The Symbolism of the Mayan Numbers

[Myriel RAouine]

The Symbolism of the Mayan Numbers

". . . Solamente habia immovilidad y silencio en la obscuridad, en la noche. Sólo Tzacol (el Creador), Butol (el Formador), Tepeu (el Gobernante), Gucumatz (la Serpiente Emplumada), Alom (la Madre) y Caholom (el Padre) estaban en el agua rodeados de claridad . . ." (Popol Vuh).

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At early stages, the Maya perceived that the natural events recur in a cyclical manner and that are combined each other according to proportions and numerical parameters. The sequence of lunar cycles within a year, the conjunctions and eclipses, the periodicity of the solar flares and even the apparent repetition of major cataclysms registered in their history was a definitive urge to express that the Universe obeys the laws of the alpha and omega, that everything is measured and everything can be anticipated if the numbers are known for which are the cause of the manifestation. In the Kahlay of the Conquest, of Chilam Balam of Chumayel, there is a poetic fragment that I can not resist the temptation to translate because it describes eloquently that attitude toward Life although some historians have confused with the fatalist determinism of a culture situated in a prolonged descending slope. I judge it as a scientific positivism that anticipated our times recognizing the inevitable periodicity of the ecological cycles, the relativity of any temporal glory, and reflecting the anguish of knowing what the future is.

So, the fragment read like this: ". . . Every month, every year, every sun, every spirit, walk and pass when it has completed its just measure. Also, every blood and dynasty reaches the place of solitude as it takes the power and the throne. Measured was the time when the Itzáes praise the magnificence of the Three; measured was the time they could find the goodness of the Sun; measured was the time they could look over them the knitting of the stars; and from there, looking at them, the gods contemplated. The gods that were jailed in the stars. Then, everything was good and then, they were abated . . ."

A culture highly mathematical as the Maya had to incorporate teogonic concepts with the numerals, using them as symbolic elements to express their ideas about the Universe.

The hipostasis, perceptible manifestations of Hunab-Ku, the abstract deity, unknownable and without possible representation of the Mayas, are clearly expressed in the Popol Vuh under the symbolic names of Tzacol, Bitol, Alom, Cajalom, Tepeu and Gucumatz. Each one of these designations has a clear and simple ethymology that has been elucidated by several authors with congruent results.

Tzacol means "Creator", Bitol is the "Former", Alom is the cosmic female progenitor, Cajalom is the cosmic male progenitor, Tepeu means the "Governor", and Gucumatz (Kukulcan, in maya) is the "Plumed Serpent": the Quetzalcoatl of the Toltecs and Mexicas.

It is not required a big effort to reconstruct the essential thinking of the Mayan philosophers that reunited in these six teogonic personalities the visible and comprehensible attributes of an abstract deity revealing its presence. To return with imagination of what the Cosmos would have been, descending through the evolutive scale of beings and things, we reach a hypothetical starting point of all Creation where the postulates compel us to accept the supernatural intervention of a Creator. It is evident that the creation represents a foreign act to the natural order of the Universe because from there the Law of the Conservation of Energy is manifested invariably and nothing can be created or destroyed but only modified in appearance or manifestation. In other words, since energy acquired its expression it has remained unaltered in total magnitude: neither the transformation of matter into energy, neither the confirmed existence of anti-matter, neither the phenomena related with the possible displacement of some molecules in a fourth geometrical dimension modify or invalidate this conservative principle. However, the theoretical movement that for the first time manifested the energy of the Universe, in any of its primitive expressions, establishes the problem of the Creation. This event implies the birth of energy from nothing without antecedents of any previous form. This origin is not explained within the the natural order. It is of supernatural order and required from the Maya thinking, the intervention and willingness of an entity: God with the personality of Tzacol, the Creator.

The number ONE represents Tzacol, " . . . In the One, Chuén, says Chilam Balam of Chumayel took itself his divinity and made the sky and earth. . ." In the so called Book of the Spirits, the document states: " . . . From the abyss matter was born and the Power carved the Great Stone of Grace; there there was no sky. And seven sacred stones were born, seven warriors suspended in the spirit . . . seven chosen flames . . . and they moved! And seven were their graces also and seven were their qualities. And it happened in the immensity of the nights; there where there was no God because they have not received their own God who was within the Grace, within the darkness . . . there where there was no space or matter . . ."

This passage reflects the energetic concept of the Maya Universe, in spite of the Spanish version contaminated with other concepts covering the symbol of the "stone" (concrete nature), "grace" (substance or essence), "flames" (manifested energy) and "darkness" (space).

Tzacol is, therefore, the first hipostasis or sensible manifestation of God. He is the Huehuetéotl, the creator of Fire. A fire that Heraclitus postulated as the constitutive energy of all Universe in constant return. Tzacol is the red sun born from the darkness in the Eastern horizon during the Winter solstice. The glyph of the numeral One is a dot or point: a small circle that reminds us the shape of an spore, or an ovule and a germinated egg of the Indostan cosmogenesis. It is seen in the fretwork of the Mayan facades that are eloquent pictograms of the ideas this culture had about the Universe.

