History of Tibetan Astronomy
The history of the Tibetan astronomy is to show the development of the historic Tibet (popular science tib. : Rig gnas ; "City of Knowledge") about the structure of the earth and the universe , about the calculation of the structure and components of the Tibetan astronomical calendar , on the calculation of the movement of the ten planets known in Tibet including the sun and moon as well as the comet Encke and on the calculation of solar and lunar eclipses . The astronomical calculations were carried out with the Tibetan sand tobacco .
The Tibetan astronomy is of Indian origin, being on the astronomical teachings of the first chapter of the Kalachakra is based, an Indian tantric teaching text whose Sanskrit -Textversion may not have originated before 1027 and the first time in the second half of the 11th century, the Tibetan translated has been.
Origin according to mythological Buddhist tradition
According to Tibetan tradition, the tantric teaching system Kālacakra, "wheel of time", was given by the historical Buddha shortly before or after his death at the South Indian stūpa of Dhānyakaṭaka in front of a mythical audience at the request of Sucandra (Tib .: zla ba bzang po ), a king of the fabled kingdom of Shambhala . Sucandra is said to have written down these teachings in a 12,000-verse work called Root Tantra (Mūlatantra). The root tantra written by Sucandra is said to have been lost, apart from a few quotations in later works.
The authoritative text for the development of Tibetan astronomy is the first chapter of the work known as Kālacakratantra , which is attributed to another mythical king of Shambhala, namely Jamyang Dragpa (Tib .: 'jam dbyangs grags pa ) and a shortened version of the lost root -Tantra should be. The Tibetan title of this work is: mChog gi dang po sangs rgyas las phyung ba rgyud kyi rgyal-po dus kyi 'khor lo (“The king of tantras revealed by Buddha, the first of the most high, the wheel of time”).
The first chapter of this work contains a description of cosmography and the implementation of astronomical calculations, as they are usually presented in numerous practical arithmetic books of Indian astronomy and calendar calculation. In Sanskrit , such arithmetic books are called Karaņa or later in Tibetan byed rtsis ("practical arithmetic").
The calculation variables used to facilitate the practical implementation of the invoices are shortened or rounded up in such a work. For example, in order to simplify the calculations, fewer numbers are used after the decimal point than would be required exactly. The practical arithmetic books were created against the background of large, systematic Indian treatises on astronomical calculations, which are called Siddhānta, and in which calculations are made with more complex numerical values and long periods of time. This was not considered necessary for everyday use.
From the perspective of the scientific history of Indian astronomy, the astronomical content of the kālacakratantra is therefore not of particular importance. The first chapter of the Kālacakratantra, however, served to export a large part of the highly developed astronomical knowledge of the Indians to Tibet, where it was valued as an authoritative proclamation of the historical Buddha, and was highly valued and a peculiar further development.
Astrological content can hardly be found in the first chapter of the Kālacakratantra.
Of great importance for the development of Tibetan astronomy was the commentary Vimalaprabhā (" Flawless Shine") on the Kālacakratantra, which was also ascribed to a mythical king of Shambhala, namely Pema Karpo (Tib .: padma dkar po ), the successor to Jamyang Dragpa.
This commentary contains numerous quotations from the root tantra that were important for the later development of Tibetan astronomy. The author of the Vimalaprabhā can be ascribed to serious misjudgments in the commentary, which resulted from an evident ignorance of the relationship between Karaņa and Siddhānta works of Indian astronomy. In the Vimalaprabhā, for example, there is an indication that unbelievers have maliciously falsified the true astronomy taught by the Buddha, which is contained in the root tantra, and that these falsifications were spread in the first chapter of the Kālacakratantra.
These hints, as well as the indication of some deviating values from the root tantra that were believed to be correct, were an essential drive for the development of Tibetan astronomy, which ultimately saw itself as a 'reconstruction of the true Siddhānta astronomy taught by Buddha' and in Tibetan as a grub rtsis was called.
The Vimalaprabhā emphasizes two values in particular, which are said to have been essential for the astronomy of root tantra. One value is the factor for converting the length of a mean solar month or a mean zodiac day into mean lunar months or mean lunar days , the one with
A =
can be specified. This value means that 67 mean synodic or lunar months correspond to 65 solar months.
The second conversion factor relates to the ratio of the length of a mean lunar day to the length of a natural day. This corresponds to a mean lunar day
B =
natural days.
