Invictus 1 -0- 1

[Yygdrasilian]

prisca sapienta

Tradition attributes the introduction of figurate numbers in Greek mathematics to Pythagoras, though all One really needs to obtain the archetypal sequences of our natural numbers is a stack of pebbles and time to spare. There is a pure, ancient wisdom embedded in The Book of Thoth that utilizes these Key numbers, modeling a topological space that seamlessly integrates the Pythagorean quadrivium of arithmetic, astronomy, music (harmonics) & geometry.

Of particular interest to the alchemically inclined, the sum of our Triumphs: 231
21st(+0) Triangular, 11th Hexagonal, 8th Octahedron, 6th Heptadecagonal
http://en.wikipedia.org/wiki/Category:Figurate_numbers


. . . . . . . . . ^ . . . . .
. . . . . . . XX...XI. . . (20+11+2)=33
. . . . . . .Fire... “11” <--------------> 2³
. . . . . . /............\ . .
. . . . . . . . II . . . . . .
. . . . . . . . ☽ . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . 2 ☽ . . . .
. . . . . . . Swords . .
. . . . . . . . . . . . . . .
. . . . . . . .2 ♀ . . .
. . . . . . . Cups . . . .
. . . . . . . . . . . . . . .
. . . . . . . 2 ♂ . . . .
. . . . . . . Wands . . .
. . . . . . . . . . . . . . .
. . . . . . . 2 ♃ . . . .
. . . . . . . Disks . . . .
. . . . . . . . . . . . . . .
. . 3 ♄ ~ ~ ~ ~ ~ ~ ~ ~ ~ 3 ♂
. . swords ~ ~ ~ ~ ~ ~ ~ ~ disks
. . . . . 3 ☿ ~ ~ ~ ~ ~ 3 ☉
. . . . . cups ~ ~ ~ ~ ~ wands
. . . . . . . . . . . . III ♀
. . . . . . . . . . XII Water
. . . . . . . . . . . XXI ♄

176 = ☿ Spin:Orbit resonance = 3:2


( 11 <------> 8 )


217 = ]1+[ 6³ = arc˚ venus-earth synodic period
9th centered hexagonal

. . ./4\. . . . . . /4\ . . . . . . /4\ . . . . . /4\
. . / ♃ \ . . . . /....\ . . . . . /....\ . . . . / ☉\
. . \ \ . . . / ☽ \ . . . . / ♀ \ . . ./ /
. . . \ . 0=22 . . . . IV= . . . XIII= . /
. . . . \_________________________/
. . . . 3 ♄ ~ ~ ~ ~ ~ ~ ~ ~ ~ 3 ♂
. . . . swords ~ ~ ~ ~ ~ ~ ~ ~ disks
. . . . . . .3 ☿ ~ ~ ~ ~ ~ ~ 3☉
. . . . . . . cups ~ ~ ~ ~ ~ wands
. . . . . . . . . . . . . . III ♀
. . . . . . . . . . . . .XII Water
. . . . . . . . . . . . . . XXI ♄

226 = ]1+[ 225 = ♀orbit
10th centered pentagonal


Tempore patet occulta veritas...

 

[Yygdrasilian]

The 3rd Heptacontaoctagonal Number

As a matrix for comprehending a relationship between the Golden Ratio & the Octave, as well as a mnemonic for mapping the circle of Fifths &/or circle of Fourths onto the chromatic Scale, the 8th Octahedron (=231) is subdivided between its' 8th & 11th courses (Notes G & A, respectively) when unison is set at Note D. This conforms to the Pythagorean tuning of the chromatic scale that produces the Ionian mode. By placing the Perfect Fifth at Note A (Key pitch) and the Perfect Fourth at Note G, One subdivides the 13 courses of the 8th Octahedron in accord with the Fibonacci sequence both structurally and astronomically.

To illustrate:
Summing from the first course (or ‘layer’) of the 8th Octahedron, the Perfect Fourth (4:3) is set after the 8th course [176 = ∑ (courses 1-8)], while the Perfect Fifth (3:2) is set before the 11th [226 = ∑ (courses 1-11)].

