The Pythagorean Tradition in Freemasonry
by Wor.Bro. The Rev. J. R. Cleland, M.A. D.D.
Source : http://www.boudicca.de/areas-e.htm
Over the Gates of the ancient
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
their systems of learning and polity 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
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
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 fron the various systems to which he gained
Thus he studied Astronomy and Astrology both in Chaldea and in
Esoteric Sciences among the Brahmans of
Europe, he settled at
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
Not only was he the greatest mathematician, geometer and astonomer 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
Mysteries of Byblus and
Mysteries of the Phoenecians, and also that he spent two and twenty years in the adyta
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
even by Christian writers". The
three degrees of the
HEARERS, who studied for three years in silence.
MATHEMATICI, learning Geometry and Music, the nature of Number, Form, Colour,
PHYSICI, who learned to master Cosmogony and Metaphysics. They were then
prepared for the Mysteries.
The School at
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
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
for intercommunication. Pythagoras in
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 symbolised 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 divire lore." 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 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
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 proceded 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
on Earth as in Heaven. The whole
conception apppears originally in
we cannot go into that now. The Western Teacher who first formulated it was
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 possibilitiss, as sunliqht contains all colours in
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 "sumnit of the Many" and simpler. One is the
first of a series, nonexistant unless followed by other numbers, whereas the Monad
includos all numbers, holds division in check. One is the apez of all numbers which
spread fron it to the base, 10. Pythagoras realised the fundamental basis of numbers
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 arithmancy 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 religiouis, as God, both understanding the same thing.
They had many names for such number. Their One corresponds to the Advaitya, 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 begining 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 tte 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
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, the 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 Genises 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 between two analagous 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
of its toil and take its place in the building of the
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 rivealed to him that this point was attachad to and formd 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
Advancing to the E. he passes through a symbolic figure of 9, 12, and 15 units,
the Pythagorean proportion found in
second dimension of space and becomes a three-dimensional beinp 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.
Proceding 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. ard 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 new 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 outsite 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 produce; by our Third
Regular Step, a four-dimensionial 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
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 irrer 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 Tomple, to find the wages of Truth. Tired of chasing an illusion, thay 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.
History of Science, Mathematics,