## Ancient Timekeepers, Part 4: Calendars

All calendars began with **people recording time by using natural cycles: days, lunar cycles (months), and solar cycles (years). **Ancient peoples have attempted to organize these cycles into calendars to keep track of time and to be able to predict future events of importance to them, such as seasons (e.g. the annual Nile flood in ancient Egypt), eclipses etc. **The main problem was that these natural cycles did not divide evenly.**

Today, the solar **year is 365.242199 days** long (or 365 days 5 hours 48 minutes 46 seconds) and the time between **full moons is 29.530589 days. Therefore in 1 year there are 12.37 moon cycles (365.24 / 29.53 = 12.37).**

The Moon makes a complete orbit around the Earth with respect to the fixed stars about once every** 27.3 days** (**sidereal** period). However, since the Earth is moving in its orbit about the Sun at the same time, it takes slightly longer **for the Moon to show the same phase to Earth, which is about 29.5 days **(its **synodic** period).

*Moon’s Synodic and Sidereal month. Click to enlarge*

**Nature’s Nearly Perfect Calendar**

**The Moon** could be **“Nature’s perfect clock”** if the **solar cycle period **were** exactly divisible by the period of the lunar cycle.**

For example if the solar year were exactly **364 days** (instead of 365.24 ) and lunar cycle exactly **28 days **(instead of 29.53), we would have a “perfect calendar” based on **13 months of 28 days** per month, with each month having 4 weeks of 7 days. Such calendar was proposed as ** “13 Moon Calendar”** (discussed later in this article) with the **365th day** called the “Day Out of Time”.

Another “perfect calendar” would require **solar year to have 360 days and lunar cycle 30 days:**

- The “perfect” Earth would take
**360 days**to complete**360 degree circular solar orbit (1 deg per day).** - The “perfect” Moon would take
**30 days**to complete**360 degree circular orbit around the Earth (12 deg per day).** - In such case, we could have a year based on
**12 months of 30 days**. Each month would have 5 weeks of 6 days each.

We can only wonder if these numbers were true for the Earth in the the early period of the solar system…

### The Solar and Lunar Cycles

Although the “ideal” periods of the solar and lunar cycle are described by **numbers very close to the current values**, **calendars must reflect the correct numbers in order to properly keep track of time and have seasons in sync.**

At present the time for Earth to complete full orbit around the Sun in “Solar Days” is**365.242199 days*** long (365 days 5 hours 48 minutes 46 seconds). Earth orbits the Sun once every 366.242 times it rotates about its own axis in relation to stars but in relation to the sun it turns only 365.242 times to complete its orbit.

*Earth moves 1 degree on its orbit around the sun in 365.242/360 = 1.0145611 solar days (or 366.242/360=1.0173388 sidereal days).

This is over-rotation by 5.242 degree. How far on the orbit the earth travels during one full solar rotation (in one full day)?

360/365.242 = **0.98565 degree** or **59.1389 seconds. **During 1 degree orbital travel, earth rotates (in relation to stars) 1 + 0.0173388 times on its axis (360 + 6.242) degrees.

The time between **full moons is 29.530589 days. **

**So a month measured by the moon doesn’t equal an even number of days**, and **a solar year is not equal to a certain number of moon cycles** (months or “moon”ths).

Before we continue with the calendar basics, it is worth to answer this question: ** What does the orbit of the Moon around the Sun look like?** Most people (almost all mathematicians) tend to believe that it will have loops and look something like the picture below:

The orbit of the moon around the earth is nearly circular and its orbit around the sun also looks like a circle. It is not a perfect circle, but is close to a 13-gon with rounded corners (see the image below — not to scale). It is locally convex in the sense that it has no loops and the curvature never changes sign ( considering the sidereal month of 27.32 days instead of the synodic month of 29.54 days, number of orbits around the earth is 365.25/27.32 = 13.37.)

There are several ways to see this. Since the eccentricities are small, we can assume that the orbits of the Earth around the Sun and the Moon around the Earth are both circles. The radius of the Earth’s orbit is about 400 times the radius of the Moon’s orbit. The Moon makes about 13 revolutions in the course of a year. **The speed of the Earth around the Sun is about 30 times the speed of the Moon around the Earth.** That means that the speed of the Moon around the Sun will vary between about 103% and 97% of the speed of the Earth around the Sun. In particular, the speed of the Moon around the Sun will never be negative, so the Moon will never loop backwards.

*Note: Length of the lunar month can be well approximated by 1447 / 49 (error: 1 day after about 3 millennia)***. 235 lunar months made up almost exactly 19 solar years (period called Metonic Cycle). **

Using modern measurements, 365.2425/29.53059 = 234.997 (well approximated by 235)

Using modern measurements, 365.2425/29.53059 = 234.997 (well approximated by 235)

**.**

In other words, after 235 synodic months the phases of the moon recur on the same days of the year.

In other words, after 235 synodic months the phases of the moon recur on the same days of the year.

*If we coordinate the 13 Moon, 28-day pattern plus the 365th day (Day out of Time) with the 260-day pattern, we arrive at a cycle of 18,980 days, or 52 years, or 73 of the 260-day patterns.*

**The Lunar Month**

The moon repeats its cycle of phases every **29.53 days**, and since it is a mysterious heavenly object, **it is ideal for religious observances.** Religious observances can be **coordinated with the phases of the moon**, and time divided into months (“moonths”), each month beginning when the thin crescent of the new moon is seen in the twilight.

**The month can then be divided into days**, which now are more memorable by being part of the longer cycle, and certain things are done on certain days.

The problem is that **the month is not an integral number of days.** This only worries the orderly mind, which wants some fixed number of days so the future can be precisely planned.** One solution, which is actually used, is to alternate months of 29 and 30 days, which only slowly gets out of register with the moon.**

What happens when we are in the evening of the 30th day of some month, and the new crescent is not seen as it should be? Well, we could start the month anyway, or we could add a day, called an **intercalary day**, hoping to see the crescent the next evening. Both methods have been used, but the latter is the most popular with the precise minds. This day we can make a holiday, or the occasion for an extra gift to the priests, or a day for athletic contests or drinking.

### **The Solar Calendar**

There is another great and very obvious cycle, the year. **The observant notice that the sun moves northward and southward, through the equinoxes and solstices, as the cycle of nature in the temperate latitudes takes place.** **For an agricultural society, this cycle is of practical importance.** Besides, it is also a good impetus for religious observances.

The **year is about 365.24 days long, or 12.37 lunations, unfortunately. The cycles of day, month and year do not mesh evenly.**

One alternative is simply to neglect the year, and base the calendar so that it stays in step with the moon, using an intercalary day now and again. 12 months are arbitrarily defined to be a year. This gives about a 354-day year, which is 11 days short of a real year. In about 33 years, the months would go completely through the seasons. **People who don’t do much agriculture are happy with such a calendar, which is called lunar.**

If you can’t do this, several shifts are possible. First, you can **insert 11 extra days in every year**, and devote them to a general festival or something.** Or, you can insert a whole month every two or three years,** as necessary,** to keep the months in register with the seasons.** King Numa Pompilius’ calendar of 713 BC was of the latter type, with **12 lunar months every year, and extra months thrown in now and then.** It replaced Romulus’s calendar of **10 months and only 303 days which began on 1 March, and gave the ordinal names to the months (September, October, etc.) from the order they had in that calendar. These compromise calendars are termed luni-solar.**