01 = 1
----------0 : C
02 = 5
----------1 : C#
03 = 14
----------2 : D=unison
04 = 30
----------3 : D#
05 = 55
----------4 : E
06 = 91
----------5 : F
07 = 140
----------6 : F#
11 = 176 ☿
------------------------------------Note G = 4:3
09 = 201
----------8 : G#
10 = (216 +1) ♀
------------------------------------Note A = 3:2
08 = (225 +1) ♀
----------10 : A#
12 = 230
----------11 : B
13 = 231


176 = the number of days in Mercury’s 3:2 Spin-Orbit Resonance = 8x22
---------------------------------> (4:3) Perfect Fourth

217 = ]+1[ 216 = 6x6x6 = arc degrees between Earth-Venus conjunctions (5:8)
---------------------------------> (3:2) Perfect Fifth
226 = ]+1[ 225 = days of Venus orbit (13:8)


1, 1, 2, 3, 5, 8, 13...

 

[Yygdrasilian]

30th Parallel Puzzle-box

220 = 10th Tetrahedral number
∑ (0-10) = 55 (x4 = 220)
∑ (trumps) = 231 + 220 = 451

Digit ∑ (planets) = 22 <--------(♂= )------------> ∑ (planets) = 76
∑ (zodiac) = 139 <--------------(♂= )-------> Digit ∑ (zodiac) = 76
451 - 139 = 312

312
231
123

∑ (trumps) = 231<------------------------------------------> Digit ∑ = 96
∑ (zodiac) = 123 <-------( ☽= ) (♂= )-------> Digit ∑ (zodiac) = 69
∑ (zodiac) = 127<---------------------------------> Digit ∑ (zodiac) = 73

123-gonal Numbers: 1, 123, 366, 730...
231-gonal Numbers: 1, 231, 690...
321-gonal Numbers: 1, 321, 960...

231 = 6th Heptadecagonal, 18th Heptadecagonal = 2313
321 = centered 32-gonal, 6th 23-gonal

231.321...
x 10 degrees²
= c / π

c = speed of light = 299,792,458 meters per second (m/s)
1 meter = distance trave11ed through free space by Light in 1/299,792,458th of a second

127 = ∑ (zodiac) <--------------------------------------> 72 = ∑ (planets)
127.272 = 1400 / 11 ≈ 400/π
12.7272 = 140 / 11 ≈ 40/π = steradians per sphere = 4π
1.27272 = 14 / 11 ≈ 4/π = 1 steradian (unit of solid angle measure)
11 / 14 = .78571418... ≈ 1/4π = fractional area of sphere in steradians
http://en.wikipedia.org/wiki/Solid_angle
http://en.wikipedia.org/wiki/Steradian
http://en.wikipedia.org/wiki/Unit_sphere
http://en.wikipedia.org/wiki/Unit_circle
http://en.wikipedia.org/wiki/Radian

Tetrahedron
4π/4 = solid angle subtended at center of tetrahedron by one face = π steradians

Cube
2π/3 = solid angle subtended at center by one face = π(.666...) steradians

./ 6☉]............../ 6 ☽ ] as above...
/ -cups-].....☉...../ disks ]
.[ ----- ] . . . . . . . [ ----- ]
.[ 6 ♃ ] . . .♃ . . . [ 6☿ ]
.[wands] . . . . . . .[swords]
.[ ----- ] . . . ☿ . . .[ ----- ] Realms&Exiles (♃☿) diagram obtains golden apple
[ -VI - ] . . . . . .[ -XV- ]
. . . . . . . . . / \
. . . . . . . . ./ - \
. . . . . . . . / --- \
. . . . . . . ./ ----- \
. . . . . . ./ -- -- \
. . . . . . /[ -XIV-- ]\
. . . . . . .[ ------- ]
. . . . . . .[ 5 ☿ ]
. . . . . . .[ disks- ]
. . . . . . .[ ------- ]
. . . . . . .[ --5♄- ]
. . . . . . .[ wands ]
. . . . . . .[ ------- ]
. . . . . . .[ 5 ♂ ]
. . . . . . .[ -cups- ]
. . . . . . .[ ------- ]
. . . . . . .[ 5 ♀ ]
. . . . . . .[swords ]
. . . . . . .[ ------- ]
. . . . . . .[ --V - ] ...so below
. . . . . . . YESOD
http://www.math.washington.edu/~greenber/PiPyr.html

“The surprise caused by the discovery of an Egyptian book:
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?”

