Tuesday, January 31, 2017

The New Model of the Universe

360° + 1 = 361 = 19 x 19
Note: 19 is the number of The Sun tarot card which is fitting for the SOLAR symbol of ⊙, the universal symbol of THE UNIVERSE. In the Flower of Life there are also 19 interlocking circles, and 19 veils the spectrum 1-9 (hence the Hebrew Eve = 19 = חוה), and signifies the fractal TENSEGRITY of the THE GEOMETRY of Ο Αριθμος, ‘The Numbers’ that coalesce into the Μονας, or Monad. Crowley also notes in Liber 777 that 361 veils the Tree of Life itself as the Supernal Triad (3), Yetzirah (6) and the pendant Malkuth (1). Thus, the Tree of Life has been effectually folded back up into a perfect balance.

     While I still plan to continue reading more of The Libri of Aleister Crowley on YouTube (See המלכ רשעא, and ItsAllInTheEgg), I plan on analyzing various other authors and subjects that I have come across in the past year which need more analysis. I am also currently involved in other mundane matters that take time and energy so I plan on focusing on staying on a particular topic per month. I am currently in the process of reading Konx Om Pax (1907), which consists of Liber 95 - The Wake World, Liber 41 - Thien Tao, The Synagogue of Satan, Ali Sloper and The Stone of Abiegnus which I plan to post as soon as I can.

     First to be considered here is the work of the Russian P.D. Ouspensky and his Armenian predecessor and teacher, G.I. Gurdjieff. Pyotr Demianovich Ouspenskii (Пётр Демья́нович Успе́нский) was born March 5, 1878 and died October 2, 1947. George Ivanovich Gurdjieff was born January 13, 1866/72/77? and died October 29, 1949. Gurdjieff's teachings were more mystical and ambiguous, but Ouspensky worked to make them more apprehend-able to general readers with his books, though they go a bit deeper into certain philosophical speculations of his own about the Fourth Dimension, the Fourth Way, and more. The Fourth Way teachings, from what I have read so far, seem to be quite pertinent for many reasons. I shall however say at the outset that this post is not specifically about these men or their ideas, and I will probably mention numerous other things in due course but as I read, integrate and understand more I will continue adding additional considerations in forthcoming posts.

     Although I have seen The Fourth Way numerous times at various bookstores over the years, it is usually in tattered paperback condition and I didn't think it would be that relevant... so I never paid much attention to it. Then, a few months ago I came across Tertium Organum, and after reading the Introduction and first few pages of Chapter 1 I was intrigued and started looking more into the author and his ideas - having been already interested in Hinton's theories on The Fourth Dimension. I found a sturdy hardcover version of The Fourth Way and found that it is actually serendipitous that much of what it focuses on is what I personally feel I need to hear/(read) and put into practice right now in my life. I very much need to synthesize and put into use my knowledge and power, but in order to do that I have had to do much personal analysis and work to really know how. The idea of psychology first and foremost being a study of oneself which The Fourth Way heavily emphasizes is very important to me, and for the past year I have been having to face certain hidden, subconscious and hard-to-face aspects of my inner and outer self - and the statement Ouspensky makes, that our tendency to lie to ourselves is one of the biggest obstacles in the way of attainment of true awakening, rings true to me now perhaps more than it would have in the past - and something tells me it is perhaps one of the most relevant yet nearly forgotten books for all of us at this time.

     A primary teaching of both Ouspensky and Gurdjieff is that man is naturally very much mechanical, and because of his mechanical nature is largely asleep even when waking. Much of what we consider 'thinking' is actually reaction, or cause and effect-based responses which we have little to no real control over while confined to lower-mind dominated states of consciousness. The Higher or Transcendent Mind is that which one gradually comes to become aware of, or remember rather, through the processes of Initiation and Self-Remembering, and through which in working in accord with allows for individual and collective Evolutionary progress. Max Heindel, author of The Rosicrucian Cosmo-conception terms this process Epigenesis

     "The Force within the evolving being which makes evolution what it is and not a mere unfoldment of latent germinal possibilities; which makes the evolution of each individual differ from that of every other; which provides the element of originality and gives scope to the creative ability which the evolving being is to cultivate that he may become a God--that Force is called "Genius," and as previously explained, its manifestation is "Epigenesis."
      Many of the advanced philosophies of modern times recognize involution and evolution. Science recognizes only the latter, because it (Science) deals only with the Form side of manifestation. Involution belongs to the Life side; but the most advanced scientists regard Epigenesis as a demonstrable fact. The Rosicrucian Cosmo-Conception combines all three as necessary to full understanding of the past, present and future development of the System to which we belong." -Chapter 7, The Scheme of Evolution

     In physics, the field of mechanics is generally split among Classical Mechanics and Quantum Mechanics with sub-groups under these; the former dealing with ordinary physical objects and the latter dealing primarily with the sub-atomic level of physical objects and their dynamic interactions on the sub-atomic or meta-physical level. I want to here also quote Arthur Koestler since his statements on these matters are still very much relevant for us now and still have yet to sink in:

