Search This Blog

Sunday, November 21, 2021

History of calendars

From Wikipedia, the free encyclopedia

The history of calendars, that is, of people creating and using methods for keeping track of days and larger divisions of time, covers a practice with ancient roots.

Archeologists have reconstructed methods of timekeeping that go back to prehistoric times at least as old as the Neolithic. The natural units for timekeeping used by most historical societies are the day, the solar year and the lunation. Calendars are explicit schemes used for timekeeping. The first historically attested and formulized calendars date to the Bronze Age, dependent on the development of writing in the ancient Near East. The Sumerian calendar was the earliest, followed by the Egyptian, Assyrian and Elamite calendars.

A larger number of calendar systems of the ancient Near East appear in the Iron Age archaeological record, based on the Assyrian and Babylonian calendars. This includes the calendar of the Persian Empire, which in turn gave rise to the Zoroastrian calendar as well as the Hebrew calendar.

Calendars in antiquity were usually lunisolar, depending on the introduction of intercalary months to align the solar and the lunar years. This was mostly based on observation, but there may have been early attempts to model the pattern of intercalation algorithmically, as evidenced in the fragmentary 2nd-century Coligny calendar. Nevertheless, the Roman calendar contained very ancient remnants of a pre-Etruscan 10-month solar year.

The Roman calendar was reformed by Julius Caesar in 45 BC. The Julian calendar was no longer dependent on the observation of the new moon but simply followed an algorithm of introducing a leap day every four years. This created a dissociation of the calendar month from the lunation.

In the 11th century in Persia, a calendar reform led by Khayyam was announced in 1079, when the length of the year was measured as 365.24219858156 days. Given that the length of the year is changing in the sixth decimal place over a person's lifetime, this is outstandingly accurate. For comparison the length of the year at the end of the 19th century was 365.242196 days, while today it is 365.242190 days.

The Gregorian calendar was introduced as a refinement of the Julian calendar in 1582, and is today in worldwide use as the "de facto" calendar for secular purposes.

Etymology

The term calendar itself is taken from the calends, the term for the first day of the month in the Roman calendar, related to the verb calare "to call out", referring to the calling or the announcement that the new moon was just seen. Latin calendarium meant "account book, register", as accounts were settled and debts were collected on the calends of each month.

The Latin term was adopted in Old French as calendier and from there into Middle English as calender by the 13th century. The spelling calendar is from Early Modern English.

An alternative hypothesis connects "calendar" with koledari in Slavic, pre-Christian tradition, which was later incorporated into Christmas. Kolo means "circle, cycle" and dar means "a gift".

Equinox seen from the astronomical calendar of Pizzo Vento at Fondachelli-Fantina, Sicily

Prehistory

A number of prehistoric structures have been proposed as having had the purpose of timekeeping (typically keeping track of the course of the solar year). This includes many megalithic structures, and reconstructed arrangements going back far into the Neolithic period.

In Victoria, Australia, a Wurdi Youang stone arrangement could date back more than 11,000 years, with some estimates dating it to be older than 20,000 years. This estimate is based on the inaccuracy of the calendar, which is consistent with how the Earth's supposed orbit is thought to have changed during that time. The site is found near the world's oldest known site of permanent aquaculture.

A ceramic artefact from Bulgaria, known as the Slatino furnace model, has been pronounced by local archaeologists and media to be the oldest known calendar representation, a claim not endorsed in mainstream views.

A mesolithic arrangement of twelve pits and an arc found in Warren Field, Aberdeenshire, Scotland, dated to roughly 10,000 years ago, has been described as a lunar calendar and was dubbed the "world's oldest known calendar" in 2013.

The Oldest European calendar other than the one found in Scotland, is the one found near to Vukovar in modern-day Croatia. It is a ceramic vessel bearing inscribed ideograms of celestial objects.

Ancient Near East

The ancient Sumerian calendar divided a year into 12 lunar months of 29 or 30 days. Each month began with the sighting of a new moon. Sumerian months had no uniform name throughout Sumer because of the religious diversity. This resulted in scribes and scholars referring to them as "the first month", "the fifth month", etc. To keep the lunar year of 354 days in step with the solar year of 365.242 days an extra month was added periodically, much like a Gregorian leap year. There were no weeks in the Sumerian calendar. Holy days and time off from work were usually celebrated on the first, seventh and fifteenth of each month. In addition to these holy days, there were also feast days which varied from city to city.

Antiquity

Babylonia and Persia

Although the earliest evidence of Iranian calendrical traditions is from the second millennium BC, predating the appearance of the Iranian prophet Zoroaster, the first fully preserved calendar is that of the Achaemenids. Throughout recorded history, Persians have been keen on the idea and importance of having a calendar. They were among the first cultures to use a solar calendar and have long favoured a solar over lunar and lunisolar approaches. The sun has always been a symbol in Iranian culture and is closely related to the folklore regarding Cyrus the Great.

Old Persian calendar

Old Persian inscriptions and tablets indicate that early Iranians used a 360-day calendar based on the solar observation directly and modified for their beliefs. Days were not named. The months had two or three divisions depending on the phase of the moon. Twelve months of 30 days were named for festivals or activities of the pastoral year. A 13th month was added every six years to keep the calendar synchronized with the seasons.