 

[kapoore]

Hi Yygdrasilian,
I do get some of your speculations, such as the number 231 and 153 being significant to a understanding of the hidden Tarot. For example, in the World card from the earliest decks there has been the mandorla of the fish. This particular shape is formed from the ratio of 265/153, which is approximately the square root of three. Then, 231 is the sum of all the numbers leading up to 21. I think the mandorla is sufficient evidence that our Tarot creator was up to something with a hidden number riddle. Also, 231 does contain 153 through addition/subtraction. Add the first 12 numbers (1+2+3..=78). Add all the numbers up to 21 (1+2+3...=231). The difference between 231 and 78 is 153. If you add another section of 21 you get an even more significant number. Add 20+19+18..13=132. Twice 132 is 264 which is a very close approximate to 265 and the ratio of the mandorla. In other words, within the number 21 it's possible to separate out numbers that have historical power, and apparently geometric potential as Yygg points out. And, of course, you are correct as well that cosmic cycles in general follow a similar pattern which the Magi knew, for example the whole idea of the music of the spheres. The problem is that these cycles lack enough precision to be important for modern calculations. But, perhaps, within these cycles and with an occult understanding that I don't quite get, other more precise predictions might be possible. I think this might be the direction that you are going...

When we were dialoguing yesterday on the Kabbalah/Tarot thread I should have asked you the right question that didn't occur to me until later. You said there that you had discovered the quadrivium in the cypher manuscript and Crowley's books. I would love some citation on that. This, I believe, would be important for the history of the cards, which as I see it is a sort of jigsaw puzzle. Sharing your information on Crowley and the quadrivium would open up a section that I haven't explored. Thanks, Kapoore

 

[Yygdrasilian]

Lamp

Aloha, Kapoore...
& Mahalo.

The problem is that these cycles lack enough precision to be important for modern calculations. But, perhaps, within these cycles and with an occult understanding that I don't quite get, other more precise predictions might be possible. I think this might be the direction that you are going...

Gaining access to the various applications of this System, One begins to comprehend its power as both a mnemonic device and problem-solving T☉☉L.

When we were dialoguing yesterday on the Kabbalah/Tarot thread I should have asked you the right question that didn't occur to me until later. You said there that you had discovered the quadrivium in the cypher manuscript and Crowley's books. I would love some citation on that. This, I believe, would be important for the history of the cards, which as I see it is a sort of jigsaw puzzle. Sharing your information on Crowley and the quadrivium would open up a section that I haven't explored.

In a letter from the ‘Society of Hidden Masters’ written by Crowley (to himself) he remarks that his publication of 777 in 1909 revealed the initiated attributions entrusted to him at a “Secret Lecture on the Tarot” by the Order A..A.., winter of 1898/9. Elaborating upon the subject, Dion Fortune wrote, “...it may be justifiable to say that if he did receive the Unwritten Qabalah, it has for some years ceased to be unwritten, for after a quarrel with MacGregor Mathers, Aleister Crowley . . . published the lot.” (The Mystical Qabalah, 21)
http://en.wikipedia.org/wiki/Cipher_Manuscripts
The Manuscripts’ correspondences appear to decrypt Tarot for partition by digital Root.
“You might as well object to the mnemonic value of Arabic modifications of roots." (-AC, 777)
http://www.hermetic.com/crowley/crowley-harris.html

These are the components of our puzzle to be arranged on the 2-d orthogonal projection of our ‘gameboard’ Tree
(≈ http://upload.wikimedia.org/wikipedia/commons/c/c8/Decad.svg). The Tzaddi/HeH transposition lends symmetry to these attributions with respect to their ecliptic positions and our 11<--->8 switch. This Hyperbola also coincides with the realm/exile & exaltation/fall of the Sun (Gold) and Saturn (Lead). CROSSing their BRIDGE obtains the zodiacal glyphs assembled into a geometric diagram for obtaining ɸ (the golden 'apple') from our vesica pisces.

