When the Earth Was Flat (eBook)

Dirk L. Couprie is a retired scholar (University of Leiden). Doctoral dissertation at University of Amsterdam with a thesis on Anaximander.Current position: leader of a project on Presocratic Philosophy at the philosophical department of the faculty of philosophy and arts, University of West Bohemia in Pilsen.Areas of work: Presocratic philosophy, more especially Presocratic cosmology; also ancient cosmology in a broader perspective (ancient Egyptian, ancient Jewish, ancient Chinese).

Spherical versus Flat Foreword AcknowledgementsReferencesIntroduction                                                                                                                     Chapter 1        Preliminaries on Sources and Methodology          Sources          Methodology          ReferencesPart One     Ancient Greece Chapter 2        Peculiarities of Presocratic Flat Earth Cosmology           The shape of the earth Arguments concerning the shape of the earth          Geographical issues          The tilt of the celestial axis          The alleged tilt of the earth          Climatological issues             Falling on a flat earth          Distance of the heavens          Temporal issues          ReferencesChapter 3        Anaximander’s Images          Introduction          The cosmic tree          The tilted tree          The reversal in the relationship between air and fire          Tamed fire          Turning wheels          Two images for escaping fire          Tilted wheels          ReferencesChapter 4        Anaximander’s Phenomenological Astronomy          Closing fire spots          Phases of the moon Lunar eclipses          Solar eclipses          ReferencesChapter 5        Anaximander’s Numbers          Introduction          An ordered universe          Anaximander’s numbers of the heavenly bodies          Tannery and the standard interpretation          The problem of the sun’s distance           Attempts to explain the origin of Anaximander’s cosmological numbers          An interpretation dating from before Tannery          The sun’s angular diameter          Skeptical conclusions and a possible way out          A new interpretation: the numbers as a calculator for the lunar cycle          Conclusions          ReferencesChapter 6        Anaximenes’ Cosmology          The cap simile; Graham and the top hat          The tilted earth interpretation of the cap simile          Bicknell’s interpretation of the cap simile          McKirahan’s interpretation of the cap simile          Fehling and the flat heaven          A fresh look at the doxography          Anonymous texts and Kirk’s interpretation          Towards an interpretation of Anaximenes’ cosmology          Concluding remarks           ReferencesChapter 7        Xenophanes’ Cosmology          A cosmological quotation from Xenophanes’ poemXenophanes’ text in the interpretation of Aristotle, Achilles Tatius, Empedocles, pseudo-Aristotle, and Simplicius          Xenophanes’ text in the interpretation of Aëtius, Strabo, and CiceroXenophanes’ text in the interpretation of Diogenes of Oinoanda, Hippolytus, and pseudo-Plutarch          Xenophanes’ text in the interpretation of some recent authors           Xenophanes’ text in the interpretation of Mourelatos          The nature and movements of the celestial bodies          The interpretation of an enigmatic text: Drozdek and Mourelatos          Mourelatos’ interpretation illustrated by GrahamA cosmic railway system and a cosmic ballet          The different paths of the heavenly bodies according to Mourelatos and Graham          Some more textual and conceptual problems          The earth not infinitely extended, neither in surface nor in depthThe two meanings of ἄπειρος          A spherical cosmos and a hemispherical heaven          The “many suns”          The curved paths of the celestial bodies           All disappearances of heavenly bodies are quenchings          Final remarks          ReferencesChapter 8        Anaxagoras on The Milky Way and Lunar Eclipses          Introduction          The Milky Way           Anaxagoras on the Milky WayIntroductory remarks on eclipses          Anaxagoras’ alleged explanation of lunar eclipses The incompatibility of Anaxagoras’ theory of the Milky Way with his alleged explanation of lunar eclipses           Invisible heavenly bodies below the moonAttempts to understand the invisible bodies as an additional cause of lunar eclipses          Invisible bodies as Anaxagoras’ only theory of lunar eclipses          The possible origin of a misunderstanding          Concluding remarks          ReferencesAddendum to Chapter 8: “Crepuscular” Lunar Eclipses During Anaxagoras’ Lifetime          ReferencesChapter 9        Anaxagoras on The Light and Phases of the MoonIntroductionCould Anaxagoras have given the correct explanation of the moon’s phases?Anaxagoras on the light of the moon in Aëtius 2.25 and analogous textsAnaxagoras on the light of the moon in Aëtius 2.28 and analogous textsAnaxagoras on the light of the moon in Aëtius 2.29 and analogous textsAnaxagoras on the light of the moon in Aëtius 2.30 and analogous textsProblems and past suggestions to solve themThe ambiguity of “received light”The moon’s light and phases according to Anaxagoras’ suggestions for a new interpretationConclusion          ReferencesChapter 10      Anaxagoras and the Measurement of the Sun and MoonThe doxographical evidence Did Anaxagoras measure the size of the sun and moon with the help of a solar eclipse?Solar eclipses; umbra, penumbra, and antumbra Graham and Hintz on the eclipse of February 17, 478 BCFurther critical remarks on Graham and Hintz’ attemptFehling’s attemptAn extrapolation of Thales’ method to measure the height of a pyramid          ReferencesChapter 11      Aristotle’s Arguments for the Sphericity of the EarthIntroduction The first empirical argumentThe second empirical argumentThe third empirical argumentEmpirical arguments that Aristotle did not useAristotle on empirical arguments for a flat earth Theoretical arguments for a spherical earthFinal remarks          ReferencesPart Two    Ancient ChinaChapter 12      An Ancient Chinese Flat Earth Cosmology. Main FeaturesThe gai tian model of a flat earth and a flat heavenThe movements of the heavenly bodies and the location of ZhouThe shadow rule and the fundamental cosmic measurementsSome more calculationsThe incorrectness of the shadow ruleThe horizon and the rising and setting sun as optical illusionsQuestionable interpretations of the heavens as an optical illusionThe heaven as an optical illusion and the range of visibilityThe interrelation of the range of visibility and the area of sunlightAnother interpretation of the three-dimensional shape of sunlightThe size of the area of sunlight (first approach); the circle of the equinoxThe size of the area of sunlight (second approach); the xuan jiHow we see the sun; the shadow rule once again The limited applicability of the shadow ruleThe cardinal directions          ReferencesChapter 13      An Ancient Chinese Flat Earth Cosmology. Details and CalculationsThe location of ZhouMeasuring the sun’s diameterThe extension of the solar illuminationGeographical measurementsSunrise and sunset seen from ZhouThe seven heng and the limit of the cosmosAn extrapolation: the southern poleThe heaven shaped like a truncated conical rain hat?A short evaluation of the gai tian system in the Zhou bi          ReferencesChapter 14      Ancient Chinese Versus Greek Flat Earth Cosmology Two kinds of flat earth cosmology comparedGreek influence on the gai tian flat earth cosmology?          ReferencesChapter 15      Two Appendices: Cosmas Indicopleustes and Samuel Birley Rowbotham Cosmas Indicopleustes and the shadow ruleRowbotham: the world not a globe          ReferencesList of AbbreviationsList of IllustrationsQuotations from Ancient Greek and Roman AuthorsQuotations from the Zhou bi and Ancient Chinese Authors Bibliography