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Nahua/Maya Number system

The Skull Motif and the Mayan Discovery of Zero
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Seven
The Skull Motif and the Mayan Discovery of Ten
 
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"It is evident that the cult of the skull or at least skull worship, has been in the past a worldwide practice among ancient peoples," Dorland says.  "From the Pacific islands to Tibet, from Egypt to Mexico, skull worship is found in every corner of the globe.  And it seems that almost all of this practice held the skull in extremely high esteem.  It was worshipped and adored and saved and revered.  The symbol of the skull as a gruesome ugly death head, seems to be most common in the last fifteen hundred years.
 
 
"The actual quartz crystal skull is a magnificently sophisticated bit of masterful art and it has nothing at all to do with death or mortality in the eyes of its original makers.  It was believed to be a godhead-symbol of all encompassing knowledged and wisdom.  I believe it was a fountainhead of power and magical talisman."
 
 
Dorland, in his research, speculates that the Mitchell-Hedges skull could even represent earlier deities. He points out two possibilities: Ea and Mazda.
 
 
"Ea was one of the three deities of the Babylonian pantheon and the lord of all wisdom.  Mazda was an ancient Iranian god, illuminator of the universe and another likely candidate.  I think it logical that Ea and Mazda could possibly be the same god, simply evolving in different areas.  Both, for example, were gods of wisdom, both possessed a great and encompassing love of man, and both were great magicians.
 
 
 
"Ea was the god of water and Mazda the god of light.  Ea, being the water god, would be sculptured in a material that represents exactly what he was: wisdom and water.  The human brain box signifying wisdom and the quartz crystal symbolizing water.  It would have been relatively simple to manufacture the skull from gold or silver but it would not be suitable for a water god."
 
 
Dorland has been unable to find any other god that would be so suitable to be carved from pure rock quartz.
 
 
But nowhere in the world has the skull motif had a greater importance than in the Central American cultures, both modern and pre-Hispanic. In these cultures, the skull motif shows up in an astounding variety of forms.  For instance, the center of the Aztec-Calendar is a fleshless face; the Aztec god Xolotl, twin of Quetzalcoatl, had the face of a skull; mosaic inlays of skulls were made by the Nahuas and the skull was an important thematic element in the gold work of the Mixtecs.
 
 
In Mexico, the skull is constantly used as an element in ceramics, reliefs and sculptures.  It is used in arches and pageantry, crafts, politics, the manufacture of toys; even tiny sugar skulls are a popular confection among the children.
 
 
One of the most popular holidays of the year is the Feast of All Saints--the Mexican Halloween.  Many reasons have been offered as an explanation for the prevalence of the skull motif in these cultures but none so intriguing as the possibility that the skull could possibly be related to the development of the mathematical concept of zero by the Mayas.
 
 
It has been pointed out, notably in Indian Historian, the quarterly publication of the American Indian Historical Society, that the skull motif was closely related to the Maya discovery of zero.  The Mayas invented the sero around 200 B.C.--long before the concept evolved in other civilizations.  It has further been suggested that the Mitchell-Hedges crystal skull served as the archetype of the Mayan head variant for ten and that the skull was made as a sort of standard for the concept. 
 
 
Around a thousand years before the early Hindus civilization was credited with the development of the concept of zero, this idea was already firmly planted in the intellects of the high Maya priests.  Further, this mathematical concept did not reach Western Europe until the Middle Ages--centuries after its development in the Western Hemisphere.
 
 
The possibility that Thor Hyerdahl suggests--that man traveled westward across the Pacific--might well explain the expansion of this concept from a Central American culture to a civilization of the East.
 
 
At any rate, there is little quarrel among authorities that sometime around 200 B.C. the Mayan concept of zero was developed.  And as the late authority on the ancient Maya, Sylvanus G. Morley, commented, they developed man's first positional arithmetical system, one involving the concept of zero "which even today stands as one of the brillian achievements of the human mind."
 
 
In what way, however, does the concept of a skull with a detachable jawbone and the prevalence of the skull symbolism in Central American cultures have to do with mathematics?  The answer porbably lies in the fact that the Mayan system of notation is based on the number twenty (vigesimal) rather than by tens [as] in our decimal system.  And just as we use both Roman* and Arabic numerals, two sets of symbols were used by that culture, both employing the concept of zero. [*The concept of zero is lacking in this notation.  To reach the number of nineteen using the symbols of I, V, and X, a subtractive process must be employed.  The dot-bar system of the Mayas requires but simple addition.]
 
 
One is known as the "normal form", a system of bar and dot numerals in which a dot has the value of one and the bar a value of five.  In various combination the numbers from one to nineteen could be written.  Zero in this system is symbolized by the glyph of a shell.
 

The other method of numerical notation is usually referred to as the "head variant" system and uses the head symbols of deities to represent the numbers from zero to thirteen.  But most significant is that this system utilized the symbol of the detached skeletal jawbone to represent the number ten.  Thus if the fleshless jawbone were added to the head variant figure for seven, the number would automatically become seventeen.  This is an amazing concept considering the age in which this was discovered--equaling or perhaps even outstripping the contributions of a Pythagoras, a Euclid or an Archimedes.
 
 
Was it a mere accident that the jawbone of a skeleton was chosen to prepresent such an important mathematical concept?  Certainly a less macabre symbol could have been employed. But symbolism of the most basic themes were used throughout the culture--a culture which recognized the head as the brain box and the carrier of intellect and rationality.  What symbol of the human anatomy, stripped of all its fleshly characteristics, could serve better as the archetype of man's intellectual potential?  And so the selection was accepted, probably was passed into law and became the most important mathematical symbol ever to develop in this culture. 
 
 
The use of the skull and its detached jawbone, it may be concluded, would make maximum effective use of the symbolism that employed the concept of zero.  The symbol was constantly kept before the eyes of the people in their day-to-day existence by its obiquitousness in erected stelae, friezes and other artifacts.
 
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Taken from:
The crystal skull; the story of the mystery, myth and magic of the Mitchell-Hedges crystal skull discovered in a lost Mayan city during a search for Atlantis
by Garvin, Richard M.  [Chapter Seven]
 
 
Read Also:
 

Mayan Numbers

History of Zero

Current Mayan Date

 
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