Reading the astrological/alchemical glyphs, as with viewing the Qabala Tree, requires a consideration of their form in more than 2-dimensions. This is KEY to understanding their shared context and applications as a Pythagorean mathematical TooL...
♂http://en.wikipedia.org/wiki/Archimedes#The_Archimedes_Screw
http://en.wikipedia.org/wiki/Archytas

∑ (zodiac) = 127
127th triangular number = 8128
http://en.wikipedia.org/wiki/Perfect_number

∑ (planets) = 72 ( - ☉19 = 53) http://www.hermetic.com/gdlibrary/cipher/folio53.htm
53 x5 = 265

∑ (elements) = 32 ( + ☉19 = 51) http://www.hermetic.com/gdlibrary/cipher/cipher51.htm 51º51’
51 x3 = 153

Whatever we choose to believe regarding the origins of Tarot should address the enigmatic properties of this numerological artifice. The attributions ‘revealed’ by Aleister Crowley are clearly the product of intentional design and can be demonstrated to exhibit characteristics coinciding with descriptions of the Pythagorean mystery school as well as Key measurements of the Great Pyramid. Thus, it may be argued that there is, in fact, a basis for An Egyptian Theory of Origin after all.


Imagine that.

 

[kapoore]

Hi Yydrasilian,
I have skimmed through the sites you offered as an explanation of the quadrivium. Am I right in guessing that the quadrivium is to be found in the technique of "projected geometry" that is in the Thoth deck? Would you mind naming the cards I should study and how the math works in each card.

As far as the cypher manuscript goes I can't decipher it, but I thought the Wiki article was a good summary of history surrounding it. I thought it was particularly interesting that the method came from Trithemius, which is more familiar turf for me.

I do think the Tarot has something to do with the "exhaustive method," that is that the infinite cannot coincide with the finite, and that the polygons will not ever absolutely arrive at the circle no matter how many sides they assume. Again, is this incorporated into the Crowley deck?

So, I thank you, but I am afraid I am still a little lost as to the quadrivium and the Crowley deck. I have a good library and so you can cite pages for me in either the Cypher, the Golden Dawn by Israel Regardie, or the Book of Thoth. Or as I said above describe the geometry on the cards... Kapoore

 

[Yygdrasilian]

Scarlet Letter

Projective geometry appears to explain certain Forms and phenomena in Nature - as if our space-time continuum were itself a projection from ‘HigHer dimensions’. The use of Projective Synthetic Geometry in the Crowley-Harris deck is perhaps a subtle clue to this effect.
http://user.cyberlink.ch/~koenig/dplanet/stephen/claas/olive_e.html
http://www.tarotforum.net/showthread.php?t=121902

In applying the Tzaddi<---->HeH transposition, Crowley maps a Hyperbola onto the zodiacal ecliptic where previously there had only been the Parabolic curve indicated by 8<--->11. It is a curious feature when One considers the Whitehead Link mapping our Planets from their Tree to Tarot sequence, as the complement of this link has a hyperbolic structure “...obtained by making the octahedron an ideal regular octahedron in hyperbolic space” (see 3.3.9: http://books.google.com/books?id=9k...v=onepage&q=whitehead link octahedron&f=false). Borromean Rings similarly have a hyperbolic complement, obtained from gluing 2 ideal octahedra; which may help explain the link’s presence atop The Hierophant’s STAFF - symbolizing our pOrtal to ‘manifolds’ of greater dimensional complexity.

Utilized as a method of loci mnemonic, One essentially identifies with the cosmic architecture thus provided. Its’ integration of the quadrivium is then a matrix for ‘working out’ certain ‘calculations’ and can be used as a primer for conceptualizing the geometry of 3+ dimensions.
http://upload.wikimedia.org/wikipedia/commons/c/c8/Decad.svg
http://upload.wikimedia.org/wikipedia/commons/b/b4/Hamming_distance_4_bit_binary_example.svg
http://en.wikipedia.org/wiki/Hypercube_graph
http://casa.colorado.edu/~ajsh/sr/hypercubes.html

 

[Yygdrasilian]

Merry X-mas, Mr. Crowley (2.0)

Let us imagine a most auspicious event within the katarchic astrology of ancient times - an 'old school' reading of omens practiced in The Temple. Being far more than some minor highlight in YHVH’s sacrificial schedule, say this day ‘initiated’ a new Aeon: YHShVH (Jesus) :the dying god in the Age of Aries (Chrysomallos) passing the torch unto the dying god in Pisces (Chrystos).

