The Holy Grail
It's fair to say the chief corollary of Einstein's special and general theories of relativity is that time doesn't really exist. As Julian Barbour points out in his outstandingly challenging and marvelous End of Time, Einstein’s general theory of relativity is best formalized in terms of what is now called geometrodynamics. That deep structure intrinsic to Einstein’s theory was not discovered until the late 1950s, by physicists Paul Dirac, Richard Arnowitt, Stanley Deser and Charles Misner. The elements of geometrodynamics are the members of the set of mass-embellished Riemmanian 3-spaces — i.e. they are chunks of solid space that have “mass” associated with each point (mass being a uniquely invariant form of “charge” that has the units of “energy”). Each of these chunks of space — painted, if you will, with mass — is a continuum (although the mass associated with a point can be perfectly zero). Each is finite (although each corresponds to an instantaneous snap-shot, as it were, of the whole universe). Each has associated with every of its infinite points a 3-dimensional curvature (i.e. the objects are generally non-Euclidean, although said curvature may be 0). Barbour emphasizes that this set can be considered as corresponding quite perfectly to the set of souls — Leibniz’s monads, to be precise.
Einstein’s theories, however, along with Schrödinger’s wave mechanical atomic theory are remarkably and it seems resolutely reflective of Spinoza’s philosophy, which philosophy stands in extreme contrast to Leibniz’s. Indeed, both Einstein and Schrödinger considered Spinoza the greatest philosopher ever. Heisenberg’s quantum mechanical atomic theory, on the other hand, along with Bohr’s Copenhagen Interpretation thereof stand poignantly in contrast to Einstein’s and Schrödinger’s theories and correspond deeply — although rather irresolutely — to Leibniz’s philosophy. Hence I think a physical theory which resolves to reflect the philosophy of Leibniz is waiting to be discovered.
Indeed, Leibniz’s philosophy seems to lend itself to physics extremely well. “As far as I am aware,” writes Julian Barbour, “Leibnizian ideas offer the only genuine alternative to Cartesian–Newtonian materialism which is capable of expression in mathematical form.” Physicist Lee Smolin, whose specialty is quantum gravitational theory and who became a proponent of Leibniz by way of conversations with Barbour, notes in his Life of the Cosmos:
Julian [Barbour] is not the only deep thinker in science who considers himself a follower of Leibniz. So also do many others such as David Finkelstein, Louis Kauffman and John Wheeler. We must ask why, if it was based on the worse [non-purely-relational, absolute] philosophy, was it Newton’s physics, and not Leibniz’s, that triumphed and became the basis of science for the next two centuries. Certainly Leibniz was also not dumb. One philosophy professor I know calls him the smartest person who ever lived.
To pursue such alternative theory we should take a tack contrariwise to Einstein and Schrödinger by placing unity and multiplicity on an equal footing and from that lone principle develop a theory of physics. That’s the Leibnizian way. What’s more, precisely that footing can be considered the true principle of relativity: the principle that others exist, i.e. the belief that I, the fundamentally individual observer, am nevertheless related to other fundamentally individual, Cartesian I’s — i.e. other (and the only other) substances. This is the most basic, the most natural, of all beliefs. Being a belief, this principle is precisely a form of mysticism. Moreover, being a belief in an infinity of others, this principle of relativity is the extreme form of mysticism. In contrast the God-is-the-only-substance sort of solipsism at bottom of Spinoza's philosophy is purely reasonable. To call mystical that which favors unity over multiplicity has long been the fashion; but such trumping is in truth simply reasonable.
The greatest mystic ever was not Spinoza but Leibniz.
I suspect that the price Spinoza and Einstein and company had and have to pay for their extreme economy with Occam's Razor is the price of failure itself. By way of admitting mysticism in an extreme (yet extremely rarefied) way, we may be able to reach a bona fide theory of everything and perhaps even a final physics. Such theory would ironically be understood as the greatest symbol of mystery. Not surprisingly, though, the theory would as such be a Faustian deal — precisely as is Heisenberg’s Uncertainty Principle in orthodox atomic theory.
Indeed, the essentially prehistoric, mytho-logical principle of relativity I point to can at bottom of a new, more general quantum theory play the very mystical role which the Uncertainty Principle plays at bottom of Heisenberg and Bohr's quantum theory. Unlike the Uncertainty Principle and the singular quantum of action it accommodates, said principle of relativity would clearly serve as a basis for cosmology, i.e. for a description of the whole as well as the part. The physical theory stemming from that principle would be a quantum theory either of space or of time: the stuff of the theory would either be space or time, quanta of space or time. Which is to say, the intrinsically quantum mathematics of such theory would be symbolic either of space or of time; it would, respectively, be either a model or purely a symbol.
Barbour is developing such a quantum theory of space, a theory in which time is emergent from space, secondary to it. I'm suggesting such a quantum theory of time, in which space is secondary to time. The mathematics of my theory is fractal and holographic, at once far more simple and complex yet remarkably mapable to the aforementioned set of Riemannian 3-spaces suggestive of Barbour’s theory. According to my approach, space does not exist but is rather a hologram of time; each observer, i.e. each particular quantum of time, harbors quantum yet non-divisive structure which can be considered perfectly symbolic of a postulated multiplicity of others.
Now, Leibniz correctly argued that such members of a multiplicity-in-unity cannot be said to have parts, lest said members be not true individual (i.e. indivisible) members of the set. Yet in the absence of space the quanta inherent to an observer are not truly parts, not truly divisions, not mechanical; they are merely the structure of time, existentially inflective/reflective of all that is extrinsic to (i.e. outside) a particular individual. What's more, corollary of the extremely mysterious, paradoxical principle of truly general relativity which I point to above is the notion that said particles of reality mysteriously influence each other. Which is to say, the true principle of relativity absolves us of any need to explain such influence; the influence would simply be a manifestation of the one Force, if you will, which Force would be co-existence itself. As such, the particles of time — the souls, Cartesian I's, observers — can best be considered not monads but pleiads.
In other words, a little mystery goes a long, long way — all the way. Leave that door open just a crack and all of existence is in the house.
You have to admit, if a person could derive a successful physics from and only from the single chief principle (i.e. belief) by which that person lives — namely the principle that heshe is not alone, that others exist — it would be extremely beautiful. For this reason alone we are obliged to explore whether that theory might exist. I expect such exploration should progress via a single best mathematical symbol of said principle of relativity. Such symbol, coupled to the hypothesis that the structure of a person’s experience perfectly matches it, could be identified as physics itself. Thus the belief in others including an absolute, singular, yet immanent, extremely incarnate God would virtually be reduced to fact, and physics itself would stand as the best, most potent symbol of the extreme mystery of co-existence, of otherness, of difference, sameness, relativity, kinship, peace.
The age has come for the world to acknowledge that people and souls in general are not separated by space and matter and linear time but by separation itself. Likewise, people are not related by local causality but by causality or relativity itself. Such recognition, I think, is the basis of true peace.
What the heavens were to prehistoric humanity the microscope is to the modern world. Whereas the circumpolar precessional ellipse was the Holy Grail of old — shining invisibly every clear night before all eyes but seen only by the very few — the quantum of action is the Holy Grail of our day. The periodicity of the grandest scale corresponds to the quantum structure characterizing the smallest. The Holy Grail in general is not merely a best symbol of the cyclical, fractal, holographic nature of the individual, of the Quest, and likewise of multiplicity-in-unity; rather it is the individual, it is the Quest, it is multiplicity-in-unity — it is the Force. Hence the end of physics in terms of a Holy Grail is not to be thought of as an end but rather as a beginning or better still a touchstone, a simple, elemental, irreducible yet extremely complex vein merely representing the infinite plenum. Such physics is existential DNA, if you will; and indeed, as we relegate space to secondary status we necessarily do the same to the theory of evolution. At every past debate between a creationist and an evolutionist there should have been on stage an empty chair representing an existentialist. Increasingly that chair will be present and occupied.
As someone once said, “What really counts is what you learn after you know everything.”
According to the new yet essentially mytho-logical theory that I’m here outlining, the merely physical (i.e. the structure of one’s experience, the structure of a soul, the structure of reality, the structure of the observer, of what is observed) should perfectly correspond to the best symbol of the whole supposedly plural set of souls (i.e. real quanta). This is to say, the structure intrinsic to any one person (the structure of that person’s experience) should correspond to the best — the most beautiful, the simplest yet most general — symbol of the souls supposedly extrinsic yet related to that person. A physics based on this principle of relativity would be the best argument against any but the weakest form of solipsism, which weakest form it would be identical to. Precisely this heuristic quality of physics should not surprise us. Physics, after all, is primarily an accounting for the particularity of experience, and the particularity of experience is precisely what suggests to an individual that he or she is not alone.
On this view the principle of relativity can itself be considered an extremum principle, for an individual generally experiences an extremum of particularity, i.e. of discontinuity — what Sartre called “nothingness.” This intrinsic nothingness is concomitant of the multiplicity of souls; in other words, it corresponds but is not identical to the supposed extrinsic nothingness: the separation (mere, non-extensive) of souls, the freedom (in this most basic sense) of souls (from one another, that is). Insofar as the particularity intrinsic to a soul corresponds to the infinite multiplicity of souls, that particularity is a sort of maximum. But in the sense that this particularity is likewise limited, such that only a finite number of unique structural quanta (if not a finite number of real quanta) may be immediately experienced by any single soul (other than God), it is minimized. Thus the principle of relativity has as a corollary what might otherwise be called the principle of plenitude, where plenitude signifies at once the infinite multiplicity of souls (i.e. real quantumness) and the uniquely finite, rarefied discontinuity (i.e. merely essential quantumness) instantly (at least) intrinsic to any single soul.
Permit me to add that we can fairly call this complex plenitude the basis of liberty. For whereas the word freedom connotes the simple, White/Apollonian paradigm, the word liberty connotes the complex, Red/Dionysian paradigm: freedom alloyed with bondage, multiplicity alloyed with finity, variety alloyed with periodicity, generality alloyed with simplicity which dualities are akin to the orthodox physical dualities of particle and wave, space and time, momentum and energy.
More to the point is the analogy between said extremum principle and the famous principle of action an extremum principle that has been developed and handed down to us as a basis of physics by the likes of Aristotle, Hero of Alexandria, Fermat, Leibniz, Maupertuis, Euler, Lagrange, Gauss, Hamilton, Jacobi, Dirichlet, Helmholtz, Planck, and Dirac. Indeed, I think this analogy is better considered an identity. I consider the principle of relativity identical to the principle of action. This identification suggests that the concepts of plenitude, liberty and action are to be considered significant of the same kind of thing: reality, soul, experience, what Sartre called “being” (in contrast to nothingness).