With good astronomy, it is perceived that **the sun makes an annual journey through the stars on the path called the ecliptic.** Of course, the average person can’t see the stars and the sun at the same time, so this takes a degree of scientific sophistication. One can **divide the ecliptic into 12 segments of 30° each, the signs of the Zodiac.** The passage of the sun through each segment is a **zodiacal month.** These months **are not equal in length.** Those of the winter are shorter than average, and those of the summer longer than average. It is possible to design a calendar with, say, 12 months of arbitrary but unvarying lengths that correspond roughly with the sun’s residence in each sign. **The Egyptians logically took 30 days in each month, making 360 days in the year. Such a calendar is solar. The Egyptian year, being a little short, moved through the seasons slowly in a 72-year cycle.** Since the **actual year was of importance** to them–it timed the rise of the Nile–**5 intercalary days were added to get an alternative 365-day year.** This ran through the seasons only once in 1,520 years or so. **Since events were dated not only by these calendars, but also by the heliacal rising of Sirius, the differences allow precise calibration of Egyptian dates**, something not possible anywhere else. **Egyptians had little interest in the moon’s phases, since their religion was tied to the solar year and the Nile.**

### The Metonic Cycle

**Meton of Athens** was a Greek mathematician, astronomer, geometer, and engineer who lived in Athens in the** 5th century BC.** He is best known for calculations involving the eponymous **19-year (6,939.602 days) Metonic cycle** which he introduced **in 432 BC into the lunisolar Attic calendar.** **Meton approximated the cycle to a whole number (6940) of days**, obtained by 125 long months of 30 days and 110 short months of 29 days. In the following century** Greek astronomer Callippus** developed the **Callippic cycle** of four 19-year periods for a 76-year cycle with a **mean year of exactly 365.25 days.**

Ironically, whereas the **Metonic cycle overestimates the length of a solar year by 5 minutes**, the Callippic cycle underestimates the length of a solar year by 11 minutes, and therefore produces results that are less accurate than those produced using the Metonic cycle.

The world’s oldest known astronomical calculator, the Antikythera Mechanism (2nd century BC), performs calculations based on both the Metonic, and Callipic calendar cycles, with separate dials for each.

It seems that **Meton** was not aware of precession and **did not make a distinction between sidereal years** (currently: **365.256363** days) and **tropical years** (currently: **365.242190** days).

**Most calendars, like our Gregorian calendar, follow the seasons and are based on the tropical year. 19 tropical years are shorter than 235 synodic months by about 2 hours.** The **Metonic cycle’s error** is then **one full day every 219 years**, or 12.4 parts per million.

**19 tropical years = 6939.602 days**- 235 synodic months (lunar phases) = 6939.688 days (Metonic period by definition)
- 254 sidereal months (lunar orbits) = 6939.702 days (19+235=254)
- 255 draconic months (lunar nodes) = 6939.1161 days

Note that the 19-year cycle is also close (to somewhat more than half a day) to **255 draconic months, so it is also an eclipse cycle, which lasts only for about 4 or 5 recurrences of eclipses.** The Octon is a 1/5 of a Metonic cycle (47 synodic months, 3.8 years), and it recurs about 20 to 25 cycles.

This cycle appears to be a coincidence (although only a moderate one). The periods of the Moon’s orbit around the Earth and the Earth’s orbit around the Sun are believed to be independent, and have no known physical resonance. An example of a non-coincidental cycle is the orbit of Mercury, with its 3:2 spin-orbit resonance.

**A lunar year of 12 synodic months is about 354 days on average, 11 days short of the 365-day solar year. Therefore, in a lunisolar calendar, every 3 years or so there is a difference of more than a full lunar month between the lunar and solar years**, and an extra (embolismic) month should be inserted (intercalation). The Athenians appear initially not to have had a regular means of intercalating a 13th month; instead, the question of when to add a month was decided by an official. **Meton’s discovery made it possible to propose a regular intercalation scheme.** **The Babylonians appear to have introduced this scheme well before Meton, about 500 BC.**

The Metonic cycle is related to two less accurate sub-cycles:

**8 years = 99 lunations (an Octaeteris)**to within 1.5 days, i.e. an error of one day in 5 years; and**11 years ( i.e. 19 less 8 ) = 136 lunations**within 1.5 days, i.e. an error of one day in 7.3 years.

By combining appropriate numbers of 11-year and 19-year periods, it is possible to generate ever more accurate cycles. For example simple arithmetic shows that:

**687 tropical years**= 250921.39 days**8497 lunations**= 250921.41 days

giving an error of only about **half an hour in 687 years (2.5 seconds a year)**, although this is subject to secular variation in the length of the tropical year and the lunation.

**Calendars**

**A calendar is a system of organizing time.** It is used for social, religious, commercial, or administrative purposes. **Timekeeping is done by giving names** to **periods of time, **typically** days, weeks, months, and years.** **Periods in a calendar** (such as years and months) are **synchronized with the cycle of the sun or the moon **(ancient astronomers also used planet Venus and/or star Sirius) .

The astronomical day had begun at noon ever since Ptolemy chose to begin the days in his astronomical periods at noon. He chose noon because the **transit of the Sun across the observer’s meridian occurs at the same apparent time every day of the year, unlike sunrise or sunset,** which vary by several hours. Midnight was not even considered because it could not be accurately determined using water clocks. Nevertheless, he double-dated most nighttime observations with both **Egyptian days beginning at sunrise and Babylonian days beginning at sunset.**

**Julian Day**

Probably most fundamental calendar is a count of days. A calendar that is a **pure count of days is the Julian Day**.

The Julian day number is based on the **Julian Period proposed by Joseph Scaliger in 1583**, at the time of the Gregorian calendar reform, but** it is the multiple of three calendar cycles used with the Julian calendar:** 15 (indiction cycle) × 19 (Metonic cycle) × 28 (Solar cycle) = **7980 years**

Day 1 was **January 1, 4713 BC Greenwich noon**, and we are now up in the millions, but this count is reliable, and the best way to find the time between two events. The Julian Day is divided decimally, and begins at noon at Greenwich. It is the least confusing way to identify a particular day. Julian day is used in the Julian date (JD) system of time measurement for scientific use by the astronomy community, presenting the interval of time in days and fractions of a day. For example, the decimal parts of a Julian date: 0.1 = 2.4 hours or 144 minutes or 8640 seconds, 0.01 = 0.24 hours or 14.4 minutes or 864 seconds, and so on…

**The Julian Calendar**

The **Julian calendar began in 45 BC** (709 AUC) as a reform of the Roman calendar by Julius Caesar. It was chosen after consultation with the astronomer Sosigenes of Alexandria and was probably designed to approximate the tropical year (known at least since Hipparchus).

**The Julian calendar has a regular year of 365 days divided into 12 months with a leap day added to February every four years. The Julian year is, therefore, on average 365.25 days long.** The motivation for most calendars is to **fix the number of days between return of the cycle of seasons (from Spring equinox to the next Spring equinox, for example), so that the calendar could be used as an aid to planting and other season-related activities. The cycle of seasons (tropical year) had been known since ancient times to be about 365 and 1/4 days long.**

**The Gregorian Calendar**

The more modern Gregorian calendar eventually **superseded the Julian calendar: the reason is that a tropical year (or solar year) is actually about 11 minutes shorter than 365.25 days. **These extra 11 minutes per year in the Julian calendar caused it to** gain about three days every four centuries, when compared to the observed equinox times and the seasons. In the Gregorian calendar system, first proposed in the 16th century, this problem was dealt with by dropping some calendar days, in order to re-align the calendar and the equinox times. Subsequently, the Gregorian calendar drops three leap year days across every four centuries.**

**Did you know?**

**The months named September through December, which literally mean 7-10, are actually months 9-12**

The 12 month calendar which currently serves as the world standard of time is called the Gregorian Calendar, named for Pope Gregory XIIIth who “revised” the previous Julian calendar (named for Julius Caesar). October 5, 1582 was followed by October 16th, 1582, correcting for the Julian calendar which had slipped behind the Spring Equinox by 10 days. Aside from an improved leap year calculation, Pope Gregory’s calendar has no structural differences from Julius Caesar’s calendar.

The Julian calendar, (instituted in 46-45 B.C.) was preceded by the calendar of the Roman Empire, which was originally a calendar of only 10 months. Their year originally started in March (Martius) and the 2 winter months before then were known as “dead time” – they were unnamed. On the original Roman count, September (which literally means 7) was the 7th month, October (which means 8 – like octagon) was the 8th month, November (9) was the ninth, and December (10) was the tenth and last month.

