Chronologies and Julian days

Joseph Justus Scaliger

One of the fundamental concerns of civilized man is the study of the past, natural or human. For this, it is necessary to be able to fix the date on which each event took place. This is the goal of a science called chronology.

If the exact date of an event is known, we can define it by giving the day, month and year in which it took place. For example, we can say that the Second World War began on September 1, 1939. We have no problem with the day and the month, but how are the years numbered? Obviously we must take an origin or starting point that everybody will agree to use.

This dating system causes a curious effect: the numbers assigned to the years after the origin grow towards the future, while the previous years grow towards the past. Thus, the year 2000 of our era came after the year 1000, but the year 2000 B.C.E. came before 1000 B.C.E. (see below the meaning of these acronyms). The years prior to the origin work as negative numbers.

Proposals for a reform of the calendar

As we saw in the previous post in these threads, the Gregorian calendar is practically perfect in terms of the duration of the year, since its error is about three days every ten thousand years, so we won’t have to worry about introducing new corrections until about the year 3500.

However, the calendar also affects the distribution of the year in months, weeks and days; and there, our calendar has some drawbacks: first, the months have variable durations; second, the week and the year do not keep pace: an ordinary year of 365 days contains 52 weeks and one day; a leap year, 52 weeks and two days. Therefore, the position in the week of every day of the month varies from year to year. For instance, July 1st 2020 was a Wednesday; the same date in 2021 will be a Thursday; in 2022, a Friday; in 2023, a Saturday; and in 2024, a Monday. The leap is one day in normal years and two days in leap years for all days after February 29th, and in the following year for days before that date. That is the reason for the English name leap year, for the succession of the days of the week for a given date leaps in those years.

The main consequence is this: we cannot have a unique calendar, valid for every year. The cycle of the days of the week is repeated with a periodicity of 28 years (the product of the seven days of the week by the four leap year cycle), but in fact there are just fourteen different calendars: seven for normal years, seven for leap years. In addition, it’s difficult to know, without consulting a calendar, on which day of the week falls a certain date. This is annoying, especially in a world as copious in commercial and administrative activities as ours. Wouldn't it be possible to avoid it?

Modern attempts to reform the calendar go in that direction. In 1954, the UN adopted a resolution, at the proposal of the Indian Union, in which all member countries were asked to study the possibility of reaching an agreement to universally adopt a calendar reform that would affect the division of the year in months and weeks. Two proposals received the attention of the international organization. The first, the international fixed calendar, divides the year into thirteen months of 28 days, plus a supernumerary day (two, in the case of leap years), which would not occupy a place in the week. The names of the months would be the same as now, except for the additional month, called sol, which would be located between June and July. All months would be identical, for they’d cover four exact weeks, and all would start on Sunday. We would have a unique calendar, valid for every month and every year: the one in the following table. The extra day, the year end day, would be placed between Saturday, December 28th and Sunday, January 1st of the following year. The other extra day in leap years would be located between Saturday June 28th and Sunday Sun 1th. This calendar has a drawback: the thirteen months of the year don’t distribute well between the four seasons: each season would last three months and one week.

S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28

International fixed calendar

The world calendar avoids this problem by dividing the year into twelve months, three per season, with the same names as the current months. The three months of each quarter would last, respectively, thirty-one, thirty, and thirty days. Each quarter would consist of thirteen weeks (ninety-one days) and would always start on a Sunday. In this case, the quarter calendar in the following table would apply to all quarters and all years. The first month of the table would apply to January, April, July and October. The second, to February, May, August and November. The third, to March, June, September and December. The additional day that would complete the 365 of the ordinary years, the world day, would be placed between Saturday, December 30th and Sunday, January 1st of the following year. The extra day of leap years would be placed between Saturday June 30th and Sunday July 1st.

The main difficulty to reach an agreement for a reform of the calendar has a religious origin: Jews, Adventists and Seventh-day Baptists oppose breaking the strict succession of the days of the week with the insertion of extra days, which would affect the interval between two consecutive Sabbaths, for them untouchable. The Catholic Church and many Protestant churches, on the other hand, don’t seem to have a problem to accept the change. Since these proposals were made, 66 years ago, nothing has been done. Change does not appear to be imminent.

