Brief expositions on the nature, significance, and utility of symbols used in religion, philosophy, science, and art.
The symbolism of Numbers is one of the indispensable foundations of all Science, and has been taught by most of the great mystics and religious philosophers.
The precise formulation of scientific laws is impossible without the elements of numeration.
“Number was called Arithmos (as that which measures and orderly arranges all things, and unites them in harmonious proportion.” (Thomas Taylor.)
“All things are assimilated to Numbers.” says the Pythagorean maxim.
The characteristics of Time and Space and Motion would be meaningless without numerical presentation of some description.
Everything subsisting according to Nature has its Number. The name of a thing is its Word, or reason of existence: the number of a thing is its Power – passive or active – by which it represents its Word or Name.
The inter-relations of the Numbers of all things, when expressed with exactitude, represent the fundamental Laws upon which the operations of the Cosmos depend.
And this holds good even when Science leaves the domains of Nature and enters the realms of Spirit or Super-Nature.
The numbers One to Ten are the keys of all mysteries.
“Number is the governing and self-begotten bond of the perpetual permanency of mundane natures.” (Philolaus, the Pythagorean.)
In other words, the spiritual and immutable principles and laws behind all material and mutable natures are, in a certain sense, Numbers. But they are not the ordinary numerals of arithmetic.
It may be said that there are three Orders of Numbers, corresponding to the Natural, Spiritual, and Divine Sciences.
(1) Mathematical Numbers, which are units or numerical components; for example, the number ten is composed of ten units, or of any series of components equivalent to ten.
These are the numbers which, with their divisions and fractions, are employed in the Natural Sciences as well as in other spheres of practical mundane activity.
Their Symbolism is literal and precise, but not arbitrary and variable.
They have geometrical expression.
(2) Ideal Numbers. These are not composed of units, save the first unit, which is Unity itself. They are Ideas and Archetypes.
“According to Pythagoras and Plato every Ideal number is an Idea and has a paradigmatic peculiarity.” (Thomas Taylor.)
For instance, the Duad is the Idea or Paradigm of Two-ness or Duality in all its phases. As an Idea it is one and not two, therefore it is equivalent quantitatively – but not qualitatively – to the Monad which is the prototype of One-ness.
The Ideal Numbers are from One to Ten; all other series of numbers above the decad are composed of different combinations and unions of the Ideal Numbers. For example, eleven may represent the idea of ten combined with the idea of one; or of the idea of one united with the idea of two repeated five times; or of the duad joined with the idea of three triads; and so on.
Each Ideal Number is an aspect of the Primal Monad, in fact, as an Idea, each is itself monadic. Thus the Hebdomad is not seven units, nor is it the union of the triad and the tetrad; but rather is it the one septenary principle of all creation, which, as such, is an indivisible wholeness.
Hence, Ideal Numbers are distinct individual types and wholeness, each representing its own archetypal principle – self-prolific and self-subsistent, – independent of all other numbers, except The ONE, Who, however, is not a number.
“Ideal Numbers, according to Pythagoras, are generated from the Monad and the indefinite Duad: each of them is One, and no one is a part of another.” (Thomas Taylor.)
The indefinite Duad, among other things, is the initial idea of progression, by which the principle of Plurality emanates from the Monad, or the principle of Unity.
According to Syrianus, Pythagoras in the “Sacred Discourse,” states that “Number is the ruler of types and ideas, and the cause of the divine and, angelic progressions.”
(3) Divine Numbers. The Monad of Monads is God as the ONE. In Him all Ideal Numbers subsist superessentially. They are Infinite and Divine because they symbolize the Powers and Attributes of the Infinite One.
Although each superessential Number is infinite this does not imply duplication or triplication of infinity, for the Infinite One is transcendentally beyond all ideas of increase or multiplication.
But even as Archetypes are Divine Thoughts of Ideal Perfections, so Divine Numbers are expressive of the Divine Infinite Powers according to which all things abide in, proceed from, and return to the Superessential Absolute ONE.
(1) THE MONAD.
(a) Mathematically, the figure 1 is the root of all numbers: as such it is indivisible. Fractions do not really split up the unit, but are themselves components of lesser units.
All mathematical numbers proceed from unity as its modes and products, but unity is in and of itself.
Unity multiplied by unity remains unity.
Nothing can ever exist unless it is one, hence all things possess oneness, proceed from the one, through different media, and because of this receive their own particular individuality.
Geometrically, One is represented by the Dot or Point.
(b) Ideally, Number One is the Primal Monad or Subjective Idea of Unity and Integral Oneness.