When the Romans eventually named the unnamed months, they became January and February (Januarius and Februarius) however they were at the end of the year. 153 B.C the Romans decided that January 1 would be the beginning of the year, and they did not bother to adjust the rest of the names of the months – hence we are left with these illogical names where the 12th month of our year is named for the 10th month, etc. We have been following this calendar from the Roman Empire for almost 2200 years!

As for the rest of the names of the months: January is derived from the God of the doorway; February is an obscure word referring to a divinatory rite using animal entrails; Mars refers to the planet and god of war; April and May refer to goddesses of the spring; June to the wife of Jupiter. July is named after Julius Caesar and August is named after his nephew Augustus Caesar.

The word “calendar” itself is derived from a the Latin word calendarium meaning “account book,” the first day of every Roman month being “calends” or the date of payment of debts. This confirms the depths of the societal programming that “time is money.”

**13 Moon Calendar**

*A Culture of Peace through a Calendar of Peace*

The 13 Moon Natural Time Calendar is based upon Dreamspell – a universal application of the mathematics and cosmology of the Classic Mayan Calendar and Prophecy of 2012 as deciphered and presented by Jose and Lloydine Arguelles.

Around the world, people of diverse beliefs and cultures are unifying with the 13 moon calendar as a global harmonic standard – thirteen moons of 28 days, with one day to celebrate “Peace Through Culture” before each new year (July 26).

**Introduction to the 13 Moon Calendar:**

The Thirteen Moon/28 day calendar is a perpetual, harmonic calendar. It is called a Moon Calendar because it is based on the female 28-day (average) menstruation cycle, which is also the average lunar cycle. The measure of the moon from new moon to new moon is called the synodic cycle and is 29.5 days in length.

However, the sidereal lunar cycle which measures the moon from where it reappears in the same place in the sky is only 27.1 days in length. So 28 days is the average lunar cycle.

In actuality the moon goes around the Earth thirteen times a year. This means that the 13 Moon calendar is a genuine solar-lunar calendar which measures the Earth’s orbit around the sun by the lunar average of 28 days.

**Thirteen perfect months of 28 days = 52 perfect weeks of 7 days = 364 days.**

The 365th day is called the “Day Out of Time” because it is no day of the week or month at all. This day which falls on the Gregorian correlate date of July 25 is a day for forgiveness and for the artistic celebration of life and freedom.

The synchronization, or new year’s date of the 13 Moon calendar is July 26. This corresponds to the rising of the great star Sirius. This makes the 13 Moon Calendar a tool for harmonizing ourselves with the galaxy.

This is not the first time people have used a 13 Moon calendar. The Druids kept a “tree” calendar, a count of 13 moons of 28 days each, plus one day. The Incas, ancient Egyptians, Mayans and the Polynesians all kept a 13 moon/28 day count. The Lakota Indians kept a 13 moon/28 day count based on the “keya”, or turtle, since the turtle has 13 scales on its back.

One of the great advantages of the 13 Moon Calendar is that day/date calculations are amazingly simple. The first day of every Moon is always a 13 Moon Dali. The last day of every Moon is always a 13 Moon Silio. (Note: the old paradigm names of the days in a week are replaced by galactic names which describe seven primary plasmas – electronically charged particles which activate our magnetic field. Thus, each week has the following 7 days: Dali / Friday, Seli / Saturday, Gamma / Sunday, Kali / Monday, Alpha / Tuesday, Limi / Wednesday, Silio / Thursday.)

The Gregorian calendar makes day/date calculations very difficult because the months are of unequal measure so the days and dates of the week vary from month to month and year to year. On the new 13 Moon Calendars, the Gregorian correlate dates are found at the bottom of each 13 Moon date. Find your birthday, every year it will always be on the same day of the same 13 Moon week.

Time is a frequency – the frequency of synchronicity.

The 13 Moon calendar is truly unique because it is synchronized with the Harmonic Module, the universal **13:20** timing frequency. **Originally used by the Maya, the most sophisticated timekeepers ever known, the Harmonic Module consists of 20 icons or solar seals and thirteen galactic tones, 1-13.** The resulting 260 permutations combined with the perfect harmony of the 13 Moon calendar give each day a unique quality. The two cycles – 13 Moons/28 days and the 260-day Harmonic Module perfectly mesh every 52 years! Each year your birthday moves up one tone and ahead five icons. In the center of the Harmonic Module is a black pattern of 52 “galactic activation portals.” See if you can find the sequence of 13 sets of four, counting from the four corners inward. Notice that the numbers of each set of four equals 28. 13 sets x 28 = 364, the number of days in the 13 Moon calendar!

In the 13 Moon calendar the obscurely named Gregorian months are replaced by names which correspond to a fourth-dimensional cosmology of time.

**Perfect Periodicity****For every one time we go around the Sun,the Moon goes around Earth 13 times.**

The year has already been divided by Nature-13 ‘moon’ths of perpetual harmony.

—

### The Intercalary days

The Julian Calendar lengthened some of the months to give a 365-day year without intercalary days, and in addition added an intercalary day every fourth year, now 29 February, to give an average 365.25 day year. The longer months were placed in the summer because the sun’s movement through the stars is slower in these months. A further correction of omitting the extra day on even century years, except every 400 years, keeps the calendar in close synchronization with the seasons. This is the Gregorian Calendar, but the difference from the Julian is piddling. No great scientific insight was necessary to devise this correction. **This calendar, which is now all but universally used for civil purposes,** is a **purely solar calendar.**

The week is a purely arbitrary grouping of days, mainly to give names to the days for convenience. Weeks go on oblivious of any astronomical happenings. The day of the week can be found from the Julian Day by simply dividing by 7. **The Chinese week was five days, named for the five Chinese elements.** The **revolting French had a 10-day week.** The **revolting Russians had a 5-day week** with a month of 6 weeks at first, then a 6-day week with 5 weeks in a month later. **The Mayas and Aztecs used 13-day and 20-day divisions simultaneously.**

It requires some intelligence to work out a system of arranging and naming days to stay in step with the moon and sun, but no more science than simply counting days. Errors will become evident after the passage of a sufficient interval of time. The lazy will merely intercalate days as necessary, the clever will think up formulas for adding the extra days in advance. No extra precision of measurement is necessary.

**Because a calendar system counts years or days from some early date does not mean that the calendar existed at that date.** Any calendar can be extrapolated backwards to create a proleptic calendar for expressing dates before the calendar actually existed.** The Julian Day starts in 4,713 BC, but no one could have known it at the time, since the Julian Day was not devised until the 17th century.**

*References:* Wikipedia, M. Westrheim, *Calendars of the World*

## Early Calendars

Why do we divide the circle into** 360 degrees?** Why the year is divided into** 12 months?** Why a week has **7 days?**

Considering we use decimal system wouldn’t be easier to divide circle into **10, 100 and 1000 equal parts?**

The answer could be related to the fact that our year has 365 days…**Earth rotates 365 times (366 in relation to stars) **around its axis while completing** 1 full orbit **around the Sun.

Note: This number is very different for other planets of the Solar System, for example **Mercury makes 1.5 rotation per its “year”** (orbit around the sun); for **Venus this number is 0.925** (Venusian sidereal day lasts longer than a *Venusian year*, in addition Venus has retrograde rotation); **Mars rotates 668.5921 times during one orbit about the Sun.**

Interestingly, the average length of a Martian sidereal day is 24h 37m 22.663s (based on SI units), and the length of its solar day (often called a sol) is 88,775.24409 seconds or 24h 39m 35.24409s. The corresponding values for Earth are 23h 56m 04.2s and 24h 00m 00.002s, respectively. This yields a conversion factor of 1.027491 days/sol. Thus **solar day on Mars is only about 2.7% longer than Earth’s solar day.**

**The Babylonians were the first to recognize that astronomical phenomena are periodic** and apply mathematics to their predictions.

