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Nahua/Maya Number system

World Tree Axis: Dzibilchalt˙n
On the Mexican Calendar and its Cycles
The Maya Cycles
The Maya Creation
The Zuni and Hopi Calendar
On the Maya number system
Codex Mendoza / Mexican Numbers
The Calendar Wheel
The Calendar, The Seasonal Round, and Moon Ceremonies
Sun Calendars of U.S. First Americans
Maya numbers / Maya Mathematics
The "Five Suns', the Mexican Calendar, and Mexican Creation Story
The Skull Motif and the Mayan Discovery of Zero
Roman Numerals
On Numbers, the Syllabary, and Symbols
Oldest Known Maya Mural
Index of Links to Mexican and Mayan Codexes [& on the Number System]

By Awake! Writer in Ecuador
(December 22, 2005)
Debate over the exact shape of the earth raged at the prestigious Academy of Science of Paris in 1735.  Supporters of Isaac Newton's theories concluded that the earth was a sphere with slightly flattened poles.  Supporters of the Cassini school of thought said that the flattening occurred at the equator. 
Therefore, in 1736, two expeditions were sent to measure the earth's curvature. One went to Lapland, headed toward the North Pole, and the other went to present-day Ecuador, to the equator. ('Ecuador' is Spanish for 'equator').  The Investigation proved Newton's supporters to be correct.
In 1936, to commemorate the 200th anniversary of that French mission, a monument was constructed near Ecuador's capital, Quito. The monument is located at the line reckoned by the 18th century French scientists to be zero degrees latitude, or the equator.  To this day countless tourists visit the monument, called the Middle of the World.  Here they can straddle the equator and be in two hemispheres at once.  Or can they? 
Not really.  Recent findings have slightly relocated the equator.  Amazingly, centuries before the French sages arrived, the native peoples inhabiting the area had already pinpointed this precise location.  But how?
The True Equator
 in 1997 the seemingly insignificant ruins of a semicircular wall were discovered on top of Mount Catequilla, which lies a little to the north of Quito.  Using the satellite technology of the Global Positioning System (GPS), investigator Cristobal Cobo discovered that one end of this wall was located precisely on the equator.  (On the other hand, GPS places the famous Middle of the World monument some 1,000 feet to the south of the true equator).
The wall's allignment with the true equator might have easily been brushed aside as coincidental.  However, a line connecting the two ends of the wall creates a 23.5-degree angle to the equator.  This is almost precisely the angle at which earth's axis is tilted.  (exact tilt is 23.45-degrees).  Further, one end of the connecting line points to the rising of the sun on the solstice in December; and the other end, to the setting of the sun on the solstice in June.  More discoveries followed. 
Using the theodilite on top of Catequilla, researchers noted that the pre-Inca pyramids of Cochasqui were aligned at an angle that coincided with the rising of the sun on the solstice of June. Sifnificantly, Pambamarca, another archaeolofical sire, is found at an angle that coincides with the siring of the sun on the solstice in December. 
Could it be that Catequilla was used as the hub of astronomical observation?  Were other sites specifically built in line with astronomical calculations obtained from this hub? 