Translation into Tibetan
The Kālacakratantra as well as the Vimalaprabhā in their present version date from the 11th century. Both works were translated into Tibetan in the second half of the 11th century by the Indian scholar Somanātha and the Tibetan translator Drolo Sherab Drag (Tib .: 'bro lo shes-rab grags ).
Beginnings of the development of a separate science of astronomy in Tibet (12th century and beginning of the 13th century)
The transmission of Indian astronomical knowledge in the context of the tantric meditation cycle Kālacakratantra to Tibet initially had no meaning for the Tibetan calendar, nor did it result in any significant preoccupation among Tibetans with questions of the complicated calculations of Indian astronomy. This required the extraction of astronomical knowledge from the Kālacakra tantra cycle and representation in its own astronomical texts.
In the 11th and the beginning of the 12th centuries, this task was again taken over by two Indian Buddhist scholars interested in astronomy who contributed to the spread of Buddhism in Tibet.
The first of these two scholars was Abhayākaragupta (1084-1130), known in Tibet under the name Lobpön ("teacher") Abhaya, who under the title Kālacakrāvatāra presented the astronomical contents of the Kālacakratantra in a separate treatise and then translated this work into Tibetan through the Nyinphugpa Chökyi Dragpa (Tib .: nyin phug pa chos kyi grags pa ) (1094–1186).
The second of these two scholars was the famous Kashmiri scholar Śākyaśrībhadra (1127-1225), who wrote three writings on astronomy based on the teachings of the Kālacakratantra, in which he calculated the calendar, the calculation of the solar and lunar eclipses and the movement of the five planets Mercury , Mars, Venus, Jupiter and Saturn. Śakyaśrībhadra visited Tibet in 1204 and stayed there until 1214.
He became one of the outstanding teachers of Sakya Paṇḍita Künga Gyeltshen (1182–1251). From the biography of Sakya Paṇḍita Künga Gyeltshen it can be inferred that he has completed a thorough practical training in calendar calculation and astronomy of Kālacakratantra. He was the first of the Sakya hierarchs we know to have received such training.
This training included, among other things, the practical implementation of addition, subtraction, division and multiplication using the sand abacus , the calculation of the five components of the calendar calculation, the calculation of solar and lunar eclipses, the lengths of the 5 planets and the position of the comet Encke. Sakya Paṇḍita did not write his own contributions to Tibetan astronomy and calendar calculations.
First astronomical textbooks by Tibetan authors (2nd half of the 13th century)
In view of the increasing interest in computational astronomy, the first textbooks on this subject by Tibetan authors soon appeared. The first Tibetan author from whom we have such writings was the famous Tibetan clergyman Chögyel Phagpa (1235–1280).
Chögyel Phagpa wrote nine papers on calendar calculation and astronomy. In all cases, these are practical arithmetic books. The treatises of Chögyel Phagpas are the oldest of the accounts of kālacakra astronomy known to us in the Tibetan language, which are not translations from Indian. In terms of content, Chögyel Phagpa still largely follows the explanations of the Kālacakratantra.
The calendar based on the Kālacakratantra was introduced by him into Tibet and established as the authoritative calendar taught by the Buddha. In this respect, Chögyel Phagpa laid the political basis for the later independent development of Tibetan astronomy and calendar calculation.
Another important clergyman who contributed to the spread of astronomical knowledge in Tibet is the 3rd Karmapa Rangjung Dorje (1284–1339). Rangjung Dorje wrote the first of two textbooks in 1318 that deal with astronomy and calendar calculations as well as astrology.
The textbooks of Rangjung Dorje are also practical arithmetic books that are fully in the tradition of the Kālacakratantra and thus offer little new in terms of scientific history compared to the works of Chögyel Phagpa, with one exception. On approx. 4 ½ pages he explains shortened calculations for the mean movement of the sun, moon, planets and lunar nodes . This is the earliest attempt known so far to calculate the orbital times of these celestial bodies or the mean change in their ecliptical lengths per specific time unit . In addition, he established the Kālacakra astronomy and calendar calculation in the Kagyu school with his two treatises . He has not yet made any significant contribution to the further development of the content of Tibetan astronomy.
Commentary on the program texts of the practical arithmetic books (14th century)
The practical arithmetic books of the gradually spreading astronomy in Tibet, written in verse, were all program texts with arithmetic instructions for the sandabacus, which hardly gave any explanations about what was actually calculated and why. This required oral instruction from a teacher until the beginning of the 14th century. This did not change for the representations in the later practical arithmetic books until modern times. In order to make the problem clear, the program text presented in connection with the calculations with the sandabakus is explained again in the following , whereby the interpretive terms from astronomy have been replaced by the literal meaning of the Tibetan terms:
"(1.) Place the" pure month number "in five places .
