Qaballah and Tarot: Lesson IX

8/9/2019 Qaballah and Tarot: Lesson IX

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Qaballah & Tarot: A Basic Course in Nine LessonsLesson VIII: Applications of Tarot and Qaballah in Magick and Related Disciplines

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Yael R. Dragwyla First North American rightsEmail: [email protected] 13,100 wordshttp://polaris93.livejournal.com/

Qaballah and Tarot: A Basic Course in Nine

Lessons

Lesson IX:

New Directions in Qaballah and Tarot – An

Introduction

A. New Qaballahs

1. Extensions or Modifications of the Tree of Life Based UponTraditional Structures

By definition, a Qaballah is just a set of numbers plus an alphabet which is arranged in some fixed,given order in terms of some indexing set. In the West, this indexing set is the Key Scale, consisting of alist of positive integers 1-n, where n = x + y, x being the quantity of numbers in the numerical subset of the Qaballah and y that of the characters in its alphabetical subset.

The numerical subset of the Qaballah usually consists of x = m positive integers 1-m, where m is the base of the numbering-system used by the culture which has produced the Qaballah under consideration.Additionally, with each of the y characters in the alphabetic subset of the Qaballah a unique cardinalvalue is associated.

The elements of such a system may be arrayed in a diagram in the following way: the x numbers in the

numerical subset of the Qaballah are each associated with a Sephirah, represented as a point in the diagram(sometimes shown enclosed as a circle or other regular figure). Each of these points is then connected withat least two other points in the diagram by line segments, one for each pair of interconnected points; andwith each such ray is uniquely associated exactly one of the y characters of the alphabetic subset of theQaballah.

The Hebrew Qaballah is the traditional, classic, and definitive example. Its set of numbers comprisesthe counting numbers 1-10; throughout, it is based squarely upon a base-10 number-system, not only in thenumber of its Sephiroth, the conceptual point-set associated with the ten digits of its strictly numericalsubset, but also in the ordinal values* associated with its alphabetic subset, the 22 letters of the Hebrewalphabet. The diagram by which this system is mapped is the Tree of Life, as defined and described in




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previous lessons. The Key indexing system associated with the overall set of numbers and alphabeticcharacters consists of the counting numbers 1-32, exactly one for each of the ten Sephirothic numbers and22 alphabetic Paths of this Qaballah.

*Ordinal numbers are any numbers used to indicate order in a particular series, e.g., second, fifth, ninth,

etc. They are distinguished from cardinal numbers, which are any numbers used in counting or showing how many, e.g., 2, 6, 1,000, etc.

Beginning with this classical system, we can construct other, quite legitimate Qaballahs and their associated Trees of Life by means of various additions, subtractions, or other modifications. But we mustdo so according to certain rules, just as new mathematical systems having seemingly little or nothing incommon with the original, classic set of positive integers and basic operations of arithmetic over that setstill come into existence as the result of a series of precisely defined, logically justifiable modifications of that system or of the basic concepts that underlie it. Though the Qaballim we finally end up with as a resultof these transformations of the original Qaballah may seem to have little in common with their progenitor,they must not only conform to certain strict criteria as to their structures and uses, but must also be the end-

products of precisely defined and logically, philosophically, and historically defensible modifications of theoriginal.Above all, a Qaballah comprises a set of concepts, represented by Sephiroth, each of which is

associated with a number and a corresponding point-nexus on the Tree of Life. These Sephiroth are allinterrelated by Atua or Paths, each of which is associated with a literal (alphabetic) character. Classically,of course, there are ten Sephiroth and 22 Atua:

Of the Sephiroth there are ten and not nine, ten and not eleven. Ten.

Until recently, the inviolability of this principle was held to as strongly by Qaballists as earlier cultures heldto the impossibility of the zero, negative numbers, irrationals, and other “weird perversions” of the earliestnotions of number and structure, which originally included only the set of counting numbers, the operationsof basic arithmetic, and the plane geometry of Euclid and Pythagoras. But

‘The time has come,’ the Walrus said,‘To talk of many things:Of positive curvature of space,Of surds and groups and rings.’

So it is with the Qaballah. We can increase the number of Sephiroth, or decrease them in number. We canassociate them with a number-base other than the familiar decimal system. We can even associate themwith numbers other than counting numbers: with zero, or rational but non-integral numbers, or negativenumbers, or irrationals, imaginaries, complex numbers, transfinite numbers, or any other sort of numbers.Once we have determined what our set of Sephiroth will be, how many of them there will be, and what setof numbers, of what kind, will be associated with them, we have a number of ways to determine how many

Atua we must have by which to interrelate these Sephiroth. If we have x Sephiroth, we must have at least x Atua – enough to ensure that each Sephirah can be uniquely related to at least two other Sephiroth, these

relations being signified by the Atua. On the other hand, we can have at most

x

Σ I = 1 + 2 + … + x = x ⋅ (x + 1) / 2i=1

Atua, if an Atua is defined as representing a relationship in both directions between the members of a pair of Sephirim related to each other by means of it, or x2 Atua if in each case it represents only one of the two possible directions of such a relationship.* Having determined, within these limits, how many Atua we can






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2. A new, sui generis English-language Qaballah: Liber Al vel Legis

and the cybernetic revolution

On April 8-10, 1904 e.v., in Cairo Egypt, Aleister Crowley wrote a remarkable document which has been variously titled Liber Al vel Legis (The Book of the Law), Liber AL, Document XXXI (the originalhandwritten draft of the book), and Document CCXX (the typescript copy of the original manuscript). Thisfollowed his Cairo Working of March 20 of that same year, in which he attempted to contact certain entities by invocation in the Great Pyramid, near Cairo. The writing of the book was apparently one of themanifest results of that invocation.* According to a number of esoteric schools, the reception from Inner Planes sources, whatever they actually may have been,1 and transcription of this document by Crowley,signaled the closing out of the Aeon of Osiris (the Age of Pisces**) and the beginning of the Aeon of Horus (the Age of Aquarius†). Thus 1904 e.v.2 is Year Zero of the Thelemic calendar, the one kept bythose esoteric schools which believe that the Cairo Working and the writing of Liber AL initiated the newAeon of Horus/Aquarius.3

*Or, possibly, transcribed from dictation from preternatural sources, as he himself claimed. See Aleister Crowley, The Confessions of Aleister Crowley: An Autohagiography (New York: Hill and Wang,

1969), passim. Cf. Endnote 1 of this lesson, for more on this.

**The 2,160 years or so during which at the Vernal Equinox each year the Sun stands within the boundaries of the Constellation Pisces, in terms of celestial longitude.

†The 2,160-year period during which at the Vernal Equinox each year the Sun stands within the boundariesof the Constellation Aquarius, in terms of celestial longitude.

