TONATIERRA

Xinachtli – The Seed

The work of Tonatierra in the area of education and culture over the past 11 years has lead to the development of a curriculum of Indigenous community cultural empowerment called the Xinachtli (Seed). With the momentum of an idea whose time has come, the Xinachtli has been described as evidence of a paradigm shift in strategy and practice for community development initiatives serving the Xicano Mexicano community. In implementation at the community level Tonatierra delivers contracted services in the form of Xinachtli curriculum presentations and training for youth groups, schools, parent groups, teachers, administrators, and social service professionals. The Xinachtli project has been recognized nationally and internationally as one of the most effective models for addressing the issues of Indigenous Xicano youths in terms of alienation and violence which derives as a result of colonization.

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NEMONTEMI

Tamechtlahpahloa, Greetings to all, the following is an offereing from our relative in El Paso, TX, Carlos Aceves, related to the teaching and learning’s that is derived from the studies of the Tonalmachiotl.  A new presentation will be offered each day of the Nemontemi that bridges the year mahtlactli calli, 10 House and mahtlactli ihuan ce tochtli, 11 Rabbit.

Tonalpohualli

Tonal Machiotl is a product of Tloque Nauoque/Hunab K’u, the “giver of all measurement and movement.” Through the geometric manifestation of circle united with square, Tonal Machiotl is thirteen wheels working together to track, measure, and calculate the cycles of Creation. My friend Andrés Juárez said it best, “The Aztec Calendar is a model of kinship with Creation.”

A cycle specific to human beings is Tonalpohualli, the cycle of human life. This cycle centers around one quantity—260 days. There are two other numbers integral to this count—13 and 20. Thirteen has two functions, one as 13 x 20 = 260, and 260 + 13 = 273.

To understand their role we need to identify and track the 8 points of vital importance to life on Earth: two equinoxes, two solstices, the point at which the Earth is farthest from the Sun (aphelion), the point at which she is closest to the Sun (aphelion), and the two points at which they are equidistant from Tonatiuh (equihelion).

The aphelion happens 13 days after the summer solstice, the perihelion 13 days after the winter solstice, and both equihelions happen 13 days after each equinox.

Using the four celestial occurrences (aphelion, perihelion, equihelions) we arrive at 273.  From aphelion to Spring there are 273 days. The same is true from the Fall equihelion to the summer solstice, from perihelion to Fall equihelion, and from Spring equihelion to winter solstice. What is significant about 273 is that those are the number of days in a human gestation period from conception to birth.

Tradition tells that the human season (first of nine in a human being’s life) is marked by five stages: conception, housing in the womb, housing of the heart, housing of the brain, housing of the tonalli, and birth. Tonalli, the animating force which Sun, nests on the opening atop the skull, the moyera at day 260 of gestation. At that moment the tonalli begins descending into the body (it takes two years to full enter) and integrating with the other animating forces: teyolia, ihiyotl, and atalchinolli. The first step of integration takes 13 days, and we are ready to be born at 273 days.

Tonal Machiotl’s wheel of 20 days functions on a count of 13. In counting the days, after thirteen we return to one. Here the day-glyphs tochtli, tecpatl, calli, and acatl not only serve as one of the twenty days but also as the names of the years (we are entering the year tochtli) and the 13^th day after which each season begins.

The equihelion after Fall corresponds to tochtli. The Afelion correspond to acatl, perihelion to tecpatl, and the equihelion of Spring to calli. As we track the year through Tonal Machiotl we can identify these positions and their parent seasons through the number 13.

On a personal level, the birth of an individual can also be tracked. Thirteen days prior to birth is the housing of the tonalli, the vibration frequency we share with the sun. Tradition tells us that every 260 days our solar frequency begins a re-adjustment in its relationship with the other animating forces and that this adjustment takes 13 days. We undergo a “rebirth” every 273 days.

This is not a mystical concept. We have seen how these numbers correspond to positions of Earth in relation to Sun. Each one of us is a smaller planet, also orbiting the Sun. Our entire being is made up of the unity of Earth and Sun. Current science, the very one we teach our children through their elementary and secondary school years is that this orbit creates accumulative changes that culminate in many pivotal changes of which the Seasons are only one aspect. All this is due to the radiation, gravity, heat, motion, weather, tides, and the space-time continuum.

Our bodies, as they orbit the Sun along with the Earth go through no less changes and adjustments. We too have our individual aphelion, perihelion, and equhelions. We too have our seasons. Tonal Machiotl tracks, records, and calculates those as well as the celestial bodies that make up of significant Creation.

