Customer Review

May 30, 2010
This is of course the book in which Kepler presents his famous polyhedral theory of planetary distances, which Kepler summarises thus on the opening page:

"Greetings, friendly reader. The nature of the universe, God's plan for creating it, God's source for the numbers, ... the reason why there are six orbits, the spaces which fall between al the spheres...---here Pythagoras reveals all this to you by five figures." (p. 49)

Although this theory itself is very famous, the details of Kepler's reasoning are not, so I would like to convey its flavour by means of a few examples. Consider first the issue of how to justify the ordering of the polyhedra that matches the planetary distances. This arrangement is justified by a myriad dubious arguments, of which the following is a representative sample:

"[The regular polyhedra] are classified into three primaries, the cube, tetrahedron and dodecahedron, and two secondaries, the octahedron and the icosahedron. For the correctness of this distinction, note the properties of each class. ... 2. Every one of the primaries has its particular type of face: the cube has the square, the pyramid the triangle, the dodecahedron the pentagon; the secondaries borrow the triangular face from the pyramid. ... 6. It is characteristic of the primaries to stand upright, of the secondaries to balance on a vertex. For if you roll the latter onto their base, or stand the former on a vertex, in either case the onlooker will avert his eyes at the awkwardness of the spectacle. ... Therefore, since there was an obvious distinction between the solids, nothing could be more appropriate than that our Earth, the pinnacle and pattern of the whole universe, and therefore the most important of the moving stars, should by its orbit differentiate between the two classes stated, and should be allotted the position which we have attributed to it above." (p. 105)

Once this role of the earth as a divider is recognised, the five remaining planets become associated with one polyhedron each. This leads to "an astrological game" (p. 119) with such conclusions as: "Woman is always fickle and capricious; and the shape of Venus [i.e. the icosahedron] is the most capricious and variable of all [i.e. has the most faces]." (p. 117)

Lest anyone should look disparagingly on such "games," Kepler provides a beautiful statement of the purpose of astronomy:

"As we do not ask what hope or gain makes a little bird warble, since we know that it takes delight in singing because it is for that very singing that a bird was made, so there is no need to ask why the human mind undertakes such toil in seeking out these secrets of the heavens. ... The reason why there is such a great variety of things, and treasuries so well concealed in the fabric of the heavens, is so that fresh nourishment should never be lacking for the human mind, and it ... should have in this universe an inexhaustible workshop in which to busy itself." (p. 55)
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