The illusory potential collision of Mars and the Sun when considering the motions of the sun and planets as described by Tycho Brahe arises because of an attempt to represent their motions in two reference frames simultaneously. The ingenious demonstration by Margolis (1998) removes the problem by providing a clear, unambiguous reference frame in which to view the motions. This case illustrates the danger of overlooking reference frames as a fundamental aspect of cognitive coding.
2. The cognitive illusion described by Margolis can be paraphrased as follows:
"When looking at path-diagrams of the movements of the sun and planets in the Tycho model, why does it appear that there could be a collision between Mars and the Sun?"
3. The reason for this illusion is that the planetary motions in the Tychonic model are described in two reference frames at the same time: one reference frame relative to the earth and another relative to the sun. When looking at the static picture, we are asked to try to visualize the motion of Mars in these two reference frames at the same time, which is impossible. All movement has to be specified in a single reference frame (see Harris, Zikovitz, & Kopinska 1998 for a recent review), but although it is a simple matter to convert from one frame to another mathematically, only one can be used at a time. Therefore we assume cognitively, as we must, that everything shown in Tycho's diagram is in the same reference system, that is, the planets and the sun and their orbits are all represented relative to the earth. And if that is true then it follows that there will indeed occasionally be collisions between any bodies with intersecting orbits.
4. The reason that Margolis's ingenious cut-out demonstration works is that it forces us to use a single reference frame, consisting of the picture of the earth and the background to which the picture is attached, in which to make decisions about the movements of the various bodies. The lines on the original drawing are a hopeless mixture, with some belonging to one reference frame and some to another. By drawing the lines belonging to one frame on one piece of paper and the lines from the other on another, physically separated sheet, Margolis's demonstration makes it very clear perceptually which reference frame to use. A similarly effective demonstration can be made by fixing the sun and moving the rest of the diagram around it. Indeed, convincing demonstrations can be made choosing any planet (with their appropriate orbits) as the reference point, since the motion of any of them can be expressed equivalently as motion of that planet around the sun or of the sun around the planet. All of these demonstrations provide a single, clear, consistent reference frame and hence result in a clear perception of the events with no illusory collisions.
5. The reduction to a single reference frame and the resultant clarity are illustrated in the Figure accompanying this commentary.
The top row shows rotation in a sun-based frame with the right hand panel depicting the only lines that should be drawn in a sun-based diagram. The second row shows rotation in an earth-based frame with the right hand panel again depicting the only lines from the original that have a basis for appearing in such a diagram. There is no ambiguity and the positions of all the bodies relative to the reference point can immediately be seen.
See also the animated version:
6. This rather intellectual case of imagined movements draws attention to a general principle in real-world perception and cognitive mapping. When any movement or position is utilized, it must always be coded neurally in a single reference frame, otherwise ambiguity will result when trying to decode or interpret that neural signal. Each task for which the information is to be used requires that the reference frame be unambiguous, although there can be several tasks running at the same time, each with its own frame. Errors in reference frame specification lead to perceptual and motor errors which can be as least as calamitous for the survival of the organism as the collision of planets. Precise specification of that reference frame is the first duty of the cognitive neuroscientist.
Harris, L.R., Zikovitz, D.C., and Kopinska, A.E. (1998) Frames of reference with examples from driving and auditory localization. In: Harris, L.R. and Jenkin, M. (Eds.) Vision and Action. Cambridge University Press.
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