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## #1 2023-05-04 17:48:22

Jai Ganesh
Registered: 2005-06-28
Posts: 47,795

### Chronology

Chronology

Gist

Chronology: the order in which a series of events happened; a list of these events in order.

Summary

Chronology (from Latin chronologia, from Ancient Greek "time"; and  -logia) is the science of arranging events in their order of occurrence in time. Consider, for example, the use of a timeline or sequence of events. It is also "the determination of the actual temporal sequence of past events".

Chronology is a part of periodization. It is also a part of the discipline of history including earth history, the earth sciences, and study of the geologic time scale.

Related fields

Chronology is the science of locating historical events in time. It relies upon chronometry, which is also known as timekeeping, and historiography, which examines the writing of history and the use of historical methods. Radiocarbon dating estimates the age of formerly living things by measuring the proportion of carbon-14 isotope in their carbon content. Dendrochronology estimates the age of trees by correlation of the various growth rings in their wood to known year-by-year reference sequences in the region to reflect year-to-year climatic variation. Dendrochronology is used in turn as a calibration reference for radiocarbon dating curves.

Calendar and era

The familiar terms calendar and era (within the meaning of a coherent system of numbered calendar years) concern two complementary fundamental concepts of chronology. For example, during eight centuries the calendar belonging to the Christian era, which era was taken in use in the 8th century by Bede, was the Julian calendar, but after the year 1582 it was the Gregorian calendar. Dionysius Exiguus (about the year 500) was the founder of that era, which is nowadays the most widespread dating system on earth. An epoch is the date (year usually) when an era begins.

Ab Urbe condita era

Ab Urbe condita is Latin for "from the founding of the City (Rome)", traditionally set in 753 BC. It was used to identify the Roman year by a few Roman historians. Modern historians use it much more frequently than the Romans themselves did; the dominant method of identifying Roman years was to name the two consuls who held office that year. Before the advent of the modern critical edition of historical Roman works, AUC was indiscriminately added to them by earlier editors, making it appear more widely used than it actually was.

It was used systematically for the first time only about the year 400, by the Iberian historian Orosius. Pope Boniface IV, in about the year 600, seems to have been the first who made a connection between these this era and Anno Domini. (AD 1 = AUC 754.)

Astronomical era

Dionysius Exiguus' Anno Domini era (which contains only calendar years AD) was extended by Bede to the complete Christian era (which contains, in addition all calendar years BC, but no year zero). Ten centuries after Bede, the French astronomers Philippe de la Hire (in the year 1702) and Jacques Cassini (in the year 1740), purely to simplify certain calculations, put the Julian Dating System (proposed in the year 1583 by Joseph Scaliger) and with it an astronomical era into use, which contains a leap year zero, which precedes the year 1 (AD).

Prehistory

While of critical importance to the historian, methods of determining chronology are used in most disciplines of science, especially astronomy, geology, paleontology and archaeology.

In the absence of written history, with its chronicles and king lists, late 19th century archaeologists found that they could develop relative chronologies based on pottery techniques and styles. In the field of Egyptology, William Flinders Petrie pioneered sequence dating to penetrate pre-dynastic Neolithic times, using groups of contemporary artefacts deposited together at a single time in graves and working backwards methodically from the earliest historical phases of Egypt. This method of dating is known as seriation.

Known wares discovered at strata in sometimes quite distant sites, the product of trade, helped extend the network of chronologies. Some cultures have retained the name applied to them in reference to characteristic forms, for lack of an idea of what they called themselves: "The Beaker People" in northern Europe during the 3rd millennium BCE, for example. The study of the means of placing pottery and other cultural artifacts into some kind of order proceeds in two phases, classification and typology: Classification creates categories for the purposes of description, and typology seeks to identify and analyse changes that allow artifacts to be placed into sequences.