This document, Liber AL, makes many prophecies, some of which may already have come to pass, anda few of which may be coming to pass now, or will in the near future. (See, e.g., AL 3:46.) Most of these prophecies, if indeed they ever do prove out, to be tested in the future, perhaps the far future (see, e.g., AL

3:34). However, among them is the following:

Thou shalt obtain the order & value of the English alphabet; thou shalt find new symbolsto attribute them unto.

– AL, 2:55

There is also

The Perfect and the Perfect are one Perfect and not two; nay, are none! Nothing is asecret key of this law. Sixty-one the Jews call it*; I call it eight, eighty, four hundredand eighteen.** But they have the half; unite by thine art so that all disappear.

– AL, 1:45-47

From this last was derived the Thelemic principle

2 = 0




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where “2” is ordinal and “0” cardinal. That is, “2” refers to “two things,” each the complement, negative,or inverse of the other, and “0” to “zero” in the ordinary as well as the esoteric sense of that term. This is aWestern refinement of the principles of Taoism and the Tantric philosophy, according to which samadhi isattained by the literal, fleshly union of Yang and Yin as man and woman.†

*The Hebrew word for “Nothing” is AIN . The sum of the numerical value of its letters, Aleph-Yod-Nun = 1+ 10 + 50 = 61.

**Fans of Stephen King will be interested to learn that he was born at 4:18 a.m. on September 21, 1947, inPortland, ME. In his natal chart, he has the Fixed Star Spica – the “most fortunate Star in the heavens” – conjunct the Third House cusp and Jupiter, the great Benefic, in Scorpio in that House(among other things, the Third House rules writing, and Scorpio rules death and horror). He has Algol, the “mostmalefic Star in the heavens,” conjunct his Midheaven (10 th House cusp) and North Node of the Moon;the Midheaven rules career and the North Node of the Moon is a benefic, like Jupiter, Venus, and thePart of Fortune. Considering all the mentions of “kings” in Liber AL, maybe somebody could do

something interesting with this in a sensational horror novel . . .

†In the East, this union is represented by the T’ao symbol in Chinese cosmology,

and by various Hindu mandalas. In the West, it is represented by the Star of David

or, as traced:

1=4*

7 6

* *




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* *3 2

*

5=8

(tracing figure from point to point in order as indicated by the numbers; Points 1 and 5 are notconnected) and the Unicursal Hexagram

or, as traced:

1=7

*

3 5* *

0*

* *6 2

*4

(tracing from point to point as indicated, ignoring the center, which stands for the Sun).

– All of which would be only a curiosity for scholars and lunatics, except that long after 1904, andeven after Crowley’s death (which occurred in 1947 e.v.), since the late 1940s a brand-new industry hascome into being which has brought with it its inevitable attendant technological revolution: thecybernetic/electronic industry and the computer revolution. Computers are quite real – at the moment, as amatter of fact, I am in fact writing this text using an IBM Aptiva Pentium and WORD for Windows 7.0software, and many of you may be reading this by aid of a similar PC or Mac! – and now an inextricable part of today’s everyday, physical world, plainly here to stay. Yet the underlying principle of all their operations, and the way in which they store, process, and retrieve information within themselves or fromother sources, is eerily evocative of the seemingly purely mystical unearthly passages from Liber ALquoted above.




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First, almost all digital computers store and process information in the form of binary numbers, vector strings of 1’s and 0’s representing numbers in base-2 format.* Both numerical and non-numerical data arerepresented this way in computers. When the data are numerical and are operated upon arithmetically inthe computer, the operations by which they are thus manipulated obey the laws of Böolean algebra.Addition under Böolean algebra is very simple:

0 + 0 = 0

0 + 1 = 1 + 0 = 1

1 + 1 = 0

(with 1 to “carry” into the next higher binary position). But in our more usual, base-10 arithmetic:

1 + 1 = 2;

so we have

02 = 1 + 1 = 210,

or

2 = 0!

Even remembering here that “0” really means “zero 1’s, plus one 2 raised to the first power = 0 1 + 21” – that “0” is thus really “102,” just as “2” is really “210” – this mundane ghost of AL 1:45-47 is strikinglyevident.

*Some digital computers do exist which use a trinary or base-2 numbering-system, based on the set of integers {0,1,2}, stored in the form of positive, negative, and null electromagnetic charges. However,

these have problems, especially concerning their lowered efficiency and speed as compared with binary storage and processing. Analog computers, on the other hand, rather than processing discretenumbers, deal with continuously changing phenomena and the data that comes from them. Goodexamples of an analog computer is a non-digital clock with hands that move around the face of acircular dial, meters used to monitor use of gas and electricity by the utility companies, hydraulic-flowsystems, and so forth.

Second, since, in computers, non-numerical data must be encoded in this same binary format, thenwhatever literal data is stored and processed – data originally entered as letters, digits for report format, andspecial characters such as blanks, punctuation symbols, mathematical operators, etc. – it is in the form of these same binary numbers (though in this case, usually these numbers aren’t arithmetically operated on).Since computers can’t deal with ambiguously presented data, in order to store and manipulate such

characters in a computer, then, to each such alphanumerical character there must be assigned exactly onedistinct binary number which is assigned to no other character.

More than one lexicon of such numerical assignments to various character alphabets have beencreated, because of fierce competition in the industry; but as no one line of computers or major subset of the industry uses more than one such lexicon for its computers, this isn’t a problem. In fact, almost allcomputers now use the ASCII lexicon. Years ago, the major holdout was IBM, which used the EBCDICcharacter formats; but IBM, like all other major computer-technology companies the world over, has sincegone to ASCII, in order to ensure the easy, rapid transmission of data between computers, especially viaInternet.




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Now, to paraphrase Gertrude Stein, “a number is a number is a number is a number,” regardless of the base-system in which it is expressed. Thus

10102 =1013 = 224 = 205 = 146 = 137 =128 = 119 = 1010.

So the numerical equivalents of any characters listed in any such lexicon may be expressed in decimal or

other formats besides binary format. Therefore it might be handy to show the decimal as well as the binaryencoding for each character in a given lexicon under examination. The basic working character set is asfollows*:

Character N10** N2† Q‡

“B” (SPACE) 32 100000 Ain

! 33 100001 0“ 34 100010 1# 35 100011 2$ 36 100100 3

% 37 100101 4& 38 100110 5

‘ 39 100111 6( 40 101000 7) 41 101001 8* 42 101010 9+ 43 101011 10, 44 101100 11- 45 101101 12. 46 101110 13/ 47 101111 140 48 110000 151 49 110001 162 50 110010 173 51 110011 184 52 110100 195 53 110101 206 54 110110 217 55 110111 228 56 111000 239 57 111001 24: 58 111010 25; 59 111011 26

< 60 111100 27= 61 111101 28> 62 111110 29? 63 111111 30

@ 64 1000000 31A 65 1000001 32

B 66 1000010 33C 67 1000011 34D 68 1000100 35E 69 1000101 36F 70 1000110 37G 71 1000111 38H 72 1001000 39I 73 1001001 40J 74 1001010 41




