The Geomantic Pyramid, by Frater Pyramidatus

8/6/2019 The Geomantic Pyramid, by Frater Pyramidatus

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The Geomantic Pyramidby Frater Pyramidatus

2011 Brian Adam Newman

Do what thou wilt shall be the whole of the Law

In 2010 I published, electronically, A Geomantic Curiosity , which revealed, as far as I cantell for the first time, the mathematical and scientifically flawless key to the art of Lineal

Geomancy. One cannot say it received a negative response, nor a mixed one, because quite franklyno one seemed interested. Even on specialist forums in cyberspace the paper merely clocked up ahandful of warm comments, with perhaps two enthusiastic cheers.

Despite this Lineal Geomancy needs revivification into a solid pillar of Hermetic instruction, besides other branches like astrology, the Qabalah, ceremonial magick and the Tarot. I shopped inGlastonbury recently and, of thousands of volumes on the occult in general, only three on this Artreared their diminutive heads. All seemed only to paraphrase Agrippa and Barrett.

All this superstitious secrecy is very silly. All numerical keys have been published . A greatexample is W. S. Andrews and Magic Squares and Cubes ; which shows people were actively

publishing every number key discernible, and over a century ago. It seems that poor old Geomancyhad to wait a little longer. In all honesty the information I adumbrate probably has been published decades ago, I just couldn't find it in the literature of straight-cut Hermetics. So I don't claim to be a

pioneer, simply someone trying to 'reboot' this antiquated tradition. This data was not in the GoldenDawn books I had, nor in Crowley, nor Zalewski, nor the infamous www.abrahadabra.com , nor elsewhere in cyberspace; even the well known Hermetic author John Michael Greer thanked me for these insights.

People should also realise that computer circuits have been around for longer than actualelectronic computers. All the truth tables and bit parity checks on a P. C. were more or less thrashedout a hundred years before the pocket calculator by people engaged in the same, seemingly boring,numerical escapades as myself.

A political note... In the year 2011 I think we could all settle on the following axiomaticstatement: We are becoming increasingly dependent on machines we do not understand.Everything we do today is dictated, in subtle and direct ways, by devices. We need technology tolive. In this unprecedented climate I think people should be encouraged to more and more studyHermetics to stem the flow of a culture plummeting towards a suicidal cybernetic maelstrom of unfathomable complexity. Our planet is on a precipice, terrifying and alluring, where only ahandful of psychopaths need 'pull the plug' for our top-heavy utilitarian utopia to crumble evenmore quickly than the five decades it has taken to develop such a monstrous edifice. I believe the

more people induced to study Hermetics the better it will be for everyone. As a Scientific IlluministI have never adopted the stance of Ludd, but I worry about the educational deficit amongst not onlyour youth, but seemingly most people I meet. We are trained as specialists in universities, to
http://www.abrahadabra.com/http://www.abrahadabra.com/


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Each Unique Shield is generated from four Mothers, hence each Ruling Figure has four expressions that create it. Every tableau is purely dependent from only four Mothers. It isunnecessary to show each Unique Shield in full, we simply place the Mothers only as a basis for our work. This fits in better with the fourfold development of the Pyramid.

We position the Mothers in a two-by-two square; the first on the top left, the second on thetop right, the third on the bottom left, and then the final Mother on the bottom right.

We then arrange them according to the Qemea scheme given in A Geomantic Curiousity .(However in this paper I have rotated this decimal square 90 degrees.)

We place the four Mothers appropriate under each square. We also acquire another magicsquare when we consider the base as an eight-by-eight in that each column and row totals to 48

points. This diagram is partly shaded, purely for ease of reference.


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The Ruling Figures

We have our 16 Figures tallied with the decimal key. This decimal key is one of manymagic squares of Jupiter, and totals to 34 in every way. If we add up the points in each GeomanticFigure they total to 24 every way.

For the Four Elements we ascribe them to the Figures in the following way.

Fire 1 Via Fire 2 Fortuna Minor Air 3 Puella Air 4 Laetitia

Water 5 Caput Draconis Water 6 RubeusEarth 7 Fortuna Major Earth 8 PopulusFire 9 Puer Fire 10 Cauda DraconisAir 11 Carcer Air 12 AmissioWater 13 Acquisitio Water 14 ConjunctioEarth 15 Tristitia Earth 16 Populus

This ascribes the Four Elements, in pairs, according to the traditional Geomantic order of theElements of Fire, Air, Water and Earth. This is also the Platonic ordering of the Elements; that isthe tetrahedron, octahedron, icosahedron and cube (finally we have the dodecahedron answering toSpirit, but that is beyond our scope of working). We now have the following Elementallysymmetrical square.


