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Calendars are one of the more fascinating aspects of civilized man’s reaction to Time.  On the one hand, calendars are extremely practical, ranging in everything from when to plant food crops (and thereby expect a good harvest -- and have food to eat), to when to chop timber, to when to set up your next appointment.   

Clearly, knowing that a warm spell in winter is not the same as the advent of spring is very important to the farmer.  Knowing also that a late spring does not imply a late fall is also critically important information.  Agriculture usage is obviously based on the desire to avoid attempting to harvest crops in the dead of winter.  

The example of chopping timber, meanwhile, is based upon an observation by James Lynch, an American scientist, who learned from Costa Rican farmers that a tree cut down during a new moon is quickly ravaged by insects, while one cut down several days before a full moon will stay free of termites for years.  In other words, not only is the solar cycle important, but so also is the lunar cycle.  

As for keeping appointments, it is said, for example, that there are three stages of mankind in the use of calendars:  

            1) Where will we find food today? [What’s the weather likely to be like today and what will be its effects on our finding food?],

            2) Where will we find food for the winter? [How many days do we have to find food before the winter sets in?], and

            3) Where shall we do lunch?  

A truly excellent website, <http://webexhibits.org/calendars/index.html>, (from where the tree and termite story came) provides a host of insights into the subject of calendars -- most everything anyone might want to know about the history of mankind’s efforts to subdivide a year for the purposes of predicting the controllable aspects of his future.  

For our purposes, we will begin by noting that Cro-Magnon Man may have been tinkering with calendars some 15,000 years ago -- or at least such is the interpretation of at least one researcher investigating the Lascaux caves in France.  Since then, calendars have been developed by the Sumerians, Egyptians, Babylonians, Celts, Greeks, Friends, Romans, Countrymen, and various groups -- such as Hebrews, Mayans, Christians, and believers in Islam.  In all cases, religion was intermixed with the mathematics of the calendars.  


Historically, calendars have been based on astronomical events, the two most likely of which deal with the sun and the moon.  Their cycles (i.e. years and months) are important in the construction and understanding of most calendars.  The more obvious means is to use the moon, inasmuch as it’s cycle is shorter and easier to grasp. The time from one new moon to the next is called a synodic month, and its length is currently 29.5305889 days.  No kidding.  Someone actually determined it to seven decimal places -- despite the fact that it varies slightly.  For example, in 1900 its length was 29.5305886 days, and in 2100 it will be 29.5305891 days.  Fortunately this variation should not effect your weekend plans.  

But also very important, particularly from the agricultural viewpoint, is a calendar based on the earth's motion around the sun (i.e. one year). The time from one fixed point, such as a solstice or equinox (solstices being far easier to ascertain), to the next is called a tropical year.  Its length is currently 365.242190 days, but it too varies.  In 1900 its length was 365.242196 days, and 200 years later, it will be 365.242184 days.  Yes, the years are getting shorter, as you suspected, and you have less and less time to get your work done!

It’s noteworthy that these extraordinarily accurate numbers are only averages.  The actual length of any given year can vary by several minutes (i.e. 0.002 days) due to the influence of other planets.  Similarly, the time from one new moon to the next may vary by several hours (i.e. 0.1 days) due to a number of factors, including changes in the distance from the sun to the earth, gravitational effects, and the moon's orbital inclination.  (The moon is often less inclined to some things, depending upon its mood/phase.)

The length of the tropical year divided by the length of the synodic month is 12.3683..., not a simple relationship between the two.  Thus, any assumption of 12 months per year will quickly lead to inconsistencies between the tropical and synodic calendars.  However, 19 tropical years equals 234.997 synodic months, which is really close to 235.  Thus every 19 years, the phases of the moon will fall on the same dates -- except for the skewness introduced by leap years.  19 years is known as the Metonic cycle (named after Meton, an Athenian astronomer from the 5th century B.C.E., who first made note of it).

