# Abstract Series Num.10-19

 The Aztec Calendar: The Inner Rings ---A Possible Method of Calculation; Science in Ancient Artwork Nš10, New Orleans, 30 March 1995, 17pp. The 260 day-count calendar reflects a 146 year cycle, which forms a reckoning system equivalent to the 104 year-cycle of the 365 day-count, and to the year-cycle of the 584 day-count. Extract: The peoples of ancient Mesoamerica were concerned with counting the cycles of time. To think, however, that the Aztec Calendar's intricacy in design might represent a mere reckoning of the days would appear rather simplistic; too much meets the eye to be reduced to merely counting the number of days in a year. Most interpretations, however, treat the numbers of day represented in the calendar, concluding generally that the Aztec Calendar reflects the 260c and the 365c calendars. In this analysis, we shall consider the logic of the Aztec Calendar's elements, their number and design with respect to the reckoning of the years and cycles, or calendar rounds. We shall not consider only the mexica system, but also the maya system which appears to have had enormous influence then. We shall examine the inner rings, reserving the analysis of the outer ring, the Ring of Serpents for a later essay. Cosmic Time: The 260c Calendar; Science in Ancient Artwork Nš11, New Orleans, 6 April 1995, 10pp. The yearly cycle numbers of the ancient Mesoamerica reckoning system are projected on to an analysis of the inner rings of the Aztec Calendar. Extract: In our examination of the reckoning systems of ancient Mesoamerica, we are attempting to comprehend the way in which the significant cycle numbers may be related. There does appear to exist a particular mathematical logic behind the numbers. One possible relationship may be discerned among the 65-year cycle of the Venus 584 day-count; the 52-year cycle of Earth's 365 day-count; and a 73-year cycle of the ancient 260 day-count. As we have seen in previous studies (Earth/matriX nš8), by comparing the 365c and the 584c, intervals occur at every 260-year period on the Venus table. which coincide with intervals the distinct day-counts coincide in numbers of days, and thereby whole cycles may be counted for the orbits of Earth and Venus. In that previous essay, we suggested that the 260c-calendar may have been derived mathematically from this 260-year interval pattern. The 260c could then have served as a method of calculation for whole cycles between the 365c and the 584c. It was further suggested that this possible mathematical origin to the 260c may have also been related to the Great Sun Cycle of 26,000 years, where by it is also obvious that 260 represents a fractal of 26,000. Let us further examine, then, the nature of the 260 calendar as of the implications of the distinct cycles and their corresponding day-count. Let us explore how the cycle numbers 52, 65 and 73 relate in distinct manners to the 365, 584 and 260 day-counts. Numbers in Ancient Mesoamerica: Duplatio and Mediatio; Science in Ancient Artwork Nš12, New Orleans, 24 April 1995, 16pp. The Dresden Codex numbers (236/90/250/8) represent day/year counts and constant numbers for a method of astronomical computation. Extract: Little is known about the way in which the ancient astronomers achieved their calculations for whole cycles of the orbits of the planetary bodies in the solar system. In this series of essays, we have suggested different methods of calculation regarding examples of ancient artwork in Mesoamerica. One author (Harleston) emphasizes the point that, in fact, the ancient astronomers were not creating art as such, but rather working out cosmic knowledge. In a sense, that is why we have draw attention to the concept of science in this series of essays on ancient artwork. Exactly how they achieved their science seems to have been long lost throughout history. Let us attempt to reconstruct a possible insight into the method of calculation regarding ancient reckoning systems in Mesoamerica. In order develop this, we begin by considering that the numbers themselves reflect a specific design,. The logic of the numbers, of the day-counts, the year-counts, the calendar rounds, and the cycle numbers may reveal the manner in which they were obtained. The Aztec Calendar: The Ring of Flames; Science in Ancient Artwork Nš13, New Orleans, 30 April 1995, 12pp. The Ring of Flames of the Aztec Calendar reflects the day-counts of 365 and 584, and related to the design of the spatial allotment thereof. Extract: This essay treats a possible method of calculation regarding the Ring of Flames of the Aztec Calendar, and the relationship there of with the precession of the equinoxes. The 52-year cycle of the 365 day-count reckoning system is analyzed with respect to the spatial division of the design of the Aztec Calendar. The relationship of the 365c reckoning system and the Sun's Great Cycle (ca. 26000 years) is shown to be the result of design, and not a mere coincidence of numbers. A discussion and interpretation of the day-glyph numbers 13, acatl, examine its possible relation to the precession of the equinoxes. The Aztec Calendar: The Ring of Serpents; Earth/matriX, Science in Ancient Artwork Nš14, New Orleans, 14 May 1995, 12pp. The concept of the underworld, mictlan, is discussed regarding the Aztec Calendar and the day-count for Earth and Venus. Extract: The space allotment and the placement of specific elements within the Aztec Calendar are not apparently due to mere artistic expression. Rather, they reflect science, knowledge within astronomy, mathematics, and geometry; as well as creative art. The complexity of design and the depth of knowledge become quite apparent in the Ring of serpents (xiuhcoatls). The outermost ring of the Aztec Calendar etched upon its face, the Ring of