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I PASS BY, I WALK and DANCE GUIDED by HARMONIOUS COUNTING Mathematical Theory of the Universe Origin and the Order of the C I PASS BY, I WALK AND DANCE GUIDED BY HARMONIOUS COUNTING Mathematical theory of the Universe origin and the order of the corn account, within the Dance of the Anahuac Nation. Everardo Lara González FOREWORD This work continues the first research initiated in 1987 and published in 1993, under the name Mathematics and Symbolism in the Native dance of Mexico. I consider that, since that year, I was involved in the very first intuition of math within the traditional dance of the Anahuac. This mathematical intuition arose through the teachings generously transmitted by two persons, outstanding in their own specific areas of study: Engineer David Esparza Hidalgo, with regard to the mathematical knowledge of the Nepohualtzintzin, who devoted himself for more than thirty years of his life to the research of the Mesoamerican calculating system, as well as the contribution of the general captain of the Mesoamerican Dance, Ignacio Cortés, founder of the Tenoch group and one of the sponsors of the process for getting away from syncretism within this discipline and who, within his rehearsals of the traditional dance, suggested the presence of numbers within the rhythmic process. Afterwards, Master Cruz Hernández Ibarra, captain of the traditional dance belonging to the Mesa del Santo Niño de Atocha, kindly accepted to give information by means of interviews which were videotaped; in those interviews he teaches us about the symbolisms of certain steps within the different dances. Hernández Ibarra learned directly from Captains Gabriel Osorio and Carmelo Morales, from the zone of Guanajuato. Master Cruz’ trajectory in the traditional dance dates back to 1946 and he considers that nobody is the exclusive owner of knowledge; therefore, this must be spread towards childhood and youth as well. The intuition of the symbolism which is implicit in the dancing steps is completed thanks to the teachings received from Professor Encarnación Martínez who was, respectively, disciple of the illustrious Professor Marcelo Torreblanca. Gabriel Hernández Ramos, captain of dance in the Volcanoes Zone, provides the compilation of the Half Sun and Xochitl dances, 1 With regard to the Dance of the Half Sun, David Mazatl Velázquez refers that this one belongs to the Guanajuato Zone, where he saw it with the dancers belonging to the word of the maximum dance chief of that zone: Natividad Reyna. Brother, Sister, dance and dance without rest, do not let fatigue nor pain exist in your legs, in your heart or your thought; today, more than ever, we do need your harmony. Dance and dance without rest, make your body and your feather whirl turning your energy around touching the four corners of the infinite and the bowels of our Mother Earth. Brother, Sister, dance and dance without rest, teach your people, your children above all, how to love Nature, as well as the Universe and the remembrance of the origin of Creation. Brother, Sister, dance and dance without rest… Everardo Lara González. 2 General Index PROLOGUE.................................................................................................3 REFLEXION...............................................................................................13 The Dance among the Aztekatl…………………………………………..15 The dancing warrior…………………………………………………… 15 INTRODUCTION…………………………………………………… 19 FIRST CHAPTER Mathematical founding of quality………………………………………..23 1.1 Numeric symbols in Mesoamerica……………………………………25 1.2 Metaphoric symbolism of the numbers……………………………….25 1.2.1 Symbolism of the zero…………………………………………..26 1.2.2 Symbolism of the zero within the Dance………………………..27 1.2.3 Symbolism of number two……………………………………….28 1.2.4 Symbolism of number two within the Dance……………………...29 1.2.5 Symbolism of number four……………………………………… 30 1.2.6 Symbolism of number four within the Dance…………………….31 1.2.7 Symbolism of number seven………………………………………32 1.2.8 Symbolism of number sever within the Dance……………………34 1.2.9 Symbolism of number thirteen…………………………………….34 1.2.10 Number 13, as a symbol of expansion and simplicity of harmony..35 1.2.11 Symbolism of number 13 within the Dance………………………38 1.2.12 Symbolism of number twenty…………………………………… 39 1.2.13 Symbolism of number 20 within the Dance………………………41 1.3 Theory of the mathematical metaphor of the nahuatl language about the origin of the Universe…………………………………………….43 1.3.1 Theory of the Big Explosion……………………………………….43 1.3.2 Mathematical metaphor of the nahuatl language…………………..43 1.3.3 Supreme Geometry……………………………………………… 44 1.4. Numeric association…………………………………………........46 1.4.1 Number four association…………………………………………..46 1.4.2 Number seven association…………………………………………46 1.4.3 Number thirteen association……………………………………….46 1.5 