When the puzzle box opens up, you’ll see what I mean, but the for the time being use the following attributes as a guide, if necessary. I found them by looking at the symbols themselves as each embodying a distinctive meaning manifest in a type of motion, action, or intelligence. As if the shape of the glyphs were each designed to show their intent.

The partitioning of the Tarot deck by digital root was the method of connecting them together into sets. These in turn fit together in a kind of narrative describing the journey through a geometric lattice known as the ‘Tree of Life’. This method is outlined in further detail in Ring Two below.

It may be helpful to bear in mind that these astrological glyphs were also used by the alchemists.

12

Let the glyphs of the zodiac represent different types of motion or action.

In this sense, the imagery associated with each sign complements the function of the glyph.

♈ ARIES (the Ram): Pressing - Pushing

♉ TAURUS (the Bull): Grounding

♊ GEMINI (the Twins): Cleaving - Twinning

♋ CANCER (the Crab): Cycling

♌ LEO (the Lion): Ignition - the Creative ‘spark’

♍ VIRGO (the Virgin): Bringing to Fruition

♎ LIBRA (the Scales): Balancing

♏ SCORPIO (Fish - Serpent - Scorpion - Eagle): Metamorphosis

♐ SAGITTARIUS (the Archer): Penetration

♑ CAPRICORN (the Goat-Fish): Progression - Evolution

♒ AQUARIUS: (the Cup-bearer): Reflection

♓ PISCES (Two ‘Fish’ going opposite ways): Expansion - Return

7

Let the Planets serve as forms of intelligence, personified in their ‘densest’ form as metals, or in purer form as the archetypal ‘gods’ & ‘goddesses’.

♄ SATURN (Lead): Measure - Mortality - Understanding

♃ JUPITER (Tin): Harmonizing - Ruling - Orchestrating

♂ MARS (Iron): Enforcing - Activating - Conflicting

☉ SUN (Gold): Illuminates - Enlightens

♀ VENUS (Copper): Attraction - Embodying

☿ MERCURY (Mercury): Integration - Synthesis - Communication

☽ MOON (Silver): Tides - Phases

3

Let the Elements represent different faculties of Being.

As the Matter, or Body, from which we undertake this work, EARTH need not be represented among the Elements of the major arcana.

There are, of course, volumes of lore written on the interpretation of these symbols.

The present thesis maintains a self-initiation defense, predicated on the basic proposition that, given the context provided by the integration of Tarot & Qabalah, they form a unified whole that is self-explanatory by virtue of its’ architecture being founded on a ‘simple’ geometric diagram.

But, like any puzzle, its’ solution requires Play.

## Thursday, August 26, 2010

## Wednesday, June 9, 2010

### BORROMEAN RINGS (2/3)

RING TWO:

an elixir of memory & wisdom

Socrates I can tell something I have heard of the ancients; but whether it is true, they only know. But if we ourselves should find it out, should we care any longer for human opinions?

Phaedrus A ridiculous question! But tell me what you say you have heard.

Socrates I heard, then, that at Naucratis, in Egypt, was one of the ancient gods of that country, the one whose sacred bird is called the ibis, and the name of the god himself was Thoth. He it was who invented numbers and arithmetic and geometry and astronomy, also draughts and dice, and, most important of all, letters. Now the king of all Egypt at that time was the god Thamus, who lived in the great city of the upper region, which the Greeks call the Egyptian Thebes, and they call the god himself Ammon. To him came Thoth to show his inventions, saying that they ought to be imparted to the other Egyptians. But Thamus asked what use there was in each, and as Thoth enumerated their uses, expressed praise or blame, according as he approved.

The story goes that Thamus said many things to Thoth in praise or blame of the various arts, which it would take too long to repeat; but when they came to the letters, “This invention, O king,” said Thoth, “will make the Egyptians wiser and will improve their memories; for it is an elixir of memory and wisdom that I have discovered.” But Thamus replied, “Most ingenious Thoth, one man has the ability to beget arts, but the ability to judge of their usefulness or harmfulness to their users belongs to another; and now you, who are the father of letters, have been led by your affection to ascribe to them a power the opposite of that which they really possess. For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practice their memory. Their trust in writing, produced by external characters which are no part of themselves, will discourage the use of their own memory within them. You have invented an elixir not of memory, but of reminding; and you offer your pupils the appearance of wisdom, not true wisdom, for they will read many things without instruction and will therefore seem to know many things, when they are for the most part ignorant and hard to get along with, since they are not wise, but only appear wise.

http://www.ancient-hebrew.org/3_home.html

There’s a kind of Game that can be played with Tarot cards. Not the trick-taking variety of gambling associated with their emergence in northern Italy [c. 1441], nor the divinatory permutations combined within the fortune teller’s craft. This game imparts a book of secrets preserving a most ancient teaching concealed within the sequence of Letters comprising the Hebrew alphabet. In this respect, Tarot can be used as a cipher-text for performing a kind of alchemical card trick.