The orthodox “quantum” of action is in fact a function, not truly a quantum (i.e. not a number). That function is best considered significant of a principle of extreme action and, deeper yet, of plenitude, relativity. The only physical “events” that can occur are those which correspond to this principle; and these events are precisely intrinsic nothingness, the stuff of mere physics (what Einstein called “being”), the structure (or “essence,” as Sartre called it) of experience.
The principle of relativity is likewise equivalent if not identical to what Einstein called “Mach’s Principle.” Mach’s Principle, which stems from Bishop Berkeley, can be understood as equivalent if not identical to the following: The inertial motion of a particle — i.e. motion which is considered unaccelerated and therefore, in this special sense, not consequent of what we classically and hence typically call a force — must nevertheless be described as caused by something and must therefore be considered forced by something contrary to but ultimately of the same kind as that which causes accelerated motion; and whereas accelerated motion is described as being generally in immediate spatial connection with its cause (i.e. with a typical, local force) and in this sense as having no spatial memory, if you will, inertial motion should be understood as being generally in nonimmediate spatial connection with its cause (i.e. with nonlocal, atypical force) and in this sense as having spatial memory, i.e. as being caused not only by a particular instance of force but moreover by everything in existence; in a merely pictorial sense, that “everything” could be described as the instantaneous configuration of all the particles of the universe; in a philosophical sense, that “everything” could be described as God (per Spinoza) or as the set of monads (per Leibniz).
Physics logically aims to minimize the number of forces involved in a theory. Mach’s Principle suggests that this impetus toward simplicity requires us to understand force as being generally non-local, an action-at-a-distance. Like all “forces,” this Force cannot be derived; it is unexplainable in terms of mechanism; indeed it is not meant to be explained as such; it must be merely postulated; it is extremely mysterious. Nonetheless, such postulate can be extremely useful in the physical sense and, ironically, can be perfectly determined, i.e. mathematically symbolized, rendered free of arbitariness, and in this sense considered ironically absolute.
Mach’s Principle suggests that the key to orthodox physics is our understanding of mass particles (whether they be mathematical points or not) and the mere separation thereof (i.e. length, distance); in other words, the key is our understanding of the spontaneous mass-symmetry breaking. According to the principle of relativity as I generalize it above, mass and length and spontaneous symmetry breaking are all mere aspects of a single best mathematical symbol of the set of real particles: the Leibnizian set of souls, others, monads, what I think we should consider pleiads.
As such, all the motion that I — the Cartesian I, a unique particle of reality/consciousness; i.e. the weakest anthropic principle — experience (observe) can be considered inertial motion caused only by my existential relationship with all other souls. Yet each soul is itself a unique force capable of generating motion. An individual soul is naturally aware of generating such motion. When such singular motion intrudes into that soul (i.e. into that soul's experience), the soul naturally recognizes it especially as being attributable to another singular soul, i.e. as being evidence that others exist — and ultimately obliging one (in a moral sense) to believe (or at least assume) this principle (of relativity), as per the Turing Test.
A few paragraphs below is a representation of what I consider the single best symbol of the truly general principle of relativity, i.e. of the Force. This representation — at once symbol and pure structure — should especially be compared to the orthodox representation of the so-called hydrogen atom energy levels (second image below). In terms of contemporary superstring theory (so-called M theory), said pure structure may be considered the superstring, the brane, the only physical being, the general structure and symbol of time; it corresponds at once to both matter (including radiation/light) and space. Likewise this structure can be considered the initial conditions of the universe and, more generally, the boundary conditions, although such considerations are merely poetic insofar as the notions of beginning and creation and symmetry breaking (indeed symmetry itself) and boundaries are not extremely fundamental.
Thus we see physics reduced to light, and light identified as symbol: the single best symbol of the principle of relativity: the principle that countless other souls exist.
The mystery of time, we may fairly say, is identical to the mystery of existence; and this mystery is inextricably alloyed to the mystery of the supposed multeity-in-unity of souls.
Here, then, is the symbol I am referring to. I consider this symbol the essence of Julian Barbour’s Platonia reduced to a single most simple yet general and in this complex sense extremely beautiful (á la the action principle) and necessarily quantum determination.
Compare this symbol to the following representation of the energy levels of the orthodox hydrogen atom.
The vertical lines in the symbol above (i.e. the top image) are included as mere pointers to the corresponding zero-dimensional divisions of the unit line. These divisions signify the “nothingness” of Sartre’s philosophy; i.e. they correspond to the separation between — that is, the freedom of — souls. The whole unit line — dual in the sense that it is at once absent any divisions and inclusive of an infinite number of divisions — symbolizes Zeus, Jupiter, Ainsoph, Allah, God, i.e. the single greatest soul of them all. In the latter sense this complex line represents the real matrix, the cosmos, the set of souls, the set of Hermes-types, the completely sacrificed (as it were) aspect of God, God incarnate. Each division of the unit line corresponds to a unique soul. Precisely a single such division corresponds to you and only to you. The finite set of unique line segments to the right (by convention) of your particular division is the set of all possible physical quanta in your experience.
Which is to say, I think the symbol above is the true Holy Grail. It could even be considered the true “blood-line” of Jesus Christ. Adam is an atom. Every soul, a Christ. The cosmos is a single, extremely complex, infinite molecule of souls evidenced most saliently by the timeless hologram we call the hydrogen atom.
This remarkable structure — this extremely beautiful symbol — is typically referred to as the Fibonacci geometry. But in a fundamental sense it is not a geometry, for it is not intended as a model of the classical, spatial universe, i.e. of the universe supposed a container or a 3+-dimensional configuration space. Hence I call this determination the Fibonacci structure or the Fibonacci symbol. In a sense this structure the general structure of soul is 1-dimensional. But each unique quantum of the structure is best considered a unique force, a dimension of reality, and in this sense the structure consists of an infinite number of dimensions. The order of a soul, on the other hand, may be most simply and generally described in terms of a 2-dimensional ramification of or emergence from this structure. Order as such would be holographic in relation to the notion of space-as-container. Regardless, order would be what Douglas Hofstadter called a “tangled hierachy” in contrast to an “inviolate level.” Orthodox physics has naturally addressed order only, i.e. emergent entities, but now the age has come for it to address and fundamentally identify itself with the inviolate level.
In a sense what I have done here is simply replace the aforementioned set of mass-embellished Riemannian 3-spaces, which quantum set of continuum parts has been shown by Dirac and company to be the truly elemental basis of Einstein's general theory of relativity, with the much more simple yet thoroughly quantum Fibonacci structure.
According to my understanding the classical, geometric, spatial model of the universe is false. There essentially is no unlimited configuration space. There essentially is no set of Riemannian-like spaces. In fact there essentially is no space at all, just the (absolutely immediate) structure of experience. (In saying this I’m just repeating Leibniz.) The job of physics is and in truth always has been to address this structure and this structure only.
Einstein didn’t completely deconstruct the concept of simultaneity, for that job requires the deconstruction of space itself. The stars and galaxies and such are remarkable intimations of infinity though they do not represent a huge space that simultaneously contains myriad far flung life-bearing planets and intelligent civilizations. Rather, I think, they represent the infinite set of souls which are separated by separation itself yet are each non-locally interacting with every other. That extreme, non-local causation — that extreme synchronicity, that extreme coherence/entanglement of an infinite set of otherwise unique quanta of time — may provide a basis for understanding Fermi’s Paradox. It seems to me that the bell curve assumed in that paradox as representing the number of planets bearing civilizations simultaneously capable of a certain mode of, say, space travel stems from the assumption that non-local causation is not important. My suggestion is that such causation is all-important. Quantum mechanics — in which entanglement/correlation is the general case — seems to similarly apotheosize non-local causation. Hence, I think, said bell curve should be more like an impulse function, what engineers call a delta function. Therefore we might say that life is progressing “everywhere in the universe” like water rising in a flooded room. Such image is consistent with Einsteinian-type space–time, which space–time does indeed conserve a fundamental kind of simultaneity. However, I'm saying space–time is but an imperfect concept used to describe an observer's immediate experience. Reality, I'm saying, is an infinite set consisting of unique quanta of time — observers, “dynamos,” as Leibniz called his monads (his Monadology he called a “dynamics”) — that are all non-locally yet thoroughly interacting with every other, each of them flowing through every other, infinitely in contact with each other. The aliens, I'm saying, are all “here” already, though nearly all of them are here very subtly, apparent only in terms of the supposed inanimate aspects of our experience, especially the hydrogen atom.
On such view, there is no real simultaneity — precisely because the only real things are unique souls, unique observers, and these can be considered quanta of time. As there is no such thing as 2 identical observers, there is no such thing as 2 observers at the same time. I imagine the structure of reality is a fractal, such that the quanta of time (souls) tend to be bunched up here and there in the set, i.e. the differences between members of these bunches are especially small. Such bunches correspond to, say, “planets” bearing intelligent life, and they are akin to “elementary” particles of the standard model of particle physics. Likewise there are bunches of bunches, and as such there is a sense in which myriad planets bearing life that is intelligent but incapable of interstellar travel are in a pseudo-simultaneous relationship with each other.
The real difference between observers/monads/pleiads is, I think, akin to the determinable “intrinsic difference” central to Barbour's reasoning. As Barbour points out, such difference can be stated in terms of a single scalar number. He speculates that the proper algorithm for determining such number — namely the algorithm which assigns such scalar to a particular monad and corresponds to the “probability” which Schrödinger's basic, time-independent equation assigns to a configuration of mass-point particles — depends on the complexity/variety intrinsic to a monad. Therefore the sort of interplanetary pseudo-simultaneity I suggest above can be said to qualify as pseudo-simultaneity inasmuch as the observers constituting the planets share a certain degree of complexity/variety. I imagine that the intrinsic difference between 2 technologically intelligent monads from 2 different, if you will, planets where obvious extra-planetary life is scientifically recognized is typically much, much smaller than the intrinsic difference between such an intelligent monad who is among her planet's first generation to observe extra-planetary life scientifically and another from another planet where such observations have never been made. Inasmuch, “we today on Earth” may be considered monads/pleiads existing at a sort of level in the set of all souls, a level which is characterized by a degree of complexity/variety corresponding to intelligent technological life that has not yet been obviously invaded, so to speak, by other such life. Nevertheless, the hierarchical and seemingly fractal structure we Earthlings presently observe and describe in orthodox physical terms — e.g. in terms of hydrogen atom energy levels, solar systems, galaxies, clusters of galaxies, etc. — can be said to represent (perfectly, I say) the structure of the set of all life forms.
