The Pythagorean Tradition in Freemasonry

by Wor.Bro. The Rev. J. R. Cleland, M.A. D.D.

Over the Gates of the ancient Temples of the Mysteries was written this
injunction, "Man, Know Thyself". It meant that each Candidate must try
to contact that Inner Self which is the only Reality, - Paul Brunton
calls it the Overself, - that Self which lies at the very Centre of his
Being, in the Silence and Darkness of the Holy Place which, to those who
have penetrated to the Sanctum Sanctorum, becomes the deafening Music of
the Spheres and the blinding Light of Truth. As the DORMER is the window
giving light to the Sanctum Sanctorum, it is but right that here, among
your members who have chosen to work under that name, one should attempt
to find some light upon the Secret of Secrets, which each must
ultimately solve for himself, which "no man knoweth" save "he that
overcometh", he that has mastered it for himself. It "passeth all
understanding" and is the mystery of his own being.

Freemasonry is closely allied to the ancient Mysteries and, if properly
understood, and in spite of repeated revision and remoulding at the
hands of the ignorant and sometimes the malicious, it contains "all that
is necessary to salvation", salvation from the only "sin" that
ultimately matters, that which lies at the root of all other sin and
error, the sin of ignorance of the self and of its high calling.

The First T.B. opens with the statement that "the usages and customs
among Freemasons have ever borne a near affinity to those of the Ancient
Egyptians; The Philosophers of Egypt, unwilling to expose their
mysteries to vulgar eyes, concealed their systems of learning and policy
under heiroglyphical figures, which were communicated only to their
chief priests and wise men, who were bound by solemn oath never to
reveal them. The system of Pythagoras was founded upon similar
principles and maintained under the same conditions."

We might, therefore, reasonably expect that a study of the system
originated, or adopted, by the great teacher, Pythagoras, would tend to
throw some light upon this Masonic Craft of ours. There are four
questions which we might put to ourselves in this connection:-

1. Who was Pythagoras?

2. What was the basis of his philosophy?

3. What are his and its connections with Freemasonry as we know it?

4. Can we from a study of these, formulate a code, and by following it,
open up a path, whereby, if trodden by the individual student, he can,
and should, reach that state, which, for want of a better name, we may
call "Realisation", - the full knowledge of that which alone is real, -
The Oneself?

I believe that all these questions can be answered and, tonight, I am
going to make an attempt to condense the answers, as I see them, into
one short paper. It would be impossible to go into each one fully, and,
in process of condensation, the answers will overlap; but I will try to
state them as simply as possible and I hope I may succeed in making the
general outline, at least, clear. It can only be an outline, for that
which must ultimately be sought is beyond form, formless. It can never
be filled in fully in words. The connection with Freemasonry will, I
think, make itself clear, if we attempt to answer the other three
questions.

First, then, just who was, or rather in, Pythagoras. As the most famous
of Greek Philosophers, he was born at Samos about 586 B.C. His father
was Mnesarchuss, a man of learning and of noble birth. As a boy,
Pythagoras had every advantage of education and, later, seems to have
travelled all over the world and to have formulated his philosophy upon
basic principles culled from the various systems to which he gained
access. Thus he studied Astronomy and Astrology both in Chaldea and in
Egypt, and the Esoteric Sciences among the Brahmans of India. To this
day his memory is preserved in India under the name of Yavanacharya, the
Ionian Teacher. Returning to Europe, he settled at Crotona, in Magna
Grecia, where he established a School, to which were attracted all the
best intellects of the civilized world. He left no writings himself, so
we have to piece together the details of his philosophy from the
writings of his followers. To him we owe the word Philosopher. He was
the first to teach the heliocentric system i n Europe and no one of his
time was so proficient in Geometry. Not only was he the greatest
mathematician, geometer and astronomer of historical antiquity, but he
also held highest place among scholars and metaphysicians. His fame
cannot perish. He taught much of the Ancient Secret Wisdom, the truth of
re-incarnation, the necessity for return to a natural system of diet,
the rule of Justice in the whole Universe and the certainty of ultimate
attainment of perfection by all beings. He realised that the solution of
the great problem of Eternity belongs neither to religion, to
superstition not to gross materialism. The harmony and balance of the
two-fold evolution - of Spirit and of Matter, - have been made clear
only in the Universal Numerals of of Pythagoras, who built his whole
system entirely upon the so-called "Metrical Speech" of the Vedas. In
both Pythagorean and Brahman Philosophy the esoteric significance is
derived from numbers. One of the few commentators who have paid just
tribute to the high mental development of the old Greek and Latin
writers, Thomas Taylor, says "Since Pythagoras, as Iamblichus informs
us, was initiated in all the Mysteries of Byblus and Tyre, in the sacred
operations of the Syrians and in the Mysteries of the Phoenecians, and
also that he spent two and twenty years in the adyta of the Temples in
Egypt, associated with the magicians of Babylon and was instructed by
them in their venerable knowledge, it is not at all wonderful that he
was skilled in Magic, or theurgy, and was therefore able to perform
things which surpas merely human power, and which appear to be perfectly
incredible to the vulgar."

