Towers of The Moon


At most, 6 circles can divide a plane into 32 regions: ✡
1+2+3+4 = ▵
At most, 5 circles can divide a plane into 22 regions: ☆

✡ - ▵ = ☆

To ‘calculate’ is a verb derived from the latin word for pebble, calculus, specifically used in reference to a small stone used for counting. And there was once a mathematician-philosopher of antiquity who painted a picture of 32 wondrous paths of wisdom, composed of 10 numbers + 22 letters. Playing with the shapes of 32, 10 and 22, this anonymous mystic cryptographer partitioned the letters further to echo those figurative patterns, inducing a property of recursion within the architecture of a ‘sacred’ alphabet very closely related to our own.

"To understand recursion, you must understand recursion."

But does that make it “true”?


Mise en Abyme

Recursion within recursion: self-similar repeating patterns illustrate 32 wondrous paths articulated in a mysterious ‘Book of Formation’ (Sepher Yetzirah). Was it an accident? By weave of circles and array of stones those paths partition into stars and polygons, hidden within stars and polygons, all abiding in mutual symmetry. A fractal alphabet.

If consciously engineered, its cipher went unspoken: to number the sequence of 22 letters 0 - 21, as zero posed a paradox too great among the ancients to be included among their numbers. For how could ‘nothing’ be some thing? Though known of, zero remained hidden from the mathematics of antiquity, even by the unknown author of the 32 paths. Yet it unlocks a secret function in that account of letters & numbers - a distinctive attribute sharing certain similarities with the composition of a Tarot deck.

Naturally, bearing structural resemblance to such a recursive artifice as the Book of Formation (however adeptly concealed), speculations concerning Tarot’s origins are prone to get tangled in the strange loops of what fractal kingdom is fashioned from that cipher. Its’ self-similar repeating patterns evoke synchronicity by propagating ‘meaningful’ coincidences, and in that respect shares more than just a structural resemblance to Tarot. It may account for its utility as an oracular device.

But the more pertinent question: to what degree knowledge of this cipher influenced the development of Tarot from its earliest Renaissance formulations to its subsequent standardization during the Enlightenment. To suggest that degree were “zero” is perhaps too good a pun on The Fool (cifra) to be taken seriously, but is that itself a judgment tangled in recursions?

A Fool does play a significant role with respect to a Tower within the traditional lore of Judaism (Midrash) complementing Biblical allegory. Therein “Kesil”, the “fool” king Nimrod fabled to have commanded Babel’s tower built, was reputedly punished for his hubris by being pinned to the starry night with Orion’s belt - an asterism whose constellation straddles the celestial equator (0º). Notably, the tale stems from a Biblical episode concerning the confusion of languages [Genesis 11:7 ≈ π/2] where, to thwart common purpose among humans, YaHVeH jumbled the letters of the spoken word. By subdividing their single communal unity into categories of native self & foreign other, by introducing xenophobia, humanity becomes mired in an oppositional thinking toward the differences between communities and cultures deemed too alien to be treated humanely. In effect, war was born.

⨺ (0) The Fool (alef) Air - ox
♂ (16) The Tower (peh) Mouth
The confusion of speech - breath made sound - inflicted upon an otherwise unified people at Tower’s fall, unleashes Mars/Aries by engendering conflict between them. Deeper still, language itself seems wholly dependent upon oppositional concepts for meaningfully nuanced expression: war/peace, love/hate, self/other, etc. - words defined as much by what they are not, as what they are supposed to be. Though not exactly at war with what they signify, the words of any language inflict an arbitrary sort of violence merely by their separate and independent existence from that which they are intended to represent.

Given the poignancy of the Babel myth with respect to such a cryptic play on letters & numbers, we might reasonably ask whether there are other notable instances of synchrony between Tarot & the Book of Formation specific to Judeo-Christian allegory & exegesis. How many would it take to constitute a reasonable argument for more than zero degrees influence between systems? 231, or more? 343? Supposing the correlation weren’t just occult superstition, could one even navigate such a recursive domain and keep one’s logic sound? Could a modus operandi be discerned and described without getting lost in the infinite regress of self-similar patterns reiterated within one another?

Well, for the sake of some argument, as opposed to none, let us further consider how the imagery of Tarot might be utilized as a guide to decrypting the Book of Formation, and the soundness of the logic will speak for itself.