In much the same way that Checkers or Chess possess their field of play in the form of a checkered board, Tarot utilizes the matrix of 10 points (sefirot) and 22 inter-connecting lines (pathways) known as the ‘Tree of Life’. By using the simple number trick of adding the individual digits of a number together until reaching a single digit sum, One is able to group the Tarot’s enumeration of Hebrew Letters into 9 sets.

This method of assembling our ‘game-pieces’ is a formulaic device for establishing the components of an even larger puzzle - One we are to construct upon our ‘game-board,’ the Tree of Life. To be more precise, the arrangement of these components upon the Tree constructs an allegorical scenario wherein the alchemical craft of transmuting Lead into Gold serves as a metaphor for the perfection of our ‘puzzle’.

Herein lies an aenigma that has been the Philosopher’s Riddle for ages - One which has taken many guises but always adheres to a retrievable pattern based not merely upon an archetype of the collective unconscious, but structured around a set of relations integrating the mathematics of acoustic geometry with the proportions of regular solids & periodic cycles of planetary alignment - together articulating a model of the cosmos whose musical & celestial harmony lay at the heart of antiquity’s mystery traditions.

While examining the ‘mechanics’ of this System, it is advised that the reader consider this a map only, and not ‘the territory’. The benefits to be derived from exploring such an aenigma are primarily realized through treading its’ pathways for One self. The poise of its’ symbols articulated as One express an architectural view to Numbers as they move thru Space (geometry) and Time (music) in a way that visually balances rational forms, like cubes & octahedrons, with irrational quantities such as pi, the golden ratio, and the square roots of 2 & 3.

On a practical level, this activity is of benefit in constructing what is called a ‘method of loci’ mnemonic TooL - an Art of Memory formed around a recursive pattern in nature, broadly applicable to a wide variety of subjects by virtue of its’ ubiquity. Through repeated distillations it begins to take shape, coming into clearer focus as One gains greater familiarity with the Knowledge it maps and the Understanding that contains.

The rationale behind its’ Table of Correspondences is drawn from the sequence and classification of letters comprising the Hebrew alphabet. It was ‘adopted’ during their Babylonian captivity (7th-6th century, BC), when what had been the ruling class (patriarchs, priests, etc.) within the kingdom of Judea became the servants of the Chaldeans - a culture highly esteemed for their advancements in mathematics, astronomy & geometry. The archaic Hebrew alphabet was at this time replaced by a box script form of Aramaic (the language spoken by the Chaldeans) that then became the basis of the current letters in use. Our cipher-text, as it exists today, stems from the assignment of these ‘newer’ letters to the symbols depicted by hieroglyphs from which the more ancient Hebrew letters had been derived. In a very real sense, the one was grafted unto the other. They had much in common already, having both been based on the Phoenician (or, rather, Canaanite) alphabet from which Latin & Greek were also similarly descended.

Replacing the current symbols tied to their Hebrew letters with those of these ancient glyphs depicts an older version of our Game - their differences reflecting a change of idiom consistent with the transition from the Age of Aries to that of Pisces within the exeligmos of equinoctial precessions.

It has been surmised that these letters broke down into 3 categories based on the type of sound(s) they indicated. One of the earliest known manuscripts (c. 2nd-3rd century AD) containing the basic tenets of the Jewish mystic tradition that would become known as Kabbalah, the Sepher Yetzirah (“Book of Formation”) describes 10 Numbers (sefirot) and 22 Letters as the medium through which the Hebrews’ creator god, Yahweh [YHVH], manifests the universe & everything in it. Classifying each of the letters as either one of 3 mothers (element), 7 double (planet) or 12 simples (zodiac), this book ‘forms’ the alphabetical structure that, when de-ciphered with the Tarot de Marseilles, exhibits a collection of mathematical constants specific to our study of the Great Pyramid in RING ONE.

Developed in the intermediary zone between the ancient Egyptian & Mesopotamian cultures, our earliest alphabets may have retained the texture of a much older system; perhaps One that was known to the high priests of the Gods’ own scribe, Thoth. But whether his ibis-headedness truly invented these Letters & Numbers himself is beside the point: their cipher-text, in its’ current form, demonstrates an internally self-consistent logic for integrating his reputed inventions (writing, arithmetic, geometry, measurement, music, architecture, medicine, alchemy, gambling, astrology & the calendar) into a single, potent mnemonic TooL. One that explains much regarding many specific allegories used in both Semitic & Indo-European mythology; as well as their attending star lore.

