northanger (northanger) wrote,

projective geometry

"Nothingness with twinkles. . . but what twinkles!"

Abrahadabra: the Word of the Aeon given in Liber AL .... Abrahadabra a Key of the Pentagram .... Also, by Aiq Bkr, it = 22; and 418 = 19 x 22. 19 = Manifestation; it therefore manifests the 22 Keys of R.O.T.A. The first meaning is ABRAH DBR, The Voice of the Chief Seer. It resolves into Pentagram and Hexagram as follows: [3rd method]: Dividing as 3 and 8, we get the Triangle of Horus dominating the Stooping Dragon. —Sepher Sephiroth (#418)

[I]nstructions were given on a new way to use the Tablets for magickal workings. The method involves the transformation of the two-dimensional Tablets into a three-dimensional structure that is the Temple of the Tablet. The Temple demonstrates the fundamental geometric, energetic, and spiritual properties of the Enochian magickal system through a form embodying the character of its active, intelligent energies. —Enochian Temples, Benjamin Rowe

[C]reated you a circle, a plan, in which the powers of the Tablets might be seen in another fashion, one which reflects the intent of the creators in a sense other than that shown in the Tablets. And in the space, this circle, a city was born; not of your intent, but of the action of those forces which you brought to bear. —Circle City: The magickal record of the first Comselha Working, Benjamin Rowe

I am here to introduce you to the details of the work we do here in your name and God's. For it is the work of the builders, the creators, those who make God's ideas into form, that is done here. And so do I greet you in the manner of those builders. —ANLOSh Describes Comselha, in Circle City: The magickal record of the first Comselha Working, Benjamin Rowe

The medallion had the image of the wheel in low relief, with a jewel in the center. But there was something odd about it. Viewed straight on, the spokes of the wheel were straight; viewed from an angle, the spokes bowed in the direction of the tilt. {Note: More accurately, when tilted to the right, the spokes bowed in a clockwise direction around the center; when to the left, they bowed in a counterclockwise direction} On the back were engraved five rows of letters, each letter individually boxed: Turning again to the front I saw that the jewel had the enochian B character within it, as if lines of white fire had been encased in the jewel. And again there appeared to be a tiny diamond point in the exact center of the jewel. —Circle City: The magickal record of the first Comselha Working, Benjamin Rowe

These historical data are necessary to explain why all previous packs are of little more than archaeological interest; for the New Aeon demanded a new system of symbolism. Thus, in particular, the old conception of the Earth as a passive, immobile, even dead, even "evil" element, had to go. It was imperative to restore the King-Scale colour attribution to that of the Aeon of Isis, Emerald Green, as was understood by the Egyptian Hierophants. This green is, however, not the original vegetable green of Isis, but the new green of spring following the resurrection of Osiris as Horus. Nor are the Disks any more to be considered as Coins; the Disk is a whirling emblem. Naturally so; since it is now know that every Star, every true Planet, is a whirling sphere. The Atom, again, is no more the hard, intractable, dead Particle of Dalton, but a system of whirling forces, comparable to the Solar hierarchy itself. This thesis dovetails perfectly with the new Doctrine of Tetragrammaton, where the Earthy component, Hé final, the Daughter, is set upon the Throne of the Mother, to awaken the Eld of the All-Father. The NAME itself, accordingly, is no longer a fixed symbol, emblem of extension and limit, but a continuously revolving sphere; in the words of Zoroaster, "rebounding, whirling forth, crying aloud". —The Book of Thoth (Ace of Disks), Aleister Crowley & Frieda Harris

Quite why Crowley feels the need to cite Papus at this point only becomes clear when we study Table 1, where the Heh(f) of Heh(f) position is given as infinity. As we know, technical analysis shows the Earth element not to exist in terms of YHV, and there is the famous phrase 'Kether is in Malkuth, but after another way'. Crowley incorporated this concept in the Princess of Disks, last of the Court cards —The Fool and the Pole Star, Paul Hughes-Barlow

[25-Feb|1:36pm] ~ someone brought to my attention incorrect link on Paul's paper. Here's a working link: "That the cards of the Book of Thoth can be combined to create new visual ideas and concepts can be seen in Frieda Harris' use of Goethe's geometrical symbolism."

