Why are the primary mythological colors black, white and red? Perhaps because black and white can be considered at once different in kind from each other and different in kind from color itself, while red is the most profound color proper, at least inasmuch as it’s the color of blood and thus of life in general. Similarly the Earth is black, the stars white, and the planets often red. Color theory itself can be precisely if rather crudely based on such a trinity: “brightness” is a measure of the amount of black coupled to a color, “saturation” is a measure of the amount of white likewise coupled, and “hue” is a measure of the amount of the color itself.
Among the all-time great color theorists are England’s remarkably White/Apollonian Sir Isaac Newton and Austria’s famous, aforementioned, chiefly White/Apollonian physicist Erwin Schrödinger. Schrödinger became nearly as well known for his Vedic advocacy of the unity of minds/consciousnesses indeed the singularly prime existence of Mind, fairly considered identical to Spinoza’s concept of God/Nature as he was for his physics. Color theory, as Schrödinger’s biographer Walter Moore emphasizes, “stands at the crux of the ancient mind–body problem.” According to the Red/Dionysian paradigm the mind–body problem is better considered the mind–body duality or complementarity, akin to yin–yang, Red–White, particle–wave. Indeed the philosopher/physicist Rene Descartes’ great discovery, stemming from the work of Giordono Bruno (first to employ the word monad) and Galileo, was that mind and extension are incommensurate, extension being the essence of body (matter) according to Descartes. Newton conserving the notion of extension as physically fundamental exiled (but did not kill) Descartes’ theory of mind. Newton and extension were St. George; Descartes and mind, the dragon. Noam Chomsky, from his Language and Thought:
As is well-known, the Cartesian program collapsed within a generation. It is commonly derided today as the belief that there is “a ghost in the machine.” But that conclusion mistakes what happened. It was the Cartesian theory of body that collapsed; the theory of mind, such as it was, remained unaffected. Newton demonstrated that the Cartesian theory of the material world was fatally inadequate, unable to account for the most elementary properties of motion….
Returning to Newton’s demolition of the common sense theory of body, the natural conclusion is that human thought and action are properties of organized matter, like “powers of attraction and repulsion,” electrical charge, and so on. The conclusion was drawn very soon, most forcefully by La Mettrie, a generation later by the eminent chemist Joseph Priestley, though neither attempted to deal with the properties of mind identified by the Cartesians, just as they have been put aside in the revival of “cognitive science” since the 1950s….
Here’s Schrödinger, from his Mind and Matter:
… The material world has only been constructed at the price of taking the self, that is, mind, out of it, removing it; mind is no part of it, obviously, therefore it can neither act on it nor be acted on by any of its parts. (This was stated in a very brief and clear sentence by Spinoza [“the greatest philosopher of the seventeenth century,” as Schrödinger refers to him; here’s the sentence Schrödinger refers to, from Spinoza’s Ethics, Pt III, Prop. 2: “Neither can the body determine the mind to think, nor the mind determine the body to motion or rest or anything else (if such there be).”] …)
It is very difficult for us to take stock of the fact that localization of the personality, of the conscious mind, inside the body is only symbolic, just an aid for practical use.
Descartes’ mindbody theory was Aristotelian. The Aristotelian is fundamentally complex, Red/Dionysian, involving as substance both “body” (matter) and “form” (soul, mind) and moreover being hierarchical, plenist, providential in a word, organic. This is to say, Aristotle’s cosmos is holistic, holographic: the whole expresses the parts and any part expresses the whole. Gottfried Wilhelm Leibniz the Red/Dionysian German philosopher, mathematician, contemporary and chief rival of both Spinoza and Newton not only conserves this complexity, he makes it a principle of his cosmology, the “principle of macrocosm and microcosm,” he calls it, whereby each of his real particles (“monads”) is a “universe in prototype.” The Vedic doctrine “All is One” (Atman is Brahman), says Leibniz, is best considered complementary to the doctrine “One is All.” Modern physical theories are similarly complex insofar as they fundamentally involve dualities: e.g. position and momentum, space and time, particle and wave, real and imaginary number components. Yet mind remains exiled from physics, even from atomic theory, which is bounded by the notions of randomness and “observer-created reality” only inasmuch as these notions are involved in one or another interpretation of the theory’s 2 equivalent but not identical indeed deeply contrasting mathematical formalisms, these being Heisenberg’s Red/Dionysian matrix (alias quantum, as in monad) mechanics and Schrödinger’s White/Apollonian wave (as in continuum, unity) mechanics.
The pair of orthodox atomic formalisms are together a duality that resonates with the dualities each contain. Naturally the question suggests itself: Is one of these formalisms fundamentally better? If so, which? Both formalisms chiefly address the concept of difference. Heisenberg’s does not allow difference to be vanishingly small. Schrödinger’s does. Which is to say, Heisenberg’s is quantum, Schrödinger’s continuum. Heisenberg’s is based upon said dualities whereas Schrödinger’s is based on mathematical points. Heisenberg is telling us that there is something extremely complex — indeed, absolutely mysterious — about difference. Whereas Schrödinger is telling us that the extreme multiplicity of the wave-mechanical “configuration space” of mass points meets its opposite: a simple, comprehensible unity. With Schrödinger difference takes a back seat to unity. With Heisenberg we see a way to the following, contrary resolution of the mind–body problem: although extension is not commensurate with mind, difference can be!
Leibniz used precisely this commensurability between real difference and mind to conserve Aristotle’s organic philosophy vis-à-vis Spinoza’s and Newton’s expressions of monism. Leibniz termed this conservation his “system of pre-established harmony.” We will do well to consider this system a theory of relativity, i.e. a theory of difference. Likewise we should recognize Leibniz and Heisenberg as being at once the greatest mystics and the greatest defenders of orthodoxy the world has ever seen; whilst Spinoza and Newton and in turn Schrödinger and Einstein are to be considered the greatest gnostics ever, for they assert that there is nothing fundamentally unfathomable, incomprehensible — nothing (or next to nothing) fundamentally mysterious — about experience.
Schrödinger termed Leibniz’s system of pre-established harmony a “doctrine of Monads” and called it “unappealing,” “fearful,” even “horrible.” Why? Because the quanta of this system — the monads, as Leibniz indeed calls them, i.e. minds/souls — are related to each other in terms only of the pre-established harmony which they altogether amount to. As Leibniz said, these real quanta are “windowless.” The infinite set of monads is maximally a community, but it is a community which harbors absolutely no actual communication. You could say the communication between monads is all pre-established. Why does Leibniz call these quanta monads and describe them as being related to each other in such a massively yet exclusively parallel way — indeed, in a purely mystical way? Because logically a true quantum (i.e. unit) harbors no true parts, and logically there can be no mechanical/localizeable connection between quanta. In other words, there is no logical way to describe these quanta as mechanically/locally interacting with each other. (A translation of Leibniz’s remarkably concise Monadology is available free of charge online.)
Plurality implies mystery. Leibniz tried to conserve plurality and reason — and himself. In 1714 he wrote to a correspondent:
[I]t is precisely by means of the monads that Spinozism is destroyed. For there are as many true substances — as many living mirrors of the Universe, always subsisting, as it were, or concentrated Universes — as there are Monads; whereas, according to Spinoza, there is but one sole substance. He would be right, if there were no Monads.”
Plurality is Leibniz’s chief principle and therefore his only principle. Leibniz is better known as an advocate of the principle of sufficient reason, stated in his words as follows:
[I]t is necessary to refer everything to some reason, and we cannot stop until we have arrived at a first cause — or it must be admitted that something can exist without a reason for its existence, and this admission destroys the demonstration of the existence of God and of many philosophical theorems.
If Leibniz would have described God as being not a creator of the monads but merely a member — albeit the greatest member — of the Existential set of real quanta, he not only would have lost his ultimate reason for the existence of the quanta, he would have been widely branded a heretic (perhaps even a greater heretic than Spinoza) and may have been executed for it — a fate indeed suffered by many of his coevals. Leibniz ultimately conserved the principle of sufficient reason to save his neck. In truth he is the greatest mystic ever. In my opinion if Leibniz could have completely given himself over to the mystery which is truly the singular basis of his system, he would have been able to argue that the quanta thereof do interact with each other albeit in an absolutely mysterious way. Indeed, such generally mystical interaction — such non-local and indeed extreme causation, such extreme-action-despite-separation — seems but corollary of the very principle of plurality, i.e. of the true principle of relativity, alias, you might say, a principle of plenitude.
The depth, antiquity and richness of the principle of plenitude that is, of Black/Baroque community is exceedingly remarkable, as A. O. Lovejoy explains so well in his classic Great Chain of Being. Consider in this respect the word cornucopia. This word derives from the Latin words corn, “horn,” and cōpia, “plenty,” the latter consisting of co + opia/ops, as in the Latin opus and the Sanskrit apas — both meaning “work” and both being closely related to the Greek apis, “honey bee” and as in the goddesses Ops/Rhea, Eur–Opa, Penel–Ope, Op–Helia (Ophelia, Ops–Helen), where ops is typically taken to mean “eye,” “light,” “face,” “voice,” “snake,” and “power” (altogether as in Medusa) but is also equivalent to the P-I-E opi and the Greek epi, “back,” as in Epimetheus, he who thinks of the past. Leonard Shlain notes in his insightful Art and Physics:
The preclassical Greeks did not distinguish between “eye” and “light”: either word could be used to describe something beloved or admired. Eyes seemed to emanate light and sources of light were as large eyes. The sun could be called an eye and one’s eye was referred to as a light.
Yet the Sun has a dark side: The P-I-E Ops Kolyo is beautiful to behold from the front, yet her whole backside is writhing of snakes and worms. The root op- is the basis of the English root af-, as in after the letters p and f being closely related. The title/name Aphrodite who, incidentally, is associated with the initial metal worked by humans, copper is equivalent to Op-ro-dite, wherein the ro signifies redness, running, periodic movement and dite signifies whiteness, brightness, as in Diana (Di-Ana). Similarly if we consider the Ap prefix symbolic of the White/Apollonian, we see her name as literally White–Red diety; and recognizing Ap as being just as equivalent to Ops, we see her as the Black–White–Red diety. Aphrodite’s association with sea foam, Greek aphro, is on analogy with the surf’s dark power and periodicity as well as its white, semen-like essence, and only secondarily on analogy with its whiteness. Her association with the horse ros, as in Aphrodite’s flower, the red rose is on analogy with running horses and sea foam, as in the horses leading Poseidon’s chariot and as in the periodicity exhibited by animals of the herding sort, i.e. of the gregarious sort, this latter word from the P-I-E ger. This ger is basis of the Greek word meaning “crane,” geranos, and is closely related to the name Cronus (alias Kronos, Saturn) i.e. Geranos, the annual (periodic) herding animal in general. Geranos contrasts with Ur–anos, Uranos being father of Cronus. Similarly Cronus’s mother, wife of Uranos, is Gaia, whose name is cognate with ger and likewise cognate with ge, as in geo and meaning “commonality, community, plurality,” i.e. the Black/Baroque. Cronus = Aphrodite. Here we have the basis of the word grail. Among other germane relatives are Greece, grey (as in the grey-eyed goddess Athena) and the P-I-E gherd, “to surround, enclose, hedge, gird,” and ghordo, “enclosure,” and likewise the Sanskrit grhá, “enclosure,” and the Lithuanian gardas, “pen” or “fold.”
Similarly we have the Latin opera, meaning “a peasant’s day’s labor,” and operire, “to cover,” which words are closely related to the Old High German helan (cognate with Helen), “to conceal,” and the Greek kalyptein, “to hide,” as in eclipse and apocalypse, and kalos, “beautiful,” and are likewise related to the Black/Baroque names Kalypso, Kali, and Kolyo, the latter being the chief P-I-E goddess. The very title Latin comes from latere, “to hide.” Virgil says this title signifies Saturn/Kronos’s (profound) concealment in that peninsular countryside, the god hiding himself from his upstart son Jupiter/Zeus. Likewise Atlas, another Titanic equivalent to Zeus, is positioned by Zeus underneath the world (ostensibly holding it up). The Titans Epimetheus (past-thinker) and Prometheus (future-thinker) famously sided with Zeus against Cronus and Atlas and the other Titans; thus they participate in several trinities akin to Past–Present–Future: Epimetheus–Cronus–Prometheus, Epimetheus–Atlas–Prometheus, Epimetheus–Zeus–Prometheus.