I know all this sounds crazy, yet I’m more reporter than prophet when I exclaim that the biggest surprise waiting for us in space is the fact that space does not exist. The elephant in the room is the room itself, which is precisely why that elephant is so hard to recognize much less to acknowledge. Likewise, biological evolution isn’t best considered real; along with space and causality, it only seems to be real. Nor is any form of creationism ultimately a credible explanation of existence. Existence cannot be explained, and physics is merely the structure of one’s (absolutely immediate) experience. Sure, the structure of one’s experience seems to correspond to concepts such as space and evolution, but this correspondence is not perfect.
Literature is rife with messages indicating the apotheosis and holographic nature of time. One of the most salient is from Jorge Luis Borges' “A New Refutation of Time”:
Time is the substance I am made of. Time is a river which sweeps me along, but I am the river; it is a tiger which destroys me, but I am the tiger; it is a fire which consumes me, but I am the fire. The world, unfortunately, is real; I, unfortunately, am Borges.
Thomas Wolfe writes in Look Homeward Angel, “... every moment is a window on all time.” T. S. Eliot says in “Burnt Norton”:
At the still point of the turning world. Neither flesh nor
William Blake writes:
in your bosom you bear your Heaven
In his "Address to the Jews" prefacing the second Book of Jerusalem Blake refers to the cosmic figure of Adam Kadmon:
You have a tradition, that Man anciently contain'd in his
"This externalization of the physical universe," comments scholar Kathleen Raine, "seemed to Blake the tragedy of modern Western civilization. The 'starry heavens' have become exteriorized in what Blake calls the 'void outside of existence' of the Newtonian universe."
Notice the equivalence to St. George and the Dragon.
Raine, from her Yeats the initiate: essays in certain themes in the work
The human "body", according to the tradition in which both Blake and Yeats must be understood, is not in space. Swedenborg (from whom both poets learned in great part the system they share) taught that (of the Lord) "his Human Body cannot be thought of as great or small, or of any stature, because this also attributes space." "He is the same in the first things as in the last, the greatest and the least." The "true man" is mind, or as Blake names it, Imagination, the "spiritual body" of St. Paul.
Relative to the corpus of philosophy as well these statements should not come as a surprise. Physics, not philosophy, has failed to promote time over space. The ancient Greek philosopher Zeno of Elea pointed out the paradoxical relationship between motion (whether continuous or discrete) and space. Descartes who systematically doubted everything except his experience of doubt itself (“I think [i.e. doubt] therefore I am”) reduced the ancient mind–body problem to the incommensurability of mind (doubt) and extension. He then built a physics based on extension alone. Newton soon demolished that physics, but he left Descartes’ theory of mind intact — and it remains so to this day. Contemporary with Newton, Leibniz described physics not as extension but as the (immediate) structure of mind (i.e. of soul, monad). Leibniz’s “system of monads” is fundamentally a general theory of relativity, wherein the things related are minds and only minds. Leibniz describes these minds, these real related quanta, as “windowless” in the sense that there is no way to explain how they can be influenced by each other because there is no sense to the notion of a mechanical bridge between them and there cannot truly be parts within an individual. In contrast I assert that such influence and such intrinsic physical (in contrast to extrinsic, real) quanta are corollary of the principle of relativity itself, i.e. the principle that others exist. This is to say: separation, or relation, implies non-causal, unexplainable influence, action-at-a-distance (action-despite-separation); it also implies a multiplicity that is reflected inside the individual, i.e. inside the indivi-dual (or, more generally, the indivi-multiple). Leibniz considers mind “simple substance,” by which he means without parts — and by this he means indivisible. Hence his term monad. I point out that indivisibility is different than divided. (This difference might be considered the basis of Existentialism.) Leibniz’s substances are simple, White/Apollonian. Mine are complex, Red/Dionysian. His are monads. Mine are pleiads.
Consider in this light the following passage from Descartes’ third meditation, in which passage he describes the two different notions of the Sun which are in their own ways fundamental to him:
One is, as it were, created by the senses, and it could most easily be counted among those which I think are acquired; it makes the sun seem very small to me. The other, in contrast, results from calculations in astronomy, meaning that it is either gained from concepts that are innate within me or which I have produced in some other way; it presents the sun to me as something several times larger than the earth.
And here’s Ernst Mach, from his 1872 lecture, The History and Root of the Axiom of Conservation of Effort:
[F]echner [in his lecture “On the Law of Causality”] formulated the law of causality very pointedly, stating “that everywhere and at all times, inasmuch as the same circumstances reoccur, the same outcome reoccurs; to the extent that the same circumstances do not occur, the same outcome will not occur.” This, as Fechner says in a latter passage, “relates whatever happens everywhere and at all times.”
Now, I believe that I must add, and I have already done this elsewhere, that explicitly involving space and time in the law of causality is at least superfluous. Since we recognize what we call time and space by using other particular phenomena. When, for instance, we express the positions of heavenly bodies as functions of time, i.e., functions of the rotational angle of the earth, we have done nothing other than to determine how the positions of the heavenly bodies depend on one another.
Concerning Mach and space, Michael Heidelberger comments in his outstanding Nature from Within: Gustav Theodor Fechner and His Psychophysical Worldview (which work is extremely relevant to the present chapter):
After studying [Johann Freidrich] Herbart’s treatment of space, Mach was convinced that it is not even necessary to think of atoms as spatial: “Indeed, we need not even imagine atoms as extended in space. For as we have seen [in Herbart’s work] space is nothing original and results very probably from an indirect co-effect of several reals.”
According to Herbart the spatiality of our sensations is caused by the reminiscence and reproduction of previously experienced series of ideas stored in consciousness. Our sensations are three-dimensional because through vision we can follow-through perceptions in the directions of the three coordinates of space. However, as Mach discovered, Herbart could not explain why some series of perceptions are only one-dimensional for example, why hearing is one dimensional, even though our ears, like our eyes and our sense of touch, can follow through series of perceptions in all different directions.
Now if someone who could only hear would try to develop a worldview based on his perceived linear space, he would fall considerably short of his goal because this type of space cannot encompass the variety of real relations. But we have no more reason to believe that we can press the entire world, including things unobservable, into the space presented to our eyes. Yet this is the case for all molecular theories. We possess one sense that, in terms of the variety of relations it can grasp, is richer than any other. It is the mind. It is superior to the senses. It alone can establish a lasting and sufficient worldview.
As long as we have no series of perceptions for atoms, there is no justification for assuming that the 'series of perceptions' that, for us, make up the object “atom” constitute diversity of a three-dimensional kind.
We are also not justified in attributing solidity to atoms .
Yet all these difficulties are not what make Mach into a anti-metaphysical anti-atomist. He first becomes a devotee of the metaphysical doctrine of monads. Since the success of physics has led us to believe that appearances are caused by atoms, and we know nothing to say about atoms, our last recourse is to attribute non-material properties to them: “Let’s confess it straightaway! We cannot reasonably discover any external side to atoms, so if we are to think anything at all, we must attribute an internal side to them, an inwardness [subjectivity] analogous to our own souls. In fact, how could a soul originate as a combination of atoms in an organism, if its germ were not already contained in the atom?”
Then there’s Roger Penrose, from his “Theory of quantized directions,” an unpublished manuscript:
A reformulation is suggested in which quantities normally requiring continuous coordinates for their description are eliminated from primary consideration. In particular, since space and time have therefore to be eliminated, what might be called a form of Mach’s principle must be invoked: a relationship of an object to some background space should not be considered — only the relationships of objects to each other can have significance.
Consider as well the following outtakes from Lee Smolin’s 2006 gem, The Trouble with Physics — perhaps the most elucidating popular science book I've read:
No observation in the last thirty years has been more upsetting than the discovery of the dark energy in 1998. What we mean when we say that energy is dark is that it seems to differ from all forms of energy and matter previously known, in that it is not associated with any particles or waves. It is just there.
We do not know what the dark energy is . What happened in 1998 was that observations of supernovas in distant galaxies indicated that the expansion of the universe was accelerating in a way that could best be explained by the existence of dark energy.
One thing that the dark energy might be is something called the cosmological constant. This term refers to a form of energy with a remarkable feature: The properties of the energy, such as its density, appear exactly the same to all observers, no matter where they are in space and time and no matter how they are moving. [In other words, this energy is constant (i.e. unvarying in time) and invariant (i.e. unvarying per observer, i.e. universal). Einstein’s postulation that these two qualities characterize the speed of light serves — along with the principle of relavitity of motion — as the basis of his special theory of relativity and hence as a fundamental element of his general relativity theory as well. There is at least this deep connection between the cosmological constant and light.] Because it seems to have no origin or explanation in terms of particles or waves moving in space, it is called cosmological — that is, it is a feature of the whole universe and not any particular thing in it.
People soon began to understand that quantum theory had something to say about the cosmological constant. Unfortunately it was the opposite of what we wanted to hear. Quantum theory — in particular, the Uncertainty Principle — appeared to require a huge cosmological constant. We know this is wrong, because it implies that the universe would have expanded so fast that no structure at all could have formed. The fact that there are galaxies puts very strong limits on how big the cosmological constant can be. Those limits are some 120 orders of magnitude smaller than the predictions given by quantum theory; it might just qualify as the worst prediction ever made by a scientific theory.
Something is badly wrong here. A reasonable person could take the view that a radically new idea is needed and that no progress can be made in the unifciation of gravity and quantum theory until this discrepancy is explained. Several of the most sensible people feel this way. One of them is the German theoretical physicist Olaf Dreyer, who argues that the incompatibility between quantum theory and general relativity can be resolved only if we give up the idea that space is fundamental. He proposes that space itself emerges from a more fundamental description that is quite different. This point of view is also argued by several theorists who did great work in the field of condensed-matter physics, such as Nobel laureate Robert Laughlin and the Russian physicist Grigori Volovik. But most of us who work on fundamental physics simply ignore this question and go on studying our different approaches, even if at the end of the day they do nothing to resolve it.
And so far, string theory has nothing to say about the greatest mystery of all, which is the meaning of quantum theory.
The principles that are hardest to give up are those that appeal to our need for symmetry and elevate an observed symmetry to a necessity. Modern physics is based on a collection of symmetries, which are believed to enshrine the most basic principles. No less than the ancients, many modern theorists believe instinctively that the fundamental theory must be the most symmetric possible law.
We need a theory about what makes up space, a background-independent theory.
The main unifying idea is simple to state: Don’t start with space, or anything moving in space. Start with something that is purely quantum-mechanical and has, instead of space, some kind of purely quantum structure.