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K 75 1001011 42L 76 1001100 43

M 77 1001101 44 N 78 1001110 45O 79 1001111 46P 80 1010000 47Q 81 1010001 48R 82 1010010 49S 83 1010011 50T 84 1010100 51U 85 1010101 52V 86 1010110 53W 87 1010111 54X 88 1011000 55Y 89 1011001 56Z 90 1011010 57[ 91 1011011 58\ 92 1011100 59] 93 1011101 60. 94 1011110 61

_ 95 1011111 62` 96 1100000 63a 97 1100001 64

b 98 1100010 65c 99 1100011 66d 100 1100100 67e 101 1100101 68f 102 1100110 69g 103 1100111 70h 104 1101000 71i 105 1101001 72 j 106 1101010 73k 107 1101011 74

l 108 1101100 75m 109 1101101 76n 110 1101110 77o 111 1101111 78 p 112 1110000 79q 113 1110001 80r 114 1110010 81s 115 1110011 82t 116 1110100 83u 117 1110101 84v 118 1110110 85w 119 1110111 86x 120 1111000 87

y 121 1111001 88z 122 1111010 89{ 123 1111011 90| 124 1111100 91

} 125 1111101 92~ 126 1111110 93




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Table 1

*Machine operation codes and special character-codes such as those for, e.g., ♣, ♦, ♥, ♠, i, k, Y, Σ , ∞,etc., not included.

**Value of number encoding ASCII character in base-10 format = Key Number in new, 16-Sephiroth

English-language Qaballah.

†Value of number encoding ASCII character in base-2 format.

‡Value of number in new, 16-Sephiroth English-language Qaballah.

This includes lower- as well as upper-case letters, the digits 0-9, standard punctuation symbols,mathematical operators, a few other standard characters and the SPACE. This lexicon is a preferred one,

since almost all sectors of the industry now use it, as does the Internet. Notice that, unlike IBM’s oldEBCDIC or the even more primitive, original BCD, the numbers encoding these characters are in acontinuous sequence, in this case beginning at 1000002 = 3210, for “ ” (SPACE), and ending at 11111102,for “~.” This continuity also makes it preferable for Qaballistic purposes to those which aren’t completelycontinuous in character assignments, such as IBM’s old EBCDIC, not to mention Honeywell’s atrocity of a lexicon (which has since fallen by the wayside, deservedly so).

Notice that the listing in Table 1, above, begins at Key 33 (if we don’t use Key 32 = “ ” [SPACE]).This is legitimate, Qaballistically speaking, since SPACEs are so prevalent in all texts used by human beings that they can be assumed to be ubiquitous background noise which can be ignored. Otherwise wewould unnecessarily compound our actuarial miseries when doing Gematria.

Further, the traditional Key Scale ends with Key 32, so if we equate SPACE with Key 32 andeverything prior to it, we can add the new Key system (33-126) to the old one, such that it begins right after the old one ends, with Key 33 = “!”. It is as if this new Key Scale were specifically designed to be added

on to the old one in this way, leaving the latter one completely intact, to expand it without in any waydistorting, obscuring, or destroying it.

If, however, we add the new system to the traditional one, so that we have 126 Keys in all, ten of which are Sephiroth and 116 of which are Atua, we end up with a Qaballah seriously in need of modification. If we have 116 Atua, then we must have either at least 15 Sephiroth to accommodate them asinterconnections of the Sephiroth, if our Atua are to be “two way,”* or at least 11, if they are to be “one-way.”** If we do add such Sephiroth, the system will in fact work. But, given this, since the ASCIIlexicon is a truly bijective association between numbers and literals, it is thus a true Qaballah, one which isquite capable of satisfying the requirements of Liber Al 2:55.

*Since 14 x (14+1)/2 = 105 < 116 < 120 = 15 x (15+1)/2 ⇒less than 15 Sephiroth will not work.

**(10)2

= 100 < 116 < 121 = (11)2

⇒implies, in this case, that less than 11 Sephiroth will not work.

As said before, the basic ASCII lexicon contains 94 characters in all, from “!” through “~”. So it canalso be bijectively associated with the Periodic Table of the Chemical Elements, from element Z=1(hydrogen) through element Z=94 (plutonium), so that each Key/ASCII character is thus uniquelyassociated with exactly one chemical element. Now hydrogen, unlike all the other chemical elements,normally contains no neutrons. In a way, it isn’t really an element as such at all – rather, it is a “pre-element” or “proto-element,” the basic building-block out of which all the “real” elements are formed.




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From this point of view, then, helium (Z=2) is actually the first “real” element, lithium (Z=3) the second,and so on through plutonium (Z=94), which would be the 93rd element. We might then consider hydrogento be “element zero,” since it precedes helium by atomic number as well as weight.

Likewise, while the ASCII Keys go from 33 to 126, if we subtract 33 from each Key (N 10 in the tableabove), the ordinal value of its associated literal, we get the numbers 0-93 as a result. Let the result soobtained for each character in the listing (Q, in the table above) be its cardinal value in the same way that,e.g., the cardinal value of the Hebrew letter

Kaphis 20, while its ordinal value (the order of its appearance

in that alphabet) is 11. If this is done, then the cardinal value of each character in the ASCII Key list givenin Table 1 is equal to the atomic (Z) number less 1 of exactly one chemical element in the Periodic Table of the Chemical Elements. E.g., ASCII Key 33, corresponding to the character “!”, would have a cardinalvalue of 33 - 33 = 0, equal to the atomic number of hydrogen (Z=1) minus 1; ASCII Key 126, associatedwith “~”, would have a cardinal value of 126 - 33 = 93, equal to the atomic number of plutonium (Z=94)minus 1; etc. Thus the cardinal value of each ASCII character listed in Table 1 would be equal to theordinal value of one of the chemical elements (beginning with helium, and excluding hydrogen).

This has several interesting implications. First, according to Crowley, the number of the “current” or energy-flow of the New Aeon of Horus/Aquarius is 93, while the formula of this new Aeon is

Do what thou Wilt shall be the whole of the Law; love is the Law, love under Will.

Aleister Crowley, Liber 77 4

The Greek word for Will, True Will, or Good Will, is Θ ε λ ε µ α (Thelema); that for Perfected Love or

Divine Love (Love-in-God) is Α γ α π ε ( Agape). The values of the letters of these words as spelled inGreek letters5 in each case have a sum of 93.*

*For an analysis of the Magickal meanings of the numbers 0-93, see Aleister Crowley’s The Book of Lies,

Which is also Falsely Called BREAKS, the Wanderings or Falsifications of the One Thought of Frater

Perdurabo (Aleister Crowley) Which Thought is Itself Untrue, a Reprint With an Additional

Commentary to Each Chapter (New York: Samuel Weiser, Inc.1975.