**Early people could either try to stay in sync with the moon, perhaps making months alternating combinations of 29 and 30 days, with special rules to re-sync occasionally with a solar year by adding leap months (such as the Jewish or Chinese calendar) or abandon lunar cycles and concentrate on the solar year (such as the Ancient Egyptian calendar of 12 same-sized months).**

**Calendars in Ancient Egypt**

**Calendars in Ancient Egypt**

**The Ancient Egyptians are credited with the first calendar of 12 months, each consisting of 30 days, comprising a year.** They **added 5 days at the end of the year to synchronize** somewhat with the solar year. By making all their months an even 30 days,** they abandoned trying to sync with lunar cycles and concentrated instead on aligning with the solar year.** The Egyptians recognized that this calendar didn’t quite align with a actual year. Since the traditional Egyptian calendar of **365 days fell about one-fourth of a day short of the natural year, the ancients assumed that the helical rising of Sirius would move through the Egyptian calendar in 365 x 4 = 1,460 Julian years (that is, one Sothic peniod).**

**The earliest Egyptian calendar was based on the moon’s cycles, but the lunar calendar failed to predict a critical event in their lives: the annual flooding of the Nile river.** The Egyptians soon noticed that** the first day the “Dog Star,” which we call Sirius, was visible right before sunrise was special.** The Egyptians were probably the first to adopt a mainly solar calendar. This so-called ‘heliacal rising’ always preceded the flood by a few days.

They eventually had a system of **36 stars to mark out the year** and in the end had** three different calendars working concurrently for over 2000 years**: a **stellar calendar** for agriculture, a **solar year** of 365 days (12 months x 30 + 5 extra) and a **quasi-lunar calendar** for festivals. The later Egyptian calendars developed sophisticated Zodiac systems. According to the famed Egyptologist J. H. Breasted,** the earliest date known in the Egyptian calendar corresponds to 4,236 B.C.E. in terms of the Gregorian calendar.**

*Source:* wikipedia and http://www.webexhibits.org/calendars/calendar-ancient.html

**Calendars in Ancient Mesoamerica**

Among their other accomplishments, the** ancient Mayas invented a calendar of remarkable accuracy and complexity.**

The Maya calendar was adopted by the other Mesoamerican nations, such as the Aztecs and the Toltec, which adopted the mechanics of the calendar unaltered but changed the names of the days of the week and the months. The Maya calendar uses **three different dating systems in parallel, the Long Count, the Tzolkin (divine calendar), and the Haab (civil calendar).** Of these, only the Haab has a direct relationship to the length of the year.

The length of the **Tzolkin year was 260 days** and the length of the **Haab year was 365 days.** **The smallest number that can be divided evenly by 260 and 365 is 18,980**, or 365×52; this was known as **the Calendar Round.** If a day is, for example, “4 Ahau 8 Cumku,” the next day falling on “4 Ahau 8 Cumku” would be 18,980 days or about** 52 years later.**

Tzolkin Calendar: 13 x 20 = 260

For 365 and 260 the “least common multiple ( the smallest positive integer that is a multiple of two integers) is 18980 (365×260/5). [ 365 x 1 = 73 x 5 and 260 x 1 = 52 x 5 ].

**The Long Count** is really a mixed **base-20/base-18 representation of a number** (*see Maya numerals below*), representing the number of days since the start of the Mayan era. It is thus akin to the Julian Day Number.

- The basic unit is the kin (day), which is the last component of the Long Count. Going from right to left the remaining components are:

- uinal (1 uinal = 20 kin = 20 days)
**tun (1 tun = 18 uinal = 360 days = approx. 1 year)**- katun (1 katun = 20 tun = 7,200 days = approx. 20 years)
- baktun (1 baktun = 20 katun = 144,000 days = approx. 394 years)

The kin, tun, and katun are numbered from 0 to 19.

The uinal are numbered from 0 to 17.

The baktun are numbered from 1 to 13.

Logically, the first date in the Long Count should be 0.0.0.0.0, but as the baktun (the first component) are numbered from 1 to 13 rather than 0 to 12, this first date is actually written 13.0.0.0.0.

The authorities disagree on what 13.0.0.0.0 corresponds to in our calendar. I have come across three possible equivalences:

- 13.0.0.0.0 = 8 Sep 3114 BC (Julian) = 13 Aug 3114 BC (Gregorian)
- 13.0.0.0.0 = 6 Sep 3114 BC (Julian) = 11 Aug 3114 BC (Gregorian)
- 13.0.0.0.0 = 11 Nov 3374 BC (Julian) = 15 Oct 3374 BC (Gregorian)

Assuming one of the first two equivalences, the** Long Count will again reach 13.0.0.0.0 on 21 or 23 December AD 2012** – a not too distant future. This is not “the end of time” but a beginning of the new Long Count cycle.

**Tzolkin**

The Tzolkin date is a combination of two “week” lengths. While our calendar uses a single week of seven days, the Mayan calendar used two different lengths of week:

- a numbered week of 13 days, in which the days were numbered from 1 to 13
- a named week of 20 days

**Haab – The Civil Calendar**

The Haab was the civil calendar of the Mayas. It consisted of **18 “months” of 20 days each, followed by 5 extra days**, known as Uayeb. **This gives a year length of 365 days.**

In contrast to the Tzolkin dates, the Haab month names changed every 20 days instead of daily.

The days of the month were numbered from 0 to 19. This use of a 0th day of the month in a civil calendar is unique to the Maya system; it is believed that the Mayas discovered the number zero, and the uses to which it could be put, centuries before it was discovered in Europe or Asia.

**Although there were only 365 days in the Haab year, the Mayas were aware that a year is slightly longer than 365 days.**

When the Long Count was put into motion, it was started at 7.13.0.0.0, and 0 Yaxkin corresponded with Midwinter Day, as it did at 13.0.0.0.0 back in 3114 B.C.E. The available evidence indicates that the Mayas estimated that **a 365-day year precessed through all the seasons twice in** 7.13.0.0.0 or** 1,101,600 days.** We can therefore derive a value for the Mayan estimate of the year by dividing 1,101,600 by 365, subtracting 2, and taking that number and dividing 1,101,600 by the result, which gives us an answer of **365.242036 days, which is slightly more accurate than the 365.2425 days of the Gregorian calendar (we use today). **Note: the solar year is** 365.242199 **days long

**.)**

**Aztec Calendar**

The Aztec calendar is the calendar system that was used by the Aztecs as well as other Pre-Columbian peoples of central Mexico. It is one of the Mesoamerican calendars, sharing the basic structure of calendars from throughout ancient Mesoamerica. The calendar consisted of a 365-day calendar cycle called xiuhpohualli (year count) and a 260-day ritual cycle called tonalpohualli (day count). These two cycles together formed a 52-year “century,” sometimes called the “calendar round”. The Aztec Calendar is no less accurate than the Mayan Calendar and conversely.

*The Aztec Calendar, on display at the Museo Nacional de Antropologia in Mexico City, Mexico.*

*Colorized graphic depicting the Aztec Calendar. Click to enlarge.*

*First drawing in the book “Descripción histórica y cronológica de las dos piedras que con ocasión del nuevo empedrado que se está formando en la plaza principal de México, se hallaron en ella el año de 1790″(or “Historical and chronological description of the two stones found during the new paving of the Mexico’s main plaza.” in English ) by Antonio de Leon y Gama (1792). The book describes Aztec calendars and specifically the discovery of the Aztec calendar stone in México. The image depicts an aztec sun calendar.*

*Click to enlarge. Image Source: http://www.azteccalendar.info/*

*One of the best and most accurate graphics showing minute details of the “Sun Stone” (Aztec Calendar). Created by Ken Bakeman. Click to Enlarge.*

Aztec Calendar Links:

- http://www.azteccalendar.info/Wiki/
- http://www.kenbakeman.com/
- Aztec Calendar Handbook

**Chichen Itza Pyramid Calendar**

The Pyramid of Kukulkan at Chichén Itzá, constructed circa 1050 was built during the late Mayan period, when Toltecs from Tula became politically powerful. **The pyramid was used as a calendar:** four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year.

