Maya Vigesimal Place Numeration System & the Invention of Zero
At the core of all advancements in the sciences are numbers and methodology. While, the invention of systems to handle numbers is taken for granted by most people. In the early periods of human civilization, having the means to place symbolic representations for numeric values was a dilemma needing to be solved. So too, as the need to calculate and record longer numbers becomes evident, so too does the necessity for having an ability to handle numbers of increasing value in an efficient way. The system that we use today for counting numbers is scientifically called place numeration. It utilizes two significant leaps of mental achievement in the advancement of humanity. The first was a development of the concept of zero. That is, the symbolic representation for an identity of null to be used in the expression of mathematics. The second is an actual usage of this momumental concept of the zero to act as a space place holder for the counting of numbers as we still commonly see done today in our modern decimal (10-based) numeric system. In place numeration, there is a position for units and also subsequently placed multiples of those units (either top to bottom, or right to left, etc.) used to efficiently notate extremely long numbers which also aids in the task of larger calculations. This is especially relevant for advanced mathematics used in astronomy. Unlike our modern decimal based system, which is often said to be corresponding with the counting of numbers on our fingers and hands; the Maya used a vigesimal (20-based) system. This is often compared to the counting of numbers using both the fingers and toes of both our hands and feet. In other words, intead of being a 10-based counting system, their system was twice the speed. Also unlike our modern convention which shows positional increase in value from right to left by a factor of 10 (10's, 100's, 1000's, etc.) with numbers read left to right; in the ancient Maya vigesimal system, numerical positions increase from bottom to top by a factor of 20 (20's, 400's, 8000's, etc.) with numbers being read from top to bottom. Maya numbers were primarily written in a dot bar system with the simple glyph of a shell to show zero. Much more ornate character glyph portraits were also used to represent the zero, base numbers, time periods, and other numbers of special spiritual and cosmological significance.
While, the dot bar system was apparently adopted from the simple math of their predecessors the Olmecs. It was the Maya who added the monumental concept of zero to usher in a much greater understanding of the more advanced mathematics needed for the study of our universe, in addition to their complex overall system of numerology and mass calendrical calculations which would later be used by all of the other cultures in the New World. Yet, this was not just an influence for the New World. Historians initially believed that the first usage of zero and place numeration had occurred in India around the 8th Century then passing to Western civilization via Arabia and then to Moorish Spain. Today, we now know that the concept of zero and place numeration were already being fully used in Mesoamerica for over a thousand years before this. Most modern scholars now acknowledge that it was the Maya were the first people on earth to grasp this essential concept of zero [11, p.22]. This is quite a statement, especially when considering that both the ancient Greeks and Romans, who despite all of their engineering and artistic achievments, had still not conceived of this important concept during their golden ages, thus being confined to usage of mere simple geometry and short calculations of addition and subtraction [27, p.74]. In a similar vein, it is also equally impressive that the Maya, along with the other cultures of the New World, were the last people on earth to arrive at their respective permanent settlements after eons of migration in the primal stage of humanity. In this respect, not only were they the first, but also the fastest in their endogenous (without external influence) conception of this major feat for humanity. This attribute of original conception is also exhibited in many other areas of Mesoamerican culture. Namely, the Mesoamericans developed their own: architecture, art, costumes, customs, dance, economy, educational system, horticulture, language, medicine, mores, music, religion, socio-political hierarchies, trade associations, traditions, and writing, etc. berift of any influence from the Old World. So too, within all these areas of advanced society, the Maya added their own flair.
End of the Maya Calendar's 13th Baktun - The Beginning of a 14th New World Era
On December 21, 2012, the 13th Baktun of the Maya Calendar's Long Count cycle will complete. Whenever people say that the Maya Calendar is coming to an end, that is completely wrong. It is only the end of one Long Count period cycle. One completed cycle of the Maya Long Count Calendar occurs every 13 Baktuns or 1,872,000 days (roughly 5,125 years). This is often referred to as the "Great Cycle" with the current 13th Baktun scheduled to end on the Maya Calendar Round date of 4 Ajaw, 3 Kank'in. While, there is much discussion about the completion of the Maya calendar's 13th Baktun, and the popular media's portrayal of it as a Maya doomsday prophecy; the truth of the matter is, that, there's only one known ancient Maya artifact which references this particular day. This type of statement is wholly the invention of Western scholars, North American (U.S.) specifically, and mass media. The only known Maya artifcat existing that references this date is on what is known as the Tortuguero Monument 6. This artifact has a current tepid speculation purporting that it may have referenced a return of the Mesoamerican cultures' set of nine gods known as the "Lords of the Night". Now, what exactly this ancient Maya mythology entails for our modern human experience only time will tell. Nevertheless, to be sure, the Maya themselves (both past and present) have never predicted a world end on this date. Thus, the superiority of Maya Calendar system along with our planet and it's inhabitants are very likely to still exist well past 12/21/12. An example of how the public needs to think regarding these matters is that the Gregorian Calendar we commonly use today won't end on 12/31/12 either. It too will renew. The Maya just accounted for very long cycles uncommon to us today. Below is a chart breakdown of the cycle periods leading to the end of the Maya Calendar's 13th Baktun cycle and the beginning of it's 14th new era.