Laboratory techniques developed particularly after mid-20th century helped constantly revise and refine the chronologies developed for specific cultural areas. Unrelated dating methods help reinforce a chronology, an axiom of corroborative evidence. Ideally, archaeological materials used for dating a site should complement each other and provide a means of cross-checking. Conclusions drawn from just one unsupported technique are usually regarded as unreliable.

Details

Chronology is any method used to order time and to place events in the sequence in which they occurred. The systems of chronology used to record human history, which are closely related to calendar systems, vary in scope, accuracy, and method according to the purpose, degree of sophistication, and skills of the peoples using them.

Scientific chronology, which seeks to place all happenings in the order in which they occurred and at correctly proportioned intervals on a fixed scale, is used in many disciplines and can be utilized to cover vast epochs. Astronomy, for example, measures the sequence of cosmic phenomena in thousands of millions of years; geology and paleontology, when tracing the evolution of Earth and of life, use similar epochs of hundreds or thousands of millions of years. Geochronology reckons the more distant periods with which it deals on a similar scale; but it descends as far as human prehistoric and even historic times, and its shorter subdivisions consist only of thousands of years. Shortest of all are the chronological scales used in the recording of human events in a more or less systematic and permanent manner. These vary in scope, accuracy, and method according to the purpose, degree of sophistication, and skill of the peoples using them, as do the calendrical systems with which they are inextricably bound up. For further details see the article calendar.

It is difficult to fix ancient historical chronologies in relation to scientific chronology. The terms of reference of ancient peoples were vague and inconsistent when judged by modern standards, and many of their inscriptions and writings have inevitably disappeared. The gaps in their records are increasingly filled in and their inconsistencies removed by the results of archaeological excavation. Guided by these findings, scholars can confirm, refute, or amend chronological reconstructions already tentatively made. Astronomical calculation and dating by radioactive-carbon content are also helpful in the work of fixing ancient chronologies.

Chinese

Chinese legendary history can be traced back to 2697 BC, the first year of Huang Ti (Chinese: Yellow Emperor), who was followed by many successors and by the three dynasties, the Hsia, the Shang, and the Chou. Recent archaeological findings, however, have established an authentic chronology beginning with the Shang dynasty, though the exact date of its end remains a controversial topic among experts. The so-called oracle-bone inscriptions of the last nine Shang kings (1324–1122 BC) record the number of months up to the 12th, with periodical additions of a 13th month, and regular religious services on the summer and winter solstice days, all of which indicates the adjustment of the length of the lunar year by means of calculations based on the solar year. Individual days in the inscriptions are named according to the designations in the sexagenary cycle formed by the combination of the 10 celestial stems and 12 terrestrial branches. Every set of 60 days is divided into six 10-day “weeks.” Also recorded are numerous eclipses that can be used to verify the accuracy of the Shang chronology. In the oracular sentences of the last Shang king, Chou Hsin, the year of his reign is referred to as “the King’s nth annual sacrifice.”

From the beginning of the following (Chou) dynasty, the word year was etymologically identical with “harvest.” Thus, “King X’s nth harvest” meant the nth year of his reign. The lunar month was then divided into four quarters—Ch’u-chi, Tsai-sheng pa, Chi-sheng pa and Chi-szu pa—and the practice of using the 60 cyclical names for the days was continued. Thus, in the inscription on a Chou bronze vessel, a typical date would read: “In the King’s nth harvest, in the nth quarter of the nth month, on the day X-y, etc.”

The tradition of recording events by referring to the king’s regnal year continued until 163 BC, when a new system, nien-hao (“reign-period title”), was introduced by Emperor Han Wen Ti of the Former Han dynasty (206 BC–AD 8). Thereafter, every emperor proclaimed a new nien-hao for his reign at the beginning of the year following his accession (sometimes an emperor redesignated his nien-hao on special occasions during his reign). A typical date in the nien-hao system might read, “the third year of the Wan-li reign period” (Wan-li san nien). In order to date any event in Chinese history, it is necessary to convert the year in the period of the designated nien-hao into the Western calendar.