For entrance to the School ot Pythagoras the qualifications were high
and rigorously enforced and, once entered, the candidate came under very
strict rules as regards diet, exercise and study. Besides this outer
discipline there were pledged disciples who were expected to pass
through three degrees, during a probation of five years. Of the outer
disciples, leading an ordinary family social life, G.R.S. Mead says,
"The authors of antiquity are agreed that this discipline had succeeded
in producing the highest examples, not only of the purest chastity and
sentiment, but also a simplicity of manners, a delicacy and a taste for
serious pursuits which was unparalleled. This is admitted even by
Christian writers". The three degrees of the Inner School were:

HEARERS, who studied for three years in silence.

MATHEMATICI, learning Geometry and Music, the nature of Number, Form,
Colour, Sound.

PHYSICI, who learned to master Cosmogony and Metaphysics. They were then
prepared for the Mysteries.

The School at Crotona was closed at the and of the sixth century B.C.,
being persecuted by the Civil Power; but other communities carried on
the tradition. Mead says that Plato intellectualized it to protect it
from profanation, which was on the increase, and the Mysteries of
Elusis, although they had lost its spirit and substance, still preserved
some of its rites.

The root of all such teachings seems to have lain in Central Asia,
whence Initiates spread to every land, carrying the same doctrines,
using the same methods, working towards the same final goal. There was a
common language and symbolism which served for intercommunication.
Pythagoras in India received a high Initiation and later, Appolonius of
Tyana followed in his steps. Typically Indian are the dying words of
Plotinus, noblest of the Neo-platonists "Now I seek to lead back the
self within me to the All-self." One great teacher has said, "The end of
knowledge is to know God - not only believe; to become one with God -
not only to worship afar off." We gain a hint in the Kathopanishat (V1-
17) "Let a man with firmness separate it (the soul) from his own body,
as a grass stalk from its sheath," to which point we will return later.

Pythagoras gave the "knowledge of things that are" to his disciples and
his knowledge of Music is said to have been such that he could use it to
control men's wildest passions and to illuminate their minds. Iamblichus
quotes instances and advises Porphyry to remove from his thoughts the
image of the thing symbolized and to reach its intellectual meaning. Of
the use of symbols Proclus remarks, "The Orphic method aimed at
revealing divine things by means of symbols, a method common to all
writers of divine lo re." Great stress was laid upon the fact that
numbers should be studied for the better comprehension of life, and not
or use in commerce.

I am tempted to think that Pythagoras is a title, rather than a real
name and it is significant that his father Mnesarchus, the nearest
translation of which is "Ruler of Memory." Pythagoras, as a title, is
identical, in root meaning, with Hiram Abif and with the Egyptian
Thoth-Hermes. The root Pytha is the Sanscrit Pitta and the Latin Pater
and the Greek, , all meaning Father. It is again the same root as the
Egyptian Phtha, one of the names of Thoth and Abif also means Father.
Goras is the Sanscrit root t Guru meaning Teacher, and the same root is
found in Huram or Hiram. The Egyptian root is ChR Horus. ChR-Mes or
Horus-Moses means Son of Horus. We may note here that Mercury, the latin
equivalent of the Greek Hermes is a corruption of the Syrian Mar-Kurios
meaning Son of the Lord.