Put into movement the cosmic mechanism the existing matter begun its ascending evolution toward more complex forms of organization allowing to reduce the entropy and taking advantage of the obtained energy. From the infinite number of transformations that ocurred some of them persisted representing a better functional perfection. Attempting to understand this admirable concatenation of factors, the Mayas touched again the supernatural frontier and required of the intervention of an abstract God invested in a new personality. The "Former." This is Bitol, similar to a crafter, modeling the clay of the Creation in the evolutionary process toward their mysterious designs.

The warm and tranquile waters of the Precambrian sea incubated the first cultures of living cells. The first fermentations of the animated existence. In these waters, says the Popol Vuh and modern science, evolution operated toward living beings until one day these living organisms emerged from the sea and invaded the beaches and spread over the land. This wave breaking near the beach is the ideogram of Bitol, the "Former" of the Universe. Wave and backflow, evolution and involution, constitute the geometrical design of the series of fretwork extensively used in the Maya architecture.

The polarity is the motor principle of the Cosmos. From the atraction and repulsion that establishes the movement of the atoms and molecules. The equilibrium of the bodies at rest, of the bodies in movement, of the activities of beings, polarity rules all of them. By virtue of this principle, a portion of the Universe participates of a polarity that can be qualified as "femenine", "negative" or "passive" (please ignore the political correctness) and the other half as "masculine", "positive" or "active." To use these tems "negative" or "positive" I am not implying a relative importance of one over the other. They are qualities of identical magnitude, complimentary and essential in the cosmic scheme. Can we conceive the existence of an atom without electrons? Of an electric current without positive and negative poles? Of a generation without polarity in the sexual creation? It is necessary that the capacity of giving exist to have the capacity of receiving, it is precise to have the container to hold the content.

Alom and Cajalom, " . . . the mother and father of Life, of everything created, the ones that give the breath and the thinking, the ones that give the children. . ." These are the words of the Popol Vuh. In Alom it is represented the essence of all that is conceived, all that has the capacity to give and to receive. She is the electron, the Mother Earth, the Moon. She is the conscience and the flower. Beautiful is the symbol chosen by the Mayas: the flower. Like her, the flower is the femenine condiment by excellence. Alom is Mother Earth. She receives the golden seed of corn, able to germinate and nourish the womb like mother to child. Alom is the conscience, the lotus receiving the vibrations of the surrounded Universe and translated concrete images. She receives the inspiration to produce the ideas. The flower appears in the Mayan fretwork with an intimate and simple design different from other geometrical forms to give the master touch of beauty and humanization of the scientific coolness of the abstract designs. The numeral FOUR and the SQUARE are symbolically equivalent.

Cajalom, on the other hand, is the father of Life and his functions as progenitor are evidently set when the sun is placed in the zenith. It is from that position energy is sent with more power. From there, at the intersection of the six cosmic roads (the points of orientation of the Sun), in the center of the cross, in the heart of the sky, the Maya ideogram of Cajalom is designed: The Maya Cross. The symbol of Cajalom is the cosmic cross formed by the vertical coming from the zenith to the center of Earth and the horizontal that is the way of the Sun (from East to West). In the center of the cross is the Sun. The numeral symbol is FIVE, but as we see later it is transformed into SEVEN by the adition of the sun at the center, also of the cross of the six arms formed by the horizontal plane. Girard (1) has explained this on the numeral SEVEN called the God 7 or "the maintenance God."

Tepeu is the Governor. He is a God with an ordering personality extending to the most remote corner of the Universe the invariable law of causality, of the proportion and similarity. His ideogram is IK that appears in the Mayan fretwork in two positions: upward and downward. It exemplifies the hermetic concept "as above, so below, what has been, will be again." Its numeral is SIX and it is related with the causal trinity: thesis, antithesis and synthesis, acting upward and downward.

Gucumatz, that is Kukulcán-Quetzalcoatl, is the Plumed Serpent. Omnipresent theme in the Toltecs, Zapotecs and Mayan representations. It hides a teaching and symbolism of great depth.

The senses of man are limited in number as well as in sensibility. From there, all things that are presented have a dual aspect. One part of nature is available to our senses and another escape to us. The first is concrete and the second is abstract. In representing this fact the Maya symbolism makes a tool of its imaginative resources.

If we try to find in the physical world a synonim or parallel to describe a set of intangible things, it is difficult to find a better example than the air surrounding us. This untouchable environment is practically unreachable to our senses but we know it exists because its presence is manifested in the movement of the leaves of trees, the dust and other light bodies. The symbol of air, and in consequence the symbol of the abstract or spiritual (that is conventionally assigned) is the bird because air is its natural media. The element where the bird lives and interacts.

On the other hand, the material, the tangible and earthly is represented with the serpent. The simbolic representation is evident if we recall that everything that is perceived by our senses comes from Earth. It the serpent the animal that lives and drag over the ground. The plastic beauty of the serpent exemplifies the Mayan concept of the cyclical recurrence of phenomena, the poison that represents the danger in the appearance of all material forms. Its total symbolism has reserved a sacred place in the Egyptian, Hebrew, Caldean, Babylonic, Hindu cultures.