Zoroastrian calendar

The first calendars based on Zoroastrian cosmology appeared in the later Achaemenid period (650 to 330 BC). They evolved over the centuries, but month names changed little until now.

The unified Achaemenid Empire required a distinctive Iranian calendar, and one was devised in Egyptian tradition, with 12 months of 30 days, each dedicated to a yazata (Eyzad), and four divisions resembling the Semitic week. Four days per month were dedicated to Ahura Mazda and seven were named after the six Amesha Spentas. Thirteen days were named after Fire, Water, Sun, Moon, Tiri and Geush Urvan (the soul of all animals), Mithra, Sraosha (Soroush, yazata of prayer), Rashnu (the Judge), Fravashi, Bahram (yazata of victory), Raman (Ramesh meaning peace), and Vata, the divinity of the wind. Three were dedicated to the female divinities, Daena (yazata of religion and personified conscious), Ashi (yazata of fortune) and Arshtat (justice). The remaining four were dedicated to Asman (lord of sky or Heaven), Zam (earth), Manthra Spenta (the Bounteous Sacred Word) and Anaghra Raocha (the 'Endless Light' of paradise).

Modifications by Parthians, Ardashir I, Hormizd I, Yazdgerd III

The Parthians (Arsacid dynasty) adopted the same calendar system with minor modifications, and dated their era from 248 BC, the date they succeeded the Seleucids. Their names for the months and days are Parthian equivalents of the Avestan ones used previously, differing slightly from the Middle Persian names used by the Sassanians. For example, in Achaemenid times the modern Persian month 'Day' was called Dadvah (Creator), in Parthian it was Datush, and the Sassanians named it Dadv/Dai (Dadar in Pahlavi).

When in April of AD 224 the Parthian dynasty fell and was replaced by the Sasanid, the new king, Ardashir I, abolished the official Babylonian calendar and replaced it with the Zoroastrian. This involved a correction to the places of the gahanbar, which had slipped back in the seasons since they were fixed. These were placed eight months later, as were the epagemonai, the 'Gatha' or 'Gah' days after the ancient Zoroastrian hymns of the same name. Other countries, such as the Armenians and Choresmians, did not accept the change.

The formation of the current Persian calendar in the 11th century

Toghril Beg, the founder of the Seljuq dynasty, had made Esfahan the capital of his domains and his grandson Malik-Shah was the ruler of that city from 1073. An invitation was sent to Khayyam from Malik-Shah and from his vizier Nizam al-Mulk asking Khayyam to go to Esfahan to set up an Observatory there. Other leading astronomers were also brought to the Observatory in Esfahan and for 18 years Khayyam led the scientists and produced work of outstanding quality. During this time Khayyam led work on compiling astronomical tables and he also contributed to calendar reform in 1079.

Cowell quotes the Calcutta Review No 59:

When the Malik Shah determined to reform the calendar, Omar was one of the eight learned men employed to do it, the result was the Jalali era (so called from Jalal-ud-din, one of the king's names) – 'a computation of time,' says Gibbon, 'which surpasses the Julian, and approaches the accuracy of the Gregorian style.'

Khayyam measured the length of the year as 365.24219858156 days. Two comments on this result. Firstly it shows an incredible confidence to attempt to give the result to this degree of accuracy. We know now that the length of the year is changing in the sixth decimal place over a person's lifetime. Secondly it is outstandingly accurate. For comparison the length of the year at the end of the 19th century was 365.242196 days, while today it is 365.242190 days.

Classical Greece

The Greeks, as early as the time of Homer, appear to have been familiar with the division of the year into the twelve lunar months but no intercalary month Embolimos or day is then mentioned. Independent of the division of a month into days, it was divided into periods according to the increase and decrease of the moon. Thus, the first day or new moon was called Noumenia. The month in which the year began, as well as the names of the months, differed among the states, and in some parts even no names existed for the months, as they were distinguished only numerically, as the first, second, third, fourth month, etc.

The ancient Athenian calendar was a lunisolar calendar with 354-day years, consisting of twelve months of alternating length of 29 or 30 days. To keep the calendar in line with the solar year of 365.242189 days, an extra, intercalary month was added in the years: 3, 6, 8, 11, 14, 17, 19 of the 19-years Metonic cycle. See About the structure of the Attic Calendar The Athenian months were called Hekatombion, Metageitnion, Boedromion, Pyanepsion, Maimakterion, Poseidon, Gamelion, Anthesterion, Elaphebolion, Munychion, Thargelion, and Skirophorion. The intercalary month usually came after Poseidon, and was called second Poseidon. See also: Athenian Calendar. A reconstruction of the Attic Calendar is given by Academy of Episteme.