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Each Geomantic Figure has three levels, and you can break down each Figure into a permutation of the Elements.

We take a column of two dots as representing Fire, a column of four dots as Earth, anupward pointing triangle of dots as Air, and a downward pointing triangle of dots as Water.

Thus Populus would be Earth/Earth/Earth; Via would be Fire/Fire/Fire; and AlbusEarth/Water/Air. Calling these the three 'terms' of the Figure is my own literary device; as isdefining the top term as the 'first', the middle the 'second', and the lowest as the 'third'.

Each of the first terms of the Ruling Figures correspond to our scheme of the Four Elementswithout flaw.

The Four Elements are equally distributed in every row and column, and although notequally given in the diagonals they are in the four corners, in the corner groupings of four squares,and two other groupings of four squares.

Each Figure also has three numbers drawn from the Platonic Solids of the tetrahedron,octahedron, icosahedron and cube (or 'hexahedron'). These polygons are formed by lines drawnacross the interstices of the economical groupings of spheres. The most spheres that can be insimultaneous contact is four; if we draw lines across their interstices we produce a tetrahedron,composed of four equilateral triangles. The next figure is the octahedron, composed of eightspheres; then the icosahedron, cube and finally the dodecahedron which is composed of 32 spheres.You might assume the cube as the third in this series, but it is actually always the fourth. The

ancients allocated Fire to the tetrahedron because it pointed upwards; the cube to Earth because of its stability; the icosahedron to Water because it 'rolled' better than the others, amongst many other reasons. Thus the Platonic Order is Fire, Air, Water, Earth and Spirit. In the Hermetic Qabalah it is


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generally different. Each Figure has its four rows allocated to this sequence with Fire at the highestrow, and Earth lowest.

We perform arithmetic, permuting the rows in each Figure with geometrical attributes of thePlatonic Solids; arriving at three numbers for each Figure which collectively possess symmetrical

properties.

The table below gives basic data for the Platonic Solids, excluding the dodecahedron.

We take each Geomantic Figure and either deal with the points, lines or faces. As the rowsin each Figure correspond, via Element, to the four Solids, this is remarkably simple. We giveexamples which employ the faces of the Solids.

Via has one point in each row. We multiply the number of faces in each Solid once: 4 + 8 +20 + 6 = 38. For Populus we have two points in each row, and we simply double the previous sum,and get 76. If we have one point per row we multiply by one, if two points we double. With Albus,for example, we take the top row of two points and take the number of faces in a tetrahedron twice,the faces in an octahedron twice, the faces in an icosahedron once, and the faces found in a cubetwice: (2*4) + (2*8) + (1*20) + (2*6) = 56. The other two numbers assigned to each Figure followthe same logic with the number of lines and points in each Solid.

The numbers total equally in each row and column. Those generated from the faces areespecially useful in being unique for each Figure.

The following table provides this arithmetic.


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The sum of the point generated figures totals 180 across each row/column; that of the lines360; and that of the faces 228. Only the numbers for the faces generate a unique number each time,as previously stated; however 228 is also the value in Hebrew of OTz ChIIM, 'The Tree of Life',and KRVB, 'Cherubim'. These two isopsephisms are illuminating when we think of the Cherubimas being the Fixed Zodiac signs, and the Four Beasts that protect the Supernals of the Tree of Lifefrom the Stooping Dragon that arose after The Fall [sic]. For which see Israel Regardie's TheGolden Dawn , and many other places.

We now have a magic square symmetrical in (at least) Geomantic, Elemental, decimal andPlatonic Solid geometry; and we progress to the next level of the Pyramid. The diagram belowgives the combined symbolism.


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The Square of Saturn and the 'Westernised' I Ching

The logic that springs from the Ruling Figures to the Square of Saturn is not mathematicalas hitherto. I am using Yetziratic , so called, correspondences to develop the next level.

The Qemea of Saturn is a three-by-three square of the numbers one to nine, arranged so that

each row, column and diagonal totals to 15. It is called the Square of Saturn because the thirdSphere on the Qabalistic Tree of Life, Binah, is traditionally associated with the planet Saturn. (Itwould be nave, if not presumptuous, to assume that this configuration actually has anything to dowith the planet Saturn.) This is upside-down from what is typically displayed in Hermetic texts.

Each grouping of four squares of Ruling Figures corresponds to a single square in the three- by-three arrangement.


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The Yetziratic symbolism within this three-by-three square is fundamentally based on theoutermost corners of the Ruling Figures grid, and the Elements allocated.

The group of four squares in the top left corresponds to Fire as this Element tallies with thatof the top left individual square. And thus for the other corner groups of four squares, with Air inthe bottom left, Water in the bottom right and Earth in the top right.

