Owen Gingerich's (1998) commentary on Topper (1998) draws attention to the most striking aspect of "Tycho's illusion". At least for people (such as Gingerich) who are highly expert in the substantive issues a mere look at the cutout actually turning convincingly undoes a strong prior conviction. What warrants careful attention to this illusion is not only its long life (400 years), but the remarkable effectiveness of merely showing Tycho's own diagram (which prompts the illusion) in a novel way.
2. As described in my target article (Margolis 1998a, para 16), Gingerich and I had a copy of the Tychonic diagram in front of us as I (with handwaving and pointing) tried to explain why there was really no such inconsistency. Gingerich, who happened to have recently gotten a circle-cutting compass, proposed that he just cut up the diagram in the way I was proposing, and see what happened when we made this working model of a solid spheres Tychonic system. So instead of having to envision a mental rotation (of the annual component in Tycho's diagram), we could now look at a physical rotation (making and then actually moving the cutout shown in Fig. 5 of my article.) For most people in my experience, this turns out to immediately cure the illusion, but in particular for those who are expert in the matter, hence those who would not be distracted by secondary difficulties about how Tycho's system works.
3. It is the combination of the stubbornness of this illusion without the cutout (400 years of that) with the immediate effectiveness of a simple remedy that made this oddity seem of real psychological interest. In particular, no one (it seemed -- and still seems -- to me) could plausibly argue that the illusion was merely transient, or would not fool really knowledgeable people, or that there was more than one "right" way to see the issue, etc. etc., as is currently being discussed in the recent Psycoloquy target article by Krueger (1998) and the comments on it, and before that by many similar exchanges over almost three decades.
4. It may help to add something to my previous response (Margolis 1998b) to Topper (1998) and Munafo & Tijsseling (1998). In Tycho's static diagram, he very understandably drew a line to show the path of the sun around the Earth, along with a set of lines to show the simultaneous paths of the planets around the sun. But then not only Tycho but also both his admirers and his critics over the four centuries since have taken it as obvious that in a world of solid spheres, the sun and each of the five planets would be moved by its individual sphere, yielding a collision (or more exactly but very clumsily, an impermissible interpenetration) of the spheres of Mars and the sun.
5. The cutout, however, shows that intuition to be a mistake. What in a solid Ptolemaic world are six nested spheres become in a Tychonic world a single sphere carrying the sun and the orbits of the five planets. All move together in a single annual motion around the Earth. In this Tychonic solar system, the rotating orbits of the planets must indeed be physically real things with the sun at their center. That set of objects is in turn carried by a single physically real annual "sphere" which fills the whole space between the Earth-moon region and the sphere of the fixed stars. There is no need for a physical orbit to carry the sun, since (as is plain when you move the cutout) the annual rotation carries the sun through its orbit without any such assistance. The path of the sun in Tycho's diagram can then be seen to be like the line showing the equator on a map. Depending on what you are trying to show, it may (or may not) be useful to show that line. But either way, it is not a physical object that Mars could bump into, any more than a ship could bump into the equator. A reader in doubt ought to look again at Fig. 5 in my target article, together with the two animations which now accompany it.
Margolis (1998) Figure 5.
6. The cutout shown in Fig. 5 of my article was explicitly made by cutting up Tycho's own diagram. So it has the path of the sun still drawn on it, with the accompanying text explaining why that solar orbit is not a physical object. The same holds for the animation of that cutout provided by Harris (1998).
Harris (1998) Revised Animation.
7. Munafo & Tijsseling's animation is an independent production, correctly omitting any such path.
Munafo & Tijsseling (1998) Figure 1.
In their animation, a viewer can see the sun move around its orbit, so that it would be redundant and indeed confusing to show a line for that orbit. (But Munafo & Tijsseling's animation might be misleading on another point, because, unlike my Fig. 5 or the Harris animation, they fail to show the central region, which is not involved in the annual motion, in a color distinct from the region which does rotate annually.)
8. A way to envision the Tychonic situation might be this: Think of the single Tychonic "sphere" as being like the platform of a merry-go-round. It rotates around the unmoving Earth and its immediate neighborhood as the merry-go-round rotates around the machinery fixed at its center. That rotation, in combination with the simultaneous rotation of the heliocentric planetary orbits carried by that sphere, produces what is in fact seen by an Earthbound observer.
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
Harris, L. (1998) The Mars/sun Collision Illusion: motion is not visualizable in two different reference frames simultaneously PSYCOLOQUY 9 (34) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.33.cognitive-illusion.2.harris
Krueger, J. (1998). The bet on bias: a foregone conclusion? PSYCOLOQUY 9(46) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.46.social-bias.1.krueger
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
Munafo, M. & Tijsseling, A. (1998) Movement in a Solid Sphere:. PSYCOLOQUY 9(44) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.44.cognitive-illusion.9.munafo
Topper, D. (1998) Margolis's Delusion: a Critique of "tycho's Illusion". PSYCOLOQUY 9(42) Z ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.42.cognitive-illusion.7.topper