Now plutonium, which, as discussed above, is the 93rd “real” element, wasn’t even known to exist untilthe 1940s. Since then, however, the entire world has come to know all too much about it. Pluto, the Planetthat rules this metal, wasn’t even seen via telescope, let alone photographed, until 1930, well before Hismetal was refined in the early 1940s, decades after 1904. Crowley believed that Pluto was the Lord of Magick, its chief ruler. Uranus is the higher octave of Mercury and rules all Western esoteric theory and practice, not just Thelemic Magick, or even Magick in general; according to Crowley, Pluto is the ruler of Magick per se, Uranus of the more general category of the occult, which includes Magick but also a greatdeal else, as well. So while Uranus rules Aquarius, and the Age of Aquarius, Pluto is the Lord of the rawenergy that fuels that Age, and of the special technology, Thelemic Magick, that is its hallmark.

When the New Age supposedly was initiated in 1904 via the Cairo Working, astronomy had yet todiscover the Planet of the Age, Pluto; technology had yet to produce its cybernetic validation; the WorldWars, which were about to propel an unwilling world into the Atomic Age, hadn’t yet occurred;revelations concerning the ghastly facts of epidemic child-abuse in the Western World and its cover-up by

Sigmund Freud et al. lay exactly eight decades in the future*; and the Magickal metal, plutonium, wasn’teven a gleam in a chemist’s eye. Crowley couldn’t have known about any of these things, at least by anymeans recognized by science today. Yet all of them were discovered, invented, or came to pass in thedecades since 1904, demonstrating by their very natures real and Magickally legitimate fulfillment of important portions of Liber Al , and its prophecies as well as much of the rest of the so-called ThelemicHoly Books6 and their assertions.




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*Pluto, as Lord of Scorpio rules the Underworld and things kept undercover; abuse of power; sex as a biological and spiritual phenomenon; revelation of scandal and related matters. As lord of Aries, Herules the dawn, the beginnings of things, birth, and the energy of early childhood.

On the other hand, 11 is the number of Magick. It is the Key Number of the Hebrew letter Aleph,

associated with Trump 0, The Fool .* Its Planet is Uranus, Who rules Magick in the general sense as wellas the other occult Arts and Sciences such as astronomy, Alchemy, etc. In Hebrew, the number 11 isequivalent to IA (Yod-Aleph), a primordial name of God, the sum of the value whose Hebrew letters is 10 +1 = 11. It is the number of Da’ath, the energy of the Tree of Life itself. Also, 93 = 3 31; 31 is equivalentto AL or EL ( Aleph-Lamed ), another ancient name of God, the sum of the values of the letters of which,when spelled in Hebrew, is 1 + 30 = 31, and 3 is the number o Binah, whose Planet is Uranus. Thus 93 isdoubly, even trebly Magickal, and is so by the action of inherent primordial divinity through Magick actingon the Universe. 3 11 = 33, the first Key Number or ordinal value of the ASCII character-list (see Table 1,above), and it is by subtracting 33 from the Key Number of each character in the basic ASCII lexicon thatwe get its cardinal value, a member of the set of counting numbers {0-93}.

*See Lesson III in this course for a complete description of this Trump.

Thus this English-language ASCII Qaballah is rich with Magickal associations via the Key system, andin this way is also fit to become the English-language Qaballah referred to in Liber AL. All that needs to bedone is to establish a table of associations for it similar to those for the Hebrew alphabet given in Liber 777 ,in addition to its cardinal and ordinal numbering system and the Periodic Table of the Chemical Elements,and design a proper Tarot pack for it.

The ASCII lexicon is a product of the computer revolution, specifically designed for use in machinescapable of working only with binary numbers. Note that our new Qaballah is thus ultimately based upon anumbering system other than the decimal, conforming to an algebra other than that tailored to decimalnumbers. It thereby already goes far outside the bounds of the conceptual universe – the World of Yetzirah

– of the older Hebrew Qaballists, so there is little reason at that point to avoid altering the number of Sephiroth on the Tree of Life, hence its geometry, to enable it to accommodate this cybernetic alphabet andthe Keys 33-126 which index it. Remember, if we use only these 94 literals as our Atua, then since

13 × (13 + 1)/2 = 91 < 94 < 105 = 14 × (14 + 1)/2

and

92 = 81 < 94 < 102 = 100,

if our Atua are to be “two-way,” we need at least 14 Sephiroth to accommodate them, while if they are to be “one-way,” we require at least 10 (for which, of course, the traditional 10 would do very well).Similarly, if we add these 94 new literals to the traditional ones, thus obtaining 94 + 22 = 116 literals in all,we require at least 15 Sephiroth for “two-way” Atua and at least 11 if they are to be “one-way.”

3. New Maps for Magick: Redesigning the Tree of Life

The Tree or Life, conceived of as a 2-dimensional map of n points with up to n × (n + 1)/2connections,* is in fact a representation of the path which energy takes as it manifests in more and moretangible form and then returns to subtler and subtler states again, but now in more complex form than whenit began its descent of the Tree of Life into the realm of manifestation. It is thus a map of athermodynamically active, multi-dimensional system,7 and whatever else they may represent, one of its twodimensions, the vertical, thus also represents time (ruled by Saturn, Keys 3 and 32), while the other, thehorizontal, simultaneously represents all three physical dimensions of space (ruled by Jupiter, Keys 4 and




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21). Thus Key 1, Kether , and Key 10, Malkuth, are “Alpha” and “Omega,” representing the terminals of universal processes. However we may modify the Tree of Life, we must at least retain those two points asfirst and last upon it.

*That is, for “two-way” Atua. For “one-way” Atua, at most only n2 are required..

Remember also that the Middle Pillar of the Tree of Life represents consciousness, as aligned withForm (the Left-Hand Pillar of Severity) and Function (the Right-Hand Pillar of Mercy), the subjective or subtle aspects of reality. This, too, must be kept, regardless of any other modifications we make of the Treeof Life.

For a 15-Sephiroth, 2-dimensional Tree of Life, we might therefore have, e.g.,








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expanding it into more than two dimensions, or adding to the number of its Sephiroth or Atua, increases itsvalue in this respect, then such modifications are perfectly legitimate and permissible.

4. Alien Magicks: To Reintegrate the Tree (with Apologies to Larry

Niven)

How would a resident of another Planet of the Solar System design a Tree of Life? What sort of Treewould a denizen of the Sun come up with? How about an inhabitant of a Planet of another Star, or of thatStar itself, or of a space-ship culture which never took up a stable orbit around any Planet or Star design aTree of Life?

