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

Thematic Thread on Time: Previous Next

Thematic Thread on Science and History: Previous Next

Manuel Alfonseca

Is there a fifth force in Nature?

The standard model of particle physics recognizes the existence of four fundamental forces (their correct name is interactions):

• Gravitation: Newton called thus the force of attraction between any two masses at a distance. For Einstein, according to General Relativity, gravitation is the curvature of space as a consequence of the presence of a mass, which affects the movement of nearby masses. This force, which is always attractive, has an infinite range, although its effect decreases in inverse ratio of the square of the distance, and is the weakest of the four, but its effect is dominant at cosmic and planetary distances, as well as on the Earth's surface.

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.

The mystery of Planet X

Urbain Le Verrier

In 1845, some 60 years after the discovery of planet Uranus, the French astronomer Urbain Le Verrier tried to solve the problem posed by the discrepancies of a few minutes of arc between the observed orbit of this planet and the predictions made by applying Newton’s theory. Le Verrier thought the problem could be solved if there were another unknown planet beyond Uranus. On September 23, 1846, the German astronomer Galle discovered this new planet, which received the name of Neptune. The success of the prediction became top-notch scientific news and boosted Newton's theory of gravitation.

For decades, some unexplained irregularities in the orbits of Uranus and Neptune were attributed to the existence of another possible planet, located even further from the sun. In 1906, Percival Lowell undertook, at his private observatory in Falstaff, Arizona, a search program for the so-called Planet X, not because of its number in the list of planets (which would be 9), but because the letter X traditionally represents the unknown in a mathematical expression. In 1930, after Lowell's death, Clyde Tombaugh discovered Pluto, which came to be considered planet number 9, but as its small mass was insufficient to explain the discrepancies, the X in the name of planet X automatically came also to mean number 10, in accordance with the meaning of that letter in the Roman numeral system.

In 1987, the search for planet X was still unsuccessful. From the analysis of the orbits of Pioneer X and XI, it was deduced that none of those space capsules had been subject to the influence of the mysterious planet X, so if this planet existed, it must be in a very elliptical orbit, inclined at least by 30º with respect to the plane of the trajectory of the two space capsules.

In 1992, it was proposed that planet X might not be a planet, but a swarm of bodies the size of Pluto (1,000 at least). In 1999, the analysis of the orbits of some comets gave rise to the proposal of the existence of a planet the size of Jupiter (or even larger) 25,000 astronomical units from the sun. An astronomical unit (1 AU) is the distance from Earth to the sun. This possibility was later rejected when NASA's WISE satellite ruled out the existence of an unknown body the size of Saturn less than half a light-year from the sun (about 30,000 AU). Nor can there be any Jupiter-sized body less than 1.5 light-years away (90,000 AU).

In 2001, the analysis of the orbit of Comet 2000 CR105 gave rise to the proposal of the existence of an unknown planet, intermediate in size between Mars and Earth, at the distance of the Kuiper Belt, an accumulation of objects beyond Neptune, between 30 and 55 astronomical units of the sun.

Pluto

On August 24, 2006, the International Astronomical Union decided that Pluto would no longer be considered a planet, moving it to the category of dwarf planet or plutoid, together with other bodies, such as Ceres, the largest of the asteroids, and Eris, more massive than Pluto and located farther away. With this change, automatically, planet X became known again with the alternative name of planet 9, and the double meaning of the letter X was no longer applicable.

Starting in 2016, the analysis of the orbits of several recently discovered bodies in the Kuiper belt and some simulations, suggested the idea that there could be an unknown planet up to 10 times larger than Earth, or another body of equivalent mass, at 500 or 600 AU from the sun. In comparison, Neptune's distance from the sun is less than 30 astronomical units, and its mass about 17 times that of Earth.

From Investigación y Ciencia, April 2016

The latest theory suggests that planet 9 might not be a planet, but a primordial black hole about 10 times more massive than Earth, located about 500 AU from the sun, which would have been formed shortly after the Big Bang, and which would be much more difficult to detect than a planet. However, there are proposals to locate its exact position, such as one, made in 2020, which would consist of sending a fleet of spacecraft weighing about 100 grams each, accelerated by laser beams to a speed of 300 km/second, with which they could reach that distance in about 10 years. They would send radio pulses that would make it possible to detect if the small probes had been subjected, somewhere in their trajectory, to the attraction of an unknown body. Edward Witten, one of the authors of the proposal, is skeptical and says that it is far from clear that this approach is practical, while other researchers, such as Mike Brown, assert that there is zero reason to think that Planet Nine is a black hole.

Meanwhile, there are other options. A theory dating back to 1984 argues that the sun could be part of a binary star system, and that its companion (nicknamed Nemesis, the Greek goddess of revenge) would have to move through an extremely elongated orbit that would take it to a maximum distance of the sun of 88,000 astronomical units (more than a light-year). When the star, which could be a brown dwarf (which would make it very difficult to locate), approached the sun once every 26 million years, its influence on the Oort comet cloud would cause many of them to rush over the inner solar system. Their impacts with the Earth would cause massive extinctions, similar to that at the end of the Cretaceous period that put an end to dinosaurs. This theory lost weight when it was found that the 26 million-year period of mass extinctions could, after all, be a statistical artifact.

The same post in Spanish

Thematic Thread on Space Exploration: Previous Next

Manuel Alfonseca

Pandemics and scapegoats

Emperor Marcus Aurelius

Human beings have an irresistible tendency to blame others for our misfortunes and our mistakes. In fact, this is a symptom of low maturity, very clear in children, who when they are caught red-handed doing something they shouldn’t, they always try to justify themselves by blaming someone else. But the trend is so widespread that it applies not just to children, but to most human beings.

In the particular case of pandemics, this is seen quite clearly. Epidemic diseases were almost unknown before the invention of cities, which took place some 10,000 years ago. But for a pandemic to be possible (an epidemic affecting a considerable part of the world), the world had to wait until there were great empires, with many internal and external commercial relations.

Literature and Science: Huxley and Heisenberg

Aldous Huxley

In 1963, the year of his death, Aldous Huxley published an essay titled Literature and Science. In it, he raises the existence of two different specialized languages, literary and scientific, different from the vulgar language, each of which is directed towards a specific objective:

• The purpose of literature is to describe, in the best possible way, man's most private experiences, especially those that deal with our feelings. To do this, it creates a specific language, where the ambiguity of words is the fundamental element giving strength. For Huxley, the term literature can be applied to all possible forms of the art of writing: poetry, drama, novel and essay, whose relationship with science he analyzes successively.
• Science, on the contrary, seeks to univocally describe the public (or less private) experiences of man, those that have to do with objective reality. To do this, the scientific language must be as far as possible free of ambiguity. Each term must have a univocal and unambiguous meaning. In the best case (as in physics) scientific language can be reduced to mathematical formulas.