Margolis (1998) argues that a solid-spheres version of the Tycho model of planetary orbits is indeed possible, and only appears impossible because of a cognitive illusion. This is not quite the case, as can be clearly seen from an animated version of the Tychonic system.
2. Tycho's system of planetary orbits came at a time when both the geocentric view of the universe and the notion of solid spheres carrying the planets was under question. Observations such as that of the comet of 1577 made it increasingly difficult to believe in an essentially solid universe, since the motion of such comets would be through the substance of the spheres. Indeed, it was observations such as these that convinced Tycho to abandon the notion of solid spheres. The question posed by Margolis (1998) is whether the Tychonic system could exist in a solid-spheres universe, notwithstanding the separate issue of the motion of comets and other transient heavenly bodies.
3. The simple answer to this question is that such a system is not possible, but not for the illusory reason which Margolis correctly undermines. The issue resides in the definition of "solid," which is relevant to any discussion of heavenly spheres. It is clear from Margolis's argument that if the spheres were solid, in the way a tennis ball is solid, the system would be viable, since the intersection of the orbits of Mars and the Sun is illusory. The spheres, however, were not regarded as "solid" in this sense by the contemporaries of Tycho but as "solid" in the way a golf ball is solid. Anything carried within these spheres would therefore have to be embedded within the substance of the sphere and would hence be unable to move. This is not a problem for spheres themselves, as these can orbit freely within each other (so that, with the exception of the innermost sphere, the spheres are not in fact spheres at all but thick-bodied globes). The problem arises with the position of the Earth and Moon within the substance of the sphere of Mars. Viewing a model of the Tychonic system in which the independent motion of planets can be seen illustrates the difficulty (Figure 1).
4. If the sphere of Mars is free to move as it is in this diagram, the motion of Mars relative to the Earth has two components (Mars around the Sun, and Sun around the Earth) and gives rise to the observed movement of Mars relative to the Earth. In this case, however, the Earth and Moon are moving continuously THROUGH the substance of the sphere of Mars. This is surely impossible in a solid, crystalline sphere. The alternative is that the Earth and Moon remain embedded within the sphere of Mars, which would mean that the Earth and Mars remain fixed relative to each other. This patently fails to match astronomical observations.
5. This illustrates the paradigm shift which was occurring in the time during which the Tychonic system was developed. A compromise between the Ptolemaic and Copernican system was suggested by Tycho which, implicitly, rendered impossible one of the central Ptolemaic concepts. It is interesting that Tycho did not in fact cite this incongruity of the nature of a solid spheres universe when abandoning this concept, relying instead on other arguments such as the motion of comets through the spheres.
ACKNOWLEDGEMENT: We would like to thank Prof. Christopher Green for discussions that alerted us to the anomaly discussed in this commentary.
Green, C. (1998). An Empirical Test of Margolis's Theory of the Tycho Illusion. http://www.yorku.ca/faculty/academic/christo/papers/tycho-exp.htm
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