(Based on the original German article "Der Schalt-Zyklus des Maya Kalenders" by Karl-Heinz Homann)

The Maya had a precise calendar system based on the tropical year, as well as an outstanding knowledge of lunar phases, solar eclipse cycles and Venus phases & transits*.

* [see also: INTERPRETATION OF THE MEXICA CALENDAR - A variant diagnosis of the Mesoamerican Calendar and the Precession Phenomenon by Marcos Adrián Villaseñor ]

Only an advanced culture would use equinoctial points and the nodes of Moon & Earth (Saros cycle) and Venus & Earth, for instance, to measure time. There is little dispute that the Sumerians were at the origin of civilizations. They were excellent mathematicians and builders, as well as outstanding astronomers. The names for the constellations of the Zodiac originated with the Sumerians, and we find their perfected calendar system later in Egypt, in Central America among the Maya, in South America at Tiahuanaco and even Stonehenge. However, for the purpose of examining its basic mathematical principle, we shall focus for now on the Mayan calendar.

Scholars have unearthed, studied and interpreted as much as they could find, and when there was a lack of evidence or knowledge, Gods and myths served as explanations until only symbols, religious calendars, rituals and places of cult worship remained. While the real significance of the Mayan calendar seems to have been lost, we cannot deny the fact that it employs the same fundamental 4-year leap system, which originated with the Sumerians and still applies to our modern calendar. But in order to achieve greater accuracy over longer time frames, the ancient calendar makers discovered mathematical combinations and devised an ingenious system of leap-days that makes our modern calendar look primitive in comparison.

Calendars are chronological instruments to count days, months and years. However, without a precise knowledge of the fundamental time period, which forms the mathematical basis of the calendar system, the names given to days and groups of days have even less meaning than religious symbols. The basic unit for calculating time is the period it takes for Earth to make a complete revolution around the Sun. This time interval is the so-called solar -, tropical – or equinoctial year, and modern observations have shown that it consists of 365.24219878 mean solar days.

The ancient calendar makers were fully aware of the fact that this year does not consist of 365.25 days or more. Otherwise there would have been no need for them to devise a leap-day system that requires the omission of one day approximately every 128.18 tropical years. In our modern calendar (Gregorian) we adjust for that cycle by omitting one leap day every century that cannot be divided evenly by 400. Hence, 3 leap-days are omitted in a period of 400 years. Since 400 ÷ 3 = 133.33, the leap-day system of the Gregorian calendar is fairly close to the 128.18 year cycle. However, it requires a further correction of one day every 3320 years.

It appears the ancient inventors of the calendar understood that a discrepancy in Earth’s orbital period of just one minute per year would cause a difference of more than 4 days in a period of 6000 years. In fact, modern astronomy tells us that a daily time difference of nearly 10 milliseconds between the mean solar day and the mean sidereal day results in a time difference of more than 20 minutes per orbit!

As we will examine later, the Mayans chose a combination of the number 365, 20 and 13, producing a period of 52 years. Since 2.5 × 52 years = 130 years, the accuracy of their calendar was somewhat greater than our modern calendar. In Stonehenge, the calendar makers decided to use a different combination of numbers (30, 40, 19), resulting in a cycle of 152 years. While this number guarantees the accuracy of the calendar for longer time frames, it had a certain disadvantage, which is probably one reason why Stonehenge is shrouded in mystery. There is another combination of numbers resulting in a direct cycle of 136 years that is even closer to the "magic" 128 year cycle, than any multiples of 52 or fractions of 400 or 152. But that combination has another disadvantage, which the calendar makers of Stonehenge also discovered (and which will be subject of a future article).

History has shown that the Egyptians had lost the ancient knowledge of the true Sothic calendar - the flooding of the Nile occurred for them earlier each year. Later, the descendants of the Romans ignored this additional leap-day every 128 years and during the medieval times (in 1582 AD) they were forced to correct their calendar by 10 days. But before one can devise a reliable and perfect calendar system, one had to observe celestial phenomena for a very long period of time.

Evidently, some "pioneers of the stone-age" were skilled builders, superb mathematicians and superior astronomers. Understanding that life and the universe had a purpose, they did not rely on coincidences. All of their calculations, whether predictions of solar eclipses or the phases of Venus and the Moon, were derived from the tropical year or Earth’s 360° orbit around the Sun. They were aware of the 251-year Venus transit cycle, which still remains obscure to modern astronomers. Mayan cities, Teotihuacan, as well as Dendera and other temples in Egypt, have a 16° to 17° east of true north orientation (general axes of the constructions), representing the star Sirius which plays a central role. The ancient astronomers realized that the motion of our Sun around its dual and around the Zodiac determines the calendar, and thus they did not require a wobbling Earth to accurately calculate celestial mechanical phenomena.

The calendar, which originated with the Sumerian, came from Egypt to Mesoamerica. The Maya inherited it from the Olmec and the Toltec, and is, in effect, a precise chronometer consisting of three different wheels. Considering that a combination of these wheels could form a straightforward "gear mechanism", the biggest wheel has 365 "teeth", the intermediate wheel has 20 and the smallest 13 teeth (see diagrams below)*.

* (Graphic Design courtesy of John N. Harris)

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