No very extensive knowledge of occult mathematics is required by beginners in Tarot-study. All that is absolutely
necessary may be stated in a few paragraphs. It is developed from the Qabalistic doctrine of a ten-fold emanation from
the Absolute.
The Absolute is Ain Suph, No Limit. From Kapila and the Bhavagad Gita to Spinoza and Sir William Hamilton,
philosophers always describe it by negatives. Boehme, for example, says: “It may fitly be compared to Nothing, for it is
deeper than anything, and is as nothing with respect to all things.” The idea of depth emphasized by Boehme echoes
Lao-tze, who calls the Absolute “the Mother-deep.” This feminine aspect of the Absolute is recognized by all deep
thinkers, for that in which lies the potentiality of all things must be as truly Mother as Father. This feminine potency is
represented by the zero-sign, 0, a circle or oval, symbol of the Great Mother and of the egg of the universe. The
Changeless 0, which cannot be added to, subtracted from, multiplied, nor divided, is a perfect numerical symbol for Ain.
Suph. In the major trumps of the Tarot it is represented by The Fool.
The initial emanation from Ain Suph is Kether, the Crown, identical with the Supernal Source in all but name, the
Creative Principle in the beginning. The inherent mental quality of the Supernal Originating Principle is implied through
the Qabalah. Its primary expression, therefore, cannot be other than some form of Will; and the first conceivable
manifestation of that Will in beginning the creative process would be the selection of a particular point in space at which
to start. Hence Qabalists call Kether the Primal Will, and sometimes refer to it as the “Small Point.” The point
corresponds geometrically to 1, which represents what Eliphas Levi terms “the relative unity, manifested, possessing
duality, the beginning of numerical sequence.” The student should note particularly that the number 1 possesses
duality. This idea is a key to many occult truths.
The duad is Chokmah* , Wisdom. the number of science, since all scientific knowledge is based upon comparison; of
Woman as the wife of Man., of antagonism, opposition, and polarity; and also of equilibrium. The duad is the especial
symbol of Memory, because every recollection duplicates an original experience. Perfect memory is required to
continue a creative process springing from a Limitless Absolute and begun by an Infinite Will; and this perfect
recollection of every stage of development is the essence of that Wisdom by which, says the Bible, the Lord founded
the earth. Whosoever can understand the saying, “God creates by remembering Himself,” is very near to the real
meaning of the duad. He will understand, moreover, why the full significance of this number must be concealed from the
profane.
* The aspect of Chokmah represented in the Tarot by the number 2, and the High Priestess, is the Lesser Chokmah
mentioned in the twenty--first chapter of the Lesser Holy, Assembly,. It is female in respect to Kether.
The triad is Binah (BINH), Understanding, which, says The Lesser Holy Assembly, “comprehendeth all things. . . . For in
the word BINH are shown Father, Mother, and Son; since by the letters IH Father and Mother are denoted, and the
letters BN, denoting the Son are amalgamated with them.” Binah is the Great Sea, Mare-Mary the Great Mother. Her
ancient symbol is an equilateral triangle with the apex turned downward-the Phoenician character for the letter Daleth.
Papus says: The hieroglyphic meaning of Daleth is the womb. It suggests an object giving plentiful nourishment, the
source of future growth.” By gematria, BINH = 2+10+50+5 = 67 = 13 = 4, and the value of Daleth is 4. Again, since BINH
= 67=13, it suggests the selfdivision of the One which is the foundation of the creative process, for the Name of the
One is IHVH = 26, and 13 (BINH) =26 --'2, or IHVH divided by Chokmah (2). Finally, in the Tarot Daleth is The Empress,
who corresponds to the number 3. This number denotes extension, expansion, increase, growth, and generative
activity.
In some respects, Chesed, the fourth Sephirah, is a repetition of Kether, because its number, 4, is 10 by extension ( 1
+2+3+4), and the reduction of 10 (1+0) is 1. As Kether is “The Crown,” so is Chesed sometimes called Gedulah,, or
“Majesty.” Mercy, or Benevolence, the self-imparting aspect of the Primal Will, is the fundamental meaning of this
number, which the Tarot symbolizes by The Emperor.
