Guess the Most Stable and Predictable Calendar of the World?

Our life is governed by the Sun as regulator of day light and not governed by the stars. A day is the time measure for Earth to rotate once on its axis. It is not meant an equivalent of 360 degree as measured with reference to a particular star, like moon, (a “sidereal” day). The acceptance of Gregorian calendar was not easy for most of the rulers of the time. Omitting 10 days from the calendar resulted lot of confusions and difficulties for the international travelers, transactions of amounts, rents and change in planed actives, resulted in number of disputes among the people, latter resolved by the courts.

In fact the interval used is the mean solar day: the actual solar day vary throughout the year, some are shorter than 24 hours and other longer, by up to 28 second- this shows how some days seem to drag! The Earth has to rotate through 360 degree for a star to appear on the same meridian. But the earth moves round the Sun, so the Earth has to rotate an extra degree or two for the sun to cross the same meridian on successive days.

Explaining a Month

The month and year are not simple multiples of the day, and neither are they themselves commensurable. The Earth’s movement around the Sun, one solar day corresponds to a rotation of about 3610, and it is this that determines the “day” which we define as 24 hours. The “month” in which most of the people are interested is not the simple orbital time of moon, which averages about 27.32 days, but the more readily observed period from, say full Moon to full Moon (the synodic month), which averages 29.530 587 9 days always.

Cycle of an Year

While describing the cycle of “year”, again we have to be careful as it brings changes of seasons for us. The Earth complete its one orbit of the Sun exactly in 365.356 360 042 days (a sidereal year); but we are more interested in the year as measured by the seasons, which is not the same. You know why? Because the Earth is slowly precessing, its equatorial plane changes, and so therefore, do the points where the Sun appears to cross the equator. The time between successive Spring equinoxes, which gives us more important tropical year, turns out to be 365.242 198 79 days, about 20 minute shorter than the sidereal year and this is understandable.

Hijra Calendar as the Most Accurate Depiction of Time Universe

The best surviving example of highly stable and predictable system based on the lunar (Moon) month is the calendar of Islam called Hijra Calendar.

The basic year in this calendar consists of 12 months alternating in length between 30 and 29 days. However, the last month Dul Hija (Zulhig) is observed to be given an extra day in 11 year out of each 11 years out of each 30-years cycle. This increases the average length of the Islamic month from 29.50 days to 29.530 5 days-only about 8 second less than the average synodic month.

In fact, Hijra calendar entirely disregards the solar year, so that the seasons move right through the calendar in about 33 years tropical years. This calendar has its starting point which begin with the migration of Prophet of Islam Muhammad (may peace be upon him) from Mecca in AD 622. Because the year in Islamic calendar averages only about 354.33 days, the dates of New Year and other Islamic festivals change relentlessly from year to year in solar calendars such as Gregorian. Thus for example, the dates of Islamic New Years (1st day of month of Muharram) 1437 A.H. and 1438 A.H. are 14 October, 2015 and 3 October 2016 respectively then 1439 A.H. would be 22 September 2017.

Luni-Solar Calendars

Renditions of Luni-solar calendars, which attempts to combine lunar months with solar years, were devised as long as 3000 B.C. by the Mesopotamians, probably by adapting earlier strictly lunar systems.

The basic year of 12 lunar months is, as we have seen, about 11 days shorter than the tropical year, so to correct for this short-fall an additional month is inserted periodically. A possible algorithm for such additional month added in seven years out of every 19 years, the average calendar year would only about six minute longer than tropical year. This was a basis of several Babylonian calendars and of their Greek derivatives. A close relative of these is the Jewish calendar which has 12 months of 29 or 30 days with an additional month added to year 3, 6, 8, 11, 17 and 19 in each 19-years cycle. 

Again, because of the variation between 12 and 13 month years, the seasonal points (equinoxes, solstices) varying date by up to 15 days, as does the start of the Jewish New Year, on the Gregorian calendar. Thus for example, the dates of Jewish New Years (1st day of month of Nissan) 5775 and 5776 are 21 March, 2015 and 9 April , 2016 respectively and 5777 would be 28 March, 2017. 

The Julian Calendar

The Julian calendar from which present Gregorian calendar was introduced had difficulties due to Roman version of the luni-solar system. The Pre-Julian year consisted of 12 “lunar” months, four of 31 days, seven with 29 days and one with 28 days, counting 355 days a year (the then Romans deliberatively avoided 30 as unlucky number to count a month in the calendar). To bring it in to line with the solar year, an additional month was inserted every other year, with a length alternating in between 22 and 23 days. In fact there is evidence that this was done by shortening the February in every second year to 24 or 23 days, and inserting the "intercalary" month of 27 days before the beginning of March.

Got it, well? It is almost embarrassing to relate that this left the pre-Julian with an average year of 366 ? days-an inaccuracy of about one day which demanded yet more occasional “adjustment”. 

In fact, from 200 B.C. onwards the calendar descended gently in to chaos, so that by the time of Julius Caesar it was several weeks out of phase with the seasons. Then, Julius sought the help of Sosigenes who was an Gastronomist from Alexandria, charged to compile new system. 

Julian calendar was opted on 1 January, 45 B.C., with the reforms introduced represented radical changes, discarding all the lunar features in favour of a purely solar calendar. An algorithm was that in every cycle of four years, three normal years of 365 days were followed by a fourth “leap” year which had an extra day. January, March, May, July (Quintilis), September and November were given 31 days, the remaining months' 30 days, except February which had 29 days (the extra day was introduced in the leap years by duplicating 24 February- the sixth day before March ends - hence the surviving description of leap years as “bissextile“ years.