During the Chou dynasty the civil year began with the new moon, which occurred before or on the day of the winter solstice. This “first month” of the Chou year (Chou cheng) was equivalent to the 11th month of the Hsia year (Hsia cheng) or to the 12th month of the Shang year. The first emperor, Shih Huang-ti, of the short-lived Ch’in dynasty (221–206 BC) made the year begin one month earlier—i.e., with the lunation (the period of time between one new moon and the next) before the one in which the winter solstice occurred. The Ch’in year was continuously used until 104 BC, when Emperor Han Wu Ti promulgated the T’ai-ch’u calendar by reverting to the Hsia cheng—i.e., by taking the third month of the Chou year, or the second lunation after the winter solstice, as the first month of the civil year. This lunar year (or Hsia cheng) was used till the last day of the Ch’ing, or Manchu, dynasty (1644–1911/12). When in 1911 the first republic was founded, the solar year was officially adopted, but successive governments kept the nien-hao tradition by referring any date to the number of years since the establishment of the republic—e.g., 1948 was chronicled “the 37th year of the republic.” In 1949, when the People’s Republic of China was proclaimed, the old system was replaced by the Gregorian calendar.

Japanese

The principal chronicles describing the origins of Japanese history are the Nihon shoki (“Chronicle of Japan”) and the Koji-ki (“Record of Ancient Matters”). The Nihon shoki (compiled in AD 720) assembled information in a chronological order of days, months, and years starting several years before 660 BC, which was the year of the enthronement of the first Japanese emperor, who was posthumously named Jimmu. The Koji-ki (compiled in AD 712) related events under the reign of each emperor without a strict chronological order. Sometimes the Koji-ki gave the years of emperors’ deaths and their ages at death. This information is different from that recorded in the Nihon shoki.

Native Japanese scholars since Fujiwara Teikan in the 18th century have realized that the Nihon shoki was historically inadequate and different from the Koji-ki, at least insofar as the chronological information is concerned. They have suggested that the foundation year of Japan was 600 years later than stated in the Nihon shoki. Naka Michiyo (late 19th century) argued with minute detail about the question of Japanese chronology. His ideas were supplemented by those of other Japanese scholars, who pointed out that: (1) the reigns of the earlier Japanese emperors as stated in the Nihon shoki are unnaturally long; (2) the date of the enthronement of the emperor Jimmu should be reconsidered; (3) a chronological gap exists between the Nihon shoki and contemporary Chinese and Korean chronicles. In comparison with Korean chronicles, they argued, the Nihon shoki has created an intentional expansion of chronology—i.e., the entries about the empress Jingō and the emperor Ōjin can be identified with historical facts relating to the Korea of the 4th and 5th centuries and therefore must be placed 120 years later than mentioned in the Nihon shoki. When comparing the Nihon shoki with Chinese chronicles, one finds the chronological gap somewhat reduced. The Chinese chronicles provide information about the tributes sent individually by five Japanese “kings” to Liu-Sung and Southern Ch’i during the 5th century. There are still questions about the identification of these kings, but it is generally accepted that the “king” written in Chinese character as Wu must be the Japanese emperor Yūryaku. By the late 5th century the gap between Japanese and Korean records, on the one hand, and Japanese and Chinese, on the other hand, disappears.

The intentional expansion of the chronology of the Nihon shoki was adopted by its compilers, who identified Queen Himiko (Pimihu) of Yamatai of the chronicle of Wei China with the Empress Jingō of Japanese legend.