Serpents, reflects the same method of employing symbols and apparently constant numbered elements. As we have analyzed in previous essays, each concentric ring entails a specific amount of constant elements to which particular valences may be assigned. The Legend of the Four Suns; Science in Ancient Artwork Nš15, New Orleans, 21 May 1995, 10pp. The legend of the "Four Suns" is discussed in terms of the 52c cycle and the Dresden codex numbers. Extract: The legend of the four suns, followed by the fifth sun, is most undoubtedly a reflection of ancient belief, and possibly founded in history. To what extent, however, do the numbers of the versions of the codices and tradition reflect a faithful representation of the original legend may never be known. The 676-pattern is cited in this version as having been annotated in 1558; 37 years after the conquest of Mexico. A side from the obvious relationship of constant numbers (multiples of 4s, 10s etc.), and cycle numbers (52, 65, 73, etc.) in the dates and periods cited for the four suns, might there not be another aspect assigned to these numbers as having specific significance. One could also see these numbers as enshrouding an identification of specific numbers that were significant then, in post-conquest Mexico. The Maya Long Count and the Sidereal Orbit of Venus; Science in Ancient Artwork Nš16, New Orleans, May 1995, 11pp. The maya Long Count is shown to be a function of the sidereal orbit of Venus. Extract: This essay forms part of a series in which I attempt to discern how the computations of whole cycles within the different reckoning systems of ancient Mesoamerica may have been effected. The historically significant day-counts and their corresponding cycle numbers, of the maya and mexica cultures, reveal an apparent logic of numbers grounded upon the relation of the synodic orbit of Venus and the solar year of Earth. To date many astronomers belive that the ancient maya people did not even conceive of the Universe as planetary bodies that orbited one another. The fact that calculations were based upon the apparent orbit of Venus, its synodic orbit, would seem to prove such an idea. For the synodic orbit is the time reckoned from the perspective of the observer on Earth watching Venus move in the sky. However, if the maya long count system, based on the 360 day-count would reflect the sidereal orbit, then that might suggest that the ancient maya, in fact, knew of the sidereal orbit of Venus. Such a recognition on the part of the maya would further suggest that they understood the nature of the solar system, and calculated the actual physical orbiting of the Sun by Venus; a feat which is not restricted to the perspective upon Earth. Human reasoning and analysis could have led them to design such a system of reckoning. In this essay, I attempt to demonstrate the manner in which the maya long count (360c) relates to the sidereal orbit of Venus, if considered to represent 225 days. The relation 225:360 is mathematically the same as that of 365:584. In other words, both the sidereal and synodic orbits of Venus relate to Earth's approximate solar year by a ratio of .625 exactly. If this were the case, then their having designed a system based on the 360 day/count was surely and precisely by design; not in error. The maya knew that the Earth's solar year was 365 days/years; that is why they chose the figure 360 for the sidereal count of Venus computations. The Reckoning Systems of Ancient Mesoamerica: The Synodic and the Sidereal Orbits of Venus; Science in Ancient Artwork Nš17, New Orleans, May 1995, 14pp. The constant and cycle numbers of the 260 day-counts are discussed. Extract: In this essay, then we shall examine the tables of constant numbers and a possible relationship of the 360 day-count (360c) reckoning system with the synodic (584c) and the sidereal (225c) orbits of the planet Venus. We should emphasize once again, as in previous essays, that the day-counts corresponding to the planet Venus are those used by the ancient astronomers, given the fact that the actual orbit of Venus varies by a couple days each year; where by the average orbital time is cited today as being 583.92 days. The ancient astronomers were evidently interested in calculating whole cycles, the comparison of orbital times among the planetary bodies in the solar system in terms of whole number. Such an intention would immediately reflect the fact that they knew the orbital times occurred in numerical fractions, which they could allow to remain or eliminate in a knowledgeable fashion. The Reckoning Systems of Ancient Mesoamerica: Day-Count and Constant Numbers; Science in Ancient Artwork Nš18, New Orleans, May 1995, 11pp. The day-counts and the constant numbers of the reckoning system of ancient Mesoamerica are analyzed regarding the logic of numbers. Extract: The significant numbers of the reckoning systems of ancient Mesoamerica consist of day/year count numbers, cycle numbers, and constants. These numbers appear to from a logically structured system, which serve as the basic for the different reckoning systems of ancient Mesoamerica. The day/year counts that reflect the orbital times of the planetary bodies are accompanied by cycle counts, which may also represent day/years counts. For example, the 365 day-count (365c) and the 584 day-count (584c) of Earth and Venus respectively, are accompanied by the cycle counts of the 52 and 65, or 104 and 65, again respectively. These cycle-count numbers may also represent day or years themselves in the method of calculation devised by the ancient astronomers. The Method of Calculation of the Reckoning System of Ancient Mesoamerica; Science in Ancient Artwork Nš19, New Orleans, 30 May 1995, 11pp. The method of astronomical computation is explained as orbital times.