http://SaturnianCosmology.Org/ mirrored file For complete access to all the files of this collection see http://SaturnianCosmology.org/search.php ========================================================== web hosting domain names photo sharing Project Ahau I endure in order to equalize, Transcending opportunity. I seal the store of death. With the cosmic tone of presence. I am guided by the power of heart. Chilam Balam and Tzacol asking themselves what Java is. They laugh when they understand Java is a program developed without cosmic synergy. Electric Seed Logo | Control | Developers | Logistics | Status | Files | Search | Briefings | INTRODUCTION Welcome to the Project Ahau. The mission of my work is to demonstrate the abilities of Mayan computers and implement the development of neurographics: architectural-oriented graphics created by neurological inputs. Thousands years ago, the Mayas occupied a unique domain called virtual space. In there, they created computer chips associated with pyramids in the real world to remind us of the harmony of the Universe. And then, they left their carcasses . . . so we may face them in cyberspace one more time. Facing the uncertainties of nature and the extension of the mathematical science that the Mayas could have owned, opinions are divided. While some scholars reject "a prori" that the Mayas had something else than a pathetical obsession of counting, one by one, some investigators show the incredible accomplishments that represented the precise determination of astronomical cycles, the exact proportion of architectonic constructions and the imaginative achievements internalized in the discovery of zero, the invention of the numerical positions and the utilization of a vigesimal system. Landa (1) says . . . "Their counting is 5 by 5 until 20 and 20 by 20 until 100, and 100 by 100 until 400, and 400 by 400 until 8,000, and this count was used for the cocoa trading. They have other large counts that are extended ad infinitum counting 8,000 twenty times that are 160,000, and turning to 20, duplicating these 160,000 and after that duplication is made without end, THEY COUNT ON THE GROUND." This afirmation is incongruent with Eligio Ancona (2) who comments ". . . They did not have notions of arithmetic, if we are to believe Landa who assure us that the Mayas did not known other operation that throwing beans on the ground or other flat surface to make their additions and subtractions. But this asertion can be disproved by the ingenious numerical combinations they used in their chronological system . . ." The ancestral use of grains of corn to make their counts seem to be corroborated from diverse sources: Sánchez de Aguilar (3) said that the Mayas "throw their luck with a fistful of corn" and it is very suggestive to read in the Popol Vuh a paragraph where our cosmic grandfathers, Ixpiyacoc and Ixmucané before the formation of the human race, they make an augury based on mysterious calculations using corn grains and tzité. Recinos (4) identifies the tzité as the Erythrina corallodendron - Arbol de Pito, in Guatemala, and "colorín" in Mejico, and states that the fruit is a shell that encapsulates red grains similar to beans which the natives Mayas still use for magical spells. From the examination of the mathematical aspects of Maya culture emerges the need to know how these corn grains and tzité were handled to calculate numerical operations. In further elaboration, not only they symbolized the unity with each grain or simulated bars and dots but they manipulated the grains as tokens or chips to add, subtract, multiply and divide. It was until I had the opportunity to watch a Maya collaborator explain the way the H-Men (shaman) of one of our native groups calculated the distribution of a estate using corn grains and wooden sticks. I recognized the way that took me to the re-discovery of the techniques that undoubtedly were routine for the Mayan mathematicians. The inference that the red grains of tzité were used to represent the number 5 and equivalent to the bar of the Maya numeration was a fact that I was deducted logically. But the missing point was the fact that the H-Men while they placed the tokens on the ground, they placed the tokens in a square matrix of 9 squares (3 x 3), previously traced on the ground. The use of that board (similar to a chessboard) escaped to my attention and to many historians and scholars. The archaeological evidence that has facilitated these board activities have not been discovered or acknowledge as such. However, it will be demonstrated in further sections that the calculations techniques are simple and it only needs a systematized rationale of the order of the numbers for an operator executes the most complex operations without mistakes. Consequently, the stelas and codexes do not have to reflect the sequence of numerical operations because they only perpetuated the final results of these calculations. Curiously, it is not in the Maya area but the Peruvian where it reaches a full confirmation with similar results, if not identical. Before the Spaniard Conquest, these