The Pythagorean system of Cosmology is based upon the Decad, 10, or to
use the name of the symbol associated with its name, the Tetractys. This
Tetractys is represented in United Grand Lodge of England by a single
great Hebrew Yod, or "I," placed immediately over the Grand Master's
Throne, Yod being the tenth letter of the Hebrew alphabet and that also
being its numerical value. The "pillar and circle," also 10, the perfect
number of the Pythagoreans became later, among th Jews, a pre-eminently
Phallic number, among whom it represented Jehovah as Male-Female. This
Decad, representing the Universe and its evolution out of Silence and
the Unknown depths of spirit, was presented to the student in Dual
Aspect. It applied first to the Macrocosm, from which it descended to
the Microcosm. To-day, upon four-square bases, we have, in our Lodges,
or should have, two pillars, each bearing aloft a circle in perpetuation
of this symbolism.

Both the purely intellectual and metaphysical, or "inner science" and
the purely materialistic or "surface science", can be expounded by, and
contained in, the Decad, study being by the deductive method of Plato or
by the inductive method of Aristotle. Plato commenced with Divine
Comprehension, and multiplicity proceeded step by step from Unity, the
digits appearing only to be returned to the Circle of the All-pervading
Absolute. Aristotle started with perception by the senses, the Decad
being regarded either as the unity which multiplies or as the matter
which differentiates, its study being limited to two dimensions, to the
Cross, or the 7; proceeding from the 10, the perfect number, on Earth as
in Heaven. The whole conception appears originally in India, but we
cannot go into that now. The Western Teacher who first formulated it was
Pythagoras.

Primarily numbers are symbols of the beginning and development of a
universe, so the simplest way of bringing home to you their significance
will be to take the first cycle of Creation, leading to full
manifestation of the ultimate physical atom, and the building therefrom
of matter, as we know it. I shall run through the stages very rapidly
and leave it to you to go more fully into the subject should it appeal.

First, then, we have the Zero, nought, the Circle appears the Point at
the Centre, potentiality, showing the Circle as not barren. In
Arithmetic "0" is nothing, but, added to other numbers, is all things.
Without it multiplicity cannot go beyond 9. This Circle-potential is the
first number of the Cosmos, symbol of the Unknown, the Illimitable,
containing all numbers as possibilities, as sunlight contains all
colours in whiteness.

The 0 the Circle or Ovum is Passive, and requires vivification before it
can fructify and produce. The point, or centre, then becomes active and
from it arises the Line, - the diameter which bisects the Circle,
thereby polarising it. This is the Monad, the First Power of the
Universe creating Polarity, opposites in Unity.

Some ancient philosophers spoke indiscriminately of Monad and One, but
the Platonists drew sharp distinction, speaking of the Monad as that
containing distinct yet profoundlly united multitude, whereas the One is
the "summit of the Many" and simpler. One is the first of a series,
nonexistent unless followed by other numbers, whereas the Monad includes
all numbers, holds division in check. One is the apex of all numbers
which spread from it to the base, 10. Pythagoras realised the
fundamental basis of num bers as Rhythm. In it was based the generation
of all things. Numbers, to Pythagoras, were names and descriptions of
Cosmic Ideas and Happenings. One writer quotes him as saying, "There is
a mysterious connection between the gods and numbers, on which the
science of arithmatic is based. The soul is a world that is self moving;
the soul contains in itself, and is, the quaternary, the tetractys, the
perfect cube, and another says "Pythagoras is not reported as saying
that the gods are numbers, or that all things are numbers, as some of
his followers and critics affirm." Everything with the Pythagoreans,
ideas, injustice, separation, mixture and even man and his horse, were
all numbers" according to Aristotle. When speaking of the Monad or One,
they actually referred to that which was before Creation, and, if
philosophically minded, referred to it as the "Primordial Cross," if
religious, as God, both understanding the same thing. They had many
names for such number. Their One corresponds to the Advaity, the one
without a second of the Hindoos, creator and cause of all numbers.

