Initiation into Pythagorean Number Philosophy

Pythagorean Number Philosophy is based on the pattern of the first ten Numbers.  These Numbers are the core pattern of philosophical laws for contemplating the mysteries of The ONE.

Understanding the Number pattern from the Monad to the Decad is the first stage in an alchemical process to harmonize personal consciousness with the flow of universal consciousness.  Through a crystallization process this pattern is hard-wired into our subconscious Net of associations, and becomes a platform for stepping into mystical states where pure knowing is achieved (gnosis via mathesis).

The Pythagoreans gathered around the holy Tetractys as the principal symbol of their philosophy of Numbers.  It displays the progression of the Monad to the Decad as a dot-pattern in the form of a triangle, called a figurate.

The Tetractys, symbol of Pythagorean Number Philosophy

The Tetractys encodes many secrets of the universe, and is to be taken as a cosmological symbol.  There are 4 levels, symbolizing 4 philosophical or metaphysical worlds.  The numerical progression of levels (1:2:3:4) gives the fundamental harmonic proportions used for constructing the Pythagorean Diatonic scale.

In total we have 10 dots, which are viewed as the 10 aspects or qualities of being within The ONE.  This was taken to be the complete map of all that is, since all other numbers could be reduced to one of these.  The use of base-10 counting was seen as a reflection of this philosophical truth within human understanding.


As a figurate, the Tetractys is the 4th Triangular Number.  The Triangular Numbers are given as the sums of consecutive numbers, beginning with 1.  So 1+2=3, 1+2+3=6, and 1+2+3+4=10, making 10 the 4th Triangular.  Taken philosophically, since 10 reduces to 1 (1+0=1) we have that 4 is really 1.  So there is a pattern from 1 to 2 to 3 to 4, but 4 is really 1.  Since we return to 1, we must continue to 2 and 3, but then 2+3=5, 1+2+3=6, 4+3=7, 1+3+4=8, 2+3+4=9, and 1+2+3+4=10.  So by staying within 1 to 4, we can generate all 10.


When seen from modern mathematics, these calculations would seem infantile, but when viewed philosophically, we can see why the Tetractys could merit such veneration.  We may not be surprised, then, to recall that the Divine Names in most ancient mysteries were spelled with 4 letters.  In Greek ThEOS and in Hebrew YHVH.  The latter is known as the Tetragrammaton, or 4-letter Name, which encodes a profound universal pattern of Numbers, which I shall explain in future posts.

The Pythagorean doctrine of the Decad may be responsible for the Qabalistic doctrine of Ten Sephiroth.  The Qabalists also based their metaphysical system on a system of Ten, and while the earliest of Qabalistic texts refering to these Ten Sephiroth, the Sepher Yetzirah, is generally dated by scholars to be at least several hundered years after the time of Pythagoras, but the correspondence between the two is nearly the same.  They can be studied in conjunction, yielding the fruits of cross-fertilization.


The First Stage of Self-Initiation into Pythagorean Number Philosophy is to develop in one's consciousness the ideas and images that follow from contemplating the following series of seed-ideas.


The Numbers:


1 - MONAD - Beginning, Wholeness, Unity
2 - DYAD - Duplication, Reflection, Extension
3 - TRIAD - Multiplication, Growth, Expansion
4 - TETRAD - Order, Regularity, Structure
5 - PENTAD - Mediation, Adaptation, Modification
6 - HEXAD - Reciprocation, Symmetry, Harmony
7 - HEPTAD - Equilibrium, Poise, Rest
8 - OCTAD - Rhythm, Vibration, Pulsation
9 - ENNEAD - Perfection, Attainment, Mastery
10 - DECAD - Completion, Fulfillment, Validity


Once the mathematician-alchemist has distilled and digested this Number pattern, repeated study leads to crystallization and a kind of prototype for the Stone of the philosophers.

The Philosophy begins by establishing the Greek names for the numbers, to remind us that they are to be thought of as philosophical qualities.  Then we try to understand the Numbers as states in a dynamical movement, as indicated by the meanings of the key-words.  These key-words have been chosen very carefully by the philosophers so that they may help you unlock the secrets which lie hidden within our philosophy.

In future posts, we will explore the link of Number to Geometry.  The geometry associated with the Numbers gives us a way to visualize the pattern in ways that lead to better understanding, but also gives us a Path to follow and a way to Truth.  We will also see how Letters can stand in for Geometry, leading to a sacred script for describing and preserving the mystical experiences of the mathematician-philosophers.