Another important cognate is the Latin optimus, equivalent to the Greek aristos, as in Aristotle and aristocrat. This word refers not only to the high, Apollonian social position characterizing aristocrats but also to the land and more generally the property they own, property being the basis of aristocracy. Looking at the etymology of property we see that it stems from the Latin translation of the Greek idiòtēs, meaning “peculiar nature, specific character.” An aristocrat, then, is essentially an eccentric, a man with qualities. In a word, he believes himself to be a unqiue quantum. Which is to say, he believes in quantum theory, in plurality, in the principle of relativity, hence he can believe in hierarchy. Moreover, he believes in prophecy, which word — apparently cognate with property — comes to us from the Greek prophēteíā, meaning not the ability to predict essentially random future events but rather the gift of interpreting the will of the gods, i.e. the gift of understanding destiny. Here we have the meaning of the adage, “Character is destiny.”
According to the Golden/Legal philosophy, property as well as the cosmos it can at best be thought to signify is ultimately providential and hierarchical. Importantly, however, this philosophy does not believe property can really be possessed, for the only thing that can be possessed is one's quantum self — and even that possession is crucifed for better and worse on an infinity of other selves. Property, according to this philosophy, is rather akin to physics: it is secondary, derivative; nevertheless in its purest form — namely art — it is significant of reality.
All this goes to say that every circumstance is naturally an opportunity. This is the meaning of the word optimism. And this is the most important meaning of the myth of the Golden Age. Optimism focuses neither on the future nor on the other; it focuses on the present and the self, albeit with the aid of and interest in all time, all others. Optimism is the recognition that one is vested in everything yet eternally in possession of only one’s self.
Now, if Leibniz had considered plenitude in this more general, prehistoric, magico-providential sense — i.e. in this fully optimistic sense — maybe he would have considered the non-vanishing differences (or, you might say, nothingnesses) between monads, i.e. extrinsic to any single monad, as having corollaries intrinsic to a monad and thus being pseudo-divisive and pseudo-integral to that monad. Those corollaries seem to correspond to Leibniz’s idea of the physical as being secondary though not illusory. The physical is perhaps best considered the structure of any single monad (i.e. observer). A monad whose structure (physics) is quantum in a way which reflects the plurality of monads is perhaps better considered not a monad but a pleiad. Such soul/observer could thus find a virtual confirmation of its belief that it is not alone. Which is to say, such physics would be an extreme solace and likewise a perfect expression of the principle of relativity.
Fairly calling the difference between such souls curvature, we can recognize here the basis of Gauss’s Theorema Egregium, each soul being a sort of quantum geometry embedded in a quantum geometry. As the experts on Einstein’s general theory of relativity know, the structure of that theory corresponds quite perfectly to Theorema Egregium. At once window and light, the holographic structure which I suggest is native to the soul/observer/pleiad would subsume all the primary entities of orthodox physical theory: “radiation,” “particles having rest mass,” and “space.”
Physics as such would be a sort of picture or, better, symbol of real, plural plenitude. What’s more, this physics would correspond to the magical admittance of real action-despite-separation and would therefore be a sort of symbol thereof. Furthermore, this physics would be in contrast but not opposition to mind; it would literally be commensurate with mind. Such structure would not be a creation of mind, not merely mathematical; it would, rather, be concomitant with mind (i.e. with the plenum); it would be the structure of experience, of existence, the absolute and discrete (rather than continuous) rock bottom of physics; and as such it would be precisely heuristic signifying the extreme mysteriousness of existence.
Leibniz was the greatest mystic of all time, but he was not mystic enough. He developed his philosophy largely and perhaps chiefly to counter the monism of Spinoza and of Newton. “Spinoza’s teaching,” concludes Matthew Stewart in his notable Courier and the Heretic, “is that there is no unfathomable mystery in the world.” Of this trinity, perhaps only Spinoza fully extended his own principles. Leibniz and Newton were holding back, if not disimulating in the highest degree.
Newton atomist, puritan, known for his prematurely white hair, a lifelong virgin postulated absolute space and absolute time as fundamental (mathematical) entities of physics and as “attributes” of God. He constructed his physics not according to the (holistic) organic analogy but merely according to mathematical description of observation. Such divorced mathematics could not be considered significant of God; at best (or worst) it could only be attributed to God. Likewise, and after the fashion of (White/Apollonian) Zoroastrianism and courtly love, Newton considered God a different kind of entity than are human minds/souls — this especially in contrast to Leibniz, who once asserted in a note to himself that “God is a certain substance, a person, a mind,” and much later formally and publicly called God the “monad of monads,” thus implying purposefully or otherwise that God did not create the other monads but is merely co-existant with them. Newton considered God chiefly in terms of apocalyptic prophecy. Nearly an expert regarding the Bible, Newton calculated that Jesus Christ the son of God would return in the year 2060. Nevertheless, Newton (heretically) concluded that God Himself is fundamentally singular rather than fundamentally a trinity. Newton’s essentially continuum physics corresponds precisely to this monism. God is the only substance. Human and other souls are not real, quantum particles, not true substances, rather they are merely aspects of the only such particle — God — and that particle must be a continuum. Newton was moreover the greatest alchemist of his day, a fact which further marks him a neo-Zoroastrian, a sort of Manichaean or Cathar. In his Psychology and Alchemy Carl Jung, who studied alchemy for decades, intimated the Zoroastrian thrust of alchemy:
For the alchemist the one primarily in need of redemption is not man, but the deity who is lost and sleeping in matter. Only as a secondary consideration does he hope that some benefit may accrue to himself from the transformed substance as the panacea, the medicina catholica, just as it may to the imperfect bodies, the base or "sick" metals, etc. His attention is not directed to his own salvation through God's grace, but to the liberation of God from the darkness of matter. By applying himself to this miraculous work he benefits from its salutary effect, but only incidentally. He may approach the work as one in need of salvation, but he knows that his salvation depends on the success of the work, on whether he can free the divine soul. To this end he needs meditation, fasting, and prayer; more, he needs the help of the Holy Ghost as his paredroz [ministering spirit]. Since it is not man but matter that must be redeemed, the spirit that manifests itself in the transformation is not the "Son of Man" but as Khunrath very properly puts it, the filius macrocosmi. Therefore, what comes out of the transformation is not Christ but an ineffable material being named the "stone," which displays the most paradoxical qualities apart from possessing corpus, anima, spiritus, and supernatural powers. One might be tempted to explain the symbolism of alchemical transformation as a parody of the Mass were it not pagan in origin and much older than the latter.
The substance that harbors the divine secret is everywhere, including the human body. It can be had for the asking and can be found anywhere, even in the most loathsome filth.
Virtually the same could be said of Spinozism. (Still, there’s fundamental room to interpret alchemy according to the anti-Spinozist belief in a plurality of substance/soul. Indeed, Leibniz himself was deeply and vigorously interested in alchemy.) Likewise another famous Swiss, Denis de Rougemont, writes in his classic Love and the Western World: “The condemnation of the flesh, which is now viewed by some as characteristically Christian, is in fact of Manichaean and ‘heretical’ origin. … Catharist dualism issues in an eschatological monism.” The ideal of unity with a lover anticipates the ideal of unity with God. Courtly love anticipates Spinoza and Newton and hence modernism, Musil’s Man without Qualities — and Erwin Schrödinger.
Newton lived by himself in a Cambridge house where all the furnishings were colored red. Schrödinger was a deuteroanomalous trichromat: his perception of the color red was much greater than normal, a condition occurring in about 2 percent of the human population. Among Schrödinger’s favorite stories was Poe’s Masque of the Red Death. And among his favorite paintings, Dürer’s Adoration of the Trinity, alias All-Saints. It’s as if Newton and Schrödinger were naturally wedded to the color, complexity and mysticism antithetical to their White/Apollonian idealism/monism, like children who are strangely attracted to the most mysterious, frightening character of a fairy tale.
Schrödinger worked chiefly on color theory from 1918 to 1920, at the University of Vienna. Through 1925 he continued to publish papers on the subject — becoming recognized as the world authority.
Schrödinger’s extreme interest in color theory is all too often explained-away as a philosophical indulgence. But Schrödinger following Einstein sought to base his physics on principle, i.e. on philosophy, namely on a principle of reality (if not relativity). It seems he expected that both atomic theory and Einstein’s general relativity could be understood as generalizations of color theory. In this respect, the following outtake from Moore’s excellent biography of Schrödinger (which outtake I’ve embellished with several of my comments, in brackets) is extremely interesting:
Erwin based his analysis of color vision on the three-color theory of Thomas Young (1806), surely the most prescient work in all of psychoanalysis, which was rediscovered, developed, and extended by Hermann Helmholtz in the latter part of the nineteenth century. The Young–Helmholtz theory is based on the hypothesis (since proven) that the normal (trichromat) human retina contains three types of receptors, each with a particular spectral response curve; these may be called red, green, and blue receptors on the basis of their response curves. Any spectral color (light) F or any mixture of such colors can be matched by a linear combination of the three basic colors, R, G, B, so that one can write F = x1R + x2G + x3B.
… The geometry of color space is not the ordinary Euclidean variety that we learn in high school. It is more general geometry, called affine geometry, of which the Euclidean variety is a special restricted case. Affine [cognate with the word affinity] geometry deals with those properties of figures which are unchanged when the original coordinates of the points, x, y, z, are transformed to new coordinates, x′, y′, z′, by a system of linear [my emphasis] equations [i.e. it deals with properties that are “invariant”] .
x′ = a11x + a12y + a13z
y′ = a21x + a22y + a23z
z′ = a31x + a32y + a33z
This set of linear equations with constant coefficients aik defines an affine transformation, which plays the role in affine geometry that the concept of congruence has in Euclidean geometry. A general affine transformation corresponds to a displacement (e.g., translation, rotation, reflection in a plane) plus a dilation, i.e., an expansion or contraction of space in three mutually perpendicular directions. A dilation transforms each line into a parallel line. The importance of affine geometry is greatly enhanced owing to the fact that [its] more general transformations become linear in the limit of very small displacements. Thus any geometry that deals with infinitesimal displacements, i.e., differential geometry, is necessarily affine. [Importantly, the reverse is not true: a geometry which is affine is not necessarily differential. Schrödinger comments: “The color space owes its existence as well as its affine structure to the equality relation [i.e. transformation within any single dimension] quite without reference to the vectorial or point space which serves for its elucidation.” Which is to say, the concept of transformation is a principle whereas the number and kind of dimensions to which this principle applies is merely conventional. This is Einstein’s expression of the relativity principle.]
In affine geometry, the basic elements are points A, B, C, etc. [i.e. coincidences], segments AB, BC, etc. [i.e. lengths], and the idea of intermediacy, e.g. of B in a segment ABC. In affine geometry, lengths of segments can be [meaningfully] compared only if they are collinear or lie on parallel lines. …
Schrödinger pointed out that the empirical data of elementary color theory are derived exclusively from sensations of equality between color samples, which are best compared by presenting two adjacent color areas to the observer. It is possible to match one of the qualities of hue, brightness, or saturation, when the other two are kept the same. When one of these qualities is altered continuously, the observer does not perceive a change until a certain minimal difference has been presented; this is called the threshold of distinction. All colors that are at the same threshold of distinction from a given color are said to be at the same distance from it. Thus the difference in stimulus required to reach the threshold of distinction defines a unit length along any vector in color space. By proceeding with stepwise matches it is thus possible to compare lengths along collinear vectors by the number of thresholds required to cover the distance in question.
Elementary color theory is not so simple as it may seem. There is an infinity of different spectral distributions of energy (or of reflectances or transmittances) which can match any given color in the visible range. Helmholtz was the first really to understand this fact. The visual system performs a formidable job of reductions of physical data before it presents a color sensation to the mind. …
Advanced color theory is concerned with questions such as how to measure a difference of brightness between two colors that have different hues ... Instead of trying to match two closely neighboring colors exactly, Helmholtz introduced [my emphasis] a “principle of greatest similarity” [i.e. he imposed a constraint, a condition]; all those colors that appear equally most similar to a given color are said to be at the same distance ds from it. He wrote ds because the colors are very close together and the finite distance is approximated by the differential. [Here we have the essence of ds as Einstein, and Newton before him, famously used it: vanishing, non-quantum difference. The differential stands in contrast to Leibniz’s quantum (i.e. discrete) difference dx — which dx corresponds to Leibniz’s monads. In a major contribution made recently, contemporary English physicist and cosmologist Julian Barbour, whose career is closely linked to Schrödinger’s, has shown that the concept of “greatest similarity” which Helmholtz felt obliged to impose upon affine geometry is inherent in (i.e. a property of) affine geometry in general; there is no need to impose it unless, that is, you want it (i.e. the property of similarity between any 2 lines in the geometry) to be essentially quantum.] The differential distance or line element is expressed as
ds2 = aik dxi dxk [aik = aki]
(The usual convention of summation over repeated subscripts is followed, with the sums from i, k = 1 to 3.) [The condition aik = aki is the aforementioned commutation postulate (i.e. law) of multiplication. The absence of this postulate which absence, I say, is corollary of the generally quantum essence of experience is the crux of Heisenberg’s matrix (a.k.a. “quantum”) mechanics.] In advanced color theory, therefore, a metric has been introduced, and the geometry is no longer affine, but Riemannian. It is interesting that this is the same kind of geometry used by Einstein in his general theory of relativity, although his space is four-dimensional (space–time) whereas the color space is three-dimensional. [The ds2 term is “generally,” i.e. in Riemannian geometry (which itself is clearly a mere subset of geometry), called the metric form and the aik term is called the metric tensor.]
