatics.[48] 

 

 

Even if we consider these, as Plato did his creation myth in the Timaeus, as just “likely stories,” they nevertheless point out that intuitions that can guide cultures at the Weltanschauung level belong to the “constructive” sphere of Chockmah.  And other structures which suggest “likely stories” for the guiding intuitional “consciousness maps” of other cultures – associated with the non-algorithmic mysteriousness of a culture’s “Prime Symbol” in Oswald Spengler’s sense – can also be discerned here.  For many “simple questions” (with impossibly hard “constructive” solutions) can be asked in Ramsey Graph land.  Here’s another Gardner talks about, which has some very surprising properties:

 

Consider a cube with lines joining every pair of corners.  The result is a complete graph on eight points, except now we have added a Euclidean geometric structure.  Imagine the lines of this spatial K₈ arbitrarily colored red and blue.  Can it be done in such a way that no monochromatic K₄ results that lies on a plane?  The answer is yes, and it is not hard to do.

 

Let us generalize to n-dimensional cubes.  A hypercube has 2ⁿ corners.  On the four-dimensional hypercube, it also is possible to two-color the lines of the complete graph of 2⁴, or 16, points so that no one-color complete planar graph of four points results.  The same can be done with the 2⁵ hypercube of 32 points.  This suggests the following Euclidean Ramsey problem:  What is the smallest dimension of a hyper­cube such that if the lines joining all pairs of corners are two-colored, a planar K₄ of one color will be forced?[49]

 

Ron Graham, then the head of the Discrete Mathematics Department at Bell Labs and one of the world’s top combinatorialists (and ex-professional trampolinist and former president of the International Juggler’s Association), was able to prove the existence of an answer.  But the existence proof required computations of an upper bound “so vast that it holds the record for the largest number ever used in a serious mathematical proof” – and required a special notation, introduced by Donald E. Knuth, just a few months before Paris and Harrington’s proof was revealed.  And yet . . . “Ramsey-theory experts believe the actual Ramsey number for this problem is probably 6.  As Stanislaw M. Ulam has said many times in his lectures, ‘The infinite we shall do right away.  The finite may take a little longer.’”[50]

 

What is curious is that “probably 6” means play would take place on a 64-vertex “game board” whose lattice would be that of the I Ching:  the collection, with commentary, of  64 “hexa­gram” oracles, which is the closest thing, in China, to the Kabbalah in terms of “diagram status”:  that is, it has shaped the metaphysics of its indigenous culture in a comparably monolithic way.  And, for what it’s worth, Spengler was of the opinion that the “Prime Symbol” of ancient Chinese culture was the plane – and it is the planar constraint on the solution space that “made” the problem whose answer is “probably 6” in the first place!

 

I have long thought of this general situation as akin to a cheap-laugh-getting trick that used to crack me up when watching certain silly silent movies.  Two people from very different cultures (typically, some Great White Hunter and a Pygmy chief deep in the Congo) are trying to communi­cate.  When one says something sound-bite-sized, the translation sometimes needs a full screen of small print; when one de­livers a long monologue, the translation might be one or two words.  The surprising effect of these imbal­ances led me to call it “haha wobble,” and I’ve come to see it as quite ubiquitous.  A client will have some simple-sounding thing he wants me to do for him with a software application; I tell him no way, I’d have to go into the API and write a layer of C code “under the hood” to pull it off.  Other times, the same client will have something he wants that sounds so difficult to him that he’s afraid to even mention it – but once I ex­tract the request from him, it will often be the case that I can make the changes needed while we’re talk­ing on the phone.  These differences between “constructive” and “effective” abound in real life.

 

But what is it, in simple terms, that makes “constructive” phenomena so intractable?  In a word:  symmetry – or rather, the absence of same.  When we come down to the third Sefirah, we enter the realm of the readily axiomatized, hence inherently repeatable, ergo amenable to simplification by symmetry argu­ments.  Quantum mechanics itself is built upon the stunning realization of Emmy Noether that all the con­ser­vation laws of physics are essentially just symmetries – hence, analogues of the Platonics, or more ela­bo­rate geometric forms, underwrite the complicated messinesses of real-world phenomena.

 

We saw in the third installment how close in spirit to Plato’s vision of ideal geometric forms modern physics is.  We heard no less than Werner Heisenberg say of Plato’s vision that it was likely right in principle, even if we dismiss the actual machinery of creation he proposed.  The passage is worth repeating now, as it gives a wonderful depiction of Binah’s interface to the realm of the Created things:

 

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.