A simplified explanation of the Long Count Calendar would be that it is a continuous "non-repeating" linear count utilizing 5 Mesoamerican cycles of time anchored to a starting base date and correlated to reoccur once every 5,125 years. With regard to the Maya Long Count Calendar specifically, the five cycles of time used for the Long Count recording of any date after the base starting point of 3114 BCE were called the: Baktun (144,000 days), Katun (7,200 days), Tun (360 days), Winal (20 days), and Kin (1 day).
Maya Long Count recordings were commonly used by all Mayan kings who ordered that certain dates of historic significance be carved into stone stelae (monuments) for posterity. The Long Count dates were given as a permutation of rows and columns where the Maya numbers are (primarilly) written in a system of dots and bars using the simple glyph of an eye-shaped shell to represent zero and various glyphs for the personification of days. The ancient Maya taught that with each cycle of time, there exists a specific set of unique characteristics. Thus gylphs of facial symbols were also used to denote the Maya pantheon of deities associated with their own attributes and cycles of time, in addition to the component numbers and zero (see above).
To the point: Because there has never been in any form of an ancient Maya artifact found, whether that be a Mayan book, carving, or inscription of any kind, anything to support the assertion that our ancient Maya ancestors believed the world would end in 2012. Many people are specifically asking. So then, where exactly did this current frenzy of discussion about a Mayan doomsday prophecy originate? To be simple; it was from a book originally published in 1966 entitled, "The Maya", written by the then associate professor at Yale University, Michael D. Coe. On page 149 of his original publication (now in its eighth editon), Professor Coe wrote: "There is a suggestion [ from who? ].. that Armageddon would overtake the degenerate peoples of the world and all creation on the final day of the thirteenth [ Baktun ].. Thus ... our present universe be annihilated [on December 21, 2012]" Ever since the publication of this presumed authority's presumptuous statement, starting in the mid 1970s there has been a bevy of various authors who have latched onto these words without caring to do any further independent investigation of the veracity of such a pronouncement on their own. Hence the spread of a reckless and flippant falsity. So much for the superiority of an Ivy league mind.
4 Ajaw, 8 Kumk'u, or August 11, 3114 BCE, is an important date. According to Ernst Förstemann, a German librarian with access to the Dresden Codex, and the majority of Western scholars who have followed his line of thinking ever since, it was the ancient Maya date given for the creation of our universe or world. According to Maya elders and a majority of the Mexican archeologists who remain unaffected by a U.S./Eurocentric perspective, it's the starting point of record for Maya civilization and its calendar cycles. This is a vast difference. It's similar to the major difference of thinking that argues whether Columbus discovered America. Arrogance of attitude and a lack of acknowledgement for the words of our Maya elders and their aids has been and continues to remain a problem on study of the Maya. Below is a listing of some prominent Mexican archeologists (none of whom entertained the silly notion that our world would end on December 21, 2012): Jorge R. Acosta, Marcos E. Becerra, Alfonso Caso y Andrade, Manuel Gamio, Eduardo Matos Moctezuma, Lorenzo Ochoa Salas, Eduardo Pareyón Moreno, Alberto Ruz Lhuillier, and Monica Pellecer Alecio, a Guatemalan archaeologist.
Harvard archeologist, Herbert J. Spinden, wrote the following about the Maya calendar in his book, The Reduction of Mayan Dates (1924).
The invention of the Central American calendar in the Seventh century before Christ may be described with all propriety as one of the most outstanding intellectual achievements in the history of man. This calendar solved with conspicuous success the great problem of measuring and defining time which confronts all civilized nations. Moreover it requird the elaboration of one of the four or five original systems of writing the parts of speech in graphic symbols, and it conjoined with this supplementary invention of hieroglyphs the earliest discovery of the device of figures with place values in the notation of numbers. This time machine of ancient America was distinctly a scientific construction, the product of critical scrutiny of various natural phenomena by master minds among the Mayas. It permitted a school of astronomer-priests to keep accurate records of celestial occurrences over a range of many centuries, with the ultimate reduction of the accumulated data through logical inferences to patterns of truth."