Geburah, Strength or Severity, also named justice (Din), or Fear (Pechad), is the Sephirah corresponding to the
number 5. This number is the mean term between 1, the beginning of the integral series, and 9, its end. Hence it
implies balance, or equilibrium. That this is the rootquality of justice needs no demonstration. Equilibrium, moreover, is
the Great Arcanum of magic. The search for it entails trials of the utmost rigor and severity trials which inspire the
unprepared with chilling fear., but when they are passed, the seeker finds in balance an exhaustless source of
strength. Therefore, in the Tarot is this number and Sephirah represented by The Hierophant, the “revealer of the
mysteries” of the Great Arcanum.
From 5 proceeds 6, for the extension of 5 is 15, and by reduction 15 is 6. This number also proceeds directly from 3 by
extension; and as 3 is itself the extension of 2, the number 6 is really involved in, or implied by, the duad. Of this its
geometrical symbol is a reminder, for the hexagram, or six-pointed star, is composed of two interlaced equilateral
triangles, a double triad. This is what Eliphas Levi means when he says that in a certain aspect “the senary is only the
duad exalted and carried to its extreme power.” The corresponding Sephirah is Tiphareth, Beauty; and as all true
beauty implies rhythm, harmony, and symmetry, it is not difficult to understand why the hexagram, the geometrical basis
of the snow-flake, is regarded by Qabalists as its most appropriate symbol. There Are other, and deeper,
correspondences, moreover, between the number 6 and the idea of Beauty. Upon these I hope to be able to dwell at
greater length when I come to the interpretation of the sixth major trump, The Lovers.
The union of 1 and 6 produces 7, which in this aspect is a symbol of the harmonious
manifestation of the specializing power represented by 1. But it is as the sum of 3 and 4, represented by the figure of
an equilateral triangle surmounting a square, that the septenary reveals its deepest meaning. As the sum of the triad
and the tetrad, 7 is the sacred number of all religions, and, especially, a summary of the whole secret doctrine of Israel.
It corresponds to the Sephirah Netzach, Victory, and is represented in the major trumps by The Chariot.
The number 8 is that of the Sephirah Hod, Eternal Order, or Splendor. Eliphas Levi says: “It represents motion, Yet
also, and more than all, stability; it reconciles the opposed laws of nature. explains eternity by time, faith by knowledge,
God by man. It is the number of eternal Introduction to the Study of Tarot life, which is maintained by the equilibrium of
motion.” This is the only cube among the integers, formed by the double multiplication of the duad (2 x 2 x 2). Here' for
discerning students, is an important clue to the occult significance of 8. Another is that by its extension it produces 36,
a number representing the combination of the triad and the senary or Understanding and Beauty. Finally, the Sephirah
Hod is the seat of “The Intelligence of the Secret,” and the secret is that of the direction of the Great Magical Agent.
Even the shape of the figure 8 is a hint of that secret. Far more than a hint is given in the symbolism of the eighth major
trump in Mr. Waite's pack, entitled Strength.
In 8, because its extension is 36--3+6=9, is concealed the potency of 9, and the nature of that potency is revealed by
the fact that in the symbolism of number 9 stands for prophecy and initiation. In occult mathematics, therefore, initiation
and prophecy are considered to be manifestations of the power of the duad, because they are expressed by a number
which results from the extension of the cube of the duad. That they are so in fact is understood by every occultist who
has mastered even the rudiments of' the Sacred Science. As the final term of the integral series, 9 signifies completion.
Hence it is a symbol of perfection, entirety, and realization; and it denotes those who have reached the heights of
attainment-the experts, virtuosi, adepts, and illuminati. It is the number of Yesod, the Sephirah of Foundation, the seat
of “Pure Intelligence.” In the Tarot it corresponds to The Hermit.
