SACRED COSMOLOGY
FEDERICO GONZALEZ
NUMERICAL AND
GEOMETRICAL SYMBOLS
For a traditional society, the concept of number is diametrically opposed
to the one that might be held by a profane society such as ours. This calls
for emphasis, since it was traditional societies that created numbers as
concepts of relation that their sages and inspired men obtained by revelation.
Modern society, meanwhile has pressed them into service exclusively for
its material ends, ignoring their meaning-without any attention to their
authentic sense, their true essence. In other words, modern society has
demeaned numbers by taking account only of their quantitative values, rejecting
the qualities of numbers, the ideas and concepts that they express.
At the same time, we of the contemporary era take our numerical code simply
as a given, without stopping to ask ourselves of what this system is a manifestation.
Numbers expressed (and still express) ideas: metaphysical concepts concerning
everything numbered, or participating in the categories of the numerable-that
is, concerning what is "countable," finite, and successive. On
the other hand, these "numerations" are the harmonious measure
of all things, and the form in which these things related between each other.
They are rhythmic standards, modules, and cycles that generate-in their
quality as concepts-"proportion," and reveal the secret "ciphers"
of the cosmos, of which they are active components. Obviously oneness does
not correspond to the same idea as twoness or threeness, and does not manifest
the same thing. Today, however, this is left out of consideration by the
diminished, humdrum, horizontal view that we have of these concepts when
we regard them as simple factors of quantitative multiplication.
Let us further indicate that these numerations refer to different energies,
and to the ordered intervention of these energies in the universe. After
all, as we have said, they attest the interrelations of the creative elements-their
waves, their vibrations-that join together in the numerical corpus. To give
a very simple example: even persons of very little mental acumen know that
it is not the same for a person to be alone (one) as to be a member of a
pair (two) or to belong to a triangle (three). Number obviously alters our
relations with others and our being in the world, since it actively intervenes
in situations as a component of the same, as it signs or marks them with
its conceptual and vital seal. And yet, generally speaking, even the simplest
sense of the idea of number escapes men and women of this century. Indeed,
most of them have never reflected on numbers, nor are they interested in
the subject. But what is really arresting is the fact that not only have
the common masses lost all notion of the fact that number is the sign of
a quality that it represents and fixes-of a concept that it expresses in
unequivocal fashion, a concept capable of articulating itself, and entering
into interplay with, other concepts-but even today's mathematicians (who
one supposes to be specialists) are ignorant, up to our very day, of the
real conceptual (and emotional) charge carried by numbers. These persons
proceed on quantitative criteria, those of the marketplace-fundamentally
suited for the commercial and the material, but not for Knowledge.
Traditional arithmetic corresponds to geometry, and numbers to geometrical
figures, forming complementary symbolic codes that manifest identical concepts,
correspondences, and analogies. At the same time, in the first three numbers,
all of the others are synthesized. From the union of oneness and duality
(which is its reflection), that is, from triad, proceed all of the other
numbers, and from this primordial triangle all figures derive.
There is also, for traditional civilizations, a direct relationship between
numbers and letters of the alphabet, to the point where, with many alphabets,
numbers were represented by letters, and had no special signs of their own.
This is not the case with the early American cultures, which knew no alphabet,
but we wish to call attention to this correspondence because not only the
alphabetical code, but the numerical one, as well, describe all reality:
that is, everything that is numerable or namable-in the sense of "ciphers,"
harmonious measures, "proportions"-in sum, the totality of the
cosmos, of the knowable.
This threeness or triad, to which we have referred earlier in our pages,
has always been considered sacred-like oneness, duality, and all numbers-by
virtue of its very properties and particular attributes. These properties
and attributes are manifested in its threefold nature, which of itself is
the inevitable expression of a principle, an archetypal fact, that solidifies
in a series, as a representation of ideas and energies that materialize
in magical, mysterious fashion while obeying precise, universal laws, which
the numerical codes and their geometrical correspondences symbolize.