Thus many quantum-gravity theorists believe that there is a deeper level of reality, where space does not exist (this is taking background independence to its logical extreme). [My emphasis.] It is thus not surprising to hear Edward Witten say, as he did in a recent talk at the Kavli Institute for Theoretical Physics at UC Santa Barbara, that “most string theorists suspect that spacetime is an 'emergent phenomenon' in the language of condensed matter physics.”
What many of us in quantum gravity mean when we say that space is emergent is that the continuum of space is an illusion. [Yet this is not going far enough, for these physicists conserve the classical idea of space in terms of a tinker-toy (i.e. quantum) structure defined against a three-dimensional background space (albeit featureless except for its topology) and a classical background time. They thus also conserve the classical notion of local causality.]
[F]or the last decade [Gerard 't Hooft] has been one of the boldest thinkers on foundational issues. His main idea is called the holographic principle. As he formulates it, there is no space. Everything that happens in a region we are used to thinking of as space can be represented as taking place on a surface surrounding that space. [Yet even a surface is a two-dimensional volume, a space.]
Indeed, 't Hooft’s ideas were in part an inspiration for Juan Maldacena, and some think the holographic principle will turn out to be one of the basic principles of string theory.
I believe there is something basic we are all missing, some wrong assumption we are all making. If this is so, then we need to isolate the wrong assumption and replace it with a new idea.
What could that wrong idea be? My guess is that it involves two things: the foundations of quantum mechanics and the nature of time. I strongly suspect that the key is time.
We have to find a way to unfreeze time — to represent time without turning it into space. I have no idea how to do this. I can’t conceive of a mathematics that doesn’t represent a world as if it were frozen in eternity. It’s terribly hard to represent time, and that’s why there’s a good chance that this representation is the missing piece.
That last paragraph from Smolin bears repeating and further emphasis:
We have to find a way to unfreeze time — to represent time without turning it into space. I have no idea how to do this. I can’t conceive of a mathematics that doesn’t represent a world as if it were frozen in eternity. It’s terribly hard to represent time, and that’s why there’s a good chance that this representation is the missing piece.
Even by Einstein’s formulation of relativity theory space (that which is measured by a ruler) and physical time (that which is measured by a clock; i.e. the periodicity of space) are abrogated in favor of their marriage (which marriage does not simply unify them but signifies the notion that time is more than just the periodicity of space, i.e. time is different than space and in this sense it is meta-physical) equated to a similar marriage of momentum and energy (alias matter). That equation seems to signify that energy is likewise really meta-physical and perhaps identical to meta-physical time. In other words, the equation suggests that the classical conjugation of these variables energy x time, which has the units of action is significant of reality. Which is to say, physical action as in the quantum of action is our best symbol for reality. Einstein’s performance of these marriages and their equation (his further marriage of those marriages) follows from his apotheosis of light per se. Light is more fundamental physically than are space and time and matter. Sure enough, with the publication of his “general” theory of relativity Einstein determined himself to spend the rest of his life generalizing that theory by way of light. “For the rest of my life I want to reflect on what light is,” he commented. (I imagine he emphasized the “is.”) Light, in fact, was the focus of Einstein’s entire career. Leonard Shlain, from his Art and Physics:
According to Einstein, light is elevated to a supremacy over both space and time. Indeed, it seems to be the very source of space and time. Prosaically, we believe light rays journey light-years across vast intergalactic distances. On the contrary, as the physicist Edward Harrison wrote:
Spacetime is constructed in such a way that the distance traveled by light is always zero. Light rays ... travel no distance whatever in spacetime. In the world of spacetime we are in contact with the stars.
In other words, Einstein’s general theory of relativity conserves the naïve yet useful concepts of space and time and momentum and energy while advancing the idea that the concept of light is more profound.
Shlain fairly suggests that modern visual art especially as it comes to us via Manet, Monet and Cézanne signifies the secondary or derivative nature of both space and physical time and that the greatness of such art indeed the greatness of modern art in general, including music and literature depends on this essentially prehistoric understanding of experience.
Consider the following from William Ivins’ Art and Geometry: A Study in Space Intuitions:
An odd and interesting fact is that physiological optics and perspective are actually in many ways very different from the monocular optics and perspective of the geometer and the photographic lens, and that our eyes, when we can invent situations in which they are not dominated by “conditioning,” give us returns that frequently are at variance with the constructions of the drawing board and the camera. All the world talks about “photographic distortion,” but without realizing that the “distortion” is no more in the photograph than it is in our mental habits and our visual mechanisms.
… [T]he forms produced by our modern geometrical perspective are conventions which, in spite of their practical utility and philosophical importance, are only a loose general rationalization of the actual sense returns of physiological binocular vision. …
Across the centuries the religious subject matter of art gradually became dramatic. This drama was full of action. Action implied relationships between human figures located in the same visual spaces and not in different ones. The artists began to dislike action at a distance, much as later philosophers and physicists have disliked it. By the end of the thirteenth century this had begun to have the most positive effects in both painting and sculpture. The artists saw groups as dramatic wholes and not as spatially unorganised congeries of symbols. …
Before the invention of the phonetic alphabet, man lived in a world where all the senses were balanced and simultaneous, a closed world of tribal depth and resonance, an oral culture structured by a dominant auditory sense of life. The ear, as opposed to the cool and neutral eye, is sensitive, hyperaesthetic and all-inclusive, and contributes to the seamless web of tribal kinship and interdependence in which all members of the group existed in harmony. The primary medium was speech, and thus no man knew appreciably more or less than any other which meant that there was little individualism and specialization, the hallmarks of “civilized” Western man. Tribal cultures even today simply cannot comprehend the concept of the individual or of the separate and independent citizen. Oral cultures act and react simultaneously, whereas the capacity to act without reacting, without involvement, is the special gift of “detached” literate man. Another basic characteristic distinguishing tribal man from his literate successors is that he lived in a world of acoustic space, which gave him a radically different concept of time–space relationships. Our own Western time-space concepts derive from the environment created by the discovery of phonetic writing, as does our entire concept of Western civilization. The man of the tribal world led a complex, kaleidoscopic life precisely because the ear, unlike the eye, cannot be focused and is synaesthetic rather than analytical and linear. Speech is an utterance, or more precisely, an outering, of all our senses at once; the auditory field is simultaneous, the visual successive …. The writings of Egyptian, Babylonian, Mayan and Chinese cultures were an extension of the senses in that they gave pictorial expression to reality, and they demanded many signs to cover the wide range of data in their experience — unlike phonetic writing, which uses semantically meaningless letters to correspond to semantically meaningless sounds and is able, with only a handful of letters, to encompass all meanings and all languages. This demanded the separation of both sights and sounds from their semantic and dramatic meanings in order to render visible the actual sound of speech, thus placing a barrier between men and objects and creating a dualism between sight and sound. It divorced the visual function from the interplay with the other senses and thus led to the rejection from consciousness of vital areas of our sensory experience and the resultant atrophy of the unconscious. The balance of the sensorium — or Gestalt interplay of all the senses — and the psychic and social harmony it engendered was disrupted, and the visual function was overdeveloped. This was true of no other writing system. … It’s metaphorically significant, I suspect, that the old Greek myth has Cadmus, who brought the alphabet to man, sowing dragon’s teeth that sprang up from the Earth as armed men. … It’s television that is primarily responsible for ending the visual supremacy that characterized all mechanical technology, although each of the other electric media have played contributing roles …. [T]he clash of the old segmented visual culture and the new integral electronic culture creates a crisis of identity, a vacuum of the self, which generates tremendous violence violence that is simply an identity quest, private or corporate, social or commercial …. [T]his is an age of information overload. … [T]he electric media always produce psychically integrating and socially decentralizing effects …. All over the world, we can see how the rise of the electric media are stimulating the rise of ministates …. [A] global theatre in which the entire world is a Happening. … The day of the individualist, of privacy, of fragmented or “applied” knowledge, of “points of view” and specialist goals is being replaced by the over-all awareness of a mosaic world in which space and time are overcome by television, jets and computers a simultaneous, “all-at-once” world in which everything resonates with everything else ….
E. H. Gombrich, in his Art and Illusion: A Study in the Psychology of Pictorial Representation, ties in Greek narration; and he sees in the transition, so distasteful to Plato, from heroic, holistic (Red/Dionysian, I say) high Classicism to free, particular (White/Apollonian) Hellenism, evidence of an emergent paradigm of space–time as stage or container:
… [W]hen classical sculptors and painters discovered the character of Greek narration, they set up a chain reaction which transformed the methods of representing the human body — and indeed more than that …. For what is the character of Greek narration as we know it from Homer? Briefly, it is concerned not only with the “what” but also with the “how” of mythical events. … [W]here the poet was given the license to vary and embroider the myth and to dwell on the “how” in the recital of epic events, the way was open for the visual artist to do likewise. … [A]nd so there would be every incentive for artists to explore the possibility of a convincing stage on which to place the hero in convincing light and space. … It is surely no accident that the tricks of illusionist art, perspective and modeling in light and shade, were connected in classical antiquity with the designing of theatrical scenery. It is here, in the context of plays based on the ancient mythical tales, that the re-enactment of events according to the poet’s vision and insight comes to its climax and is increasingly assisted by the illusions of art. … [M]y hypothesis would be merely that the Homeric freedom of narration was as necessary as the acquired skill of craftsmanship to open the way for the Greek revolution …. Once we are “set” for this kind of appeal to our imagination, we will try to look through the picture into the imagined space and the imagined minds behind its surface …. Narrative art is bound to lead to space and the exploration of visual effects, and the reading of these effects in their turn demands a different “mental set” from the magic rune with is enduring potency. But Plato was right when he felt that something had been sacrificed to this change: the timeless function of the potent image … had to be discarded in favor of an imaginary fleeting moment of time …. We remember that this was one of the shortcomings that Plato held against the [mimetic] painter, who could not represent the couch as it is but only as it appears from one side. If the painting is to make us into spectators of an imaginary scene, it has to sacrifice the diagrammatic completeness that was demanded by the earlier functions of art …. Psychologists who wanted to test the taste of Australian aborigines and showed them pictures of birds found it a disturbing element that the natives “disliked the absence of full representation, as when the foot of a bird was missing in an attempt to convey perspective.” In other words, they share Plato’s objection to the sacrifices of illusionism …. The creation of an imaginative realm led to an acknowledgement of what we call “art” and the celebration of those rare spirits who could explore and extend this realm.
R. W. Southern, in his classic The Making of the Middle Ages, emphasizes a strikingly similar though rather reversed contrast between the so-called Dark Ages and the Middle Ages: “The change in emphasis from localism to universality, the emergence of systemic thought, the rise of logic to these we may add a change which in a certain sense comprehends them all: the change from Epic to Romance.”