The Duad, 2, is termed the cause of dissimilitude, matter. It is
considered to be feminine, as the matrix or all things, and is the
symbol of growth. Two cannot be produced from One, so duality is
considered as the actual beginning of manifestation; It is the drawing
apart of God as Life and God as Substance, 1 X 1 is l and nothing but 1
so 1 needs 2, as Life needs Substance for manifestation and
multiplication. 1 entering into relation with 2 gives rise to 3. Life,
1, ensouling Form, 2, becomes linked to it, 3, after being polarised, 2,
from itself, 1. Opposites are essential to any creative purpose. 2 is
therefore called the "First Number". Cornelius Agrippa calls it so
because "it is the first magnitude and the common measure of all
numbers, or, as the Pythagoreans term it, a confusion of unities. Thus,
God, as One, the producer and clause of Persistence, polarizes, His
Unity and draws apart from His substance, Subsistence, and, then
vivifies it, producing Existence. 1 is potentially 2 for polarity is
everywhere, as are pairs of opposites.

Avicebron of Cordova (1021-70) speaks of the affinity between "to be"
and numbers and says 3 is the root of all things; for Spirit, 1, and
Matter, 2, linked by Will, the bond between, form the Triad. He ways,
"All existing things are constituted after the nature of numbers.....The
Highest Abstract God is the indivisible, metaphysical unity". So 3, as
relating the action of the two opposites is rightly considered the
number of true beginning, without which no production is possible. One,
potential, like a ring of magnetized steel, is powerless until broken,
or polarized, and the opposites are themselves useless until there is a
relation between them. 3 is then the number of active growth and
production. There are three distinct steps to be taken by the student
before he can enter the "outer court" of the Mysteries:-

1. He must collect together his forces and prepare to learn.

2. He must eliminate and subtract gross matter.

3. He must amalgamate or synthesise the result.

or in more familiar words

1. He must come of his own free will and accord.

2. He must be deprived of all metals and material valuables.

3. He must be properly prepared.

The third step of apprenticeship gains approbation from a master and
leads the student to a position where he can grasp the work with his
whole nature.

The number 3 is most important and, masonically, so far as the Craft is
concerned, must be studied in conjunction with 5 and 7. I will return to
this point.

The idea of the fundamental Trinity presupposes a condition of being
before the worlds were created.

4 is significant of system and order. Plutarch states that it is because
of 4 that every body has its origin. It is Foundation, and does not
relate to the building of physical forms and bodies, which is the
function of 8, but to that of the Cosmic stones, the ultimate atoms out
of which these forms will be built. Philo says it is the first number to
show the nature of solidity. Mathematically it is Foundation, for,
without it, no progression beyond 6 is possible, but with it completion
in 10, that is, th e complete cycle, can be reached. Three components
blending equally gives 6 and no more but predomination of any one of
them would lead to 7 or more, for 1 plus 2 plus 3 equals 6 and also 1 X
2 X 3 equals 6 each of which requires the addition of 4 to complete the
cycle (or circle).

5 has a root meaning of "harvesting", the arranging in sheaves of
produced substance, hitherto potential, now becoming matter. Five forms
are combined in the foundation of the chemical atoms. It is a matter of
rebirth and actual material commencement. That matter should be ensouled
is not sufficient. Both matter and life must be qualified that gradation
and diversity may result. Each chapter of the first ten chapters of
Genesis is said to refer to one of these numerical steps and it should
be noted that chapter V contains a description of all emanated things
and is devoted solely to generation. D'Olivet reads it as a story of
Cosmic generation. The Pythagorean name was cardiatis or cardialts, as
the heart of things manifest, change of quality, the fire which "changes
all things triply extended or which have length, breadth and depth into
the sameness of a sphere and producing light." It is eminently a
"circular number" and spherical, restoring itself in every
multiplication. Note here the F.C's steps. By 5 arranging matter ready
for use, three fundamental qualities are produced in the prepared matter
and the three aspects of Diety find reflection in them, Will or Strength
to Create, Love or Wisdom to Preserve, and activity or Beauty to
Transmute or to send forth Creation, producing 6, representing that
period in the creative process in which Triple spirit enters into
Matter, already prepared as a triplicity to receive it. The double
triangle is its symbol. Allendy defines it as a static correspondence
bet ween two analogous terms and not a transitory action or passage from
one state to another. It is the instrument of progression but not the
progression itself."