The central set of four squares correspond to Spirit, as this Element is said traditionally tobind and separate the others.


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The set of four squares in the upper middle correspond to Sol as it is between the Elementsof Fire and Earth; the former representing the energy of Sol, and the latter its gravitational fulcrum.

Luna is allocated to the set of four squares in the lower middle, between the Elements of Air and Water; the former is Qabalistically equated with intellect and the Astral Plane, and the Sphere of Yesod (the Moon), the latter because of Her effect on the ebb and flow of tides.

The set of four squares on the middle left are attributed to Lingam, or the phallus; as a posited combination of the active principles of Fire and Air.


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The set of squares on the middle right is allocated to Yoni, or the kteis; as a positedcombination of the passive elements of Water and Earth.

We arrive at this three-by-three arrangement.

We have allied the Yetziratic symbols with the integers of the traditional Qemea of Saturn.The following symbol string arises, which is polarised linearly.

There are other wonderful synchronisations in Sol being the first, or highest, of thesenumbers; and in Luna being nine in this scheme and the Qabalistic Tree of Life. Fire is next toLingam, and Water next to Yoni. The progression of the Four Elements is the same as the Zodiacal(Fire, Earth, Air & Water). Spirit is in the middle and functions as a mirror polarising the rest.

If we ascribe the trigrams of the I Ching, as 'westernised' by Crowley, we discover a circular symmetry similar to the traditional Wheels of the Trigrams discussed by Richard Wilhelm.


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This configuration is different from those found in Wilhelm. However, we still acquire asymmetry in that each of the reflected pairs of trigram are composed of nine parts; if we take theliberty of expressing a yin as two components, and yang as one.

The Polarised Capstone

This is simply a two-by-two square, with each being ascribed one of the Four Elements, andeach being either positive/masculine or negative/feminine.

We take the Square of Saturn beneath and find the four squares of the upper left are Fire,Lingam, Spirit and Sol and thus Fire/Masculine. The bottom right set of four squares are Water,Yoni, Spirit and Luna and therefore Earth/Feminine. The top right set is more feminine in its partsthan the bottom left, so the former is Water/Feminine, the latter Air/Masculine.

You may think this last level as overly simplistic, which it may be. However, it helps youuse the Pyramid from a magical perspective if one wishes to 'explore' the binary permutations fromthe top down, or vice versa.

We have two symbols detailed here, three symbols on the three-by-three, and four symbols

with the square detailing the Ruling Figures. Our Geomantic Pyramid is complete.

When we permute the four levels, stepping down the Pyramid stage by stage, we have four


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to the fourth power permutations, or 256. This is a curious device slightly akin to the ElementalWatchtowers of Dr. Dee and Sir Kelly, as developed by the Hermetic Order of the Golden Dawn.

Poetic Mnemonics and the Unique Shields

I have contrived a poem that helps one remember the 16 sets of four Mothers that generate

each Unique Shield, and their Ruling Figures.

It is a 16 line poem, the initial letter of each of the first four words of each line being anotarius of the Mothers. As the translations, from the Latin, of the Geomantic Figures hardly startwith unique initials I have taken the liberty of renaming some of them.

Via P ath Cauda Draconis Tail of the DragonPuella M aiden Fortuna Minor L esser FortunePuer Boy Amissio F orfeitureCarcer Incarceration Laetitia J oy

Caput Draconis H ead of the Dragon Conjunctio C onjunctionAcquisitio Acquisition Rubeus R ednessFortuna Major G reater Fortune Albus W hitenessTristitia Sorrow Populus P opulation

The Ruling Figures are determined from the number of syllables, so that if the first word hasone syllable, then the highest row of the figure, that of Fire, has one dot; if two syllables two dots.Thus the four initial words give out the four Mothers of each Unique Shield, and the Ruling Figure.This short, ostensibly hyperbolic, poem deals with the notions of ascension and atonement.

Freedom's Frontier

By Her still wings I slowly fly,All my worries gently do die...The heavens soar wide, softly quiver,Clouds mingled golden silver.

Mellowed by sounds with wingd feet,Holy is wonder! Gallant retreat!Madly thinking some word may unseal,Hallowed frenzies! Glories surreal!

Rare jewels Herself by wisdom gave,Just let all turmoil wave on wave,Rest joyful. Moving by Her dream,Love's raiment! I tremble serene.

Reigning joy! Thankful height!Jazzy lights by contoured night,Rapture's journey! Twisting mirth!Little remains but far-flung Earth.

Love is the law, love under will

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The Geomantic Pyramid, by Frater Pyramidatus