*The ancient Mayan Pyramid at Chichen Itza, Yucatan, Mexico. Copyright World-Mysteries.com*

**Mesoamerican Archaeoastronomy**

** Using the summer solstice to calibrate the secular calendar**

By about 1000 B.C., knowledge of the calendars and the principle of orientation based on solstices had spread into the Olmec metropolitan area and priests had come up with a formula for recording when the zenithal sun was passing overhead at Izapa!

In reality, the formula was as simple as it was ingenious. The problem at San Lorenzo had been that the priests had no way of knowing when it was August 13, because in their part of the world the zenithal passage of the sun did not occur on that date. Thus, they had settled on using one of the solstices instead, because the date of the sun’s turning point was the same everywhere, they had discovered. Whereas at San Lorenzo they were obliged to use the winter solstice sunset to calibrate their calendar, when La Venta was founded it appears that they could once more think in terms of the summer solstice, as had originally been done in Izapa. Indeed, the only difference was that instead of marking the sunrise as they did at Izapa, they were obliged to use the sunset at La Venta.

Once back in the mental groove of **using the summer solstice to calibrate the secular calendar,** it would not have been long before some priest realized that the beginning date of the sacred almanac can itself be calibrated by reference to the summer solstice. In effect, he was recognizing that, if the solstice occurred on June 22 and the “beginning of time” occurred on August 13, there was a fixed interval of time between these two dates. Using our modern calendar to demonstrate his thought process, we would count 8 days to complete the month of June, add 31 more for the month of July, and then count 13 until the sunset of August 13, yielding a total of **52 days**. (For anyone used to thinking in “bundles” of 20′s and 13′s, what a neat package this was — 4 rounds of 13 days = 52 days.) **Thus, no matter where one wanted to build a ceremonial center, one could always find out when it was August 13.** All that was required was to **count 52 days from the time that the sun turns around in the north and mark the horizon at sunset!**

Although both the 260-day sacred almanac and the 365-day secular calendar predated the Maya by well over a millennium, and the “principle” of using key calendar dates to define urban locations and the Long Count itself had likewise been developed by the Olmecs several centuries before the Maya emerged as a civilized society, it was the latter who seized upon these intellectual tools and honed them to the highest level of sophistication of any of the native peoples of Mesoamerica.

**In the flat and featureless landscape of Yucatán, it had been a rather simple matter to lay out a new city oriented to the sunset on “the day the world began” because the “summer solstice + 52 days” formula had already been developed.**

With the discovery of the Long Count with its **“grand cycle” of 5125 years,** Olmecs had a means of defining every day that passed as being absolutely unique. And the position of every day within that round of 13 baktuns, or 1,872,000 days, was numbered consecutively from “the beginning.”

**The imprecision of the Short Count, or defining a day within a given 52-year period,** was gone. Human life spans lost their meaning when compared to the “life spans” of the sun, moon, and stars, and of the celestial rhythms which governed their movements. (Learn more about The Long Count- Astronomical Precision ).

Read More: Mesoamerican Calendars

### Pre-Columbian Calendar of South America

**The Gate of the Sun and Cracking the Muisca Calendar by Jim Allen**

*Copyright Jim Allen, Presented with permission of the author.*

The **Muisca were a pre-Columbian people** who lived in the territory now known as Columbia in South America.

In 1795, Dr Jose Domingo Duquesne, a priest of the church of Gachancipa in Columbia published a paper detailing the Muisca calendar, which information he claimed to have received from the Indians themselves. His paper was later ridiculed as being nothing but an invention of his.

Yet the figures given by Duquesne do in fact relate to a lunar calendar although Duquesne himself may not have fully understood the workings of it since it seems possible that the calendar was more sophisticated than might appear at first glance, and two types of lunar month may have been used, the Sidereal Lunar Month when the moon returns to the same position relative to the stars (27.32 days) and the Synodic Month which is the period between full moon and full moon (29.53 days).

**Background**

At Tiwanaku we found how the solar year was divided into 20 months of 18 days and also interlocked with the Inca calendar of 12 sidereal lunar months of 27.32 days (making 328 days) so that 3 x solar years also equalled 40 sidereal lunar months and the two calendars came together every 18 solar years which equalled 20 Inca years when the cycle started all over again (also known as the Saros Cycle).

**Duquesne**

At first difficult to read and understand, Duquesne’s *(shortcut to Wikipedia info about Duquesne)* paper begins with a background about the Americas and the Egyptians and how the Muiscas counted by their fingers with names for each number up to ten, and then on to twenty.

He then relates their calendar to harvesting and sowing and begins:

*El año constaba de veinte lunas, y el siglo de veinte años* (the year consisted of twenty moons, and the century of twenty years) then goes on to relate this to lunar phases and harvests.

The first thought on reading this, was that as at Tiwanku, they might have divided the Solar Year into twenty for their months, but the text implies that 20 lunar months made the year and it also implies that Synodic or phase months were intended. This year of twenty months he tells us was called a “Zocam” year. Now a period of 20 x 20 months which Duquesne mentions might seem worthy of fitting into an Aztec or Mayan calendar since 20 x 20 gives 400, but further down the text, if we read closely, Duquesne says that

*“Twenty moons, then, made the year. When these were finished, they counted another twenty, and thus succesively, continuing in a continuous circle until concluding twenty times twenty. The inclusion of one moon, which it is necessary to make after the thirty-sixth, so that the lunar year corresponded to the solar year, and thus they conserved the regularity of the seasons, which they did with consumate ease.”*

Now, here is a question, not of translation, but of meaning. Because a little further along, Duquesne explains how the year of 37 months was a period of 36 months plus a “deaf” month so that the year adjusts to the solar year. This year of 37 months is called an “Acrotom” year. He also tells us that 20 x 37 of these months corresponds to 60 of our years, divided into four parts so that each part was ten Muisca years which equalled fifteen of ours.

From this we can easily work out that 60 of our solar years divided by 20 x 37 gives a month of 29.61 days suggesting that here, the synodic or phase month from full moon to full moon was intended since the synodic month has an average of 29.53 days.

*Above, the Synodic month is based upon the time taken from full moon to full moon.*

But returning to the earlier statement

*“Twenty moons, then, made the year. When these were finished, they counted another twenty, and thus succesively, continuing in a continuous circle until concluding twenty times twenty. The inclusion of one moon, which it is necessary to make after the thirty-sixth, so that the lunar year corresponded to the solar year, and thus they conserved the regularity of the seasons, which they did with consumate ease”.*

What I think is meant here, is that they counted in twenty times twenty then added an extra month in the same manner as they added an extra month to 36 months to make 37, so the real figure here is not 20 x 20 = 400 but 20 x 20 + 1 = 401.

There is also another difference.

I think** they were running two calendars in parallel with each other**, so the 37 month calendar was in Synodic Months of 29.53 days while the 20 month and 401 month calendar was in Sideral Lunar Months of 27.32 days, although at the same time Duquesne counts the 37 month year as being 20 months + 17 months (because the counting system was based on twenties) making 37 months when the solar and lunar calender synchronised, in this instance these 20 would be synodic months the same as the 17 months and he also explains this another way, as the extra month being inserted at the end of every three lunar years so they counted two x lunar years of 12 months then one of 13 months, the thirteenth month being the “sordo” (deaf) or extra month. So after 1 x Muisca year of 37 synodic months (3 solar years), sowing would begin again on the same day in January, while the intervening two years had a system of counting the months on the fingers as Duquesne puts it…

But returning to the calendar of 20 months running continuously as 20 x 20 months with an extra month inserted to give 401 months, we can check the figure of 401 Sidereal Lunar Months to see if it relates to a solar year and 401 x 27.32 days comes to a great period of 30 Solar Years, which in turn equals 10 Muisca Acrotom years of 37 x synodic months of 29.53 days….