Other Sources to consult (besides all works by Arturo Meza)

Fundamentos astron♀micos del Tonalpohualli David Wood Cano

The Aztec Calendar Handbook Randall C. Jimenez

The 8 Calendars of the Maya Hunbatz Men

The 13 Toltec Constellations: pre- Columbian astronomy Arturo Rodriguez

Los Computos Aztecas y la Geometría David Esparza Hidalgo

www.aztekayolokalli.com Mazatzin

www.xinchtli.com Carlos Aceves (Yolohuitzcalotl)

Lesson 4

Two “new years”

Tonal Machiotl’s geometry is given by Tloque Nauoque, a concept that has its geometric representation as the unity of the circle and square. Thus Tonal Machiotl is a geometric instrument in which its wheels are meant to turn to track motion.

We know that Earth’s orbit is elliptical yet it is represented as a circle in Tonal Machiotl. To understand how let’s return to the geometric figure of the first level of Tloque Naouque—where Tonal Machiotl is conceived out of the sequence of circle and square unified.

At the corner where the first square embraces the circle edge of Tonal Machiotl there is a smaller square that can be formed. That square as you remember is the same size as the square that forms around the central face. It is also the square that makes it possible to compute the circumference (C) of the circle—3 x length of side (s) of larger square + length of side of smaller square or as western math puts it: C = 3.14 if s = 1. Remember that 3.14 is the constant Pi.

Trace a line from the tip of the corner of the smaller square to the center of the face (nose). Then trace another line from the opposite corner to the same center. You will have drawn a “pizza slice” figure going from the small square to the center.

If we replicate this “pizza slice” around the circle of Tonal Machiotl, we will find that there are 18 slices and a smaller fractional space left. This natural division of the circle into 18 slices account for the 18 months of Tonal Machiotl, the fraction accounts for the 5.25 days. Thus, 365.25—the amount of days of one Earth orbit of the Sun.

If you draw a circle around the smaller square to form a smaller Tloque Nauoque geometric figure, you will see that they are like two gear wheels. As the larger wheel turns, so does the small wheel. One turn of the large wheel places the small wheel at the next corner with an extra ¼ turn.

Right below it, marked by the smaller Sun ray is the glyph for the year. Their sequence is tecpatl, calli, tochtli, and acatl. In other words, the rotational relationship between the Tonal Machiotl wheel and the smaller Tloque Nauoque wheel natural tracks the passing of days into the next year. The extra ¼ rotation indicates what time of day that year begins: tochtli (sunrise), acatl (sunset), tecpatl (midnight), and calli (noon).

The mathematics of Earth’s orbit is 18 segments multiplied by 20 day glyphs equals 360 plus the fractional segment of 5.25 giving us a total of 365.25. The fractional segment are the Nemontemi days.

Two Yancuic Xihuitl

Returning to the geometric divisions of Tonal Machiotl within Tloque Nauoque that show the tropics and equator, we realize that the equator line divides the 20 day glyphy wheel in half—ten days above the equator and ten days below.

As the sun rises over the equator, Tonal Machiotl marks this time by geometrically placing tens days on each side of the equator. One complete turn of the day glyph wheel tracks the Sun returning from the southern (Condor) side of Abya Yala into the northern (Eagle) side. As we are in the Eagle side, there are literally “two new years” or yancuic xihuitl. The first is ten days before the Sun reaches the equator, the second is ten days later at the Spring Equinox at the point of crossing over. In other words, March 11 and March 20.

What is important about this is that the basis for the date of the Aztec New is not the count left by the Catholic friars, but Creation’s date upon when She places the Sun over the midline of Earth. At whatever day and time the Spring Equinox occurs, ten days before is the Aztec New Year.

Lesson 3

Eight are the birds, therein is the answer to an age old question—are the Evening and Morning Stars one? If we stay in one place and follow the Sun from sunrise to sunset, our left hand is the Evening Star, our right hand the Morning Star. Just as we disappear in our dreams, so does the Evening Star vanish only reappear as the Morning Star. Each one of our hands is a bird with a four-feathered tail. As they come together at the center of our heart, they become one with four feathers on each wing.

Written above is a loose retelling of Tradition, part of the numerology the late maestro Domingo Martinez Paredes used to explain Mayan cosmogony. The Nahuatlaca and Maya were the “twins” on the continent consciously working to create a society where humans could expressed their highest creativity without destroy the greatest beauty given us, Creation. Hence, it is an accepted fact the Tonal Machiotl and the Mayan Calendar are the same Wheel of Creation.