The method of designating a year by the kan-shi (sexagenary cycle) appears to have begun about the reign of Emperor Yūryaku, when, as mentioned above, the gap between the continental and Japanese chronologies was bridged. The inscription on remarkable copper images of Buddha cast just after the period of Prince Shōtoku’s regency (AD 593–621) bears a nengō (nien-hao, or reign-year title), although not a strictly authorized one. It was at this time that the Chinese luni-solar calendar system was adopted. The first official nengō was Taika, which was adopted by the imperial court in 645. Since 701, when the second title, Taihō, was adopted, the reign-year system has been continuously used in relation to the emperors’ reigns up to the present day. In medieval times Japanese chronology underwent a remarkable evolution: (1) when the Imperial dynasty split into two courts (1336–92), two series of nengō began to be used; (2) during the Ashikaga period some private nengō again appeared; (3) some dates of the authorized “central” calendars did not correspond with those of locally compiled calendars. Moreover, military leaders would not accept some of the new nengō. Minamoto Yoritomo, for example, did not use the nengō that was adopted by the emperor Antoku and the Taira regime, and Ashikaga Mochiuji and Ashikaga Shigeuji did not use the official, respectively Eikyō and Kōshō, nengō.

In the Tokugawa period (1603–1867), gaps between central and provincial calendars disappeared, especially after the establishment of the Jōkyō calendar, the first native calendar compiled in Japan, instead of the Chinese-based one that was in use until this period. On January 1, 1873, Emperor Meiji adopted the Gregorian calendar in use in the West and at the same time adopted the “Japanese Era,” with Emperor Jimmu as its founder, in addition to the nengō system.

Indian

Two kinds of chronological systems have been used in India by the Hindus from antiquity. The first requires the years to be reckoned from some historical event. The second starts the reckoning from the position of some heavenly body. The historical system, the more common in modern times, exists side-by-side with Muslim and international systems successively introduced.

The inscriptions of the Buddhist king Aśoka (c. 265–238 BC) give the first epigraphical evidence of the mode of reckoning from a king’s consecration (abhiṣeka). In these inscriptions (Middle Indian language in India or Greek and Aramaean in what is now Qandahār, Afghanistan) the dates are indicated by the number of complete years elapsed since the king’s consecration. But the earlier existence of a reckoning of duration of reigns and dynasties is evidenced by the testimony of the Greek historian Megasthenes, who in 302 BC was the ambassador of Seleucus I Nicator, founder of the Seleucid Empire, to the court of Chandragupta Maurya, Aśoka’s grandfather. According to Megasthenes, the people of the Magadha kingdom, with its capital Pāṭaliputra (Patna), kept very long dynastic lists, preserved in the later Sanskrit Purāṇas (legends of the gods and heroes) and later Buddhist and Jain chronicles. They generally indicate, in years or parts of years, the duration of each reign.

Similar records of other periods and regions exist, and a relative chronology may be established. Unfortunately, it is not always possible to connect them with any absolute chronology, the precise dates of the reigns given being still unsettled. For example, in the Scythian period of the history of northern India, several inscriptions are dated from the beginning of the reign of Kaniṣka, the greatest king of the Asian (Kushān) invaders, but his dates are still uncertain (AD 78, 128–129, 144, etc., have been suggested for the beginning of a Kaniṣka era).

Other records give regnal years that can be linked with absolute chronology through other data—e.g., those of several rulers of the Rāṣṭrakūṭa of the Deccan.

Later, instead of the beginning of a reign or of a dynasty, the death of a religious founder was adopted as the starting point of an era. Among Buddhists the death of the Buddha and among the Jains the death of the Jina were taken as the beginning of eras. The Jain era (vīrasaṃvat) began in 528 BC. Several Buddhist sects (no longer existing in India) adopted different dates for the death (Nirvāṇa) of the Buddha. The Buddhist era prevailing in Ceylon and Buddhist Southeast Asia begins in 544 BC.

Historical events, now obscure, were the basis of the two most popular Indian eras: the Vikrama and the Śaka.