7 represents the progressive atomization of matter, without which
building is impossible. The ancient Greeks called it Justice and
represented it as a pair of scales, the bar pivoting about a point and
supporting two hemispherical pans, each supported by 3 chains. 7 is to 3
as 3 is to 1. As 3 represents the development of a principle, so does 7
represent it doubly represented, that is to say not only manifested but
objectively realised. Everywhere in nature we find this 7, in ourselves,
in colour, music, the Arts, in healing and so on, balancing three on the
life side against three on the form side with one giving synthosis.

Now, I think we may stop here, for this is the point to which the Craft
of Freemasonry brings us. To complete the major cycle one has to
consider the Holy Royal Arch and the Installation of W.M. which leads to
it.

Before passing to one last point I want to take up, let me give the
parallels briefly:-

In the making of a Freemason there must first be the man himself, the
Circle, No-number. Next comes that preparation in the heart which makes
him the Circle-potential. The Unknown God, transcendent within-all men
has become immanent in him. Then he takes his first step towards the
door of the Lodge, The First step of a Series, he separates himself from
the vulgar crowd and becomes a free unit, "Free and of Good Report." He
becomes polarized, realising dimly that to is not only Body but also
Spirit, he gains forward "In Strength." The E.A. degree is founded upon
the number 3, and in it, by the union of his opposites, he makes
production possible, he reaches "Plenty". In the F.C. degree he is able
"To Establish" himself upon a sure foundation, begins to realise his
real self. He gains control of matter and of "Worldly Possessions",
producing multiplication of ports. The M.M. degree is founded on the
number Seven, which, so we saw represented full atomization. Here the
One Rock of the Quarry has become the individualized multiplicity of
prepared stones, ready for the building. Each is a complete work in
itself but has to die as such in order to reach a reunion with the
companions of its toil and take its place in the building of the Temple,
the new cycle of 7 which it inaugurates.

Now for my last point. Several of the ancient Philosophers, including
both both Plato and Aristotle, hint that man is something more than the
three-dimensional being that he appears to be, at first sight. We cannot
go into full evidence here, but Plato's beautiful allegory of the men
chained in a cave with the light behind them and seeing only their own
shadows and those of the passersby, thrown upon the flat surface of the
opposite wall, should be called to mind. He tries to show how difficult
it would be for one who had escaped and returned to his chained
companions to bring to them any realisation of three dimensions. This
seems to be a clear hint, and a study of Dimensional Masonry bears it
out.

Before entering the Lodge for the first time, the Candidate is
symbolically unaware of the existence of Spiritual Dimensions: Yes, in
this three-dimensional world of ours, he has reached a stage where the
unfolding of spiritual consciousness has become for him a definite aim.
He has, in this sense, become one-pointed. So, when he comes to the door
of the Lodge, he enters upon an undimensional Euclidean Point, having
neither length, breadth nor thickness. Only at a later stage, when he
has been restored to light, is it revealed to him that this point was
attached to and formed part of a straight line, a one-dimensional
instrument, held by a brother whose grip was separated from it by a
cross-piece, which, by its very position, indicated its
two-dimensionality. Thus, the candidate transcended the first dimension
of space and became a two-dimensional being.

Advancing to the E. he passes through a symbolic figure of 9, 12, and 15
units, indicating the Pythagorean proportion found in Euclid, 1, 47.
Thus he surpasses the second dimension of space and becomes a
three-dimensional being capable of ruling and preparing a plate surface
by knocking off all superfluous knobs and excrescences, roughly squaring
the faces of the Ashlar in its rough form and preparing it for the hand
of the more expert workman. This stone is placed upon the pedestal of
the J.W. and should appear in the Ceremony in the N.E. corner of the
Lodge.

Proceeding onwards he enters upon the next stage upon an instrument
which, although it is used upon three-dimensional work, is itself
two-dimensional and which can be used to test the rectangularity of the
previous advance. He then advance in a manner typical of
three-dimensional motion. Under no conceivable circumstances can this
advance take place in less than three dimensions. Now he produces a
smooth stone, the Perfect Ashlar, which has place on the pedestal of tho
S.W. and appears ceremonially in the S .E. corner of the Lodge.