D	L	M	X	J	V	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31

D	L	M	X	J	V	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30

D	L	M	X	J	V	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30

World calendar

The same post in Spanish

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Thematic Thread on Science and History: Previous Next

Manuel Alfonseca

The Gregorian calendar

Roger Bacon

After the fall of the Western Roman Empire, the Julian calendar remained in force for more than a millennium. Although very approximate, it was not perfect. The duration it assigned to the year was 365.25 days, while its actual duration is 365.2421988... days. Consequently, the error made is 0.0078011... days per year, about 11 minutes and 14 seconds, which may seem small, but over a thousand years, several days are accumulated. The error amounts to approximately one day every 128 years, or about three days every 400 years.

In the 13th century, since the Council of Nicaea, the accumulated error was equal to eight days, so the spring equinox no longer fell on March 21, but took place on the 13th of the same month. The English philosopher and scientist Roger Bacon noticed the error. In 1263, he wrote to Pope Urban VII explaining the problem. However, although Bacon's project had the support of his successor, Pope Clement IV, the time was not conducive to reforms: the Holy Roman-Germanic Empire of the Hohenstaufen had collapsed. The second half of the 13th century is characterized, in central Europe, by factional fights: Guelphs and Ghibellines in Italy. Under these conditions, no reform of the calendar was undertaken. Two centuries later, the attempts of the German scholar Nicholas of Cusa and the German astronomer Regiomontanus were also unsuccessful.

The Roman calendar

Commemorative coin in honor of
Numa Pompilius

According to Plutarch, the Roman calendar was established by the second king of Rome, Numa Pompilius (753-674 BC), who at first divided the year into ten months, beginning in March, and gave numerical names to the fifth to tenth months, but later added two extra months (January and February), and moved the beginning of the year to January 1st. The months of the early Roman calendar, therefore, were these: Ianuarius, Februarius, Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November and December. It will be noted that, by adding two months at the beginning, the numbers of the fifth to tenth months became seventh to twelfth, but the names were already fixed and nobody bothered to correct them and adapt to the new situation. Plutarch comments on the origin of the month names:

The first month, consecrated by Romulus to Mars, was called Martius, and the second Aprilis, named after Aphrodite, who is Venus, because in this month sacrifices are made to this Goddess... The next month is called Maius, after Maia, as it is devoted to Mercury [son of Maia]; and Iunius is named after the goddess Juno. But there are some who argue that they take their denomination from the oldest and the youngest; because the eldest are called maiores, and the youngest iuniores... The first, Ianuarius, comes from Janus [the god of the doors].

The Roman months were lunar, alternating 28 and 29 days. As twelve lunar months fall short of the year by more than 11 days, from time to time an additional month was added (the thirteenth month), but a regular system was not established for the addition, as they did in Babylon and Greece. The decision to add the additional month was taken by the pontifex maximus, the main religious authority. But this position was political and fell under the party game, which was especially virulent in the last years of the republic. As the political magistracies lasted a year, the additional month was inserted when the pontifex wished to prolong the government of the party holding power, and omitted it when the magistrates belonged to the opposite party. The result was chaotic. By mid-first century B.C., the total error amounted to eighty days, almost a season.

Dating the crucifixion of Jesus Christ

Christ crucified, wood carving
by Manuel Alfonseca Santana

During their deportation in Babylon, the Jewish people adopted a lunar Babylonian calendar and took it with them at their return to Palestine. Ordinarily their year consisted of twelve lunar months, but as this made them lose on average eleven days every year against the solar cycle, occasionally it was necessary to introduce an intercalary month, thus some of their years had thirteen months.

At the beginning of our era there was no rigid rule for the proclamation of the intercalated months. Every year the Sanhedrin (the Jewish Supreme Court) decreed whether or not an extra month would be intercalated. For this they used several criteria, first of all that the Passover celebration had to take place after the spring equinox, but if the crop had been very bad and the first fruits, to be offered in that festivity, were not mature, or if the sacrificial lambs had not grown enough, the council could decide to insert a new month, delaying a full cycle the celebration of the Passover.