However little these modules in their exterior expressive form be the same
as we have today in our recent Arabic notation, the archetypes to which
both refer are identical, the laws of the cosmos the same-for every time
and place-and the model of the universe one only. We shall see, then, that
Western numerology corresponds perfectly with the Indian, although the latter
was commonly vigesimal (and, accordingly, decimal as well, both having the
number five as a common base). We shall say something about these first
five basic numbers, common to various peoples, but especially to the indigenous
peoples and Christians, since this is the subject with which we are concerned.
We have somewhat anticipated our discussion of the triad, as basic form
or archetype, a concept present in all manifested things, which are generated
by its multiplication.1 We have also asserted that it is produced by the
amalgam of the primordial oneness with its own reflection. Now we shall
add that this fact, whose design is successive (1, 2, 3), is actually simultaneous
and eternal, and that from it proceed all numbers, or all manifested beings.
Now let us see something about oneness and duality-concepts to be found
at the foundation and origin of every traditional civilization or culture,
among them those of America.
We have called attention to duality, twoness, on various occasions, as the
fundamental mover of the beliefs and cultures of the Precolumbians. This
is especially clear among the Incas and the Aztecs, to take them as two
examples of civilizations that were already developed by the time the Europeans
arrived. In the former, Manco Capac and Mama Ocllo, equivalated to the sun
and the moon, gold and silver, together establish Cuzco, which is divided
at its center into two parts, one masculine and active, the other feminine
and passive, which were denominated as the high part and the low part, and
which we equivalate to the vertical and the horizontal.
Indeed, if we regard two energies symbolized by the above-and-below, one
rising and the other falling, we find that there is a neutral point, common
to both, at which their oppositions do not exist. That center or middle,
in which the contraries complement each other, creates a plane (or world)
where that conjunction occurs-a reflection of the original metaphysical
oneness, which gave rise to the manifestation of arithmetical singularity,
represented by the number one or the geometrical point. It is this point
or center that generates the plane (or world) in question-in this case the
Incan civilization-acting on it as a reflection of the invisible axis. To
put it another way: the center acts upon the world as a reflex of the active,
vertical energy that conditions horizontal reception by coupling with it,
and thus creating the said plane (or world). The limits of this world are
constantly given by its own progression-which, although it can be considered
indefinite, is marked by its own numerical laws that succeed one another
ad infinitum.
Thus the number four signs the first manifestation-the first action of the
three ontological or primordial principles in the world (3 + 1 = 4)-the
creational plan and its limitations, thanks to which latter any being or
object can be constituted, and then assimilated to the world, especially
to the earth.2
We must explain that all of this dialectical production is successive, and
that, in regard to it, the energy of oneness, constantly adding itself to
the energy of the preceding number, transforms the latter into its own quality,
while remaining ever-present and inalterable throughout the numerical series.
Let us add that, in numerology, zero is a concept not only indicating lack
of quantity or absence of numerical determination, but also serving as a
mechanism of position and order in the tens, hundreds, thousands, and so
on, which makes for great manageability when it comes to notation, and great
facility in the calculation of large units. The Mayas knew the zero, and
made use of the positional notation in their numerals, the only difference
being that their system was vigesimal instead of decimal. Actually, they
used the zero long before Europe did so: until the eighth century of our
era, the system of position that we share today was not used. Of Hindu origin,
our present system was propagated in the Middle East and Europe by the Arabs,
although its dissemination occurred only between the tenth and twelfth centuries.
That system has obvious advantages over Roman numerals.
It is interesting to recall that the system of counting and calculating
with pebbles (or grains of maize) of different colors or placed in different
groups, common to the Precolumbian traditions and attested by various chroniclers,
is basically the same as that with which the Pythagoreans effected their
"measures," and their abstract "speculations."