 

The Sefirah of Binah (or more properly, perhaps, the path from Chakhmah to Binah on the Light­ning Flash) is traditionally associated with the origin of Time was we know it:  the less-than-godly realm, that is, where things are deferred, delayed, destroyed and created, and almost never instantaneously real­ized.  We might call this, then, the backdrop of Creation, or the gateway into and away from Manifesta­tion.  And it is here, in the realm of the Third Intelli­gence, that a crucial phenomenon emerges.  I will introduce it through the backdoor of a well-known co­nun­drum from quantum mechanics, the two-slit experiment.

 

There’s an old Sid Caesar routine where his German scientist character is being introduced by Carl Reiner’s talk-show host.  Asked what he finds to be the most amazing technological feat of our time, Cae­sar’s scientist says the lunch-box thermos.  Surprised, Reiner’s interviewer asks him why he thinks this.  “Vell, vhen you put sumting in dere dat’s hot, it stays hot; vhen you put sumting in dere dat’s cold, it stays cold.”  Reiner, looking puzzled, says:  “So?”  Caesar, eyes bugging, exhorts, “How does it know?”

 

This is the basic quandary with the two-slit experiment, too.  When one slit is left open, electrons passing through it act like particles, leaving a sensible distribution of evidences of their passing on the screen in the back of the box.  When two slits are open, though, electrons act like waves, somehow passing through both slits simultaneously, and leaving evidence of interference effects that are wave motion’s trademark.  How, indeed, does the electron “know”?

 

A most roundabout way to approach this problem was derived by a Russian sociologist with a pen­­­chant for mathematical modeling, Vladimir Lefebvre.  He took his cue from a well-known suggestion of Niels Bohr, who had wondered if the phenomenon of complementarity observed in quantum theory might not also obtain in the areas of human cognition and psychology.  In Atomic Physics and Human Know­ledge, Bohr wrote as follows:

 

In introspection it is clearly impossible to distinguish sharply between the phenomena themselves and their conscious perception, and although we may often speak of lending our attention to some particular aspect of a psychical experience, it will appear on closer examination that we really have to do, in such cases, with mutually exclusive situations.  We all know the old saying that, if we try to analyze our own emotions, we hardly poss­ess them any longer, and in that sense we recognize between psychical experiences, for the description of which words such as “thoughts” and “feelings” are adequately used, a complementary relationship similar to that between the experiences regarding the beha­viour of atoms obtained under different experimental arrangements and described by means of different analogies taken from our usual ideas.[51]

 

Lefebvre had meanwhile been inspired to develop an algebraic model of ethical cognition based on an exponential representation of Boolean functions.  The model allowed a connection to be made be­tween the individual’s behavior and the structure of his inner world:  specifically, it allowed a recursive depiction of his images of others, their images of him, his image of their images of him, their images of his images of them, and so on . . .  which secondary images are collectively called “registrations.”  This is, of course, quite similar formally to the “renormalization” of virtual particles epitomized, say, in Feynman diagrams.  But even this formal similarity did not prepare him for what he found:

 

With the help of Boolean functions, an individual is represented as an automaton with two inputs and one output.  The inputs correspond to the environment’s demands which are coded as either “good” or “bad.”  The output is the individual’s response….  Thus in this model an individual is an “observer” of his own images and images of his images, etc….  If the values of images’ inputs and registrations’ inputs coincide with each other, we say that the registrations are correct.   In the opposite case we say that the registrations are incorrect… This allows us to imitate the inner feelings of an individual and to connect his inner states with his responses.  Psychology suggests that in the realm of moral feelings a substantial role is played by such feelings as repentance and condemnation, that is, observing the “evil” in oneself and the “evil” in one’s partner.[52]

 

Boolean renderings of the familiar notions of “guilt,” “condemnation,” and “suffering” then be­come readily generated.  The notions can be expressed either as “impulses” or as impulse frequencies – these latter being interpreted as feelings of guilt, condemnation, suffering, and their compounds.  “And here we come to a surprising thing:  if an individual has at least one correct registration of input impulses, feel­ing of suffering is a simple arithmetic sum… However, if an individual does not have any correct registra­tions, the equation changes” – to include an interference term, exactly analogous to the wave interference effect in the two-slit experiment!  “This means that the correct registration on the one hand and the obser­va­tion of interference on the other are complementary events.”[53]  Moreover, as he shows in detail, his “for­mulae describing individuals, situations, and their relations” offer an exact “analog of amplitude corre­la­tions in quantum mechanics.”  Then he deadpans this closing thought: “One may suppose that this paral­lel would be useful not only for the psychologist, but also for the physicist since in physics neither ampli­tudes of probabilities, nor their modules (as it seems to the present author) have clear interpretation.”[54]

