In "Tycho's Illusion," Margolis (1998) argues that for the past 400 years it has erroneously been believed that the spheres of Mars and the sun collide on the Tychonic cosmological system. Using a simple cut-out exercise with Tycho's diagram, Margolis contends that no such collision occurs. But his cut-out is incomplete. The spheres do collide.
Margolis contends that, on the contrary, such a collision is an illusion; despite the intersection of their orbits, the spheres of Mars and the sun do not collide.
2. This is perhaps a moot point, but it could be argued that Margolis's thesis, even if correct, is irrelevant, since Tycho's system, as he conceived it, did not entail spheres. Through his study of the motion of comets, Tycho concluded that such spheres did not exist, and hence commenced the search for another mechanism to explain the orbits of the planets -- a problem tackled by some of the best minds of the time, from Kepler to Newton. Nevertheless, Margolis's thesis, even if anachronistic, must not go unchallenged, because, in fact, no one has been fooled these 400 years.
3. The Tychonic system was a compromise between the (geocentric) Ptolemaic system from ancient times, and the (heliocentric) Copernican system of 1543. In Tycho's system, the earth is immovable at the center of the sphere of the fixed stars, with the moon and sun moving around the earth. The planets, however, then orbit the sun in the following order: Mercury, Venus, Mars, Jupiter, and Saturn. Because of the relative distances of the planets from the sun (based in Copernicus's calculation), the orbits of Mars and the sun overlap on this model. (See Figure 1)
4. Margolis's argument (and evidence) for his thesis is based on the following exercise with Figure 1. He tells the reader to cut out the model around (or below) the orbit of the moon and also below the sphere of the fixed stars: the resulting cut-out (or template) thus contains the orbit of the sun and the orbits of the planets. Now, placing this template over the original diagram, one is next told to rotate the template around the earth, hence putting the sun and planets in motion. Since there is no resulting collision, Margolis maintains that such a belief has been a 400 year illusion.
5. But of course there is no collision using the template this way, because the planets are not, in turn, moving around the sun (as they must do in the Tychonic system). The cut-out alone is incomplete; it only accounts for the motion of the sun around the earth, with the planets fixed in their orbits. Try to cut out the orbit of Mars in the template and rotate it around the sun. This cannot be done, because the spheres of Mars and the sun (if there were such spheres) overlap and hence collide. (On the other hand, Mars and the sun, as planets moving on individual orbits, do not collide.)
6. In sum, there is no 400 year illusion. Instead, Margolis has deluded himself into believing so.
Margolis, H. (1998) Tycho's Illusion: How It Lasted 400 Years, and What That Implies About Human Cognition PSYCOLOQUY 9 (32) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.32.cognitive-illusion.1.margolis