If ever the whole system contained in the Tarot came to be worked out, which will scarcely be in our time, it might even prove that its attribution to the Hebrew alphabet obtains only in the lesser degrees. —Preface to Tarot of the Bohemians, A. E. Waite (quoted here: The Influence of Papus on the Major Arcana)

In Crowley's own Magical Diary for May 3, 1920 he writes a new commentary to replace Levi's own poem on the Court Cards: “Why do the Tarot Cards give the Knight as the father, the King as the son? It is an echo of the legend of the wandering Knight who wins the Queen and whose son becomes the King.” —Hidden and Secret Meanings: The Court Cards (Part II), David Allen Hulse

GLGL is the mathematical key. It instructs us on how to arrange the 22 Hebrew letters within the Jacob's Wheel mandala by giving us the 'magic number' 33. GLGL is valued 66, where GL = 33, so that GL + GL = 33 + 33. This is the key formula ... The Jacob's Wheel mandala's basic blueprint contains the numbers from one to 21, and consists of seven rows of three numbers where each row (or 'spoke' of the wheel) adds up to 33. The JW mandala uses the ordinal values of the Hebrew letters (1 to 21) to determine the correct arrangement (as depicted below). The 22nd Hebrew letter is positioned at the centre of the mandala. —Jacob's Wheel - The Key, Mallukh AHI

The North Pole and the Princesses. The Big Dipper, The Plough, the Great Bear, or Ursa Major is the constellation whose stars point to the North Pole. The Pole Star varies over extended lengths of time due to Precession. The Tarot cards have been given astrological attributions as is well known, but there has been a tradition of rulership over various parts of the heavens. The Princesses are unique in Tarot, in that they are given rulership over the quadrants of the world —The Fool and the Pole Star, Paul Hughes-Barlow

In the Book "T", it is written: "Also the Dragon (i.e. Draco, the constellation at the Northern pole of the Heavens) surroundeth the Pole Kether of the Celestial Heavens." It is further laid down that the Four Aces, (symbolized by the Princesses and Amazons), rule the Celestial Heavens from the Northern Pole of the Zodiac unto the 45th degree of Latitude North of the Ecliptic, and from the Thrones of the Four Aces which rule in Kether. —The Golden Dawn, Israel Regardie

Note the ambiguity between the Aces and the Princesses. Regardie equates them as being one and the same. Elsewhere in the Golden Dawn book (Llewellyn edn), Regardie remarks on the "... five divisions of the Tarot". In Hebrew, "Throne" is equivalent to Chariot, an implicit reference to the Merkaba Vision in Ezekiel. The Throne is also a symbol of Binah, the Great Mother. —The Fool and the Pole Star, Paul Hughes-Barlow

The Princesses rule the Four Parts of the Celestial Heavens which lie around the north Pole, and above the respective Cherubic Signs of the Zodiac, and they form the Thrones of the Powers of the Four Aces. The twelve cards, the Four Kings, Queens and Princes rule the dominion of the Celestial Heavens, between the realm of the Four Princesses and the Zodiac, as is hereafter shewn. And they, as it were, link together the signs. —A Description of the Cards of the Tarot

Now as the North Pole corresponds with Kether, and the South Pole corresponds with Malkuth, the central Pillar of the Sephirotic Tree will form the invisible Axis of the Sphere, the Central point coinciding with Tiphareth. This latter Sephirah together with that of Yesod will be completely hidden from view, so that Tiphareth will be the exact centre of the Sphere. Regard thou then the form of this Constellation of the Dragon. It is convoluted in the four places answering unto the rule of the Aces. Head, First convolution is the Ace of Cups. Second convolution is the Ace of Swords. Third convolution is the Ace of Pentacles. Fourth convolution is the Ace of Wands. This convoluted course will represent the Law of the Aces. Now in the Four Faces of YHVH, Fire and Water be contrary, and also Earth and Air be contrary. The throne of the Element will attract and seize, as it were, the Force of that element, so that herein be the Forces of Antipathy and of Sympathy, or what are known chemically as attraction and repulsion. —pp. 602-603, The Golden Dawn (Of the Operation and Rule of the Tree of Life in the Celestial Heavens Projected as if in a Solid Sphere), Israel Regardie

On page 610 of Regardie's book, "The Golden Dawn" is a table Showing the Order of the Passage of the 4 Aces, above the Signs, in the dominion of the Princesses (see table here). Another view: The 1st, 2nd, 3rd and 4th Order of Passage for each sign creates four different permutations of Tetragrammaton that appear to correspond with the Princesses (90 degrees, or three signs). Assuming "1st Order" is the first letter (YHVH), then the permutations "switch" the order of the zodiac, and the thrones "switch" from Fixed to Cardinal signs.