Yet their integration depends upon keys that aren’t printed until the 17th century: the matrix of 10 interconnected points referred to as ‘the Tree of Life’; and the Tarot de Marseilles pattern that standardized the Tarot deck format. To what degree either represent a much older tradition of esoteric transmission is a matter of conjecture to which many authors in the intervening centuries have proffered a wide range opinions. Our concern here is less with the specifics of that debate than with the unique structure created by their synthesis - how these Keys unlock the Hebrew alphabet’s cipher-text of correspondences and arrange them into a unified whole. In order to see how this is done requires looking at their distribution in more than 2 dimensions.

Again, the reader is advised that this is only an introduction to this System - a reminder, of sorts - and only succeeds in distilling the ‘elixir of memory & wisdom’ through repeated use.

The TREE of LIFE: projections of light & shadow

Anthanasius Kircher (1601–1680) was a Jesuit scholar & polymath employed by the Collegio Romano whose breadth of inquiry spawned a host of books on topics ranging across fields diverse as magnetism, linguistics, optics, music, mathematics & geology. A ‘pioneer’ in the attempt to reconstruct the lost art of reading Egyptian hieroglyphics, he compiled his 20 years’ research drawing from Chaldean astrology, Pythagorean mathematics, Greek & Latin mythology, alchemy, and the Hebrew Kabbalah into the 4-folio volume, Oedipus Aegypticus (c. 1652-4).

Providing one of the earliest renditions of the Tree of Life exhibiting the structure & symmetry of a projection, Kircher elaborated upon an earlier version of the diagram provided by a Christian convert from Judaism, Phillipe d’Aquin (1625), by designating which of the 22 letters corresponded to each of the pathways interconnecting its’ 10 sefirot.

Kircher had already written one of earliest accounts on projecting images in his Ars Magna Lucis et Umbrae (“The Great Art of Light and Shadow”, 1646) wherein he suggested such methods were used by the priesthood of Solomon’s Temple and warns against their unscrupulous abuse. As all that’s required to project the 3-d skeleton of a cube (or of any solid) is enough light to cast its’ shadow upon a 2-d plane, the technology for obtaining such a matrix was well within the reach of ancient geometers.

Why it should be of particular interest within Judaism becomes easier to see when we examine the architecture of the Temple itself. Its’ inner sanctum, known as the Holy of Holies, was the ancient Hebrews’ repository for their most sacred relics: the rod of Aron, a pot of manna, and the Ark of the Covenant (containing the 10 ‘words’ brought down Mt. Zion by the Semitic ancestor-hero, Moses). A feature of temple architecture classified as the adyton, it was adjacent to a longer hall called the cella. Described in the Torah’s Book of Kings as being in the shape of a Cube inlaid with Gold, the Holy of Holies was considered the dwelling place of “the name”, YHVH - a symbolic formula of letters embodying the ritual function of the Ark itself as ‘the footstool of God.’

One way of looking at the Tree of Life is as a portable version of the Temple itself; and, just as with Solomon’s Temple after the Babylonian conquest, or the fall of the second Temple at the hands of the Romans, the edifice has been broken into fragments. Even when it stood, the ritual object embodying their covenant with the Divine was supposed to have contained his ‘10 words’ already smashed to bits. In this sense, our ‘Game’ is essentially a process of rebuilding the Temple from all its’ scattered pieces, re-assembling them in much the same way as in the Egyptian myth of Isis’ journey to collect the pieces of her dismembered husband, Osiris, before resurrecting him and conceiving their child, the Sun god, Horus. The formula itself is a geometric expression of mathematically constant proportions, which remain consistent from culture to culture throughout the ages - only the mythology draped over it changes.

Kircher’s Tree disseminated a piece of this Knowledge. Within the same decade master card printer Jean Noblet would provide another: a deck of cards whose mathematical structure parallels the ritual function & sacred architecture of SOLomon’s Golden Cube.

[22/56 ≈ π/8] : [22/14 ≈ π/2] = 4:1 (double octave) = XVI:IV

‘TAROT de MARSEILLES’: the Book of Thoth

Though its’ precise origins remain a mystery, the earliest known Tarot emerged in northern Italy at the dawn of the renaissance - a collection of hand-painted images brought together under the auspices of gambling. These decks and the games played with them had faded into obscurity within Italy by the time Noblet’s printing press issued the pattern of 78 cards we recognize today as the standard Tarot. But, despite having worked from the city of Paris, the structure of his and other decks of this type mostly originating in France are now collectively referred to as Tarot de Marseilles.

Exactly when Tarot’s structural parallels to Kabbala began influencing their composition & design may never be firmly established due to the tradition of secrecy attending the esoteric transmission of Knowledge among its’ adepts; but the earliest explicit mention of major arcana corresponding to the Hebrew alphabet doesn’t appear in print until 1781 with a pair of essays written by Antoine Court de Gebèlin & the Comte de Mellet, and featured within the 8th volume of de Gebèlin’s encyclopedic, Le Monde Primitif (1781).