I see the following periodicity in history: Trojanism (Red/Dionysian) to Greek Classicism (White/Apollonian) to Romanism (Red/Dionysian) to the Dark Ages (White/Apollonian; extremes meet) to the Middle Ages (Red/Dionysian) to the Renaissance and the Age of Reason (White/Apollonian) to the Romantic and the Modern (Red/Dionysian).
The concepts at bottom of orthodox physics are too White/Apollonian, too simple, too naïve. As Einstein wrote to Schrödinger: “Hardly any of the fellows … can get out of the network of already accepted concepts, instead, comically, they only wriggle about inside.” In this respect, consider again the following from Arthur Fine’s renowned 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 [i.e. a corollary of the Principle of Separation], even if one not so highly prized.
Einstein defines physical theory as “a conceptual model for the comprehension of the interpersonal [my emphasis], whose authority lies solely in its verification.” Referring to quantum mechanics, he writes, “What does not satisfy me in that theory, from the standpoint of principle, is its attitude towards that which appears to me to be the programmatic aim of all physics: the complete description of any (individual) real situation (as it supposedly exists irrespective of any act of observation or substantiation).” Note the parenthetical use of the word individual, the parenthesis indicating Einstein’s feeling that the local/monadic/soulful viewpoint is so natural that a person is hardly required to acknowledge it as an assumption. In his “Autobiographical notes” Einstein explicates this assumption and in the process he implies that (any strong) solipsism is the chief principle to be countered, i.e. by a contrary principle, what I call the principle of relativity, the principle that others (i.e. other reals, other souls) exist:
A basic conceptual distinction, which is a necessary prerequisite of scientific and pre-scientific thinking, is the distinction between “sense-impressions” (and the recollection of such) on the one hand and mere ideas on the other. There is no such thing as a conceptual definition of this distinction …. Yet, one needs this distinction in order to be able to overcome solipsism …. But this is only the first step. We represent the sense-impressions as conditioned by an “objective” and by a “subjective” factor. For this conceptual distinction there also is no logical-philosophical justification. But if we reject it, we cannot escape solipsism.
“Body and soul,” he writes elsewhere, “are not two different things, but only two ways of perceiving the same thing.”
In his World as I See It, Einstein points up his belief that a Holy Grail of physics — in the sense of Grail-as-pathway — can be found:
If it is true that this axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? Nay more, has this right way any existence outside our illusions? … I answer without any hesitation that there is, in my opinion, a right way, and that we are capable of finding it …. I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other, which furnish the key to the understanding of natural phenomena …. In a certain sense, I hold it to be true that pure thought [mathematics] can grasp reality, as the ancients dreamed.
The “purely algebraical” physics anticipated by Einstein has been anticipated more strongly by some of his greatest successors. As I noted earlier, among Paul Dirac’s pet ideas was the notion that the basis of mathematics in general is due for a change. Consider in this respect the following account of Dirac’s method, as it were, this from Moore’s biography of Schrödinger:
Dirac’s approach to theoretical physics was quite different from that of Schrödinger; he was not interested in construction of … physical models, but was content to let mathematics be his guide, confident that if the mathematical analysis was reasonable, the physical picture would in most instances emerge eventually ….
Heisenberg’s matrix mechanical (alias quantum mechanical) formulation of atomic theory exemplified such approach. Heisenberg described the line of thought that led to his Uncertainty Principle: “Instead of asking: How can one using the known mathematical scheme express a given experimental situation? the other question was put: Is it true, perhaps, that only such experimental situations can arise in nature as can be expressed in the mathematical formalism?” Heisenberg arrived at that formalism simply by generalizing the mathematics used to account for the classical conjugate physical variables i.e. the classical married variables, in the sense that the more precisely you measure the one the less precisely you can concomitantly measure the other, e.g. position and momentum, energy and time, all of these conjugates/dualities having the units of action. He did this just by discarding the constraining commutative law of multiplication. You see, according to that law a x b = b x a. Without that all too familiar law/imposition, the directionality is given its due as a difference: a x b ≠ b x a, i.e. by simple algebra a x b - b x a ≠ 0. Heisenberg literally saw that this inequality made room for the non-zero quantum of action: a x b - b x a = the quantum of action. Already in full recognition of the dizzying, magical, principled nature of the quantum of action itself, Heisenberg now recognized that its equivalent in classical physical terms is the aforenoted equation a x b - b x a ≠ 0. He thus recognized that insofar as the quantum of action is simple (like a monad is simple) and is a principle unto itself — and insofar as classical physical terms are fundamental to any measurement — this physical equation which accommodates the quantum of action should be considered a principle: the Uncertainty Principle.
Consequently Heisenberg and Bohr and company were obliged to abandon the classical concept of a continuum path of a particle, which abandoment can be considered but a single step from abandoning the concept of space itself. Yet they conserved the concept of space and its classical corollaries because, generally in accord with Kantian philosophy, they believed that any measurement must consist of precisely such terms.
Physics can fairly be defined as measurement/control theory, although as with all theory it must be based on a principle/belief (or set thereof) which is necessarily unmeasureable/mysterious. Since the classical physical terms are seemingly the only terms of measurement/control, and since they seem to be fundamentally inapplicable to any supposed intrinsic structure of the quantum of action, that mysterious unit as it were was indeed embraced by Heisenberg and Bohr as being a simple unit, a simple quantum, without any intrinsic physical structure and inherently fundamental. This is the meaning of the Uncertainty Principle; which is to say, this is the meaning of quantum/matrix mechanics (again, in contrast to Schrödinger’s wave mechanical formulation of atomic theory). But if we can allow ourselves to consider measurement a more general thing than the control of classical physical concepts of space and time — especially of space, for time is classically measured in terms of space — then we can conserve the notion that physics is essentially measurement/control theory whilst we seek (and perhaps find) a different, deeper (if you will) meaning of atomic theory. This is to say, we can consider the quantum of action as being symbolic or corollary of some principle or set of principles and as probably having intrinsic physical structure. This is basically the way Schrödinger and Einstein considered atomic theory, although true to Spinoza they considered the quantum of action a mere corollary of an underlying continuum unity/reality; to their thinking the quantum of action was at best merely phenomenological, something to be acknowledged but basically looked past, a barrier to be overcome rather than something providential, something heuristic, something precisely indicative of a deeper, wider reality. Likewise Schrödinger and Einstein famously refused to abandon the classical notion of continuum particle paths; hence it’s fair to say that they conserved the classical concept of space more strongly than did Heisenberg and Bohr.
Dirac considered matrix mechanics “the general theory of all quantities that do not satisfy the commutative law of multiplication.” Writing to Heisenberg in 1967 Dirac said in regard to Heisenberg’s new and controversial unified quantum field theory:
My main objection to your work is that I do not think your basic (non-linear field) equation has sufficient mathematical beauty to be a fundamental equation of physics. The correct equation, when it is discovered, will probably involve some new kind of mathematics and will excite great interest among the pure mathematicians, just like Einstein’s theory of the gravitational field did (and still does). The existing mathematical formalism just seems to me inadequate.
Dirac in 1977 wrote:
… 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, 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.
Mathematics was Dirac’s muse. To his way of thinking Heisenberg had begun correctly, greatly satisfying the gods, if you will, by sacrificing the classical concept of continuum particle paths upon the profoundly heuristic altar of mathematics, but unfortunately Heisenberg stopped attending this altar; contrariwise Schrödinger always attended the altar but he never brought with him a sufficient sacrifice.
Dirac called for sacrifices such as the following suggested by the contemporary Dutch physicist Gerard ’t Hooft, one of the greats of particle physics. In his contribution to Jan Hilgevoord’s anthology Physics and Our View of the World ’t Hooft writes:
“Superstring theory” is almost certainly not the answer [i.e. not the way to express the supposed “single ultimate Law of Physics underlying all particles and forces”].
… I will try to explain what I mean by the complete merging of theoretical physics with mathematics [i.e. the form in which said Law may need to be expressed; my emphasis]. …
Allow me for a short while to speculate that there is indeed a simple dynamical law [my emphasis; physics, I think, is not in itself dynamical but rather it is significant of dynamos, souls], waiting to be discovered. As I explained and emphasized earlier, the practical implications would hardly be noticeable. It is almost certain that such a law will rapidly produce chaotic behavior, so that even the most elementary calculations using this law as a starting point will be cumbersome at best, impossible in most cases.
But from a more philosophical viewpoint the implications would be immense. We would have to conclude that what we used to call “Nature” is actually something like a mathematical processor, much like the processors we have inside our computers, just quite a bit bigger and faster.
It is not obvious that Nature’s own mathematical processor works like ordinary ones. Most physicists would argue that, since we have quantum mechanics, Nature’s processor will have to obey “quantum logic” instead of ordinary logic. This is a widespread belief which, as I stated earlier, I do not share. What physicists at present call “quantum logic” may well be nothing but the best representation of our present understanding of the laws of physics, but may not necessarily be the ultimate truth. From a philosophical point of view it could not have been otherwise than that our first attempts at formulating the laws of physics should contain statistical elements; all those degrees of freedom or variables that we do not understand at present just look like random noise to us. Experts will no doubt recognize in these words the “conjecture of the hidden variables”. Since several simplistic versions of such theories have been ruled out in the past, the notion of hidden variables is no longer very popular in theoretical physics. So I will try not to emphasize my personal belief in some more advanced version of hidden variables, but I won’t hide it either.
Whatever the logic, quantum or classical, random or deterministic, let us suppose that there exists a well-formulated physical law …. Then I claim that there should also exist some prescription concerning the order in which the law or laws should be applied to calculate how the numerous physical degrees of freedom evolve. It is this order that I would identify with “time”. One must first calculate how “early” degrees of freedom evolve, and only then one has the necessary data to calculate how “later” degrees of freedom will behave. Without a good prescription of the logical order the laws will not be unambiguous. …
I can even go a step further. If our universal law [i.e. the aforementioned ultimate Law of Physics] is sufficiently simple, one could just as well conclude that the entire universe [i.e. the structure of experience in general] is nothing but an enormous series of mathematical combinatorial “theorems”. The mathematical theorems are time ordered. Time ordering is indeed also the order of logic: first come the theorems that were relatively easy to prove, then come the theorems that require the previous theorems to be proven first. Now many mathematical theorems are in some sense “equivalent”: they require tremendously complex calculations for their proofs, but one theorem follows directly if we know the other. …
A simple example of an infinite series of “theorems” is the series of prime numbers [my emphasis]. To prove that a large number is a prime number you first need to know the smaller prime numbers. Thus, the series of prime numbers in some sense form their own universe indeed, one can represent the prime numbers as a four-dimensional table just like our real universe! If mathematicians could prove that all combinatorial theorems in number theory ultimately are connected to knowing the complete series of prime numbers, then our universe “is” the series of prime numbers! This is what I referred to in the summary as the complete merging of theoretical physics with pure mathematics.