An end result is that the Christian (or Gregorian) calendar is a solar calendar, with the months having no connection with the moon’s motion.  Meanwhile, the Islamic calendar is a lunar calendar, with the year having no connection with the earth’s motion about the sun.  Finally, the Jewish calendar combines both, in that its years are solar based, and its months, lunar based.  (Hint: The Jews knew about the Metonic cycle!)


Calendars are fundamental to the manner in which a civilization or culture thinks, and far and away more than merely useful devices for keeping track of appointments, or even of knowing when to plant and when to harvest -- activities considerably more important than knowing when to fold and when to hold ‘em. But seriously, even the Days of the Week have significance far beyond an apparent arbitrary cycle of seven days.  To appreciate this statement, consider the following calendars:

The Chinese Calendar, for example, began with the “string of pearls” incidence in 2637 B.C.E.  This refers to an alignment of the visible planets, such that they appeared before dawn (and were thus visible), and were strung out like a “string of pearls.”  This alignment was considered sufficiently significant that the Chinese Calendar is based on this date.  The fact that the Spring Equinox was also involved made the timing a popular favorite.

The Hebrew calendar, on the other hand, date the years by counting from the creation of the world (another, one would assume, sufficiently significant event), which is assumed to have taken place in 3761 B.C.E.  Possibly on a Tuesday.

The Mayan Calendar bases their calendar on a starting date, referred to as “”, and this may have been their idea of the date of the creation of the world as well.

The Egyptian calendar was initially based on the lunar cycle, but this early version failed in its most important test: predicting the annual flooding of the Nile river. The Egyptians then noticed that the “helical rising” (i.e. being visible just before sunrise) of Sirius in Canis Major -- what the Egyptians referred to the “Dog Star,” -- always preceded the flooding of the Nile by a few days. The Egyptians subsequently became one of the first to adopt a stellar calendar.  But they kept the lunar calendar as well.  They even created a third calendar, a solar one.  Some they used for agriculture, some for religious festivals, and some for civil matters.  The Egyptians were into plurality.

The Babylonians, meanwhile, were mostly into confusion, calendar-wise.  Their first attempt was a lunar calendar with alternating 29 and 30 day months.  But this required the addition on three extra months every eight years in order to eliminate the differences between the lunar and solar years.  Basically, whenever the king felt the calendar was out of whack -- or to distract his subjects from lousy economic conditions (in the true tradition of heads of state the world over) -- he would order an extra month.  Around 300 B.C.E., the Babylonians wised up and began to use a more reliable system.

It is interesting to note how often Emperors (Chinese, Babylonian, whatever) or other heads of state have had to step in and make periodic calendar adjustments -- and probably lop off the heads of a few less-than-competent priest-astronomer-time-clock types.


Various ancient calendars developed their own unique characteristics.  Some of these innovations include multiple calendars for different uses (Egyptian), the perspective of a very long view of events (Mayans), a tradition of simply ignoring portions of the year (early Romans), and one which is basically divorced from natural rhythms (Gregorian).

The Egyptians used a stellar calendar connected to 36 stars to subdivide the year, which they used for agriculture.  They also developed a sophisticated Zodiac system (using the same symbols of Astrology as are employed today).  The latter was thus a solar calendar, which was used for civil matters (administrative and governmental functions).  This solar calendar used 360 days (i.e. 12 months, with 30 day months). The Egyptians also included three seasons of four months each (the five intercalary days in the depths of winter being left out in the cold... so to speak).  Meanwhile their lunar calendar continued to regulate religious affairs and everyday life -- like when to check the other calendars.  Stuff like that.

The use of 365 days, in lieu of 365.24..., eventually got them into trouble, with their year falling behind the solar year by one day every four years.  The good news was that every 1,460 years, everything was in agreement again.  The bad news is: this “Sothic cycle” was not considered a real politically-viable solution to the problem -- in other words, it was beyond the next election, next dynasty, and next generation.  Eventually a 25-year cycle was introduced, and the civilization pretty much died out before this particular socio- political prop went out of fashion.

