History of Western Philosophy - Bertrand Russell [128]
Copernicus perhaps came to know something, though not much, of the almost forgotten hypothesis of Aristarchus, and was encouraged by finding ancient authority for his innovation. Otherwise, the effect of this hypothesis on subsequent astronomy was practically nil.
Ancient astronomers, in estimating the sizes of the earth, moon, and sun, and the distances of the moon and sun, used methods which were theoretically valid, but they were hampered by the lack of instruments of precision. Many of their results, in view of this lack, were surprisingly good. Eratosthenes estimated the earth's diameter at 7,850 miles, which is only about fifty miles short of the truth. Ptolemy estimated the mean distance of
the moon at 29 1/2 times the earth's diameter; the correct figure is about 30.2. None of them got anywhere near the size and distance of the sun, which all under-estimated. Their estimates, in terms of the earth's diameter, were:
Aristarchus, 180;
Hipparchus, 1,245;
Posidonius, 6,545.
The correct figure is 11,726. It will be seen that these estimates continually improved (that of Ptolemy, however, showed a retrogression); that of Posidonius5 is about half the correct figure. On the whole, their picture of the solar system was not so very far from the truth.
Greek astronomy was geometrical, not dynamic. The ancients thought of the motions of the heavenly bodies as uniform and circular, or compounded of circular motions. They had not the conception of force. There were spheres which moved as a whole, and on which the various heavenly bodies were fixed. With Newton and gravitation a new point of view, less geometrical, was introduced. It is curious to observe that there is a reversion to the geometrical point of view in Einstein's General Theory of Relativity, from which the conception of force, in the Newtonian sense, has been banished.
The problem for the astronomer is this: given the apparent motions of the heavenly bodies on the celestial sphere, to introduce, by hypothesis, a third co-ordinate, depth, in such a way as to make the description of the phenomena as simple as possible. The merit of the Copernican hypothesis is not truth, but simplicity; in view of the relativity of motion, no question of truth is involved. The Greeks, in their search for hypotheses which would 'save the phenomena', were in effect, though not altogether in intention, tackling the problem in the scientifically correct way. A comparison with their predecessors, and with their successors until Copernicus, must convince every student of their truly astonishing genius.
Two very great men, Archimedes and Apollonius, in the third century B.C., complete the list of first-class Greek mathematicians. Archimedes was a friend, probably a cousin, of the king of Syracuse, and was killed when that city was captured by the Romans in 212 B.C. Apollonius, from his youth, lived at Alexandria. Archimedes was not only a mathematician, but also a physicist and student of hydrostatics. Apollonius is chiefly noted for his work on conic sections. I shall say no more about them, as they came too late to influence philosophy.
After these two men, though respectable work continued to be done in Alexandria, the great age was ended. Under the Roman domination, the Greeks lost the self-confidence that belongs to political liberty, and in losing it acquired a paralysing respect for their predecessors. The Roman soldier who killed Archimedes was a symbol of the death of original