This suggestion by ’t Hooft is the initial reason why I focused on the Fibonacci series of numbers as a possible basis of physics. I eventually coupled that focus to several important recognitions: (a) the Fibonacci series is best considered a series of lengths relative to a unit line (i.e. as being a structure, a geometry, if you will); (b) such quantum structure is strikingly analogous to the albeit continuous, mass-embellished Riemannian 3-spaces which are the most simple basis of the orthodox general theory of relativity; (c) similarly the measurement of length is, as Mach emphasized, “the foundation of all measurement”; and (d) the Fibonacci structure is a fractal, and as such each quasi-recrudesence of the whole within the whole can be considered a particle (more specifically, you might say, a holon). (Strictly speaking such recrudesence “occurs” at every Fibonacci division of the unit line; but some of these occurences/divisions represent the whole much more saliently.)
According to our prehistoric heritage, distance is — precisely like the hydrogen atom — hierarchical. What’s more, primitively speaking distance is not extension but rather the structure of immediacy, which immediacy is, according to the principle of relativity, a medium. Space does not really exist. Space, indeed, has never happened to you. You have never been in space. Space — as a mere yet almost extremely useful concept — has been in you. Everything that has happened to you has been absolutely immediate to you. This fact is just as true for, say, the astronauts of the Apollo missions to the Moon. The Moon exists, but only in terms of the structure of (immediate) experience. Nowhere is the Moon but distributed within the essence of each of the infinite number of minds which are inasmuch tempted to travel to it. Infinity is an awful lot to be related to. It does all the heavy lifting. Infinity gives to airy nothing not only a local habitation and a name but a virtual concreteness. It all but multiplies entities. The Moon is as concrete as concrete gets, but that doesn't mean it really exists. A center of the cosmos, the Moon exists nowhere and everywhen. The Moon is a nexus of Time within all times — as is every object of significance, every measurable thing. Ironically, the exploration of the universe will involve the abandonment space. The universe will be explored on the basis of a physical theory according to which space does not exist. The concept of space is very useful but not extremely useful, for it cannot be used to explain all the physical structure we experience. To put this another way, the present impasse in physics is so great it can only be overcome by removing from it something as big as space itself.
Why do I consider the Fibonacci structure the single best possible symbol of the set of souls/monads/observers? The Fibonacci structure is corollary of the following relationship: segment AC′ is to segment AC as segment BC′ is to segment BA, where B, C, and C′ can fairly be said to represent any 3 segments of a finite line which are immediately similar to each other, i.e. minimally different.
As such, every segment of the Fibonacci structure is unique yet related to every other such segment — and this in the simplest way possible. Thus we have an optimal mathematical mingling of simplicity and generality. In a word, we have an extremely beautiful structure. Corollary of the entire Fibonacci structure is an infinite algebraic series, the famous Fibonacci series (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …) in which each term happens to be the sum of the pair immediately “previous.” These numbers are the denominators of the fractions produced by the holistic rule that codes the Fibonacci structure. The Golden Mean, as you may know, is precisely the limiting value, as the Fibonacci series of numbers grows, of the ratio between any single number in the series and its immediate predecessor in the series: Phi = 1.61803…. This Golden Mean or Golden Ratio is an irrational “number”; it cannot be perfectly written as a ratio. In other words, the Golden Mean is a function, not a number. The Fibonacci structure can also be symbolized by the equation n2 = n + 1 or (taking the square root) n = √(n +1) or (dividing both sides by n) n = 1 + 1/n or (repeatedly replacing the particular, far n by the whole symbol of n)
This sort of fraction is called a continued fraction, but I like to call it a functional fraction instead. Because this particular functional fraction is composed of 1’s only, it converges very slowly — extremely slowly. In this sense the Golden Mean — the limit of this functional fraction, i.e. the “number” toward which the function converges — is the most irrational of all so-called irrational numbers; i.e. it resists being represented as a fraction more than does any other irrational number.
Obviously this (or these) equations — especially the corollary functional fraction — are extremely beautiful, in the mathematical sense. Indeed I think we have here the equation(s) adumbrated by the great physicist Paul Dirac: the general equation of so-called particles (both of “matter” and of “space”), the “quantum” (in truth, function) of action, the so-called Hamiltonian, the best possible symbol of the principle of (extreme) action. Likewise we have the new, non-whole-number mathematics anticipated by Dirac; as well as the new, non-continuum, non-spacetime i.e. non-field mathematics Einstein thought could be the only alternative mathematical basis of physics (although, as he said, he had “not the slightest idea what kind of elementary concepts could be used in such theory”). As such, I think the various versions of the final equation of physics are those presented above.
But how can all the tremendously rich order of the universe be reducible to the Fibonacci structure? As I’ve said, the goal of physics is to describe space and matter and light and boundary conditions as being the same kind of thing. More poignantly put, all physical structure should be considered both light and boundary conditions. But light as such should be considered symbolic of time in general, i.e. of action in general, of dynamos. Time is meta-physical. Time is a soul and moreover the whole set thereof. Which is to say, time is experience, reality in contrast to (physical, spatial/material/radiational, mathematical) being (i.e. determination). There is precisely no need to explain time. Time rather is undoubtedly experienced, and it is generally postulated in terms of the principle of relativity. In other words, light — including what we call space and matter — is the structure of time, the essence of existence. Light and matter do not really move through (or on) space; they along with space are really intrinsic to a soul; they are the mere structure of a soul.
But again, how can all the tremendously rich order of the universe be reducible to the mere Fibonacci structure? Answer: Because the Fibonacci structure corresponds to the so-called hydrogen atom. The initial 3 segments within the structure correspond to the 3 “quarks” which constitute the proton. The term quark, owes to physicist Murray Gell-Mann’s reading of Finnegans Wake: “three quarks for Muster Mark ….” Gell-Mann is famous for discovering quarks in 1964 or so and for mainly in consequence receiving the 1969 Nobel Prize in physics. Yet in 1969 Gell-Mann’s colleague and foil at the California Institute of Technology, the even greater physicist Richard Feynman, quite independently developed and proposed a model of nuclear collisions that was based on pointlike particles he called “partons” embedded in protons, which protons he imagined as being 2‑dimensional pancakes. These partons were soon understood to be equivalent to the quarks and gluons elemental to Gell-Mann and company’s quantum chromodynamics (QCD), which remains our theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton and neutron. Yet as James Gleick emphasizes in his biography of Feynman, Genius: “Gell-Mann, more than any other physicist of the sixties and seventies, defined the mainstream of the physics that Feynman had reminded himself to disregard.” About partons, Gleick continues:
Feynman’s essential insight was to place himself once again in the electron, to see what the electron would see at light speed. He would see the protons flashing toward him — and they were therefore flattened relativistically into pancakes. Relativity also slowed their internal clocks, in effect, and from the electron’s point of view, froze the partons into immobility.
It’s a remarkably small leap from Feynman’s frozen pointlike particles embedded in a 2-dimensional pancake-of-a-proton to the finite 1-dimensional lines of the Fibonacci structure understood as the face of an infinitely complex and extremely symbolic yet extremely simple frozen clock, the ultimate universal clock. (Even a frozen clock represents time: it symbolizes time.) And indeed, why stop at 2 dimensions? Why not go on to 1 dimension, or to an infinite number? The Fibonacci structure gives us both and thus it gives us a completely non-arbitrary dimensionality.
According to my analysis presented in the subsequent volume of this trilogy, the 4th Fibonacci segment is the single least resonant segment — i.e. the least holistic, least beautiful segment — in the entire Fibonacci structure. Inasmuch, that segment is a pseudo separation, a pseudo transition, a virtual break between the 3 segments that go before it and the infinite number thereof which follow, and it is the most extreme such within the entire structure. Moreover, the Fibonacci structure is a fractal; it quasi-recrudesces within itself an infinite number of times. In other words, the Fibonacci structure is quasi-periodic. To see this fractal/quasi-periodic essence, peruse the list of Fibonacci numbers presented at www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html, noting only the character (and perhaps its immediate neighbor or neighbors) occupying the highest place, i.e. the character (or characters) to far left. … In general such recrudescences occur absolutely ubiquitously throughout the structure; but the most salient recrudescences occur every 67 divisions of the unit line. (Recall in this respect that the Fibonacci series exhibits marked 5-fold, 12-fold and 60-fold symmetries as well.) According to my theory each such 67-fold recrudescence corresponds to a unique “electron energy level” in contemporary orthodox physics, the 3 subsequent Fibonacci segments corresponding to the so-called electron itself. As such the beginning of the 2nd electron energy level corresponds to the 134th Fibonacci division, while the outer termination of that level corresponds to the 137th Fibonacci division. Here we have the basis of the so-called “fine structure constant,” the dimensionless scalar absolutely and extremely crucial to but not determined by contemporary orthodox physics. For orthodox physics to accurately predict experimental results, the value of this constant must be set to 137.0359975 ± 0.00000050. Yet the great cosmologist Arthur Eddington famously although rather imprecisely reasoned that the fine structure constant should be exactly 137.
With respect to this number 137 the following coincidences are fun to consider. Suffering a chronic disease of the spine, Alexander Pope grew to be only 1.37 meters (4 feet 6 inches) tall. The great physicist Wolfgang Pauli’s untimely death occurred in hosptial room 137. Levi, father of the priests of Israel, died aged 137 years. Amram of the house of Levi, and father to Aaron and Moses, died aged 137 years. The unique numerical values associated with the characters in the Hebrew word Kabbalah sum to 137. The largest prime factor of 123456787654321 is 137. (Hence 137 is curiously related to the numbers 8, 7 and 15, the number 8 being significant of the existential, the complete, the feminine, and the number 7 being significant of the dynamic, the incomplete, the masculine. When the Osiris–Orion constellation is at the greatest height of its 25,776-year precessional cycle (e.g. c. 2070 CE), if you stand on the equator and look straight south and then bend your head back so that you can observe the starry environs about the celestial north pole, 137 degrees back from the southern horizon is the furthest angle of sight which will still allow you to fully see Osiris–Orion.