The Mayans, meanwhile, had a unique feature of their calendar, which came to be known as the Long Count.  While distantly related to the Julian Day Number (a simple count of each day from a specific date -- currently, January 1, 1900), the Long Count is much more interesting in that it involves a mixed base-20/base-18 representation of a number.  (We use a base-10, i.e. there are ten different symbols, 0, 1, 2... 9.  Base-2 uses only 0 and 1 -- convenient for computers -- and Base-8 uses 0, 1, 2...7.)

The Mayans’ Long Count began with a number written as “”.  (13 is a biggie with the Mayans as an important number in its own right, and interestingly enough is held over by popular demand in our modern day playing cards, each suit having 13 cards.)  As to the precise date in the modern Gregorian calendar, there is some disagreement among scholars as to the beginning of the Long Count.  Three possibilities are:

   = 8 Sep 3114 BC (Julian) = 13 Aug 3114 BC (Gregorian)

   = 6 Sep 3114 BC (Julian) = 11 Aug 3114 BC (Gregorian)

   = 11 Nov 3374 BC (Julian) = 15 Oct 3374 BC (Gregorian)

Assuming one of the first two possibilities, the Long Count will again reach on 21 or 23 December 2012 A.D. -- what is commonly known as the End of the Mayan Calendar, and possibly the end of Time as we know it.

[This might indeed effect your weekend plans!  At the same time, it is not necessarily prudent for you to plan your finances such that you run out of money just prior to Christmas of 2012.  Or to wait until Christmas Day to open your presents, either!  It’s a tricky question as to just how much planning to do beyond December 21, 2012 A.D.!  Keep in mind that there is also an alternative view with respect to the Mayan Calendar in terms of what 2012 A.D. actually means.]

The Mayans were apparently aware that the solar year was longer than 365 days, and estimated that the solar year precessed through all of the seasons twice in 1,101,600 days.  Based on this, the Mayan estimate of the year appears to be 365.242036 days, which is slightly more accurate than the 365.2425 days of the Gregorian calendar!  Because of this greater accuracy, advocates of the Mayan Calendar like to suggest that the Mayans knew a great deal more than they’re generally given credit for.  This leads them to point out that the ramifications of the end of the Long Count should be, perhaps, taken much more seriously.  These same advocates also like to emphasis the greater adherence to natural rhythms of the Mayan Calendar over the Gregorian.  [E.g., the 13 lunar moons in a year.]

The early Romans borrowed parts of their earliest known calendar from the Greeks -- which traditionally was true of the Romans borrowing most every artifact of culture the Greeks had.  The early Roman Calendar consisted of 10 months in a year of 304 days.  No kidding.  The Romans seemed to have simply ignored the remaining 61.24 days, all of which fell in the middle of the winter.  (So much for the opera season!)  The 10 months that were included were named Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December. The last six names, obviously, were taken from the words for five, six, seven, eight, nine, and ten. 

By tradition, Romulus, the legendary first ruler of Rome, is alleged to have introduced this calendar circa 700 B.C.E.  Later, the Roman ruler Numa Pompilius added January and February to the calendar, bringing the Roman year to 355 days long.  Then in order to make the calendar correspond to the solar year, Numa lso added every other year a month called Mercedinus.  Mercedinus was inserted after February 23 or 24, and the last days of February were moved to the end of Mercedinus -- while the normal month of February lost as many days.  In the years when it was inserted, Mercedinus added 22 or 23 days to the year.  (And you thought the Babylonian Calendar was fouled up!)

In their earliest incarnation, Roman months were identical to the lunar cycle.  Each moon was divided into three sections (three being inevitably more a natural division of the ancients, than say, four).  These sections corresponded to three phases of the moon: new, first quarter, and full -- or in Roman jargon: Kalends, Nones, and Ides.  Accordingly, when Shakespeare’s Julius Caesar was warned of the “Ides of March”, he was being warned of the time of March’s full moon (not necessarily the fifteenth as some have surmised).  [BTW, the “Ides of April” (tax time) are infinitely more threatening.)