 

 

If we contrast and compare Lefebvre’s conclusions with Cochran’s, we might be tempted to think of the movement from Keter’s unitary experience of a kind of “Collective Unconscious” in the waking state, to a universe with multiple centers of consciousness (within which “incorrect registrations” become possible) as sufficient grounds for introducing evil into Creation.  One might be tempted to expand on this supposition, by recalling arguments made in Part IV, between Notes 63-72, concerning the peculiar nature of the “para­meter” sitting in Keter’s place, the Double Cusp’s highest-order monomial control, or “top”:  

 

But we sense the possibilities for re-enchantment when we realize that this peculiar control in fact provides a measure of the “cross-ratio,” and that each of its infinity of possible values is associa­ted with a distinct manifold:  like Cusa’s painting, myriad differentiably distinct viewpoints (one “Tegern­see monk” per “differentiable manifold”) are underwritten in a unitary manner from the topological “God’s-eye view” perspective.   

 

And if one is so tempted, one will sense a necessary link between the origins of individual free­dom and cosmic evil – and hence, will be keeping compa­ny with Kabbalists and Tayyibites, who saw the origin of Evil as contained within the Third Intelligence:  like the pre-Gödel, pre-Heisenberg scientist,

 

The Third Intelligence inquired and sought the source of its own origin.  What could be apparently more natural?  Yet it was a misconceived plan fraught with very dangerous consequences, like an innocent and unknowing intruder in the control room of an atomic reactor, toying with the buttons and seeking to access the full power of the energy source as “a good thing”….

 

[T]he Third Divine Entity sought to encompass its own origin and to plumb the very depths and sources of its being – a route that would perforce have to lead into the Un­mani­fest, the Mystery of Mysteries that by its very nature cannot be unveiled with impunity to the one so seeking:  the veiling is inherent and necessary for the eternal provision of immortal being….  To seek to manifest the source of life out of the unmani­fest, could end only in the manifestation of death, for such a seeker thereby would suc­ceed only in cutting himself off from the circuit and flow of life in so trying , even though unwittingly, to preempt it.  No manifest being can contain the unmanifest infinite.[55]

The tragic flaw of the Third Archangelic Power is its containing, as its boundary condition sepa­rating it from its “constructive” predecessor (a separation made explicit in Turing’s “Halting Problem,” for in­stance), the necessary intrusion of Time.  Prior to its level, the fantasy of all fast-food consumers is a given:  “No waiting!”  But the intrusion of the phenomenology of Derrida’s starting point, the “différance” of delay and differentia­tion, is introduced herein, and the rest is the inevitable consequence:

 

The Third Divine Entity dreamed a dream of finding that source explicitly and controlling it to be within himself (as he mistakenly thought was the case with the Second and First Intelligences).  That dream and wish albeit momentary, had on that level of power and perception dire consequences, the first of which was a retarding of the consciousness of the Third Intelligence by reason of this thus introduced blockage or fallacy that could by its very nature not advance, but only hold back.  The basic term used in the tradition is takhalluf, to stay back because of being delayed, retarded, or postponed.  Etymologically related words that clarify the usage in our tradition are tahaluf:  to be self-constrained by some prior allegiance; takalluf:  a self-caused constraint; and finally the very illuminating takalif:  self-caused costs or difficulties from the word kulfa, trouble.

 

The reason for such grave consequences of a released desire on the part of the Third Archangelic Power is bound with the fact embedded in ancient traditions preserved in Homeric Greece of the … mere wish or willing propensity of a god being equivalent to the determined … implementing, focused will of a man.  But the implications go deeper, since the reason that it is so depends on the fact that the gods are not in our kind of time.  Duration of things, yes, and changes, too – but all without waiting time, which is the chief characteristic of what we humans call our time.  We must wait for any idea or plan to be enacted and then mature to fruition or full manifestation….

 

All this happened instanter, for in the world-out-of-waiting-time there is no delay.  Imme­diately with that momentary dream of absolute self-containment on the part of the Third Entity, arose within its being the monstrous image of all evil, called in the Yemenite tradition, “the Image of Iblis” (i.e. of Satan), the concept going back to the Egyptian god  of evil, Set….  Note that all possibilities must exist in invok­able form in the unmanifest, or else there could not be free choice, which is the hallmark of love, by which love in turn is guaranteed since non-voluntary love is a contradiction in terms.  Thus the very nature of love guarantees both the possibility (under free choice) of evil and its ultimate defeat if manifested.