In addition to their regular, "festival" calendar, the Athenians maintained a second, political calendar . This "conciliar" calendar divided the year into "prytanies", one for each of the "phylai", the subdivisions of Athenian citizens. The number of phylai, and hence the number of prytanies, varied over time. Until 307 BC, there were 10 phylai. After that the number varies between 11 and 13 (usually 12). Even more confusing, while the conciliar and festival years were about the same length in the 4th century BC, such was not regularly the case earlier or later. Documents dated by prytany are frequently very difficult to assign to a particular equivalent in the Julian calendar.

The table of Greek Olympiads, following the four-year cycles between the Olympic Games from 1 July 776 BC, continued until the end of the 4th century AD. The Babylonian Era of Nabonassar, beginning on 26 February 747 BC, was used by the Greeks of Alexandria. It was later known in the Middle Ages from the works of Ptolemy.

Hellenistic period

The Greek calendars were greatly diversified by the Hellenistic period, with separate traditions in every Greek state. Of primary importance for the reconstruction of the regional Greek calendars is the calendar of Delphi, because of the numerous documents found there recording the manumission of slaves, many of which are dated both in the Delphian and in a regional calendar.

The Macedonian Era of the Seleucids, which began with the conquest of Babylon by Seleucus Nicator in 312 BC. It became widely used in the Levant. The Jews knew it as the "era of contracts", and used it in Europe until the 15th century.

The Roman Republican calendar numbered years based on the sitting consuls. References to the year of consulship were used in both conversation and official records. Romans from the same family often had the same praenomen, which sometimes makes it difficult to distinguish them, and there were two consuls at any one time, each of whom might sometimes hold the appointment more than once, meaning that it was (and is) necessary to be well educated in history to understand the references. The Romans had an eight-day week, with the market-day falling every eight days. It was called a nundinum or 'nine-day' in inclusive counting.

Most of the regional Hindu calendars are inherited from a system standardized in classical Hindu astronomy as adopted via Indo-Greek transmission in the final centuries BC, and reformed by Gupta era astronomers such as Āryabhaṭa and Varāhamihira.

China

Before the Spring and Autumn period (before 770 BC), the Chinese calendars were solar calendars. In the so-called five-phase calendar, the year consists of 10 months and a transition, each month being 36 days long, and the transitions 5 or 6 days. During the Warring States period (~475–220 BC), the primitive lunisolar calendars were established under the Zhou Dynasty, known as the six ancient calendars (simplified Chinese: 古六历; traditional Chinese: 古六曆). The months of these calendars begin on the day with the new moon, with 12 or 13 months (lunations) in a year. The intercalary month is placed at the end of the year. In Qin China, the Qin calendar (simplified Chinese: 秦历; traditional Chinese: 秦曆) was introduced. It follows the rules of Zhuanxu's calendar, but the months order follows the Xia's calendar.

Vedic and Pre-Vedic Era /Ancient India

Timekeeping was important to Vedic rituals, and Jyotisha was the Vedic-era field of tracking and predicting the movements of astronomical bodies in order to keep time, in order to fix the day and time of these rituals, which were developed around the end of 2nd millennium BC as mentioned in "Sathapatha Brahmana". This study was one of the six ancient Vedangas, or ancillary science connected with the Vedas – the scriptures of Hinduism, which was quoted by 5th-century BC scholar Yaska. The ancient extant text on Jyotisha is the Vedanga-Jyotisha, which exists in two editions, one linked to Rigveda and other to Yajurveda. The Rigveda version is variously attributed to sage Lagadha, and sometimes to sage Shuci. The Yajurveda version credits no particular sage, has survived into the modern era with a commentary of Somakara, and is the more studied version.

The Jyotisha text Brahma-siddhanta, probably composed in the 5th century AD, discusses how to use the movement of planets, sun and moon to keep time and calendar. This text also lists trigonometry and mathematical formulae to support its theory of orbits, predict planetary positions and calculate relative mean positions of celestial nodes and apsides. The text is notable for presenting very large integers, such as 4.32 billion years as the lifetime of the current universe.

Water clock and sun dials are mentioned in many ancient Hindu texts such as the Arthashastra. The Jyotisha texts present mathematical formulae to predict the length of day time, sun rise and moon cycles.

The modern Hindu calendar, sometimes referred to as Panchanga, is a collective term for the various lunisolar calendars traditionally used in Hinduism. They adopt a similar underlying concept for timekeeping, but differ in their relative emphasis on the moon cycle or the sun cycle, the names of months and when they consider the New Year to start. The ancient Hindu calendar is similar in conceptual design to the Jewish calendar, but different from the Gregorian calendar. Unlike the Gregorian calendar which adds additional days to the lunar month to adjust for the mismatch between twelve lunar cycles (354 lunar days) and nearly 365 solar days, the Hindu calendar maintains the integrity of the lunar month, but inserts an extra full month according to complex rules, every few years, to ensure that the festivals and crop related rituals fall in the appropriate season.

The Hindu calendars have been in use in the Indian subcontinent since ancient times, and remain in use by the Hindus in India and Nepal, particularly to set Hindu festival dates. Early Buddhist and Jain communities of India adopted the ancient Hindu calendar, later Vikrami calendar and then local Buddhist calendars. Buddhist and Jain festivals continue to be scheduled according to a lunar system in the luni-solar calendar.