As the last of the integers, the number 9 really completes the series of simple mathematical ideas from which all others
are derived; but in the scheme of the Sephiroth the number 10 is included. It is assigned to Malkuth, the Kingdom,
declared by Qabalists to be the Shekinah, or divine halo which encircles all the other nine Sephiroth, and encompasses
the whole in its presence. The number 10 represents the combination of the Manifest (1) and the Unmanifest (0), the
particular and the universal, the Primal Will (Kether) and the Limitless Absolute (Ain Suph). It is a sign of the totality of
existence, of the perfection and consummation of all things. As the extension of 4, it is the sum of the monad, the duad,
the triad, and the tetrad, and so combines all the fundamental mathematical conceptions of the Sacred Science. It is
also produced by the reduction of the extension of 7 (28 =2+8 =10). Finally, it is the number which brings all the
integers back to unity, since 10 =1+0 =1 ; and its own extension, 55, is not only the double pentad, but is also
significant of the eternal self-reproduction of the Divine Kingdom, since 55=5+5=10. Its representative in the major
trumps is The Wheel of Fortune.
The student who has read, in Chapter 1, that the twenty-two major trumps correspond to the twenty-two letters of the
Hebrew alphabet, may wonder why I am now assigning them to the Sephiroth. The reason is that each trump has a
double significance. For the paths between the Sephiroth, indicated by the twenty-two letters, are really only forms or
stages of the activity of the Sephiroth themselves. And the student will find, as he progresses in his study of the cards,
that whatever apparent confusion may arise from the fact that each trump has two meanings will disappear when the
full extent of each meaning is grasped, simply because the two are really aspects of a single truth.
In conclusion, let me give a simple rule for determining the Sephirotic correspondence of any major trump bearing a
number higher than 10. First, reduce the number to an integer; second, find the extension of that integer, and reduce it
also.
Example:
What is the Sephirotic value of trump 17, The Star ?
17==1+7= 8, therefore The Star represents an aspect of Splendor, the eighth Sephirah, and should be compared, for
study, with Strength.
The extension of 8 is 36. This may be articulated as 3 and 6, hence we know that The Star represents, in the
extension, or development, of the power symbolized by it, a combination of the principles represented by The Empress
and The Lovers, or the Sephiroth Binah and Tiphareth.
The reduction of 36 is 9. Hence we may study The Hermit for a symbolic presentation of the secret doctrine about what
results from the development of the activity represented by The Star.
These considerations, combined with what we shall learn of each card by the analysis of its symbolism in connection
with the secret meaning of the Hebrew letter to which it corresponds, will enable us to establish our study of the Tarot
upon a sure foundation. In succeeding chapters I shall endeavour to furnish outlines for such study.
In the Tarot the archetypal triad of involution is represented by the Fool, the Magician, and the High Priestess. Readers
who possess the cards can better follow the explanation of the symbols if they will place these three trumps on a table,
with the Magician immediately below the Fool, and the left upper corner of the next card just touching the right lower
corner of the picture of the Magician, so that his left hand will be pointing toward the black pillar on the High Priestess'
right. In this arrangement, the Fool stands in the place of Ain Suph, and the Magician and High Priestess indicate the
positions of Kether and Chokmah on the Qabalistic “Tree of Life.”
The Fool is Yod of Yod, the archetypal active principle of involution before manifestation, not as It really is, because
the Absolute transcends finite comprehension, but as It has revealed Itself, in a measure, to the wise. He is Ain, No-
thing, Ain Suph, No Limit, and Ain Suph Aur, Limitless Light. This last designation is the keynote of occult doctrine.
What it implies is confirmed by the discoveries of modern scientists, although they approach Truth by other paths than
those of occultism.
Because we must think of the Absolute in terms of our own experience, It presents Itself to us in human form (The
Fool); but behind this personal seeming the sages discern something highertypified in this picture by the white sun-an
Impersonal Power, manifesting as the Limitless Energy radiated to the planets of innumerable world systems by their
suns. In manifestation, that Energy, symbolized also by the fair hair of the traveler, is temporarily limited by living
organisms. Of these the vegetable kingdom, represented by the green wreath, is the primary class, from which, in
course of evolution, spring animal organisms, typified by the red feather.