The Gregorian Calendar (or Christian Calendar) is the defacto calendar of choice in the modern world.  A physician from Naples, Aloysius Lilius, first proposed it, after which it was adopted by Pope Gregory XIII in accordance with instructions from the Council of Trent (1545-1563) to correct for errors in the older Julian Calendar.  It was decreed by Pope Gregory XIII in a papal bull, Inter Gravissimas, on February 24, 1582.  (Typically, the man with the idea did not have his name attached to the end result.)

The Gregorian calendar is based on a tropical year of 365 days, with a leap year (adding an extra day every four years).  However, this does not apply to the century mark years which are not evenly divisible by 400 (e.g. 1800 or 1900 are both not leap years, whereas 2000 is a leap year).  In other words, there are 97 leap years every 400 years.  (See also -- if you dare -- Gregorian Conspiracies?.)

This use of Fudge’s Factor and Finagler’s Theorem still does not quite make it -- i.e. the Gregorian Calendar continues to be less accurate than the Mayan Calendar.  However, there is, in addition to a 400 year rule, a possible 4000 year rule.  The idea has been suggested by several individuals, including the noted astronomer John Herschel (1792-1871) that a better approximation than the 97/400 leap year rule, would be a 969/4000 leap year rule.  I.e. drop one leap year from the current Gregorian calendar every 4000 years.  Given the fact that the ancient Egyptians had calendars that lasted some 2000 years, this would put the modern world in serious competition for longest running show.

However, the 4000 year rule has not been officially adopted (again the political problem of too long a time before it makes a difference).  Also, if the End of the Mayan Calendar is indeed the “end of time as we know it”, it simply won’t make any difference!

Meanwhile, the Orthodox church in Greece, when it switched to the Gregorian calendar in the 1920s, attempted to improve on the Gregorian leap year rules, by replacing the "divisible by 400" rule by a rule which said that any century mark which when divided by 900 left a remainder of 200 or 600 was a leap year.  This had the effect of making 1900, 2100, 2200, 2300, 2500, 2600, 2700, and 2800 all non-leap years, whereas 2000, 2400, and 2900 would be leap years.  Thus there will be no conflict with the Gregorian until 2800.  Interestingly enough, this version is slightly more accurate than the Gregorian, with the Greek version obtaining an average year of 365.24222 days.

It might be pointed out in passing that “leap day” is actually February 24th.  This derives from the Roman calendar and the celebration of feast days.  Not the 29th.  Sorry.


 Comparing dates between different calendars is difficult at best.  Years, on the other hand, are less inhibiting (even when they begin at different points in the year).  But roughly, the Gregorian years of 2000, 2012 and 2013 correspond, for example, to the following:

                        Gregorian                     2000                2012                2013

                        Chinese                        4698                4710                4711

                        Hebrew (*AM)            5761                5773                5774

                        Egyptian                       6236                6248                6249

                        Mayan                          5114                5126                      0!

*AM stands for Anno Mundi, the Year of the World).


The accuracy of calendars for the last three and a half thousand years has obviously been of concern to Kings, Emperors, Popes, and anyone attempting to correlate daily events with the rhythms of nature.  A tropical year of 365.242190 days (and one which is slowly growing shorter) is obviously not a trivial matter for accuracy prone individuals.  There is the distinct likelihood, however, that the ancients had it rather easier in this regard.

In times past, the number of days of the year was apparently 360 days!

In such times, the allegedly arbitrary division of the circle into 360 degrees would have corresponded rather nicely to the days of the year.  And in fact 360 day calendars were in use for nearly a thousand years, until sometime in the eighth century B.C.E., civilizations all over the world began junking their calendars and starting over.  Rather abruptly, the lunar month lengths were no longer fixed, but based instead upon sky observations.  It became the rule that priest-astronomers would declare when a new month began (i.e. at the first sighting of a new moon), and the length of a month became simply the time from one new lunar crescent to the next.