Roman Empire

The old Roman year had 304 days divided into 10 months, beginning with March. However the ancient historian Livy gave credit to the second early Roman king Numa Pompilius for devising a calendar of 12 months. The extra months Ianuarius and Februarius had been invented, supposedly by Numa Pompilius, as stop-gaps. Julius Caesar realized that the system had become inoperable, so he effected drastic changes in the year of his third consulship. The New Year in 709 AUC began on 1 January and ran over 365 days until 31 December. Further adjustments were made under Augustus, who introduced the concept of the "leap year" in 757 AUC (AD 4). The resultant Julian calendar remained in almost universal use in Europe until 1582, and in some countries until as late as the twentieth century.

Marcus Terentius Varro introduced the Ab urbe condita epoch, assuming a foundation of Rome in 753 BC. The system remained in use during the early Middle Ages until the widespread adoption of the Dionysian era in the Carolingian period.

In the Roman Empire, the AUC year could be used alongside the consular year, so that the consulship of Quintus Fufius Calenus and Publius Vatinius could be determined as 707 AUC (or 47 BC), the third consulship of Caius Julius Caesar, with Marcus Aemilius Lepidus, as 708 AUC (or 46 BC), and the fourth consulship of Gaius Julius Caesar as 709 AUC (or 45 BC).

The seven-day week has a tradition reaching back to the ancient Near East, but the introduction of the "planetary week" which remains in modern use dates to the Roman Empire period (see also names of the days of the week).

Middle Ages

Christian Europe

Page of a 10th-century calendar from Einsiedeln Abbey (16 March to 9 April)
 
The page for May in the Bedford Psalter and Hours ms. (British Library Add MS 42131, fol. 3r, early 15th century)

The oldest calendar of saints of the Church of Rome was compiled in the mid-4th century, under Pope Julius I or Pope Liberius. It contained both pagan and Christian festivals. The oldest extant manuscript of the early Christian calendar is the so-called Calendar of Filocalus, produced in AD 354. A more extensive martyrology was compiled by Jerome in the early 5th century. Jean Mabillon published a calendar of the church of Carthage made in ca. AD 483. The Anno Domini epoch is introduced in the 6th century. Extant calendars of the early medieval period are based on Jerome's system of numbering of the years of the Metonic cycle, later called the Golden Numbers. A Carolingian-era calendar published by Luc d'Achery is entitled Incipit Ordo Solaris Anni cum Litteris a S. Hieronymo superpositis, ad explorandum Septimanae Diem, et Lunae Aetatem investigandam in unoquoque Die per xix Annos. ("here begins the order of the solar year with the letters placed by Saint Jerome, for the purpose of finding the day of the week and the age of the Moon for any day within [the cycle of] 19 years"). The Leiden Aratea, a Carolingian copy (dated 816) of an astronomical treatise of Germanicus, is an important source for the transmission of the ancient Christian calendar to the medieval period.

In the 8th century, the Anglo-Saxon historian Bede the Venerable used another Latin term, "ante uero incarnationis dominicae tempus" ("the time before the Lord's true incarnation", equivalent to the English "before Christ"), to identify years before the first year of this era. According to the Catholic Encyclopedia, even Popes continued to date documents according to regnal years, and usage of AD only gradually became common in Europe from the 11th to the 14th centuries. In 1422, Portugal became the last Western European country to adopt the Anno Domini system.

The Icelandic calendar was introduced in the 10th century. While the ancient Germanic calendars were based on lunar months, the new Icelandic calendar introduced a purely solar reckoning, with a year having a fixed number of weeks (52 weeks or 364 days). This necessitated the introduction of "leap weeks" instead of the Julian leap days.

In 1267, the medieval scientist Roger Bacon stated the times of full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates. Although a third for 160 of a second remains in some languages, for example Arabic ثالثة, the modern second is further divided decimally.

Rival calendar eras to Anno Domini remained in use in Christian Europe. In Spain, the "Era of the Caesars" was dated from Octavian's conquest of Iberia in 39 BC. It was adopted by the Visigoths and remained in use in Catalonia until 1180, Castille until 1382 and Portugal until 1415.

For chronological purposes, the flaw of the Anno Domini system was that dates have to be reckoned backwards or forwards according as they are BC or AD. According to the Catholic Encyclopedia, "in an ideally perfect system all events would be reckoned in one sequence. The difficulty was to find a starting point whence to reckon, for the beginnings of history in which this should naturally be placed are those of which chronologically we know least." For both Christians and Jews, the prime historical date was the Year of Creation, or Annus Mundi. The Eastern Orthodox Church fixed the date of Creation at 5509 BC. This remained the basis of the ecclesiastical calendar in the Greek and Russian Orthodox world until modern times. The Coptic Church fixed on 5500 BC. Later, the Church of England, under Archbishop Ussher in 1650, would pick 4004 BC.

Islamic calendar

The Islamic calendar is based on the prohibition of intercalation (nasi') by Muhammad, in Islamic tradition dated to a sermon held on 9 Dhu al-Hijjah AH 10 (Julian date: 6 March 632). This resulted in an observationally based lunar calendar shifting relative to the seasons of the solar year.

