From the standpoint of everyday experience, we are aware of
the universe as an incredibly diverse system made up of a multiplicity
of apparent unities. A duck is a unity, made of a multiplicity
of cells, each of which is a unity made up of a multiplicity of
molecules, each of which is a unity made up of a multiplicity of
atoms, each of which is a unity made up of a multiplicity of
'particles ' for whose description ordinary language will no longer
suffice. Seen one way they are particles, or unities ; seen another
way, they are modes of behavior of energy; and it is energy that is
now regarded as the ultimate unity underlying the material universe.
The same line of thinking followed into the macrocosmic sphere leads
to the same conclusion. The duck is a unity, which is one aspect of
the planet earth, which is a unity, which in its turn is part of the
solar system, which is a unity, etc . . .and on and on to the galaxies
which, combined, make up the unimaginable unity we call the 'universe'.
Positivists and certain linguistic philosophers may argue that the
concept 'universe' is a fallacy, that the universe is an illusion,
no more than the sum of its parts. But in that case a duck, or
a positivist , is also a fallacy and an illusion, and no more than the
sum of its parts.
Multiplicity presupposes unity. Multiplicity is meaningless unless
unity also has meaning. Both terms confer a real, not merely
abstract, meaning upon number.
It is the manner in which our senses receive information that creates
an automatic, often insuperable problem.
Multiplicity assaults our senses on every front, while the unities
we call 'duck', 'cell ' and 'molecule' are provisional and relative
and we know this. We are such philosophically provisional , relative
unities ourselves. Philosophically, logically, we may postulate
an ultimate unity , but it is impalpable to our senses.
We are obliged to acknowledge the limits of reason, and to
acknowledge the necessary reality of realism to which reason
has no access. And while reason will not in itself set men going
along the paths of an initiative tradition (that is the function of
conscience), reason is enough to invalidate skepticism.
It is the senses that make us skeptics. When scientists and
intellectuals claim that their atheism or agnosticism is forced
upon them by 'reason' , they lie. They have simply failed to apply
their reason to the relative and provisional data returned by
the senses.
What is today called Pythagorean number mysticism is Egyptian in
origin (if not older still) and corresponds to the underlying
philosophy behind all the arts and sciences of Egypt. In effect,
what Pythagoras did was to undramatise myth — a strategy that had
the advantage of talking directly to those capable of thinking along
these lines.

The work of Schwaller de Lubicz and the independent but complementary
work of a few other contemporary thinkers (J. G . Bennett, for example)
has made it possible to reexpress Pythagorean theory in a way
acceptable to our thinking.

When we reapply this to Egyptian myth it becomes clear that these
curious tales are based upon an understanding of number and the
interplay of number, not upon animism, tribal superstitions, priestly
feuds, the raw material of history or dreams.

Number: key to function, process and principle
1
One, the Absolute or unity, created multiplicity out of itself.
One became Two.
This Schwaller de Lubicz calls the 'Primordial Scission '
(Division, Separation). It is forever unfathomable and
incomprehensible to human faculties (although language allows us
to express what we cannot comprehend).
The creation of the universe is a mystery. But in Egypt this
was regarded as the only ineluctable mystery — beyond the Primordial
Scission, all is in principle comprehensible. And if it
is objected that a philosophy founded upon a mystery is
unsatisfactory, it must be remembered that modern science is rife
not only with mysteries, but with abstractions corresponding
to no possible experience in reality : the zero, which is
a negation;infinity, which is an abstraction ; and the square root of
minus one, which is both a negation and an abstraction.
Egypt carefully avoided the abstract.
Turn (transcendent cause), in regarding himself, created
Atum out of Nun, the primeval waters.
In our terms unity, the Absolute or unpolarized energy, in
becoming conscious of itself, creates polarized energy. One
becomes simultaneously Two and Three.
Two, regarded by itself, is divisive by nature. Two represents
the principle of multiplicity ; Two , unchecked, is the call to
chaos. Two is the Fall.
But Two is reconciled to unity, included within unity, by
the simultaneous creation of Three. Three represents the principle
of reconciliation, of relationship. (This three in one is of
course the Christian trinity, the same trinity that is described
in innumerable mythologies throughout the world.)
Numbers are neither abstractions nor entities in themselves.