The Vikrama era (58 BC) is said in the Jain book Kālakācāryakathā to have been founded after a victory of King Vikramāditya over the Śaka. But some scholars credit the Scytho-Parthian ruler Azes with the foundation of this era. It is sometimes called the Mālava era because Vikramāditya ruled over the Mālava country, but it was not confined to this region, being widespread throughout India. The years reckoned in this era are generally indicated with the word vikramasaṃvat, or simply saṃvat. They are elapsed years. In the north the custom is to begin each year with Caitra (March–April) and each month with the full moon. But in the south and in Gujarāt the years begin with Kārttika (October–November) and the months with the new moon; in part of Gujarāt, the new moon of Āṣāḍha (June–July) is taken as the beginning of the year. To reduce Vikrama dates to dates AD, 57 must be subtracted from the former for dates before January 1 and 56 for dates after.

The Śaka, or Salivāhana, era (AD 78), now used throughout India, is the most important of all. It has been used not only in many Indian inscriptions but also in ancient Sanskrit inscriptions in Indochina and Indonesia. The reformed calendar promulgated by the Indian government from 1957 is reckoned by this era. It is variously alleged to have been founded by King Kaniṣka or by the Hindu king Salivāhana or by the satrap Nahapāna. According to different practices, the reckoning used to refer to elapsed years in the north or current years in the south and was either solar or luni-solar. The luni-solar months begin with full moon in the north and with new moon in the south. To reduce Śaka dates (elapsed years) to dates AD, 78 must be added for a date within the period ending with the day equivalent to December 31 and 79 for a later date. For Śaka current years the numbers to be added are 77 and 78. The official Śaka year is the elapsed year, starting from the day following that of the vernal equinox. A normal year consists of 365 days, while the leap year has 366. The first month is Chaitra, with 30 days in a normal year and 31 in a leap year; the five following months have 31 days, the others 30.

A Nepalese era (AD 878) of obscure origin was commonly used in Nepal until modern times. The years were elapsed, starting from Kārttika, with months beginning at new moon. Another era, the use of which is limited to the Malabār Coast (Malayalam-speaking area) and to the Tirunelveli district of the Tamil-speaking area, is connected with the legend of the hero Paraśurāma, an avatar (incarnation) of the god Vishnu. It is called the Kollam era (AD 825). Its years are current and solar; they start when the Sun enters into the zodiacal sign of Virgo in north Malabār and when it enters into Leo in south Malabār. It is sometimes divided into cycles of 1,000 years reckoned from 1176 BC. Thus, AD 825 would have been the first year of the era’s third millennium.

Eras based on astronomical speculation

During the period of elaboration of the classical Hindu astronomy, which was definitively expounded in the treatises called siddhāntas and by authors such as Aryabhata (born AD 476), Varāhamihira, Brahmagupta (7th century AD), etc., the ancient Vedic notions on the cycle of years, embracing round numbers of solar and lunar years together, were developed. On the one hand, greater cycles were calculated in order to include the revolutions of planets, and the theory was elaborated of a general conjunction of heavenly bodies at 0° longitude after the completion of each cycle. On the other hand, cosmologists speculated as to the existence of several successive cycles constituting successive periods of evolution and involution of the universe. The period calculated as the basis of the chronology of the universe was the mahāyuga, consisting of 4,320,000 sidereal years. It was divided into four yugas, or stages, on the hypothesis of an original “order” (dharma) established in the first stage, the Kṛta Yuga, gradually decaying in the three others, the Tretā, Dvāpara, and Kali yugas. The respective durations of these four yugas were 1,728,000, 1,296,000, 864,000, and 432,000 years. According to the astronomer Aryabhata, however, the duration of each of the four yugas was the same—i.e., 1,080,000 years. The basic figures in these calculations were derived from the Brahmanical reckoning of a year of 10,800 muhūrta (see calendar: The Hindu calendar), together with combinations of other basic numbers, such as four phases, 27 nakṣatras, etc. The movement of the equinoxes was at the same time interpreted not as a circular precession but as a libration (periodic oscillation) at the rate of 54 seconds of arc per year. It is in accordance with these principles that the calculation of the beginning of the Kali Yuga was done in order to fix for this chronology a point starting at the beginning of the agreed world cycle. Such a beginning could not be observed, since it was purely theoretical, consisting of a general conjunction of planets at longitude 0°, the last point of the nakṣatra Revati (Pisces). It has been calculated as corresponding to February 18, 3102 BC (old style), 0 hour, and taken as the beginning of the Kali era. In this era, the years are mostly reckoned as elapsed and solar or luni-solar.