Answering the question of the first and last “stars” of the night sky was crucial because as we know now the cycles of Venus are key in the tracking of astronomical cycles in Tonal Machiotl. Since Venus disappears after rising at dusk, the ancients asked a rather simple but scientific question to find the answer.

Tezcatlipoca, Xolotl, and Quetzalcoatl

Is there an astronomical phenomenon that is unique but common to Morning and Evening Stars?

Observation demonstrated that there is. Every eight years (April 3 o 4 by the Gregorian Calendar) a star cluster called the Pleiades (known commonly as the seven sisters) align with Venus. The seven star cluster looks like the proverbial question sign and Venus as the large “dot”.

The answer is recorded in four ways on Tonal Machiotl.

If you take the square (or circle) formed by the central face and bring it down you will find that the square fits snuggly around the faces of Tezcatlipoca (to the left) and Quetzalcoatl (to the right).  The message is clear: the two faces are actually one. The Evening and Morning Stars are One. On this part of Tonal Machiotl, Tezcatlipoca represents the Evening Star while Quetzalcoatl the Morning Star. Xolotl is Venus when she disappears and becomes the nahual (reflection) of Quetzalcoatl. It is from Xolotl that the Morning Star reappears.

Another way that this unity is marked is by looking at the “eyes” that surround the “horns” of the Twins. Each have seven. These eyes are the seven main stars of the Pleiades aligning with Venus as one planet, though manifested as two stars.

Tracking this celestial cycle is done through the “solar rays” of Tonal Machiotl. There are eight, representing each a year of this cycle.

Finally there is the “wheel of Venus”, the one that has a series of square glyphs with five dots, four on the corners and one in the center.  It lies just above the twenty-day ring.

The five dots on each glyph represents the five patterns of Venus in the sky. The 8 arrows is their repetition (5 patterns that repeat every eight years—8 feathers on the wings, five fingers of the hand that forms each bird).

This Venus wheel turns 13 times to every 8 turns of the solar rays-wheel because the seven Pleiades align with Venus every 13 orbits of that planet, which equates to 8 orbits of Earth. This synchronicity appears to happen on the 240^th day of the orbit of Venus. Thus Tonal Machiotl shows 40 Venus glyphs time 5 dots is 200. Then we add the number of “dots” on the eight Venus markers just above the ring of corn which gives us 40.

Attached is a photograph of the alignment that answers the question—are the Morning and Evening Stars one?

Naui-Macuilli: Lesson two

Four are the people, five is the world. We reproduce through a pattern of four: mother-father/daughter-son. With the five fingers of our hand we create our world out of Earth using the special relationship of four fingers and one thumb. Unlike our relatives we can create our world in numerous ways, is our gift and our curse. That is why the ancients taught “live with purpose to reconstruct through numbers.”

In our first lesson we learned that the center face of Tonal Machiotl has a square, created using the “helmet” line above the eyes. This square is equal to the first smaller square created at the first transition of a 13 step sequence of Tloque Nauoque (circle to square). This gave us the first clue of the fractal geometry operating—remember we discovered the unity of the two constants, Pi and Phi (something extremely difficult to do in western matematics). Now we can continue another fractal geometric sequence that allows for further recording/calculating of cycles.

1. Create pentagon using the base of the square as one of the five sides.

2. Extend each side of the pentagon to create a five pointed star.

3. Using the points of the star create a second (larger) pentagon.

4. Extend each side of this pentagon to create another star.

5. Use the points to create a third pentagon.

If you have done this correctly you will find that Tonal Machiotl is inside the third pentagon. In mathematics this pattern is called a “fractal nest.” Our fractal nest has three levels, but it can be extended towards infinity outward and infinite, the unity of the outer and inner space. This is the pattern nature follows when creating any form.

The beginning sequence (at the face) allows Tonal Machiotl to mirror the relationship of fingers (4) and thumb (5), which is also one (4 + 1 = 5). Geometrically it also reflects what western math calls the Pythagorean Theorem—a2 = b2 + c2 (each side is squared—multiplied by itself). The multiplication of the two quantities 4 x 5 = 20, which is one reason why Tonal Machiotl uses a twenty day count. This is also expessed in the human body, four limbs x five digits = 20. In the fourth lesson we will see how this geometry allows for the recording/calculating the relationship of the human gestation cycle (273 days) to the orbit of Earth (365.25 days), which we know as Tonalpohualli.

