Abstracts of Symposium 2

Comparison and Connection in the Astral Sciences across Eurasia

Yuzhen Guan
The Culminating Stars in Chinese and Babylonian Astronomy

Rising time schemes are Babylonian cuneiform texts dealing with culminating stars at the time of sunrise and sunset. There are two kinds of such schemes, either in a calendar-based framework, to record culminating points monthly, or even daily; or in a zodiac-based framework, to mark the culminating points corresponding to particular points of the zodiac signs. Similarly, there is a long tradition of observing and recording the culminating stars zhongxing 中星 in Chinese astronomy. The treatises, including dynastic histories indicate that there are two stages of understanding culminating stars in traditional Chinese astronomy: first, observing the culminating stars during morning and evening twilight on particular days as recorded in the Shangshu尚書, Xiaxiaozheng夏小正, etc; second, providing calculating procedures in Tang and Song official calendrical systems. This research aim to investigates the different views and uses of culmination in Babylonian astronomy and ancient Chinese astronomy.

Alexander Jones
Transmissions of the Babylonian zodiac

There were plural transmissions of the Babylonian zodiac to the Mediterranean civilizations (Greek, Egyptian, Roman), reflecting both the multiplicity of uses of the zodiac and the complexities of contact between Babylonia and its neighbours. While mathematical astronomy in the service of astrological computation provided a vehicle for what one might call the “metric” concept of the zodiac as a scale for quantifying the apparent positions and motions of the heavenly bodies, other adaptations and applications of the zodiac preceded and coexisted with this technical use, as can be shown from various sources including inscriptions, technical and nontechnical literature preserved through the medieval tradition, and iconographic representations.

John Steele
The Length of Life in Babylonian and Greek Astrology

Several Babylonian nativity omens predict for an individual that his or her “days will be long” or “days will be short”, meaning that he or she will life a long or a short life. In this paper I present the first evidence for a more detailed Babylonian astrological scheme which linked an exact number of year that an individual will live with the signs of the zodiac. I then compare this scheme with schemes for predicting the length of life known from Greek astrology in order to see whether there are any common features and whether there is any evidence that the Greek schemes were based upon a Babylonian original.

Erica L. Meszaros
The Legacy of Babylonian Astronomers in the Language of Greek and Roman Authors

Greek and Roman astronomy made use of observational data, astronomical parameters, systems of mathematical astronomy, and measurement systems borrowed from Babylonia. Despite this clear influence, Babylonian astronomers are infrequently referenced by name in later Greek and Latin texts. Berossus, Sudines, Kidenas, and Nabourianos are named in the works of Pliny the Elder, Strabo, Vettius Valens, and others, but these four comprise the limited examples where such naming occurs. Since specific references to named individuals are rare, the language used in these instances may provide a unique method for understanding how Babylonian astronomers were viewed in Greek and Roman cultures. Does this language suggest attitudes of respect and reverence, or mundane reference to established practice? This presentation examines the language used to describe Babylonian astronomers in Greek and Latin texts and seeks to identify if this language differs from that used to discuss astronomers from other cultures in order to contribute to a more complete understanding of the relationship between Babylonian astronomers and the Greeks and Romans who made use of their work.

Zhang Nan
Research on astronomical instruments used and manufactured by Zhang Heng and Ptolemy

During the similar period, Zhang Heng and Ptolemy became the masters of astronomy in their own civilizations, and established the Han Dynasty paradigm and Ptolemy tradition that respectively influenced the East Asia and Europe for more than a thousand years. This paper attempts to use the astronomical instruments as a research perspective, starting from the two clues of observation instruments and demonstration instruments, and discussing the astronomical theories and ideas embodied in instruments from the astronomical observation to the demonstration.
The instruments described in Almagest became the starting-point for the instrumentation of astronomy in western Europe, such as the meridian ring, equatorial ring, armillary sphere, astrolabe and more. In early imperial China, Eastern Han Dynasty, the records of Zhang Heng’s astronomical instruments are scattered in some ancient books, also formed a continuation of the tradition of astronomical instrument manufacturing, what we currently know includes observation armillary sphere, water-power movement celestial globe and a little sphere (小浑) for coordinate transformation and calculation. The origin, structure, method of use and function of these instruments are all issues that we need to address.

Rui Zhang
From Aratus to Geminus: ‘Phenomena’ in the Hellenistic Period

In Plato’s time, ‘phenomena’ denotes the intermediary between the data and the theory of heavenly bodies’ motions. In the Hellenistic Period, Aratus’ Phenomena and Geminus’ Introduction to the Phenomena focus on basic knowledge without giving complicated theoretical proof. Both books contain knowledge in similar subjects such as constellations, axis and poles, days of the month, celestial circles, weather signs and so on. This study investigates the changing of the meaning of ‘phenomena’ from Aratus to Geminus by means of comparing different interpretations when dealing with the same phenomena in the two books. Aratus’ Phenomena attempts to approach the truth by imagination based on the description of observations, like what Plato did, while in Geminus’ Introduction to the Phenomena, phenomena has already become pure astronomical knowledge with no signs of philosophical influence.