According to Iamblichus, it is the cause of
sameness and union.
It symbolizes singleness, simplicity, definition,
identity, unification, and universality.
Since it contains an infinite number of unities it
signifies that infinite potentiality of which all numerical progression is
the never-ending process of actualization. And, for the same reason it
denotes the Will in all its aspects.
The higher any number is, the higher is the
actualized-potentiality which it symbolizes.
The Monad is also the Archetypal Man who is the
One Idea of Pan-humanity and the unitary embodiment of divine perfections.
(c) Superessentially, One is the Absolute, Who
is superlative in His Ineffable Unity.
There is none before Him; but all are from Him.
He is the Beginning without a beginning; and,
at the same time, the End, without a progression; the Alpha and Omega, the
One without a second.
Infinity added to Itself is still Infinity: God
is the All comprehending ONE to Whom nothing can ever be added, even in a
2. THE DUAD.
(a) Mathematically, the figure 2 is negative
and feminine, like all even numbers. As the first multiplication of the
number one it is the beginning of numerical sequence. It is really the first
Geometrically it is the Line extended from the
(b) Ideally, it is the Duad of duads and the
Idea of Twoness, not of two units, but of Duality, the bifold or binary
principle of things. It is indefinite receptivity, and, in the abstract
sense, denotes Matter and Passivity. It is the first Chaos or Void
conceivable as separate from and relative to the Absolute One, hence in a
passive, but not active sense, it is the principle of separation and
relativity; of division and differentiation; of reflectiveness and
reproduction; of polarity and the pairs of opposites.
(c) Divinely, it is God’s reflection of Himself,
so that He is at once the Transcendental Immanence, and the Father-Mother of
3. THE TRIAD.
(a) The figure 3 is the first relative number:
unity being absolute. It is positive and masculine like all odd numbers.
It proceeds from the indefinite duad, and, as the
triangle, is the first defined and enclosed figure or superficies.
(b) As an abstract Idea, three is the Triad of
triads and the universal ternary principle. It is the actualization of the
passive-potentiality of the duad.
It symbolizes activity of all kinds, and since
it comprehends the Actor, the Acting, and the Action, as well as the Knower,
the Knowing, and the Known, it is that Cosmic Ideation by which all things
are generated and made manifest in successive stages of beginning, middle,
end. It is the union of the positive and negative by Action and thus denotes
fecundity and vitalization; harmony and order. It is the principle of all
trilogies and the basic tripartite classification.
It is Subjective-Objective-Projective;
Static-Dynamic-Ideal; Being-Life-Intellect; Time-Space-Motion;
Length-Breadth-Thickness; Quantity-Quality-Intensity; Past-Present-Future;
Above-Below-Between; Spirit-Soul- Body; Will-Heart-Mind; Father-Mother-Son;
Iamblichus says: “The Triad is truly
all-harmonic, containing all ratios in itself and unfolding in itself the
second, or duadic, distribution of things.”
(c) Divinely, it is God as the
Manifest-and-at-the-sametime-Unmanifest: the Good-the True-the Beautiful;
the Divine Trinity or Tri-Unity of the Three Co-eternal Con-substantial
4. THE TETRAD
(a) The figure 4 is the natural effect of the
action of the triad. It is the Square and the fundamental concrete numeral.
(b) Ideally, it is the number of Manifestation
because it is the result of ternion Ideation and denotes the Four Planes:
Divine-Creative-Formative- Material: as well as the Four Limbs of the
whirling Cosmic Cross of the Manifested Worlds.
It symbolizes Law because it comprehends the
Four Chief Orders: Divine-Celestial-Human-Natural.
It is called the Key-bearer and Key-keeper, because it
Four Basic Causes: Final-Efficient-Formal-Material.
It is the Fertile Fount of Nature because it
includes the Four Elements: Earth-Air-Water-Fire, and the Four Seasons or
Periods of natural evolution, as well as the four qualities:
It is Objectivity, because it outlines the Four
Quarters and Regions.
It is the Heavenly City because it is the
Quarternion Redemption and the Universal integration, by the Four Cardinal
Virtues and similar means.
It is Revelation because, among other things,
it is the Possession of the Four Divine Inspirations of Plato: the Musical,
the Telestic, the Prophetic, and the Amatory.