Once more he passes on his way and enters upon, another stage of his
quest, this time upon an instrument which is used in the depicting and
measurement of the three-dimensional advance he has previously made. He
now reaches the supreme test. Three stops he takes, each indicating an
advance in a different direction and together showing that conquest of
the three-dimensional world has been achieved. Then, boldly he marches
forward, and indicates, in a very beautiful piece of symbolism, his
passage into a n ew world, a world almost inconceivable to our untutored
finite minds, the FOURTH DIMENSION of space. The Stone he can now
prepare is of a shape normally outside our consciousness.

It may be noted here that the W.T.'s in each degree of the Craft, and
those of an I.M., indicate work in 1, 2, and 3 dimensions, the conquest,
in each case, of the three boundaries of our three dimensional
existence, length, breadth and thickness.

This third stone is one over which there has been much wrangling,
discussion and wild speculation, yet its essential qualities would seem
to be sufficiently obvious. Most writers tacitly accept the Perfect
Ashlar as the last possible stage in the preparation of of the stone,
but this is true only of the three-dimensional world. If there are other
dimensions, there will be further stages in the preparation, and it is
significant that we find references to yet another stone, whose true
place is on the Master 's Pedestal, and, it its ceremonial position,
"With the centre", perpendicular, perpendicular, or perpend, to
three-dimensional space. This is the PERPEND ASHLAR, and the reason why
it cannot be seen in its completeness in the Lodge is that, existing in
the Fourth Dimension, the only part we could perceive would be a perfect
cube, suspended in space, to ever point to which it would be
perpendicular. Mr. C.H. Hinton (in "The Fourth Dimension" calls it the
Tessoract. It is to be noted that each Regular step is rectangular,
taken symbolically at right angles to the last position. We move a point
to produce a line; we move a line at right angles to the previous motion
to obtain a superficies. This is the First Regular Step and from it we
obtain a rectangular plane figure, a square; we now move our square at
right angles to both the former directions of motion and the result is a
solid cube, the Second Regular Step; and now we move this cube at right
angles to all three directions of motion already used, and pro duce; by
our Third Regular Step, a four-dimensional figure, the Tesseract. Even
then the journey is incomplete, for, as an I.M., the zealous brother
uses tools belonging to the three dimensions of our space to prepare
himself to work freely in the four-dimensional atmosphere of the Holy
Royal Arch, wherein the whole scheme of Creation of Man as a reflection
or form created by God "in the image of His own Eternity" and the method
of the return of that image into the substance of T.G.A.O.T.U. in
unfolded in the consciousness of the Initiate.

Thus far I have tried to answer the first three questions put at the
beginning of this paper. Pythagoras, is, we have seen, fundamentally
involved in our symbolism. We have taken a very hurried glance at the
relevent portions of his Philosophy, and we have seen the same
fundamentals running through our rituals.

Now, very briefly to answer the fourth question.

We can, I think, say definitely that there is no Royal Road to
Perfection. Each must find a way for himself. But signposts are not
wanting, for to those who choose to raise their eyes from the plane of
Matter, they point a clear way. The first and most important comes early
in our Masonic knowledge." This can only come from the age-old
three-fold method of advance being applied; CONCENTRATION, MEDITATION,
CONTEMPLATION. These we must apply daily to some portion of our
Ceremonies, Tools and other Symbols, seeking ever to find their inner
significance.

At no time in the Era of Recorded History has the application of these
methods been more difficult than it is to-day in the Western world, but
at no time has so much help been available to those who conscientiously
attempt to apply them. In this Machine-tyrranized Age it is difficult to
attain the necessary leisure, peace, quiet, stillness and silence, and
the forgetfulness of the rush and hurry of the world in its search for
the transient and worthless. Yet, even now, there are many signs that
the world is getting tired of its own shallowness and sensationalism and
is turning to things that are more worth while.

Perhaps the time is nearer than we think when men will at last seek the
Middle Chamber of their own Temple, to find the wages of Truth. Tired of
chasing an illusion, they may seek the reality within, the Overself,
which lies sheathed, as lies a grass-stalk in its husk, within the husk
of Personality, ready to be drawn out into tho Light of T.G.A.O.T.U.

Peace to All Beings, Amen.