Numbers are names applied to the functions and principles
upon which the universe is created and maintained. Through
the study of number — perhaps only through the study of number
— these functions and principles can be understood. Generally
speaking, we take these functions and principles for
granted; we do not even realize they underlie all our experience
and that, at the same time, we are largely ignorant of them. We
can only measure results, which provide us with quantitative
data but not with understanding. We experience the world in terms of
birth, growth, fertilisation, maturation, senescence, death,
renewal. We experience in terms of time and space, distance,
direction, velocity.
But contemporary science can account for this only in partial,
superficial, quantitative terms. And either it refuses to
admit these shortcomings, or to the manifold mysteries it
applies meaningless but impressive labels. Eloquent in the
emperor's new vocabulary, it insists the mystery is solved.
'Selection pressure', 'survival value', 'interaction between genetics
and environment' — analyze any or all of these terms and
you will find underlying all the mysteries of fecundation,
birth, growth, maturation, senescence, death, renewal. None
can be accounted for by the scientific method.
Yet through a restated Pythagorean number mystic is man
insight can be gained into their nature. The philosophy based
upon Pythagorean is miscalled by Schwaller de Lubicz 'the
only true philosophy'. This is not arrogance but a recognition
of the fact that by this means we can begin to understand the
world as we experience it.
2
The Absolute, unity, in becoming conscious of itself creates
multiplicity, or polarity. One becomes Two.
Two is not One plus One. Metaphysically, Two can never be
the sum of One plus One since, metaphysically, there is only
one One , which is All.
Two expresses fundamental opposition, fundamental contrariety
of nature: polarization. And polarity is fundamental to
all phenomena without exception. In Egyptian myth, this
fundamental opposition is vividly depicted in the interminable
conflict between Seth and Horus (ultimately reconciled
after the death of the king).
The Primordial Scission provokes, postulates, reaction.
Modern science is aware of the fundamental polarity of phenomena
— though without acknowledging its implications or
its necessarily transcendent nature. Energy is the measurable
expression of the revolt of spirit against its imprisonment in
matter. There is no way to express this fundamental verity in
acceptable scientific language. Yet the language of myth
expresses it eloquently: in Egypt, Ptah, the creator of forms, is
depicted as imprisoned, bound in swaddling clothes.
Polarity is fundamental to all phenomena without exception,
but it changes in aspect according to the situation. This
fact is taken into account in common language. We apply different
names according to the situation or category of phenomena.
Negative, positive ; active , passive ; male , female ;
initiating, resisting ; affirming, denying ; yes, no; true , false —
each pair represents a different aspect of the same, fundamental
principle of polarity.
For purposes of clarity and precision , we carefully distinguish
among these sets of polarities according to their specific
function within a given situation. And it is true that by doing
so, we may gain in clarity and precision. At the same time we
may — and in science invariably do — lose sight of the cosmic,
all pervading nature of polarity. In myth, this danger is
avoided. In myth the cosmic nature is intensified, and the individual
scholar, philosopher or artist utilizes that precise aspect
of the principle that applies to his task or quest, whatever it
may be. Precision and clarity are not purchased at the price of
diffusion.
Two, regarded in itself, represents a state of primordial or
principal tension. It is a hypothetical condition of eternally
unreconciled opposites. (In nature, such a state does not exist.)
Two is static. In the world of Two,nothing can happen.
3
A relationship must be established between opposing forces .
The establishment of relationship is, in itself, that third force.
One, in becoming Two, becomes Three simultaneously. The 'becoming' is
the third force, automatically providing the
innate and necessary (and mysterious) reconciling principle.
Here we come to an insoluble problem in both language and
logic. The logical mind is polar by nature and cannot accept or
comprehend the principle of relationship. Throughout history,
scholars , theologians and mystics have been faced with
the problem of explaining the trinity in discursive language.
(Plato wrestled manfully with it in his description of the
'world soul' ; to all but Pythagorean it seems gibberish). Yet
the principle of Three is easily applied to daily life where,
again according to the nature of the situation, we apply a different
name.
Male/female is not a relationship. For there to be relationship
there must be 'love ' or at least 'desire'. A sculptor and a
block of wood will not produce a statue. The sculptor must
have 'inspiration'. Sodium/chlorine is not in itself enough to
produce a chemical reaction ; there must be 'affinity'. Even the
rationalist, the determinist, pays unwitting homage to the
principle: unable to account for the physical world through
genetics and environment, he calls in 'interaction', which is a
label applied to a mystery.