techniques included the utilization of grains with two different colors placed on a board similar to the checker board. Garcilaso de la Vega (5) says of the Incas . . . "From the arithmetic they know and in an admirable manner, the knots represented by threads of diverse colors give a method to count taxes and contributions in the Inca Empire by charge and discharge." Acosta (6) says that in 1590 . . . "to make a difficult calculation for which an operator is required to use a pen and ink, the natives (of Perú) use their grains of corn. They place one here, three in other position and eight somewhere. They move the grains, one here, three there and the fact is they can complete the calculation without one mistake. In reality, they have better methods than us . . ." Guamán Poma de Ayala (7) reiterates a similar finding. He affirmed they counted with boards and registered the calculations in "quipos" made with knotted threads of several colors. His illustration shows a drawing of the Mayor Controller and Treasurer Tauantinsuio Quipoc Curaca Cóndor Chava holding a quipu in his hands and to one side a board is drawn with twenty squares containing small circles, some blacks, some whites. Another evidence is the Maya vocabulary. In the Diccionario de Motul (8) as is in the Pío Pérez (9) and the most modern one of Don Ermilo Solís Alcalá (10) confirm that the Maya language had words for the operations of addition, subtraction, multiplication and division. Addition is BUC-XOC and to add is BUX-XOCIL or CUCH-XOCH; subtraction has varied phonetic forms and depends what is subtracted. To subtract in height is CABALTAL and to reduce is CHICHANCUNAH. Multiplication is DZAAC-XOC and division is HATZIL or HATZ-XOCH. The dice game is named HAXBIL-BUL and is derived from HAXBIL (drill) and BUL (riddle game), however BUUL is also assigned to grains and we already know how the grains were related to fortunetelling and mathematical calculations that the Spaniards called superstitions. The Mayan language, so rich in words, also has suffixes and prefixes highly differentiated that are attached to numerals to count distinct things. Lopez Otero (11) has researched this as explained in this table. Concepts such as "infinite" (BAKLIZ, MAXULUNTE); "cero" (MIXBAAL, ICH); "remnant" (U YALA); "equality" (CETIL), "identity" (LEILIL); "fraction" (XETT); and many others with a semantic vinculation with mathematics have survived in our times. This section opens an avenue to rediscover new concepts that can be applied currently. From different cultures, from Chinese abacus to Keltic numerical inscriptions, all have basic elements of a archaic system of arithmetic that could be explained by convergence and linked to an impressive list of parallel cultural features, sometimes identical in conventional details, reinforce the theory of diffusionism notably. In other words, all of the Maya elements that have been compared with equivalents in the Old World could have been originated in America thousands of years before they appeared in Europe and Asia and that their diffusion was more widespread that originally suspected. In this project, I don't pretend to have complete knowledge. I only expect to demonstrate that the Mayas using grains of two colors or little stones and sticks representing the numbers 1 and 5 and placing them on a board drawn on the ground, it is possible to create the fundamental algorithms of mathematics with a precision and order of magnitudes consonant with the chronological evidence, astronomy, engineering and architecture. The visitor to this Web site can judge for himself if this purpose has been fulfilled. To this point, I have not decided the best way to present it in the Web. Perhaps, a collaboration of the more professional programmers interested in developing a Maya Java computer to further present it to Sun, for example, is the most adequate way to present these novel concepts and then proceed with a copyright notice. Meantime, I will continue elaborating further sections of the Maya's computer concepts. References 1. Landa, Diego de. Relacion de las Cosas de Yucatán. Edición de Pebro Robedo. México. 1938. p. 112. 2. Ancona, Eligio. Historia de Yucatán. Imp. de M. Heredia Argüelles. Yuc. 1878. p. 141. 3. Sánchez de Aguilar, Informe contra Idolurum Cultores. 4. Recinos, Adrian. Popol Vuh. Fondo de Cultura Económica, México. 1949. p. 97. 5. Vega, Inca Garcilaso de La. Comentarios Reales de los Incas. Emecé Editores, S.A., Buenos Aires, 1945. p.119. 6. Acosta. Quotation made by Henry Wassen "The Ancient Peruvian Abacus," Göteborg, 1931. 7.Guamán Poma de Ayala, Felipe. Nueva Economica y Buen Gobierno. Université de París, 1936. p.361. 8. Ciudad Real, Fr. Antonio De. Diccionario de Motul (1578). Edición de Juan Martínez Hernández. Mérida. 1929. 9. Pío Pérez, Juan. Coordinación Alfabetica de las Voces del Idioma Maya. Imp. de la Ermita. Mérida. 1898. 10. Solís Alcalá, Dr. Ermilo, Diccionario Español - Maya. Ed. Yikal Maya Than. Mérida.1949. web hosting ? domain names ? video sharing online games ? photo sharing free blog ? advertising online