Calendars…………………………………………………………...47 1.5.1 Calendar of the human beings’ destinies……………………………47 1.5.2 Astronomic calendars………………………………………………48 1.5.3 Association of number 73…………………………………………..48 1.5.4 Sublime numeric association of number 52………………………..49 1.5.5 Sublime numeric association of number 104………………………50 3 1.6 Numeric association within the Dance……………………………….50 1.6.1 Association between the solar calendar and the sidereal calendar…50 1.6.2 Association between the solar calendar and the calendar of Venus..51 1.6.3 Association of the Great ceremony of the New Fire………………51 1.7 The square root within the Dance…………………………………..53 SECOND CHAPTER 2. Mathematical founding in the education……………………………...55 “Heart and rostrum”, mathematical metaphor in the education………57 2.1 The rostrum in the ceremonies and within the Dance………………...58 2.2 Metals and precious stones within the Dance………………………..61 THIRD CHAPTER The myths in the mathematical origin of the Universe…………………..63 3.1 The magical world of the Anahuac gods…………………………….64 The god looks for his woman…………………………………………64 The Omeyocan, place of duality………………………………………65 The sons of the Divine Couple………………………………………..66 The four sons ask their father for a knack…………………………….67 Quetzalcoatl and Huitzilopochtli, the creators of fire…………………68 Chantico, goddess of the volcanic fire……………………………… 70 The half sun…………………………………………………………..71 The half sun is placed…………………………………………………72 The first man…………………………………………………………..73 Oxomo…………………………………………………………………75 The meeting……………………………………………………………77 Riddles and sorceries…………………………………………………..77 The calendar……………………………………………………………79 3.2. Legend of the suns in the Nahuatl language………………………….82 First Sun. Version of the Chimalpopoca Codex………………………..82 First Sun. Version of the Aztec myths and legends……………………82 This was the end of the first sun, called the Jaguar Sun……………….83 Second Sun. Version of the Chimalpopoca Codex…………………….83 Second Sun. Version of the Aztec myths and legends…………………84 Third Sun. Version of the Chimalpopoca Codex………………………84 Third Sun. Version of the Aztec myths and legends…………………..85 Fourth Sun. Version of the Chimalpopoca Codex…………………….85 Fourth Sun. Version of the Aztec myths and legends…………………88 The true maize…………………………………………………………90 Fifth Sun, version of the Chimalpopoca Codex……………………….91 Fifth Sun……………………………………………………………….92 4 FOURTH CHAPTER The ancestral Dance……………………………………………………97 4.1 Maceualiztli. Dance of the cosmic harmony…………………….102 4.2 Netotiliztli. Dance of the pleasure in private events……………..103 4.3 Calendar in the ancestral dance…………………………………..103 4.3.1 Xiuhpohualli, solar calendar……………………………………103 4.3.2 Tonalpohualli, ritual calendar…………………………………..104 4.3.3 Symbolic relationship between the Tonalpohualli and features of the person……………………………………………105 4.3.4 Deities of the Tonalpohualli…………………………………….108 4.4 Chronicles about the ancestral dance……………………………...108 4.4.1 Fray Bernardino de Sahagún…………………………………….109 4.4.2 Fray Toribio de Benavente or “Motolinía” *…………………..114 Attitude in the Maceualiztli dance………………………………119 Attires…………………………………………………………….119 Calendar………………………………………………………….120 4.4.3 Fray Diego Durán………………………………………………..120 Dance of the Permission…………………………………………121 Flyers’ dance……………………………………………………..121 Divine chants……………………………………………………..122 About the attire: ………………………………………………….122 Mayahuel dance…………………………………………………..122 Special attire………………………………………………………122 4.4.4 Fray José de Acosta……………………………………………….130 Dance and games…………………………………………………131 The order within the Dance: ………………………………….131 In the ceremonial centers the use of luxurious attires was common 131 4.4.5 Father Francisco Javier Clavijero……………………………… 132 The order within the Dance: ……………………………………132 The chants and the music within the Dance: ……………………132 Presence of buffoons: ……………………………………………132 Representations of the Dance: …………………………………...133 5 FIFTH CHAPTER The music………………………………………………………………..134 SIXTH CHAPTER The chanting…………………………………………………………….136 Words used for the chanting…………………………………………….138 SEVENTH CHAPTER Offerings………………………………………………………139 7.1 Offering of fire…………………………………………………….139 7.2 Burning of incense of the earth……………………………………140 7.3 Casting food and libation…………………………………………..140 7.4 General awaked night or vigil……………………………………...140 7.5 Penitential abstinence………………………………………………140 7.6 Swallowing snakes…………………………………………………141 7.7 Making birds fly…………………………………………………….141 7.8 Processions………………………………………………………….141 7.9 Woman like falsetto singing………………………………………..141 7.10 Zigzagging…………………………………………………………141 7.11 Striping…………………………………………………………….142 7.12 How the incense was offered………………………………………142 EIGHTH CHAPTER The attire 8.1 The masculine attire…………………………………………………143 8.2 The feminine attire………………………………………………….147 NINTH CHAPTER The traditional dance since the beginning of the Colonial period……….148
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