In Hindu tradition the beginning of the Kali era was connected with (1) events of the Mahābhārata war; (2) King Yudhiṣṭhira’s accession to the throne; (3) 36 years later, King Parikṣit’s consecration; and (4) the death of Lord Krishna. Years of the era are still regularly given in Hindu almanacs.

An era resting upon a fictitious assumption of a complete 100-year revolution of the Ursa Major, the Great Bear (saptarṣi), around the northern pole was the Saptarṣi, or Laukika, era (3076 BC), formerly used in Kashmir and the Punjab. The alleged movement of this constellation has been used in Purāṇa compilations and even by astronomers for indicating the centuries.

Two chronological cycles were worked out on a basis of the planet Jupiter’s revolutions, one corresponding to a single year of Jupiter consisting of 12 solar years and the other to five of Jupiter’s years. The second, the bṛhaspaticakra, starts, according to different traditions, from AD 427 or from 3116 BC. Before AD 907 one year was periodically omitted in order to keep the cycle in concordance with the solar years. Since 907 the special names by which every year of the cycle is designated are simply given to present years of the almanac.

Side-by-side with Hindu and foreign eras adopted in India, several eras were created in the country under foreign influence, chiefly of the Mughal emperor Akbar: Bengali San (AD 593), Amli of Orissa and Vilayati (AD 592), Faṣlī (AD 590, 592, or 593 according to the district), and Sursan of Mahārāshtra (599).

Egyptian

At the end of the 4th millennium BC, when King Menes, the first king of a united Egypt, started his reign, the ancient Egyptians began to name each year by its main events, presumably to facilitate the dating of documents. These names were entered into an official register together with the height of the Nile during its annual inundation. Short notes at first, the year names developed into lengthy records of historical and religious events, especially of royal grants to the gods. These lists grew into annals, which were kept during the entire history of Egypt so that later kings could, after important events, consult the annals and ascertain whether a comparable occurrence had happened before. Unfortunately, these annals are lost. Only fragments from the 1st to the 5th dynasty (c. 3100–c. 2345 BC) are preserved, copied on stone. These fragments, however, are in such poor condition that they raise more chronological problems than they solve.

The Egyptian priests of the Ramesside period (c. 1300 BC) copied the names and reigns of the kings from Menes down to their time from the annals, omitting all references to events. Even this king list would have given a safe foundation of an Egyptian chronology, but the only extant copy, on a papyrus now kept at the Museo Egizio in Turin, has survived only in shreds, entire sections having been lost. Extracts from this king list, which name only the more important kings, are preserved in the temples of the kings Seti I and Ramses II at Abydos and on the wall of a private tomb at Ṣaqqārah (now in the Egyptian Museum), but they give little help in chronological matters.

Theoretically, the Egyptian civil year began when the Dog Star, Sirius (Egyptian Sothis), could first be seen on the eastern horizon just before the rising of the Sun (i.e., 19/20 of July). As the civil calendar of the ancient Egyptians consisted of 12 months (each of 30 days) and five odd days (called epagomenal days), the civil year was a quarter of a day too short in relation to the rising of Sothis, so that the new year advanced by one day every four years. New Year’s Day and the rising of Sothis coincided again only after approximately 1,460 years, the so-called Sothic cycle. Dated documents mentioning the rising of Sothis can be translated into the present calendar by multiplying the number of days elapsed since the first day of the year by four and subtracting this sum from the date of the beginning of the particular Sothic cycle. The dates for the start of each Sothic cycle are fortunately known because the Roman historian Censorinus fixed the coincidence of New Year’s Day and heliacal rising of Sothis in AD 139. Taking into account a slight difference between a Sothic year and a year of the fixed stars, the years 1322, 2782, and 4242 BC are taken as starting points of a Sothic cycle.