Though widely panned today by many historians for ‘dubiously’ attributing authorship of Tarot to the Egyptian god Thoth, the eponymous claim may have stemmed from their involvement in Freemasonry. A member of Les Neuf Sœurs, de Gebèlin’s 9 volume work on the ‘enlightened & advanced’ civilizations of antiquity enjoyed a readership which included both the King of France and the President of the United States. Suffice to say, he was likely well-placed within that fraternal brotherhood whose own origin mythos centered around the construction of Solomon’s Temple and the allegorical assassination of it’s Master Mason for not divulging the secrets of his Craft.

Notably, more than just the addition of iconography is attained by integrating Tarot with the Hebrew alphabet; for the Marseilles pattern also established the numerical ranking of major arcana. A critical Key, but still essentially useless lest the player know where the Cipher is put - in this case both a visual & numerical conundrum, or ‘punning riddle’, suitable for a fooL.

Prior to the invention of symbols to represent numerals, the Letters were accorded values that also reflected their sequence within the alphabet. Wedded to the Tarot de Marseilles pattern, their sequence remains the same, but assigns a new value to each number depending solely upon the placement of the Sifr (the arabic root from which both ‘cipher’ and ‘zero’ are derived). When 0=aleph, the first letter, their subdivision by element, planet & zodiac give values whose combination describe proportions consistent with the diagram seen in RING ONE.

Only then does partition of the deck by digital root connect the Letters subdivided into these 9 sets to the Numbers relevant for their assemblage upon the Tree of Life.

Similar to a puzzle made by cutting a picture into many interlocking pieces, there is a ‘completed’ object in which all components of the partitioned Tarot fit together & reinforce One another by their own peculiar, internal logic. Playing with this aenigma is a process of repeated distillations, bringing the object into clearer focus, recognizing in its’ architecture not merely the interlinking of arcane symbols within an octahedral matrix, but also an allegorical key for unlocking the use of symbol within Indo-European & Semitic mythology and star lore.

When examining the zodiacal glyphs it is as if we are looking at this object broken into pieces and then ‘projected’ onto a 2-dimensional surface. One might say that distilling the solution to this particular puzzle requires continually translating its’ partition of glyphs into higher dimensions. This is also consistent with the type of motion or ‘intelligence’ being indicated by each glyph’s design. For example, how Scorpio ♏ depicts a spiral (as seen from its’ side) of transformation through which metamorphosis incurs change; this same spiral is connected to a ‘hymen’ in the glyph ♍ for Virgo, specifying a type of metamorphosis: gestating in the womb of creative ferment until mature enough to cross a Virgin threshold.

Each partitioned set may also be read as a chapter within a narrative describing the Soul’s journey through the Tree of Life. The process of determining what sequence the chapters are ordered in leads to an Understanding of how the game-pieces are to be arranged upon the game-board. Implicit within their sequence is a philosophy on the progression of Number and Form.

Yet, even after having fit together all these pieces on our game-board, there is still an operation to be performed - an error in The System that requires adjustment. Winning the Game is a matter of solving the riddle posed by this specific dilemma, and concerns the mutual use of all these glyphs among both the alchemists & astrologers of the past.

Prizing a certain secrecy which could only be overcome with a requisite modicum of technical proficiency & education, those adept at the alchemical craft used the mythology associated with our planets and constellations to create allegories from ancient lore that could be used to represent specific chemical processes and philosophical concepts. However inscrutable or bizarre this means of communication might seem to the influent, this discourse of riddling becomes accessible when the cipher-textual properties of Tarot are properly applied.

If we scrutinize the iconography of the major arcana, matched against the simple letters pertaining to the zodiac, it becomes apparent there is a fundamental flaw: Libra’s scales of Justice [VIII] have switched places with the Strength [XI] of Leo’s lion. This transposition of symbols within the deck is instructive in many respects, and is utilized within the context of our Game to transform ‘Lead’ into ‘Gold’ by completing a matrix of geometric relations at the 11th point (Gnosis) within the Tree of Life necessary for the 2-d ‘projection’ of a Cube & Octahedron.

Before ever becoming a ‘standardized pattern’, the Tarot arcana representing the cardinal virtues - Temperance, Justice & Strength - tended to vary position more than any other cards within the sequences of older decks. Ironically, the position they ultimately assume in Noblet’s Tarot are poised at the crux of this Puzzle: a crossroads in the Tree's pathways leading to where its’ golden apples grow.

Phaedrus Socrates, you easily make up stories of Egypt or any country you please.