In Lesson V we examined the astrology of the Lower Arcana of the Tarot. Since the Lower Arcanarepresent the Sephiroth, number for number, just as the Greater Trumps represent the Atua, this astrology isin turn also the astrology of the Sephiroth. Notice that in descending order of their Key Numbers, theSephiroth are associated with Planets or Lights with increasingly slower average apparent motions throughthe Heavens. That is, ignoring Malkuth, which represents Earth and the Observer, the Sephiroth areassociated with the Planets and Lights, in decreasing order of the speed of apparent motion of the latter, asfollows:

Sephirah Sephirah No. Planet/Light Symbol Av. apparent motion

Yesod 9 Luna g 12°-15°/day Hod 8 Mercury h 2°/day Netzach 7 Venus i 1½°/day

Tiphareth 6 Sol f 1°/dayGeburah 5 Mars k ½°/dayChesed 4 Jupiter l 2½°/month

Da’ath “11” Saturn m 12½°/year Binah 3 Uranus n 4.29°/year Chokmah 2 Neptune o 2.14°/year

Kether 1 Pluto p 1.45°/year

Notice also that in this same order, the Sephiroth represent the increasing average distance of the Planets

and Lights from Earth, as follows:

Sephirah Sephirah No. Planet/Light Symbol Perigee Perihelion

Yesod 9 Luna g 4.0 × 105 km 1.47 × 108 km Hod 8 Mercury h 7.8 × 107 km* 4.59 × 107 km Netzach 7 Venus i 4.0 × 107 km* 1.07 × 108 kmTiphareth 6 Sol f 1.47 × 108 km N. A.

Geburah 5 Mars k 5.84 × 107 km** 2.06 × 108 kmChesed 4 Jupiter l 5.89 × 108 km** 7.41 × 108 km

Da’ath “11” Saturn m 1.20 × 109 km** 1.35 × 109 km Binah 3 Uranus n 2.59 × 109 km** 2.74 × 109 kmChokmah 2 Neptune o 4.31 × 109 km** 4.46 × 109 km

Kether 1 Pluto p 4.28 × 109

km** 4.43 × 109

km†

*At inferior conjunction.

**At opposition.




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†But Neptune’s aphelion distance is 4.54 × 109 km, whereas Pluto’s is 7.36 × 109 km. So whereas at His

farthest from Earth, Neptune’s distance from us is 4.56 × 109 km, Pluto’s apogee distance is 7.38 ×109 km.

If we lived on, say, Mars, the “Planets” moving most quickly through our heavens would be Phobosand Deimos, the moons of Mars. Next most swift would be Mercury, then Venus, then Earth,10 then Sol,and then, in order, Jupiter, Saturn, Uranus, Neptune, and Pluto. And this ordering of the Planets and Lightswould then also be in accord with their increasing average distance from Mars. By Key Number, theSephiroth on the Martian Tree of Life might accordingly have the following astronomical/astrologicalcorrelates:

Key Number Sephirah Planet/Light

1 Kether Pluto2 Chokmah Neptune3 Binah Uranus

Da’ath Saturn

4 Chesed Jupiter 5 Geburah Sol6 Tiphareth Earth/Luna (a double Sephirah!)7 Netzach Venus8 Hod Mercury9 Yesod Phobos/Deimos (another doublet)10 Malkuth Mars (the “Earth” of this system)

Of course, the geometry of this version of the Tree would have to be modified from that of the traditionalTree of Life to make Sol – Who is represented in this version of the Tree by Sephirah 5 rather than S . 6 – appear as the central organizing principle of the Solar System and the spiritual heavens which it really is.Accordingly, Sephirah 5 would have the Solar place on the Middle Pillar of this version of the Tree, rather

than Sephirah 6, which would have its place on one of the side Pillars.If, on the other hand, we lived on Venus, our version of the Tree of Life might be as follows:

Key Number Sephirah Planet/Light

1 Kether Pluto2 Chokmah Neptune3 Binah Uranus

Da’ath Saturn4 Chesed Jupiter 5 Geburah Mars6 Tiphareth Earth/Luna (a double Sephirah!)7 Netzach Sol8 Hod Mercury9 Malkuth Venus (the “Earth” of this system)

Again, this version of the Tree would require a suitably modified geometry. Also, notice that it has onlynine Sephiroth rather than ten. (Does this perhaps imply that people on Venus each have three hands, eachof which has two fingers and a thumb, something like the anatomical arrangements of lamviin of the worldcalled Sodde Lydfe, chronicled in surmale Mymysiir Offe Woom’s marvelous autobiographical presentation, Their Majesties’ Bucketeers?*)






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The Tree of Life as a concept is itself part of Olam Yetsirah , the Formative World. Hence it is a mapthat includes itself as part of the territory it maps. This is a characteristic of recursive languages, languageswhich can refer to themselves – or rather to simplified examples of themselves – as part of the conceptualuniverse which they map.11

In line with this, the Tree of Life is also a fractal structure. Each Sephirah and Atu of the Tree of Lifecan itself also be regarded as a Tree of Life in its own right, though one whose major character isdetermined by the nature of the element of the original Tree in which the smaller one is included. In turn,each element of the Tree of Life corresponding to that element of the original Tree is likewise a Tree of Life in its own right, each element of which is in turn a Tree of Life, . . ., and so on ad infinitum.

An analogous structure exists in library science in the form of the Dewey Decimal System of book cataloguing. In theory, no matter how complex the definition of any given subject, a call-number can bedetermined for it in that indexing system by first determining the broadest category of books to which it belongs, then, within that, the number of the greatest sub-category of the original category to which the book belongs, and so on until a unique number if the form of a linear array of digits is formed by thismethod. Read from left to right, the first digit in this digit-string is the one assigned to the first, major category; the second, the one assigned to the first sub-category of the original category; and so on down tothe last sub-sub-. . . . - sub-category and the digit assigned to it. The resulting decimal number is thereforethe cataloging number for the book.

For example, suppose that “religion and philosophy” is a primary category, to which is assigned thenumber 200. Then suppose “religious biography” is a sub-category within that one, to which is assigned

the number 290. Then suppose that “English religious leaders” would be a sub-sub-category, to which isassigned the number 299. If this process is carried out far enough, one could derive a unique number 299.abcdefgh to categorize a biography on the life and works of nearly any particular English religiousleader. (This example isn’t necessarily anything like the actual Dewey Decimal System. It is used solelyto give an idea of how such assignments can be made.)

Similarly, any idea, any concept at all of which we can conceive can be assigned its place on the Treeof Life by associating it first with that element of the Tree of Life with which is correlated the most generalcategory to which the concept may be assigned; then to that element of the Tree of Life comprised by theSephirah associated with that first, most general category, with which is associated the most general sub-category within the original one to which the concept may be assigned; and so on down, from level tolevel, element within element within element, until the concept is completely categorized by and associatedwith some ultimate sub-sub-sub- . . . -sub-element of the Tree. Thus the Tree of Life replicates itself at all possible magnifications, a fractal structure of great delicacy and precision. Fractals are the mathematical

analogues of linguistic recursions. The Tree of Life most elegantly exhibits both these properties – fractalization and recursion – and analysis of it in terms of these can be extremely useful.

