Book of Law Study Group 1.50

Welcome to the Hypersphere

Luckily, our Hierophant offers a Key: there is a path to ‘Borromean Rings’ - but the enigma they give a view to is a tricky concept ‘to grasp’. Perhaps the Trick is in letting go of concepts that no longer apply...

The complements of certain knots and links in the ‘3-sphere’ are cusped hyperbolic manifolds. Gaining familiarity with these structures literally provides One an added dimension of meaning to this and other aspects of The Book of Thoth, and its’ interface with the Qabalah Tree.

Interested parties are referred to:

Example: 2.19 Borromean Rings
[hyperbola & octahedra]

Example: 2.18 Whitehead Link
[transposition of 8-11 & Tzaddi-Heh]
[planetary seq. conversion Tree to Tarot]

http://books.google.com/books?id=Ny...6-nJBQ&sa=X&oi=book_result&ct=result&resnum=8
Discrete Groups in Space and Uniformization Problems
By Boris Nikolaevich Apanasov

8th octahedron = 231

Thus ye have star & star, system & system; let not one know well the other!

Click to expand...

Is this saying in the ordeals we are each on our own? Or that the ordeals are different for each of us? Perhaps that we cannot predict what would be the best ordeal for another...

Yygdrasilian said:

Luckily, our Hierophant offers a Key: there is a path to ‘Borromean Rings’ - but the enigma they give a view to is a tricky concept ‘to grasp’. Perhaps the Trick is in letting go of concepts that no longer apply...

Click to expand...

Thats interesting Yyg. I found an article on Borromean Rings on wikipedia, for those not familiar with what they are.
http://en.wikipedia.org/wiki/Borromean_rings

The Hierophant card in the Thoth holds a sceptre (?) topped by Borromean rings. Do you view this feature on the card as trying to indicate the three linked ordeals?

There is a word to say about the Hierophantic task. Behold! there are three ordeals in one, and it may be given in three ways.

Click to expand...

If so, what about the same feature on the Ace of Cups?

Corpus Hypercubus

Similia said:

The Hierophant card in the Thoth holds a sceptre (?) topped by Borromean rings. Do you view this feature on the card as trying to indicate the three linked ordeals?

Click to expand...

Yes.
The Question is: What to make of the ordeals...

The strange loops in Thoth’s book appear to have these 3-manifold hyperbolic complements in common. In a very real sense, they are Knots & Links defined by matrices of Pythagorean solids glued together in a ‘higher’ dimension. So, however One interprets its metaphysical implications, this system can be shown to exhibit properties of hyperspatial geometry.

Looking at the 8th Octahedron as a harmonic Key ( http://www.tarotforum.net/showpost.php?p=1894530&postcount=14 ), the Borromean Rings appear to correlate with the point where the end and the beginning of an Octave meet: Note C, between the 13th and 14th Intervals. When calculated in equal temperament with a reference of 440Hz= Note A above middle C, the frequency of the middle C note is between 261 & 262 Hz (cycles per second).

261 = number of Tesseract nets, Harshad number, and 9th Nonagonal number.
262 = meander number, open meander number, untouchable number.

Taking the Hypersphere into consideration, the properties of these numbers (realized as their ‘shapes’) would seem to indicate a kind of pOrtal to hyperspace at the very ‘point’ where Ouroboros bites its’ tail. In this sense, the shaft of the Hierophant’s sceptre (or, STAFF) may be seen to represent XIV: Art...

................/\.............
.............../...\............
............../.....\.............
............/.. ...\........... Path 25: Yesod-Tipareth
.........../[..XIV..]\......... 14th Interval
............[........]..........
............[5 ☿ ]...........
............[.disks]..........
............[........]..........
............[ 5 ♄ ]..........
............[wands]..........
............[........]..........
............[5 ♂]..........
............[.cups.]..........
............[........]..........
............[5 ♀ ].......... 1☉1 Invictus : Failure ♀ the consequence of remaining In 3's CUP
............[sword].......... Narcissus
............[........]..........
............[....V...]..........
............[......].......... 1☉1 Invictus : Success ☽
{9/YESOD = ☽ } The Foundation : “Hail, thou One, who shinest from the Moon”


...and Borromean Rings may be comprehended as an intersection between the world of our senses and ‘What Truths Beyond.’
Thus, the Hierophantic task is a word; and that word is a Name embodying the formula for One’s apotheosis: YHShVH

Could these ordeals be inherent properties of One's alchemical transmutation from the holographic delusion of material existence into ...Enlightenment? The gross must pass through Fire for the same reason The Surgeons must teach: as none of the psychic residue of dualistic egotism can ‘exist’ in higher dimensional states - a realm of consciousness where the consistency of matter (if it can be called such) has as much solidity as its ‘equivalent’ in Dreams.

Yet the gross must also ‘pass’ through fire by raising Shin up the axis mundi of 11/CROSS:
http://www.tarotforum.net/showpost.php?p=1885516&postcount=12

So, the task is a word; and that word is a Name.
And the Zero of our calendar’s year count resides at the ‘birthday’ of that Name.
Upon the Ace of CUPs, the Borromean Rings may offer a clue regarding One who attains this mastery over the Elements.
For it behooves All to consider the relation 'between' Art & Science.