Socrates They used to say, my friend, that the words of the oak in the holy place of Zeus at Dodona were the first prophetic utterances. The people of that time, not being so wise as you young folks, were content in their simplicity to hear an oak or a rock, provided only it spoke the truth; but to you, perhaps, it makes a difference who the speaker is and where he comes from, for you do not consider only whether his words are true or not.

Phaedrus Your rebuke is just; and I think the Theban is right in what he says about letters.

RING THREE: Hera’s Orchard

(under construction)

## Tuesday, May 18, 2010

### BORROMEAN RINGS (1/3)

“If one proceeded to announce that there is still nowadays a work of the former Egyptians, one of their books that escaped the flames that devoured their superb libraries, and which contains their purest doctrines on interesting subjects, everyone who heard, undoubtedly, would hasten to study such an invaluable book, such a marvel. If one also said that this book is very widespread in most of Europe, that for a number of centuries it has been in the hands of everyone, the surprise would be certain to increase. Would it not reach its height, if one gave assurances that no one ever suspected that it was Egyptian; that those who possessed it did not value it, that nobody ever sought to decipher a sheet of it; that the fruit of an exquisite wisdom is regarded as a cluster of extravagant figures which do not mean anything by themselves? Would it not be thought that the speaker wanted to amuse himself, and played on the credulity of his listeners?”

BORROMEAN RINGS

Viewed in this diagram, we are looking at a 2-dimensional map of Earth from its side, represented by One ring of our choosing (blue):

Orient the planet so the Great Pyramid at Giza (30˚N) lays at one of the vertices, the Earth’s center at another, and its axis’ North pole at the third.

Exploring this set of relations, it can be demonstrated that the architectural proportions of the Great Pyramid at Giza exhibit a means of utilizing the measure of Earth to express the mathematical constant, π. To understand how we must suspend, for a moment, our habit of thinking of number in purely quantitative terms and consider the ways in which some numbers are also inherently bound to specific geometric forms - like with ‘square’ (1² 2² 3² 4² 5²...) or ‘cubed’ (1³ 2³ 3³ 4³ 5³...) numbers we see a sum attached to a particular shape. Other shapes each possess their own sequence of numbers also attached to their change in proportion.

These are called ‘figurate numbers’, and tradition has it they were introduced into Greek mathematics by the pre-Socratic philosopher, Pythagoras, in the 6th century BC. A student of the ancient mystery schools, it is likely he acquired this knowledge during his journeys to Chaldea & Egypt; but all that is really required to calculate the number sequences tied to these shapes is a stack of pebbles and time to spare, counting out the variety of polygons & devising ways of stacking them to construct polyhedrons.

To the careful interpreter of nature a pattern was discernible amidst this numerical data - One that, properly placed, could be applied to the measure of all things. It is suggested here that the Great Pyramid at Giza, in relation to the 3-Ring structure given above, embodies this application.

Let us then imagine the Great Pyramid as keystone to a system of ‘projective numerology’ - an application of mathematics using figurate numbers to model distances and proportions as shapes, and translating them into their related forms as ‘seen’ from different angles & in other dimensions.

At the root of any square pyramid’s architecture is its’ seked - an ancient Egyptian ratio of angular measure used to determine the slope of a pyramid’s sides and thus its’ height.

Utilizing the seked of the Great Pyramid, the perimeter of a square pyramidal base equals the circumference of a circle whose radius is equal to that pyramid’s height.

Within our 2-dimensional map, as our planet rotates upon its’ axis, the Pyramid appears to move from one end of a vesica piscis to the other, as if turning on a Wheel whose rim is the 30th parallel. Thus, in one quarter turn (11/14 ≈ π/4) the Pyramid appears to move in a perpendicular line to the base of the equilateral Triangle articulated within our 3-ring diagram.

The distance of this perpendicular line from the Great Pyramid to the Earth’s polar axis is 3430 nautical miles, or 10x the cube of seven.

Let us then imagine this distance as a stack of 10 cubes, 7x7x7.

A ‘quarter turn’ (11/14) of the Earth thus ‘apportions’ a 10x10 square of these cubes:

10² x 14/11 = 127.27272727...

So, by the logic induced with this arrangement of proportions, distances can be pictured in the mind’s Eye as figurate numbers of octahedral symmetry with 7-unit sides. Reading the Run & Rise of the Great Pyramid’s seked both forward and backward we get a formula for modeling a linear distance of the Earth’s measure as a column made of figurative cubes.

[3d:2d = 343 : 127 ]

As such, we can picture the square pyramid monument atop this ‘column’ as pointing to the center of an imaginary 11th cube.

It follows, then, that a 12-hour rotation (180˚) measures a distance from center-point to center-point of the cubes at either end of a column 22 cubes of 7 long.