Further Amazing Discoveries
As more astronomical alignments were plotted on a map, a figure began to emerge --an eight-pointed star.  This figure is found on ancient ceramics and has often been explained as a simple representation of the sun.  Since early inhabitants of this land were sun worshippers.  Ceramic fragments excavated on Catequilla have been analyzed and were found to date back nearly a thousand years.  To this day the indigenous tribes weave an eight pointed star into their tapestries and clothing, as their ancestors apparently did.  However, their ancestors may well have attributed more to this figure than is commonly suspected.
The Quista-to Project, directed by Cobo, is amassing compelling evidence of the astronomical acumen of the early natives. ('Quitsa-to' comes from the language of the Tsachila Indians and means 'Middle of the World.' Some believe that Quito is a name derived from this term.)   More than a dozen archaeological sites and many ancient towns have been found to line up perfectly along the astronomical star figure when it is superimposed over the equator with Catequilla at its center. 
Even more astounding is the fact that the location of the then undiscovered ruins was predicted.  How was this done?  In September 1999 the Quitsa-to Project recommended that excavations be made in the Altamira sector of Quito, on one of the 23.5-degrees spokes from Catequilla.  There, a great necropolis was found, along with numerous ceramics from colonial, Inca, and pre-Inca periods. 
Some of the Catequilla radiuses also fall across churches built during the Spanish colonial era.  Cobo explains that in 1570 the council of Lima insisted on building 'churches, convents-monasteries, chapels and crosses upon all pegan 'guacas' and worship places of native people.'  Why did they do this? 
Well, these places of worship were considered heathen by the Spaniard Crown.  So they were destroyed, and Catholic churches were built on the original sites.  Building churches on ancient sun temples made it easier to convert the natives to Catholicism. 
The Church of San Francisco in the old colonial sector of Quito lies on one of the Catequilla radiuses.  It was built in the 16th century upon a pre-Inca structure and was constructed in such a way that the rays of the rising sun of the solstice in December penetrate the cupola of the church, striking a triangle above the altar.  As the sun rises farther, the light bean progresses downward and creates a brillian glow on the face of an image entitled 'God the Father.'  This effect occurs precisely on the December solstice!  In other local churches, such sunlight displays were also incorporated into the architecture for the purpose of converting the sun-worshipping natives to Catholicism. 
How did they know?
How could that ancient civilization have known that Catequilla was the 'middle of the World?'  There is only one place where objects cast no shadow at midday on the equinoxes:  the equator.  So the Quitsa-to Project proposes that careful observation of shadows would have indicated the equator's location to the ancients. 
Furthermore, Mount Catequilla is a natural astronomical observatory that would not go unnoticed by people who worshipped the sun.  The mountain rises a thousand feet from its base and lies between the eastern and western ranges of the Andes Mountains.  Therefore, the rising and setting of the sun each day would have definite points of reference against the spectacular backdrop of the Andes.  For example, the magnificent snowcapped volcanoes Cayambe and Antisana pierce the eastern horizon with their three-mile-high peaks--conspicuous markers for monitoring solar movement. 
Mount Catequilla also offers an unobstructed 360-degree view of about 20 ancient towns and some 50 archaeological sites, all visible without the use of optical instruments.  Moreover, both the southern and northern skies are visible from Catequilla because of its position on the zero degree parallel.  Thus, Catequilla can be called the true middle of the world, for there is no other place on the equator that offers ll these advantages at an altitude of over 10, 000 feet above sea level. 
The greater part of the equator passes through ocean or tropical jungle, where vegetation obstructs celestial observation.  Additionally, such vegetation does not provide stable points of reference from which to draw conclusions, since the foliage is in constant change as it grows and dies.  Only in Kenya are there mountains near the equator, but these are not flanked on either side by mountain ranges, as is Catequilla.  Yes, Catequilla occupies a privilege location, uniquely suited to astronomical observation. 
Who were they?
Who were these ancient astronomers?  The Quitsa-to Project suggests that Indigenous tribes, such as the Quitu or Cara, might have been the original possessors of this knowledge.  However, the project is still in its infancy, and much remains to be learned. 
Yet, some basic precepts of the early inhabitatants are evident.  Understanding the sun's apparent movements would be necessary for formulating calendars useful to agriculture.  Since the sun is crucial for sustaining life, it is no wonder that the sun was worshipped.  Thus, solar observation and calculation were taken from a secular level to a sacred level.
Religious zeal evidently motivated the people to study meticulously the heavens and their luminaries.  Over the centuries their studies apparently resulted in an impressive accumulation of astronomical knowledge that is only now being revealed through the amazing discoveries surrounding Catequilla. 

See also,


The Solstice and the Equinox
Because of the earth's 23.5-degree tilt, the sun does not rise and set in the same place each day.  Rather, it gradually migrates north and south of the equator. Of course, this is an apparent migration of the sun, since it is the earth that changes its position throughout its year-long trip around the sun.
Once a year, when earth's orbit positions the planet's axis at full tilt toward the sun in the Northern Hemisphere, the sun will rise at its farthest northerly point: 23.5 degrees to the north of the equator.  This occurs about June 21.  When the Southern Hemisphere is at its maximum tilt toward the sun, the sin rises at its farthest southerly point: 23.5 degrees to the south of the equator.  This occurs about December 21.  These two extremes points are referred to as solstices.  "Solstices" means "motionless sun."
Midway between the solstices, however, the sun is aligned vertically above the equator of the earth.  This occurrence is known as an equinox, which means that day and night are of equal length everywhere on earth.  About March 20 and September 21, the sun rises exactly in the east, follows the equator for 12 hours, and sets exactly in the west.  At midday on an equinox, the sun is at its zenith over the equator and no objects will cast a shadow there. 

Solstice:  December 20, 21, 22, or 23
Equinox:  March 19, 20, or 21
Solstice:  June 20, 21, or 22
Equinox:  September 21, 22, 23, or 24

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