(2.) From above, multiply successively by “eye” (2), “cardinal direction” (10), “snake god sense organ” (58), “body” (1), “moon planet” (17).
(3.) From above add one after the other “Suchein” (25), “Treasure” (8), “Zero Body” (10), “Vedas” (4), “Teeth” (32).
(4.) Upward conversion using the values “mountain taste” (67), “season” (6), “sky taste” (60), “zero intermediate direction” (60), “wheel” (27).
(5.) The rest, after deleting the highest point, is the mean sun. "
The Tibetan astronomy student was orally explained by his teacher what “pure number of months ”, namely the number of previously calculated past synodic months , or what “mean sun”, namely “mean length of the sun at the end of the relevant synodic month” means , but there is no explanation in the practical arithmetic books. The same applies to the meaning of the numbers that have to be added or multiplied according to the above calculation rule.
The first comprehensive explanation of the astronomical contents of the astronomical arithmetic books came from one of the most famous scholars of the Tibetan Middle Ages, namely Butön Rinchen Drub . Butön wrote several works on astronomy and calendar calculation. Particularly noteworthy is the first major written in prose commentary work for Kalacakra -Astronomie and calendar account entitled "textbook on the calculations of the Kalachakra, something that pleased the scholars" (Tib .: dpal dus kyi 'khor lo'i rtsis kyi bcos bstan mkhas pa rnams dga 'bar byed pa ) which he completed on November 14, 1326.
This work, which comprises 244 pages, is the first previously known treatise on astronomy and calendar calculation, which does not have the mere form of a practical arithmetic book, but tries to explain the meaning of the arithmetic operations to be carried out on a large scale. In this respect, Butön's work was groundbreaking for the systematic development of Tibetan astronomy and the Tibetan calendar calculation .
Butön was very well aware of the numerical reductions in the Kālacakratantra and their interpretation as malicious falsifications by the Vimalaprabhā. Accordingly, there are also first attempts to introduce new calculation methods based on the transmitted so-called “true values”. In the end he did not succeed because he could not solve the mathematical difficulties of the corresponding arithmetic calculations with the Sandabacus.
The Origin of the Phug-pa School of Tibetan Astronomy (15th Century)
The 15th century was an extremely fruitful period for the development of Tibetan astronomy. One of the most important representatives of this development was the scholar Phugpa Lhündrub Gyatsho (Tib .: phug pa lhun grub rgya mtsho ). The most important school tradition of Tibetan astronomy, the Phugpa School (Tib .: phug lugs ), was named after him. In his Padma dkar-po'i zhal lung ("Instruction of the (King of Shambhala) Padma dkar po "), which was completed in 1447 and written in prose, he presents the new approaches to an astronomical overall picture. The extensive treatise by Phugpa Lhündrub Gyatsho was supplemented by several additional texts by the astronomer and mathematician Norsang Gyatsho (Tib .: nor bzang rgya mtsho ). This created a teaching building that was characterized by the following main focuses:
Theory of the mean motion of all planets known in Tibet
With the theory of the mean movement of all planets known in Tibet, called "analysis (of the movement of the planets) according to the three types of day" (Tib .: zhag gsum rnam dbye ), on the one hand, mathematically correct calculation rules for determining the sidereal times of rotation (Tib. : dkyil 'khor ) for all planets including the sun, moon and lunar orbit nodes in natural days , zodiac days and lunar days . For the sun and moon, only the values taken from Vimalaprabhā were used
A = and
B =
used and with
the period of revolution of the suns in lunar days and with
the period of revolution of the suns in natural days
calculated, with 360 being the period of revolution of the sun in solar days.
For the sidereal orbital periods of the planets Mercury, Venus, Mars, Jupiter and Saturn, the values of the kālacakratantra given in natural days were used.
On the other hand, this part of the astronomy of the Phugpa School contains calculations for the change in the mean ecliptical longitudes (Tib .: rtag longs ) of all planets per natural day, zodiac day and lunar day.
The major conjunction and the correction of the initial values
According to the ideas of Indian astronomy, world history takes place in large time cycles, also called world ages ( cf.Kalpa ), at the beginning of which all movable celestial bodies have the ecliptical length 0, i.e. stood at the fixed starting point of the ecliptic , and the point in time at 1st day of the 1st month of the 1st year of a year cycle fell. The Kālacakratantra as a practical arithmetic book uses a less distant point in time as an epoch , namely the beginning of the month Caitra (Tib .: nag zla ba ) of the year 806. The initial values given for this point in time in the Kālacakratantra were of course not 0. However, it contains the Kālacakratantra information on time periods at the beginning of which a major conjunction is said to have taken place.