Every three solar years equals the Muisca “Acrotom” year of 37 Synodic Months of 29.53 days and at the same time corresponds to 40 Sidereal Lunar Months of 27.32 days, and every one and a half solar years corresponds to a “sidereal lunar year” of 20 Sidereal Lunar Months which is the true “Zocam” year of the Muiscas.

So to sum up so far,

1 x Tiwankau Solar year = 20 “months” of 18 days (using a rounded-off 360 day year divided by 20).

1 x Tiwanaku Lunar year = 12 sidereal lunar months of 27.32 days (328 days) – also used by Incas.

1 x Muisca Zocam year = 20 sidereal lunar months of 27.32 days = 1½ solar years

2 x Muisca Zocam years of 20 sidereal months of 27.32 days = 1 Muisca Acrotom year of 37 synodic months

1 x Muisca Acrotom year = 37 x synodic months of 29.53 days

1 x Muisca Acrotom year = 3 x solar years = 40 x sidereal lunar months of 27.32 days = 2 x Muisca Zocam years

½ Muisca Acrotom year = 1½ solar years = 20 x sidereal lunar months of 27.32 days = 1 x Muisca Zocam year

18 solar years = 20 Inca years = 6 x Muisca years of 37 x 29.61 days = the Saros Cycle

10 Muisca Acrotom years = 30 solar years = 401 sidereal lunar months of 27.32 days = 20 Zocam years.

20 Muisca Acrotom years = 60 solar years = 2 x 401 sidereal lunar months of 27.32 days = 40 Zocam years.

It might appear that Duquesne made an error when stating that “the ‘century’ of the Muiscas consisted of 20 intercalcated years of 37 months each, which corresponded to 60 of our years, which comprised four revolutions counted in fives, each one of which equalled ten Muisca years, and fifteen of ours until completing the twenty….”

Since 1 x Muisca year of 37 months equals 3 solar years, then 10 x Muisca years should be 30 solar years as per the table above, and since Duquesne was talking about how they counted up to twenty in periods of fives which corresponded to five fingers, what he should have said here was that each of the five was five Muisca years of 37 months equalling fifteeen of ours. But in fact he is correct except it is 10 x Sidereal lunar month years of 20 x 27.32 days which equal the fifteen solar years…..

5 Muisca Acrotom years of 37 synodic months of 29.53 days would be 15 solar years

10 Muisca Zocam years of 20 sidereal months of 27.32 days would be 15 solar years

I suspect therefore, and it is fairly clear, that the 20 month year which Duquesne called the “Zocam” year was actually the sidereal year of 20 sidereal months but the name may have mis-understood by Duquesne as a period of 20 synodic months if Duquesne were unaware of a different type of lunar month in use, otherwise there would have been little point in having years of 20 synodic months running continuously when they were actually grouped in 37 month years and by contrast 2 x 20 sidereal months mesh both with the Acrotom year and solar year at 3 year intervals and over longer periods.

To see how they compare at three year intervals,

37 synodic months of 29.53 days would be 1092.61 days

40 sidereal months of 27.32 days would be 1092.8 days

3 solar years of 365.2524 days would be 1095.72 days

Because of the small discrepency, over long periods of time some adjustments would probably be necessary such as the extra month inserted after 400 sidereal months on the Zocam calendar making

401 sidereal months of 27.32 days = 10955.32 days

10 Muisca Acrotom years = 370 synodic months of 29.53 days = 10926 days

but if they added another month that would bring them to 10955.5 days and back into line with the Zocam sidereal lunar calendar and closer to the 30 solar years of 365.24 days = 10957.26 days

The Muisca “Acrotom” 37 month synodic month calendar with the phases of the moon was probably a more “user friendly” calendar for the man in the field, whereas the “Zocam” 20 month sidereal lunar calendar was probably of more interest to the time keeping priesthood and for bringing the other calendar into alignment periodically.

Duquesne also tell us that the Muisca “week” was a period of three days, and at face value, this would appear to have no relationship to the Muisca calendar whether using sidereal or synodic months, but then the calendar itself, in spite of Duquesne’s explanation as a usage for agriculture does not seem really practical for agriculture or at least not as practical as the Tiwanaku one but perhaps having the advantage that no construction of pillars or standing stones was required.

The calendar which is practical for agriculture is the one found at Tiwanaku where the solar year is divided by twenty and determined by the setting of the sun over a pillar, so it would be fairly easy to note the same pillar where the sun would return to each year, and this is the calendar which is easily divided into periods of three days, and period of nine days were also known to have been worked in that region.

So perhaps the Muisca also ran a solar calendar, undiscovered but in the same style as Tiwanaku, or perhaps their customs were left over from some forgotten era, based on the same mathematicas as Tiwanaku with it’s interlocking sidereal lunar calendar and counting in twenties.

* Note to advanced visitors: * Click here for the scientific dissertation

*(4 MB, PDF – slow loading)*by Manuel Arturo Izquierdo Pena:

*“The Muisca Calendar: An approximation to the timekeeping system of the ancient native people of the northeastern Andes of Colombia”.***Appendix A.1**contains (in Spanish) “

**dedicada al s. d. d. Jose Celestino de Mutis, director general de la expedicion botanica por s. m.por el d. d.**

*Disertacion sobre el Calendario de los Muyscas, Indios naturales de este nuevo reino de Granada.***Jose Domingo Duquesne de la Madrid**, cura de la iglesia de gachancipa de los mismos indios. Ano de

**1795**.

**Calendario de los Muyscas, Indios naturales del Nuevo Reino de Granada.**

**Return to Tiwanaku**

The Muisca calendar then, is another important piece in the jigsaw of the lost knowledge of the Andes.

If the origins of the Muisca calendar were to be found at Tiwanaku, then perhaps they were also built into the Gate of the Sun which gives the clues to the workings of the Tiwanaku calendar.

Many people have studied the icons on the Gate of the Sun at Tiwanaku and tried to relate them to a calendar. The icons are called “chasquis” or Messengers of the Gods and because there are fifteen of them on each side, some people have thought that they represented a thirty day month in a solar year of twelve months. But as explained earlier, this calendar at Tiwanku is not based upon a divison of the solar year into twelve, but into twenty, and this is represented by the eleven smaller icons forming the freize at the bottom which represents the eleven pillars on the west side of the Kalasasayo which is the actual calendar. So if you count from the central icon or pillar out to the right hand end, then back past the central icon to the left hand end, then back to the centre, you will have effectively counted in twenty divisons and followed the path of the sun over a year.

So if the chasquis do not relate to the days in whichever number of days we choose for the months of the year, could it be that the chasquis represent the years themselves?

*Top part of the “Gate of the Sun” at Tiwanaku, Bolivia*

*Above, detail of the “Gate of the Sun” at Tiwanaku, Bolivia showing the principal grouping of thirty “chasqui” figures with beneath them the freize showing eleven icons and forty condors heads arranged in two rows of twenty heads. *

If each chasqui were to represent a solar year, then each column of three chasquis would represent three revolutions of the sun around the eleven pillar calendar wall and three solar years are equivalent to 1 x Muisca Acrotom year of 37 synodic months of 29.53 days and also equivalent to 2 x Muisca Zocam years of 20 sidereal months of 27.32 days.