Of specific note, in ancient times, the Mayans had a tradition of a 360-day year.  Then in the 4th century B.C.E., they took a different approach from both Europeans and Asians, and began maintaining three different calendars. In one of these calendars, they divided a 365-day year into eighteen 20-day months, which was then followed by a five-day period that was no part of any month.  The five-day period was considered to be unlucky. 

The Celtic cultures supposedly used the same 360 day year for month calculation and then referred to the 5.24 extra days as special days at the end of the year (and not part of the monthly scenario at all).

We might wonder what happened.  After all, a 5.24 day error, in about 11 or 12 years amounts to a two-month error -- which agriculturally would have been disastrous!  Heads of calendar-providers would surely have rolled, if such an error had been practiced for lo unto a thousand years.  Such an error is not conceivable.

Thus, the question becomes, did something happen to change the number of days in the year from 360 to 365.24?  The answer is:  Almost certainly!

Immanuel Velikovsky was one of the first to notice the 360 ancient day, and not dismiss it as the mistakes or ramblings of an ancient culture.  In his classic 1950 volume, Worlds in Collision, Velikovsky claimed that the events of the Exodus (circa. 1460 B.C.E.) was due in large part to an interplanetary contact of the Earth with another heavenly body -- in his view, Venus.  Then later, in or about the 8th century B.C.E., Mars became the interacting body, and led to a change in the number of days in the year.  The enormous destruction and other effects of this encounter might be an explanation for why the Mayans thought the extra 5.24 days were “unlucky”!  [Think of its equivalent as adding an extra work day to the Days of the Week!]

The idea of other planets having made close encounters with the Earth in ancient times has been met with derision and thoroughly unscientific skepticism by the mainstream scientific community.  Even today, the idea is dismissed out of hand.  After all, as Thomas Kuhn has so eloquently shown, scientists’ preference for one paradigm (e.g. “Be happy; everything’s stable and safe in the solar system”) over another (e.g. “occasionally, there will be comets, planets, and other intruders impacting our Earth in one form or another”) is determined by a host of non-scientific, non-empirical factors.  (For example, Einstein’s theory of special relativity was once challenged by one alleged scientist as being wrong because the end result of Einstein’s famous twin paradox “would have allowed people to cheat death”.)

Suffice it to say that the mainstream scientific community has been notably unscientific in its condemnation of Velikovsky, while others with a more rational frame of mind have taken the time to study the possibilities, and found much additional evidence.  The ten volumes of Pensee (published by the Student Academic Freedom Forum, Portland, Oregon) and the Immanuel Velikovsky website <http://www.varchive.org/> provide an enormously more balanced, scientific view. 

From a physics perspective, the relevant question is whether or not such an interplanetary exchange would change the days of the year from 360 to 365. 

The means of doing so are discussed in some detail in Sun Stand Thou Still, where the alleged Venus-Earth interaction is demonstrated to be energetically plausible.  Robert W. Bass has also noted in Pensee’s 8th volume that “it is perfectly possible, according to Newton’s Laws of Dynamics and Gravitation when three or more bodies are involved, for planets to nearly collide and then relax into an apparently stable Bode’s Law type of configuration within a relatively short time.”

For the moment, if we assume an interplanetary contact has changed the number of days in the year from 360 to 365.24, what precisely does this imply?

On the one hand, we might assume that the mechanics discussed in Sun Stand Thou Still are valid (i.e. the crust of the earth slips on the continuing rotation of the Earth’s core -- producing the perception on the surface of the Earth of the rotation ceasing).  If we also assume that the earth continues to remain at the same distance from the sun, and at the same orbital speed, then we logically note that an increase in the number of days per year implies a shorter distance along the earth’s orbit per rotation (day), and thus a more rapid rotation of the Earth on its axis. 