Phugpa Lhündrub Gyatsho was able to prove mathematically that with the initial values of the Kālacakratantra the event of a great conjunction (Tib .: stong 'jug ; "entry into the void") could never take place.
He explained this fundamental flaw in the figures of the Kālacakratantra, based on the Vimalaprabhā, by saying that the malicious unbelievers had falsified the Buddha's figures.
As a consequence, he proposed a change in the initial values, which in particular changed the inclusion of leap months in the Tibetan calendar. The Phugpa School finally calculated the fantastic number of 279 623 511 548 502 090 600 years for the period between two major conjunctions. Expressed in number names , these are 279 trillion, 623 quadrillion, 511 trillion, 548 billion, 502 million, 90 thousand and 6 hundred years.
The Solstice Watch and the Crisis in Buddhist Astronomy
For the Tibetan astronomers, observing the starry sky played a completely subordinate role. In any case, systematic observations of the starry sky did not take place, as a computer system taught by Buddha was available with which the changes in the starry sky could be calculated. This attitude was not clouded by the fact that traditional astronomy was numerically falsified.
There were, however, two phenomena in which one could not escape observation: One was the answer to the question whether the calculated solar and lunar eclipses actually took place, which occasionally was not the case. Since the arrival of solar and lunar eclipses was announced in advance by public notices because of their great astrological significance, false prognoses were extremely embarrassing for the astronomers.
In the second half of the 17th century, the Tibetan government under Sanggye Gyatsho imposed sanctions on astronomers who made false announcements about solar and lunar eclipses. In response, the astronomers discontinued public announcements.
Another astronomical phenomenon that was traditionally observed was the winter and summer solstices . According to the Kālacakratantra, the winter solstice takes place with the entry of the sun into the zodiac sign Capricorn and the summer solstice with the entry of the sun into the zodiac sign Cancer .
In his work Kālacakrāvatāra, written in the first half of the 12th century, the Indian teacher Abhayākaragupta (1084–1130) described a method by which the time of the solstices could be measured using a measuring stick called a gnomon (Tib .: thur shing ). Corresponding measurements have now shown that the winter solstice took place with the entry of the sun into the zodiac sign Sagittarius and the summer solstice with the entry of the sun into the zodiac sign Gemini .
In December 1466 and December 1467, Norsang Gyatsho, accompanied by witnesses, again took measurements to determine the winter solstices. He determined that the winter solstice occurred on December 22nd in both years, exactly 7 days after the sun entered the zodiac sign Sagittarius.
These measured deviations at the times of the solstices from the information in the Kālacakratantra could not be explained by the argument that they were falsified by unbelievers. So was the astronomy revealed by Buddha flawed?
The solution to the resulting crisis of credibility resulted from a closer examination of the peculiar world model of Tibetan astronomy. According to this, the sun and moon circled around a central world mountain (cf. Meru ), in the south of which was the triangular continent Jambudvīpa (Tib .: 'dzam bu gling ) with the countries Shambhala, China, Tibet and India etc. Summer and winter solstices were explained by the fact that the sun was high in the north near the world mountain in summer, while in winter it circled the world mountain deeper in the south at a greater distance. The model of solar movement developed from this led to the conclusion that winter and solstices varied in an east-west direction, i.e. according to the geographical longitude .
Although this is inconsistent with reality, the Tibetan astronomers tried on this basis to explain the deviations of their measurements of the solstices from the information in the Kālacakratantra. Since the Buddha had preached the teachings of the “wheel of time” in South India, the geographical longitude of Tibet was to be set at more than 30 degrees east of India. Thus, based on a false assumption about the variation of the solstices, Tibet was moved geographically to the east. This change in situation also had a major impact on the Tibetan calendar.
Fundamental change in the calculation rules for calendar calculations and astronomy
Phugpa Lhündrub Gyatsho presented two fundamentally different models for performing the calendar calculation and the other astronomical calculations.
In the first model, called exact byed rtsis , he gave a representation of the arithmetic rules of the Kālacakratantra, which he cleared of all abbreviations and computational roundings while retaining the initial values.