And so, let us return to our division of energies into above/below, ascending/descending,
or of two forces mutually opposed but complementing each other at some point
(and radiating outward in a horizontal plane in which these energies also
project themselves in the same fashion, now standing in a two-to-two opposition
and meeting at the point of intersection, the fifth, the quintessence, the
center, the axis or heart of the figure). We see the validity of transposing
the entire process and synthesizing it in the opposition of vertical/horizontal,
high/low, heaven/earth, active/passive, male/female, since from this primordial
opposition and of its complementarity spring all of the things of the universe.
The binary is likewise revealed in the myth of the foundation of the Aztec
city, and in the manifestations of that society. As we know, at the arrival
of the Spaniards, the principal temple of Tenochtitlan was crowned with
a double sanctuary. One of these (painted red) was dedicated to Huitzilopochtli,
image of the ascending (from the earth to heaven) sun,-the sun of the zenith,
the south, and noon. The other (painted blue) was consecrated to Tlaloc,
god of rain, associated with thunder, lightning, thunderbolt and water,
the deity who descends (from heaven to earth), and who is akin to the gods
of fertility and the moon, the numina of vegetation and generation which
are possible only when the energies of sun and rain-ascending and descending-of
heaven and earth, of the eagle and the serpent, join together as one, to
the exclusion of neither pole.3
It would be superfluous to cite further examples of duality, as they are
innumerable in the Precolumbian tradition, and readers can discover them
for themselves. But we do wish to indicate the conception of the binary
that is entertained by modern society-that is, the conception of duality
with which it has outfitted us, this particular baggage of our convictions
and the difference between it and the one held by a traditional society.
In this respect, let us observe that the traditional conception does not
reject evil (or the descending, passive, subterranean, or horizontal energy,
in varying terminologies). Rather it accepts it, in conformity with the
knowledge it possesses of cosmogony and theogony, which testifies to the
continuous recycling of two universal energies, contrary forces that are
not mutually exclusive but that this cosmogony and theogony incorporate
as integral parts of reality and life. With each other (and in the mutual
relations to which they give rise), these forces or principles constitute
a complex of modules, measures, archetypal emanations, which, in their "coagulation,"
are even manifested as phenomena. The gods personify these opposed forces
in many-faceted wise, which is the case, among many others, with the struggle
of Tezcatlipoca as the nocturnal, dark deity and Quetzalcoatl as the diurnal,
luminous god, just as between the latter and his twin, Xolotl, sometimes
represented by a skull. The two forces are constantly at war with each other,
and thereby balance each other, as we see so well in the perennial cosmic
drama exemplified by the interplay of tensions prevailing in any quadrangle
or any quaternary, where the forces are in opposition by pairs, two to two.4
Just oppositely, we moderns have been educated in a milieu that always obliges
us to choose between good and evil, and this is the principal cause, the
root, of our conditioning. Worse, the only escape from the disjunction is
the choice of an alleged goodness ascribed to one of the poles-monism-to
the exclusion of the other, which is left entirely out of consideration,
as it is ascribed a negative value, which need not be taken into account,
but rather torn up by the roots. We fail to notice that the primacy we attribute
to one of the factors of the duality good/evil is bestowed by evaluations
that are altogether relative, circumstantial, or of purely personal or group
interest, such as current society's "ideologies," usages, customs,
phobias, and manias, channeled by means of nation, state, class, and even
ethnic group, to all of which we necessarily belong. The same occurs with
the attractive and the ugly, liking or disgust, the useful and the useless.
All of these values are of a nature as variable as their contraries, with
which they could be exchanged, and to which are attributed a supposed definitive,
objective truth.
The quaternary as a concept of creational manifestation-as the idea of generation
and limit, or as the form of the earth (figured by the square or by the
cross)-is basic in the early American cultures, and we should like to emphasize
that this last geometrical form is equivalent to the circle (a rotating
cross generates a circumference). The reason is that they each symbolize
the same creational plane, alternately in its static and in its dynamic
aspect, in its contraction and its dilation, in its crystallization and
its expansion, and are assimilated respectively to the solid and the aerial,
earth and sky. That is, they constitute complementary figures, just as do
the world (horizontal plane) and man (vertical plane).
