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3.0 out of 5 stars
Inconspicuous, June 28, 2008
This review is from: Kepler's Geometrical Cosmology (Hardcover)
This is an inconspicuous survey of Kepler's cosmology. Since Stephenson has covered much the same material much more thoroughly this book is not very useful, not least owing to Field's lightweightness when it comes to mathematics (a telling example: she apparently believes, for example, that the approximation sin(x)=x for small x is valid only for radians; p. 192, 1988 Athlone ed.). Nevertheless one can of course read it with pleasure since the subject matter is so enjoyable.
The two main works examined are the Mysterium Cosmographicum and the Harmonices Mundi. The former revolves around Kepler's remarkable polyhedral theory of planetary distances. This theory is of course heavily influenced by Plato's Timaeus, which according to Kepler "is, beyond all possible doubt, a commentary on the book of Genesis ... transforming it into Pythagorean philosophy, as will be apparent to an attentive reader who compares it with Moses' own words" (p. 1).
Indeed, Kepler had initially hoped, like Timaeus, to treat all aspects of the world in a similar fashion. But this was not to be. Instead, returning to this work many years later, Kepler has reached the conclusion that "the heavens, the first of God's works, were laid out much more beautifully than the remaining small and common things" (title page of the second edition of the Mysterium Cosmographicum; p. 142).
The polyhedral theory was an empirical success. "Until quite recently, twentieth-century cosmologists would have been very pleased if their theories had fitted the observations as well as Kepler's do" (p. 38).
But Kepler was not satisfied. "Tycho's observations [enabled] Kepler to calculate more accurate values for the radii of the planetary orbs. ... [Kepler] expected that [the new values] would would be correspondingly closer to the theoretical values calculated from the polyhedral Archetype ... Since it turned out that the agreement between theory and observation was not much changed by using the new more accurate orbits, Kepler set about changing his theory" (p. 179).
"However, there was no need for any drastic modification of the [polyhedral] theory, which Kepler still regarded as intellectually satisfying, mathematically justified and in fairly good agreement with observations." (p. 94). Indeed, Kepler published a second edition of the Mysterium Cosmographicum in 1621 in his mature age.
Perhaps the main revision in the notes Kepler added for the second edition concerns his initial insistence on using only three-dimensional figures to explain the cosmos: "Oh what a mistake" (p. 172) he now says (otherwise the revisions are minor, e.g., "behold a manifest hallucination; eight is not a factor of sixty"; p. 75). This exclamation stems from the fact that the use of plane figures had in the meantime served Kepler well in the Harmonices Mundi, the closest he would get to a comprehensive cosmology à la Timaeus. Here he explains musical consonances in terms of ratios of arcs cut out of a circle by the constructible regular polygons. Kepler then found these consonances among the extremum angular velocities of the planets. In the same work he also applied the same ideas to astrology: from empirical data he had been collecting (pp. 128-130), Kepler found that the angles between planets corresponding to "powerful Configurations" were precisely the angles of "the side of a convex or star polygon" (p. 131; see Kepler's illustrations, pp. 136-141).
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