The treatment of observations in early astronomy. (English) Zbl 0787.01002
Precision of instruments, treatment of astronomical observations, and development of error theory from antiquity (esp. Aristarchos of Samos (310–230), Archimedes (287–212), Hipparchus of Nicaia (180–125) and Ptolemy of Alexandria (85–65)), up to Levi ben Gerson (1288–1344) and J. Kepler (1571–1630) are being discussed. New English translations of Ptolemy’s Almagest by G. J. Toomer (1984), and of Kepler’s New Astronomy by W. H. Donahue (1992) are regarded.
Ptolemy did not pay due attention to rounding off or to some other aspects of practical computation. Often the errors are of the same order of magnitude as the effect under consideration. It seems that Ptolemy was an opportunist, collecting data of other observers, and ready to simplify and to fudge data. His star catalog had been compiled in the main during Hipparchus’s time. Relations to other star catalogs of Al-Sufi (ca. 964) and of Ulugh Beg (1437) are considered. Better instruments and regular observations were demanded by Levi ben Gerson. Kepler had to choose between three models of the world. His main goal was checking the fitness of models, hereby he apparently applied the principle of minimax. He also adjusted certain observations by small arbitrary quantities, it is possible that he used an embryonic form of the Monte Carlo method: Some special remarks are given to his triangulation of Mars.
Ptolemy did not pay due attention to rounding off or to some other aspects of practical computation. Often the errors are of the same order of magnitude as the effect under consideration. It seems that Ptolemy was an opportunist, collecting data of other observers, and ready to simplify and to fudge data. His star catalog had been compiled in the main during Hipparchus’s time. Relations to other star catalogs of Al-Sufi (ca. 964) and of Ulugh Beg (1437) are considered. Better instruments and regular observations were demanded by Levi ben Gerson. Kepler had to choose between three models of the world. His main goal was checking the fitness of models, hereby he apparently applied the principle of minimax. He also adjusted certain observations by small arbitrary quantities, it is possible that he used an embryonic form of the Monte Carlo method: Some special remarks are given to his triangulation of Mars.
Reviewer: H.Grimm (Jena)
MSC:
| 01A20 | History of Greek and Roman mathematics |
| 01A30 | History of mathematics in the Golden Age of Islam |
| 01A40 | History of mathematics in the 15th and 16th centuries, Renaissance |
| 62-03 | History of statistics |
| 85-03 | History of astronomy and astrophysics |
| 65G50 | Roundoff error |
Keywords:
astronomy; error theory; Aristarchus; Archimedes; Hipparchus; Ptolemy; Levi ben Gerson; Kepler; principle of minimaxBiographic References:
Aristarchus of Samos; Archimedes; Hipparchus of Nicaia; Ptolemy of Alexandria; Levi ben Gerson; Kepler, JohannesReferences:
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