In this sense, five being the number of the human being, as virtual center
of the cosmic irradiation, this number, multiplied by that of the earth,
or creational plane, shapes the ensemble of manifested possibilities. For
we now have the number twenty, the "magic" measure or module common
to various Precolumbian cultures and civilizations.5
Let us recall what we declared in the foregoing chapter to the effect that
the circle as well as the square are analogous and complementary symbols.
These have been utilized by different societies with the same object, or
in one and the same society by alternation or by conjunction, as connected
to heaven and earth as a representation of the two halves of the cosmic
model.
At the same time, the symbols associated to the circle and the square, or
derived from them, share their lot, and themselves entertain a mutual correspondence.
This is the case with the circular spiral, as a representation of the evolution
and emergence of the cosmos. It is also the case with the square. These
two figures, in the volumetric, and in constructive symbolism, are the edifices,
respectively, of the ziggurat (sig-gurat, literally, "mountain")
and the pyramid as opportunities for a vertical ascent-via a succession
of steps and revealed by the immutability of an axis, which is the center
and origin of both monuments (temples).
We only wish to emphasize-and on this note we shall bring this chapter to
a close-that, for a traditional society, not only the stars, but also rocks,
plants, animals, and human beings maintain an interplay of mutual relations,
a dance of subtle possibilities. These possibilities complement one another,
in the rhythmic cadence in which they all variously develop in reciprocal
correspondence, establishing the guidelines, the measures of their interrelation,
and conjoined in number as the synthesis of the archetypal meaning that
these "modules," "measures," "ciphers," and
"proportions" comport. And it is upon this conceptual base that
one must study the Precolumbian arithmetical and geometrical symbolisms,
just as any work on the subject will have to be orientated in this direction.
NOTES
1 See René Guénon, The Great Triad (1991, trans. P. Kingsley).
2 The number four is equal to 2 x 2, or 22, that is, the total number of
possibilities of the duality multiplied by itself. Let us observe that,
in Mesoamerican civilizations, this progression is symbolized by the number
400, which is equal to 20 x 20, or the equivalent of an indefinite numerical
series.
3 Among the Mayas of today, studies have been carried out, with respect
to the health of the body, on the relationship between hot and cold, as
the opposition of two contraries that are present throughout the cosmos.
These contraries are also indicated as the dry and the humid-which must
complement each other in order to reestablish the vital equilibrium. This
way of measuring energy extends to various kinds of diseases, foods, herbs,
etc., and is transferred to personages, events, and situations. It is autochthonous,
and does not derive from Hippocratic or Arab medicine. Simply, as with so
many other things, it coincides with other traditions in its archetypal
concepts.
4 "The Canelas, of the plateau that rises to the south of the mouth
of the Amazon, are composed of two exogamous matrilineal groups, one comprising
the inhabitants of the eastern part of the circle of their habitat, the
other those of the West. During the rainy season, a race is scheduled between
the boys of these two groups, who are then painted red and black respectively.
One of the groups represents the east, the sun, day, earth, red, and the
season of drought; the other represents the west, the moon, night, water,
black, and the rainy season. These two groups, who divide up all that exists
with the same rigorous consistency as do the Iranian and Chinese religions,
promote, with their ritual activity, the beneficent rhythm of the universe
and nature" (Ake Hultkrantz, Histoire des Religions-3, Encyclopédie
de la Pléiade, Gallimard, Paris 1976.
5 As for the number nine, we wish to emphasize that, by virtue of its intrinsic
characteristics, and as an integral element of every series or group, it
introduces into the latter the concept of circularity, or the cyclical.
The same holds true for its multiples and exact submultiples.