The Supreme Spirit is forever young, forever in the morning of its power, forever on the verge of the abyss of
manifestation. It always faces unknown possibilities of self-expression transcending any height it may have reached at
a given time; hence the Fool faces west, toward a peak above and beyond his present station. It is THAT which was, is,
and shall be, and this is indicated by the Hebrew letters Yod-Heh-Vau-Heh, faintly traced on the collar of the Fool's
under garment.
This inner robe is the dazzling white Light of Perfect Wisdom (Sattva, in Hindu philosophy); and it is concealed by the
black coat of Ignorance (Tamas), lined with the red of passion, fire, and material force (Rajas). This outer garment is
embroidered with what seems to be a floral decoration, but the unit of design is a solar orb, containing a red double
solar cross, surrounded by seven triple flames. These are the seven Spirits of God, the Elohim, through whose activity
all forms are projected, according to laws analogous to those of the vegetable kingdom.
The primary manifestation of Spirit is Will, of which Attention-the wand-is the essence, and to which Memory-the wallet-
is closely linked. Wisdom, having for its essence Imagination-the rose-is the secondary expression. Upon the progress
of this vital principle in humanity depends the advancement of the sub-human forms, represented by the dog.
A key to the true significance of the title is the saying, “The wisdom of God is foolishness with men.” The name of this
trump also indicates the folly of every attempt to define the Supreme Spirit. All names are definitions, and to define God
is to blaspheme Him.
As Heh of Yod, the Magician is passive to Ain Suph, hence he is a symbolic antithesis to the Fool. He is God the
Creator in the Beginning, in contrast to God the Principle before all beginnings. He is Kether, the Primal Will which
initiates the creative process by selecting a particular point in space at which to begin.
His passive relation to Ain Suph Aur, Limitless Light, is indicated by his uplifted right hand, holding the magic wand by
means of which he draws down power from above. That power is the descending Energy typified by the Fool; and the
Magician's wand, in the arrangement of the cards explained at the beginning of this chapter, points directly to the verge
of the abyss whereon the traveler is poised.
The Magician's left hand points toward the High Priestess. It is as if he were the medium through which the Limitless
Light finds expression in Chokmah. This gesture also denotes concentration, and the selective action of Creative Will.
The same selective action is also suggested by the table, which implies definite location, and is, in one sense, a symbol
of the material universe. The emblems of the Tarot suits lying upon it are the elements used by the Magician in his
work.
Roses above his head and at his feet suggest the Hermetic axiom, “That which is above is as that which is below.” The
Magician himself, moreover, through his correspondence to Beth, corresponds to the direction Above, which indicates
that lie is “the superior nature” or Purusha of Hindu philosophers. He is the Onlooker, the objective aspect of Infinite
Intelligence, perceiving nature as something other than himself. In Egyptian mythology he is Thoth, in the mysteries of
Greece he is Hermes, and in the allegory of Genesis he is Adam, the first man, or first mode of mind.
The roses in the garden are symbols of the universal feminine principle, and they grow side by side with lilies, which
are masculine emblems. Thus the flowers, which belong to the Magician, and which he cultivates, remind us of the
doctrine that the number One possesses duality: for they denote the Law of Gender, an important aspect of the duad.
Over the Magician's head is the lemniscate symbol of the Holy Spirit. A double zero, it represents the ancient doctrine
that in creating Spirit divides itself, so that the One becomes Two.
The central point of contact is Kether, the “Small Point” of primary manifestation. Because even the Primal Will is a
limitation of Ain Suph, it possesses some degree of the quality of darkness. Hence the Magician's hair is black; but a
golden band surrounds it, to show that the Darkness is held in cheek by Light. Here is the antithesis to the Fool's
yellow hair and his green wreath.