The center point of a unit cube has a specific relationship to the vesica piscis traversed in this 12-hour ‘distance’ within our diagram, as Two rings sharing a single radius give a rational approximation for √3, which is also the space diagonal of any unit cube.

In other words, with respect to a unit cube, the √3 is the distance between opposite corners of that cube. Tracing these space diagonal lines joins the opposing corners, all of which intersect at the center of that cube, and thereby delineate the edges of six square pyramids joined at their apex.

22:7 ≈ π

To the Egyptian god Thoth, equated with the Greek god, Hermes, and particularly the Roman god, Mercury, this ratio is significant in describing the number of conjunctions aligning Mercury & Earth with the Sun every 7 years. Also known as a ‘synodic cycle’, this is an example of what ancient Greek astronomers called an exeligmos, or ‘Turn of the Wheel’ - describing any period wherein Sun, Moon, and/or planets return to conjunction(s) from which they started. The term is still used today, but is more specifically applied to the Triple Saros cycle of reckoning lunar eclipses, each 120º of longitude apart, eventually returning to a point relatively close to where they began: exeligmos. The Romans used the term annus magnus, or ‘great year’ to describe the same class of periodic event.

As we shall see, each of the planets have a harmonic ratio of conjunctions with our planet Earth, and with each other. By fixing the Earth to the center of our ecliptic plane, the motion of other planets relative to our position appear as serpentine spiro-graph patterns, looping in close when aligning into conjunction with the Sun, and looping out to trace a wide arc that coils about the Earth until looping in again for another conjunction.

Mars:Earth

Venus: Earth

Consistent within our model of 10 cubes of seven, the Great Pyramid (pointing to the center of an eleventh) also corresponds to the tip of an octahedron of 7 = 231. And it just so happens that 11x 231 is the number of days in the exeligmos of Mercury & Earth, 22:7. In addition, the measure of the Great Pyramid’s base side lengths (440 cubits each) give a total base area measuring approximately 231 meters square.

Being a close approximation of the value π, and our annus magnus with the planet Mercury (Hermes/Thoth), let us then imagine this column of 22 cubes of 7 as the staff of his Caduceus. As we shall see, the cycles of the other planets can be represented as the serpents entwined about this Staff, their helices in tune with the ratio of their exeligmos.

Imparting more than just the inevitable passage of Time, they were the very music of the spheres by which the harmony of creation was made known to the ancient Geometers. Our 3-Rings establish the base unit of an entire system of weights & measures (metrology) by symbolizing an angular dimension constructed by the movement through Time of the Great Pyramid, like the point of a metronome entrained to the Earth’s tempo. In effect attuning the mathematical constant π with Mercury's Great Year & the linear measure of Earth's size in units of angular measure. 'Squaring' the circle much like the Great Pyramid's seked.

1 nautical mile = 1.15 miles

The nautical mile used as our base unit of measure for obtaining the distance in cubes of seven is also a unit of angular measure equivalent to 1/60th degree of Earth longitude (=1 minute of arc degree). Converting this into survey land miles = 1/10² the number of days between Earth:Mercury conjunctions (=115).

22:7 = 12 hrs @ 30˚north (12x 30 = 360)

180˚ = 10,800 arc minutes of degree = 50x 216, the cube of 6

216 also equals the number of degrees between Earth:Venus conjunctions (x5 = 1 Earth:Venus pentagram = exeligmos). So, by subdividing each degree of arc into 60 minutes, Earth’s 180˚ rotation (22:7) upon its’ axis thereby possesses a kind of numerological resonance regarding its harmonic with Venus, the exeligmos of the pentagram. Reputedly a symbol of good will among the Pythagoreans, the pentagram also provides an easy means of obtaining the golden ratio.

12 : 1 = (22/7) = 60 minutes

In this way our measure of both Time & Space define each other by weaving together the value π with the ‘divine proportion’ of the golden ratio.

Of the numerous other curious facets to this TooL of Hermetic Metrology, establishing not only our system of weights & measures, its choice of cubes & octahedrons also exhibit a direct connection to speeds of both sound & light:

1 meter

=distance trave1ed by sound 1/343th of second

=distance trave1ed by light 1/299,792,458th of second

343 = cube of 7

299,792,458 = c = speed of light in meters per second

1296000 / π = number of square degrees in one whole sphere

c / 1296000 = 231.321....

231 = octahedron of 7

Stranger still, the proportions outlined above are also paralleled in the numerical structure of the Tarot de Marseilles’ pattern of 22 major arcana trumps when applied to the Hebrew alphabet - in turn derived from Egyptian (via proto-Sinaitic) hieroglyphs which depicted the symbols those letters are still associated with.

We see traces of this tradition within our own English alphabet with the letter A: also the glyph for an Ox head (turned upside-down) having the same origin as the Hebrew letter aleph.