 

The shock of this horrible manifestation awoke the Third Entity from the evil-spawning fantasy; but too late, for in that realm of supernal reality, evil was now released and made manifest.  With a shudder of revulsion, the divine being expelled the horrid image; but that being contained also within itself the seeds of countless other potential and similar beings, who were now all infested…[56]

 

The Kabbalists speak now of the “Bursting of Vessels” – and the incipient need for the Humpty Dumpty work of tikkun or “rectification”:  the retrieving of the Divine Sparks scattered by the catastrophe that marked the Fall into material existence, and returning of them to their proper home.  But of course, the great gift won at such a price is individualized freedom.  In this sense, the “Bursting” is an orgasmic act of “going to seed” – an act of dissemination and universal creativity as well as of decay and dissolution.  As such, it is the non-Sefirotic (be­cause unstable) mani­festation of Da’at or “Knowledge.” 

 

And here we can let modern mathematics add its own two cents’ worth to the myth.  For the catastrophic outcome just narrated is a built-in feature of the Double Cusp’s dynamics.  Da’at is always drawn on the axis which joins Tiferet to Keter; hence, if my own reading is to be consistent, there must be some critical condition associated with this dimension of control, from which all else follows.  In fact, there is, and it is associated in my mind with a motif from contemporary myth, the “Borg ship” of  the sci-fi series Star Trek.

 

As any fan of android Data and U.S.S. Enterprise Captain Jean-Luc Picard needn’t be told, the Borg collective comprise a demonic variant – denizens of a sort of Bentham-like Panoptikon – of the “Col­lec­tive Unconscious” all-is-oneness of Keter’s realm.  They are on a mission to “assimilate” all intelli­gent life-forms into their prosthetic dystopia.  And the distinctive feature of their intrusion into the normal state of things is the presence of their bizarre mode of transport:  the Cube-shaped space ship.

 

On planet earth, the closest thing to such a vehicle, to my way of thinking, would be a square sea-going ship.  And such ships do, in fact, exist:  offshore oil-rigs, before they’ve been moored to their drilling sites, are just such ungainly vessels.  And during their brief period of being ferried into place, they are ex­ceedingly vulnerable to hurricanes and other sources of turbulence.  Exceptionally so, in fact (even, to some degree, once locked in place).  And the reason?  Their square shape has a lot to do with it.  What happens?  Their stability is governed by a form of Double Cusp where the “parameter” can pass through crucial val­ues – values which, though two points equidistant around the origin in theory, in practice are guaranteed to be passed through if the parameter is subjected to a sufficiently wide range of continuous variations.  And if these values are traversed?  The 8-dimensional control space suddenly becomes infinite!

 

The “generic section” of the Double Cusp looks like two orthogonal ellipses in a 2-D cut through its “behavior space,” allowing for a maximum or “fountain” in the central region the ellipses share, and minima or “pockets” in the four lobes depending from it.  By working the controls, deformations of this “generic section” can lead to a huge variety of interrelations between the four minima or “stable states,” in a manner semioticians relate to the four “noun cases” of a standard Indo-European sentence.  But when the drilling rig hits sufficiently choppy seas, the infinite number of controls easily cause the “generic section” itself to careen wildly, so that it effectively traces out all possible positions of itself, inducing a blurred surface which is known as the “sombrero” or “Mexican hat.”[57]

 

Yet this very same surface can be thought of in a different sense:  put an object at the top of the sombrero, then shake the table it rests on.  The object will fall from its metastable placement into the curled trough demarcated by the rim of the hat:  to physicists, this is the “false vacuum” model behind the Higgs mechanism (whose “Higgs particle” is the last piece of the “standard model” not yet in evidence).  The model, that is, governing the “filling up” of a particle’s “gas tank” with the stuff we call mass – the Fall into material existence.

 

*              *              *              *              *

               

Some closing thoughts:  in Musès’s account of the Tayyibite doctrines, he tells us “This chapter which is essentially historical (a major aspect of time) couldn’t have been completed before 1970 when a key breakthrough was made in our knowledge of the ancient Egyptian world-view.”[58]  This breakthrough was the discover of the Temple of Opet at Karnak, with surprisingly well-preserved wall figures which Jean-Claude Goyon, in the late 70s, showed were duplicates of an extremely important, but almost destroy­ed, initiatory temple constructed by the XXV^th Dynasty pharaoh Taharka – a temple which, in its turn, was built as an act of historical homage, duplicating texts and images, otherwise largely lost, of crucial V^th Dy­nasty “Pyramid Texts.”  One subterranean crypt at the Taharka temple was concerned with a pantheon of Ten Deific Souls of the Most Hidden One (Amun Re); Goyon’s analyses of the Opet find strongly suggest these Ten are the prototypes for Kabbalistic Sefirot and Tayyibite Intelligences.