As you can observe, the second pentagon lies within the circle of the 20 day glyph. This allows us to tract two important cycles of Venus, which is one of the celestial bodies that Tonal Machiotl also uses to track other cycles. One of the cycles of Venus is that she follows five patterns in the sky of 584 days (represented by the 5 sides of the pentagon) that repeat every 8 years.

The other cycle of Venus is that of her transits across the Sun. That is when the planet appears to cross the diameter of the Sun. These transits repeat themselves in pairs—that is, when a transit happens it will happen again in another 8 years. In 2004 there was a transit of Venus to be followed by another in 2012. Then they won’t happen for a number of years.

Tracking of these paired transits are done through the two rectangular bars that separate each day-glyph. Twenty repetitions of the transit pairs take approximately 26,000 years. Besides the midpoint cycle of the tropics shift (Cancer and Capricorn), this is another cycle that come together on our famed “doomsday” 2012.

Now we go to the third pentagon that embraces Tonal Machiotl. Here there are three cycles that come together. Each line of this pentagon represents the changing of the North Star. There are five stars in the galaxy that “take turns” becoming the North Star—it takes approximately 26,000 years for all five stars to be the North Star.

Another cycle is that of the Sun aligning with the dark area just above the center line of the Milky Way (galaxy). The ancients referred to this spot as the Universal Womb, which the Sun returns to every 5,125 years. Currently the Sun is at the center line and moving into the “womb”. On December 21, 2012 will begin this alignment. Five of those alignments is approximately 26,000 years.

Finally there is the teoxihuitl, the Year of Creation. Because Earth does not spin perfectly, but wobbles on its spin, there is a shift from facing one point in the galaxy then very slowly (from out viewpoint) “wobbling” around the galaxy and return to that same point in approximately 26,000 years. The Nahuatlaca and Maya were not the only ones aware of this “Great Year”—the largest cycle of the celestial cycles tracked by Tonal Machiotl. The Babylonians and Egyptians also recorded it in their calendars.

Of course, an extraordinary aspect of Tonal Machiotl is that these cycles, from the Tonalpohualli, the 5 pattern cycles of Venus, to the three cycles in the Teoxihuitl—are calculating in concordance with each other. Through this Wheel of Creation we are able to know and understand our “position” with our galactic Universe.

Tomorrow’s lesson: Eight are the birds.

Lesson 1

Llegó a suceder que la niña Cipactonal nació espíritu de Tlalcihuatl y Oxomoco espirítu de Tlaltecutli. Así desde temprana vida los dedicaron a aprender todo lo que ofrece la tierra y muestra el cielo. Al crecer los casaron y siguieron trabajaron hasta la edad de 104 años. Entonces plasmaron en papel lo que hoy llamamas Tonal Machiotl y Tonalpohualli.

Tloque Nauoque

Depending on which “cuenta” or version you follow, today is a cozcacuauhtli day—the condor, twin of the eagle.  The condor is the bird of the south and the eagle of the north. The eagle can see far beyond herself. The condor can also see far beyond, but within herself. Besides the pair within the wheel of day-glyphs, these sky spirits are also manifested at the “bottom” of the Tonal Machiotl as Tezcatlipoca (looks within) and Quezalcoatl (looks beyond), the unity of night and day, the inward with the outward.

Calling the Tonal Machiotl the Aztec Calendar is a limiting term. Tonal Machiotl literally translated means “solar memory” or “the Way of Knowing the Sun.” Tonal is also one of the four animating forces of the human body besides teyolia I(heart spirit), Ihiyotl (passions housed in the liver), and atlachinolli (water that flows like fire from the bladder). The tonal is that part of us which is pure sun, from tonalli, solar vibration. It begins as a little sun above our heads at day 260 of our fetal development and begins entering the body, completing this entrance around age two. That is why the “moyera” seals at that age.

The Tonal Machiotl contains within it the Tonalpohualli, the count which links the cycles of the human body with key celestial and natural cycles such as the seasons and the orbit of the Earth.  A better “translation” for Tonal Machiotl might be “Wheel of Creation”, or what northern natives call The Medicine Wheel.

Observing through Wheel of Creation

How is it possible that a seemingly simple wheel can be used to  track and record celestial, natural, and human body cycles?