*Above, each Chasqui represents a Solar Year and counting in threes, then three Chasquis or years make* *1 x Acrotom year of 37 synodic lunar months or 2 x Zocam years of 20 x sidereal lunar months.*

*The freize beneath the Chasquis shows forty condor heads in two rows of twenty representing two x zocam years of 20 sidereal months and also indicating that the calendar is based upon divisions of twenty.*

There are fifteen chasquis on each side of the central figure and each block of 15 chasquis would represent fifteen solar years which would be

5 Muisca Acrotom years of 37 synodic months of 29.53 days or

10 Muisca Zocam years of 20 sidereal months of 27.32 days

*Above, the 15 Chasquis represent 15 solar years, equal to one quarter of the Muisca “Great Century” and respectively* *5 x Zocam years or 10 x Acrotom years.*

The total number of chasquis is thirty chasquis representing thirty solar years which would be

10 Muisca Acrotom years of 37 synodic months of 29.53 days or

20 Muisca Zocam years of 20 sidereal months of 27.32 days

The choice of thirty chasquis as thirty solar years is no random figure, because after thirty solar years have gone by, it becomes necessary to add one sidereal lunar month to the Muisca Zocam calendar making it 20 x 20 + 1 = 401 sidereal lunar months to bring it back into line with the solar year.

At the same time of adding one sidereal month to the Zocam sidereal calendar, it also becomes necessary to add one synodic lunar month to the Muisca Acrotom calendar making it 10 x 37 + 1 synodic lunar months to also bring it into line with both the sidereal lunar calendar and the actual solar year.

Each of the sections with fifteen chasquis corresponds to the period of fifteen solar years which Duquesne tells us was one quarter of the great “century” of the Muiscas so to sum up, each block of fifteen chasquis represents fifteen solar years which is 10 Muisca Zocam years or 5 Muisca Acrotom years, the two blocks together make 30 chasquis representing 30 solar years which is 20 Muisca Zocam years or 10 Muisca Acrotom years and 2 x the 30 chasquis gives 60 chasquis representing 60 solar years completing the great “century” of the Muiscas which was therefore, 40 Muisca Zocam years or 20 Muisca Acrotom years.

*Above, detail of the “Gate of the Sun” at Tiwanaku, Bolivia, the 30 Chasquis represent 30 Solar years,* *equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months.* *At the end of this period, 1 x lunar month had to be added to the lunar calendars* *to bring them back into phase with the solar year..*

*Above, the “Gate of the Sun” at Tiwanaku, Bolivia, the 30 Chasquis represent 30 Solar years,* *equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months.* *At the end of this period, 1 x lunar month had to be added to the lunar calendars* *to bring them back into phase with the solar year.* *Beneath the chasquis can be seen the freize with 11 smaller chasqui heads* *representing the 11 pillars on the calendar wall which in turn divide the solar year into* *20 months of 18 days, and the 40 condor heads represent the 40 sidereal months which mesh* *with the solar calendar every three years.*

*Above, when the sun reached the end of the pillars, it appeared to “stand still” before beginning its journey back in the opposite direction.*

**Copyright Jim Allen, Presented with permission of the author.**

http://www.atlantisbolivia.org/lostcalendarandes.htm

## Related Links and Resources

- http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.html#Calendars
- http://www.math.nus.edu.sg/aslaksen/calendar/links.html
- http://www.atlantisbolivia.org/lostcalendarandes.htm

- Archaeoastronomy: Astronomical Alignments of Ancient Structures:

http://www.world-mysteries.com/alignments/index.htm - http://www.world-mysteries.com/achronology.htm
- http://www.math.nus.edu.sg/aslaksen/teaching/heavenly.html
- Lost Civilizations of the Andes [ http://davidpratt.info/andes2.htm ]
- http://gigapan.org/gigapans/28209/
- When Time Began

## PS1 360-day Calendar

*Fixed exact Chinese day names and Mayan day names for Noah’s Flood*

by R.Schiller

Looking at the days of Noah’s 360-day calendar, notice that each date has a permanent Day name in the Chinese 10-day calendar and in the Mayan 20-day calendar. This is because the 60-day calendar fits the 360-day year exactly, the same as the Mayan 20-day calendar does. The 260-day will also do so but it spans 13 tun (years of 360 days), the 13x 360 is 6x 780-day Mars which is 18x 260. The point is that Noah’s days with the date 1 (and 11 and 21) are always Chinese day Wu. And the dates 1-1 and 1-21 and 2-11 (odd month then even month in like pattern 3-1 & 3-21 & 4-11, 5-1 & 5-21 & 6-11) are all the Mayan day imix. And 10 days after those dates the 1-11 and 2-01 and 2-21, 3-11 & 4-01 & 4-21, and 5-11 & 6-01 & 6-21) are all Mayan day Chuen (Chuwen). These repeat exactly for a year of 360 days. Thus the dates on this chart marked as Noah’s (N) have a Chinese day name and Mayan day name that is consistent relationship to the other nations’ Flood years.

*Click to Enlarge*

### Wiki Question: What is the oldest calendar in use?

My insertions into the previous answer is here.

- The Hindu calender is the oldest calender in USE.
- Hebrew calendar year is 5769.
- Chinese calendar 4706. Hindu calendar 2031.
- Gregorian calendar 2009. Byzantine calendar 7518 (as of 2009 Gregorian)
- *Proto-Bulgarian calendar 7515.

A calendar’s year of Epoch or Era does not make it the oldest. For example, the **Gregorian calendar was created in 1582 AD and yet its Era is 325 AD.** In reality its formula equals Julian from 200AD March 1 to 300AD Feb 28. But that doesnt make it 1200 years old. So too, Just because the Byzantine Epoch places Adam in 5509bc versus Alexandrian Era Adam 5500bc or Jewish Adam 3761bc,** those calendars were not created then nor began use since that year.**

The oldest in use is Chinese if 1437bc, or if China’s revision was 237bc, then Japan in 660bc is older. The Egyptian Coptic calendar was created in 28bc and it remains the same and is still in use. But Julian is older (45bc) and it is still used in astronomy. Jewish claims Adam in 3761bc, but i believe Joshua’s death began the 19-year calendar in 1443bc. This makes it older than China’s. Hindu epoch (Manu’s Flood 3102bc is Man-Nu who is the incarnation of Vish-Nu; all Turks and Arabs know that Nu is Noah), it was calculated in 702-700bc, and they also orginated the 5500bc Adam. You must remember that changing a calendar renews it. The Gregorian calendar is regarded as not being Julian. **Most religions deny their calendars were readjusted.** There are claims that the Egyptian calendar began 2770bc July 17 on Thoth 1, BUT notice there is no such Julian date before 45bc. If we take Julian dates and we go back 2700 years, then can you not see that all calendars also go back to date the years of lives that did not use those calendars?

This is why I** contend that the oldest calendar was 360-day, created before the Flood,** in Adam’s year 390, the 40th decade, they are called sars and they Chinese calendar still uses the names, but they are no longer 3600 days. Further, the Mayan calendar is shifted from my calculations of this 360-day calendar by only 20 days (a Mayan unit) in which their 5-01 to 5-19 are the same dates in their calendar as it is in Noah’s. The Mayan calendar was shifted from its creation in 1314bc to 560bc, its new year Pop 1 (after Pop zero) is Thoth 1 shifted by 16 days of Venus in 312 years. From Babylon’s king Amizaduga to their founding of Copan in 1313bc. Izapa is 1275bc not 1359bc having the same dates, but requiring the shifts of 1313bc to occur first before it can match. The solstice must drift back 12 days from 2020bc Jan 6 to 560bc Dec 25 before the Greek December 25 Christmas death of Noah can be claimed as the winter solstice sun, by Persian christ king Cyrus in 560bc, and by Budhha’s mother Maya when he was born in 560bc, and by the Maya of Copan who place Pop 0 on Dec 24 and Pop 1 on Dec 25 in 560bc…. because that’s when Noah died in 2020bc at 950 because his DNA did not have the carbon-14 atoms on its molecules like ours have.

An early reference date to the development of versions of the Hindu calendar is 3102 BC which would make this year 5111 if there is a count of years back to that date. Some more Useful knowledge as Hindu scripture with minding year 2010,currently in Nepal people use Virkam Samvat calendar which has year 2066. Before that there was calendar named caliyugat, and before that there is sanatan Hindu calendar(yugabdha) according to it, as of year 2006 running year was Yugabdha sanatan Hindu Calendar: 1986772928(as of Christian Year 2006) according to Rigveda.