The [meaningful] difference between any two colors X and Y can now be calculated as the integral of ds along the shortest path between them …, provided this integration can be carried out. The shortest path or geodesic, is the one that requires the least number of steps of greatest similarity …
On May 1, 1925, [Schrödinger] published another article on color in Die Naturwissenschaften, “On the Subjective Colors of the Stars and the Quality of Twilight Sensitivity.” …
At the very end of this paper he included a remark that must have made [his fellow Viennese] Mach turn over in his grave. “The remarkable difference of twilight colors for normal and anomalous trichromats … can, I believe, be explained by difference in the daylight system alone, while the rod color itself is ‘in reality’ the same for both and apparently for all types of eyes.”
You can see that it was largely by analogy with color theory that Schrödinger and likely Einstein as well considered the quantum of action a mere phenomenon, an illusion of sorts, whereas they considered the essence of experience and implicitly reality itself a continuum. This notion of experience as being a continuum is an extreme which meets the ostensibly opposite notion: reality as an extreme plurality (i.e. of totally, radically separate, self-contained, self-sufficient quanta). According to the Golden/Legal philosophy, on the other hand, reality is best considered an extreme plurality-in-unity, an extreme and paradoxical multeity-in-unity. As Leibniz pointed out, the (clearly White/Apollonian) notion of a set of totally separate quanta is philosophically meaningless; the members of any meaningful plurality must be fundamentally unique yet fundamentally related and extremely so. Leibniz invoked his principle of pre-established harmony to bind his otherwise totally separate quanta together.
In the present light consider paragraph 739 in part 5 of (Red/Dionysian) Goethe’s Farbenlehre (Theory of Colors):
True observers of nature, however they may differ in opinion in other respects, will agree that all which presents itself as appearance, all that we meet as phenomenon, must either indicate an original division which is capable of union, or an original unity which admits of division, and that the phenomenon will present itself accordingly. To divide the united, to unite the divided, is the life of nature; this is the eternal systole and diastole, the eternal collapsion and expansion, the inspiration and expiration of the world in which we live and move.
Thus Goethe, too, expressed the principle of relativity via color theory.
Surely Bohr and Heisenberg and company understood Leibniz’s and Goethe’s indefatigable position regarding the conservation of plurality. But why did they assert that the quantum of action must be considered at once eternally fundamental and singular, a sort of unity? Doesn’t the correspondence between Leibniz’s dx and his set of monads couple to a self-evident analogy between dx and the quantum of action such that Bohr and Heisenberg would expect the quantum of action to be in truth a set of quanta of action akin to the set of monads? The answer involves measurement (or control) theory. Supposedly, measurement of an atom and indeed measurement in general is determinable (controllable) using essentially thermodynamical, classical abstractions. In other words, measurement — control, communication — is defined in classical, abstract terms; it is itself a classical, abstract concept, a White/Apollonian concept. These abstractions (in the literal meaning of the word: “out-takes”) and the mathematics they are coupled to leave room for but a single “quantum” of action. (Again, I use the scare-quotes to indicate that the quantum of action is in truth a function and is thus a potential symbol of a multeity-in-unity.) Likewise said abstractions do not signify some underlying — or outlying — merely postulated reality but are instead referential to (one’s) experience only. It is a principle of Bohr and Heisenberg and company’s Copenhagen Interpretation of quantum theory that physics, as it were, is complete in terms merely of measurement (control); i.e. physics is neither a model of nor some conception regarding reality nor is it even symbolic of some principle of reality, for physical principles concern what is ostensibly controllable not what is uncontrollable — and reality itself is uncontrollable, utterly mysterious, incomprehensible.
This is not to say, however, that the entire set of possible measurements cannot be consistent with a principle of (real) relativity. And it is not to say that perhaps only such principle along with a corollary symbol thereof considered an intrinsic metric is the only principle which is so consistent. Besides, it is theory, as Einstein said, that first determines what can be observed (i.e. controlled, measured). Perhaps a new theory will provide a new basis for measurement. But even if no such basis is discovered a theory could be discovered whose variables are, according to that very theory, unmeasureable (i.e. unobservable, uncontrollable) yet which theory is at once as successful as the presently orthodox quantum theoretical formalisms at accounting for atomic phenomena and is derived from a more profound principle or set of principles. Such theory would be more elegant — more beautiful, i.e. more simple if perhaps just as general — and would therefore be superior despite its “hidden variables.” In this precise sense, it is possible that a so-called hidden variables theory can be superior to orthodox quantum theory, which orthodox theory pointedly does not involve hidden variables. What’s more, if such new theory were to stem from a principle of relativity — ideally, I say, only from a principle of relativity — it would naturally subsume Einstein’s general theory of relativity and thus be superior in this general sense as well. Such theory would literally point to (i.e. signify, symbolize) not the naïve, classical notions and corollaries of control; rather it would point in the other direction, in the deeper direction, the direction of soul, of substance, toward that which cannot be controlled. In a word, such theory would point in the direction of the gods.
Despite the continuing success of the Copenhagen Interpretation, there remains the possibility that we can start from a principle of relativity, symbolize that principle mathematically and thus determine physics from below, as it were. Nobody understands this fact better than does Julian Barbour. During the last decade or so, Barbour has been joined in this deepest respect by American physicist Lee Smolin, author of the popular Life of the Cosmos and Three Roads to Quantum Gravity. Here's Barbour from his own End of Time:
[Lee] proved very receptive to the ideas of Leibniz and Mach to which I introduced him, while he encouraged me to see what application they might have to the problem to which he had decided to devote himself quantum gravity. We met several times in the next few years, and collaborated on an attempt to formulate Leibniz’s philosophical system, his ‘monadology’, in mathematical form. I think we made some real progress. … As far as I am aware, Leibnizian ideas offer the only genuine alternative to Cartesian–Newtonian materialism which is capable of expression in mathematical form. What especially attracts me to them is the importance, indeed primary status, given to structure and distinguishing attributes, and the insistence that the world does not consist of infinitely many essentially identical things atoms moving in space but is in reality a collection of infinitely many things, each constructed [if you will] according to a common principle yet all different from one another. Space and time emerge from the way in which these ultimate entities mirror each other. I feel sure that this idea has the potential to turn physics inside out to make the interestingly structured appear probable rather than improbable.
To use Einstein’s terminology, a bottom-up formulation would be complete precisely insofar as it conserves the notion that there is an essentially comprehensible (if infinitely, not irreducibly complex) reality, where the word reality means something independent of control, independent of measurement, i.e. a substance (if perhaps the only substance). In a letter to M. Laserna dated 8 January 1955 Einstein commented in this extremely important respect:
It is basic for physics that one assumes a real world existing independently from any act of perception. But this we do not know. We take it only as a programme in our scientific endeavors. This programme is, of course, prescientific and our ordinary language is already based on it.
Einstein’s use of the word act here implies the classical physical parameter action and therefore the very closely related notions of control, free will, plurality, Mach’s principle, the uncertainty principle, and the Copenhagen Interpretation. In the context of quantum theory an “act of perception” is more a measurement (i.e. an act of control, an abstraction dependent on classical physical theory) than a mere perception. I like to say we can control only what we cannot understand and we can understand only what we cannot control. This, I think, is physicist John Bell’s distinction between “observable” (i.e. controllable) and “beable.” The distinction is akin if not identical to Kant’s distinction between a thing and a thing-in-itself: a distinction, I say, between order and structure. All such distinctions adumbrate a fundamental difference between information and reality, where information is determined according to the “principle of separation” — no action-at-a-distance, or, more poignantly, no action whatsoever — sacred to Einstein. “Action,” I assert, means the uncontrollable, indescribable co-influence existing between otherwise separate substances (quanta, souls).
Schrödinger seems to have discounted the extremely important role color theory played in his formulation of atomic theory. His dissimulation in this respect can largely be understood insofar as his focus during the early 1920s shifted to the study of ideal gases. This field was the prime legacy of the Red/Dionysian physicist Ludwig Boltzmann, who was also Viennese and was a prime scientific hero of Schrödinger’s. Boltzmann advocated the reality of physical atoms in and of themselves (and was an ardent supporter of Darwinism), this in contrast to the paradigm championed by that other Viennese and Schrödinger’s only other scientific hero: the White/Apollonian Ernst Mach. According to Mach, atoms are merely provisional, conceptual devices useful in treating of a more fundamental continuum of “energy.” Here’s Walter Moore on the deep contrast between Boltzmann and Mach:
In 1895, at a conference in Lübeck [Germany], an attempt was made to resolve these conflicting views of the fundamental structure of the world. The report in favor of energetics [i.e. Mach’s paradigm] was given by Georg Helm of Dresden; behind him stood Wilhelm Ostwald of Leipzig, the leader of physical chemistry, and behind both was ranged the powerful positivist philosophy of the absent Ernst Mach. The leading opponent of energetics was Boltzmann, seconded by the mathematician Felix Klein. Arnold Sommerfeld [who collaborated with Klein, mentored Heisenberg at Munich, and first recognized the need for a “fine structure constant”] reported that the struggle between Boltzmann and Ostwald equalled outwardly and inwardly ‘the struggle of the bull with the supple matador [or the dragon and St. George, the serpent and Adam]. But this time the bull conquered the matador despite all his finesse. The arguments of Boltzmann drove through. All the young mathematicians stood on his side.’
Boltzmann’s temperament would today be diagnosed as bipolar disorder. He himself attributed his remarkable mood swings to the fact that he was born during the night between Mardi Gras and Ash Wednesday. While on holiday at the Bay of Duino near Trieste, Italy, in 1906, and while his wife and daughter were swimming in the sea, Boltzmann hanged himself. Schrödinger was left broken hearted; he had expected to begin studying under this beloved master within a few months. …
Above all else, Boltzmann was the founding master of statistical mechanics and statistical thermodynamics — both of which are consistent with if perhaps not based on the atomic hypothesis. Building on Boltzmann’s work, Bose and Einstein in 1924 and 1925 achieved together a fundamental understanding of the statistics appropriate to the particular (in contrast to wave) essence of light (which aspect of light later came to be called the photon). Einstein recognized that this statistics must apply not only to light (i.e. to carriers of force in general), but also to emitters/reflectors/absorbers of light (protons, electrons, molecules, etc). Thus a way had opened toward the notion that force and the stuff it works on (“matter”) are fundamentally the same kind of thing i.e. that physics is light, that it is the description of force only. It was on this path within earshot, as it were, of Bose and Einstein that Louis de Broglie “all of a sudden” realized that he should postulate a fundamental particle–wave duality: photons, electrons, protons, atoms, molecules, chairs, universes, what have you they are all best described as essentially dual, at once particles and waves. Schrödinger was nearby on this same path and was more inclined than were his colleagues to think that the apparent need for this postulate a need stemming from Boltzmann’s consideration of statistics as being fundamental, i.e. of randomness as being fundamental to analysis (if not being an element of reality itself) was more importantly significant of a fundamental reconcilability between the quantum-biased Red/Dionysian paradigm (advocated by Boltzmann) and the continuum-biased White/Apollonian paradigm (advocated by Mach). Schrödinger got swept up in the excitement attaching to both the de Broglie postulate and the Machian continuum and thus sailed fully beyond the complex Red/Dionysian sea into open, White/Apollonian waters. Schrödinger went so far as to describe particles in general as merely a phenomenal sort of “whitecap” [Schaumkamm] atop a continuum reality best described as a wave/force only (in the naïve sense of, say, a water wave). To Schrödinger’s chagrin this tack failed (and famously so), lending further credence to the notion that the essence of all physical elements is fundamentally dual or otherwise irreducibly complex. Although de Broglie’s postulate that particles are waves and waves are particles remains a primary truth of quantum theory, so too does the distinction between particles and forces, this because the theory still harbors two kinds of elementary particles (not to mention the multiplicity of particles within each set kindred particles): those that go to constitute emitters/reflectors/absorbers (i.e. matter; these are called fermions) and those which go to constitute forces (which are called bosons).