There are six ancient Egyptian documents extant giving Sothis dates, but only three of these are of value. The oldest is a letter from the town of Kahun warning a priest that the heliacal rising of Sothis will take place on the 16th day of the 8th month of year 7 of a king who, according to internal evidence, is Sesostris III of the 12th dynasty. This date corresponds to 1866 BC, according to the corrected Sothic cycle. The next date is given by a medical papyrus written at the beginning of the 18th dynasty, to which a calendar is added, possibly to ensure a correct conversion of dates used in the receipts to the actual timetable. Here it is said that the 9th day of the 11th month of year 9 of King Amenhotep I was the day of the heliacal rising of Sothis—i.e., 1538 BC. This date, however, is only accurate provided that the astronomical observations were taken at the old residence of Memphis; if observed at Thebes in Upper Egypt, the residence of the 18th dynasty, the date must be lowered by 20 years—i.e., 1518 BC. The third Sothis date shows that Sirius rose heliacally sometime during the reign of Thutmose III, which lasted for 54 years, on the 28th day of the 11th month; so year 1458 BC (point of observation at Memphis) or 1438 BC (point of observation at Thebes) must have belonged to the reign of this king. From these dates it is possible to calculate the absolute dates for the reigns of the 12th dynasty, as the durations of most of the reigns of the kings belonging to this dynasty are preserved on the king list of the Turin Papyrus. On the other hand, chronologists are able to compute the reigns of the kings of the 18th dynasty by utilizing the highest dates of their documents and the figures preserved by Manetho. Historians are also helped by the fact that the Egyptians sometimes identified a certain day as “exactly new moon”; they reckoned new moon from the morning after the last crescent of the waning moon had become invisible in the east just before sunrise. As there is a 25-year lunar cycle, such ancient Egyptian moon dates could be calculated with a fair amount of certainty but of course only if the ancient Egyptians themselves observed this celestial phenomenon accurately. There is some doubt, however, as it is shown by the attempts of very competent scholars to convert these moon dates. Sometimes even moon dates given by the same papyrus contradict themselves; in another case, the date given by a document had to be amended to achieve a reasonable result. These and other examples show that ancient Egyptian statements on celestial phenomena, especially on new moons, tend to be inaccurate because of faulty or inexact observations. Therefore, every date given for a fixed reign should be used with caution as the astronomical observation on which it is based may be inexact. Sometimes they are controlled by synchronism with Babylonian, Assyrian, or Hittite king lists or, later on, by the close interconnections between Greek and Egyptian history. Sometimes even biographical data are helpful. The statements found on small stelae inside the burial ground of the holy bulls of Memphis (Apis) register the dates of birth, enthronement, and death of these animals accurately. But the more time recedes, the more the chronology of the Egyptian history becomes uncertain, even when astronomical data are available. Up till now even carbon-14 data are of no great help, as uncertainties are mostly not greater than the standard deviations to be expected in a carbon-14 calculation.

Nevertheless, Egyptologists believe themselves to be on fairly firm ground when dating the beginning of the Ancient Kingdom (1st and 2nd dynasty) about 3090 BC, the beginning of the 11th dynasty at 2133 BC, and of the Middle Kingdom (12th dynasty) at 1991 BC. The New Kingdom started at 1567 or 1552 BC, depending on a choice for the first year of Ramses II of either 1290 BC or 1304 BC—one lunar cycle earlier. The following centuries still pose many chronological questions down to 664 BC, when Greek historiography took over.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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