Lyu Peng
Kuṭṭaka and Da-Yan-Shu: Indian and Chinese Methods of Solving the Congruence Problem

Around early centuries CE, India and China developed similar methods to solve the congruence problem mainly originated from calculating the epoch of the calendar. In India Kuṭṭaka (lit., pulverizer) is first described by Āryabhaṭa (b. 476) in his mathematical astronomy text Āryabhaṭīya and continuously improved by the later Indian mathematicians such as Brahmagupta (b. 598) and Bhāskarācarya (1114 – 1185). In China the rule for the congruence problem first appeared in the Sun-Zi-Suan-Jing (《孙子算经》, around 400 AD), which is also known as the Chinese Remainder Theorem. However, this rule cannot be supplied to all kinds of congruence problem. Then the universal method is designed by Qin Jiushao (秦九韶, 13th century) in his Shu-Shu-Jiu-Zhang (《数书九章》). Actually this method consists of two correlative algorithm called Da-Yan-Qiu-Yi-Shu (大衍求一术) and Da-Yan-Zong-Shu-Shu (大衍总数术). It is discovered that there are significant similarities between the Indian Kuṭṭaka and Chinese Da-Yan methods. Both of them are based on the computation of Euclidean Algorithm and designed systematically (i.e., iterative computation) and graphically (i.e., the creeper of remainders and the square of manipulating numbers). At the same time there are also some differences in the computing order and option. We will give a symbolical mathematical proof to interpret the parallel and then discuss the features of the two methods. As a result, compared with Da-Yan-Shu the Kuṭṭaka method seems to be more general, simpler and easier because Indian mathematicians are skilled at dealing with the calculation involving zero. In order to show this point, we will give an illustration of solving Qin Jiushao’s congruence problems by Indian Kuṭṭaka method.

Weixing Niu
Lunar Apogee: A Greek Astronomical Concept in China

In ancient Chinese astronomy the lunar perigee was customarily taken as the starting point in calculating lunar motion, while in Greek astronomy the lunar apogee was used. The Greek astronomy was absorbed by the Indian astronomy and was introduced into China through the spread of Buddhism. Some cases of apogee being the starting point of the Lunar Ephemerides in Chinese official calendrical system, and the Ephemerides of lunar apogee (Ketu) preserved in the Chinese-translated sutras, will be investigated in this presentation. It will also be pointed out that the calculation of lunar apogee, which was renamed as Yuebei, together with Rāhu, Ketu and Ziqi, became more and more popular in fortune-telling system in Song, Yuan and Ming Dynasties, and eventually won a legitimate status in the official calendrical system.

Pan Yue
Al-Bīrūnī’s criticism on Indian Cosmography in his “India”

Al-Bīrūnī devoted nearly ten chapters in India to Indian cosmography. He related these Indian thoughts on the genesis and structure of cosmos. He criticized such thoughts as ridiculous nonsense from the viewpoint of Greek reason, so that he wanted to show his advantage on Indian counterparts. A detailed study on these criticisms shows his psychology on Indian culture.

Christopher Cullen
New light on the conflict between European, Islamicate and Chinese astronomical traditions in late 17th century China

After the adoption of a European astronomical system by the new Qing dynasty in 1644, the administration of the Chinese astronomical establishment remained in Jesuit missionary hands for two decades, displacing both the native Chinese system and the Islamicate system that had been run in parallel with it during the previous dynasty. The conflict that modern scholars call the ‘calendar case’ li yu 曆獄 was marked by the condemnation of the practitioners of European astronomy in 1665, and their return to favour in 1669. The main outlines of this story have already been discussed by a number of scholars. There are however significant aspects of the second phase of the calendar case that have not so far been given the attention they deserve. This talk uses a careful reading of contemporary letters by the Jesuit Gabriel de Magalhães, combined with Chinese sources, to show that the story is more complex, and more interesting, than it has appeared to be so far.

Osman Süreyya Kocabaş
An Extenuated Treatise about Comets and The Pre-Modern Ottomans’ classical scientific Explanation of Comet

Cometary events were seen as one of the atmospheric phenomena or sub-lunar objects and interpreted as ominous, inauspicious facts, an ill omen, or the sign of God in the Classical Ottoman thought just like in the other cultures. Despite misapprehension of the physical nature of comet or “tailed star – kawkab al-dhanab”, it kept its position at the focus of interest of Ottoman astrologers, scholars, and ordinary people. While many Ottoman chronicles -tawarikhs- recorded, and many cosmological and astrological prophecy books mentioned and described them, comets were described as astrological facts and discussed limitedly in scientific books. Unlike the Ottomans, there are numerous observational records conducted by famous Islamic scholars such as al-Kindi, Abu Ma’shar, and al-Kuhi. Despite few sources about comets in the Ottomans, I want to emphasize in my presentation that the risalah -treatise- named Tuhfa al-albab fi bayan hukm dhawat al adhnab written in Arabic by Abd al’lah al-Maqdisi al-Azhari (d. 1668) is important because it includes some interpretations of other Islamic scholars’ descriptions. It was compiled and dedicated to Ottoman Sultan Mehmed IV. in the 17th century, just before Newton’s true description was released. The author based his theory and description of the Aristotelian exhalation theory that the interaction of four elements can cause many meteorological and atmospheric phenomena. He enlists sorts of comets in terms of their shape, discusses why their colors change, tries to explain the interaction between comets and the five planets, and also discusses if comets are a kind of sky objects like a star or not. Additionally, he answers why comets are ominous. Noticeably, this treatise has an exceptional compilation in the Ottoman literature as well as in the Islamic tradition because of being devoted to comets only.

Anna Jerratsch
The Role and Functions of Visuals in Early Modern Cometary Tracts

As frightening and impressive phenomena, comets in the early modern period encouraged intensive communication processes. German vernacular pamphlets of the 16th and 17th centuries offer a unique insight into a multifaceted discourse on the knowledge and interpretation of comets. Visual elements like pictures or diagrams are important parts of those tracts that fulfilled different functions: They were used to seek and create attention in order to attract an audience. They offered explanation and interpretation by visualizing observational results and they were used to popularize different ideas about comets. This paper evaluates these functions throughout a crucial time period of 150 years in order to elaborate on the development in how comets were perceived, explained and interpreted. This evaluation is then used to challenge traditional historiographical narratives which present the change of the knowledge on comets as a linear process of rationalization and naturalization.