Use of 365.25 day year as an approximation lead to an error of one day in each 128 years, noticeable by the slow drift in the date of the Spring Equinox. Thus over the period and till 15th century, the drift had amounted to about 13 days. Pope-Sixtus IV- who in 1474 commissioned Regiomontanus, an astronomer to put forward improvements to the calendar. He started this task but due to his assassination task could not be completed. During next century, Christopher Schlussel (Calvius) devised a new calendar, and in march 1582 Pope Gregory XIII accepted and promulgated Calvius’s proposals to take care what to do and when to do when seasons move through the year.

The Gregorian Calendar

The Gregorian calendar differs from the Julian by omitting three days after each 400 years, to bring average length of calendar year down to 365.242 5 days, compared with 365.242 2 day tropical year. This reform was enough to maintain calendar with an inaccuracy of only one day in 3300 years. Three days were omitted by ruling that all years divisible by 100 but not by 400 should be normal years, and not leap years as the Julian rule would have made them. Thus the years 1700, 1800 and 1900 were not leap years and neither will be 2100, 2200 and 2300. Thus the year 2000 remained as 366-day year.

In the year 1582 implementation of New Gregorian calendar resulted to correct the over due “seasonal drift” due to Julian inaccuracy had allowed, it was decreed that 1o days should be omitted at once, from the year 1582, and in that year, practically, 4 October was followed by 15 October. This brought the spring equinox in 1583 and subsequent years back to around 21 March- the date on which it fell in AD 325, the year of General Council of Nice (Nicea, Nicaea).

New Gregorian Calendar

The dates of Easter and other movable feast are the most confusing feature of Gregorian calendar because of retaining the luni-solar rule for determining the date of Easter, in an otherwise purely solar calendar. Easter is always the first Sunday after the Full Moon which happens upon, or is next after the 21st day of March every year; and if the Full Moon happens on Sunday, Easter is the Sunday after. This rule, which means Easter Day can be as early as 22 March or as late as 25 April.

Full Moon occurrence is highly predictable on the sky, which is used for predicting the Easter Day for any future year.

The Great Britain adopted the New Gregorian calendar through a Bill passed with out any opposition on 18 March, 1751. Macclesfield, President of Royal Society in the following year, had furnished most of the astronomical information, sported the second reading of Bill, reprinted full in Hansard, is a good summary of calendar construction and its problem. The New Gregorian calendar was not finally adopted in Russia, until after the revolution, so that the event took place on 26 October in the Julian year, corresponding to 7 November.   

There have been occasional moves to reform the present Gregorian calendar partly because its month vary in length and year is not divisible in equal quarters, particular dates fall on different day of the week from year to year. Most reform proposals are based on a 364-day year with provision of extra “free” day-two in leap years. One scheme would involve 13 months of 28 days, which would mean that the calendar for one month would apply for all months.

United Nations Debated World Calendar

Another suggested World Calendar, divides the 364-day into four equal three-month quarters, each of which would begin on Sunday. The additional day each year would be an extra Saturday, W December, at the end of the year, and in leap years there would also be an additional Saturday, L June, at the end of June. United Nations debated this World Calendar in 1956, but it was not adopted. In the United Nations, the issue of world calendar reform was formally raised by India with the lodgement of a document in 1953. Replies from various delegations expressed against calendar reform because of the undesirable effect it would have on many aspects of religious life--the observance of Sabbath in particular.

The Holy See (Vatican) did not present its position on the question even though decision of Catholic countries were dependent on its stand. Eventually, discussion on the issue was adjourned sine die (without fixing a day for future action or meeting) by the UN's Economic and Social Council during its 905th meeting on 20 April 1956. Since then, there has not been any worldwide initiative to reform the existing Gregorian calendar.

The French Republic in 1792 also developed their own Revolutionary Calendar of 12 months in which they attempted to decimalize time to make subsequent divisions strikingly very novel. Newly named 12 months consisted three weeks of 10 days, each day was divided in 10 hours, each hour consisting 100 minutes and 100 seconds in a minute.

To cope with the solar year, remaining five (or six) days were inserted as special holidays, the Sansculottides, at the end of each year, which fell in September of Gregorian calendar. The decimalized day survived for just two years, and the Revolutionary Calendar, begun in 1793, lasted until 1 January, 1806 when Napoleon-I reinstated the Gregorian system.

Modified Julian Day

Besides all above there is also a calendar called Modified Julian Day (MJD). The Modified Julian Day (MJD) is an abbreviated version of the old Julian Day (JD) dating method which has been in use for centuries by astronomers, geophysicists, chronologists, and others who needed to have an unambiguous dating system based on continuing day counts.

MJD is the integer assigned to a whole solar day in the day count starting from noon. With its origin 0000 MJD on 17 November, 1858 today on 16 January, 2017 it is 57769 MJD. On 1 January, 1900 it was 15022 MJD and 57754 MJD held on 1 January, 2017. This calendar is also used for noting historical events and purely meant for scientific dates when working with Universal Coordinated Time Scale (UTC) and Atomic Time Scale (TAI). 

Hijra calendar, without any doubt, is most accurate and highly stable calendar.