Logic and reason are faculties for discerning, distinguishing,
discriminating (note the Greek prefix di-, meaning two).
But logic and reason will not account for everyday experience:
even logicians fall in love .
The third force cannot be 'known ' by the rational faculties;
hence the aura of mystery hovering about every one of its
innumerable aspects — 'love', 'desire', 'affinity', 'attraction' ,
'inspiration'. What does the geneticist 'know ' about 'interaction'?
He can't measure it. He infers it, extrapolates from his
own experience, and by using a word from which all emotion
has been removed, assumes he is being 'rational'. He can
define 'interaction ' with no more precision than the sculptor
can define 'inspiration ' or the lover , 'desire'.
The heart, not the head, understands Three. (By 'heart ' I
mean the complex of human emotional faculties. ) 'Under standing'
is an emotional more than an intellectual function,
and it is practically a synonym for reconciliation, for relationship.
The more one understands, the more he or she is able to
reconcile, and relate. Seeming incongruities and inconsistencies. It
is possible to know a great deal and understand every little.
So, while we can not measure or know Three directly, we
experience it everywhere. From common everyday experience,
we can project and recognize the metaphysical role of Three;
we can see why trinities are universal to the mythologies of the
world. Three is the 'Word' , the 'Holy Ghost', the Absolute conscious
of itself. Man does not directly experience the Absolute
or unity or the Primordial Scission. But the famous mystical
experience, union with God, is, I believe, the direct experience
of that aspect of the Absolute that is consciousness.
The degree to which one understands Three is a fair indication
of the degree to which he or she is civilized. To acknowledge
the third force is to assent to the fundamental mystery of
creation; at the same time it is a recognition of the fundamental
need to reconcile opposites. The man who understands
Three is not easily seduced into dogmatism. He knows that
true and false in our world are relative — or if seemingly absolute,
as in logical systems, then that system itself is but relative,
and abstracted from a greater, more complex reality. The failure
to understand this result in the curious modern reasoning
that declares the part valid but the whole an illusion.
Though the third force can not be measured or known
directly, an enlightened science such as the Egyptian can deal
with it precisely. Any manifestation in the physical world
represents a moment of equilibrium between positive and
negative forces. A science that understands this also understands
that by knowing enough about those positive and negative
forces it will also , by inference , know about the ineffable
third force , since this must be equal to the opposing forces in
order to bring about that moment of balance. The ability to
make use of this knowledge is one aspect of 'magic'.
In everyday life, recognition of the role of Three is a step
toward that most difficult of feats : acceptance of the opposition.
A masterpiece of art, indeed creation of any sort, can take
place only in the face of commensurate opposition. To the
sculptor, the block of wood is his opposition in a very real
sense — as every sculptor knows. If his inspiration is insufficient
to deal with his block of wood, he will either go out and
get drunk or produce an ambitious failure. If the block of
wood is insufficient to his inspiration, he will finish with a
sense of frustrated ambition. Easy to recognize in principle,
the ability to give the opposition its due is one of the most difficult
things to put into practice. This is why the principle is
expressed and re expressed in a thousand different ways in
sacred literature's of the world. It is this, and not any sense of
obsequiousness, that is meant by the Christian dictum to 'love
thine enemy'. Try to love thine enemy!
4
Material, substance, things ; the physical world is the matrix of
all sensuous experience. But material or substance cannot be
accounted for in two terms or in three. Two is an abstract or
'spiritual' tension . Three is an abstract or 'spiritual ' relationship.
Two and three are insufficient to account for the idea of
'substance', and we can illustrate this by analogy. Lover /
beloved / desire is not yet a 'household' or even an affair. Sculptor
/ block / inspiration is not yet a statue. Sodium / chlorine /
affinity is not yet salt. To account for matter in principle
requires four terms : sculptor / block / inspiration / statue ;
lover / beloved / desire / affair ; sodium / chlorine / affinity/
salt.
Thus matter is a principle over and above polarity and relationship.
It includes, of necessity, both Two and Three, yet is
something beyond the sum of its constituents, as every sculptor
and lover knows full well. Matter or substance is both a
composite and a new unity ; it is an analogue of the absolute
unity, with its triune nature.