Referred to by 'occultists' as the Book of Thoth (though never adequately explained why), the key to unlocking this puzzle, as with any cryptological TooL, is knowing where to place the cypher, or sifr - the arabic word from which we also get Zero, or ‘nothing’, the rank of every Tarot deck’s Fool [aleph=0].

And this role proves more than suitable for One who ushers in what ultimately reveals a prank, of sorts... leading to what is arguably the greatest punch-line in history.

RING TWO: an elixir of memory & wisdom

BORROMEAN RINGS

RING ONE: hidden element

3 Rings linked together, their centers being vertices (corners) of an equilateral Triangle.

3 Rings linked together, their centers being vertices (corners) of an equilateral Triangle.

Viewed in this diagram, we are looking at a 2-dimensional map of Earth from its side, represented by One ring of our choosing (blue):

Orient the planet so the Great Pyramid at Giza (30˚N) lays at one of the vertices, the Earth’s center at another, and its axis’ North pole at the third.

Exploring this set of relations, it can be demonstrated that the architectural proportions of the Great Pyramid at Giza exhibit a means of utilizing the measure of Earth to express the mathematical constant, π. To understand how we must suspend, for a moment, our habit of thinking of number in purely quantitative terms and consider the ways in which some numbers are also inherently bound to specific geometric forms - like with ‘square’ (1² 2² 3² 4² 5²...) or ‘cubed’ (1³ 2³ 3³ 4³ 5³...) numbers we see a sum attached to a particular shape. Other shapes each possess their own sequence of numbers also attached to their change in proportion.

These are called ‘figurate numbers’, and tradition has it they were introduced into Greek mathematics by the pre-Socratic philosopher, Pythagoras, in the 6th century BC. A student of the ancient mystery schools, it is likely he acquired this knowledge during his journeys to Chaldea & Egypt; but all that is really required to calculate the number sequences tied to these shapes is a stack of pebbles and time to spare, counting out the variety of polygons & devising ways of stacking them to construct polyhedrons.

To the careful interpreter of nature a pattern was discernible amidst this numerical data - One that, properly placed, could be applied to the measure of all things. It is suggested here that the Great Pyramid at Giza, in relation to the 3-Ring structure given above, embodies this application.

Let us then imagine the Great Pyramid as keystone to a system of ‘projective numerology’ - an application of mathematics using figurate numbers to model distances and proportions as shapes, and translating them into their related forms as ‘seen’ from different angles & in other dimensions.

At the root of any square pyramid’s architecture is its’ seked - an ancient Egyptian ratio of angular measure used to determine the slope of a pyramid’s sides and thus its’ height.

Utilizing the seked of the Great Pyramid, the perimeter of a square pyramidal base equals the circumference of a circle whose radius is equal to that pyramid’s height.

Within our 2-dimensional map, as our planet rotates upon its’ axis, the Pyramid appears to move from one end of a vesica piscis to the other, as if turning on a Wheel whose rim is the 30th parallel. Thus, in one quarter turn (11/14 ≈ π/4) the Pyramid appears to move in a perpendicular line to the base of the equilateral Triangle articulated within our 3-ring diagram.

The distance of this perpendicular line from the Great Pyramid to the Earth’s polar axis is 3430 nautical miles, or 10x the cube of seven.

Let us then imagine this distance as a stack of 10 cubes, 7x7x7.

A ‘quarter turn’ (11/14) of the Earth thus ‘apportions’ a 10x10 square of these cubes:

10² x 14/11 = 127.27272727...

So, by the logic induced with this arrangement of proportions, distances can be pictured in the mind’s Eye as figurate numbers of octahedral symmetry with 7-unit sides. Reading the Run & Rise of the Great Pyramid’s seked both forward and backward we get a formula for modeling a linear distance of the Earth’s measure as a column made of figurative cubes.

[3d:2d = 343 : 127 ]

As such, we can picture the square pyramid monument atop this ‘column’ as pointing to the center of an imaginary 11th cube.

It follows, then, that a 12-hour rotation (180˚) measures a distance from center-point to center-point of the cubes at either end of a column 22 cubes of 7 long.

The center point of a unit cube has a specific relationship to the vesica piscis traversed in this 12-hour ‘distance’ within our diagram, as Two rings sharing a single radius give a rational approximation for √3, which is also the space diagonal of any unit cube.

In other words, with respect to a unit cube, the √3 is the distance between opposite corners of that cube. Tracing these space diagonal lines joins the opposing corners, all of which intersect at the center of that cube, and thereby delineate the edges of six square pyramids joined at their apex.