In terms of orthodox physics the formalisms of quantum physics coupled to the fine structure constant and the likewise dimensionless ratio of proton mass to electron mass are altogether said to determine almost completely the structure of atoms, molecules and further solid materials, as well as the behavior of light. As for said proton/electron mass ratio, it must be set to a value of 1836.1526675 ± 0.0000039 in order for orthodox physics to provide accurate predictions. As I explain in the subsequent volume of my Gravity trilogy, this value is essentially provisional yet by way of the Fibonacci structure it can in a sense be derived as being 1836.20895514, the difference between this value and the orthodox value being explainable, I presume, in terms of the provisions of orthodox physics.
The orthodox physical description of the hydrogen atom is our culture’s chief tool by which to describe the more complex atoms and molecules — even though the mathematics thereof cannot be solved for any system involving more than just 2 bodies, i.e. for any system other than mere hydrogen. I think the Fibonacci structure will prove to be a better tool for doing this indeed the best.
and a representation of the famed Fibonacci spiral.
The more a soul’s experience holographically resonates (i.e. ramifies) the whole Fibonacci structure the more ordered is that experience. Order is based on but different than structure.
This difference between order and structure is the fundamental difference that Leibniz did not account for, and as such it marks the fundamental difference between Leibniz’s theory of monads and my theory of pleiads. According to Leibniz, the action of a monad cannot be described as affecting other monads; i.e. every monad is “windowless.” I think this notion fails to give the principle of relativity its due, for such affection is supposed in the very principle of relativity. Here again is my reformulation of Mach’s principle: every action is related to every other such action within the whole set of souls (i.e. real particles, real quanta). True, there is no sense according to which this relativity can be explained; it must be postulated. The principle of (extreme) action and likewise the quantum of action cannot be explained as anything other than corollaries of the principle of relativity. Harmony is not merely “pre-established”; rather it is supposed (i.e. postulated) to be the very nature of existence in general, utterly and ubiquitously miraculous. The structure, the essence, of a soul is not affected by action. But the order of a soul is affected by all action. This is to say, the order otherwise intrinsic to a soul is determined not only by that soul but by the otherwise free action of all souls. In this sense a soul gets virtually all of its order “for free.” Again, infinity does all the heavy lifting. Order is not pre-established but actively (i.e. miraculously) created, although its structure is absolutely constant and in this sense pre-established. Order can be (albeit miraculously) controlled, but it can be understood only in terms of the Fibonacci structure. In this structural sense the universe, as I've emphasized, is hierarchical (just like the hydrogen atom), proto-mythological.
Mathematicians have hardly begun to explore the wilderness which is the Fibonacci structure, yet many recognize it as being extremely important. In this respect consider the recent pioneering work of Prof. Divakar Viswanath, a doctor of applied mathematics, formerly of the Mathematical Sciences Research Institute (MSRI) in Berkeley, California, and now of the University of Michigan. As you know, the ratio of any Fibonacci number (i.e. length) to its immediate predecessor in the series approaches Phi as the numbers get larger. Therefore we can say that the Nth Fibonacci number is approximately equal to the Nth power of Phi. This approximation gives us a way to calculate the Nth Fibonacci number without generating the entire sequence of preceding Fibonacci numbers: PhiN / √5, rounded to the nearest whole number. But, asked Viswanath, what if at each step in the construction of what is otherwise the Fibonacci sequence we at random either (a) generate the next number using the Fibonacci algorithm or (b) instead reverse that algorithm such that the next number is constructed by subtracting the present number from its immediate predecessor? What kind of order – if any — will the consequent series exhibit? Until 1999 this was an open if not unasked question. In the autumn of that year, Viswanath published his results proving that such a randomized Fibonacci algorithm is characterized by its tendency to produce a series in which the absolute value of the Nth number is approximately equal not to the Nth power of Phi but to the Nth power of another (almost surely) irrational “number”: 1.13198824… (where the “…” indicates both the supposed irrationality of this “number” – which, as with pi, is really a function — and also the fact that Viswanath’s method of approximating it, i.e. his function’s approximation of the function, is accurate to 8 digits beyond the decimal point). Way back in 1960, Hillel Furstenberg (now at the Hebrew University) and Harry Kesten (now at Cornell University) proved — using randomized matrix multiplication — that there is a general class of algorithms – including the Fibonacci algorithm – which when randomized are characterized by the tendency for the absolute value of the Nth number of their consequent series to approach the Nth power of some constant “number” (i.e. function) universal to that class of algorithms. (See the book Random Products of Matrices With Applications to Infinite-Dimensional Schrödinger Operators, by P. Bougerol and J. Lacroix, published by Birkhauser, Basel, in 1984.) Well, Viswanath finally found that “number.” Viswanath describes his approach to finding this mysterious number as follows: “The problem was that fractals were coming in the way of an exact analysis. What I did was to guess the fractal and use it to find [the number]. To do this I made use of some devilishly clever work carried out by Furstenberg in the early 1960s.” Mathematician Keith Devlin, who is Dean of Science at Saint Mary’s College of California and a senior researcher at Stanford University, comments on the importance of Viswanath’s achievement:
Does Viswanath’s new result have any applications? Probably not – unless you count the fact that an easily understood, cute, counter-intuitive result about elementary integer arithmetic can motivate a great many individuals (your present columnist included) to take a look at an area of advanced mathematics full of deep and fascinating results that has perhaps not hitherto had the attention it deserves. Indeed, in that respect, the randomized Fibonacci sequence problem resembles Fermat’s Last Theorem. It too is easy to state and to understand, and yet it’s only a hairsbreadth away from some of the deepest and most profound mathematics of all time….
If it’s “real” applications you want, however, then you don’t have to go any further than the work of Furstenberg and Kesten that lays behind Viswanath’s recent result. Applications of that work have led to advances in lasers, new industrial uses of glass, and to development of the copper spirals in birth control devices. The research which led to those advances earned the 1977 Nobel Prize in physics for the three individuals involved: Philip Anderson of Bell Laboratories, Sir Neville Mott of Cambridge University in England, and John van Vleck of Harvard. The citation that accompanied the Nobel Prize to the three researchers declared it to be “for their fundamental theoretical investigations of the electronic structure of magnetic and disordered systems.” “Disordered systems” exist within noncrystallic materials that have irregular atomic structures, making it difficult to theorize about them. The key starting point for their work was to realize the importance of electron correlation [i.e. nonlocal causation]….
Anderson’s main contribution was the discovery of a phenomenon [now] known as Anderson localization, and this is where the random matrix multiplication comes in. Imagine you have a material, say a semiconductor, with some impurities. If you pass a current through it, you might expect it to get dispersed and diffracted in a random fashion by the impurities. But in fact, at certain energies, it stays localized. The first rigorous explanation of this used Furstenberg and Kesten’s work….
A similar explanation shows why you can see through glass. The irregular molecular structure of glass – it’s really a “liquid” – should surely cause some of the incident light rays to bounce around in a seemingly random fashion, resulting in a blurred emergent image. But as we all know, that’s not what happens. Somehow, the repeated random movements lead to orderly behaviour. Furstenberg and Kesten’s work on random matrix multiplication provides the mathematical machinery required to explain how this happens.
In terms of the present book you can understand how the ultimate Holy Grail — which I think is the Fibonacci structure — maps to the antique Holy Grail, that is, to the antique universal clock, i.e. to the antique universe as a whole but especially to the stellar constellations and especially to those constellations attending the circumpolar precessional ellipses. As such, all the foregoing mythological understanding attaching to the antique Holy Grail maps to the Fibonacci structure and likewise to physics.
For instance, the Fibonacci structure is a perfect symbol of the tein-eigen — the fire-forced or fire-need — of the Scottish Beltein festival, i.e. the festival of Bel/Baal/Lucifer/Kronos/Loki/Saturn/Upuat/Hermes/Nehushtan/etc. The tein-eigen generally corresponds to the “eigen function” (i.e. “eigen state” vector) and its corresponding “eigen values” in contemporary orthodox atomic physics. The most concise meta-symbol of such is the Golden Mean itself: the irrational number 1.61803…. In this respect, note the following amazing fact: sin (666) + cos (6 x 6 x 6) = - Phi = - 1.61803…. Perhaps whoever wrote the Bible’s book of Revelation was fully aware of the Fibonacci structure and understood that it symbolizes the Red/Dionysian and, deeper still, the Black/Baroque. The book of Revelation says of itself that it was revealed on the island of Patmos. The island of Patmos is within sight of the island of Samos, birthplace of Pythagoras. “Wooded Samos,” as Homer refers to it, is where Dionysus fought the Amazons on the “blood red field” — which field is likewise famed not only for its strikingly red sediments but also for the contrasting white and for the myriad monstrous prehistoric bones (many of the mastodon) which the ancients often found there and which they supposed the remnants either of Dionysus's Indian war elephants or else of a prehistoric race of monsters they called Neades. Note the island names: Pat and Sam, White/Apollonian and Red/Dionysian, respectively. The name Patrick means something like “father, fellow.” In a word, someone of the same kind. With this name the sense of sameness, of identity, is emphasized over the sense of difference, otherness. I think the name Sam connotes the contrary emphasis. The name Sam is associated with smallness and blindness and woundedness, which imply intuitive, spiritual, poetic, prophetic, mystical, that which though extremely familiar is different than the conventional. Hence we have the French word for Saturday, Saturn's Day: Samedi, a day of blindness, darkness, death, intuition, spirituality, difference, sacredness, secretness, this immediately before the day of the Sun.