Curiously, a recent analysis of the cosmic microwave background suggests our Universe may have a topology in tune with a 3-manifold Poincaré homology sphere (also known as Poincaré dodecahedral space).
http://en.wikipedia.org/wiki/Poincaré_homology_sphere#Poincar.C3.A9_homology_sphere
http://physicsworld.com/cws/article/print/23009

Aeon418 said:

A similar transformation via the letter Heh occurs in the final verse of Liber 65, chapter 5. This time a new pentagrammaton is formed.

Crowley's commentary: Cf. verse 14: meditate strictly upon the propriety of the first appearance of this particular symbol in just this place.

The symbol is now completed by the introduction of Nuit into its midst. Compare the similar appearance of Shin in IHVH.

What letter, then significant of Nuit, will transmute ADNI as Shin does IHVH? The usual letter is Heh, "The Star,'' Atu XVII, (Aquarius) We thus obtain a Pentagrammaton whose value is 70, Ayin, the Eye, Set or Saturn, Atu XV "The Devil."

Click to expand...

Dwtw

If the key is using the letter of Aquarius, to signify Nuit and to expand the tetragrammaton of ADNI, then we should explore using the letter Tzaddi, which is the letter given to Aquarius in the Sefer Yetzirah.

In that case, ADNI = 65 becomes ADTzNI = 155.
And 155 is the gematria value of the title ADNI MLK, or Adonai the King.

Also, when we spell these five letters in full we have:

Alef = 111
Dalet = 434
Tzaddi = 104
Nun = 106
Yod = 20

Total = 775 = 5 x 155

The sum of the five letters 'spelled in full' is five times the sum of the letters themselves.

Now THAT'S a pentagrammaton for you


Litlluw
RLG

similia said:

50. There is a word to say about the Hierophantic task. Behold! there are three ordeals in one, and it may be given in three ways. The gross must pass through fire; let the fine be tried in intellect, and the lofty chosen ones in the highest. Thus ye have star & star, system & system; let not one know well the other!

Click to expand...

Dwtw

As usual, some ambiguous language allows for more than one interpretation. But at least one valid way of parsing the sentence is that there is a triple ordeal, and this ordeal can be given in three different ways.

The gross, fine, and lofty chosen ones are then the three parts of the ordeal, and the three ways it can be given is to the Hermit, the Lover, or the man of Earth.

I think the three parts of the ordeal relate easily to the three parts of the soul in Hebrew qabalah. So the gross is Nefesh, the animal soul; the fine is Ruach, the Rational soul, and the lofty chosen one is the Neschamah, the Divine part of the soul. It would be natural that the animal nature is purified by fire, the reason is tested in intellect, and the divinity goes through a method known only as 'the highest'.

IIRC, Crowley discussed this point of view in his Commentaries on AL. But the way I see it, we each have to have this triple ordeal, purifying the various parts of our soul, but we will each have different types of ordeals, depending on whether we are a Hermit, Lover, or man of Earth. Different systems for the different stars. This is why Nuit said earlier that she would not write the ordeals, because they are specific to each star. But here she can at least give the general nature of such ordeals.

Litlluw
RLG

RLG said:

Also, when we spell these five letters in full we have:

Alef = 111
Dalet = 434
Tzaddi = 104
Nun = 106
Yod = 20

Total = 775 = 5 x 155

The sum of the five letters 'spelled in full' is five times the sum of the letters themselves.

Click to expand...

Using the letter Heh also throws up an interesting result if you use the proper spelling of Heh and not the one used in the Golden Dawn manuscripts.

Aleph = 111
Daleth = 434
Heh = 6
Nun = 106
Yod = 20

Total = 677 = 666 + 11

RLG said:

Different systems for the different stars.

Click to expand...

Or a warning not to make the fatal mistake of confusing the planes?

let not one know well the other!

Aeon418 said:

Or a warning not to make the fatal mistake of confusing the planes?

let not one know well the other!

Click to expand...

I'd go along with that one. It's a bad enough practice normally but whilst undergoing an ordeal ....

And I have alwyas related the three rings on the Heirophant's staff, and the three ordeals to expressions of the three Gunas and the 'ordeal' of the three on the Wheel in the Rite of Jupiter.

The Treachery of Images

Animal Crackers said:

“I once shot an elephant in my pajamas. How he got in my pajamas I'll never know.” — Groucho

Click to expand...

Confusing the ‘planes’ sounds symptomatic of entertaining The Fallacy of Misplaced Concreteness. As if the complexity of an abstraction, or depth of one's involvement with it, could ever confer the status of Territory unto any map - no matter how convincing its’ simulacrum. Ultimately, these ‘ordeals’ of the Hierophantic task are beyond the medium of The Body, posing the enigma of Immediacy to a consciousness no longer subject to the mechanisms of physical sense perception.
Surely words must fail to describe such an ...inevitability.

Perhaps this is why Crowley chose Borromean Rings to signify that threshold.
Or maybe comprehension of 3-manifold hyperbolic geometry somehow increases One’s chances of Success on that far shore.

Who can say?

It is strange, given the direct correlations to hyperbolic geometry in this system, that ‘discussion’ tends to lean heavily on gematria. Yet we might conclude that to ‘let not one know well the other’ has been taken to mean certain topics are nOT tO be discussed where non-dues paying members might hear.

Sounds more like an entreaty to drop the pretense of duality.
For- how ‘One’ is one if otherness is not?