In Our Own Image: Personal Symmetry in Discovery
- István Hargittai &
- Magdolna Hargittai
Kluwer Academic/Plenum: 2000. 235 pp. £34.50, $49.95
Take for example Johannes Kepler, who tried to link the orbits of the six known planets to the five Archimedean solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron. He thought that a series of concentric spheres including the orbits of the planets must have some special geometric property. A cube inscribed in the sphere of Saturn's orbit would just contain the sphere for Jupiter. A tetrahedron within that sphere would contain a sphere for Mars. And so on, until Mercury's sphere lay neatly within an octahedron whose apices touched the sphere for Venus. The idea worked pretty well, but did not quite fit the distances Copernicus had calculated between the planets. In trying to eliminate the assumed error, Kepler observed that planetary orbits are not circular but elliptical. He discovered the rules that link these ellipses with the length of time a planet takes to orbit the Sun, rules that Isaac Newton was able to generalize into a law of gravitation. Ideal symmetry was abandoned, leading directly to more profound understanding.
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