At first glance the Fibonacci structure seems nothing like the antique Holy Grail. But in the etymology of the very word grail we can see the tremendous equivalence between them. The word grail is related most directly to the Medieval Latin gradalis, meaning “bowl.” Of course bowls have long been and continue to be intimately connected with the measurement of quantities (i.e. quanta). In this sense gradalis is related to the English words grade and graduation, which derive from the Latin gradus, meaning “step, degree.” The Latin gradi means “to step, to go”; and this word is cognate with the Lithuanian gridyti, “to go, to wander.” The Grail is not just the (determinate, physical) object of the mythological quest but more importantly it is that very action itself: the cyclical, heroic journey; time; reality; the soul itself, and moreover the set of souls. … The words grid, graph (meaning “to write”), and gramma (“letter”) are cognate with the above. Likewise grain (from the Latin grana, meaning “seeds”) and gram (meaning a “small weight,” like the carat we noted earlier; and also being the name of the sword which Sigurd, a.k.a. Siegfried, uses to kill the dragon Fafnir). Let’s not forget gravity and gravid. There’s also gratuity (implying, as it does, freedom) and gratitude and grace, from the Sanskrit grnāti, meaning “he praises.” What’s more we have the ancient Italian word for the Greeks: Graii, i.e. worshipers of “grey-eyed” Athena, Car/Cer/Cor/Kol/Kal/Bel/Bal/Hel/Hal/Hol, the terrible yet beautiful carrion or flesh goddess, the femme fatale, goddess of love/beauty and war, and more generally the Green Woman (Tree Woman, 3 Woman, Tres Woman, Troy Woman), whose Crone aspect is cognate and equivalent to Kronos and to the words crown, corona, chorus (“ring dance”) and cairn and to the titles/names Haran, Hermes/Carnival/Tristan/Drustan (i.e. the herm/cairn/boundary/tree/3/phallus god, the Green Man). Other notable cognates of the word grail include: the Germanic ger, “spear, true”; the name Gertrude (as in the Hamlet legend); the P-I-E gherd, “to surround, enclose, hedge, gird,” and ghordo, “enclosure,” as in the goddess Hel’s (alias Persephone’s, Core’s, etc) walled underworld bastion (equivalent to Helen’s Troy and to the Trojan Horse, i.e. the Pegasus Square constellation, representing the tomb, the womb, the night) and likewise the Sanskrit grhá, “enclosure,” and the Lithuanian gardas, “pen” or “fold”; the Greek geronas, “crane” (as in the Greek Flood story involving Megaron); and the English grand and grave (from an Old High German word meaning “to dig”). Going further we can also recognize the following cognates: grease (from the Latin crassus, meaning “fat”), greed, gregarious (meaning “of a flock or herd”), and grief. And of course there is grape, which is related to the Old High Germanic word krāpfo, meaning “hook,” although the scatological, cyclic connection here should not be lost on us. In this sense grail is related to the word series, which has the following, very interesting etymology: it comes from the Latin serere, “to join, link together”; and this is akin to the Greek eirein, “to string together,” and to the Greek hormos, “chain, necklace,” and probably also to Eire, i.e. Ireland, and perhaps to the Latin sort-, sors, “lot”; all of which are related to our irony, from the Greek eirōn, “dissembler.” The word serere is related to the goddess Selene, who — in accord with the Great Reversal — is a Moon goddess. Indeed, the word crescent, from the Latin crescere, meaning “to grow,” is clearly cognate Christ. This word crescere is further akin to the Lithuanian šerti, “to feed,” and to the Greek koros, “boy,” as well as to our words create, credence, creed, cream, crepuscular, crest, creep, and cretin (as in the innocent wretch sacrificed). The crescent Moon is mythologically recognized as being akin to the grail-as-container; likewise it is recognized equivalent to the horns of a bull. The Roman name for Selene was Luna, this from the Latin lucēre, “to shine,” which word is cognate with the Greek leukos, “white.” Also cognate, as you know by now, are the name Lucifer and the Latin word for a primordial forest grove, lucus, “land burned off within a wooded enclosure.” The words for wolf — lupus, loup, and lycos, as in Zeus lykaos, Apollo lykaos, the Lyceum, lyssa, and melissai (i.e. “honey-wolves,” “bees”) — are further cognates thereof. The Middle Dutch lupen means “to watch, peer” and is likely the root of our loop and cognate with the Latin sinus (as in sinuous and sinusoid and sine and cosine), meaning “fold” (thus Sino for the Chinese, who are — far too simply, need I say — characterized by the slight fold of skin over their eyes). Looping movement of course recalls the movements of wolves, of serpents (which shed their skin like the Moon its shadow), the famously strange movements of Mercury, Venus and Mars, the structure of the labyrinth and of the intestines, as well as the heads of Humbaba, Medusa, and the Green Man.
The aforementioned serere, “to join, link together,” is curiously similar to the mysterious siren, which word stems from the Greek seirēn but is considered of uncertain origin. The Sirens of the Odyssey surely represent Aphrodite and the college of nymphs and likewise the Pleiades, bees, the priestesses of Delphi, etc. The Chambers Dictionary of Etymology reports: “An earlier sense of a mythical serpent is recorded in Middle English in 1340, in Ayenbite of Inwyt.” Most likely siren is closely related to the Latin serenus, “clear,” and hence to the aforenoted lucus. In connection with Aphrodite and the Pleiades especially, I suspect a further close connection to the Greek kýanos, “dark blue enamel, lapis lazuli,” as in cyanide and as in the Cynaean Rocks — alias the Planctae, i.e. the Moving (as in the planets), alias the Symplegades, which twin rocks correspond to the legs of the constellation Hercules and likewise to the heroic passage from death to life, i.e. the crossing of the River Lethe, River of Forgetfulness. The word kýanos is related to the Greek kynikós, “dog-like” (as in Anubis, Upuat, and the “Fox Star” Polaris) and to the modern word kinetic, as in the movements of wolves and as in luge (or lug, log, sled and slide; note the le/li- root), which vehicle was originally pulled by wolf-dogs (perhaps bringing amber, i.e. the missing Pleiad Electra, from the far north). The Nordic lugga/lugge means especially “to pull by the hair.” Likewise the Scottish lugge means “ear,” as in Earwicker. A lugger is a boat rigged with lug sails, this perhaps from the Middle Dutch luggen, “to fish with a dragnet.” (From the Odyssey: “But if you wish to listen, let the men tie you in the lugger, hand and foot, back to the mast, lashed to the mast.”) A luff is a turning of the bow of a ship (especially a square-sailed ship) into the wind (i.e. against the proto-mythological current); and this word luff is perhaps cognate with the Old Icelandic lōfi, “palm of the hand,” as in Loki and glove and Chiron and manos and Manu and manna — this latter from the Hebrew mān. (Cannibals, recall, fancy the hand the tastiest part of the human body.) The Latin lūdere means “to play,” as in the trickster Odysseus/Ulysses and the word lied, “song.” (Note the tri- prefix of trick, as well as the li/le-prefix of lied.) Another interesting cognate is the Latin lūgubris, “mournful, mourning,” as in ululation, Ulysses, lupus, loup, lycos, Lucifer, Lug, and Luna, this latter, again, from the Latin lucēre, which word is cognate with the Greek leukos, the Greek leíā, “booty,” and the modern English lucre; and all this is cognate with the Sanskrit rujáti, “he breaks, tortures,” as in travel, from the Old French travaillier, “to torture, labor,” the latter as in opera and Ops and optimum and likewise aristocrat. The word travaillier stems from the Latin tripalis, “having three stakes.”
Now, kynikós, “dog-like,” and kýanos, “blue,” are likely cognates of cynosure, which word means “center of attraction or attention” and formerly also meant “guiding star.” This word stems from the Latin Cynosūra, “Ursa Minor,” this from the Greek kynósura, “dog’s tail.” Ursa Minor — with its guiding star Polaris, apex of the heroic journey, full point (i.e. fat or gras point, as in Mardi Gras) of the antique Holy Grail — is the adze of the famous Egyptian Opening of the Mouth ceremony (and likewise of their ceremonious 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 is the heroic cycle, the Grail. The Pleiades correspond to this Little Dipper — this Tom Thumb, this Aquarius, this god of sea and river, this god of the vine — via the blueness of loss, via the blueness of sky and water and secret. In fact the Pleiades themselves are constellated in the form of a dipper or adze. …
Shlain emphasizes the fact that the color blue is extremely unique, the most White/Apollonian color, you might ironically say. Referring to the aforenoted research by linguists Brent Berlin and Paul Kay, Shlain writes: “Only in the most mature languages, belonging to the most sophisticated civilizations, does a separate word for the color blue make an appearance, and it usually does so very late in the culture's development.”
The following quotes serve as apropos punctuation to the closure suggested in this chapter.
“Into the core of Nature”
— Johann Wolfgang von Goethe, “True Enough: To the Physicist”
We have inherited from our forefathers the keen longing for unified, all-embracing knowledge. The very name given to the highest institutions of learning reminds us, that from antiquity and throughout many centuries the universal aspect has been the only one to be given full credit. But the spread, both in width and depth, of the multifarious branches of knowledge during the last hundred odd years has confronted us with a queer dilemma. We feel clearly that we are only now beginning to acquire reliable material for welding together the sum total of all that is known into a whole; but, on the other hand, it has become next to impossible for a single mind fully to command more than a small specialized portion of it.
I can see no other escape from this dilmemma (lest our true aim be lost for ever) than that some of us should venture to embark on a synthesis of facts and theories, albeit with second-hand and incomplete knowledge of some of them and at the risk of making fools of ourselves.
So much for my apology.
— Erwin Schrödinger, What is Life?
The history of physics in this century teaches us that this abandonment of earlier concepts is much harder than the adoption of new ones. We shall have to reconcile ourselves to that. But I believe that the chance of achieving full clarity in the physics of elementary particles lies only with someone who … is in a position to make this sacrifice, not with the understanding only, but also with the heart.
You see, to me it seems as though the artists, the scientists, the philosophers were grinding lenses. It’s all a grand preparation for something that never comes off. Someday the lens is going to be perfect and then we’re all going to see clearly, see what a staggering, wonderful, beautiful world it is ….
— Henry Miller
… the mind’s awe before the cognized mystery of the world [:] science itself is now the only field through which [this] dimension of mythology can again be revealed.
— Joseph Campbell, Primitive Mythology
The current situation is obscure. Existentialism has ebbed away. The scene in which one wishes to continue asking one’s questions is dominated by a philosophy of science which itself wants to be a science, and by a social philosophy that wishes to interpret itself as a social praxis. Both are important. But the steadily renewed awakening to an awareness of the plane on which true philosophizing really begins seems to me even more important. We cannot learn this otherwise than by entering into a dialogue with the great philosophers of the past. By asking questions ceaselessly, they were led to attempt to think of the whole as whole. Almost no one knows today (or knew then) how difficult (and necessary) this attempt is.
— Carl Friedrich von Weizsäcker, The Unity of Nature
Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise? How could we have been so stupid for so long?
— John Archibald Wheeler
I’m the first to admit that my Gravity trilogy is extremely ambitious. But ambition is the very essence of cosmology. Thankfully we are obliged to think of ambition — i.e. generality — as being profoundly related to simplicity. Heisenberg noted late in his life: “If … in the intensive search for new conceptual or formal possibilities, the correct proposal for the closed theory emerges, it has from the very outset an enormous power of persuasion, precisely because it cannot be at once refuted.” I suspect that Heisenberg in penning those words recalled the breakfast he and Sommerfeld had with Bohr in 1922. Directly after that meeting Heisenberg wrote to his parents: “One can easily come to terms with Bohr. … In any case it was determined that until now a proof against my views is not to be found anywhere; at most only [false] generalities and matters of taste speak against them.”
I think my theory of relativity occupies a remarkably similar position with respect to our present body of knowledge. What’s more, the single principle at bottom of this theory is so beautiful I think we might feel sorry for God were it not essentially true.