In Gödel, Escher, Bach: An Eternal Golden Braid,12 Douglas R. Hoffstadter discusses the ideas of recursion and recursive languages and all their implications at great and delightful length (see especiallyChapter V, passim). More specifically, recursion is a characteristic of extremely high-level, flexible programming languages such as Pascal. In Fundamentals of Data Structures, Ellis Horowitz and SartajSahni describe recursivity, as follows:

. . . [One] of the most useful syntactical features for [structuring a cybernetic program tomake it easier to achieve the goal of readability and accuracy] is the procedure. Given aset of instructions which perform a logical operation, perhaps a very complex and longoperation, they can be grouped together as a procedure. The procedure name and its parameters are viewed as a new instruction which can be used in other programs. Given

the input-output specifications of a procedure, we don’t even have to know how the task is accomplished, only that it is available. This view of the procedure implies that it isinvoked, executed and returns control to the appropriate place in the calling procedure. . .. [P]rocedures may call themselves (direct recursion) before they are done or they maycall other procedures which again invoke the calling procedure (indirect recursion).These recursive mechanisms . . . can express an otherwise complex process very clearly. .. .13

From one point of view, Magick is a cybernetic language by means of which one can program and reprogram the Universe of which one is part from within that very Universe. From this point of view, the one




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from which the information and physical sciences view reality, everything that exists is information; andinformation, properly manipulated, can take on any content or form conceivable or desirable. Even so, theMagickian is him- or herself an integral part of all that is; so therefore, if he or she is to reprogram the processes and forms of the Universe to make them conform to his/her Will and Desire, then he/she must doso as part of the very system to be thus reprogrammed . He/she becomes part of the process of thatreprogramming, the primary instrument and tool of his/her own Will.

*Which can make for some interesting unexpected results of Magickal Workings, in light of Heisenberg’sUncertainty Principle. When the thing measured/manipulated is measured/manipulated by itself , prior knowledge of process, system-state, or both must go right out the window. Or, to put it another way,you can’t see where you’re going for getting there – and too bad if a nice, big brick wall gets in your way as you do so!

Since the Qaballah is recursive in the manner defined above by Horowitz and Sahni, it is thus ideal for Magickal purposes. In fact, in modifying the Qaballah and the Tree of Life as we have done here and in previous lessons of this course, we have used Qaballah is just this way: as a tool to modify itself , using the

principles of design of the traditional Qaballah and Tree of Life to produce new versions of them.

Exercise

Use of the mind in any way is Magickal. For according to both esoteric theory and the combinedexperience of many hundreds of generations of Hermeticists, there are always some manifestations inMalkuth of mental and psychic processes, just as men walking on friable soil always leave tracks of somekind, or as physical objects throw shadows of some form and some degree of darkness if there is any lightat all. Given that, what sort of changes in the material universe, if any, are likely to take place asreflections of or fallout from the process of modifying the Qaballah and the Tree of Life in the manner described above?

B. New Tarots

1. New designs

Styles in design of Tarot packs come and go – the Tarot itself remains. Preferences in design are verymuch a combination of individual taste in such matters and the esthetic dictates of the culture and historicalmilieu in which particular packs are designed and produced. This is a topic that deserves a whole book inits own right; still, we can touch on a few salient points here.

The well-known Rider pack, designed by Arthur Edward Waite and executed by Pamela ColemanSmith, is almost unique in that all the cards in it, not just the Greater Trumps and Court Cards, depictscenes from life. Each card is a little painting in its own right, featuring people engaged in various pursuitsin an urban, suburban, rural, or wilderness setting appropriate to its meaning. However, all of these peopleand most of the settings, as well as many of the activities in which the people in the scenes on the cards areengaged, are straight out of a textbook on the Middle Ages – and a highly romanticized one at that – rather than being taken from Waite’s own fin de siecle Great Britain or, indeed, any other place and period. If thecreators of the Rider pack were producing a Tarot deck today, in the late 20 th century, doubtless they’dupdate the styles of clothing worn by the people in the cards, their activities, and the settings in which thoseactivities take place, at least a little bit – perhaps all the way up to, say, Elizabethan times. At any rate, itwould be interesting to redesign this pack, using the same bold cartoon technique that Smith used in theexecution of the original, but picturing people, activities, and settings peculiar to our own times, as might be found in, e.g., late 20th-century London, New York, Moscow, Beijing, Tokyo, Johannesburg, Berlin,Paris, Beirut, Jerusalem, Teheran, or other modern major centers of human life and activity.*




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*This might be easier in some cases than in others. Some of these are still firmly embedded in the MiddleAges – say, the Middle Paleozoic. Ah, well, plus ça change, plus ça la meme chose . . .

Another possibility – assuming it really was possible; obviously, in many cases, it wouldn’t be, and an

imitation would have to serve – would be to have the most famous painters and draftsmen, both ancient andmodern, execute packs of their own, each in the unique style of the artist creating it. Assuming that theydid not abandon the criteria defining true Tarot packs, as defined in previous lessons, and kept to thestandard motifs and symbols that are invariant among legitimate packs, what sort of packs would thefollowing artists design: the painter Henri Matisse; Leonardo da Vinci; Charles Addams, the late,wonderfully macabre cartoonist; Paul Mavrides, the genius Alternative Press novelist and artist; Arthur Rakham, illustrator of Victorian children’s literature; John Tenniel, the editorial cartoonist who alsoillustrated the works of Lewis Carroll; Tenniel’s modern confrere, the illustrious Conrad of the Los

Angeles Times; M. C. Escher, with his fantastic anti-gravity waterfalls, rolling bugs, alchemicaltransformations of fish into birds and vice-versa, and multi-dimensional Möbius-strip worlds; R. Crumb or Gilbert Sheldon of underground comix fame; Walt Disney Studios; Hieronymus Bosch or his studentBrueghel, the Flemish masters whose nightmare visions anticipated the horrors of Dachau and Hiroshima;the American artist James Whistler; the science-fiction/fantasy/humor artists Michael Whelan, Frank KellyFreas, Norman Mingo, “Ghastly” Graham Ingles, Wallace Wood, Bill Elder, Don Martin, GeorgeWoodbridge, or Jack Davis, most of whom were also among the ranking artists and illustrators of MAD

Magazine; Johnny Parker, creator of the comic-strips “B.C.” and “The Wizard of Id”; Chester Gould,creator of the comic-strip “Dick Tracy”; Gary Trudeau of “Doonesbury”; Berk Breathed of “BloomCounty”; or even that greatest cartoonist of all time (say it reverently!), Gary Larson?

