In my commentary, "Margolis's Delusion" (Topper, 1998), I argued that Tycho's system of planetary motion would not work as a system of nested physical spheres -- contrary to Margolis's assertion (Margolis, 1998a,b) that it would. I now think I may have been wrong; that I "deluded" myself. Hence the "retraction" of the subtitle. But this is more than a retraction. As I also show, Margolis's argument is still insufficient for explaining how the Tychonic model may work as a physical system. True, he displays how the system would work from a geometrical viewpoint. But a physical system entails certain constraints that must be taken into account for the planets and the sun to rotate as expected. This Margolis does not do. Hence I see my argument as perhaps a supplement to his original discovery.
As Margolis then stresses, this "template" (as I call it), containing all the planets and the sun, may then rotate around the (geocentric) earth. Despite the fact that the orbits of Mars and the sun overlap, the template (as an entity unto itself) can surely rotate around the earth; as Margolis likes to point out, the orbit of the sun is then a pure mathematical line, like the equator of the earth. Moreover, one may, in turn, cut out the orbit of Mars (or any other planet), and it too will surely rotate around the sun, as dictated by Tycho. Hence, concludes Margolis, all the spheres may move without colliding. Seeing a collision is an illusion, one that has persisted for over 400 years. As I read Margolis, this is the sum of his argument regarding the possible motions of the spheres. It is also the point stressed by Gingerich (1998) in his critique of my commentary.
2. Frankly, I have no problem with this exercise with a spinning template -- as long as it is only perceived as a template of cutouts being spun by the person doing the cutting! Yes, that geometrical system works. My problem was, and partially still is, that of understanding this spinning template as reproducing possible motions of physical planetary spheres.
3. To see why I initially thought the motion was impossible, consider what is usually involved in conceiving of planetary motion caused by rotating spheres, at least as it was done from antiquity to Tycho's time. See Figure 2.
The planet (P) is attached to a small sphere (corresponding to an epicycle), and this sphere is embedded in a channel between two larger spheres, which then revolve around a center C. The earth is near (eccentric to) C on a geocentric system. The mechanism works as follows: by rotating the two larger spheres with specific relative speeds, the smaller (epicycle) sphere can be set rotating and hence produces the orbital motion plus retrograde motion for the planet from the point of view of the earth. On the Ptolemaic system this mechanical model "worked" (conceptually) because all the nested spheres were concentric to the earth, with each rotating around its own center.
4. The question that Margolis's assertion then posed for me was this: Can such a mechanical model of physical spheres work on the Tychonic system? Or, put another way: Was the geometrical cutout exercise with the template an analogue for the physical mechanical model? Seemingly not, by the following argument. First, fix the template: Note that the cutout planets could all still individually rotate around the sun as a system of spheres (analogous to the concentric planets and the sun around the earth on the Ptolemaic system). But, second, we also need to rotate the template around the earth. Of course, one could play God and push the thing around oneself (as in the cutout exercise), but in the Tychonic system something within the system needs to push it. The obvious candidate is the sun. But of course the sun (or more specifically the sun's sphere) cannot be the source of this motion because this sphere overlaps with the sphere of Mars; indeed, the sun's path is a mere geometrical line, not a physical thing. Hence I previously concluded that there was no illusion; the system, as a mechanical model of physical spheres, does not work.
5. Anticipating a counterargument, let me consider a possible retort. Because (say) the sphere of Mars "knows" how to rotate around the sun (as it obviously does), why cannot it (and all the planets) also "know" to rotate likewise around the earth, without the need for something to push it? The problem with this reasoning is that it does not take into account the necessary constraints entailed in physically rotating spheres. Within the realm of such mechanical models, spheres only "know" how to rotate around their own centers. (In modern terms, replace "know" with a motor at the center of a wheel, and the idea may not seem so remote or strange.)
6. For the sake of argument, however, assume further that Mars does "know" that it too should move around the earth as it rotates around the sun. But if so, then why include the large spheres, for they have lost their purpose for existing! Indeed, why have any spheres at all? We may as well eliminate the epicycle too, since Mars "knows" that motion. By this reductio ad absurdum logic, we are back to Babylonian astronomy, namely, simply plotting points. All cosmology since the Greeks has been thrown out. This, as I see it, is essentially the situation left by Margolis with his spinning cutout. What works geometrically may not work physically. Physical systems entail constraints. Mechanical things cannot always move as we may like.
7. Despite my original doubt about Tycho's system as a mechanical model, I now think there may be a way to make it work. My insight (if it really is an insight) came when I asked myself a different question. As the sun cannot move the template of the planets and itself, could something else do the task (besides, of course, God!)? I then realized that since antiquity the mechanical Ptolemaic model explained the daily rotation of all the heavens (sun, moon, planets, and stars) by a daily rotation of the stellar sphere. This sphere somehow pulled the (finite, geocentric) universe (except the earth) around with it in a day. That the earth was not part of this daily motion was due to the ancient idea of the separation between the celestial realm and the terrestrial realm (above and below the moon, respectively), each having different laws of motion. As the stellar sphere rotated in one day, it carried along the entire celestial world "down" to (and including) the moon; only the earth remained fixed and motionless at the center. Note that this celestial world is really the previous template plus the moon. How this large chunk of the universe could act as a single entity is not clear, but it was assumed to do so. Moreover, note also that this motion could be adapted to the physical model (Figure 2) by adding a sphere just below the moon, so that the template plus moon (both acting together rather as an epicycle) would be embedded between this sphere and the stars.
8. Now, because on the Tychonic system the earth is also at rest at the center of the stellar sphere, and the daily rotation of the heavens is controlled by the daily rotation of the stars, perhaps a similar mechanism could cause the template alone to turn in its annual motion. Imagine another sphere, below the stars but above the orbit of Saturn, which could by its annual motion pull the template around with it, without the need to have God move it around. One problem still remains, however. Whereas the stellar sphere moves everything from Saturn to the moon on its daily rotation, the motion of the template must stop before the moon, because the moon moves through the elliptic in 27 1/3 days. The way to solve this problem follows from the previous solution: embed the template, from Saturn to (but not including) the moon, between two spheres; one would be (as postulated above) just below the stellar sphere and the other above the moon. Again, the rotation would take place as in Figure 2, with the template (as a single entity) acting like an epicycle.
9. Contrived and a bit of a stretch of the imagination this model surely is. But it is a mechanical system in the spirit of celestial models since antiquity. And maybe, just maybe, it would work.
Gingerich, O. (1998) The Tycho Illusion: Performing the Cutout Correctly. PSYCOLOQUY 9(52) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.52.cognitive-illusion.11.gingerich
Margolis, H. (1998a) 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
Margolis (1998b) A "Delusion" Defended. PSYCOLOQUY 9(45) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.45.cognitive-illusion.10.margolis
Topper, D. (1998) Margolis's Delusion: a Critique of "tycho's Illusion". PSYCOLOQUY 9(42) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.42.cognitive-illusion.7.topper