     "Physics is regarded by the educated layman as the queen of the 'exact sciences', with direct access to the immutable 'laws of nature' which govern the material universe. In contrast to this, parapsychology deals with subjective, capricious and unpredictable phenomena which manifest themselves in apparently lawless ways, or in direct contradiction to the laws of nature. Physics is, as the academic jargon has it, a 'hard-nosed' science, completely down to earth, whereas parapsychologists float somewhere in nebulous Cloud-cuckoo-land.
This view of physics was indeed perfectly legitimate and immensely productive during the roughly two centuries when the term 'physics' was practically synonymous with Newtonian mechanics. To quote a contemporary physicist, Fritzof [sic] Capra:
    "Questions about the essential nature of things were answered in classical physics by the Newtonian mechanistic model of the universe which, much in the same way as the Democritean model in ancient Greece, reduced all phenomena to the motions and interactions of hard indestructible atoms. The properties of these atoms were abstracted from the macroscopic notion of billiard balls, and thus from sensory experience. Whether this notion could actually be applied to the world of atoms was not questioned." [-page 50, Chapter 3 Beyond Language, The Tao of Physics, 1975]
Or, in Newton's own words:
     "It seems probably to me that God in the beginning formed matter in solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, and with such other properties, and in such proportion to space, as most conduced to the end for which he formed them; and that these primitive particles being solids, are incomparably harder than any porous bodies compounded of them; even so very hard, as never to wear or break in pieces; no ordinary power being able to divide what God himself made one in the first creation. 

    If you leave out the reference to God, the above quotation, dating from A.D. 1704, still reflects the implicit credo of our educated laymen. Of course he knows that the formerly indivisble atoms can be split (with sinister results); but he believes - if he gives any thought to the matter - that inside the atom there are other, truly indivisible billiard balls called protons, neutrons, electrons, etc. However, if he were sufficiently interested, he would also discover that the giant atom-smashers have made mincemeat of protons, neutrons, etc.; that the ultimate (to date) elementary particles are called 'quarks', (A term borrowed from Finnegans Wake, Quark in German means curds or soft cheese of a pungent and generally evil-smelling sort.) and that some quarks have a physical attribute called 'charm'. The exotic terminology of sub-atomic physicists also includes 'the eightfold way', 'strangeness', and the 'bootstrap principle' - which goes to show that they are well aware of the surrealistic nature of the world they have created; behind the schoolboyish humour there is the awed recognition of mystery. For on this sub-microscopic level the criteria of reality are fundamentally different from those we apply on our macro-level; inside the atom our concepts of space, time, matter and causality are no longer valid, and physics turns into metaphysics with a strong flavour of mysticism. As a result of this development, the unthinkable phenomena of parapsychology appear somewhat less preposterous in the light of the unthinkable propositions of relativity and quantum physics. ...
    The concept of matter-waves, lauched in the 1920s by de Broglie and Schrodinger, completed the process of the dematerialization of matter. It had started much earlier, with Einstein's magic formula E=mc2 (Where E stands for energy, m for mass, and c for the velocity of light.) which implies that the mass of a particle must not be conceived as some stable elementary material but as a concentrated pattern of energy, locked up in what appears to us as matter. The 'stuff' of which protons and electrons are made is rather like the stuff of which dreams are made, as a glance at the illustration on p. 246 suggests. It is an example of the type of events which takes place all the time in the physcists' bubble chambers, where high-energy 'elementary' particle collide and annihilate each other or create new particles which give rise to a new chain of events. The particles in question are of course infinitesimally small and many have a lifetime much shorter than a millionth of a second; yet they leave tracks in the bubble chamber comparable to the visible trails which invisible jet-planes leave in the sky. The length, thickness and curvature of the tracks enables the physicists to decide which of the two-hundred-odd 'elementary particles' has caused it, and also to identify 'particles' previously unknown.
     But the fundamental lesson which bubble chamber and other sophisticated instruments teach the physicist is that on the sub-atomic level our concepts of space, time, matter and conventional logic no longer apply. Thus two particles may collide and  break into pieces, but these pieces may turn out to be not smaller than the original particles - because the kinetic energy liberated in the course of the collision has been transformed into 'mass'. Or a photon, the elementary unit of light, which has no mass, can give birth to an electron-positron pair which does have mass; and that pair might subsequently collide, and by the reverse process transform itself into a photon. The fantastic events in the bubble chamber have been compared to the dance of Shiva, with its rhythmic alternations of creation and destruction. 

    All this is a long way from the beguillingly simple Rutherford-Bohr model of the beginning of our century, that represented atoms as miniature solar systems, in which negatively charged electrons circle like planets around a positively charged nucleus. Alas, the model ran into one paradox after another. The electrons were found to behave quite unlike planets - they kept jumping from one orbit into another without passing through the space between them - as if the earth were instantaneously transferred into the orbit of Mars in a single jump, ignoring space. The orbits themselves were not well-defined trajectories, but wide blurred tracks, appropriate to the wave-aspect of the electron which was 'smeared' all over the orbit, and it became as meaningless to ask at what exact point in space the electron was at a given moment, as it was meaningless to try to pin down a wave. As Bertrand Russell has put it:
    "The idea that there is a hard little lump there, which is the electron or proton, is an illegitimate intrusion of common sense notions derived from touch." -An Outline of Philosophy, 1927

     The atomic nuclei in the model did not fare better than the orbiting 'planets'. The nuclei turned out to be compounds of particles, mainly protons and neutrons, held together by other particles and forces which defy any visual model or representation in terms of our sensory experience. According to one hypothesis, neutrons and protons race around inside the nucleus with velocities of about 40,000 miles per second - a quarter of the speed of light. As Capra put it: 
    "Nuclear matter is thus a form of matter entirely different from anything we experience 'up here' in our macroscopic environment. We can perhaps picture it best as tiny drops of an extremely dense liquid which is boiling and bubbling most fiercely." -The Tao of Physics, 1975