In our scenario, this ‘birthday’ - the beginning of our calendar count of years [Dec.25, BC 1] - is read by reckoning the positions of the Planets with respect to the Zodiac: http://www.fourmilab.ch/cgi-bin/You...1.5&showmd=6.0&imgsize=512&scheme=0&elements=

One may notice that, applying the Tarot attributions provided by Crowley’s Liber Thoth to this date, certain ‘couples’ are joined together in alchemical matrimony. Taking care to consider the symbolic designations given our Letters are not arbitrary, but derive from the hieroglyphs depicting those symbols, One can find a comparison to the ancient Hebrew helpful in reading these signs of great portent: http://www.ancient-hebrew.org/3_home.html

Piscean Age
XIX The Sun ☉ + “The Moon” XVIII = 37 = 666/6+6+6
The Head (Resh) + (Qoph) ‘Circle’ of Revolution ; the CROWN of a King

☉☿ conjunction (a solar messenger) ‘Chief’ Tent

X Fortune ♃ + The Hermit IX = XIX
(Jupiter+Virgo: Deus ‘born’ of a Virgin)
Palm (Kaph) + (Yod) Hand (corpus callosum)

Eye (Ayin)
XV Devil

☉Winter Solstice [ ☉= an Eye illuminated in Earth's darkest hour
XIV the tent is Propped up
☉ ‘Head’ (Resh) + (Samekh) Thorn

14---+------->☉
Osiris--------->Horus

XVI Tower ♂ + Emperor IV (mouth agape, in awe & amazement)
Mouth, or opening (Pey) + (Hey) Look! -as in a great sight pointed out
♂ = begins decan cycle (martial regulus of antimony}

III Empress + Star XVII<---->IV Emperor+Empress III
Door (Daleth) + (Tzaddi) the Path
♀ ‘Correct’ Doorway ---> ♀ Behold! the Door (venereal regulus of antimony)
( = ♂)---> (♂♀)

II High Priestess ☽ + Hierophant V
Camel (Gimel) + (Tau) a Peg
☽ Success: the shepherd has tethered his flock at the Oasis
Foundation: the tent is Pegged down


♄ --------> 1 ♄ 1
Kodesh Hakodashim (inner house) 20 x 20 x 20 cubits:
It was said the “name” of God dwelt within the adyton of Solomon’s Temple: the holy of holies surrounded by the form of a perfect unit Cube, inlaid with Gold. The shape itself was not the object of veneration, nor the Ark of the Covenant (housing the 10 ‘words’) kept within, for idolatry was explicitly condemned; yet the ‘space’ it defined did embody certain enigmatic properties that may have concerned priestly contemplations of ‘the Divine’.

Such as: what are the metaphysical implications of irrational numbers generated by the construction of a unit cube? - A relevant question of that space wherein the “name” dwelleth, whether it be within the first or second Temple, or 'other' means of contemplating emanations of the Divine with respect to certain cubic matrices.

Of particular interest to a dawning Piscean age: the space diagonal of any unit cube = the square root of three, an irrational number closely approximated by proportion of the vesica piscis (265/153) and known to the ancient world as “the measure of the fish”. It is thus possible that the pisces may also have been recognized as signifying a union between antipodal corners of the Cube: a marriage of polarities within the adytum intersecting precisely at the center point of the Hexa-hdron...

...where ‘The Sun’ is born.

 

[Yygdrasilian]

The Song of Songs

(11/8) Undecimal TriTone : 11th Harmonic
TriTone intervals, as their name indicates, each describe a ‘trinity’ of tones.
Contingent upon the accuracy of their ratio approximating √2:1, this trinity may span the geometric distance of an octave: C<----√2---->C

And, this eerily dissonant diabolus in musica also Twins the octave by VI semitones...
Being an irrational number, no ratio will ever catch ‘The Devil’ by his tail; but, in the same way the golden ratio limits consecutive numbers of the Fibonacci sequence, the silver ratio uses a recursive relation to limit consecutive numbers in the Pell sequence: the numbers used to construct fractions approaching the square root of two.

1:1
3:2
7:5
17:12 (mem mem : mem)
41:29....

Gold (n=1) and Silver (n=2) are each transmuted by the metallic means: ½(n + √(n² + 4)) and then joined by an alchemical marriage of Sun & Moon that weaves together irrational constants mathematically expressing the shape of an octave.