22:7 ≈ π

To the Egyptian god Thoth, equated with the Greek god, Hermes, and particularly the Roman god, Mercury, this ratio is significant in describing the number of conjunctions aligning Mercury & Earth with the Sun every 7 years. Also known as a ‘synodic cycle’, this is an example of what ancient Greek astronomers called an exeligmos, or ‘Turn of the Wheel’ - describing any period wherein Sun, Moon, and/or planets return to conjunction(s) from which they started. The term is still used today, but is more specifically applied to the Triple Saros cycle of reckoning lunar eclipses, each 120º of longitude apart, eventually returning to a point relatively close to where they began: exeligmos. The Romans used the term annus magnus, or ‘great year’ to describe the same class of periodic event.

As we shall see, each of the planets have a harmonic ratio of conjunctions with our planet Earth, and with each other. By fixing the Earth to the center of our ecliptic plane, the motion of other planets relative to our position appear as serpentine spiro-graph patterns, looping in close when aligning into conjunction with the Sun, and looping out to trace a wide arc that coils about the Earth until looping in again for another conjunction.

Mars:Earth

Venus: Earth

Consistent within our model of 10 cubes of seven, the Great Pyramid (pointing to the center of an eleventh) also corresponds to the tip of an octahedron of 7 = 231. And it just so happens that 11x 231 is the number of days in the exeligmos of Mercury & Earth, 22:7. In addition, the measure of the Great Pyramid’s base side lengths (440 cubits each) give a total base area measuring approximately 231 meters square.

Being a close approximation of the value π, and our annus magnus with the planet Mercury (Hermes/Thoth), let us then imagine this column of 22 cubes of 7 as the staff of his Caduceus. As we shall see, the cycles of the other planets can be represented as the serpents entwined about this Staff, their helices in tune with the ratio of their exeligmos.

Imparting more than just the inevitable passage of Time, they were the very music of the spheres by which the harmony of creation was made known to the ancient Geometers. Our 3-Rings establish the base unit of an entire system of weights & measures (metrology) by symbolizing an angular dimension constructed by the movement through Time of the Great Pyramid, like the point of a metronome entrained to the Earth’s tempo. In effect attuning the mathematical constant π with Mercury's Great Year & the linear measure of Earth's size in units of angular measure. 'Squaring' the circle much like the Great Pyramid's seked.

1 nautical mile = 1.15 miles

The nautical mile used as our base unit of measure for obtaining the distance in cubes of seven is also a unit of angular measure equivalent to 1/60th degree of Earth longitude (=1 minute of arc degree). Converting this into survey land miles = 1/10² the number of days between Earth:Mercury conjunctions (=115).

22:7 = 12 hrs @ 30˚north (12x 30 = 360)

180˚ = 10,800 arc minutes of degree = 50x 216, the cube of 6

216 also equals the number of degrees between Earth:Venus conjunctions (x5 = 1 Earth:Venus pentagram = exeligmos). So, by subdividing each degree of arc into 60 minutes, Earth’s 180˚ rotation (22:7) upon its’ axis thereby possesses a kind of numerological resonance regarding its harmonic with Venus, the exeligmos of the pentagram. Reputedly a symbol of good will among the Pythagoreans, the pentagram also provides an easy means of obtaining the golden ratio.

12 : 1 = (22/7) = 60 minutes

In this way our measure of both Time & Space define each other by weaving together the value π with the ‘divine proportion’ of the golden ratio.

Of the numerous other curious facets to this TooL of Hermetic Metrology, establishing not only our system of weights & measures, its choice of cubes & octahedrons also exhibit a direct connection to speeds of both sound & light:

1 meter

=distance trave1ed by sound 1/343th of second

=distance trave1ed by light 1/299,792,458th of second

343 = cube of 7

299,792,458 = c = speed of light in meters per second

1296000 / π = number of square degrees in one whole sphere

c / 1296000 = 231.321....

231 = octahedron of 7

Stranger still, the proportions outlined above are also paralleled in the numerical structure of the Tarot de Marseilles’ pattern of 22 major arcana trumps when applied to the Hebrew alphabet - in turn derived from Egyptian (via proto-Sinaitic) hieroglyphs which depicted the symbols those letters are still associated with.

We see traces of this tradition within our own English alphabet with the letter A: also the glyph for an Ox head (turned upside-down) having the same origin as the Hebrew letter aleph.

Referred to by 'occultists' as the Book of Thoth (though never adequately explained why), the key to unlocking this puzzle, as with any cryptological TooL, is knowing where to place the cypher, or sifr - the arabic word from which we also get Zero, or ‘nothing’, the rank of every Tarot deck’s Fool [aleph=0].

And this role proves more than suitable for One who ushers in what ultimately reveals a prank, of sorts... leading to what is arguably the greatest punch-line in history.

RING TWO: an elixir of memory & wisdom

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