In terms of said failure, Schrödinger nevertheless expressed very well a notion that neither he nor, to a markedly lesser degree, Einstein would abandon (chiefly lone wolves, they maintained a tenuous if not tentative collaboration with each other) and which in their professional circumstances they seemingly had no need to abandon: the notion that physics should be considered a Spinozistic, Machian address of a singular, essentially comprehensible yet unfathomable reality, one substance only, one entity only, namely identical to God whether nor not it be called a matter or a force. Such physics must therefore be based on continuum mathematics.
Continuum mathematics is equivalent to mathematics based on the set of whole numbers coupled to the concept of zero. Yet we can fairly say that the concept of zero is akin to a special frame of reference and inasmuch is contrary to Einstein’s expression of the principle of relativity. As Schrödinger writes in his masterfully concise Space–Time Structure, “Zero is the only number with a charter, a sort of royal privilege.” (This fact is commonly stated as the law prohibiting division by zero.) The chief assertion of a transformation equation, Schrödinger likewise emphasizes, is always this: a certain number is zero. Schrödinger here implies that the notion of a “transformation equation” indeed, the very notion of an equation in general must be fundamental to physics; equations must be the only way to determine (i.e. express) the notion of invariance at bottom of Einstein’s expression of the principle of relativity and therefore at bottom of Einstein’s general relativity. This assumption is what justifies the special status of the concept of zero and in turn the concept of infinite divisibility, i.e. the continuum. Indeed, the concept of zero is akin to Newton’s absolute space and absolute time.
But according to my understanding of the relativity principle, the notion of an equation is purely secondary. Symbolism is singularly primary. Physical invariance is a mere corollary of the supposed Black/Baroque reality, i.e. of multeity-in-unity, of the set of pleiads, and it should be determined via the single best symbol of that supposed reality. Consider in this respect the following from Arthur Fine’s reknowned Shaky Game:
I think the failure of [Einstein’s] space/time project did lead Einstein to take seriously the idea that the physics of the future may not be spatio-temporal at all.
In his review article of 1936, Einstein calls such a non space/time physics “purely algebraical” and, because the mathematical concepts for such a theory had yet to be invented, in 1936 he rejects the idea as “an attempt to breathe in empty space” (Einstein 1936, p. 319). Nearly twenty years later he is no more enthusiastic, and for exactly the same reason. “My opinion is that if the objective description through the field as an elementary concept is not possible, then one has to find a possibility to avoid the continuum (together with space and time) altogether. But I have not the slightest idea what kind of elementary concepts could be used in such a theory.” If we read these remarks in conjunction with his reply to Karl Menger in 1949 (“Adhering to the continuum originates with me not in a prejudice but arises out of the fact that I have been unable to think up anything organic to take its place.” [Schlipp 1949, p. 686]), then I think it clear that a non-spatio-temporal kind of realism (a “purely algebraical” realism) would be an acceptable alternative for Einstein to his own pet idea for a continuous field theory, even if one not so highly prized.
Paul Dirac, more strongly than Einstein, anticipated such utterly new, “purely algebraical” — i.e. quantum — physics. Among the laconic Dirac’s “pet ideas,” as his biographer Helge Kragh remarks, was the notion that the basis of mathematics in general is due for a change. Yet like Einstein, Dirac simply couldn’t conceive what this change should be. In 1979, a few years before his death, Dirac wrote regarding orthodox atomic theory: “I think it is very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct, even though for the time being physicists have to accept the Bohr probability interpretation, especially if they have examinations in front of them.” With respect to Schrödinger, Dirac in 1977 had written:
… of all the physicists that I met, I think Schrödinger was the one that I felt to be most closely similar to myself. I found myself getting into agreement with Schrödinger more rapidly than with anyone else. I believe the reason for this is that Schrödinger and I both had a very strong appreciation of mathematical beauty, and this appreciation of mathematical beauty dominates all our work. It was a sort of act of faith with us that any equations which describe fundamental laws of Nature must have great mathematical beauty in them. It was like a religion with us.
Yet Dirac was torn. In 1965, several years after Schrödinger’s death, Dirac had written: “All references to Schrödinger wave functions must be cut out as dead wood.” Dirac emphasized this assertion in his last lecture, delivered in the early 1980s. The professionals recognize this assertion as something of a mystery. Why, after all, did Dirac favor Heisenberg’s quantum-mechanical formulation of atomic theory over Schrödinger’s wave-mechanical formulation thereof? The answer certainly involves the Hamiltonian. As the outstanding physicist Eugene Wigner Dirac’s brother-in-law said in 1963: “Dirac was a captive and is now a captive of the Hamiltonian formalism and he thinks extremely strongly in terms of the Hamiltonian formalism.” The Hamiltonian is an exceedingly beautiful (i.e. simple yet general) formulation of the so-called action principle, the notion that classical physical action (e.g. position x momentum, or energy x time, or spin) is always an extremum (i.e. fundamentally describable as a minimum or maximum). The action principle comes down to us via Aristotle, Hero of Alexandria, Fermat, Leibniz, Maupertuis, Euler, Lagrange, Gauss, Hamilton, Jacobi, Dirichlet, Helmholtz, Planck, Dirac, and others. “In this development,” writes Ernst Cassirer in his Determinism and Indeterminism in Modern Physics, “the question of the metaphysical basis for the principle of least action [i.e. the action principle] was more and more lost from view.” As I pointed out earlier, action basically means interaction between quanta. The notion that the essence of nature is extreme action and the fact that the Heisenberg formalism is a codification of this notion in terms of non-commutativity, the so-called “quantum” of action (the very meat of quantum/matrix mechanics), and the Hamiltonian suggests that the Heisenberg formulation is destined to be reduced to a function of action (i.e. to the quantum of action unpacked, as it were, unfolded) and that this function is destined to be recognized as the ultimate physical mathematics and the ultimate formulation of the Hamiltonian, i.e. the ultimate formulation of the action principle. Such function and the interpretation(s) thereof — as being symbolic of an outlying, quantum reality, a set of souls — would be identical to physics in general. This function seems to be the irreducibly complex, middle road which Dirac intuited and inclined toward but never actually set foot upon.
Dirac appreciated the Hamiltonian as being not a constraint (i.e. secondary, forced upon something else more fundamental) but rather an essentially pure (i.e. self-referential) mathematics that happens to correspond to the classically controllable structure of experience. Similarly the Heisenberg formulation of atomic theory is a purely mathematical symbol which happens to correspond to what is controllable. The Schrödinger formulation, on the other hand, is not self-referential but symbolic of a supposed reality; it is pictorial, mimetic, a model, a metaphor precisely as any geometrical description of fundamental physicality (including Einstein’s general theory of relativity) is a metaphor implying that physical space is best described as being a geography of sorts. Therefore the Schrödinger formalism seems to place mathematical beauty second to naïve realist postulation, short-circuiting Dirac’s program. In this sense the Schrödinger approach damns the Hamiltonian to the status of a constraint upon superfluous metaphysical indulgence. To be sure, the Hamiltonian is also applied as a mere constraint to the Heisenberg formulation, in terms of the diagonal matrix. But because the Heisenberg formulation is merely a mathematical formalism and not as well a model, and because it directly corresponds to classical action, the way is at least open for this formulation to be simplified such that it becomes identical not only to the Hamiltonian but also to Dirac’s equation of the electron, i.e. to his inchoate equation of particles in general — including particles of space and time. Recognizing, again, that the quantum of action is in fact a function, we can therefore fairly say Dirac is suggesting or at least intuiting that both the Heisenberg formulation and the Hamiltonian are destined to be reduced via mathematical considerations which may involve Einsteinian realism and a principle of relativity to a function of action and that this function in and of itself will be physics.
Thus the mystery of the quantum of action — that is, the mystery of the very existence of atoms — could be reduced to the principle of relativity, i.e. to the mystery not only of one’s existence but also of the supposedly concomitant existence of an unlimited number of unique souls (absolute, radical others) which are nevertheless (extremely) related to each other. The existence of atoms in any single I’s experience would be explained in terms of the postulated existence of an unlimited number of other, related I’s. No mechanism could be invoked to explain this relatedness. According to the principle of relativity, we need not indeed cannot and should not explain this relatedness; rather we postulate this relatedness, this greatest of all possible mysteries, as our only principle.
In regard to the core of quantum theory, Bohr famously commented: “If a man does not feel dizzy when he first learns of the quantum of action, he has not understood a word.” Einstein mockingly called the action-at-a-distance (or non-locality, or “entanglement”) which is a prime (and general) corollary of that theory “spooky” and “telepathy” and he argued that there is no need to interpret the equivalent pair of quantum theoretical mathematical formalisms (Heisenberg’s quantum mechanics) and Schrödinger’s wave mechanics as complete (per the Copenhagen Interpretation) if, that is, we can interpret them otherwise and thus conserve the principle of separation, i.e. the principle of local causality, i.e. the principle that action requires a medium, i.e. the principle of action-by-contact, the notion that there is no action-at-a-distance. “I consider the renunciation of a spatio-temporal setting for real events to be idealistic-spiritualistic,” wrote Einstein to Schrödinger, derogatorily and in commiseration with Schrödinger. Yet it seems to be increasingly clear that the way forward involves recognizing the principle of relativity as precisely idealistic-spiritualistic. The noted dizziness and spookiness are heuristic. Henri Matisse said about art: “The only valid thing in art is the one thing that cannot be explained.” Ultimately, I think, the only valid thing in physics is the principle of relativity, understood as being identical to the principle of action and equivalent to the “quantum” action.
Thus the heroic path before us can be illumined such that we see it open onto the greatest possible mystery. Regarding that path, I’ll do well to note a few things about the boyish German genius Werner Heisenberg, Schrödinger’s most poignant counterpart. Heisenberg was something of a lifelong Boy Scout. In the Germany of Heisenberg’s youth the equivalent of the Boy Scouts was called the Neupfadfinder (New Path Finders). Consider the following from David Cassidy’s excellent biography of Heisenberg, Uncertainty:
For the Neupfadfinder [of which Heisenberg was a local leader], the coming third Reich was to be the culmination of centuries of German history, the final realization of the ideals of the first Reich, the Holy Roman Empire. Numerous petty princes and political parties would happily coexist within one apolitical empire, ruled by a single, trustworthy, God-appointed Führer. He would ensure the peace and well-being of the German people especially, of course, of the cultured upper middle class in the same way a [local] group Führer for his small Gemeinschaft [a group of about 10–15 people, typically men].
… As [Heisenberg’s Gemeinschaft] conceived it, the coming Third Reich bore a striking resemblance to the Christian concept of the coming kingdom of God …
The Holy Roman Empire was established over the course of some hundred years following the 843 CE Treaty of Verdun, which treaty split the Frankish kingdom of Charlemagne the so-called Carolingian Empire, covering much of modern-day France, Germany, Austria, Switzerland, and northern Italy into 3 parts to be shared by Charlemagne’s 3 surviving grandsons: Charles, Lothair and Louis.
The Investiture Controversy of the 10th and 11th centuries saw Pope Gregory VII assert the singular universality of the papal power. In turn he excommunicated and officially if not effectively deposed German King and Holy Roman Emperor Henry IV a move welcomed by the German aristocracy (which felt that the king had been too autocratic, too White/Apollonian you might say) and nearly fatal to the empire. Although severely and permanently weakened, the Holy Roman Empire largely recovered following Henry’s invasion of Rome; for the pope reacted to that invasion by calling in Norman allies from their presence in southern Italy, and although they saved the pope they also sacked Rome, provoking the Roman citizens to rise against the pope and force him and the Normans south, where the pope soon died. The Holy Roman Empire was not officially dissolved until 6 August 1806, when Francis II abdicated following military defeat by Napolean. Francis and his heirs nevertheless continued their political career as emperors of Austria, until 1918.
