1 The Birth of Science - MSRI

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82 3. Other Hellenistic Scientific Theories elementary geometric operations, realizable with two simple instruments: compass and protractor. In Ptolemy’s work the number of circular motions needed to obtain good agreement with experimental data is reduced to two — one deferent and one epicycle — through the introduction of eccentrics (the center of the deferent does not coincide with the earth) and equants (the circular motion is not considered to be uniform, but to have uniform angular velocity with respect to a point, the equant, which differs from the center of the circle). 135 Although these modifications disrupt the symmetry of uniform circular motion, they have the essential merit of buying flexibility without sacrificing computational ease: the use of eccentrics and equants amounts to a simple displacement of the point on which each of the two fundamental instruments — compass and protractor, respectively — is to be centered. This shows that the use of circular motions was not due, as has often been said, to reasons of symmetry or esthetics, but to the concrete need for an algorithm that could reduce the necessary calculations to simple operations realizable with elementary instruments. 136 Just as we saw in Section 2.3 regarding mathematics, the connection between theoretical scientific structures and material instruments used is further proved by the fact that in Mesopotamia the use of clay tablets page 120 as the writing material led astronomy in a different direction from Alexandrian astronomy. 137 Mesopotamian astronomy, in fact, did not employ geometric constructions like Ptolemy’s epicycles, but rather the study of numerical regularities. Although Mesopotamian astronomy is still little known, it is clear from the cuneiform tablets deciphered during the twentieth century 138 that, whereas paleo-Babylonian astronomy was prescientific and qualitative, the level of the mathematical astronomy developed in Mesopotamia during the Hellenistic period is comparable with that of the contemporary astronomy based on geometric methods. 139 Although the mathematical methods were distinct, it is obvious that there were cultural 135 On the actual use of eccentrics and equants one can read [Neugebauer: HAMA] or, for a briefer treatment, any history of astronomy. 136 It seems to me that the conclusion is not warranted that Hellenistic scientists had a preference for circles because of their “perfection”, just because this idea is present in authors of the classical and imperial periods — the more so because imperial-age authors, who no longer mastered the Hellenistic scientific method, often framed scientific results in conceptual schemes belonging to prescientific natural philosophy. 137 By Alexandrian astronomy we mean, as in the case of mathematics, the homogeneous scientific tradition developed in Hellenistic times in the Greek-speaking Mediterranean world, and having its greatest center in Alexandria. 138 The astronomical tablets deciphered prior to 1955 have been published in [Neugebauer: ACT]. 139 For a survey of what is known regarding the history of Mesopotamian astronomy in Hellenistic times one can turn to [Neugebauer: HAMA], pp. 347–558. Revision: 1.13 Date: 2002/10/16 19:04:00
3.8 Ptolemaic Astronomy 83 exchanges. This is shown not only by the fact that scientific astronomy arose in both civilizations simultaneously, but also by mutual influences. For example, Alexandrian astronomers adopted the sexagesimal Mesopotamian system, and the Mesopotamian astronomer Seleucus is referred to as a follower of Aristarchus of Samos. Revision: 1.13 Date: 2002/10/16 19:04:00
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1 The Birth of Science 1.1 The Remo
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1.1 The Removal of the Scientific R
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1.1 The Removal of the Scientific R
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1.2 On the Word “Hellenistic” 7
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1.3 Science 9 first and fourth cent
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1.3 Science 11 point. But a slightl
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1.3 Science 13 eas of technological
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1.4 Was There “Science” in Clas
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1.5 Origins of Hellenistic Science
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1.5 Origins of Hellenistic Science
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2 Hellenistic Mathematics 2.1 Precu
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2.1 Precursors of Mathematical Scie
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2.1 Precursors of Mathematical Scie
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Page 65 and 66: 3.4 Hydrostatics 65 ers more intuit
Page 67 and 68: 3.5 Pneumatics 67 The function of h
Page 69 and 70: 3.5 Pneumatics 69 air in motion; 84
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Page 93 and 94: 4.3 Military Technology 93 [The Rho
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Page 97 and 98: 4.4 Sailing and Navigation 97 The m
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Page 117 and 118: 4.10 The Lost Technology 117 era, k
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Page 121 and 122: 5 Medicine and Other Empirical Scie
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5.5 Development and End of Scientif
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5.5 Development and End of Scientif
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5.6 Botany and Zoology 137 which oc
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5.6 Botany and Zoology 139 in fossi
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5.7 Chemistry 141 specific characte
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5.7 Chemistry 143 We shall see that
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5.7 Chemistry 145 andria, in connec
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6 The Hellenistic Scientific Method
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6.1 Origins of Scientific Demonstra
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6.3 Saving the Phainomena 151 alone
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6.3 Saving the Phainomena 153 If ph
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6.4 Definitions, Scientific Terms a
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6.5 Episteme and Techne 161 Geometr
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6.6 Postulates and the Meaning of