On the other side, since the Chinese calendar is considered to be still in use, it is important to add some information for the Proto-Bulgarian calendar, which stays in the basis of it’s Chinese inheritor. In the year 1970 a group of non-Bulgarian scientists raised the question in UNESCO for the recognition of the “Bulghar” calendar as the most accurate calendar system known to man, proving that this Jupiter-to-Sun cycle (12 Earth years) based calendar dates 5505 years B.C. In other words, year 2010 is assumed to represent the year 7515. This puts the “Bulghar” calendar among the list of the oldest.

The year displayed by calendars do not indicate the calendars age. It indicates an arbitrary year from which the calendar counts. The Gregorian calender, to take the most obvious example, dates from the 16th century and is obviously not over 2000 years old. The same is true for other calendars.

On the lighter side;

See the related question for the circumstances for implementation of the first calendar. Courtesy of Ogg and Gronk.

## PS2 **Determining the longitudes, chronometry and observatory trials, a brief historical introduction**

We thank Arnaud Tellier, horological expert, former director and curator of the Patek Philippe Museum, Geneva.

With the invention of the pendulum in the late 1650s, then of the balance spring in 1675, horology could claim the status of an exact science. This considerable progress is due to Christiaan Huygens (1629-1695), Dutch mathematician, astronomer and physicist.

In the early eighteenth century, the improvement of the adjusting of timepieces became obvious; nevertheless, it was also true that the search for absolute accuracy was just at its beginning.

The precision of clocks and watches is essential since, once embarked on a ship, they can be used to determine the longitude, that is, to finds one’s position in the middle of the ocean. The maritime nations of the time – England, Spain, France and the Netherlands – were dismayed by the disasters caused by errors in longitude. For example, the loss of the squadron under the command of Sir Cloudesley Shovell (1650-1707), which shipwrecked on the Isles of Scilly (or*Sorlingues*) while believing they were in the English Channel (1707), had such a strong impact that years later the British Parliament organized a contest for “any method of defining the longitude at sea”, offering as incentive 10’000 for a result not exceeding 1 degree of error, 15’000 for 40 minutes and 20’000 for 1/2 degree or less. This was the famous contest of Queen Anne in 1714.

In London, the work of Henri Sully (1680-1729), George Graham (1673-1751) and John Harrison (1693-1776) marked the beginning of the eighteenth century. It was in 1735 that Harrison won the contest with his “H1″ chronometer, but only in 1751 was he able to obtain the first part of the award presented upon the construction of a fourth version. Later on, in 1773, the support offered by King George III (1738-1820) helped him receive the second half of the award for his fifth chronometer. It should also be noted that in 1757, in London, Thomas Mudge (1715-1794) developed the first watch equipped with a lever escapement which since then has been universally used in horology.

In France, the watchmakers were equally concerned with the longitude issue. In 1766, Pierre Le Roy (1717-1785) presented in Paris his first chronometer. He built it on entirely new principles that were preserved as the basis of the modern chronometry (detent escapement, isochronous spring; self-compensating balance equipped with adjustable compensation weights; temperature compensation with mercury). He also presented a bi-metallic compensation balance and established the “*Pierre Le Roy rule*” stating that for each spring there is a length that makes it isochronous. In 1768, his great rival, Ferdinand Berthoud (1727-1807), completed the first of his marine pieces and also invented a compensation balance. In 1770, Pierre Le Roy was awarded the two prizes offered successively by the Royal Academy of Sciences for “the best way of measuring time at sea.”

In 1772, John Arnold (1736-1799) built in London his first bi-metallic compensation balance based on the principles established by Pierre Le Roy; later on, in 1790, he improved the spring detent escapement. Another British watchmaker, Thomas Earnshaw (1749-1829), developed a marine chronometer so advanced and perfected that its basic principle remained unchanged until the advent of quartz clocks. The rivalry between the two watchmakers was as strong as the one between Le Roy and Berthoud.

Chronometry developed in England of the eighteenth century to the point of becoming an industry, while in France it also grew to be an important manufacture under the guidance of Pierre-Louis Berthoud (1754-1813), Ferdinand Berthoud’s nephew and disciple, who invented his own pivoted detent escapement.

The “*siècle des Lumières*” is the time when the marine chronometers were tested in long and perilous journeys. The nineteenth century was when the tests in the astronomical observatories helped verify scientifically several chronometers at once.

As early as 1766, the Greenwich Royal Observatory, near London, organized sporadically the first precision contests. In 1823, the British Admiralty created a contest with 300, 200 and 100 Pounds Sterling in prize money, hoping that this way it will acquire for its fleet the best chronometers. Similarly, and at the same time, the French Royal Navy paid 2400 Francs for the award winning chronometers.

In 1790, Geneva witnessed the first precision contest among chronometers held at the Society for the Advancement of the Arts. Later on, in 1816, the Astronomical Observatory of Geneva hosted the creation of a trial, which subsequently was conducted only occasionally. It was not until 1879 that this type of contest became an institution. The precision level of the watches is evaluated through a points system set at that time by Emile Plantamour (1815-1882), Director of the Observatory. This system with prizes (1st, 2nd and 3rd prize, then honorable mention or without) and different classes (marine chronometer, deck or pocket, with or without special features), was shortly after joined in 1884 by the Astronomical Observatory of Kew and Teddington in Great Britain and, in 1885, by that of the Astronomical Observatory of Besançon, in France. The contests organized by the Neuchâtel, Hamburg and Washington observatories also enjoyed greatest consideration. Unfortunately, it hasn’t been possible to standardize the tests between the different countries, so today it is impossible to compare their results. In addition to publishing the rankings in the official publications, the award winning time-pieces also received an official certificate of accuracy and a gold, silver or bronze medal.

**Patek Philippe and the Timing Competitions**

Patek Philippe watches participated with remarkable success at many of the trials which soon became very important events, nationally and internationally. In 1884 and 1895, the Geneva manufacturer managed to also win the prestigious series prize for the five most precise pocket watches. Between 1900 and 1939 – the year when the firm celebrated its centennial – it won 764 prizes in Geneva, of which 187 were first prizes; this represents more than half of the prizes awarded during that time.

Between 1943 and 1966, Patek Philippe presented 480 times to the Geneva Astronomical Observatory movements (simple, with no complications) from the D category (format not exceeding 30 mm in diameter or 706.86 mm2) and 27 times movements with a tourbillion regulator. As these movements could be presented on several occasions over the years, it would be difficult to determine the exact number of manufactured wristwatch chronometer movements. Moreover, many of them would never be sold and are currently preserved in the vaults of the manufacturer and the company’s own museum.

Patek Philippe did also compete in contests abroad. This is particularly the case during the 1960s when the manufacturer received the highest British distinction, the “Craftsmanship Test”, introduced in 1951. Only twelve watches can claim to have won it, amongst them the Patek Philippe pocket watch with tourbillon, No 198’423, having furthermore achieved the best results ever. The Observatory of Geneva tests were interrupted in 1967, with the arrival of quartz watches.

**The COSC**

Today only COSC (*Contrôle Officiel Suisse de Chronométrie* the Official Swiss Chronometer Testing Institute) performs accuracy testing and issues certificates. A law dated November 6th, 1886 on testing the accuracy of the pocket watches at the Geneva Observatory, set the conditions, certified through an official engraved hallmark, where the “Geneva quality” is applied to certain watches. This stamp has the same value as an official accuracy certificate and allows qualifying the watch as a “chronometer”. After several amendments and additions in 1891, 1931 and 1955, made necessary by the technical progress, the regulation on testing of the mechanical watches received its final form on April 5th, 1957.

{ 1 comment… read it below or add one }

Excellent work! This was very enjoyable for me. I love this site for the opportunity for good minds to express the knowledge and wisdom of our very existence. I suggest a chat room for those who contribute to this site so we may grow even more in common coherency of thought and understanding built on REASON.

CHEERS, ALEX