Here you have the Maya genius and simple naturality of the fusion of two symbols: the bird and the serpent expressing the duality of the Universe. By logic, the mathematical symbol is TWO. Matter and spirit forming a unique being undivided in the tangible and untangible Universe, indivisible and ruled by the same laws.

Now, what does it remain for the Mayas could define the concept of God? As we have seen, it resulted in six the perceptible manifestations of nature by which they inferred the existence of an abstract God and in consequence, the number 6 could represent God in a suggestive manner. But if the Mayas could have assigned it, they would pretend that this infinite God was not such thing because our human mind is able to contain the totality of these qualities.

It is now when the Mayan genius discovers the adequate symbolism: the perfect simile because in spite of the six representations, the set is not any more 6 but 7. It has been added something else that remains unnamed and contains all the rest that escape our understanding and experience. It constitutes the synergic principle that functions harmonically in all the manifestations as a group. The definition of God, consequently and similar to the Pitagoreans, rest incomplete and it is one of the most perfect formulas the human mind can formulate.

Besides the admiration that awaken us from the deep teogonic Maya thinking, we noticed we are touching the frontiers of the mathematical knowledge that the Mayas had reached in relation to the organizing principle of the Universe. Already, some investigators, among them Rafael Girard, have presented the way some numerals are transformed symbolically in others, the binomial mother-father is transformed in the numeral 3 when the child is added and linking them genetically as a functional triad: origin of the family, the tribe and of the nation. This principle is extended to other numerical representations: the four solstitial points of the horizon only can have life when the sun is placed on them, and thus, the numeral 4 is converted into 5. The four solstitial points and the two corresponding to the East and West only have meaning when the seventh element is associated, again the sun in its zenith position converting the number 6 in 7. As we see later this elemental Synergic Arithmetic (from the Greek, work in conjunction) is one of the most important contributions of the Maya thinking that we may as well understand and apply to our lives.

Continuing with the symbolism of the numerals, we can point the ambivalent character of the numbers 3 and 9, explained also by Girard. The numeral 9 links the law of cause and effect with gestation. It is the proper numeral of the Moon and her eight nightly companions (the planets?), therefore, it has a clear association with the night, the underworld, the occult and the nine lunar months of the human gestation. The numeral 9 is formed by multiplying 3 x 3 but also adding 4 + 5, 7 + 2, and 8 + 1. Each one of these symbolic operations represent something distinct. 4 + 5 is conception, 7 + 2 is incarnation, 8 + 1 is birth, and 3 x 3 is proliferation, succesive stages of procreation. The relations are extended to the nocturnal, the occult, the rituals toward the mystic birth (e.g. the Order of Balam and its nine grades). It is not my intention to enter into this fascinant theme but only to illustrate the way the Mayas utilized the numerals as symbols.

The numeral 13 is another example of which my mentor have baptized as Synergic Arithmetic. There are reasons to think that the Oxlahuntikú (13 stellar gods) were constituted by the twelve constellations of the Maya zodiac and the sun passes them in its ecliptical travel creating a functional set where the sun and the stars assume an astrological personality. This concept is illustrated in the Chilam Balam of Chumayel in two figures. The first represents the sun in its ortho zenith accompanied in each side by twelve stars while the second figure shows the twelve kings or masters of the sky and it is completed by the sun in its zenith position. From there, the number 12 is transformed in 13 by the addition of the ruling element and coordinator of the set as an organic unity necessary for the recognition of the event.

Finally, the number 20 represented the totality for the Maya: the complete and integrated. Its representation creates a new element because in the vigesimal system is expressed as a dot in the second position and zero in the first position.

Within the unit of superior range the numerical and symbolic elements are contained in the contribution for the addition operation. In there, all of them exist and each one previously explained are fused in a dot that is at the same time a small circle: an infinitesimal microcosmos withint the unlimited. Below the dot or point, is the zero. This symbolic element represents the existence when everything is completed. It indicates that perfection is reached when all the numerals concurs harmonically and are added to complete twenty. When this happens, it transcends to another functional hierarchy, leaving the shell back and the memories. Zero is therefore not a negation but the categorical affirmation of fulfillness. It is not death but total realization.

Until now, the reader has participated in the Maya thinking with its positive philosophy and creation. I hope I have lit the internal spark of the spectacular greatness of the Maya symbolism which is only a pale reflection of the most acute observers of nature and thinkers of incredible depth of the Mesoamerican era.

From the discussion of these principles I have also initiated concepts of my work in Synergic Arithmetic. In further sections of this Web site I will continue elaborating on graphical aspects that I call Neurographics: numerical graphics created by neurological inputs. Thanks to the Maya thinking, the reader will see complex equations representing matrices, tensors, etc. where the Maya fretwork takes place again in a time of chaos. It is my hope that these new concepts bring an ordered style to the Mathematics of our times and also serve as arquitectonic designs as the Mayans did.

References

1. Girard, Rafael. Los Mayas. Libromex Editores. Mexico. 1966

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[Arleem]

Thank you Dear Sonja xxx