The Fool (0), as stated, has his reasons for playing the pivotal role of cipher, especially when coupled with The Tower (16). Though neither bear much surface resemblance to their corresponding letters, they together posit a scene of pun & allegory in the service of Jewish folklore - a referentiality between cards which elicits a gnosis of symbols & numbers in sync with the 32 wondrous paths of the Book of Formation. For instance, beside their possible allusion to King Nimrod & the tower of Babel, The Fool (0) & (16) The Tower may be read as an approximate value for pi if we look at The Fool as also being the “22nd” trump (0=22) and combine him with the digital root of 16 (1+6=7).

22:7 ≈ π
Similarly, the form of zero could be viewed together with a ‘tower’ ◯ + | = Ⓘ as evocative of a certain key phrase from the Babel myth recorded in the biblical Book of Beginnings [Genesis 11:7] wherein YHVH decrees the confusion of tongues.
11:7 ≈ π/2

Among the 22 letters, the Book of Formation describes 7 of them as ‘double letters’, corresponding to the 7 planets of antiquity visible to the naked eye (including Sun & Moon). Perhaps, playing upon their title, these 7 are ‘doubled’, thereby reiterating a value for pi within the recursive structure of the 32 paths of wisdom visible in the figuration of 22 as a centered heptagon. In turn, this affiliation of the 7 planets with the days of the week shares a heptagonal symmetry with respect to the speed at which those planets were seen to race across the sky. Evenly spaced and sequentially ordered fastest to slowest around a circle, the planets are rearranged into the days of the week by connecting them with a heptagram - a fact somewhat obscured in the English speaking world by their Greco-Roman ‘gods’ having been replaced with corresponding deities from the Norse pantheon:

⊙ Sol/Helios = Sunna / Sunday
☽ Luna = Mani / Moonday
♂ Mars = Tiw / Tuesday
☿ Mercury = Wodan / Wednesday
♃ Jupiter = Thor / Thursday
♀ Venus = Freya / Friday
♄ Saturn-day

Taking into account how 6 circles, arranged symmetrically, can divide a plane into a maximum of 32 distinct regions (including the space surrounding them), 7 circles can likewise divide a plane into a maximum of 44 distinct regions. In keeping with a modus operandi of recursion, The Chariot (7) might then reiterate this numerology of linked circles through the number of times the word “Merkabah” appears within the Masoretic text of the Hebrew Bible: 44.

Similarly, the Hebrew word for Tower (Hammigdal) appears (1+6) times.

If such a line of reasoning led to the 7th trump becoming The Chariot &/or the 16th trump being The Tower, then the recursion of symmetries invoked by the Book of Formation would extend into the iconography of Tarot through puns and allegories, (re)counted from scripture, to impart exegetical knowledge. In which case, a riddle to solve within the Tarot deck (or, at least, its ‘standard’ variant) may be found in the interweaving of these symmetries with both biblical folklore and specific numerals & glyphs drawn from the mathematical constants inherent to those geometric forms.
Droste effect said:
Recursion within recursion: self-similar repeating patterns illustrate 32 wondrous paths articulated in a mysterious ‘Book of Formation’ (Sepher Yetzirah). Was it an accident? By weave of circles and array of stones those paths partition into stars and polygons, hidden within stars and polygons, all abiding in mutual symmetry. A fractal alphabet.
(5-6-7) 22-32-44

(5) 22-5-72
(6) 32-127-73
(7) 22-18

The 6 circles dividing a plane into 32 wondrous paths are reiterated with the partition of 22 letters into 3 ‘matrices’, 7 ‘doubles’, and 12 ‘simples’. Of the 3 matrices the Book of Formation describes their interplay as articulating a cosmic order:

Sepher Yetzirah said:
“Three matrices: Alef, Mem, Shin. Their basis is the scale of acquittal and the scale of guilt, and the language of law holds the balance between them.” -SY23

“Three matrices: Alef, Mem, Shin - a great secret, hidden and ineffable, and sealed with six seals. And from it goes out fire, water and aether, and it is enveloped in male and female. Know and ponder a form (a mental image) that fire evaporates water.” -SY24

“Three matrices: Alef, Mem, Shin - The offspring of the heavens - fire; the offspring of the air - aether; the offspring of earth - water; fire above, water below, and aether is the balancing item.” - SY25
(20) shin - fire △
(0) alef - air ⨺
(12) mem - water ▽

12+0+20 = 32
△ + ⨺ + ▽ = ✡

(20) Judgement
(0) The Fool
(12) The Traitor

As the “kesil” Nimrod, The Fool suffers a Judgement for his hubris. As subject to the Roman punishment for sedition, the hanged man, Jesus, suffered a Judgement for his humility. Both attained a form of ‘everlasting life’. One among the stars, the other in ‘heaven’. One punished, the other pardoned. The question of Justice and how it relates to the letter of the law will be addressed in due course. For the time being we are holding a mental image of the heavenly fire ‘above’ evaporating the terrestrial waters ‘below’, and Aether as the balancing item. Or, put another way, where The Traitor meets his ultimate Judgement an aether as symmetrically balanced as a star hexagram (△ + ▽) = ✡ evaporates from the offspring of Earth, like a soul leaving the body.