Now there will be, not one, but four formulae of the application of the Four Forces of Malkuth, unto the revolution of the Aces in Kether, and these acting not singly but simultaneously and with a different degree of force. Were Malkuth or Kether in the same plane or world the transmission of these forces from the one unto the other would proceed more or less in direct lines. In this case, seeing that Malkuth and Kether be in different planes or worlds, the lines of transmission of these forces are caught up and whirled about by the upper cone of the hour glass symbol into the vortex wherethrough passeth the thread of the unformulated, i.e. the Am Soph. Thence they are projected in a whirling convolution (yet according unto their nature) through the lower cone of the hour glass symbol unto Kether. Whence it resulteth that these formulae are of the nature of the Dragon, that is to say, moving in convolutions, and hence they are called the Dragon or Serpent Formulae. (1. Direct or Creeping Formula; 2. Looped or Flying Formula; 3. Leaping or Darting Formula; 4. Revolving or Flowing Formula) —pp, 617-621, The Golden Dawn (The Law of the Convoluted Revolution of the Forces Symbolised by the Four Aces Round the Northern Pole, Israel Regardie

So what's going on here? It's possible that the paper makes sense, but I just haven't grasped it yet. Maybe the paper is flawed as published, but there are other Golden Dawn documents I haven't seen that serve to provide a clearer picture. Then there's always the possibility that Mathers was already starting to go off his nut by the time he wrote this. But my favorite explanation is that the membership was getting bored, so Mathers wrote a complicated paper that intentionally made no sense. The dedicated initiates would strain to find the inner meaning of it, while everybody else would assume that they didn't get it because they slept through at least one of their knowledge lectures. —The Murkiest Golden Dawn Teaching, Xnoubis on Beast Bay

The Geometry [Lady Frieda Harris] used was an evolution of the strict Euclidian geometry. Its roots had been developed by the mathematician Descartes in the 17th Century. It's called "Projective Synthetic Geometry" and was developed by many mathematicians and scientists throughout Europe. Many of Descartes' ideas were based on both mathematical and mystic assumptions, e.g. his axiom of parallels meeting at infinity. The ends of parallel lines lie in two opposite directions, but the idea of the point in infinity is that the point, infinitely distant in a direction, is the same as those infinitely distant in the opposite direction. This step in the development of Projective Geometry, based on the idea of elements in infinity, brought movement and perspective to the Euclidian concept of rigid, fixed forms. In the following centuries the next step based on the idea of polarity (center and periphery) was taken; in other words, the concept of a polarity between a central point and an infinitely distant surface. These thoughts then had the consequence that each point in each conceivable space is the same distance from a surface in infinity. The next step, taken in the 20th century, comes from the concept of space, polar or opposite to our three-dimensional space. Can one move one's concept of a surface in infinity into an infinite center? —Projective Synthetic Geometry in Lady Frieda Harris' Tarot Paintings and in Aleister Crowley's Book of the Law, Claas Hoffmann

It will be seen that every form of energy in this picture is spiral. Zoroaster says, "God is he, having the head of a hawk; having a spiral force". It is interesting to notice that this oracle appears to anticipate the present Aeon, that of the hawk-headed Lord, and also of the mathematical conception of the shape of the Universe as calculated by Einstein and his school. It is only in the lower cup that the forms of energy issuing forth show rectilinear characteristics. In this may be discovered the doctrine which asserts that the blindness of humanity to all the beauty and wonder of the Universe is due to this illusion of straightness. It is significant that Riemann, Bolyai and Lobatchewsky seem to have been the mathematical prophets of the New Revelation. For the Euclidian geometry depends upon the conception of straight lines, and it was only because the Parallel Postulate was found to be incapable of proof that mathematicians began to conceive that the straight line had no true correspondence with reality. [The straight line is no more than the limit of any curve. For instance, it is an ellipse whose foci are an "infinite" distance apart. In fact, such use of the Calculus is the one certain way of ensuring "straightness".] —The Book of Thoth (XVII The Star), Aleister Crowley & Frieda Harris

Who are these people? Bolyai and Lobatchewsky are mathematicians who believed there was another geometry beyond Euclidean geometry, but they never proved it. Bernhard Riemann created the new geometry that did away with the Parallel Postulate. This happened in 1852. Riemannian geometry is all about space, curved surfaces and multiple dimensions. In 1904, Einstein was working on his Special Theory of Relativity, but he had a problem. He did not have the mathematical formulae to make his theory work, and it was not until someone showed him Riemann's theorems that he had the answer. Space-time geometry is Riemannian. —Parallel Universes & the Tarot, Paul Hughes-Barlow