 

Such was the reconstruction finished around 1977 by Goyon, and published in 1979, of a doctrine whose roots go back to an extreme antiquity, as the ancient Egyptian base-ten number system also showed, particularly in its special relating of Three and Ten – a con­nection illuminated by the obscure remnant of the tradition preserved with such remark­able detail in the backwater of medieval Yemen.  Such a persis­tence need not surprise when we know that certain rites and doctrines of ancient Egypt had a continuous exis­tence from at least the V^th  Dynasty through the Ptolemaic period – a stretch of over two millennia….

 

Let us recall that Yemen was a Pharaonic protectorate from the times of the earliest Mem­­phite Dynasties and their priesthoods, and hence a natural repository for ancient theological traditions.  That protectorate bridged the way to Syria, Iraq, and Iran – the former Assyrian, Chaldean, and Persian kingdoms – for it included the ancient 70-day caravan route that went from the old site later called Aden to the present Gulf of Aqaba.  The powerful continuance of the important pharmacological tradition of ancient Egypt in Yemen even through medieval times is another testimony to an enduringly strong culture bridge.  And, as recently as 1983, a Saudi archaeological team found among the ruins of an ancient Arabian temple a stone depicting religio-cosmological symbols from still more ancient Egypt and Chaldea.[59]

 

In my own account of the interrelatable nature of ancient Semitic and modern mathematical sym­bolisms, much of my argument could not have been framed prior to another recent window on ancient thought, George Michanowsky’s The Once and Future Star.  Ingeniously combining recent results of radio astronomy with ancient star-texts from the dawn of civilization in Sumer, he pinpoints the origin of the nar­rative of Da’at itself in actual cataclysmic events.  The Kabbalistic Lightning Flash passes through Da’at from Binah on its way to Chesed:  the region traversed is known as the “Abyss” – a term derived from an­cient Sumerian “Abzu” used to designate the location in the sky of what, for a brief time, was the brightest star (far brighter, in fact, than the full moon, and shining during the daytime like a second sun).  This star has long been a mystery to archaeologists, as its placement in the heavens was central to the most ancient recorded religions in the Middle East – and yet seemed to have no physical existence at all!  But on Octo­ber 4, 1968, in the constellation Vela, radio astronomers in Australia discovered what was then the faintest object in the heavens ever detected – the pulsar remnant, as it turned out, of the closest supernova to the earth ever to explode in the known history of mankind.

 

Thus, for a period that must have lasted at least many months, there was in our southern sky a phenomenon that, depending on the season, appeared either as a gigantic light source by night or as a somewhat smaller second sun by day.  Gradually, the radiance of this celestial prodigy diminished and, finally, faded away altogether.  It may very well have been the single most awesome sky event ever witnessed by humans.

 

The psychological impact of this celestial apparition on our culture was overwhelming.  In addi­tion, the radiation it generated may have had significant environmental and per­haps even biological conse­quences on earth.  Next to our own sun, Vela X was probably the most important star in the history of humanity.[60]

 

The supernova detonated, in all likelihood, somewhere between 4,000 and 6,000 B.C.E.  An ob­scure Egyptian goddess has her dominion over its locus, marked with a seven-pointed star (the sure mark, say archaeologists, of Sumerian origin).  The region is typically associated with “Duat,” the realm of the dead – whence, in the language of Egypt’s former slaves, “Da’at” today. 

 

The legend of the mighty star in Vela, which once had appeared and then was no longer seen, may very well have been the origin of esoteric traditions in various lands about a vitally important, currently invisible star, which some day will reveal itself again to humanity.  A variant of this theme is a belief that there are actually two suns in the sky and that one of them is normally invisible but can be seen at extraor­dinary moments in history….

 

Vela X is indeed Stella Quondam Stellaque Futura, the Once and Future Star.  For nearly a decade, we have heard this star’s radio signals and, at long last, we are able to see it again.  And during all these thousands of years, humanity’s oldest writ has preserved for us the memory of how it once shone brightly across the waters of the Sumerians’ southern ocean.  Today, more than ever, it is in truth a star to wish upon. [61]