But let’s get back to Charlemagne’s roots. As you may have discerned, Charlemagne stems from the Merovingian dynasty. The Merovingian dynasty is named after its founder Merowig (c. 450 CE). Legend says Merowig was truly, fully conceived when the already pregnant wife of his ostensible father Clodio the “Long-haired” or “Hairy,” equivalent to Claudius, “lame,” as in Hamlet’s “evil,” Set-like uncle encountered one of Poseidon’s sea monsters, a shape-shifting so-called Quinotaur, while she swam in the North Sea. The monster ravished her and thus added his seed to the mix. Thus Merowig was a duality, a son of 2 fathers. This story — with its poignant love triangle — resonates with those involving Zeus/Poseidon and Europa and Asterius (“Star Man”); Cetus and Andromeda and Perseus; the sea monster and Hesione and Hercules; the dragon and the princess and George (or Tristan or Sigurd …), the snake and Eve and Adam, Jesus and Mary and Joseph, and the legend of Merlin’s conception. The irreducibly complex offspring of such encounter, in this case Merowig, is equivalent to the hero who slays the monster/father/king to secure the lover/mother just as Cronus emasculates Uranos at the behest of Gaia (or Chthon) and thus creates the universe, Aphrodite emerging from those severed, sea-borne genitals, which genitals are equivalent to her husband/son Hephaistos (alias Mark, counterpart and in this sense equivalent to Tristan/Mars). Likewise said offspring is equivalent to the monster/father and the lover/mother, which implies that the lover/mother, too, is equivalent to the monster/father.
The hero/girl meeting the monster is the hero/girl not only equated to but also identified with the monster and with each other. If there is a single key that unlocks all mythology and likewise all psychology and sociology, these seemingly pedestrian identifications amount to it.
As for the particular identity of the Merovingian monster, the term Quinotaur is extremely mysterious. The prefix Quino- signifies 5-ness, 100-ness, dogishness/wolfishness (as in the Greek word kynós), smallness (as in the diminutizing suffixes -kin and -chen), change (as in kindle and kinetic and the Cynaen Rocks, alias the Planctae, this as in the planasthai, “wanderers,” i.e. the planets), blueness (as in the Greek word kýanos, “dark blue enamel, lapis lazuli,” and as in cyanide and also the blueish Pleiades), kinship/kingliness (from the Proto-Germanic *kunjá, “family, race,” and *kuningaz, “one descended from noble birth,” these being cognate with the Latin genus and the Sanskrit jánas, “kin,” as in Janus), and cynosure, which word means “center of attraction or attention” and formerly also meant “guiding star.” This last word stems from the Latin Cynosūra, “Ursa Minor,” from the Greek kynósura, “dog’s tail.” Ursa Minor with its guiding star Polaris is, I suggest, the adze of the famous Egyptian Opening of the Mouth ceremony (and likewise of the ceremonial cutting of the umbilical cord), and in this sense it represents Anubis and Upuat (“Opener of the Way”) and Fenrir and Hermes and Homer’s “wiley” i.e. viley, vixeny, foxey Ulyssses, as well as Finn of Irish lore and likewise Tom Sawyer and Huck Finn of American lore. The Chambers Etymological Dictionary states: “[Fox] is cognate with … Gothic faúhō. Outside the Germanic languages fox is cognate with Lithuanian paustìs, animal hair, the Russian and Polish puch woolly hair, tuft, fluff, and Sanskrit púccha-s tail … from Indo-European *puk-/pouk- (Pok.849).” Huck Finn, you see, is Tom Sawyer is Faustus is Puck, the latter from the Old Norse pūki, “devil.” Finn is Vin is Dionysus. The Pleiades alias the Kometes, “Long-haired,” as in comets, and as in the Merovingians correspond to this Little Dipper. In fact the Pleiades themselves — which are typically considered feminine — are constellated in the form of a dipper or adze. Proto-mythology, doggishness, wolfishness, foxeyness, the absent/tiny/fallen father and the totemic animal in general are likewise considered feminine.
Indeed, the number 5 is the number of Aprhodite/Venus and likewise the number symbolizing sacred, priestly knowledge. The number 100, on the other hand, is associated with the ascendant challenger, the White knight and his cohort or fellow centurians. We should be especially reminded here of the wise and learned centaur Chiron “The Hand,” as in the 5-ness of the hand and as in Roman emperor Constantine’s 5-pointed ChiRho symbol. Constantine considered the ChiRho symbolic of Christ and of the Sun. (Moreover, he thought that Christ like Ares/Mars and like Odin/Woden can determine victors in battle.) Chiron, who lives in a cave on Mount Pelion, is tutor to Diomedes, whom he renames Jason, “Healer.” Chiron is also tutor to Jason’s son by the sorceress Medea, Medeius, eventual ruler of the Medes; and to Hippolytus (the Latin Virbius), son of Theseus and Hippolyta, queen of the Amazons; and to the sea-god Achilles. The hand is closely related to the Latin carpo, “to pluck, seize, lay hand(s) on,” and to the Greek karpos, “fruit.” Of course the infamous scene in the Garden of Eden comes to mind, but so too does the story that Jesus's father was a carpenter. Chiron’s father is Centaurus (alias Quinotaurus?), son of Ixion, son of Ares/Mars. Here, then, we see a striking equivalency between Ares/Mars/Odin/Hermes, Ixion, Centaurus, Chiron, Jason, Medeius, Hippolytus (Virbius), Achilles, Jesus and Merowig. Let’s follow this lead.
Thinking he is ravishing Hera, Chiron’s grandfather Ixion ravishes Nephele (note the Ne- prefix), whom Zeus supposedly created as a phantasmal Hera look-alike. Nephele then gives birth to all the centaurs each being half horse or bull (or more generally a totem animal of any sort) and half man. The centaurs worship Dionysus. For the attempted rape of Hera, Zeus binds Ixion to a rolling wheel and damns him to Tarturus and the close company there of Sisyphus and Tantalus. Tantalus is father of Pelops, whom we will meet shortly. In all these connections we should furthermore be reminded of the centaur Nessus, who rapes Hercules’ 2nd wife Deianira and then effectively curses him to death at the hands of Deianira although Zeus plucks Hercules from near death atop the funeral pyre and transports him to Olympus, as Zeus did with Pelops and as Zeus eventually does with the Trojans Ganymede/Aquarius and Aeneas. Now, Neptune/Poseidon who built Troy’s famed walls was symbolized by the (gregarious, periodic) horse, as was Nephele/Hera. So, too, probably, was Hippolyta, the root hippo meaning “horse” and, as I will later explain, being identifiable with the name Poseidon and likewise with the Egyptian Hp/Hapi (the Greek Apis), a bull-god equivalent to the human-like god of the Nile, who goes by the same name but is pictured an androgynous old man with pendulous breasts. Here we again have the Op/Ep/Ap prefix, this in a form which is more clearly equivalent to the Hep- of Hephaistos. The actual bull representative of Hp was selected for being black yet bearing a white, crescent-like mark on its neck. Let me add that Odysseus/Ulysses in the wooden horse/bull is akin to the Quinotaur: he proto-mythologically impregnates Troy/Aphrodite, dying in the process (hence to “live” with Kalypso and eventually by way of return/resurrection to Penelope, i.e. Penel-Ops). The fleeing Aeneas legendary father of the Romans is the offspring of that meeting/sacrifice; he is equivalent to Poseidon, equivalent to Odysseus, equivalent to Jesus, equivalent to Merowig.
The black and white bull representative of Egypt’s Hp brings us back to the story of Europa, daughter of King Agenor of Tyre, Canaan. Son of Poseidon and Lybia and (younger) twin brother of Belus (i.e. Bel, the fire god; alias Hephaistos, Set) Agenor had proto-mythologically left his homeland of Egypt to settle in Canaan, where he married Telephassa/Argiope (“Distant White Light of Power”; i.e. Iseult; i.e. Gatsby’s green light across the bay, the light of the dock of Daisy’s “red-and-white” mansion). Robert Graves, from his Greek Myths:
Zeus, falling in love with Europe, sent Hermes to drive Agenor’s cattle down to the seashore at Tyre, where she and her companions used to walk. He himself joined the herd, disguised as a snow-white bull with great dewlaps and small, gem-like horns, between which ran a single black streak. Europe was struck by his beauty and, on finding him gentle as a lamb, mastered her fear and began to play with him, putting flowers in his mouth and hanging garlands from his horns; in the end, she climbed upon his shoulders, and let him amble down with her to the edge of the sea. Suddenly he swam away, while she looked back in terror at the receding shore; one of her hands clung to his right horn, the other still held a flower-basket.
Wading ashore near Cretan Gortyna, Zeus became an eagle and ravished Europe in a willow-thicket beside a spring; or, some say, under an evergreen plane-tree [with its 5-pointed leaves, the plane-tree was sacred to Helen/Aphrodite]. She bore him three sons: Minos, Rhadamanthys, and Sarpedon.
Agenor sent his  sons in search of their sister, forbidding them to return without her.
According to proto-mythology, the hero must venture from his original land/tribe to another and there find a woman he desires. There he must win her love, marry her, and remain with her people to ascend to their kingship and to eventually sacrifice himself at the behest, chiefly, of his wife. Zeus’s contrary abduction of Europa signifies the reversal of this custom; and especially it signifies the Great Reversal. The flowers with which Europa garlands him are the flowers typically lavished upon a bull before it is sacrificed; they are akin to the palms of Palm Sunday, the leis of Hawaii, the beads of Mardi Gras.
As we will later see, Agenor and Telephassa/Argiope correspond to Evenor and Leucippa, the original Atlanteans, whose daughter Clito corresponds to Europa. Clito’s 5 sets of twin sons by Poseidon (initial among them Atlas and Gadirus) correspond to Europa’s 5 brothers (including Cadmus and Phoenix).
Meroweg, like Poseidon/Hp/Hapi/Apis/Hephaistos and like Agenor and like Odysseus-in-the-horse and like Aeneas, signifies proto-mythology. The name Merowig smacks of earwig and Earwicker and the Welsh Evrawg, son of Bron and father of Peredur/Percival Evrawg’s 7th son, as in the 7 planets, and as in Hephaistos, i.e. Hp. Similarly the name Agenor smacks of Plato’s original Atlantean Evenor, husband of Leucippe (“White Horse”). The prefix Ear-/Evra-/Eve-/Eur- is closely linked to the Latin aevum, “lifetime.” Furthermore Meroweg smacks of Mercury, the shape-shifting Latin equivalent of Hermes, Odin, Odysseus and the closest planet to the Sun, never straying from her by more than 28 degrees of arc (which number 28 represents the college of Aphrodite’s nymphs, alias the Pleiades). The prefix mer — as in Mark and Mars and Mary — means “sea” and “(female) horse” and “daughter, woman” and “short” (the English merry, “pleasant,” stems from the P-I-E root mreĝhu-, “short”) and “memory, mindfulness” and “merchant, trader” and “martyr” and “boundary, sign” (as in marsh, moor, mark, Hermes and Janus). Meanwhile wig means “change, path, life, enliven,” stemming from the P-I-E *weik/wik, “set apart, strive against a foe,” and *wig, “bend, turn,” these being the basis, too, of the modern English weed and weak and the 7-day, 7-planet week again, the planets in Greek being literally the planasthai, “wanderers.”
Regarding the Merowig/earwig connection, it’s interesting to note that so-called wizards, as Robert Graves points out, commonly claimed that their ears had been licked clean by serpents, “which were held to be incarnate spirits of oracular heroes and … [wizards] were thus able to understand the language of birds and insects.” Athena, it is said, after blinding Teiresias, was emotionally moved by his suffering and therefore detached from her aegis originally a bag akin to Ouranos’s severed genitalia, i.e. akin to an ark the serpent Erichthonios and ordered it to, “Cleanse Teiresias’s ears with your tongue that he may understand the language of prophetic birds.” Erichthonios is EriChthonios, “heather of Gaia.” The bees on the heather are the serpents in the ear are (Red/Dionysian) AphroditeHephaistos in the sea-borne genitals/ark. Erichthonios is the snake/fish-tailed son of Hephaistos and Gaia, equivalent to his father and to Kronos/Cronus/Saturn and to the charioteers Poseidon and Auriga and Pelops, as well as Ganymede/Aquarius, Aeneas, Mercury, and Merowig. Precisely 300 golden bees were found in the tomb of Merowig’s son Childeric I. Napolean selected these bees to replace the Bourbon fleur-de-lys as symbol of his French Empire.