The culmination of his scientific work, however, was the submission of a calendar calculation and other astronomical calculations, which he presented under the designation grub rtsis as a reconstruction of the true calculation methods of the astronomy taught by Buddha in the root tantra. The most important basis was formed by the results that he had achieved within the framework of his theory of the mean motion of the celestial bodies and in connection with his calculations on the great conjunction.
The heyday of the Phugpa school (17th - 18th centuries)
As the successor to Phugpa Lhündrub Gyatsho and Norsang Gyatsho, the Phugpa School first refined the calculation rules for the theory of the mean movement of the heavenly bodies. The astronomer Pelgön Thrinle (Tib .: dpal mgon 'phrin las ), a nephew of the famous Phugpa Lhüngrub Gyatsho, should be mentioned here in particular . He was the court astronomer of the Phagmo Drupa rulers and was an excellent expert on the Sinotibetan divination calculations . Of his numerous writings, his work on the theory of the mean movement of the heavenly bodies is particularly noteworthy, which is the basis under the title Zhag gsum rnam dbye mkhas pa'i yid 'phrog ("Analysis according to the three types of day that robs scholars of the mind") for the corresponding explanations of the regent Sanggye Gyatsho in the 17th century.
The connection with the politics of the new central Tibetan state founded by the 5th Dalai Lama in the 17th century was of decisive importance for the rise of the Phugpa School to the most important school of Tibetan astronomy . Both the 5th Dalai Lama (1617–1682) and his regent Sanggye Gyatsho (1653–1705) were followers of the Phugpa school, so that the Grub-rtsis calendar of this school became the official calendar of the newly established state. In addition, Sanggye Gyatsho published with his Vaiḍūrya dkar-po, completed in 1685, a comprehensive representation of the calendar calculation of astronomy of the Phugpa school. This publication also contained numerous mathematical innovations.
In addition to the Vaiḍūrya dkar-po, there is another important work from the heyday of the Phugpa school: It is a treatise by the Nyingma scholar Lochen Dharmaśrī (1654–1717), which is entitled rTsis kyi man ngag nyin mor byed pa'i snang ba ("instruction on calculation science, shine of the day maker (sun)") was published. This treatise was begun by Dharmaśrī in 1681 and was not completed until April 3, 1713, 32 years later. Dharmaśrī, who also became famous for his treatise on Sinotibetan divination calculations written in 1684 , was murdered in 1717 by the Djungars who invaded Tibet because of his affiliation with the Nyingma school .
The Development of the Tshurphu School of Tibetan Astronomy (15th - 18th Centuries)
The scholars of the Phugpa School were not the only astronomers who endeavored to reshape Tibetan astronomy. In total, more than six different proposed solutions for calculating the major conjunction are said to have been submitted by different scholars. With the exception of one group, namely the writings of the tradition of the Tshurphu school, the associated works are considered to have been lost.
The Tshurphu school (tib .: mtshur lugs ) of Tibetan astronomy was named after the famous Karmapa monastery Tshurphu . The above-mentioned Karmapa Rangjung Dorje (1284–1339), who wrote his compendium of astrology (Tib .: rtsis kun bsdus pa ) in 1318, is regarded as the founder of this school . However, a development of this teaching tradition comparable to the emergence of the Phugpa school did not begin until the 15th century.
Mention should be made here of the scholar Tshurphu Jamyang Chenpo Döndrub Öser (Tib .: mtshur phu 'jam dbyangs chen po Don grub' od zer ), who was appointed abbot of Tshurphu monastery around 1407 during the lifetime of the 5th Karmapa Deshin Shegpa Held office until 1449. In 1447, the year the Padma dkar-po'i zhal lung was completed by Phugpa Lhündrub Gyatsho, Döndrub Öser completed his basic work on astronomy, with which he presented the original calculations of the root tantra at the wheel of time. Unfortunately, this paper has not yet surfaced.
An overview of the peculiarities of the astronomy of the Tshurphu School is provided by a standard work of this school presented by Karma Nleger Tendzin (Tib .: karma nges legs bstan 'dzin ) in 1732, which Nleger Tendzin wrote in the great East Tibetan monastery of Pelpung Thubten Chökhor Ling. Regarding the theory of the mean movement of the celestial bodies and the conclusions to be drawn from it, there is no essential difference to the Phugpa school. However, Nleger Tendzin assumes other values when calculating the major conjunction. This has the consequence that all initial values of his astronomical calculations differ from those of the Phugpa school. Accordingly, the calendar of this school differs considerably from that of the Phugpa school.
literature
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