Harris (1998) argues that a Tychonic illusion closely related to the one discussed in Margolis (1998a,b) is caused by the need to consider a situation in which there are two different frames. Pearson (1998) provides an argument against the conjecture that something related to blindsight is needed to account for that illusion. I reply to the two jointly as there is considerable overlap, arguing that the frames difficulty cannot account for persistent details of how people respond to Tycho's diagram, nor could the counterfactual motions that are implied by people's reactions be simultaneously both conscious and credible to the experts who in fact found them wholly credible for 400 years.
2. The direct collision Harris discusses would require Mars to collide with an object at the center of its own orbit. As soon as this is pointed out, a person ordinarily realizes that this could not happen. The interesting question about the direct collision then is why we are so readily prompted (at least momentarily) to that absurd intuition on a first encounter with Tycho's system.
3. Harris is certainly right in his concern with difficulties that can arise when a person has to envision motion in two frames. But of itself this difficulty cannot account for the illusion of a direct collision. If it did, then perhaps that same difficulty would be all that was needed to account also for the collision of orbits illusion. But if the difficulty of dealing with competing frames were sufficient for the illusory perception of the direct Mars/sun collision, then the same sort of illusory perception should extend to Venus/sun and Mercury/sun collisions, since their orbits also intersect that of the sun. But no one has illusory perceptions about that. Rather, without the "big-on-small" difficulty stressed in paragraphs 17-19 of the target article, people here have no difficulty at all in handling the two frames.
4. Occasionally someone (e.g., Kuhn 1957, p. 206) does notice that if there were a collision of orbits between the sun and Mars there would also be a parallel collision of orbits involving Venus and Mercury. But this is a derivative inference, not an immediate intuition. It is a logical inference that someone caught by the primary illusion might eventually notice, not a powerful intuition that a person immediately feels must be right. And no one at all seems to be caught even in a derivative way by the equally logical extension of the direct Mars/sun collision that Harris discusses to a parallel direct collision involving Venus (or Mercury).
5. The account of the primary (collision of orbits) illusion in my paper readily suggests an explanation of all these subsidiary points. Suppose (as proposed in paragraphs 17-19 of the target article) that the Tychonic orbits of Venus and Mercury were (correctly) perceived as carried around with the sun but (incorrectly but reflecting a strongly entrenched habit of mind) not so the larger orbits of Mars, Jupiter and Saturn. If that were actually how the planets behaved, then there would indeed be collisions between Mars and the sun when both bodies happened to be simultaneously at one of the two points of intersection of their orbits. Of course, supposing that is actually how the planets move makes no sense whatever. But we do not notice the habits of mind that prompt these illusions, as in general we do not commonly notice either our physical or mental habits.
6. This illusion of a direct collision, moreover, is so easily dispelled (paragraph 2 above) that by the time one might notice that such a collision would also entail collisions with Venus and Mercury, one would no longer be a victim of that direct collision illusion. So we see no such cases.
7. But a person can have habits that conflict with conscious beliefs. In fact, we all do. Every golfer knows that it is important to keep one's eye on the ball. And all golfers, even the very best, need to have someone else notice when they take their eye off the ball, for although they know they should not do that, and want very much not to, they sometimes do, and sometimes without being aware they have done it. Similarly, I would argue, and the 400 year record argues, a person who knows very well that a heliocentric planet cannot collide with the sun may nevertheless fail to notice a logically absurd mental rotation that prompts just that nonsensical intuition. So every expert in this matter regards this direct collision possibility as merely a beginner's blunder, but nearly everyone (perhaps literally everyone) is at least briefly caught by the illusion. And even after the intuition of a direct collision is dispelled by its transparent logical absurdity, a person is still left with the intuition that in a world of solid spheres, the orbits would collide even though the bodies cannot.
8. That intuition of a collision (or physical interpenetration) of orbits is logically just as bad as that of the direct collision. But the logic needed to show this is no longer the 1-step argument of paragraph 2. As the target article reports, it becomes easy to dispel the illusion of a collision of orbits only with the help of the moving model presented in the target article, which turns the required correct mental rotation into a physical rotation.
9. Harris provides diagrams which clearly separate the components of the system's annual rotation around the Earth in Tycho's diagram from the planets' heliocentric rotation. Given the ease with which even a few words of verbal explanation ordinarily dispel the direct collision illusion, it is not surprising that the Harris diagrams are also sufficient for that. But having made quite a few unsuccessful efforts to convince historians of astronomy of the illusion until circumstances put the cutout in my lap (paragraph 16 of the target article), I would be surprised if Harris's sun-focus diagrams were at all effective in dispelling the collision of orbits illusion, or that his Earth-centered diagrams were effective relative to the moving cutout. If so, that is interesting, for Harris's Earth-centered diagrams present successive "snapshots" of the rotation demonstrated by the cutout in the target article. Logically, that should work. But they do not provide the physical sense of a comfortable "small-on-big" rotation that is provided when a person handles the cutout, or even just sees the physically separated cutout. Harris stresses the impossibility of perceiving two frames of reference at once. But parallel to the experience we all have had from reversible gestalt figures, this does not always or even often prevent one from seeing the alternative frames closely enough together to allow short-term memory to continue to recall one frame while perceiving the other.
10. Pearson (1998) raises a different but not unrelated issue. He says nothing I want to disagree with until his remark in paragraph 9 that the Tychonic illusion is "based on an incorrect understanding of the model." This is fine regarding the direct collision discussed by Harris, for that only deceives novices. But the illusory collision of orbits that deceived Tycho, Kepler et al for 400 years affects the very best experts. They have a thorough understanding of the model but are deceived nevertheless. I can see no way to make sense of this unless the experts are responding to a tacit sense of how Tycho's system moves that, as discussed earlier, flatly violates what they know perfectly well about how Tycho's system moves.
11. This is very different from what happens in examples such as the "J-D" mental rotation Pearson discusses. Some subjects, but by no means all, have trouble with the required mental rotation. But even those who fail do not perceive something nonsensical (they do not form a mental image of a rotated JQ when they are trying to form the rotated JD). No illusory image seems to be involved, just a failure by some subjects to manage the mental rotation. So in Pearson's examples, nothing akin to blindsight needs to be conjectured.
12. But for the collision of orbits illusion, the very best experts for a very long time saw the collision as self-evident. Here there does not seem to be a failure to manage a mental rotation. Apparently it is done, since so definite and confident a conclusion is reached. But it is done outrageously wrongly! Look at Tycho's diagram, and you can't miss the sense of a collision (unless you have already looked at the same diagram using the cutout, and what's obvious earlier turns out to be obviously wrong). Neither Tycho nor anyone else saw anything to discuss. If even a few experts were uncertain, or if giving up the traditional solid spheres caused difficulties that motivated careful scrutiny, the situation certainly would have been clarified in short order (see paragraphs 22-26 of the target article).
13. So the situation was this: the imputed motions that can account for the intuition of a collision make no sense; and the victims are experts who know perfectly well that such motions would make no sense. How, then, could whatever imagery, or stand-in for imagery, which prompts the clear sense of collision be both conscious and convincing? My suggesting something akin to blindsight as involved in this illusion (target article, paragraph 21) was only a conjecture. But it still looks to me like a conjecture worth exploring.
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
Kuhn, T. 1957. The Copernican Revolution (Harvard University Press)
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, H. (1998b) Tycho's illusion and human cognition. Nature, 392, 857.
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