Erichthonios was abandoned by Gaia and found by (relatively White/Apollonian) Athena, who reared him under/in her own aegis, literally. In time he became the initial king of Athens and, what’s more, had a namesake/equivalent involved in the Trojan line of royalty, that line being as follows: Dardanos (a Latin; most beloved mortal son of Zeus, by the missing, i.e. 7th, Pleiad Electra, daughter of Atlas), Erichthonios, Tros (after whom Troy is named), Illus, Laomedon, and Ganymede. Because Dardonos’s father is Atlas, 1st son of Clito and Poseidon, the Trojan royal line is directly connected to the royal line of Atlantis. … Likewise we have the Hebrew mother (Gaia), Moses (Erichthonios), and the Egyptian princess (Athena). In a mythological sense, therefore, Merowig is Moses. Similarly Merowig is Noah in the ark/aegis is the ill infant Ali-the-son-Husayn left lying in the tent in Karbala: i.e. a representative of pre-Flood civilization, a representative of the ancestors, a representative of Atlantis. In fact the Merovingians did claim direct descent from both the Trojan royal line and from Noah. The main, proto-mythological legend about the founding of Troy says this city-state was established by the 1/3 of Crete’s population who fled that island nation under pressure of famine, led by Prince Scamander. Recall, Zeus/Poseidon had “abducted” Europa from Canaan to Crete, where she married the local ruler Asterius (“Starman”), who adopted her 3 sons by Zeus/Poseidon: Rhadamanthys, Sarpedon, and Minos (who became the cuckolded step-father of the Minotaur and hence commissioner and resident of Daedalus’s labyrinth).
Thus we have a strong connection running from Atlantis (i.e. the Golden Age) to Egypt (ancestral home of Europa’s father Agenor, Egypt was originally named Kehmet, the “Black,” in contrast to Deshret, the “Red” desert) to Canaan (alias Phoenicia, the “Red Land”) to Crete to (Red) Troy to (Red) Italy to the (Red) Merovingians to (Red) Charlemagne.
Merowig’s grandson King Clovis I alias alias Clodowech (as in Clito?) or Chlodwig, the modern French “Louis” and the modern German “Ludwig,” as in Loki and Lucifer and Leucippe is considered the initial French king. He died in 511 and his 4 sons divided the kingdom among themselves. The eldest, Theuderic I, rightfully claimed the better part of the kingdom. With its capital at Reims, this relatively Red/Dionysian north and eastern realm was called Austrasia. The remaining, relatively White/Apollonian realm with Orléans, Paris, and Soissons as its prime urbanities was split between the other brothers and generally named Neustria. Soon, intermittent yet protracted conflict emerged between this pair of kingdoms, weakening the (White/Apollonian) royalty in relation to the (Red/Dionysian) aristocracy. The climax came in 613 when old Queen Brunhilda of Austrasia proclaimed as king one of her great-grandsons and thus motivated her aristocracy to revolt against her. They allied themselves with her Neustrian nephew King Clotaire II and eventually delivered her to him. Clotaire had her tortured on the rack for 3 days and then, the chief legend goes, torn apart by 4 horses.
Brunhilda’s life became imbued with that of the mythical Brynhild a virginal, Athena-like female warrior (“shieldmaiden”) and moreover a Valkyrie, the latter especially being goddesses and “servants” of Odin and thus formed a basis of the Tristan and Iseult story, Wagner’s Brunhilde, and Tolkein’s Lord of the Rings. Brynhild, the myth says, was obliged to decide a conflict between a pair of kings. Although Odin preferred the elder king, Brynhild decided for the younger. Therefore Odin condemned her to mortality What’s more, to a coma behind a ring of fire impenetrable to all but the greatest man, who alone could wake her and marry her. That man turned out to be Sigurd, whose magical sword his father’s, a gift from Odin was named Gram (note the Gr- prefix). Sigurd was foster son of Regin — note the Re- root and the curious similarity to the aforementioned P-I-E mreĝhu-, “short” — who was smith (as in Hephaistos) of the Danish court. Regin had reforged and improved the previously broken Gram, armed Sigurd with it, and sent the young hero to recover the famed hoard of gold including especially the magical, gold-making ring Andvarinaut kept greedily by the smith’s own brother Fafnir, who had become an increasingly horrible dragon out of his cursed love for the gold and the ring at bottom of it. Originally the ring belonged to the dwarf Andvari, who — á la la Hephaistos — lived as a fish in an underground lake. The ring had entered human affairs by way of Loki, who had journeyed down to Andvari and threatened him such that Andvari surrendered the ring to him. But in so relenting, Andvari laid a curse on the ring: that it bring destruction to all who think they possess it.
As Sophocles said, “Nothing that is vast enters into the life of mortals without a curse.” And as Henry Miller wrote in Tropic of Capricorn:
Everything that happens, when it has significance, is in the nature of a contradiction. Until the one for whom this is written came along I imagined that somewhere outside, in life, as they say, lay the solution to all things. I thought when I came upon her, that I was seizing hold of life, seizing hold of something which I could bite into. Instead I lost hold of life completely. I reached out for something to attach myself to — and found nothing. But in reaching out, in the effort to grasp, to attach myself, left high and dry as I was, I nevertheless found something I had not looked for — myself. I found that what I had desired all my life was not to live — if what others are doing is called living — but to express myself. I realized that I had never the least interest in living, but only in this which I am doing now, something which is parallel to life, of it at the same time, and beyond it.
Similarly, F. Scott Fitzgerald wrote in The Crack-Up: “[T]he test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function. One should, for example, be able to see that things are hopeless and yet be determined to make them otherwise.”
The Andvarinaut and its curse resonate with the curse placed by Odin upon and around Brynhild. They also resonate with the curse placed by the mythical Greek figure Myrtilus who is etymologically linked to the Myrmidon sea-god Achilles, myrtle meaning “ever green” upon the house of Pelops and hence on Agamemnon and Menelaos. Myrtilus is a son of (Odin-like) Hermes as Ixion is a son of (Odin-like) Ares/Mars (rival/counterpart of Hephaistos), and as Remus and Romulus are twin sons of Mars by the Vestal priestess (i.e. Pleiad) Rhea Silvia, a descendant of Troy’s Aeneas. Like Hephaistos and Poseidon, Myrtilus is a charioteer. And like his rival and successor Pelops, he is a lover of Hippodameia. Myrtilus was likely considered crowned with green oak leaves, like Pelops’ grandfather Tmolus. The crown, like a ring, represents a profound curse, for it signifies its wearer’s identity as Tree Man, sacrificial man, and is likewise akin to the garlands placed by Europa on Zeus, the palms of Palm Sunday, the leis of Hawaii, the beads of Mardi Gras. The title Myrmidon is said to mean “ant person”: this as in Andvari and Ger-anos, Cr-onus, Ur-anus; and as in the Latin prefix ante-, “before”; and the Greek antí, “against, instead”; and the Proto-Germanic *ai, “off,” present in Aides/Hades, i.e. the missing father, literally the “goat-deity,” the scapegoat; and giant, i.e. Gaia-Ant; and the Greek ánthos, “flower,” from the Indo-European *ándhos, “bloom,” as in the name Antony and the title Adonis, both of which mean, among other things, “Lord,” and as in the aforementioned Erichthonios, “heather of Gaia.” Similarly we have the modern German Anderen, “others.”
The ant people are the before people, the contrasting people, the people from before the Flood, from before the Great Reversal. They are people who in myth are typically represented as fish/snake/short-people, like Andvari and like lame Noah and bow-legged, red-haired Odysseus and Erichthonios and Hephaistos and Enkidu and fairies and trolls, and like the 7 sage fish-men master craftsmen who, before the Flood, founded Gilgamesh’s Uruk and built its great walls (just as Poseidon built the walls of Troy). The suffix -vari in Andvari is cognate with the Latin varus, “bow-legged, bent,” with the Old Icelandic ver, “fishing place,” and verja, “to defend,” with the Albanian varr, “grave,” with the Tocharian B warto, “garden, forest,” and with the P-I-E wer/war, “to cover, close up, protect.” Contemporary English cognates include veer, variety, weir, weird, warm, thermal, terminus (i.e. boundary, as in herm and Hermes), and war. Generally the ant people are the ancestors. They are especially the ancestors from before the present Platonic (or Great) Age/Year, i.e. from before the last Zodiacal age of Leo (c. 10,800 BCE), which as I will soon explain is just beyond the celestial Pillars of Hercules. These ant people are the people of memory and of dream. They are Gaia’s people of the flowering heath, among whom are the Neanderthals. Even more generally however, the ant people are the others — i.e. others in general, the infinite mystical contrary kin of the “I.”
The craving for the ring is a sort of ironic deathwish, a Thanatos, to use Freud’s term. For the curse is not just the desire to possess or save the other, it is the desire to be the other and in turn all others and to thus be God, an extremely simple, reducibly complex, merely White/Apollonian God. This is the God of Spinoza and, I think, of Newton and Schrödinger and, to a considerably lesser degree, of Einstein.
The Norse fertility goddess Freya’s craving for the mysterious Brisingamen comes to mind. Note the Bri-/Bry- prefix. The Brisingamen was a golden necklace owned by the likewise mysterious Brisings or Bristlings, perhaps as in the aforenoted bristle/Pleiades connection and perhaps as in Achilles’ most notable lover, Briseis. The nymph Freya procured the necklace by having intercourse successively with its 4 dwarf makers (which number may place Freya especially in the age of Aries, 5th in the Zodiacal cycle), a promiscuity that disgusted her partner Odin she, a proto-mythological Valkyrie, being to Odin as Aphrodite is to Hephaistos as Penelope is to Odysseus/Ulysses as Helen is to Menelaos as Daisy is to Gatsby. She is likewise the love potion levied by Iseult’s sorceress mother upon Iseult and Tristan. And she is the underwater herb of immortality which Gilgamesh in reaction to the death of his hairy (indeed red-haired) rival/friend Enkidu sought and briefly possessed until a serpent rose from a well and snatched it away, returning to the depths.
Freya’s intercourse with the dwarves implies their self-sacrifice for her, and it likewise corresponds to Odin’s destined enchantment with her, i.e. to his self-sacrifice for her. Yet Freya herself suffers from the same sort of craving, her craving for the Brisingamen. Thus she — the object of the cursed cyclical hero — is all but identified with that hero. The profound implication here is that Freya represents true otherness; she is at once separate from and related to the hero. She represents the mystical multeity-in-unity. She is not the ring, not the necklace; rather she is the Holy Grail. The Grail does not represent the curse; it represents one’s acceptance of the curse by way of belief in otherness, in quantumness, in a Black/Baroque reality which would be humiliating were it not identical with all others (souls) together, including God. The Grail symbolizes not possession; it symbolizes understanding of that which cannot be possessed. In other words, the Grail symbolizes the quest, the holographic, quasic-cyclic, fractal and in these senses irreducibly complex quest. The hero is the knight, the princess, the dragon, the quest, the Grail.
In this light consider the following from near the end of F. Scott Fitzgerald’s Great Gatsby:
And as I sat there brooding on the old, unknown world, I thought of Gatsby’s wonder when he first picked out the green light at the end of Daisy’s dock. He had come a long way to this blue lawn, and his dream must have seemed so close that he could hardly fail to grasp it. He did not know that it was already behind him, somewhere back in that vast obscurity beyond the city, where the dark fields of the republic rolled on under the night.
Gatsby believed in the green light, the orgiastic future that year by year recedes before us. It eluded us then, but that’s no matter tomorrow we will run faster, stretch out our arms farther. … And one fine morning
So we beat on, boats against the current, borne back ceaselessly into the past.
Let’s take a harder look at the Pelops myth in connection with that of Sigurd, Loki, Andvari and company. The beautiful boy Pelops is dismembered by his father Tantalus and presented to the Greek gods as food with only Demeter partaking, and Zeus in turn damning Tantalus and resurrecting Pelops to replace the goddess Hebe as his own cup-bearer, just like Zeus does later with the Trojan Ganymede, alias Aquarius. Similarly the Norse boy/god Ottr is a cannibalized youth at bottom of Andvari’s curse. Note the similarlity between the names Andvari, Atlantis, and Tantalus, and likewise between Ottr and Odin, Attis, Atlas, apple, Apollo, Aphrodite, Hp/Hapi, Apis. This last name means “bee” and is the original name Apia, “Land of Bees” of the Greek peninsula which the resurrected Pelops eventually conquers and renames the Peloponnese, “Pelops’ Island.” Andvari is also equivalent to Athena’s proto-mythological North African precursor Anath/Tanith/Neith, i.e. the nether goddess whose symbol was an open hand as in Chiron, ChiRho, the 5 twins of Clito, the 5 brothers of Europa, and Helen/Aphrodite’s plane-tree. In other words, Andvari equals Freya equals Andromeda. Andromeda is Persephone is Core the latter as in the Indo-European *kor-, “turn, bend,” hence the Middle Irish cor, “circle,” and the English crown, and hence, too, curse.