In earlier books I have discussed some of the most notorious paradoxes of quantum physics: Thomson's experiments which made the same electron go through two minute holes in a screen at the same time (which, Sir Cyril Burt commented, 'is more than a ghost can do'); the paradox of 'Schrodinger's cat', which can be shown to be both alive and dead at the same time; Feynman's diagrams in which particles are made to move for a brief instant backward in time (which earned him the Nobel Prize in 1965); and the 'Einstein-Podolsky-Rosen paradox' (or EPR paradox) to which I shall briefly return. The situation has been summed up by Heisenberg himself, one of the chief architects of quantum theory:
     "The very attempt to conjure up a picture of elementary particles and think of them in visual terms is wholly to misinterpret them... Atoms are not things. The electrons which form an atom's shells are no longer things in the sense of classical physics, things which could be unambiguously described by concepts like location, velocity, energy, size. When we get down to the atomic level, the objective world in space and time no longer exists."

-continue reading Chapter 13, Physics and Metaphysics in Janus: A Summing Up


    There is an epigenesis on a sub-atomic, or metaphysical level ('Below'), as well as the macrocosmic 'environment' ('Above') - and this cohesion in various systemic patterns of complexity have given rise to conscious life as we know it. Even EVERYDAY EXPERIENCES = 999 are indubitably and inextricably in flux, yet structured according to the Laws of Nature, as are the quantum bonds between the fluid components of quantum/atomic physics. The MECHANIKOS, or Mechanical Man (Mechanic) is a prototype of the Magician and Magus who also learn the laws of nature in order to work in better accord and harmony with them to yield the maximum benefit. MECHANIKOS has the value of 269, which as brought up in the last post is also that of VIPASSANA, or 'Clear Seeing'. (Note that Initiation also includes the ability to come into awareness, or 'sight' of the elusive details of the mechanics of nature which often seem to 'blend in' with the whole rather than analyzed in high definition.) Another book I want to recommend is TECHGNOSIS by Erik Davis, as it will come up more in forthcoming posts as it has deep connections to what is discussed here, and links the mechanical with the spiritual developments of history and modernity, and aptly aligns to the value of 666 as well. I found this value to be quite fitting for the subject matter since 666 itself contains the Gnosis to our further technological integration and is itself a type of HIGH DEFINITION HOLOGRAM.

     As anyone with an understanding of BASIC MATHEMATICS has come to see the underlying reality of mathematical applicability of a multitude of formulae or functions among virtually any object, scenario, circumstance, or equation, such elastic practicality does not negate its pragmatic value nor diminish its usefulness, instead it qualitatively helps and develops a deeper awareness, understanding and solubility. Ironically, 269 is also the value of 'UNAWARE', which is interesting considering the uninitiated and il-LITERATE in Qabalah and Gematria are for the most part unaware of THE FRACTAL pattern underlying their own Logos. The central 'mainframe' of the individual is known as the AHAMKARA, or 'Created I' or Ego-function and equates with the Ruach or 'Breath' of Yetzirah, the Formative World, otherwise known as the Psyche. This 'plane' is considered 'metaphysical' being as it is indwelling or subsiding as the Foundation (the name of Yesod, the 9th Sephira) of what we know of as dense, physical 'Matter' (Malkuth).

     The spoken word, although uttered in the physical realm of vibration and causation, arrives from the Higher/Inner mind or Sanskrit manas/Greek Nous and governed largely by internal grammatical logic. When we are speaking (or writing for that matter), and with a sufficient comprehension and fluency in one's language, it is not necessary to consult with the grammatical laws of sentence structure, and etymological basises of words in order to construct and convey an idea, and for it to flow in the most optimal and least convoluted manner it need be as near to the original and essential idea as possible, often in the shortest and most convenient manner. (Marshall McLuhan's 'The Medium is the Message' comes to mind.)

     This is perhaps best shown in poetry, where with often the least amount of words the most profound and sensational ideas can be conveyed.  Art too, however, is also a prime vehicle for impressing a particular resonance through the means of pattern as well as disorder in a somewhat different way, often without the use of language or obvious mathematical bounds - and the more provocative or visionary the piece, the better the reception and effectivity. This is because art especially has that distinct quality of being able to stimulate the emotional body and Higher mind, being - when they aren't merely utilitiarian products, or imitations of art - materializations of the Genius itself upon a medium, and in essence - Magick.

     Author and creator of GENERAL SEMANTICS, Alfred Korzybski has also shown in his works Manhood and Humanity, as well as Science and Sanity, that verbal language is an inadequate medium for true human expression and communication because the rudimentary foundations of verbal expression are at non-verbal or 'silent levels' of cognition. It is interesting to find that GENERAL SEMANTICS has the value of 777, which is ascribed to Crowley's own Qabalistic texts as well as both 'THE GEOMETRY OF WORDS' and the 'WORDLESS GEOMETRY' hinted at through the general semantics of gematria itself.
     Again, 777 is the value of the Hebrew 'OLVM H'QLIPhVTh', the World of the Shells or Qliphoth, as well as 'CYMATICS', the word which signifies the vibratory form of sonic shells. By considering the mathematical underpinnings of language we can more readily see the internal constituents and logical framework in which meaning and value is conveyed. There is an internal cohesion between word-meanings and their numerical weight/value as evidenced by the many seemingly innocuous words and their correspondent relationships with similar or related word-values, such as when you subtract a particular word-value from a related Chamber-value and find one or multiple potential corollaries.