(c) Divinely, the Tetrad is the Sacred
Tetractys of Pythagoras, who says: “Divine number proceeds from the
penetralia of the undecaying Monad until it arrives at the Divine Tetrad,
which brings forth the mother of all things, the universal recipient,
venerable, immutable, and unwearied, and which is denominated the Sacred
It is God manifesting simultaneously the Powers
of the Monad-Duad-Triad-Tetrad, and since the mathematical sum of these
Numbers is Ten, the Tetractys is sometimes called the Sacred Decad.
5. THE PENTAD.
(a) Mathematically, the figure 5, as the
product of 4 plus 1, is manifestation dominated by Will; as the product of 3
and 2 it is dualistic activity; hence is called the number of Natural and
Sensible Man. As the union of the masculine and feminine numbers, it is the
Pythagorean symbol of wedlock.
It is the number of the Pentagram.
Geometrically it is the Pentagon.
(b) Ideally, it is the Power of’ the Soul over’
fourfold Nature, hence of Self-Mastery and Control.
It is Ordination as a, result of the operation of the
It is Equilibrium as a result of the integration of the
It is Synthesis as a result of fourfold causation and.
It is Realization as a result of the
actualization of the Four Divine Inspirations through mystical love.
(c) Divinely, the Pentad is the Number of Divine
Incarnation, of the Infinite Monad manifesting in the Finitude of the
6. THE HEXAD
(a) The figure 6 is the number of the Cube as well
as the Hexagram, and comprehends the significance of two multiplied by
three, of one united to five, of two united to four, and of three united to
three. Geometrically it is the Hexagon.
(b) Ideally, the Hexad is the Symbol of
Polarization, of fluctuating Activity, of Action and Re-action.
It is the incessant pulsation of all creation,
in and out, up and down, forward and backward, diastolic and systolic, by
inhalation and exhalation.
It is without finality, for it is a dualistic
progression, hence the number of Incompleteness, of that which needs
Redemption, and of all human progress through trials and ordeals,
temptations and experiences, towards the Fullness of Perfection.
(c) The Divine Hexad stands for the Six Symbolical
Days of God’s Creative Activity in which all things are produced.
7. THE HEPTAD OR HEBDOMAD.
(a) The figure 7 is the union of the triangle and
the square, the triad and the tetrad. It is the heptagon and the heptagram,
or seven-pointed star, as well as the encircled interlaced triangle or
hexagram, and the triangle within or surmounted by the square.
(b) Ideally, it is the Completeness, Stability,
and Perfection to which the hexad ultimately leads.
It embraces the Seven Worlds or Planes, and is
the septenary principle reflected in all realms and conditions of existence,
in which man labours to bring to fruition all that the Six Days of God’s
Creative Work have provided.
(c) Thus, the Divine Heptad is indeed God’s Day of
Rest, or Sabbath, and Seven is the most Sacred of all numbers.
8. THE OGDOAD.
(a) The figure 8 denotes all that is implied
by 7 + 1, 6 + 2, 5 + 3, 4 + 4, and 4 x 2.
It is the double-square, the Octagon and the
(b) The Ogdoad, as an equilibration of the Tetrad,
It symbolizes the four Causes joined with their
effects. It is equilibrium, crystallization, conservation, inertia, and
mystical or ideal inaction.
To reach the Ideal Ogdoad is to transcend the
limitations imposed by Fate, for it is the number of sempiternal plenitude
(c) It is Divine Inflexible Justice.
9. THE ENNEAD
(a) The figure 9, being the highest digit,
possesses many peculiar properties, such as the manner in which the products
of its multiplication are always reducible to itself ( 2 x 9 =18; 1 + 8 = 9
As the triplication of the triad it has a
Its mathematical value is educed by considering
its components, such as 8 +1;
7 + 2; 6 + 3; and 5 + 4.
Geometrically it is the Enneagon and the Enneagram.
(b) Ideally, the Ennead is Supernal Gnosis,
Initiation, and Perfection; for it is triple unfoldment and actualiztion of
the knowledge, life, and potentiality of the Ideal Triad.
It has profound occult relations with the
(c) Divinely, it is God’s Idea of Himself, the
Superessential Reflection of the Triple Logos.
10. THE DECAD.
(a) With the figure 10, number returns to
unity, hence it completes a mathematical cycle and its symbol is the Circle.
(b) Syrianus, the Neoplatonist, says: “The
Ideal Decad is the boundary of all things. It comprehends every number
within itself; not occultly as in the Monad, nor essentially as in the
Tetrad, but with diversity and differentiation.”
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 +10 =
55; 5 + 5 =10.)
As the end as well as the beginning of a cycle
it denotes sempiternity and perpetual Change.
(c) The Divine Decad is God as the ONE and