The four terms needed to account for matter are the famous
four elements — which are not, as modern science believes, a
primitive attempt to account for the mysteries of the material
universe, but rather a precise and sophisticated means of
describing the inherent nature of matter. The ancients did not
think that matter was actually made up of the physical realities
fire, earth , air and water. They used these four commonplace
phenomena to describe the functional roles of the four terms
necessary to matter — or, rather, to the principle of substantiality.
(At Four we have not arrived yet at the actual physical stuff
we stub our toes against.) Fire is the active, coagulating principle;
earth is the receptive, formative principle; air is the subtle,
mediating principle, that which effects the interchange of forces;
water is the composite principle, product of fire, earth and
air — and yet a 'substance ' over and above them.
Fire, air, earth, water. The ancients chose with care. To say
the same thing in modern terms requires more words, and
none stick in the memory. Active principle, receptive principle,
mediating principle, material principle — why bother
with such abstractions when fire, earth, air and water say the
same and say it better?
In Egypt, the intimate connection between Four and the
material or substantial world was applied in symbolism. We
find the four orientations, the four regions of the sky, the four
pillars of the sky (material support of the realm of the spirit),
the four sons of Horus, the four organs, the four canopic jars
into which the four organs were placed after death, the four
children of Geb, the earth.
Unity is perfect, eternal, undifferentiated consciousness.
Unity becoming conscious of itself creates differentiation,
which is polarity. Polarity, or duality, is a dual expression of
unity. Thus each aspect partakes of the nature of unity and of
the nature of duality — of the 'One' and of the 'Other', as Plato
put it.
Thus each aspect of primordial, spiritual duality is itself
dual. The primordial Scission creates a twofold antagonism,
which is reconciled by consciousness. This double reaction, or
double inversion, is the basis of the material world. If we understand
nothing of this fourfold process, we understand little of
the world of phenomena — which is our world. Symbols, studied
in the correct manner, make these processes clearer than
words. The square inscribed in a circle represents passive, potential
matter contained within unity. The same process is
shown in action, as it were, in the cross — which is rather more
than two sticks of wood upon which an upstart Jew was nailed. This is
the cross of matter, upon which all of us are
pinned. Upon the cross , the Christ, the cosmic man, is crucified.
By reconciling its polarities through his own consciousness,
he attains unity.
It is this same principle of double inversion and
reconciliation that lies behind all religious Egyptian art and
architecture. The crossed arms of the mummified pharaoh —
who (whatever his personal traits may have been) represents
successive stages of the cosmic man — holds the crossed scepter
and flail of his authority. Schematically, the point where the
two arms of the Christian cross intersect represents the act of
reconciliation, the mystical point of creation, the 'seed'. Upon
a similar scheme, the exalted, mummified pharaoh represents
the same abstract point.
The cross and the mummified pharaoh thus symbolize both
Four and Five.
5
To the Pythagorean, Five was the number of 'love' because it
represented the union of the first male number, Three, and the
first female number, Two.
Five may also be called the first 'universal ' number. One,
that is unity, containing as it does all and everything, is strictly
speaking incomprehensible. Five, incorporating the principles
of polarity and reconciliation, is the key to the understanding
of the manifested universe. For the universe, and all
phenomena without exception, are polar in nature, treble in
principle.
From the roots of Two, Three and Five all harmonic proportions
and relationships can be derived. The interplay of these
proportions and relations commands the forms of all matter,
organic and inorganic, and all processes and sequences of
growth. It may be that in the not too distant future, with the
aid of computers, science may come to a precise knowledge of
these complex interactions. But it will not succeed in doing so
until it accepts the underlying principles which the ancients
knew.
It may seem odd to saddle numbers with gender. But reflection
upon the functional role of numbers quickly justifies
such a procedure. Two, polarity, represents a state of tension;
Three, relationship, represents an act of reconciliation. Female
numbers, the even numbers, represent states or conditions;
the female is that which is acted upon. The male is that which
is initiative, active, 'creative', positive, (aggressive , rational);
the female is correspondingly receptive, passive, 'created ' (sensitive,
nuturing). This is not a tract advocating universal male
chauvinism; the universe is polar, masculine/feminine by
nature. And it is probably no accident that in countless phenomena
of the natural world, we find this relationship
between odd numbers and masculinity, even numbers and femininity.
Genital organs are usually treble. Female mammals of
all species have two (or multiples of two) breasts. In an accidental
universe, there is no reason why such uniformity should
prevail.