He set them in the Teli, the Cycle, and the Heart. (Sefer Yetzirah 6:1). The Teli. This is one of the most mysterious words in the Sefer Yetzirah. The term occurs neither in the Bible nor in the Talmud, and there is considerable discussion as to its meaning. The only place where we find a similar word is in a single reference to a weapon, where Jacob told Esau, "Take your instruments, your Teli and your bow" (Genesis 27:3) .... [it is] suggestive of a kind of bola. This is a line with a ball at the end, used to ensnare animals. It would be called a Teli because the ball hangs (talah) from the line. This is also supported by the fact that the scripture clearly states that Esau was to trap (tzad) an animal. According to many Kabbalists, the Teli mentioned here in Sefer Yetzirah is the imaginary axis around which the heavens rotate. It is seen as an imaginary line from which the celestial sphere hangs, very much like a bola from its line. Many authorities identify the Teli with the "Pole Serpent" (Nachash Bare'ach)... [Isaiah 27:1 Also, "On that day, with His great, harsh sword, God will visit and overcome the Leviathan, the Pole Serpent (Nachash Bare'ach), and the Leviathan, the Coiled Serpent (Nachash Akalkalon), and He will kill the dragon of the sea"]. The Pole Serpent is often associated with the constellation of Draco. This is not surprising, since Draco is very close to the North Pole. [Two imaginary poles: celestial and ecliptic; Draco surrounds the ecliptic pole with stars in all houses of the zodiac; Draco is associated with the Teli because all the other constellations hang from it]. Many philosophical commentaries on Sefer Yetzirah, as well as astronomical texts, interpret the Teli as being the inclination between two celestial planes. In modern astronomy, this is usually called the obliquity, and it usually denotes the inclination separating the ecliptic and the celestial equator .... There are two points where the orbit of a planet intersect the plane of the ecliptic ... ascending node (dragon's head = vernal equinox) and descending node (dragon's tail = autumnal equinox). There is also a tradition that there are two Telis or dragons, one male and the other female. These are identified as the two Leviathans, and are mentioned in the account of creation, "God created the great dragons" (Genesis 1:21). According to the Talmud, the Coiled Serpent () is the female. Some Kabbalists state that the constellation of Draco is the male Pole Serpent, while the inclination of the ecliptic is the female Coiled Serpent. The female therefore encompasses the male, this being the mystery of, "a female shall surround a male" (Jeremiah 31:22). —pp. 231-236, Sefer Yetzirah: The Book of Creation (Revised Edition), Aryeh Kaplan

Practical Kabbalists: Teli is actually a place under the firmament of Vilon inhabited by humanoid beings as pure as angels. The divine mysteries are revealed to these beings and they have the authority to reveal them to humans; Methods are given for contact. • Teli = Alludes to Spiritual World, and to hidden mysteries which cannot be grasped. • Rabbi Abraham Abulafia = the knots of the Teli are knots of love and mystical union. • Teli nodes are the points where two divergent orbits meet = physical and spiritual. • "The stormwind hangs (talah) between the two arms of God like an amulet" --Talmud • Hanging = Teli; Stormwind (sa'arah) = imitiation into prophetic/mystical; Two Arms = 2 nodes (spiritual points in which amulet hangs); Arms = Arms of the Universe, the 12 diagonal boundaries. • "What is the Teli? It is the likeness before the Blessed Holy One. It is thus written, 'His locks are hanging (taltalim)' Songs 5:11. —pp. 236-239, Sefer Yetzirah: The Book of Creation (Revised Edition), Aryeh Kaplan

The Midday, The First Is As The Third Heaven: Made Of Pillars Of Hiacynth 26, In Whom The Elders Are Become Strong. Which I Have Prepared For My Own Righteousness, Sayeth The Lord, Whose Long Continuance Shall Be As Bucklers To The Stooping Dragon, And Like Unto The Harvest Of A Widow. How Many Are There Which Remain In The Glory Of The Earth? Which Are, And Shall Not See Death Until This House Fall And The Dragon Sink? Come Away! For The Thunders Have Spoken! Come Away! For The Crowns Of The Temple And The Coats of Him That Was, Is, And Shall Be Crowned Are Divided. Come, Appear To The Terror Of The Earth, And To Our Comfort And Of Such As Are Prepared! —Eighth Enochian Key

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