The Magician's red mantle symbolizes Light and Creative Force (Rajas); his white robe denotes Purity and Wisdom
(Sattva); and his blue serpent girdle represents Time and Occult Science, because the Ancient Wisdom is the fruit of
observations and experiments begun thousands of years ago.
The High Priestess is the archetypal formative principle, Vau of Yod, which combines the potency of the Originating
Yod (The Fool) with the initiative and selection of the Creative Heh (The Magician). The Fool may be represented as a
circle, the Magician as the center, and the High Priestess as the diameter, dividing the circle into two equal parts. The
circle is Infinite Intelligence; the center is the Primal Will, and the extension of that Will toward the limitless
circumference is the Line, the geometrical correspondence to the number Two. This is Chokmah, the Sephirah of
Perfect Wisdom. The High Priestess is the feminine Chokmah, personified in proverbs as a woman, passive in her
relation to Kether.
Literally, her name means “The Superior Feminine Elder,” or the archetypal feminine principle. She is what Hindus call
Prakriti, the inferior nature of the Supreme Spirit. Yet she is one in essence with the superior nature, Purusha, from
which she proceeds. The Emerald Table of Hermes says the same thing, “As above, so below;” and the bearing of this
upon Qabalistic doctrine in the Tarot is the fact that the Sepher Yetzirah attributes to Beth (The Magician) the direction
“Above,” and to Gimel (the High Priestess) the direction “Below.” She is Eve, before her union with Adam; and she also
wears the horned crown and blue robe of Isis. The color of her vestments likewise connects her with the Virgin Mary,
and the moon at her feet suggests the goddess Artemis, or Diana, also a virgin.
In more than sex is she the antithesis of the Magician. His mantle represents Fire and Light; her garments, in both color
and line, remind us of Cold and Moisture. The Magician stands; but she sits on a cubic stone, a symbol of Salt, which
crystallizes in perfect cubes, and a reminder of the saltness of that mystic Sea which is associated with the name of
Mary. The Magician is out-ofdoors; but the High Priestess sits in a temple. He is the objective aspect of consciousness,
the Cognizer of the universe and its laws; she is the subjective aspect, reflecting what he perceives, and recording it
upon the scroll of the Memory of Nature. That scroll is inscribed with the word TORA, the four letters of which, arranged
in certain ways, afford a clue to the whole mystery of the Tarot. As written on the scroll, they are the phonetic
equivalent of the Hebrew Torah, the Law.
The pillars are those of Solomon and Hermes. Opposite in color, but alike in form, they represent Affirmation (“J” or
Jachin) and Negation (“B” or Boaz). For strength (Boaz) is rooted in resistance, or inertia - the negation of the
Establishing Principle (Jachin) of all things. The High Priestess sits between the pillars, because she is the equilibrating
principle between the “Yes” and the “No,” the initiative and the resistance, the Light and the Darkness.
From the pillars hangs a veil, embroidered with palms and pomegranates. The palms are masculine emblems, and the
pomegranates are feminine. The latter are so disposed upon the veil, that, although but seven can be seen, three
more would be shown were not the High Priestess in the way. The basis of this design is the Qabalistic “Tree of Life.”
Qabalists will notice that the crown of the High Priestess has its horns in Chokmah ,and Binah, and its orb in Daath
(Knowledge). The lower point of the solar cross on her breast touches Tiphareth; and her seat, the Cubic Stone of Salt
and of the Material Universe, is in Yesod, the Foundation, and Malkuth, the Kingdom. Lack of space forbids a more
extended explanation of this arrangement; but the keys to it are already in the possession of readers who have
mastered the elements of the preceding chapters, and it will be even more intelligible as we proceed with the
interpretation of the other major trumps.
Such is an outline of the significance of the first triad. Let the student ponder upon it, and amplify it for himself. To each
person some aspects of the doctrine of the Tarot are more obvious than others. Yet they are all related, and he who
masters these first principles may be sure that, in due time, he will find them leading him to other, and higher aspects of
that One Truth that is back of them all.
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Introduction To The Study Of The Tarot: Chapter IV & V