So Five, to the Pythagorean, was the number of love, but
given the innumerable connotations of that much abused
word, it is perhaps preferable to call Five the number of life.
Four terms are necessary to account for the idea of matter, or
substance. But these four terms are insufficient to account for
its creation. It is Five — the union of male and female — that
enables it to 'happen'.
And it is an understanding of Five in this sense that is responsible
for the peculiar reverence in which Five has been held in
so many cultures; this is why pentagram and pentagon have been sacred
symbols in esoteric organizations (and why it is so
ironic to see it currently used as the basis of the plan of the
world's largest military headquarters). In ancient Egypt, the
symbol for a star was drawn with five points. The ideal of the
realized man was to become a star, and to 'become one of the
company of Ra' .
As we apply the functional roles of number to familiar conditions
of everyday life, we can gain insight into the manner in
which they operate more easily than we can by technical
description. Roles change and become more complex within
functions. Man/woman is a polarity. But the same man and
woman, linked by desire in a relationship, are no longer the
same; and when the three term relationship turns into the
tetrad of affair, or household, the parties to it again change
functionally— as all lovers, husbands and wives know full
well. The parties involved play both active, masculine, initiating
and passive, feminine, receptive roles simultaneously. The
lover is active toward his beloved, receptive to desire; she is
receptive to his advances, but provokes desire. The sculptor is
active toward the block of wood, receptive to inspiration; the
block of wood is receptive to the chisel, provoking inspiration.
This kind of thinking underlies the vital philosophy of
Egypt.
Broadly speaking, contemporary philosophy falls into two
main camps. One, characterized by logical positivism and its
rather more sophisticated descendants, concentrates upon
logic and a scientific methodology. The other, typified by
existentialism in its various forms, concentrates upon human experience
in a personal or social context. Neither school incorporates
Pythagorean thinking, with the result that the positivists have
developed a rigorously consistent analytical tool unrelated to
human experience, while the existentialists
have made useful observations about experience, but cannot
fit them into a consistent or convincing structure. The Pythagorean
approach reveals a structure and system underlying experience.
The philosophy of ancient Egypt is not philosophy in our
sense; there are no explanatory texts. It is nevertheless a real
philosophy in the sense that it is systematic, self consistent,
coherent and organized upon principles that can be expressed
philosophically. Egypt expressed these ideas in mythology,
and it is not until that mythology is studied as the dramatization
and interplay of number that its coherence reveals itself.
From his study of the Hebrew Cabala, Chinese yin yang
philosophy, Christian mysticism, alchemy, the Hind u
pantheon and the latest work in modern physics, Schwaller de
Lubicz recognized a common Pythagorean bond uniting all.
However different the means or modes of expression, each of
these philosophies or disciplines concerns the creation of the world,
or matter, out of the void; each recognizes that the physical
world is but an aspect of energy, each — excepting modern
physics which, by concentrating on the material aspect of the
problem, can avoid its philosophical implications — recognizes
that 'life' is a fundamental universal principle, and not
an afterthought or an accident.
The number of 'love', the number sacred to Pythagoras, the
number symbolized by pentagon and pentagram, which commanded
the proportions of the Gothic cathedrals, played a crucial
but subtler role in Egypt. Apart from the hieroglyph of the
five pointed star, we find no over t instances of five sided figures.
Instead Schwaller de Lubicz found the square root of Five
commanding the proportions of the 'Holy of Holies', the
inner sanctuary of the Temple of Luxor. In other instances he
found the proportions of certain chambers dictated by the hexagon
generated from the pentagon. In others, crossed 8x11 rectangles,
the four sided generators of the pentagon from the
square, commanded the proportions of wall murals symbolically
related to those functions represented by Five.
Egypt also made extensive use of the Golden Section which,
from the Primordial Scission, commands the flow of numbers
up to Five. The pentagram, made up of Golden Section segments,
is the symbol of unremitting activity; Five is the key to
the vitality of the universe, its creative nature. In mundane
terms, Four accounts for the fact of the sculptor's statue, but
does not account for the 'doing' of it. Five terms are required to
account for the principle of 'creation'; Five is accordingly the
number of 'potentiality'. Potentiality exists outside time. Five
is therefore the number of eternity and of the principle of eternal
creation, union of male and female — and it is for this reason,
and along these lines of thought, that the ancients came to
hold Five in what looks to us like a peculiar reverence.