Or one could use characters from one’s favorite books or series of books, movies, comic-strips, baseball- or bubblegum-card series and the like, engaged in pursuits and found in settings normal to themin their original incarnations, yet still congenial to legitimate Tarot symbolism and the meanings of givencards. For example, a pack could be designed using characters, scenes, and activities taken from L. Frank Baum’s series of books on the wonderful land of Oz and its inhabitants. If all of these were taken straightout of his marvelous literary creations with little or no alteration, none of the completed designs wouldviolate the basic principles of Tarot design. The designs of cards in the Suit of Wands could be takendirectly from the Country of the Munchkins, with the Scarecrow, their local ruler, as the King of Wands;designs for the Suit of Cups could be taken from the Gilliken Country, with the Good Witch of the North as

Queen of Cups; those for the Suit of Swords could come from the Winkies, with Nick Chopper, the TinMan, as the King or Knight of Swords; and those for Discs/Pentacles/Coins could be taken from theCountry of the Quadlings, with Glinda the Good as Queen of that Suit. The Greater Trumps could be set inthe Emerald City, or taken from parts of the series not restricted to just one portion of Oz or even to Oz as awhole. For example, Trump 0, The Fool , might show Dorothy holding her little dog, Toto, as she stands onthe drab Kansas prairie, the tornado dancing ominously in the background. Trump III, The Empress, wouldof course show Her Royal Majesty Ozma, Empress of Oz. The Wizard of Oz would be perfect for Trump I,The Magus, while Glinda the Good could be the High Priestess in the Trump of that name, Trump II.

As discussed in previous lessons, the mathematical infrastructure of true Tarot packs and the symboliclanguage of their design are subject to rigid criteria, and may vary only according to equally rigid,restrictive metamathematical and philosophical principles. But the purely esthetic considerations of styleand conventions of artistic expression in Tarot cards may legitimately vary wildly, their mutations limited by little more than the extent and flexibility of the artist’s imagination – not to mention those of the courage

of prospective publishers of such packs. Designs can go from nearly purely mathematical in nature to thewildly romantic, to the bestially pornographic, to the classical elegance of Michelangelo, to the weirdnessof Salvador Dali, Michael Whelan, or Hieronymus Bosch, and still be legitimate Tarot.14

Exercise

Think up possible new designs for Tarot packs, going into as much detail as possible. Introduce themin class for open discussion and critical analysis.




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2. New Sense-Modalities for Tarot

What sort of Tarot “pack” would be useful to Helen Keller, assuming we aren’t talking about a pack done in a Braille-like bas-relief? This is an exercise for the entire class in open discussion.

Also, how would you put together a musical Tarot, and how would you package and market it for massconsumption? This is likewise a general exercise for the whole class.

C. Open Discussion

How has this course been useful to you?If you are a writer, has any of the material presented in this course been useful to you in your career, or

could it prove useful to you in your work in the future?Discuss writers such as Roger Zelazny and Samuel Delaney who are obviously familiar with Tarot,

since it is clear from their novels that they have done their homework in both Tarot and Qaballah. Havetheir literary creations, as such, benefited or suffered artistically as a result?

D. Students Grade Teacher

Please write out for Teacher your evaluation of this course, and how competently you feel she taughtit. What, if anything, do you feel should be added to or subtracted from it? What other courses/subjectswould you like to take up, now that you’ve had this course?

Has this course been useful to you in a general way or in particular ways? How could it have beenmade more useful to you? Would you have preferred emphases other than those given here by Teacher?

Would you be interested in classes on the theory, metaphysics, and principles of Ceremonial Magick, particularly as these depend upon Qaballah and the things presented in this course? How about astrologyand its correlation with Tarot and Qaballah?

Can you suggest materials and books that could have been used in this course, and would have beenuseful therein, but weren’t used?

Has Teacher been a good teacher? How could she have improved her technique, or otherwise madethis course and the way it was taught better for you?

Thank you for being such good students! Hope to see you again in my other courses! Best wishes and

hopes to all of you – and don’t forget to wear your galoshes and eat your chicken soup!

– Yael R. Dragwyla, Magistra Polaris

Endnotes

1Crowley believed that the true author of this book was an entity named “Aiwass” or “Aiwaz” whoclaimed to be his Holy Guardian Angel. However, he also said that there were three voices that dictatedthe three chapters of the book to him, which suggests that either Aiwass/z had a split personality, or that thesource of the book was other than him/her/it.

In fact, Liber Al vel Legis, with its three chapters and the Personalities that seem to be assigned to them – respectively, a feminine entity, the Mother, calling herself “Nuit,” associated with the Egyptian Mother-

Goddess Isis; a masculine entity, “Hadith,” the Father, associated with Osiris, the Slain and Risen God;and an Androgyne, “Ra-Hoor-Khuit,” associated with Horus-Set, the Twinned Child-God – has a structurewhich, on the plane of Yetsirah, closely resembles the physical Triangle of art used by Magickians inEvocation/Exorcism rites. There is a hint that the three Entities form the three sides of this Triangle, whichare also the three Supernals at the top of the Tree of Life, and together form a spiritual structure so strongthat no astral entity evoked into it can hope to break free of it unaided. If that is in fact the case, thenAiwass/z, rather than being the true author of Liber AL, may have been an astral entity partially or whollyevoked and bound by use of such a Triangle of Art on the Inner Planes, a projection of the process of thisevocation that was cast first into Yetzirah, where it manifested in Crowley’s mind as the text of the book,




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and finally into Assiah, the manifest world, where it took physical form as the completed and published book itself.*

*This idea is supported by the astrological chart erected for Crowley’s Cairo Working, one of whose products was apparently Liber AL. He began the Working in the Great Pyramid at Cairo, Egypt, on

midnight (12:00 a.m.) of March 20, 1904 e.v. In that chart, Sagittarius is rising, with Uranus inCapricorn in the First House, opposed to Neptune in Cancer in the Seventh. Crowley, the Magickian,corresponds to the chart’s First House, and thus to Uranus. So what did Neptune in the 7th, opposed toUranus, represent? Among other things, Neptune represents that aspect of evil known as the Deceiver,the Arch-Liar. It also represents the Aeon of Pisces/Osiris, which was closed out by the CairoWorking, with which began the Aeon of Aquarius/Horus. One wonders what Aiwass/z really was.

If such was in fact the case, then the text of Liber AL, as original conceived by the Supernals, mayhave been contaminated by interference from Aiwass/z, and should not be taken too literally or asunquestionable dogma. Further, what it would then represent would be an imperfect projection into thematerial world of the text of an exorcism, meant only to call up, bind, and banish the astral entity Aiwass/z,and perhaps little else. If so, any attempt to take it as prophecy or revealed doctrine would be ludicrous –

and could end in disaster.It is possible that the work represents a debate or dialectic among several entities, several competinglines of thought not all of which can be true. In that case, as well, taking it as doctrine would end inconfusion and worse, since to do so would keep one from sorting out which parts of it were true, if any, andwhich false, impelling one to act on all of them equally without discrimination.