    For example, 'VIBRATION' = 358, which is also the combination of SOUND + SILENCE, and subtracted from 777 = 419, both of these numbers happen to relate to the Serpent in Hebrew (358 = NChSh, Nachasch / 419 = TITh, Teth), which of course symbolizes the passivity and activity of the Kundalini, or Astral Light / 'One Substance' modulating its phase-state of manifestation . Relating to 'VIBRATION', 358 also enumerates 'FORMULAE', while correspondences of 419 would be 'CEREMONIAL', i.e. CEREMONIAL FORMULAE, or '419 = HOLOGRAM, and note that  'ASTRAL LIGHT' = 358 as well, illuminating and subsisting the 'NUMBER FIELD' of the Kundalini. Provided that you have an adequate database of component correspondences one could use such a method of blueprinting and analysis to investigate the interconnections and integration underlying any idea, concept or construct. Since the same 26 letters can be used to convey virtually any verbalization of meaning those letters are then to better be thought of as symbolic agents of communication of something more essential through them. In other words, common language is but the shell, or qliphothic vehicle, of thought and expression, and therefore but a simulacrum of the original intention or meaning, much as numerical symbols are but human conceptual devices used to convey alternative meanings depending on their use.

     Another simple example using 777 can be made via the word 'SPELL', which is obviously related to both basic linguistics, as well as the idea of magickal or ceremonial formulae. SPELL = 205, which subtracted from 777 = 572 = 'THE BOOK', therefore 777 = 'THE SPELL-BOOK' of CEREMONIAL FORMULAE. 572 is also 'MATHEMATICAL FORMULAS', which is what a 'Spell' is composed of in actuality. Sentences and spoken words have meaning precisely because of the logical organization in which they are composed, though this logical organizational mechanism operates from above the conscious, egoic level of awareness as evidenced by our ability to conceptualize and verbalize almost completely automatically, as if Mechanikos with Vipassana. (Note: ENGLISH VIPASSANA OF MECHANIKOS = 777.) These seemingly 'random' numerical values of words and phrases come together to consistently formulate significant equations in the Qabalah of Nine Chambers and evidences a quantum holography of data which shows that meaning which is conveyed through the device of language remains embedded in a non-local holographic format in which the part contains a seed-image of the whole, as said in regards to fractals, holons, etc.

     There may be a bit of confusion still about what the Qabalah of Nine Chambers truly represents, and this is better understood through the 'Key'(-hole) to the Chambers, signified by '0', Zero. If one is still thinking of numbers as dense, physical, immutable 'things' you are missing the point. The 'point' in mathematics is, after all, but an illusory conceptual device which has no real 'existence', and can be considered from any 'point' one chooses. The Zero can be thought of as the dynamic loop of fractal expansion effectively synonymous with Infinity, since it is both 'everywhere and nowhere' and the foundation of all being. Considering the Solar symbol of the Dot in the Circle, Zero and Infinity could be figured as the infinitesimally small 'point' which has no dimensions, and the outer rim of infinite expansion. The numerical spectrum lies between these two extremes, and can be thought of as a form of the Kundalini or Antahkarana, formulating the 'Matrix' of vibrational form. (Note: THE ANTAHKARANA = 358 = PURUSHA 'The Universal Principle' = THE PRANAVA 'The Cosmic Sound'.) Thus, this is why Zero is considered the 'Egg' of the All, and It's All in The Egg. Each Chamber is but a grade or level of density from 111 = THE AWAKENED / THE WHITE LIGHT signifying the three rays from Kether emanating into manifestation through deepening levels of cosmic integration until reaching THE ALIGNMENT with 'THE HIGHER POWER' of 999 which subsumes all others. These alignments direct the flow of the Astral Light/Ain Soph Aur/Azoth whose emanations formulate manifestation, and though they appear as mechanistic and deterministic formulae their conscious attunement enables fractal resonance and harmony whereas their misalignment causes reason for equilibrating processes. Perfect equilibrium, however, would effect a complete dissolution into the Absolute.


     999 has been left out of most analyses of Gematria, which is odd considering it is the most dense and insightful if deciphered with the Hebrew-English Gematria formula (i.e. Hebrew applied to English). 999 is the SANCTUM SANCTORUM of THE AGELESS WISDOM OF THE QABALAH and has many correlations with Quantum Mechanical terminology, such as the potential 'N-DIMENSION' [Nun final = 700] (and their EIGENSTATES.) which can imply any of THE DIMENSIONS OF SPACE which extend well beyond the 'Here and Now' of the I(s). The N-Dimension of the 0-field underlies all MATHEMATIC CONSTRUCTS, and since 999 is the correspondence to 1 in the sequence of 1,000, which itself symbolizes the Microcosm, it contains in mathematical reflection all potential coordinates of vibratory form. (Hence the EVERYDAY EXPERIENCES of 999 in APPLICATION. 999 being the inversion, or reversion rather (resurrection) , of 666 ('the Sun') - is thus the re-awakening of the Solar Soul-Conscious Self (Note: THE SOLAR-CONSCIOUS SOUL = 888 = THE COSMIC CHRIST = Ιησους, Jesus.)

