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Dot-Count Calendars Could prehistoric people have constructed and maintained a reliable lunar calendar? The answer is a definite yes! Simple lunar calendars could have been made from knotted string, inscribed on any flat surface or incorporated into architectural settings. These calendars, requiring setting only once each year, could have been accurate to one lunar period per 6500 years. With them precise lunar phase predictions can be extended several thousand years into either the past or the future. Whether such calendars ever existed remains a question yet to be answered. A quick review of sun-moon periods will help to furnish an understanding of these calendars. For our purposes a year will be considered as the time period from winter solstice to winter solstice (365.24 days) and a 'moon' as the time period from one full moon to the next (29.53 days). Therefore one year contains 12.37 moons and is the reason we usually observe 13 full moons every third year. It is this 'usually' which makes lunar prediction interesting. If the sun-moon period ratio were twelve and one-third (12.33...) then every three years the moon's phases would repeat and a calendar would be unnecessary, but a tiny fraction of 0.035 moons/year keeps accumulating and leads to one of the complex patterns which the moon follows. Central to the construction of a lunar calendar is the selection of two whole numbers whose ratio approximates the Sun-Moon ratio (see Table 1, column A). A circle is then scribed and its circumference subdivided by the larger of the two numbers. Circles for actual use need not be laid out with extreme precision as they will function as calendars rather than measuring instruments.
Column A is the ratio
A 37-3 calendar once set could run in perpetuity, except that the ratio 37/3 is slightly different from the moon/year ratio which this calendar represents. This difference accumulates and every 9.54 (see table 1, column c) years the calendar is off by one dot. It needs correcting alternate ninth and tenth years. Correction is accomplished by retarding the mark one dot at the beginning of the year to make up for the accumulated fractional difference. A correction will need to be made in 2005. Since a calendar can be checked annually against the heavens resetting would follow naturally from such observances. If for any reason the count happened to be lost it could be regained at the next winter solstice. Once a lunar calendar was set and running smoothly it would be very useful for predicting the phase of the moon at future equinoxes and solstices. The moon reached full about two hours after the moment of winter equinox at the beginning of the year 2000 (winter 1999). At that time all Dot-Count calendars world wide would have the year's first marker set on the zero dot. The occasion of a closer near simultaneous full moon winter solstice won't occur until the end of 2314 when a full moon will precede the solstice by about an hour.
The Dot-Count lunar calendar alluded to at the beginning of this page is the 235-19 model which can be fashioned out of length of string in a couple of hours. Tying 235 knots 1/2 inch apart and then joining the ends will produce a calendar about three feet in diameter. A triple knot can mark the winter solstice and a double knot at the first dot will assure proper orientation. An additional length of string tied to the winter solstice point can be knotted to indicate the starting dot for a given year should the count be lost during forward or backward runs. Every nineteenth knot is tied off with short lengths of string or similar marking devices. The whole calendar fits comfortably into a pocket and prehistoric people could have carried it wherever they traveled. For 2000 start your 235-19 lunar calendar by marking the solstice knot and every nineteenth thereafter. This particular setting will indicate full moons; however, your calendar can be set to coincide with any moon phase. Once set it will remain accurate to one moon for 6500 years. Since you now possess the deluxe model which divides the lunar cycle into nineteen parts your certainty of prediction will (on average) be at worst +/- 0.78 days. As you wouldn't wait 6500 years till your calendar is out of alignment a full nineteen knots, every 342 years (see table 1, column c) you would make careful moon phase observations at the equinox and advance the mark one knot. Or you could leave a note for your offspring to make the correction in 2332. Such a calendar made with tenth-inch beads would make an attractive and practical necklace. Those interested in even greater accuracy will have to construct a 4131-334 system which is nearly three times more exact than the 235-19. It would require about 170 feet of string and remain within one moon for 277,000 years. So, yes, it is possible that ancient peoples could have possessed a lunar calendar which would rival all but our most accurate instruments. If a prehistoric Dot-Count calendar exists in the Western hemisphere it will probably be found in Mesoamerica. As natives of the Southwest, it is our particular interest to find a Dot-Count calendar used by the Anasazi. Kiva A at Pueblo Bonito in Chaco Canyon National Monument has 34 equally spaced niches and other kivas lesser numbers. Some of the petroglyphs in the Three Rivers area of New Mexico look astonishingly like Figure 1, but again the number of dots is too few to serve as a useful lunar calendar. (see both these graphics at the top of the page) Aside from furnishing a design for your own lunar calendar, it is our hope at NavaChing that the foregoing might provide information which could enable someone to identify an operational prehistoric Dot-Count calendar. Recently, precipitation records for the Rio Grande basin (north western New Mexico) have been extended back to 136 B.C. A portion of these records are provided for those who seek Anasazi/precipitation correlations. Time of correction formulas: |