Conveniently, The Star (17), as the simple letter Tzaddi, is one of several of the letter-symbols sharing in a fishing motif. If we take Tarot's hanged man as the medium from which to catch the ichthys, an interesting 'coincidence' surfaces:

XIII: Death - Nun - Fish (ichthys)

♒ (17) The Star (tzaddi) Fishhook
▽ (12) The Traitor (mem) Water

Perhaps, then, Death may be drawn up from the offspring of Earth, evaporating where it mingles with the offspring of Heaven. The ‘balancing item’, inasmuch as The Fool conveys the fate of Nimrod, is that point where the material edifice has been demolished by the divine while the soul rises to heaven. The Star, then, serves to redeem The Traitor by drawing his Death out of the watery depths unto its meeting with Fire and the resurrection portrayed by its Judgement. As demonstrated, the intermingling of Fire (20), Air (0), and Water (12) gives rise to the 6-point symmetry of a hexagram (32). And, if one has a penchant for linking circles together, one can see how the measure of a ‘fish’ complements the ‘Star of David’.,+brah.jpg

Given that 17/12 is a rational approximation for the square of two, it would be logical to infer that the ‘fish’ refers to the axes of a vesica piscis (‘fish vessel’): the overlap between 2 circles sharing a common radius. Their ‘cross’ within the fish provides an ancient heuristic for approximating the square root of three: 265/153 = 1.73...

With respect to the miraculous catch of 153 fish written in the Gospel of John [21:11], we can acknowledge that this measure was somewhat highly regarded by the Christians. As both the square roots of two and three are intrinsic to the proportions of a cube, they might have inherited this reverence for the ichthys from the dimensions of the Holy of Holies - the gold cube adyton of Solomon’s Temple wherein ‘the name’ YHVH reputedly dwelt.

The shapes made by the sum of the 12 simple letters (127) and the sum of their digit roots (73) form a centered hexagon (127) and a star hexagram (73). Seen as projections onto a plane of a cube and a star tetrahedron, the latter could nest within the former: the symmetric faceting of the cube. The square root of two [17/12], essential for translating a star hexagram into higher dimensions, gives the proportion of a square’s diagonal to any edge. By hooking the ‘fish’, one may move the square into becoming a cube by knowing the proportion of the cube’s space diagonal to any of its edges.

Curiously, the numbers 17 and 73 together share a cartographic relationship to a specific star, the ‘dog star’ Sirius. At roughly -17º Declination on the celestial sphere, night’s brightest star disappears from view above 73ºN latitude and becomes circumpolar at 73ºS.

Yet the 17th trump, consistent with the attribution of the simple letter Tzaddi to the zodiacal house Aquarius, depicts a water-bearer. And, in a sense, The Star does bear water unto a threshold of fire. Being an air sign, Aquarius conveniently embodies a vessel for water reaching heaven. If the star ‘above’ the Aquarian were Sirius, then it’s distance in hours of Right Ascension (1+7) from the closest member of the constellation Aquarius would give us an angular measure of some importance in plotting the vertices of a hexagram composed of 2 triangles (8hrs RA = 120º = 360º/3).

The punishment of the fool “Kesil”, pinned to the night by Orion’s belt, aligns with this Star. Perhaps, then, his own stellar ‘punishment’ facilitates the resurrection of a ‘hanged man’. As The Star and a fishhook, tzaddi plays a role within the deck consistent with the recursive symmetries partitioned by the Book of Formation, acted out in accord with the cosmological order of its 3 matrices, whilst simultaneously engaging a central transcendental mystery in Christian belief through relations between geometric principles implicit in its primary symbols. By illustrating puns and allegories from Judeo-Christian tradition, Tarot brings narrative life to the 32 wondrous paths of wisdom through ‘meaningful coincidences’ between its numbered cards.

Similarly illustrating the Book of Formation, the 22 letter-paths & 10 numeral-points comprising the ‘Tree of Life’ serves as a framework for embedding its recursive features deeper. Being a geometric lattice very much dependent upon the ‘measure of the fish’, it provides a context for showing how the meaningful coincidences described above may be fit together. “Death”, as a fish (nun), poses a kind of riddle on the nature of mortality and how it is ultimately overcome. A visible parable, of sorts, on the paradox of zero: how nothing could ever be some thing.