During the Mughal rule, land taxes were collected from Bengali people according to the Islamic Hijri calendar. This calendar was a lunar calendar, and its new year did not coincide with the solar agricultural cycles. According to some sources, Mughal Emperor Akbar asked his royal astronomer Fathullah Shirazi to create a new calendar by combining the lunar Islamic calendar and solar Hindu calendar already in use, and this was known as Fasholi shan (harvest calendar). According to Amartya Sen, Akbar's official calendar "Tarikh-ilahi" with the zero year of 1556 AD was a blend of pre-existing Hindu and Islamic calendars. It was not used much in India outside of Akbar's Mughal court, and after his death the calendar he launched was abandoned. However, adds Sen, there are traces of the "Tarikh-ilahi" that survive in the Bengali calendar. Some historians attribute the Bengali calendar to the 7th-century Hindu king Shashanka.

Other

The ancient Taichu calendar of China was refined in the medieval period. The Dàmíng Calendar (大明历; 大明曆; 'brightest calendar'), created in the Liang dynasty by Zu Chongzhi, introduced the equinoxes. The use of a syzygy to determine the lunar month was first described in the Tang dynasty Wùyín Yuán Calendar (戊寅元历; 戊寅元曆; 'earth tiger epoch calendar').

The Yuan dynasty (13th/14th century) Shòushí calendar (授时历; 授时曆; 'teaching time calendar') used spherical trigonometry to find the length of the tropical year. This calendar had a 365.2425-day year, identical to the Gregorian calendar.

A number of other epichoric calendars are tentatively reconstructed for the medieval period. Such reconstructions are mostly limited to a list of month names, as is the case with the pre-Christian Germanic calendar as well as with the Bulgar calendar, which was supposedly in use among the Bulgars in the 10th century, as reconstructed from the 15th-century Nominalia of the Bulgarian khans.

Mesoamerica

Of all the ancient calendar systems, the Maya and other Mesoamerican systems are the most complex. The Mayan calendar had two years, the 260-day Sacred Round, or tzolkin, and the 365-day Vague Year, or haab.

A modern pictogram of the Mayan god Ahau, after which the 20th day of the tzolkin cycle was named

The Sacred Round of 260 days is composed of two smaller cycles: the numbers 1 through 13, coupled with 20 different day names: Imix, Ik, Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, Oc, Chuen, Eb, Ben, Ix, Men, Cib, Caban, Eiznab, Cauac, and Ahau. The Sacred Round was used to determine important activities related to the gods and humans: name individuals, predict the future, decide on auspicious dates for battles, marriages, and so on.

The two cycles of 13 and 20 intermesh and are repeated without interruption: the cycle would begin with 1 Imix, then 2 Ik, then 3 Akbal and so on until the number 13 was reached, at which point the number cycle was restarted so 13 Ben would be followed by 1 Ix, 2 Men and so on. This time Imix would be numbered 8. The cycle ended after 260 days, with the last day being 13 Ahau.

The Vague Year of 365 days is similar to our modern calendar, consisting of 18 months of 20 days each, with an unlucky five-day period at the end. The Vague Year had to do primarily with the seasons and agriculture, and was based on the solar cycle. The 18 Maya months are known, in order, as: Pop, Uo, Zip, Zotz, Tzec, Xuc, Yaxkin, Mol, Chen, Yax, Zac, Ceh, Mac, Kankin, Maun, Pax, Kayab and Cumku. The unlucky five-day period was known as Uayeb, and was considered a time which could hold danger, death and bad luck.

The Vague Year began with the month of Pop. The Maya 20-day month always begins with the seating of the month, followed by days numbered 1 to 19, then the seating of the following month, and so on. This ties in with the Maya notion that each month influences the next. The Maya new year would start with 1 Pop, followed by 2 Pop, all the way through to 19 Pop, followed by the seating of the month of Uo, written as 0 Uo, then 1 Uo, 2 Uo and so on. These two cycles coincided every 52 years. The 52-year period of time was called a "bundle" and was similar to a modern-day century.

Modern calendars

While the Gregorian calendar is now in worldwide use for secular purposes, various medieval or ancient calendars remain in regional use for religious or social purposes, including the Julian calendar, the Hebrew calendar, the Islamic calendar, various Hindu calendars, the Zoroastrian calendar, etc.

There are also various modern calendars that see limited use, either created for the use of new religious movements or reformed versions of older religious calendars, or calendars introduced by regionalist or nationalist movements.

Calendar

From Wikipedia, the free encyclopedia


November
Su Mo Tu We Th Fr Sa

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
 
2021
British calendar, 1851, gilt bronze and malachite, height: 20.3 cm, Metropolitan Museum of Art (New York City)
 

A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single, specific day within such a system. A calendar is also a physical record (often paper) of such a system. A calendar can also mean a list of planned events, such as a court calendar or a partly or fully chronological list of documents, such as a calendar of wills.