Oral Tradition (“la tradición”) tells us that Tloque Nauoque or Hunab K’u is “the giver of all measurement and motion.” This giver is represented through a geometric symbol, a circle and square intersecting at four points, either at the corners of the  or the midpoint of the sides of the square . The circle and square repeat themselves extending both outward and inward. This represents the square being transformed into a circle and then the circle into a square.

We can deduce that in using the geometry of Tloque Naouque a level is a transformation from circle to square and vice-versa. The circle symbolizes motion, the square is formation. We can see this manifested in the movement of the human hand—as we squeeze to form something we create a square. As we extend to squeeze again, we form a circle. We gyrate to compress. Similarly the human head gyrates to explore but we quantify our observations through a “square”—front, side to side, and back.

Tonal Machiotl is a product of Tloque Nauoque, the unity of circle and square. As a first lesson I invite you to graphically place the Aztec Calendar within the sequence of Tloque Nauoque. Please follow these steps.

1. Since the Wheel will be a product, not just a level of this geometry, trace a square over the Aztec Calendar, with the edge of the calendar touch the four midpoints of the sides of the square.

2. Draw (or use a compass) a circle around the square you formed, with the circle touching the corners. Now you have the Tonal Machiotl with Tloque Nauoque and as a product of that “which forms by its gyration.”

3. Tradición tells us that the sky has 13 levels, hence we need to create 13 levels here as well. Create a square using the  the Tonal Machiotl as a circle.

4. You can assume that a circle forms inside that square or actually create it, then simply form another square.

5. You will discover that a combination of 6 squares and 7 circles (13 levels) will get you to the face at the center.

This is the geometry that allows us to calculate and record a variety of Creation’s movements.  Tradición tells us that the equator and the two tropics is recorded in the Tonal Machiotl through the nose (equator) and lines connecting the smaller sun arrows just above the glyphs of tecpatl and calli (tropic of canser) and tochtli and acatl (tropic of capricorn). It is the Earth and Sun’s dance along these perimeters that create the weather and mark the 365.25 days Earth orbit.

How does the Tloque Nauoque geometry allow that?

–Trace the equator line from one end of the outer circle to its other end with a different color pen.

–Trace the tropics line the same way, from one end of the outer circle to the other.

–With a different color pen, trace a line from the center point (nose) to where the tropic of Capricorn line meets the outer circle.

–With the same pen, trace a line from the center point (nose) to where the tropic of Cancer line meets the outer circle.

You will notice that these new lines go through the two three ring circles on opposite sides of the jaguar/eagle claw glyph.

What you have now is a proportional model of the Earth (as if looking at it from outer space as a circle) so that if you were standing at the equator on the center point (nose), that would give you the same angles of latitude between the sunrise at summer on the tropic of Cancer and the sunrise of our winter at the tropic of Capricorn. The three ringed circles are designed that way to accommodate the recording of the tropics shifting. They shrink then expand then shrink—on a cycle of approximately 26,000 years! This one of several cycles linked to the much talked about “2012 doomsday”.

Verification of the Tloque Nauoque sequence

A key verification of the 13 cycle sequence (from outer circle to interior face) is found by doing a simple geometric exercise.

1. Where the first square meets the circle created by the edge of Tonal Machiotl, create a smaller square within one of the corners. This can be done accurately by dividing the first square from corner to corner into four parts. Marking a point where that line intersects the Tonal Machiotl circle and use these points to create the small square that will be house within the corner of the first square and the edge of the Tonal Machiotl.

2. This smaller square does two things. First, it is the same size as the square that can be naturally formed on the human face at the center (all human faces naturally form a square). So, 13 levels give us two squares of equal size—one at the first (outer) transformation and the other at the last (inward) transformation.

3. Also, adding three sides of the first (outer) square and one side of the smaller square will gives the circumference of the Tonal Machiotl. That is called a Pi constant.  But that is not all…!

4. The perimeter of the smaller square is also equal to the circumference of the circle that naturally forms around all human faces. That is called a Phi constant.

All human faces have a natural relationship in which the face forms a square using the chin as the base. Then using the chin and the nose, it forms a circle—and the circumference of that circle is then equal to the perimeter (addition of the four sides) of that square. This is the beginning of what mathematicians in the 20^th century coined as “fractal geometry.”

A geometric sequence that unites the constants Pi and Phi is not a trivial but quite a complex mathematical accomplishments. As you have seen, this sequence has formed a proportional map of the Earth that allows the tracking and recording of an important climatic cycle, the shifting of the tropics.