Loki’s journey to Andvari was required by Ottr’s father, the sorcerer/farmer Hreidmar (note the reid and mar roots), because Loki and Odin and Honir had mistook Ottr for a mere otter and had killed him and served him to Hreidmar as a victual in exchange for lodging. Discovering this awful fact, Hreidmar demanded an impossible sum of gold in return for the freedom of his guests-become-hostages. He let Loki search for that gold. Hence Loki’s journey to Andvari i.e. to Atlantis, the flooded/sunken age, the Golden Age, the age when the waning king and not the waxing son was sacrificed and eaten, when the finity, the mortality, the quantumness of life and love were recognized, honored, and institutionalized, instead of rejected in favor of some impossible, White/Apollonian quest for immortality and unity and likewise for perfectly blissful, simple love rather than irreducibly complex, Red/Dionysian love. Loki gave the ring and gold to Hreidmar, who was consequently killed by his son Fafnir, brother of Ottr, this with the aid of their other brother Regin, who planned to retrieve this loot from Fafnir by way of the young hero Sigurd assassinating Fafnir. But Sigurd intuited Regin’s intention, killed him, and thus kept Andvarinaut ignorant, though, of the curse it carried. In turn Sigurd rescued Brynhild, and the pair fell instantly in love. After giving Andvarinaut to Brynhild, Sigurd was bewitched by the sorceress Grimhild, queen of the Niebelungs (note the Nie- prefix), such that he forgot Brynhild and married Grimhild’s daughter Kriemhild/Gudrun instead. Gudrun’s brother Gunnar therefore wanted to court Brynhild. (Both these names, by the way, mean “white” and “war, killing,” as in Guinevere, Gwyneth, Igraine, Athena.) But Brynhild was still imprisoned behind the ring of fire, and Gunnar couldn’t penetrate it. Sigurd, however, under a spell cast by Grimhild, shape-changed himself to look exactly like Gunnar, passed through the fire, took Andvarinaut from Brynhild, and gave it to Gudrun. Still under Grimhild’s power, Sigurd furthermore helped Gunnar court and win Brynhild. But upon seeing Andvarinaut on Gudrun’s finger, Brynhild fathomed Sigurd’s betrayal and plotted his murder. Hence Gunnar’s brother murdered Sigurd, while Brynhild killed Sigurd’s 3-year-old son and then herself. You can’t keep a fatal femme down. …
The Merovingian’s internecine strife continued despite the death of Brunhilda. Concomitantly their (White/Apollonian) royal power became eclipsed by that of their house officials (essentially representing of the quantum, Red/Dionysian aristocracy). Thus the majordomo Latin for “major one of the house,” translated “Mayor of the Palace” in English, whereby dom and dame and palace and Pallas equivalencies are especially evident became the effective ruler. In Austrasia this title became hereditary following the majordomo Pippin (or Pepin) of Hertsal (Pippin the Middle, Pippin II). It was his forebear Pippin of Landen (Pippin the Elder), original Austrasian Mayor of the Palace, who, under the powerful influence of Bishop Arnulf of Metz, had led the aristocratic revolt against Brunhilda. (Pippin II was the son of Pippen the Elder’s daughter Begga and Arnulf’s son Ansegisel.) Likewise Pippin II’s son Charles Martel instead of Merovingian King Theoderic IV led the defeat of the Moors at Poitiers in 732. Martel fathered Pippin “the Short.” This Pippin III garnered support from the aristocracy for a change of dynasty. When the pope asked him for assistance against the Lombards, Pippin made the deal contingent upon the pope coronating him. Seemingly for legitimacy’s sake, Pippin first married a Merovingian princess. The pope then annoited him king. Hence in 751 the last Merovingian, Childeric III, was deposed and exiled to a monastery with his long hair cut (indeed tonsured). In 768 Pippin III died, having named as heir both his male children by said Merovingian princess: the elder Charles and the younger Carloman. But in 771 Carloman died and Charles who, like his father, married a Merovingian princess proceeded to achieve exceeding military and cultural successes: he expanded his father’s Austrasian kingdom; he promoted a liberal renaissance; and all the while he advocated the (Red/Dionysian) Roman (i.e. Western Orthodox) Christian Church in contrast to the (relatively White/Apollonian) Byzantine (i.e. Eastern Orthodox) Christian Church based in Constantinople, and also, of course, in contrast to certain heresies, most notably Arianism. Charles was sole king of the Franks until 814. It was during Christmas Day mass in the year 800, in Saint Peter’s Church in Rome, that Pope Leo III seemingly surprised Charles by placing the solar crown upon Charles’ head and coronating him Emperor of Rome. Hence we have Charles the Great, Charlemagne in French, Karl der Gross in German, Carolus Magnus in Latin (and thus the adjectival form Carolingian).
The circumstances of Charlemagne’s coronation occuring on a primary Red/Dionysian holy day in a primary Red/Dionysian city and church and conducted by a Red/Dionysian leader with, as we will see, a Red/Dionysian name, Leo, just as the name Charles/Karl/Carolus itself, like carne and Carnival, is Red/Dionysian are telling. Charles’ coronation was his Mardi Gras, his fattening for sacrifice. The solar crown is akin to Andvari’s ring and to the wreath of oak worn by Tantalus’s father, the river god Tmolus, who is involved along with Dionysus and that great exponent of a marvelously advanced but now sunken continent, the drunken satyr Silenus, in the story of Gordian King Midas he of the cursed golden touch. Likewise the crown represents the eclipse of the Sun by the Moon, i.e. the Meeting of the Sun and the Moon, the Female and the Male, the Priest and the Warrior, the pope and the king. The crown as in the word corona and the title Cronus (Kronos, Geranos) completed Charlemagne as a duality, a RheaCronus, OpsSaturn, AphroditeHephaistos, SunMercury, VenusMercury, SunMoon, RexDeus; it sealed his fate as an irreducibly complex persona who according to the cosmic order and hence for the greatest good naturally and preternaturally sacrifices himself in every moment, eventually to the point of death itself. Rhea is equivalent to the Egyptian Re (or Ra), who is proto-mythologically female, just at the German word Sonne is feminine while Mond (as in monad) is masculine.
The Sun-disc itself the Egyptians called not Re but Aten (alias Aton, Itn) as in the Greek god Adonis and the Norse Ottr. This mere disc per se corresponds to the full/fat, masculine Moon. The Sun in its full, warm, life-giving complexity is, however, proto-mythologically female. Re is Rhea/Ops, wife of Cronus/Saturn, mother of Zeus/Jupiter. She is “the face,” “the eye,” “the light,” “the voice,” “the snake,” “the power”: Europa, Penelope, Ophelia, Helen, Hel, Helios, Demeter, Core, Persephone, Aphrodite. She is “the beautiful coverer/destroyer”: Kolyo, Kali, Kalypso, Callisto, Calliope as in the Greek kalos, “beautiful,” and eclipse and apocalypse. She is “the beautiful face and voice covered,” “the veiled one,” the Sun eclipsed by the Moon, the Sun at once in mourning for and hidden behind the ever dying and rejuvenating, proto-mythologically masculine Moon.
The coronation is an eclipse, a signification of quantum complexity; it represents the irreducibly complex moment, the mythological apex and likewise Aphrodite, and Ops, and apis, “bee,” and Apia, “Land of the Bee” (renamed the Peloponnese), and Hp/Hapi, and Hephaistos, and Epimetheus . Later I will explain that the ancient Egyptians considered the Nile delta ironically the mythological high-point of their kingdom, which kingdom consisted of Lower Egypt and Upper Egypt, Red and White, respectively, connected by the Black Nile. The king of Lower Egypt, which realm was called Shemau (as in Joyce’s Shem) and included the Nile delta, was titled bit, “bee” or “he of the bee,” usually translated into English as “King of Lower Egypt.” I theorize that the Egyptians considered this king equivalent to Ptah their bound, Hephaistos-like god of creation and that this Ptah is equivalent to Peter (and hence the pope), as the name itself suggests. The Egyptians imagined honey bees the tears of Re. Such tears correspond to the ululations and semi-crocodile tears shed by women over the sacrificed hero. In other words, these tears correspond to the Meeting of the Sun and the Moon. This meeting, this apex, this Haran, is the moment of both rising and falling, White and Red the irreducibly complex moment of triumph, of quantum gravity. This is the nature of every moment, really: eclipse, coronation.
In this light, note that Myrtilus’s curse fell most heavily on the house of Pelops’ eldest son Atreus, father of Menelaos and Agamemnon. Atreus, legend says, was the first astronomer to correctly predict using mathematics an eclipse of the Sun by the Moon.
Similarly, recall that the twins Remus and Romulus are descendents of Aeneas, through their mother; their father is Mars. Julius Caesar believed that his own family descended from Ascanius, son of Aeneas and Creusa. Spengler reports of a typical Roman consul on the day of triumph: “[he] wore the armour of Jupiter Capitalinus, and in early days his face and arms were even painted red ….” The pigment used was red lead. Lead — cubic lead — is the metal of Saturn. The very word triumph stems from the Greek thriambos, meaning a hymn to Dionysus, sung in processions in his honor, and also an epithet of the god himself, the Red god of the vine/tree/threeness/middleness/carnality/carnivale/rebirth/cycles. The Roman consul, like a U.S.A. President, was essentially a dual figure, an Aeneas, an Ulysses, a Remus–Romulus, a self-sacrificer, a Kronos, a Dionysus, a Hermes, a Saturn, a Solomon, an Oðinn, a Humpty. Frazer expounds on the Roman associations with Jupiter:
… down to imperial times victorious generals celebrating a triumph, and magistrates presiding at the games in the Circus, wore the costume of Jupiter, which was borrowed for the occasion from his great temple on the Capitol; and it has been held with a high degree of probability both by ancients and moderns that in so doing they copied the traditionary attire and insignia of the Roman kings. They rode a chariot drawn by four laurel-crowned horses through the city, where every one else went on foot: they wore purple robes embroidered or spangled with gold: in the right hand they bore a branch of laurel, and in the left hand an ivory sceptre topped with an eagle: a wreath of laurel crowned their brows: their face was reddened with vermilion [i.e. mercuric sulfide, or another red pigment, such as the aforementioned red lead]; and over their head a slave held a heavy crown of massy gold fashioned in the likeness of oak leaves. In this attire the assimilation of the man to the god comes out above in the eagle-topped sceptre, the oaken crown, and the reddened face. For the eagle was the bird of Jove, the oak was his sacred tree, and the face of his image standing in his four-horse chariot on the Capitol was in like manner regularly dyed red on festivals; indeed, so important was it deemed to keep the divine features properly rouged that one of the first duties of the censors was to contract for having this done. The Greeks sometimes painted red the face or the whole body of the wine-god Dionysus. These customs may have been a substitute for an older practice of feeding a god by smearing the face, and especially the lips, of his idol with the blood of a sacrificial victim. Many examples of such a practice might be adduced from the religion of barbarous peoples. As the triumphal procession always ended in the temple of Jupiter on the Capitol, it was peculiarly appropriate that the head of the victor should be graced by a crown of oak leaves, for not only was every oak consecrated to Jupiter, but the Capitoline temple of the god was said to have been built by Romulus beside a sacred oak, venerated by the shepherds, to which the king attached the spoils won by him from the enemy’s general in battle. We are expressly told that the oak crown was sacred to Capitoline Jupiter; a passage in Ovid proves that it was regarded as the god’s special emblem.
The Roman leader participating in a triumph was Mars on Mardi Gras, Mars’ Day Fat, Fat Mars on Fat Teusday, on Fat Two’s Day, the fattened cow, the Full White Moon (Monday, One’s Day) ready on that New Year’s Day for sacrifice on Red Wednesday, Woden’s Day, Oðinn’s Day, Three’s Day, the New Year’s Day, his destiny the cubic crypt of Black Saturday, Saturn’s Day, Six’s Day — from which he will rise again, ever participating in all the cycles of the cosmos. A slave was typically employed during the triumph to stand behind the leader and whisper to him, “Sic transit gloria mundi,” meaning, “Thus passes the glory of the world.” General George Patton famously commented:
For over a thousand years Roman conquerors returning from the wars enjoyed the honor of triumph, a tumultuous parade. In the procession came trumpeteers, musicians and strange animals from conquered territories, together with carts laden with treasure and captured armaments. The conquerors rode in a triumphal chariot, the dazed prisoners walking in chains before him. Sometimes his children robed in white stood with him in the chariot or rode the trace horses. A slave stood behind the conqueror holding a golden crown and whispering in his ear a warning: that all glory is fleeting.