Periods in a calendar (such as years and months) are usually, though not necessarily, synchronized with the cycle of the sun or the moon. The most common type of pre-modern calendar was the lunisolar calendar, a lunar calendar that occasionally adds one intercalary month to remain synchronized with the solar year over the long term.

Etymology

The term calendar is taken from calendae, the term for the first day of the month in the Roman calendar, related to the verb calare 'to call out', referring to the "calling" of the new moon when it was first seen. Latin calendarium meant 'account book, register' (as accounts were settled and debts were collected on the calends of each month). The Latin term was adopted in Old French as calendier and from there in Middle English as calender by the 13th century (the spelling calendar is early modern).

History

Equinox seen from the astronomic calendar of Pizzo Vento at Fondachelli Fantina, Sicily

The course of the sun and the moon are the most salient natural, regularly recurring events useful for timekeeping, thus in pre-modern societies worldwide lunation and the year were most commonly used as time units. Nevertheless, the Roman calendar contained remnants of a very ancient pre-Etruscan 10-month solar year. The first recorded physical calendars, dependent on the development of writing in the Ancient Near East, are the Bronze Age Egyptian and Sumerian calendars.

The Vedic India developed a sophisticated time keeping methodology and calendars for Vedic rituals.

A large number of Ancient Near East calendar systems based on the Babylonian calendar date from the Iron Age, among them the calendar system of the Persian Empire, which in turn gave rise to the Zoroastrian calendar and the Hebrew calendar.

A great number of Hellenic calendars developed in Classical Greece, and in the Hellenistic period gave rise to both the ancient Roman calendar and to various Hindu calendars. According to Yukio Ohashi, Vedanga field developed from actual astronomical studies in ancient Vedic Period and not derived from other cultures.

Calendars in antiquity were lunisolar, depending on the introduction of intercalary months to align the solar and the lunar years. This was mostly based on observation, but there may have been early attempts to model the pattern of intercalation algorithmically, as evidenced in the fragmentary 2nd-century Coligny calendar.

The Roman calendar was reformed by Julius Caesar in 46 BC. The Julian calendar was no longer dependent on the observation of the new moon but simply followed an algorithm of introducing a leap day every four years. This created a dissociation of the calendar month from the lunation.

The Islamic calendar is based on the prohibition of intercalation (nasi') by Muhammad, in Islamic tradition dated to a sermon held on 9 Dhu al-Hijjah AH 10 (Julian date: 6 March 632). This resulted in an observation-based lunar calendar that shifts relative to the seasons of the solar year.

Modern reforms

The first calendar reform of the early modern era was the Gregorian calendar, introduced in 1582 based on the observation of a long-term shift between the Julian calendar and the solar year.

There have been several modern proposals for reform of the calendar, such as the World Calendar, International Fixed Calendar, Holocene calendar, and, recently, the Hanke-Henry Permanent Calendar. Such ideas are mooted from time to time but have failed to gain traction because of the loss of continuity, massive upheaval in implementation, and religious objections.

Systems

A so-called universal calendar, combining different calendars

A full calendar system has a different calendar date for every day. Thus the week cycle is by itself not a full calendar system; neither is a system to name the days within a year without a system for identifying the years.

The simplest calendar system just counts time periods from a reference date. This applies for the Julian day or Unix Time. Virtually the only possible variation is using a different reference date, in particular, one less distant in the past to make the numbers smaller. Computations in these systems are just a matter of addition and subtraction.

Other calendars have one (or multiple) larger units of time.

Calendars that contain one level of cycles:

  • week and weekday – this system (without year, the week number keeps on increasing) is not very common
  • year and ordinal date within the year, e.g., the ISO 8601 ordinal date system

Calendars with two levels of cycles:

Cycles can be synchronized with periodic phenomena:

Sun and Moon, Schedel's Nuremberg Chronicle, 1493

Very commonly a calendar includes more than one type of cycle or has both cyclic and non-cyclic elements.

Most calendars incorporate more complex cycles. For example, the vast majority of them track years, months, weeks and days. The seven-day week is practically universal, though its use varies. It has run uninterrupted for millennia.

Solar

Solar calendars assign a date to each solar day. A day may consist of the period between sunrise and sunset, with a following period of night, or it may be a period between successive events such as two sunsets. The length of the interval between two such successive events may be allowed to vary slightly during the year, or it may be averaged into a mean solar day. Other types of calendar may also use a solar day.

Lunar

Not all calendars use the solar year as a unit. A lunar calendar is one in which days are numbered within each lunar phase cycle. Because the length of the lunar month is not an even fraction of the length of the tropical year, a purely lunar calendar quickly drifts against the seasons, which do not vary much near the equator. It does, however, stay constant with respect to other phenomena, notably tides. An example is the Islamic calendar. Alexander Marshack, in a controversial reading, believed that marks on a bone baton (c. 25,000 BC) represented a lunar calendar. Other marked bones may also represent lunar calendars. Similarly, Michael Rappenglueck believes that marks on a 15,000-year-old cave painting represent a lunar calendar.

Lunisolar

A lunisolar calendar is a lunar calendar that compensates by adding an extra month as needed to realign the months with the seasons. Prominent examples of lunisolar calendar are Hindu calendar and Buddhist calendar that are popular in South Asia and Southeast Asia. Another example is the Hebrew calendar, which uses a 19-year cycle.