11 x 8th octahedron (231) = 22/7 Mercury:Earth synodic cycle ≈ π

Cˌˌˌ = [(10x Φ )²]:32 Hz
Cˌˌ = [(10x Φ )²]:16 Hz
Cˌ = [(10x Φ )²]:8 Hz
C = [(10x Φ )²]:4 Hz
c = [(10x Φ )²]:2 Hz
c′ = (10x Φ )² Hz = 261.803...
c′′= 2[(10x Φ )²] Hz
c′′′= 4[(10x Φ )²] Hz
c′′′′= 8[(10x Φ )²] Hz
c′′′′′= 16[(10x Φ )²] Hz
c′′′′′′= 32[(10x Φ )²] Hz

http://en.wikipedia.org/wiki/Solomon's_temple#Description
Euclid-Book I, Proposition 47: (a=1) (b=1) (c=√2)
In this light, One may benefit from considering the dual polyhedra relation of Cube to Octahedron.

 

[Yygdrasilian]

take an Egg & pierce it with a fiery Sword

Examination of our Letters’ pictographic origins ( http://www.ancient-hebrew.org/3_home.html ) will show the Liber Thoth attributions deviating from the ‘ancient’ Hebrew occur in both pairs of Trumps transposed - all of which converge in Tarot partition 8, the STAR:

....................... 2² Window <-------------> Fishhook 17
....................../....\..........Behold! <--------------> the Path
..................../........\...................
..♃ 8______/______\____8 ☿
........\......../..............\....../.........
..........\...../................\..../..........
............\./...................\./............
............/..\................../.\............
........../......\.............../....\...........
..♄ 8/_____\_______/____\8☉
....................\........./...................
......................\...../.....................
........................\../......Teaching <------> the Clay (O+X)
........................ 2³ OX Goad <-------> Serpent

1n either idiom our STAR is still ‘coaxed’ toward its destination.
1n the Age of Aries- a shepherd guides his flock unto the ‘correct path’.
1n Pisces- a fisher King reels in the Light by using antimony to ‘purify’ Gold:
http://books.google.com/books?id=ww...&ct=result#v=onepage&q=regulus martis&f=false

Here we may see the shuffled cards concern essential dignities for our Sun (☉) & ‘The World’ (T):

8 <------> 11 = Libra: Gold falls / Lead exalted
11 <------> 8 = Leo: Gold realm / Lead exiled
Tzaddi<---->Heh = Aries: Gold exalted / Lead falls
Heh<----->Tzaddi= Aquarius: Gold exiled / Lead realm

The decans of our minor arcana in Eight [ 8 disks ☉ / 8 sword ♃ / 8 wands ☿ / 8 cups ♄ ]
then point our way to the Tarot partition of 1+10=ELeveN, the CROSS:

. . . . . . . . . . . . . XIX
.. . . . . . . . . . . . . .☉
10 ☉---10 ♄--- X ---10 ♂---10 ☿
swords----wands--( 4 )---cups-----disks.
.. . . . . . . . . . . . . . I
. . . . . . . . . . . . . . .☿
. . . . . . . . . . . . . .Ace
. . . . . . . . . . . . . .AIR
. . . . . . . . . . . . . .Ace
. . . . . . . . . . . . WATER
. . . . . . . . . . . . . .Ace
. . . . . . . . . . . . . FIRE
. . . . . . . . . . . . . .Ace
.. . . . . . . . . . . . EARTH

♄-+----->---------------> 1 ♄ 1

Saturn ascends four One CROSSing the PILLARS:
an Asklepios (7:5) becoming our blameless TooL of peace,
Caduceus, an ancient map written from the realms & exiles
of its’ author, Thoth - messenger & scribe of The Sun.
http://upload.wikimedia.org/wikipedia/commons/c/c8/Decad.svg
http://home.hiwaay.net/~jalison/30th.html
http://books.google.com/books?id=hA...=8#v=onepage&q=geometry vesica piscis&f=false

“...... just like God cannot be properly defined, nor can be understood through words, likewise this proportion of ours cannot ever be designated through intelligible numbers, nor can it be expressed through any rational quantity, but always remains occult and secret, and is called irrational by the mathematicians.”

http://www.alchemywebsite.com/atal_11.html