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6.7 Hellenistic Science and Experim
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6.9 Where Do the Clichés about “
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7 Some Other Aspects of the Scienti
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7.2 Conscious and Unconscious Cultu
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7.3 The Theory of Dreams 187 One is
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7.3 The Theory of Dreams 189 classi
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7.4 Propositional Logic 191 Regardi
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7.5 Philological and Linguistic Stu
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7.6 Science, Figurative Arts, Liter
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7.6 Science, Figurative Arts, Liter
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8 The Decadence and End of Science
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8.1 The Crisis in Hellenistic Scien
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8.2 Rome, Science and Scientific Te
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8.2 Rome, Science and Scientific Te
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8.3 The End of Ancient Science 209
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8.3 The End of Ancient Science 211
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9 Science, Technology and Economy 9
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9.2 Scientific and Technological Po
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9.2 Scientific and Technological Po
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9.3 Economic Growth and Innovation
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9.3 Economic Growth and Innovation
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9.4 Nonagricultural Technology and
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9.5 The Role of the City in the Anc
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9.5 The Role of the City in the Anc
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9.6 The Nature of the Ancient Econo
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9.7 Ancient Science and Production
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9.7 Ancient Science and Production
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10 Lost Science Besides being just
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10.1 Eratosthenes’ Measurement of
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10.1 Eratosthenes’ Measurement of
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10.2 Lost Optics 241 subject is Pto
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10.3 The Principle of Inertia 243 T
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Plutarch, in the De facie, writes:
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10.3 The Principle of Inertia 247 A
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10.3 The Principle of Inertia 249 [
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10.4 Ptolemy and Hellenistic Astron
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10.5 A Passage of Seneca 253 The Al
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10.5 A Passage of Seneca 255 The sl
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10.6 Rays of Darkness and Triangula
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10.7 The Idea of Gravity from Arist
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10.8 The Shape of the Earth: Sling
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10.9 Precession, Comets, Etc. 271 m
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10.10 Ptolemy and Theon of Smyrna 1
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10.11 Determinism and Chance 275 vi
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10.12 Atoms, Gases and Heat 277 bas
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10.13 Combinatorics and Logic 279 m
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10.14 The First Few Definitions in
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11 The Age-Long Recovery 11.1 The E
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11.1 The Early Renaissances 291 Pis
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11.1 The Early Renaissances 293 at
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11.2 The Renaissance 295 worthy geo
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11.2 The Renaissance 297 Leonardo
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11.2 The Renaissance 299 was follow
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11.2 The Renaissance 301 tic works
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11.3 The Rediscovery of Optics in E
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11.3 The Rediscovery of Optics in E
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11.4 A Late Disciple of Archimedes
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11.5 Two Modern Scientists: Kepler
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11.5 Two Modern Scientists: Kepler
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11.6 Terrestrial Motion, Tides and
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11.6 Terrestrial Motion, Tides and
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11.7 Newton’s Natural Philosophy
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11.8 The Rift Between Mathematics a
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11.9 Ancient Science and Modern Sci
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11.10 The Removal of Ancient Scienc
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11.11 Recovery and Crisis of Scient
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References [Acerbi: Plato] Fabio Ac
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References 355 translation of Civil
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References 357 [Dijksterhuis: MWP]
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[Frege] Gottlob Frege, Begriffsschr
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References 361 [Hill: E] Donald R.
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References 363 [Lewis: TH] Michael
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References 365 [Oleson: GRWL] John
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References 367 [Rehm] Albert Rehm,
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References 369 “Zur naturwissensc
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References 371 [Wikander: IAWP] Ör
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