Subdivisions

Nearly all calendar systems group consecutive days into "months" and also into "years". In a solar calendar a year approximates Earth's tropical year (that is, the time it takes for a complete cycle of seasons), traditionally used to facilitate the planning of agricultural activities. In a lunar calendar, the month approximates the cycle of the moon phase. Consecutive days may be grouped into other periods such as the week.

Because the number of days in the tropical year is not a whole number, a solar calendar must have a different number of days in different years. This may be handled, for example, by adding an extra day in leap years. The same applies to months in a lunar calendar and also the number of months in a year in a lunisolar calendar. This is generally known as intercalation. Even if a calendar is solar, but not lunar, the year cannot be divided entirely into months that never vary in length.

Cultures may define other units of time, such as the week, for the purpose of scheduling regular activities that do not easily coincide with months or years. Many cultures use different baselines for their calendars' starting years. Historically, several countries have based their calendars on regnal years, a calendar based on the reign of their current sovereign. For example, the year 2006 in Japan is year 18 Heisei, with Heisei being the era name of Emperor Akihito.

Other types

Arithmetical and astronomical

Calendar of the Qahal, 5591 (1831)

An astronomical calendar is based on ongoing observation; examples are the religious Islamic calendar and the old religious Jewish calendar in the time of the Second Temple. Such a calendar is also referred to as an observation-based calendar. The advantage of such a calendar is that it is perfectly and perpetually accurate. The disadvantage is that working out when a particular date would occur is difficult.

An arithmetic calendar is one that is based on a strict set of rules; an example is the current Jewish calendar. Such a calendar is also referred to as a rule-based calendar. The advantage of such a calendar is the ease of calculating when a particular date occurs. The disadvantage is imperfect accuracy. Furthermore, even if the calendar is very accurate, its accuracy diminishes slowly over time, owing to changes in Earth's rotation. This limits the lifetime of an accurate arithmetic calendar to a few thousand years. After then, the rules would need to be modified from observations made since the invention of the calendar.

Complete and incomplete

Calendars may be either complete or incomplete. Complete calendars provide a way of naming each consecutive day, while incomplete calendars do not. The early Roman calendar, which had no way of designating the days of the winter months other than to lump them together as "winter", is an example of an incomplete calendar, while the Gregorian calendar is an example of a complete calendar.

Usage

The primary practical use of a calendar is to identify days: to be informed about or to agree on a future event and to record an event that has happened. Days may be significant for agricultural, civil, religious, or social reasons. For example, a calendar provides a way to determine when to start planting or harvesting, which days are religious or civil holidays, which days mark the beginning and end of business accounting periods, and which days have legal significance, such as the day taxes are due or a contract expires. Also, a calendar may, by identifying a day, provide other useful information about the day such as its season.

Calendars are also used to help people manage their personal schedules, time, and activities, particularly when individuals have numerous work, school, and family commitments. People frequently use multiple systems and may keep both a business and family calendar to help prevent them from overcommitting their time.

Calendars are also used as part of a complete timekeeping system: date and time of day together specify a moment in time. In the modern world, timekeepers can show time, date, and weekday. Some may also show the lunar phase.

Gregorian

The Gregorian calendar is the de facto international standard and is used almost everywhere in the world for civil purposes. The widely used solar aspect is a cycle of leap days in a 400-year cycle designed to keep the duration of the year aligned with the solar year. There is a lunar aspect which approximates the position of the moon during the year, and is used in the calculation of the date of Easter

Each Gregorian year has either 365 or 366 days (the leap day being inserted as 29 February), amounting to an average Gregorian year of 365.2425 days (compared to a solar year of 365.2422 days). It was introduced in 1582 as a refinement to the Julian calendar which had been in use throughout the European Middle Ages, amounting to a 0.002% correction in the length of the year.

During the Early Modern period, however, its adoption was mostly limited to Roman Catholic nations, but by the 19th century, it became widely adopted worldwide for the sake of convenience in international trade. The last European country to adopt the reform was Greece, in 1923.

The calendar epoch used by the Gregorian calendar is inherited from the medieval convention established by Dionysius Exiguus and associated with the Julian calendar. The year number is variously given as AD (for Anno Domini) or CE (for Common Era or Christian Era).

Religious

A Hindu almanac (pancanga) for the year 1871/2 from Rajasthan (Library of Congress, Asian Division)

The most important use of pre-modern calendars is keeping track of the liturgical year and the observation of religious feast days.

While the Gregorian calendar is itself historically motivated to the calculation of the Easter date, it is now in worldwide secular use as the de facto standard. Alongside the use of the Gregorian calendar for secular matters, there remain several calendars in use for religious purposes.

Eastern Christians, including the Orthodox Church, use the Julian calendar.

The Islamic calendar or Hijri calendar is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to date events in most of the Muslim countries (concurrently with the Gregorian calendar) and used by Muslims everywhere to determine the proper day on which to celebrate Islamic holy days and festivals. Its epoch is the Hijra (corresponding to AD 622) With an annual drift of 11 or 12 days, the seasonal relation is repeated approximately every 33 Islamic years.

