Cognitive illusions depend on the framework within which the components of the illusion are interpreted, and such frameworks are to a large extent learned. Hence the Tycho illusion consists of two potential illusions, depending on the framework adopted. Contemporaries of Tycho would "see" the illusion differently in some respects from the way we would. This suggests certain testable hypotheses about the nature of the Tycho illusion which are supported by empirical evidence.
2. The question can be resolved by appreciating the context within which the diagram is understood. To a contemporary of Tycho the universe consisted of a solid mass, with the planets suspended in rotating spheres. This much had been accepted since at least the time of Ptolemy. To our own contemporaries, however, the universe is understood to be essentially a vacuum, with some minor rubble disturbing this particular harmony. The only possible exceptions to this might be those historians of science who can readily appreciate the concept of a solid universe. As we have seen from the commentary on this target article to date, such a concept is not easy for a contemporary mind to appreciate. This perhaps provides us with some insight into the nature of cognitive illusions.
3. That insight is that the nature of the cognitive illusions to which we are vulnerable is a function of the framework within which we implicitly place the components of the illusion (in this case, the Tycho diagram). Moreover, this framework may be to a large extent learned. Certain illusions of perspective depend on appreciating the rules of perspective which apply to straight lines, such as railway tracks. Two converging straight lines may be seen either as two flat converging lines or two parallel receding lines. As straight lines are not a natural phenomenon, it is reasonable to assume that there is some learned component to this. This is NOT simply a special case of the general rule that objects decrease in apparent size with distance (which DOES apply to natural phenomena). Of course, some straightish lines do appear in nature, but not in the quantity (or quality, i.e. degree of straightness) that they do in technological civilizations.
4. One implication of this is that there will be two distinct kinds of illusion (or, possibly two extremes of a continuum of illusions). One kind does not depend on learning and cannot be destroyed by information or learning. For example, even after we measure the lines in the Mueller-Lyer Diagram, the illusion remains. Distinct from these cases of cognitive impenetrability (Pylyshyn, 1998) are examples such as the Tycho diagram, where the illusion can be destroyed. In these cases the illusion is likely to be in part a product of learning.
5. If we apply this to the Tycho diagram, we expect a contemporary observer to understand this within the context of planets moving in a vacuum. We accordingly expect observers to be less vulnerable to an illusion in the first place; those who do see an illusory collision should see a collision of planets (rather than an intersection of spheres). Green (1998) has gathered some empirical evidence to support this. Moreover, contrary to the suggestion of Margolis, those with a greater understanding of planetary motion (i.e. those with some background in astronomy) would be less susceptible to the illusion, because they would be even more inclined to view the model within a contemporary framework. This too is supported by empirical data (Green 1998).
6. On the other hand, those who frame the Tycho diagram within the context of a solid-spheres model of planetary motion will see an entirely different (and far stronger) illusion. The only contemporary minds who will readily see this illusion would be those to whom the concept of celestial spheres is not alien, such as the authorities on Tycho that Margolis cites. It is this illusion which Margolis discusses, but "first-time readers" may not appreciate the strength of his argument because they themselves have been party to an altogether different illusion.
Green, C.D. (1998) An Empirical Test of Margolis' Theory of the Tycho Illusion. http://www.yorku.ca/faculty/academic/christo/papers/tycho-exp.htm
Harris, L. (1998) The Mars/Sun Collision Illusion: Motion Is Not Visualizable In Two Different Reference Frames Simultaneously PSYCOLOQUY 9(33) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.33.cognitive-illusion.2.harris
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
Pearson, D. (1998) Imagery Need Not Be Blind to Fail. PSYCOLOQUY 9(34) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1998.volume.9/psyc.98.9.34.cognitive-illusion.3.pearson
Pylyshyn, Z. (1999) Is Vision Continuous with Cognition. The case for cognitive impenetrability of visual perception. Behavioral and Brain Sciences 10 (in press) http://www.cogsci.soton.ac.uk/bbs/Archive/bbs.pylyshyn.html