     999 is also THE UNIFIED ELECTROMAGNETIC FIELD which physicists and philosophers have been at wits end to formulate for quite some time, as well as the MASTER HIERARCHY (See The Externalisation of the Hierarchy by Alice Bailey) which many other Orders have sought to reflect and establish as well (Such as the Hierarchy of Masters as set forth in Theosophical literature; see the writings of Helena Blavatsky and Alice Bailey in particular.) The Qabalah of Nine Chambers rightly understood and applied can help in accessing the ACCESS CODES of THE FOUNDATION OF EXISTENCE (which Yesod as the Foundation and the precipitory flame of manasic (mental) and kamic/karmic (biological) energy crystallizes into substance (Malkuth/Matter) and perceived as 'EVERYDAY EXPERIENCES' of the mundane order, which itself is really combinations of infinite interactions and events of cyclic and novel circumstance (sub-atomic, nuclear, as well as geologic and cosmological). Thus, the Qabalah of Nine Chambers can be seen itself as a sort of filing cabinet of its own, as the Tree of Life itself has been said to be, but which exists on Akashic levels within the holonic or fractal QUANTUM LOGIC (333) SOURCE CODE (666) of the 'Zero Point'. (Note ZERO POINT + DARK ENERGY = 999).

     666 is known commonly as the 'Solar Number', being as it is the SUM (60+6+600 [Mem final]) of 1 through 36 (6x6), 6 being the number of Tiphareth, the Sun, on the Tree of Life. 666 is also the number of THE CIRCLE, which is symbolic of the micro- and macrocosmic CYCLIC LAW (=111=WHEELS, [within wheels]) of BOUNDLESS MANIFESTATION (999). 000 is The Limitless Light, thus 999 is the Boundless Manifestation of THE CONTINUUM OF MATTER, and THE STRANGE-LOOP EGG of THE KUNDALINI SPECTRUM
     666 has been veiled in many ways, consciously and unconsciously, as has been shown in numerous examples given in previous posts. When the value of GEMATRIA, 269 is subtracted we get 397, which is that of 'META-GEOMETRY' [Thus, THE FRACTAL METAGEOMETRY = 666], a subject explored extensively by Ouspensky in Tertium Organum, which I highly recommend reading. His considerations have yet to be fully understood or integrated, although it is insightful in regard to what can be gleamed through the development of qabalistic wisdom and understanding. 397 is the number of the Hebrew PhNIMI AVR, a title of Kether meaning 'The Inner Light', as well as the English 'INNER FLAME', and THE MATHEMATICAL POINT at the heart of the O which also relates. 397 is interesting because it is also mentioned in Liber OKBISh (See page 273 of The Ninth Arch, by Kenneth Grant, 2002) relating again to the 'New Knowledge' which cropped up in Opening the Watchtowers. The verse and Commentary is below:

397-21. at the heart

  397 is a form of AOSSIC (AVSShIK); “at the heart” may refer to the core of the Sigil of Aossic – an egg, or simply the cypher, zero. It may be significant that this verse is attributed to the Path of Kaph. Kaph means ‘a palm’; together with the egg, the palm forms one of the clues given by Amalantrah to Crowley in connection with the “new Knowledge” which he was to find in the egg. [See Crowley, the Abuldiz and Amalantrah Workings’.]

     This is ironic in light of the considerations above, and be it remembered that 666 is not just the number of the Sun above, but also the Sun or 'Inner Light' within at the center of the Ruach, Η Φρην, 'The Mind', or Reason - as well as 'THE LOGICAL MIND' in straightforward terms and numerical correspondence. True Awareness and Truth itself must be experienced authentically and apprehended directly independently of conditional and mechanistic circumstances and second-hand sources, though subjective experience is not considered to be as valid as the objective - it is a large factor in the apprehension of the latter and need be considered as bias and attention level/scope/focus plays a major role in the acquisition and subsequent application of data. Furthermore, something else I found relevant which Ouspensky says about Meta-geometry is also quoted below:

 ...Speaking of mathematics, it is necessary to recognize first of all, as a fundamental premise, that correspondent to each mathematical expression is always the relation of some realities.
     If there is no such a thing, if it be not true- then there is no mathematics. This is its principal substance, its principal contents. To express the correlations of magnitudes is the problem of mathematics. But these correlations must be between something. Instead of algebraical a, b, and c it must be possible to substitude some reality. This is the ABC of all mathematics; a, b, and c are credit bills; they can be good ones only if behind them there is a real something, and they can be counterfeited if behind them there is no reality whatever.
    "Dimensions" here play a very strange role. If we designate them by the algebraic symbols a, b and ce, they have the character of counterfeit credit bills. For this a, b and c it is impossible to substitute any real magnitudes which are capable of expressing the correlations of dimensions.
     Usually dimensions are represented by powers: the first, the second, the third; that is, if a line is called a, then a square, the sides of which are equal to this line, is called a(squared), and a cube, the face of which is equal to this square, is called a(cubed).
     This among other things gave Hinton the foundation on which he constructed his theory of tesseracts, four dimensional solids - a(four). But this is pure fantasy. First of all, because the representation of "dimensions" by powers is entirely conditional. It is possible to represent all powers on a line. For example, take the segment of a line equal to five millimeters; then a segment equal to twenty-five millimeters will be the square of it, i.e. a(squared) and a segment one hundred and twenty-five millimeters will be the cube - a(cubed).
     How shall we understand that mathematics does not feel dimensions - that it is impossible to express mathematically the difference between dimensions?
     It is possible to understand and explain it by one thing only - namely, that this difference does not exist.
     We really know that all three dimensions are in substance identical, that it is possible to regard each of the three dimensions either as following the sequence, the first, the second, the third, or the other way about. This alone proves that dimensions are not mathematical magnitudes. All the real properties of a thing can be expressed mathematically as quantities, i.e., numbers, showing the relation of these properties to other properties.
     But in the matter of dimensions it is as if mathematics sees more than we do, or father than we do, through some boundaries which arrest us but not it - and sees that no realities whatever correspond to our concepts of dimensions.
     If the three dimensions really corresponded to three powers, then we should have the right to say that only these three powers refer to geometry, and that all the other other powers, beginning with the fourth, lie beyond geometry.
     But even this is denied us. The representation of dimensions by powers is perfectly arbitrary.
     More accurately, geometry, from the standpoint of mathematics, is an artificial system for the solving of problems based on conditional data, deduced, probably, from the properties of our psyche.
     The system of investigation of "higher space" Hinton calls meta-geometry, and with metageometry he connects the names of Lobachevsky, Gauss, and other investigators of non-Euclidean geometry.
     We shall now consider in what relation the questions touched upon by us stand to the theories of these scientists
     Hinton deduces his hideas from Kant and Lobachevsky.
     Others, on the contrary, place Kant's ideas in opposition to those of Lobachevsky. Thus Roberto Bonola, in Non-Euclidean Geometry, declares that Lobachevsky's conception of space is contrary to that of Kant. He says:
     "The Kantian doctrine considered space as a subjective intuition, a necessary presupposition of every experience. Lobachevsky's doctrine was rather allied to sensualism and the current empiricism, and compelled geometry to take its place again among the experienced sciences." -pg. 92-93, Non-Euclidean Geometry, Robert Bonola, 1912
     Which of these views is true, and in what relation do Lobachevsky's ideas stand to our problem? The correct answer to this question is: in no relation. Non-Euclidean geometry is not metageometry, and non-Euclidean geometry stands in the same relation to metageometry as Euclidian geometry itself.
     The results of non-Euclidean geometry, which have submitted the fundamental axioms of Euclid to a revaluation, and which have found the most complete expression in the works of Bolyai, Gauss, and Lobachevsky, are embraced in the formula:
     The axioms of a given geometry express the properties of a given space.
     Thus geometry on the plane accepts all three Euclidean axioms, i.e.:
 1. A straight line is the shortest distance between two points.
 2. Any figure may be transferred into another position without changing its properties.
 3. Parallel lines do not meet.
     (This last axiom is formulated differently by Euclid.)
     In geometry on a sphere, or on a concave surface the first two axioms alone are true, because the meridians which are separated at the equator meet at the poles.
     In geometry on the surface of irregular curvatures only the first axiom is true - the second, regarding the transference of figures, is impossible because the figure taken in one part of an irregular surface can change when transferred into another place. Also, the sum of the angles of a triangle can be either more or less than two right angles.
     Therefore, axioms express the difference of properties of various kinds of surfaces.
     A geometrical axiom is a law of a given surface.
     But what is a surface?
     Lobachevsky's merit consists in that he found it necessary to revise the fundamental concepts of geometry. But he never went so far as to revalue these concepts from Kant's standpoint. At the same time he is in no sense contradictory to Kant. A surface in the mind of Lobachevsky, as a geometrician, was only a means for the generalization of certain properties on which this or that geometrical system was constructed, or the generalization of the properties of certain given lines. About the reality or the unreality of a surface, he probably never thought.
     Thus on the one hand, Bonola, who ascribed to Lobachevsky views opposite to Kant, and their nearness to "sensualism" and "current empiricism," is quite wrong, while on the other hand, it is not impossible to conceive that Hinton entirely subjectively ascribes to Gauss and Lobachevsky their inauguration of a new era in philosophy.
    Non-Euclidean geometry, including that of Lobachevsky, has no relation to metageometry whatever.
     Lobachevsky does not go outside of the three-dimensional sphere. Metageometry regards the three-dimensional sphere as a section of higher space. Among mathematicians, Riemann, who understood the relation of time to space, was the nearest of all to this idea.
     The point, of three-dimensional space, is a section of a meta-geometrical line. It is impossible to generalize on any surface whatever the lines considered in metageometry. Perhaps this last is the most important for the definition of the difference between geometries (Euclidean and non-Euclidean and metagometry). It is impossible to regard metageometrical lines as distances between points in our space, and it is impossible to represent them as forming any figures in our space.
     The consideration of the possible properties of lines lying out of our space, the relation of these lines and their angles to the lines, angles, surfaces and solids of our geometry, forms the subject of metageometry.
     The investigators of non-Euclidean geometry could not bring themselves to reject the consideration of surfaces. There is something almost tragic in this. See what surfaces Beltrami invented in his investigations of non-Euclidean geometry - one of his surfaces resembles the surface of a ventilator, another, the inner surface of a funnel. But he could not decide to reject the surface, to cast it aside once and for all, to imagine that the line can be independent of the surface, i.e. a series of lines which are parallel or nearly parallel cannot be generalized on any surface, or even in three-dimensional space.
     And because of this, both he and many other geometers, developing non-Euclidean geometry, could not transcend the three-dimensional world.
     Mechanics recognizes the line in time, i.e. such a line as it is impossible by any means to imagine upon the surface, or as the distance between two points of space. This line is taken into consideration in the calculations pertaining to machines. But geometry never touched this line, and dealt always with its sections only...