Technically, a point by itself is of zero dimension - a kind of ‘nothing’. But, having a twin, the initial point can attain dimension by connecting with another. Something, as distinguished from nothing. Having these 2 points of reference also defines a common radius for circumscribing the twin circles of the fish vessel. Thus, a form of consequence born from the creative act of ‘something arising from nothing’ delineates that fundamental measure. The ‘fish’ embodies the inherent limit imposed upon the act of genesis. A limit which the 13th trump poses as mortality. And a “Death” which may be overcome by recognizing how a 6-pointed “Star” complements the equally inherent recursion of fish, ad infinitum. Within this geometric framework, the letter-paths and numeral-points align to a ‘middle path’ consistent with the major axis of a vesica piscis:

(2) = ☾
(6) = ♊
(5) = ♐ 1+4 = (14)

♁♄☽♐♊<---1 1

As if to complement Jesus’ miraculous catch of 153 fish [John 21:11], this center axis lays out the symbolic architecture for connecting the mortal limitations of the vesica piscis to its ‘immortal’ recursion. The agency by which this occurs, both in the Tree & the Tarot, is suggested by drawing one’s attention to a conspicuously out of place piece of an otherwise symmetric whole - a flaw whose ‘correction’ both catches the measure of the fish whilst revealing its hidden star. [see Psalm 118:22]

Were we to assume that the towers of The Moon (♓) stood for the left & right hand pillars of the ‘Tree of Life’, what might we find if we walked that middle path to Kesil’s fallen Tower?

XVI The Tower
1.618... = the “golden" mean
XVIII The Moon
Inasmuch as one may interpret the ‘golden mean’ as an ‘immortal’ constant in mathematics/geometry, the numerals elicited by reading the towers of the 16th & 18th trumps as the ‘fathers’ (or vertical columns) of the kabbalist’s Tree produces a kind of literal “gold” ubiquitous in the phenomenal world.

What then of the creatures placed before that middle path?
Do they pose a riddle? -or is there no riddle to solve?


Basilisk, or "Does the Moon also fall?"

Isaac Newton said:
“I know whereof I write, for I have in the fire manifold glasses with gold in this mercury. They grow in these glasses in the form of a tree, and by a continued circulation the trees are dissolved again with the work into new mercury. I have such a vessel in the fire with gold thus dissolved, where the gold was visibly not dissolved through a corrosive into atoms but extrinsically and intrinsically into a mercury as living and mobile as any mercury found in the world. For it makes gold begin to swell, to be swollen, and to putrefy, and also to spring forth into sprouts and branches, changing colors daily, the appearances of which fascinate me everyday.” - (Keynes MS18) martis&f=false

Wolf = Antimony
Dog = Star

Begin by purifying the wolf of metals (stibnite), mixing ♋ with ▽ water.
Heat in crucible with proper measure of Iron ♂ to obtain star regulus.
Fuse star with Silver ☽ to facilitate amalgamation.
Then---☽-♋-> amalgamate with Mercury ☿
Rectify 7 times.

“...on the seventh time you will have a mercury dissolving all metals, particularly gold.”

‘Dissolve’ Regulus of Leo into 'Philosophik Mercury' prepared as above.
Place in 'manifold glasses'.
Keep heated with Fire △
And observe.


"Khnum is my Protector"

7/11 ≈ π/2
July 11 = 192nd Day
365 – 192 = 173
√3 = 1.73…

Our calendar bears the imprint of an ancient riddle concerning the nature of Time – obscured by a ‘confusion of tongues’, yet hidden in plain sight. It has been distilled through the ages, rectified & adjusted, fine-tuned to more readily help us gauge a metric upon an intangible. For though we may grasp it as a concept, witness its cyclical turn of seasons, or measure it by a music of the spheres - sun, moon, stars & planets - there is no ‘thing’ of Time we might grab hold of. It waits for no one.

Thus, a calendar is more than just a day-planner of practical use for a world of busy-bodies, it is an attempt to wrestle with that age old question: How can something come from nothing?

Days like today retain a signature of how the ancients used their alphabets symbolically to see an answer to this question by rendering it geometrically. Thus, that which eluded their literal grasp nonetheless took form in recognizable shapes deemed sacred – like shadows cast upon creation by a ‘divine light’. Through their craft of allegory and play on numbers they hoped to preserve hints and clues as to how one pieces that puzzle together. Yet, as with Time, they allude one’s grasp if taken too literally. And, in that respect, it helps to know the ‘measure-of-the-fish’.

But, if you can read the punchline in this paradigm, we might share a chuckle in finding that the Pyramid may not have ever had a Point. Or does it?