Various Hindu calendars remain in use in the Indian subcontinent, including the Nepali calendars, Bengali calendar, Malayalam calendar, Tamil calendar, Vikrama Samvat used in Northern India, and Shalivahana calendar in the Deccan states.

The Buddhist calendar and the traditional lunisolar calendars of Cambodia, Laos, Myanmar, Sri Lanka and Thailand are also based on an older version of the Hindu calendar.

Most of the Hindu calendars are inherited from a system first enunciated in Vedanga Jyotisha of Lagadha, standardized in the Sūrya Siddhānta and subsequently reformed by astronomers such as Āryabhaṭa (AD 499), Varāhamihira (6th century) and Bhāskara II (12th century).

The Hebrew calendar is used by Jews worldwide for religious and cultural affairs, also influences civil matters in Israel (such as national holidays) and can be used business dealings (such as for the dating of cheques).

Followers of the Baháʼí Faith use the Baháʼí calendar. The Baháʼí Calendar, also known as the Badi Calendar was first established by the Bab in the Kitab-i-Asma. The Baháʼí Calendar is also purely a solar calendar and comprises 19 months each having nineteen days.

National

The Chinese, Hebrew, Hindu, and Julian calendars are widely used for religious and social purposes.

The Iranian (Persian) calendar is used in Iran and some parts of Afghanistan. The Assyrian calendar is in use by the members of the Assyrian community in the Middle East (mainly Iraq, Syria, Turkey, and Iran) and the diaspora. The first year of the calendar is exactly 4750 years prior to the start of the Gregorian calendar. The Ethiopian calendar or Ethiopic calendar is the principal calendar used in Ethiopia and Eritrea, with the Oromo calendar also in use in some areas. In neighboring Somalia, the Somali calendar co-exists alongside the Gregorian and Islamic calendars. In Thailand, where the Thai solar calendar is used, the months and days have adopted the western standard, although the years are still based on the traditional Buddhist calendar.

Fiscal

The Payment of the Tithes (The tax-collector), also known as Village Lawyer, by Pieter Brueghel the Younger

A fiscal calendar generally means the accounting year of a government or a business. It is used for budgeting, keeping accounts, and taxation. It is a set of 12 months that may start at any date in a year. The US government's fiscal year starts on 1 October and ends on 30 September. The government of India's fiscal year starts on 1 April and ends on 31 March. Small traditional businesses in India start the fiscal year on Diwali festival and end the day before the next year's Diwali festival.

In accounting (and particularly accounting software), a fiscal calendar (such as a 4/4/5 calendar) fixes each month at a specific number of weeks to facilitate comparisons from month to month and year to year. January always has exactly 4 weeks (Sunday through Saturday), February has 4 weeks, March has 5 weeks, etc. Note that this calendar will normally need to add a 53rd week to every 5th or 6th year, which might be added to December or might not be, depending on how the organization uses those dates. There exists an international standard way to do this (the ISO week). The ISO week starts on a Monday and ends on a Sunday. Week 1 is always the week that contains 4 January in the Gregorian calendar.

Formats

The term calendar applies not only to a given scheme of timekeeping but also to a specific record or device displaying such a scheme, for example, an appointment book in the form of a pocket calendar (or personal organizer), desktop calendar, a wall calendar, etc.

In a paper calendar, one or two sheets can show a single day, a week, a month, or a year. If a sheet is for a single day, it easily shows the date and the weekday. If a sheet is for multiple days it shows a conversion table to convert from weekday to date and back. With a special pointing device, or by crossing out past days, it may indicate the current date and weekday. This is the most common usage of the word.

In the US Sunday is considered the first day of the week and so appears on the far left and Saturday the last day of the week appearing on the far right. In Britain, the weekend may appear at the end of the week so the first day is Monday and the last day is Sunday. The US calendar display is also used in Britain.

It is common to display the Gregorian calendar in separate monthly grids of seven columns (from Monday to Sunday, or Sunday to Saturday depending on which day is considered to start the week – this varies according to country) and five to six rows (or rarely, four rows when the month of February contains 28 days in common years beginning on the first day of the week), with the day of the month numbered in each cell, beginning with 1. The sixth row is sometimes eliminated by marking 23/30 and 24/31 together as necessary.

When working with weeks rather than months, a continuous format is sometimes more convenient, where no blank cells are inserted to ensure that the first day of a new month begins on a fresh row.

Software

Calendaring software provides users with an electronic version of a calendar, and may additionally provide an appointment book, address book, or contact list. Calendaring is a standard feature of many PDAs, EDAs, and smartphones. The software may be a local package designed for individual use (e.g., Lightning extension for Mozilla Thunderbird, Microsoft Outlook without Exchange Server, or Windows Calendar) or maybe a networked package that allows for the sharing of information between users (e.g., Mozilla Sunbird, Windows Live Calendar, Google Calendar, or Microsoft Outlook with Exchange Server).

 

Equality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Equality_...