Christian Meier, acclaimed biographer of Julius Caesar, notes that the supplicatio for Caesar’s victories in the civil war was 40 days long; his triumphal chariot was drawn by 3 white horses, and it was preceeded by 72 lictors. These numbers, as we will learn, are meant to resonate with the cosmic cycles. Meier emphasizes that in Caesar’s final year or so honors were heaped upon the de facto king Caesar as adornments are traditionally heaped upon the body of an animal before it is sacrificed. It is said that shortly before his death Caesar publicly bared his neck and chest to signify his respect for the republican notion that whoever sought kingship deserved execution. From 222 BCE to 153 BCE the Ides of March had been the day when the Roman consuls were inaugurated; and precisely in this respect, as Duncan Steel stresses, 15 March was, like 1 March and 1 January and 1 November and Rosh Hashanah (as early as 5 September and as late as 5 October), a New Year’s Day. (The U.S.A. Presidential election is held on the first Tuesday of November which is not 1 November, the Day of the Dead.) Probably this is why the augur Spurinna had been warning Caesar to beware the Ides of March. The augur surely knew or at least intuited that New Year’s Day was, in times of old, the day of regicide.…
I see the Atlantaean/Merovingian legacy passing from the Carolingians into the dawning Middle Ages via St. Anselm (10331109) and especially via the aristocratic St. Bernard (10901153) and hence to the synod at aptly named Troyes, now in northeastern France. In 1128 Bernard, who in the Investiture Controversy sided with the pope, was invited from his Clairvaux to Troyes, only some 30 miles distant. He soon played a prime role there in establishing the synod’s new order — which order we now know as the Knights Templar. Indeed, Bernard is said to have drawn up the very rules of the Knights Templar. These rules stem from St. Benedict’s rather desultory and expressive 12 acts of humility via St. Anselm’s contrastingly progressive and introspective 7 steps-toward-God and St. Bernard’s own Cistercian program of progress from body (Black) to soul (Red) to spirit (White), which religious program was echoed in the secular romantic literature expounded by Chrétien of Troyes, according to which the hero is obliged to leave the comradery and comfort of the court (Black) and endure a personal (if not lonely) and life-long quest (Red) toward unattainable, perfect love (White). Owing to St. Anselm, the Cistercian program emphasized the humanity of Christ and thus the importance of Mother Mary. This Red/Dionysian religious emphasis corresponds to the contemporaneous secular emphasis upon the quest including all the romantic baroqueness thereof. The Cistercians believed they could chiefly through exploration of the self recognize a fundamental resonance or duality if not union of logic and feeling, precision and soul, external and internal, divisibility and individuality, exceptionality and universality, transcendence and immanence/relativity, White and Red. Such duality is represented in the seal of the Knights Templar and is akin of course to the famous dualities of orthodox physics. …
Of Heisenberg’s Gemeinschaft (Gruppe Heisenberg), only one member not of course Heisenberg — is recalled as having joined the Nazi party. The Nazis consciously played upon old mythological themes, selecting, for instance, the swastika and the colors red, white and black for their symbol. Germany in the 1920s and 1930s was looking for a new Charlemagne, a new RexDeus. The Nazis understood this need but they didn’t believe in such irreducible complexity, such multeity-in-unity, such relativity, such Golden Age and a return thereto. They didn't want to believe that Nietzsche’s principle of eternal return should be applied to every moment, every scale, not only to the universe as whole and that return in general is therefore merely quasi, fractal. The Nazi leaders believed in an extremely simple return relative to which local ascendancy was virtually unchecked and therefore a matter almost entirely of will to power. In a word, they believed all existence was a monad, a simple, White/Apollonian unity. Rather than submitting to Andvari’s ring and thus eternally (in every moment) returning it to Andvari, the Nazis thought they could possess it, control it, without suffering the concomitant curse. They were monism at its worst.
The constitution of the Weimar Republic, established in Germany soon after World War I, was a beautiful, Golden/Legal document, a paean to Andvari. In this sense at least the stage was set for the requisite knight to emerge. If he had emerged, he would have come from the Red/Dionysian likes of the Neupfadfinder, not from the Nazis. Again, Cassidy:
… the Bavarian Neupfadfinder often equated the white knight with St. George the dragon slayer. As a constant reminder of their calling, a portrait of St. George as white knight slaying the evil dragon … hung over the door of the Bavarian ski hut built by Gruppe Heisenberg in the early 1920s. It was still there when Niels Bohr visited the hut over a decade later.
Although the contemporaneous German youth movement, including the Neupfadfinders, was to a considerable degree determined to advocate the Golden/Legal philosophy, the movement was too much a “freedom movement” away from the demeaning effects of industrialization, of mass civilization, of the city, which effects altogether seemed to suggest that the heroic (middle) ground lay outside the bourgeoisie. This was the flip side of communism. Superfluous fear of the White/Apollonian — in this case, over communism especially — had caused the Neupfadfinder and the like to lose their way, precisely as fear over terrorism is doing today. With over-intellectual youth (and in large part their mentors) actually taking to the hills, and with France (i.e. Neustria, you might say) and England and the USA but especially France bringing to bear against Germany (i.e. Austrasia) the Allied victory of World War I, the Gunnar-like Hitler was selected White Knight of Germany. Amid economic depression and hyperinflation, the Nazis came to power democratically. In the crowded political field of 1930, only 11 years after their founding, the Nazis received a full 18 percent of the vote 2nd place. In 1932 a pair of national elections were held, the Nazis winning 1st place in both, with 37 and 33 percent of the vote. Finally, in 1933 the Nazis received 44 percent of the vote, as much as their 3 closest rivals combined. Therefore the Nazis were invited to form the government.
I’ve digressed from Schrödinger, who spent the years of World War II in Dublin, Ireland, at the new Dublin Institute for Advanced Study. If we look back at his early life in Vienna, we see Erwin snubbed by the aristocratic family of his initial love, Felicie Krauss. He was 25, she 17. Reared a nominal Protestant (White/Apollonian) in extremely cosmopolitan Vienna, Schrödinger eventually married a Catholic (Red/Dionysian) girl from Salzburg: Annemarie Bertel. She was a teenager (in pigtails) when he met her. She seemed to him a peasant, but her father was a man of considerable standing in Salzburg. Unlike Felicie, Anny was homely and masculine; yet she was intelligent and wise. Her birthday was New Year’s Eve (Sylvesterabend).
In 1930 Erwin and Anny attended a carnival-time (alias Shrovetide or Faschingzeit) ball in Berlin dressed as the pharaohs Akhenaten and Nefertiti. The ancient Egyptians equated the husbandwife duo of Akhenaten and Nefertiti. (Note the Ne- prefix.) The ancient Egyptians equated this royal husband–wife duo with that of Shu and Tefnut, the first sexually differentiated offspring of the androgynous god of creation. As you may know, Akhenaten (c. 1350 BCE) is famous for promoting the worship of Re — now commonly though rather eroneously considered a masculine, White/Apollonian Sun god — over the other prime Egyptian gods, especially over Amen (alias Amon), equivalent to Zeus/Jupiter, which aspect of the Triple God, as we have seen, is chiefly Red/Dionysian although Zeus/Jupiter is White/Apollonian relative to Kronos/Saturn. Inasmuch, Akhenaten is commonly although, again, rather erroneously considered a monotheist, indeed the initial monotheist. According to a similar line of reasoning, his Sun worship is the basis of Judaism. Akhenaten is also famous for promoting androgynous and otherwise rather mimetic art forms. And so to the modern eye Akhenaten seems a chiefly White/Apollonian figure, significant more of unity than of duality, much less of quantum complexity. Yet his partnership with Nefertiti the ancients associated with the pair Shi and Tefnut (equivalent to Kronos/Saturn and Rhea/Ops and likewise Hephaistos and Aphrodite and also Hp/Hapi). In a sense this androgyny, and even this emphasis on the Sun, which is proto-mythologically female (note the similarity between Rhea/Ops and Re), signify a naturally, characteristically and quantumly complex man. Perhaps he attained and/or became attached to rather unprecedented White/Apollonian dimensions insofar as his wife was, in contrast, a remarkably Red/Dionysian figure, a femme fatale, and Aphrodite/Freya/Neith/Andromeda/Persephone. Upon Akhenaten’ss death Nefertiti became the first female pharoah.
Akhenaten, c. 1350 BCE, at left looking a lot like Hp/Hapi and rather Asian.
Nefertiti. The Egyptian Museum, Berlin.
The equivalency with Demeter is noteworthy. The name Demeter is cognate with the Cretan deai, “barley” which word is linked to the English day and degree and barleycorn. Cognate is the Greek moira, which means “share, phase, degree, fate, destiny,” as in the Moirai, i.e. the 3 Fates, the Triple Goddess, and as in the tao, me, maat, etc. A barleycorn is 1/360 of a meter and generally represents smallness yet genuineness and potential, as in seed, grain, and Quino, and as in the absent father, Andvari, the snake, the dog/wolf, the ancestors. Demeter is likewise closely related to the Greek dêmos, “common people, district,” which Greek word was originally dâmos, as in dame and dom and the Old Irish dām, this latter meaning “a following, crowd.” These words all stem from the Indo European *dâmos, meaning “division of the people, root”; and more generally from the root *dâ/də, “divide,” which root is present too in names/titles like Aphrodite, Diana, Odysseus, Odin, and Dien as in Dienstag, i.e. Tuesday, Tiwes’ Day, Mars’ Day, Mardi Gras, Fat Tuesday, Full Moon Tuesday, Full Moon Day, Full Monday.
The Meeting of the Sun and the Moon especially perfect in terms of the weirdly identical apparent areas of the face of the Sun and the face of the Moon as seen from Earth is a most profound duality, a feminization of the male, literally a coronation representing the cyclic transition from White to Red to Black, i.e. representing culture itself. Such coronation corresponds to a returning of the Andvarinaut to Andvari, a literal submission Andvari and his ring symbolizing not only a Golden Age, not only the previous Great Year, not only dream and the dream-time but ultimately the extreme mystery of existence, the Golden principle of relativity.
Akhenaten and Nefertiti, Erwin and Anny, Mach and Boltzman, Spinoza and Leibniz: these White–Red dualities are equivalent to Charlemagne, Merowig, Moses and Aaron, Isaac and Ishmael, Sarah and Hagar. Such dualities characterize the true heirs of the German kingdom. In a sense, Anny was the true Fürher from Austrasia/Austria.
Erwin, nevertheless, was always especially attracted to teenage girls, and he engaged in several affairs with such during his middle age. In his copy of Thornton Wilder’s Bridge of San Luis Rey (note the Luis and Rey) the following passage was underlined: “Now he discovered that secret from which one never quite recovers, that even in the most perfect love one person loves less profoundly than the other. There may be two equally good, equally gifted, equally beautiful, but there may never be two that love one another equally well.” Schrödinger had probably read this book during the spring of 1933, when he was deeply in love with Hilde March. He was also very fond of Somerset Maugham’s Summing Up, near the end of which memoir Maugham offers the following observation similar to Wilder's: “[W]hen La Rochefoucauld discovered that between two lovers there is one who loves and one who lets himself be loved he put in an epigram the discord that must ever prevent men from achieving in love perfect happiness.” Earlier in that book Maugham notes:
When novelists began to disclose the diversity that they had found in themselves or seen in others, they were accused of maligning the human race. So far as I know the first novelist who did this with deliberate intention was Stendhal in Le Rouge et le Noir. Contemporary criticism was outraged. Even Sainte-Beuve, who needed only to look into his own heart to discover what contrary qualities could exist side by side in some kind of harmony, took him to task. Julian Sorel is one of the most interesting characters that a novelist has ever created.
Eventually Erwin and Anny separated, but they did get back together in the end. “Joy and sorrow has bound us so closely together in the past 41 years,” Anny wrote while they were still living apart, “that we don’t want to be separated during the few remaining years of our lives.” During the month or so before his death Erwin was wont to say to her, “Oh since I have you again, everything is good again.” His last words were, “Anniken, stay with me so that I don’t crash.”