      His initial remarks of the conditional conceptualization and terminology of the dimensions can also be applied generally to any formulae, especially linguistically where, again, the word, symbol, number or other expression is but 'the map' rather than 'the territory', to allude to Korzybski's phrase that 'The Map is not the Territory', or the symbol is not the thing symbolized. There is however a caveat to this, in that despite the fact letters and numbers are but symbolic constructs - there is an inherent integration and conveyance of ideational, non-verbal, or essential meaning thereby and thus their job as vehicles remains useful. 'Things' are rarely so one-dimensional as to not be applicably described in a multitude of ways, though precision and acuity is important to balance the obtuseness of potential. The Solar symbol can be further considered as the Scope of COGNITION, which has a dual focus within and outwardly, and itself a symbolic cross-section of A METAGEOMETRICAL TORUS (777 = THE 361 [⊙] METAGEOMETRY). The Torus has been veiled in many symbols over time, as the 'onion-like' 'wheels within wheels' concept of the Sephiroth, the 'Heavens' and 'Hells', the 'Nine Worlds', etc. This is also synonymous with the Merkabah, 'Chariot' or 'Throne' - which reminds of Kenneth Grant's Outside the Circles of Time quote:
For there are Thrones under ground
And the Monarchs upon them
Reign over Space and Beyond

Invoke Them in Darkness, Outside
The Circles of Time

In Silence, in Sleep, in Conjurations
Of Chaos, the Deep will respond
From the Qabalahs of Besqul
     See Chapter 13 of Outside the Circles of Time, titled Qabalahs of Besqul, and page 176-178 in particular which give a typhonian model of the Qabalah of Nine Chambers (111-999). On page 59 of The Ninth Arch, Kenneth Grant mentions the Nine Arches or underground Chambers of the Masonic mythos, and also on page 19 of Beyond the Mauve Zone, 999 is mentioned as well:

"The Nu-Isis Workings had yielded the word or vibration necessary to complete and to invert the Magical Current of the Beast 666 by means of the formula 999, as demonstrated by:       Therion (666) + S'lba (333) = 999
     The number 999 is that of the Maatian 'Daughter' or 'Bride' who awakens the Eld of the Great Old Ones. Furthermore, 9 + 9 + 9 = 27, the number of the Path to which is attributed the letter Pe, meaning 'a mouth', a symbol of major importance in the gnosis of Maat. 27 is also the 'pregnant womb.' It is noteworthy, too, that 9 x 9 x 9 = 729, the number of Baphomet which Crowley received from the Wizard Amalantrah in 1918. (See The Amalantrah Working.) Baphomet is the name of the image which Crowley identified himself as Outer Head of the Order of Oriental Templars (O.T.O.) - as 'O.H.O.' this may also be rendered as Head of the Outer Ones, the Spawn of Nu-Isis. 729 is also the number of QROShTN, the 'curse of Satan', and of the Great Old One who identified himself as Amalantrah. During the Amalantrah Working there occurred the vision of an egg and a palm tree, vital symbolic links in the unwinding aeonic chain. (See Outside the Circles of Time."

(Note that The Beast 666 united with Choronzon 333 = 999, the number of central importance regarding the Manifestation of the Egg of Ma-Ion and the recalibration of THERION [Nun final] using Hebrew-English Gematria.)

     As I have shown in the preceding posts of the last year, 999 is the key-note of my own Initiations beginning on September 9, 2009 when I took an Oath to myself to discover and execute my own True Will, whatever it may be. On April 2, 2011 I happened to obtain an obsidian egg, which later while reading Outside the Circles of Time and subsequent Grant books I was slowly obtaining I realized was a talismanic link with the very Aeonic sequence which he described (see Chapter 8, Initiations of Aossic, where mention is made to the recurring egg of Crowley, Achad and Grant. (Note CROWLEY, ACHAD AND GRANT = 666 = GURDJIEFF AND OUSPENSKY.) See also Chapter 9, Ma-Ion for the meaning and significance of the 107 formula.)  2011 was to be the 107th year of the Aeon of Horus, and also the value of the FINAL HE, which Achad himself said 107 and the Egg (BITzH, 'Egg' = 107) referred to.
     107 being also the Hebrew Father (AB, 3) + Mother (AIMA, 52) + Son (BN, 52)  implies the Daughter as the 'Fourth Way', or Fourth Dimension which contains within her the Tetragrammatonic sequence, and the metageometrical VIRGIN MOTHER (=999) whose Immaculate Egg (0) emanates and embodies the Christ-Force (⊙)/Alpha-Omega. Note also that the Virgin Mother implies the Daughter.

     The Egg of 107 is also the formula of the Cartesian 'X-Y-Z', the three-dimensional field which extends indefinitely as the 'cosmic egg' of space-time, and thus the field of ULLAM, 'Consciousness', and the 'GOLD' egg of HAMSA, the Swan of Brahma and Eternity - essentially synonymous with the Egg that is '0' - and the Hand of Venus/Mary. The Egg is also related to Maat as evidenced by its appearance in the hieroglyph of the goddess. I also came to realize that THERION is also valued at 999, thus reverting the 666 formula (ThRIVN) as Grant said Nu-Isis sought to effect with the Maatian Current.
    The Egg, 0, is thus the Toroidal Zero-Point which contains (and is) the SANCTUM SANCTORUM of THE QUANTUM HOLOGRAM OF ENERGY, and thus also literally equivalent to THE AEON OF TRUTH AND JUSTICE (as well as THE INCOMING OF THE AEON OF MAAT, as Frater Achad termed his initial revelations regarding his Qabalistic insights and discoveries.) The Secret Doctrine of Witchcraft, which is merely Natural Magick or the Mechanics of Nature, is also veiled in the Qabalah of Nine Chambers - and thus the 'New Knowledge' and future technology is ephemeralized (to use the term of R. Buckminster Fuller) therein, waiting to be (re-/de-)coded. 666 is itself, again, the central Key of THE QABALAH OF NINE CHAMBERS, and happens to literally be A MATHEMATICAL FORMULA OF GOD which veils THE HIGHER POWER of 999. (Note also that VEILS = 111, implying each Chamber to be a veil of the Astral Light or Ain Soph Aur, 000.)