This is less likely than other alternatives, in that the frictional energy losses caused by the rotating core bringing the crust back up to speed would imply a slower rotation of the Earth.  There is the possibility that the other planet’s gravitational attraction might add to the rotational speed of the Earth, but inasmuch as the massive bulk of the Earth is in the core, and there is no gravitational “handle” to change its speed, this seems unlikely.

A more plausible alternative is that we assume the same time of rotation of the Earth on its axis.  This implies that there is no change due to the encounter, i.e. the core has brought the crust back up to speed with no, or very little loss).  What might have changed therefore, would be the actual orbit of the Earth around the sun (including the mean orbital speed, currently about 66,000 mph).  This might have been easily done simply by the gravitational attraction of the other planet pulling on the Earth in a direction, which slightly increased the size of the orbit -- or the mean distance from the Earth to the Sun.

How noticeable would this be?  We know that currently:

            Mean distance from earth to sun            = 92,957,200 miles

            Max distance from earth to sun             = 94,537,000 miles

            Min distance from earth to sun  = 91,377,000 miles

            Difference in Mean and Max                 =   1,579,800 miles

                        (or 1.67% eccentricity)

The change from 360 to 365.24 days is a 1.46% change in the circumference/radius of the Earth’s orbit.  This corresponds to a change in the radius of 1,353,044 miles.  Considering that this change is within the current eccentricity, this may very well have been the case. 

Times do indeed change!


 John Martineau has succinctly described a bit of “Calendar Magic”, in which discoveries by Robin Heath “has revealed simple geometrical and mathematical tools that suggest order and form within the Sun-Moon-Earth system.  Imagine we want to discover the number of full moons in a year (somewhere between twelve and thirteen).  Draw a circle, diameter thirteen, with a pentagram inside.  Its arms will then measure 12.364, the number of full moons in a year.” [to an accuracy of 99.95%] [1] 

An even more accurate method is to draw a triangle with sides of 5, 12, and 13.  If the 5 side is subdivided into the harmoic of 2:3, then the 3, 12 right triangle will have a side of 12.369, the number of full moons in a year to an accuracy of 99.999%! 

“Incredibly, all of the current major time cycles of the Sun-Moon-Earth system can be expressed as simple combinations of the numbers 18, 19, and the Golden Section.”  The revolution of the Moons Nodes (the two points where the slightly eccentric circles of the Sun’s and Moon’s orbits cross) equals 18.618 years (99.99% accuracy), such that the Saros Eclipse Cycle of 18 years (99.83% accuracy) in part derives.  19 is the number of years in the Metonic Cycle of full moons occurring on a given date (99.99%).  Meanwhile, the eclipse year -- the time it takes for the Sun to return to the same one of the Moon’s nodes, 18.618 days short of a solar year (99.99% accuracy) -- is 18.618 x 18.618 days (99.99% accuracy).  The 12 full moons of the Lunar or Islamic Year equals 18.618 x 19 days (99.82% accuracy), while the 365.242 day solar year equals 18.618 x 19.618 (99.99% accuracy).  Also, 13 full moons equals 18.618 x 20.618 days (99.99% accuracy).  “Coincidence or biophysics?”  [1]


 Finally, before we leave the subject of calendars, we might note that when the Gregorian Calendar was changed in 1582, when some ten days in October were simply deleted (the 21st following directly after the 10th), the days of the week were not changed, i.e. Wednesday, the 10th, was followed the next day by Thursday, the 21st.  There’s no record of any kind that the 7-day week cycle has ever been broken -- i.e. no calendar changes have interrupted the normal progression of the Days of the Week!  It appears the week cycles have run uninterrupted since at least the days of Moses, and possibly longer.

Why do you suppose that is?  Perhaps the 7 Days of the Week have some significance!


2012 A.D.         Paatah         Time         Creating Reality

Forward to:

Mayan Calendar         Gregorian Conspiracies?         Days of the Week



[1]  John Martineau, A Little Book of Coincidence, Wooden Books, Walker & Company, New York, 2001.


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