## Babylonian Astronomy

Although the Babylonians did not contribute to cosmology, their astronomy is of great interest because the astronomical data they accumulated would later be of the utmost importance in the development of Greek geometric astronomy and cosmology. The emergence of Babylonian astronomy was preceded many centuries earlier by the appearance of a very advanced mathematics, documented in cuneiform clay tablets dating back to 1700 b.c. and earlier. This mathematics was based on a base-60 positional numeration system and contained solutions to quadratic equations and algorithms to compute the square roots of numbers. Although there was some interest in geometry, the Babylonians emphasized the arithmetic and algebraic parts of mathematics. There was, during this older period, no comparable development of astronomy in even its most rudimentary empirical form. It was only much later, beginning around 600 b.c., that a sophisticated numerical astronomy was cultivated. The Seleucid Babylonians compiled very accurate tables giving the positions of the Sun, Moon, and planets as a function of time. They did so using the ancient mathematical tools; thus the base-60 system of notation was used to measure time and angles and has survived up to this day in timekeeping and navigation.

In considering Babylonian mathematics and astronomy we are in the unusual position of having a substantial collection of original artifactsâ€”the clay tablets on which the tables and procedures were recordedâ€”but very little or no information about the individual astronomers and no explanation of the methods and outlook that guided their work. We know that at a fairly early stage the Babylonians divided the ecliptic into twelve parts, each part being 30 degrees wide. These parts would become associated with constellations in a way that is familiar to everyone today. The zodiacal divisions, or signs, provided a convenient way of identifying the location of a celestial body, which would be given in terms of the sign and the number of degrees along the ecliptic within the sign.

Some indication of the character of Babylonian astronomy may be obtained from a tablet from 133 b.c. giving the position of the Sun each month when it is in conjunction with the Moon. (The following account is based on Neugebauer (1969, chap. 5).) The speed of the Sun's motion along the ecliptic varies, with motion being faster in the winter and slower in the summer. The total variation in speed is not large, being only about 3 percent of the average speed. Babylonian astronomers not only detected the variable solar speed but compiled tables accurately, giving it as a function of time. The table in question contains three columns. The month is listed in the first column, the number N of degrees traveled by the Sun in a one-month period following conjunction with the Moon is in the second column, and the position P of the Sun at conjunction is in the third column. (The structure of the table is indicated in table 2.1, which describes three successive rows. It should be noted that specific numbers rather than variables appear in the original table.) In order to find the position of the Sun for the next month, one adds P to N, and this gives the next entry in the third column. The second column gives the solar velocity along the ecliptic since it lists the degrees traveled by the Sun in successive, constant, one-month time periods. It turns out that the function giving the solar velocity is what is called a linear zigzag function, in which the dependent variable increases in a linear fashion, stops, and then decreases in a linear fashion.

 Degrees traveled by the Sun in one-month period following Position of Sun at Month conjunction with Moon conjunction with Moon T N P T + 1 N' P + N T + 2 N" (P + N) + N'

In a comment on this and other tables Neugebauer (1969, 110) observes that "at no point of this theory are the traces of a specific geometrical model visible." Babylonian astronomy, even more so than Babylonian mathematics, avoided any use of geometrical figures or constructions. The positivist dream of a science without hypotheses was realized by the Babylonians in their computations of planetary positions. From the existing evidence it appears that only functional numerical patterns inferred from the data were used to compile predictive tables. That the Babylonians were able to attain such high levels of observational accuracy with no underlying geometrical cosmology is one of the great marvels of ancient exact science.

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