     666 contains in holographic form THE NEW MODEL OF THE UNIVERSE, though remember that THE NEW KNOWLEDGE IS ANCIENT WISDOM, just reformulated in modern new aeon lines. See P.D. Ouspensky's A New Model of the Universe, as well as In Search of the Miraculous and note that MIRACULOUS also has the value of 666. This is the number referred to in the bible as the number of He who is said to perform the miraculous sign of bringing down fire from Heaven in the sight of men in Revelation 13:13, and being as it is the SPIRIT OF FIRE and FIRE OF SPIRIT it is the astral fusion of etheric and materialized being, and therefore the solar 'self' or 'Christ'-aspect of Spirit/Ruach which becomes awakened, strengthened and directed in the course of the Path and Grade-Work of Initiation with added depth and definition of the Chambers and their fractal Logoic logic formulating manifestation.

     The Qabalah of Nine Chambers are themselves a formulation of the Caduceus or Brass/Brazen Serpent, the fennel rod of PROMETHEUS (=1,111; Note the sequence of alignment.) who also brought the fire from Heaven to Man, for which he was punished. In the book The Apocalypse Unsealed by James M. Pryse (1910), the Nine Chambers are said to be roughly related to the Grades of Initiation, and similar to the "Wheels within Wheels", or layers of an onion motif common in certain depictions of the Tree of Life. The sequence 1-9, 10-90, and 100-900 or 111-222-333-444-555-666-777-888-999 acts as a holographic index or channel of of emanation from 0 (Nought; LA) to ⛒ (Malkuth/Manifestation; AL). This latter symbol is that of Malkuth, as well as the 'Mark of the Beast' or THE SWASTIKA embedding spirit in matter, or essence in form and also  represents the locus of the Akashic 'I' confined to the Elemental cross or wheel of Samsara in space-time(-spirit-matter). This Qabalistic Index conveys the ACCESS CODES (=999=) to THE LOGOS' LOGIC underlying all MATHEMATIC CONSTRUCTS of THE PLEROMA OF NINE NUMBERS. (Note: THE PLEROMA & KENOMA KEY = 666; THE KEY OF THE PLEROMA-TOTALITY & KENOMA-VOID = 999 = THE NUMBER OF THE KEY OF IT ALL. The Pleroma is the Divine Totality of the Powers of Emanation and the Kenoma is the Emptiness or 'Void Outside' [of manifestation].

     This fusion between the Pleroma, 999 and Void, 0 is typified by '1', which in the Tarot is attributed to The Magus card yet also relating to Beth, the 2nd letter which means 'House'. This is the 'Double Wanded One' of Liber AL.III.34 and 72 which symbolizes the double-current of the CADUCEUS (=333) of HERMES (=555) (Note: HERMES CADUCEUS = 888 = THE PHILOSOPHER'S STONE = THE AZOTh = MANIFESTATIVN) The 1 contains in itself a seed-image of all potentialities, thus 999 is THERION - the Magus (1) who has achieved the 1,000 petal lotus of Nerodha-Samapatti, the attainment of Extinction wherein the 'Self' is realized as identical to the All and is (re)absorbed into its Supreme Unity. Thus, THERION as the Beast 999 is 1 with THE HIGHER POWER, [O] BEING GOD THE MOST HIGH [=GOD IS THE MOST HIGH]. (Note: DUAL-WANDED = 111, therefore the HERMES' DUAL-WANDED CADUCEUS = 999.)

     Also of note is the formula which subsists both 999 and 666, 333 has many resonances with concepts of QUANTUM LOGIC, such as the HIDDEN VARIABLE theory as well the NON-LOCALITY of holons/fractal information, which the DATA-COMPLEX of the Qabalah of Nine Chambers itself demonstrates. 666 is yet further the number of QUANTUM MULTI-DIMENSIONALITY, as well as THE QUANTUM LEVEL OF METAPHYSICS - or - METAPHYSICS OF THE QUANTUM LEVEL. I have shown in detail how 666 is the central key of THE QABALAH OF NINE CHAMBERS being itself THE FULLEST CHAMBER, from THE NUCLEUS OF AN ATOM to the GEOMETRIC EMERGENCE of THE CRYSTALLIZED ENERGY from THE PSYCHIC HYPER-PLANE that intersects and subsists the PHYSICAL MATERIAL PLANE and extends through the SPACE, TIME & LIGHT of all METRIC SPACE as THE ULTIMATE UNIFIED FIELD of ATOMIC METAPHYSICS. As THE KEY OF THE AXLE, or THE KEY OF THE AEON rather, 666 is literally the key which unlocks the Axle of the Aeonic sequence of space-time causality in which RETRO-CAUSATIONS (=999) are of equal weight as CAUSALITY PHYSICS in THE SPACE-TIME MULTIVERSE / THE MATRIX OF QUANTUM GEOMETRY that is THE UNIFIED FIELD OF BEING AND EXISTENCE.