The idea that Aiwass/z had or was a split personality – and that, as this being was supposedly part of Crowley’s own being, thus implying that Crowley himself had a schizoid personality – may not be far off the mark. From his own writings and elsewhere, there is a great deal of evidence that Crowley wasseverely psychoneurotic, as many people of his age and culture were. Aleister Crowley was born onOctober 12, 1875 into an upper-middle class Victorian English household. Like many contemporaries of his class, he may well have been severely abused, probably sexually, when he was small by some adult or adults in or known to his family. Such abuse of small children can cause personality dissociation as well asa host of other emotional and mental developmental pathologies, and if Crowley suffered from such acondition, it would have been no surprise, given his origins.

See Geoffrey Masson’s Assault on Truth: Freud’s Suppression of the Seduction Theory (New York:Farrar-Straus-Giroux, 1984) for an excellent overview of the epidemic, systematic abuse of small children by adults and the conspiracy by the medical, legal, and other professions to hide the fact of it during thatera.

2“e.v.” = Era Vulgaris or “Common Age,’ i.e., the Christian Era, Anno Domini.

3There have been many arguments over just when the Aeon of Pisces/Osiris ended and that of Horus/Aquarius began or will begin. A major reason for this is the fact that unlike the astrological Signs or Solar Months, each of which comprises exactly 30° of arc of the Ecliptic (the Sun’s yearly path around thesky among the Stars), the twelve Zodiacal Constellations are not all of equal size. Some Constellations aremuch larger than others (though of course since together they cover the round of the Ecliptic, the sum of their widths must be exactly 360° and their average size 30°).

The Vernal Coleur – the celestial longitude of the Sun on the first day of Spring in a given year – changes from one Zodiacal Constellation to the one just West of it along the Ecliptic over a span of timethat depends upon how wide that Constellation and the ones flanking it are. So the arguments about whenexactly the Aeon of Pisces/Osiris ended/will end and that of Aquarius/Horus began/will begin really turn onhow wide the longitudinal boundaries of these Constellations are.

The Constellations aren’t absolutely static, fixed pieces of sky whose geometric interrelationships areforever immutable. Like the continents of the Earth, which slide on their plates across the face of the globeas the Aeons pass, losing and gaining pieces as they crash into one another like Leviathans rampagingthrough the inconceivable deeps of the Night of Time, the Constellations are constantly changing in size








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Similarly, each of these may be conceived as being constructed of nine smaller squares, the length of a sideof each one-third that of the parent square. Cut out the center sub-square of each of these remaining eightsquares; eight sub-squares will remain. Continue this process indefinitely, producing the following result,which has a boundary of infinite length and zero area:

Sierpinski Carpet

(another fractal)

The three-dimensional analog of the Sierpinski Carpet is the Menger Sponge, a solid-looking lattice

with infinite surface area and zero volume. Given a cube of volume X3

, drill a column through the middleof each side of the cube to the other side of the cube, parallel to the sides above, below, and to either side of it, such that the column has a square cross-section equal in area to one-ninth that of a side of the cube, i.e.,X2/9. This completely excises the center of the original cube, the center having a volume of X3/27, as wellas a cube of equal volume out of the center of each of the six faces of the original cube. Repeat the processwith each of the remaining 20 cubicles of volume X3/27 still left of the original volume, and so on ad

infinitum:






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Menger Sponge

(a fractal solid of infinite surface area and zero volume)

MENGER SPONGE: Mathematicians in the early 20th centuryconceived various weird objects made by adding or removing infinitelymany parts. One such shape is the Sierpinski Carpet, shown above,constructed by cutting out the center one-ninth of a square, then cuttingout the centers of the eight smaller remaining squares; and so on. The3-dimensional analog of the Sierpinski Carpet is the Menger Sponge, asolid-looking lattice that has an infinite surface but zero volume.

These examples are also found in James Gleick’s Chaos: Making a New Science (New York: PenguinBooks, 1987), pp. 96-103. This book is of inestimable value to the student, and an asset to any esoteric or Hermetic library.

10By average distance from Mars. For example, while Earth is far closer to Mars at its periarion(closest approach to Mars) than is Mercury at its own periarion, Mercury is always closer to Mars at any part of its orbit than is Earth at aparion (greatest distance from Mars), and the average apparent angular

motion of either of these bodies would then vary inversely as their average distance from Mars.

11See Ellis Horowitz and Sartaj Sahni’s Fundamental Data Structures (Potomac, MD: Computer Science Press, Inc., 1977), pp. 22-26 and passim, for a lucid and readable explanation of recursion as usedin computer programming languages in particular. The concept applies to language as a general phenomenon, as well, and thus to the technical languages of the esoteric Arts and Sciences.

12Douglas R. Hoffstadter, Gödel, Escher, Bach: An Eternal Golden Braid (New York: VantageBooks, 1980).

13Horowitz and Sahni, op. cit., pp. 22-23.

14 Nota bene: Useful color assignments á la the King, Queen, Prince, and Princess Scales of color

assignments found in 777 and Other Qabalistic Writings of Aleister Crowley (op. cit., scales XV-XVIII)might be as follows:

Those parts of the electromagnetic spectrum below (less energetic than) visual red (for example, infra-red, microwave, radio, UHF, VHF, etc.) are associated with the Pillar of Power, which includes the

Sephirah i = √-1, 0 (Zero), and the Null or Empty Set Ø. Sephirah i = √-1 is associated with the highest-energy parts of that sub-red portion of the spectrum, that is, near infrared, Sephirah Ø (Null Set) isassociated with the lowest-energy part, the background energy of the universe left over from the Big Bang,which has an average temperature of 3° Kelvin (i.e., 3 degrees Celsius above Absolute Zero temperature,where Celsius intervals of temperature are identical to those of the Centigrade scale), and Zero representseverything in between.

Similarly, the Pillar of Grace, consisting of Sephirah ℵ2 (the Number of All Possible Mathematical

Structures), ℵ1 (the Number of All Possible Mathematical Curves), and ℵ0 (the Number of All Numbers,representing the Real Line, the set of all Real numbers), may be usefully associated with those portions of

the electromagnetic spectrum above (more energetic than) visual purple, as follows. ℵ2 is associated withgamma radiation, the most energetic form of hyper-purple electromagnetic radiation; ℵ0 is associated with

near ultraviolet, the least energetic form of such radiation; and ℵ1 is associated with everything in between.

This sort of arrangement gives at least the beginnings of a way to assign colors to the new Sephirothand Paths after the fashion of color assignments to traditional Paths. In general, these new color assignments would not be visible to the unaided human eye, but they would be detectable usinginstrumentation of the sort we have in plentitude now; and for the near-infrared and near-ultraviolet, quitea few no-human beings, including bees and some other insects, some birds, some plants, etc., respond



Qaballah and Tarot: Lesson IX

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