Separate visual representations for perception and for visually guided behavior

Converging evidence from several sources indicates that two distinct representations of visual space mediate perception and visually guided behavior, respectively. The two maps of visual space follow different rules; spatial values in either one can be biased without affecting the other. Ordinarily the two maps give equivalent responses because both are veridically in register with the world; special techniques are required to pull them apart. One such technique is saccadic suppression: small target displacements during saccadic eye movements are not preceived, though the displacements can change eye movements or pointing to the target. A second way to separate cognitive and motor-oriented maps is with induced motion: a slowly moving frame will make a fixed target appear to drift in the opposite direction, while motor behavior toward the target is unchanged. The same result occurs with stroboscopic induced motion, where the frame jump abruptly and the target seems to jump in the opposite direction. A third method of separating cognitive and motor maps, requiring no motion of target, background or eye, is the Roelofs effect: a target surrounded by an off-center rectangular frame will appear to be off-center in the direction opposite the frame. Again the effect influences perception, but in half of the subjects it does not influence pointing to the target. This experience also reveals more characteristics of the maps and their interactions with one another, the motor map apparently has little or no memory, and must be fed from the biased cognitive map if an enforced delay occurs between stimulus presentation and motor response. In designing spatial displays, the results mean that what you see isn't necessarily what you get. Displays must be designed with either perception or visually guided behavior in mind

Chimneys, leopard spots, and the identities of Basmajian and Bridgeman

We give a simple geometric argument to derive in a common manner orthospectrum identities of Basmajian and Bridgeman. Our method also considerably simplifies the determination of the summands in these identities. For example, for every odd integer n, there is a rational function q_n of degree 2(n-2) so that if M is a compact hyperbolic manifold of dimension n with totally geodesic boundary S, there is an identity \chi(S) = \sum_i q_n(e^{l_i}) where the sum is taken over the orthospectrum of M. When n=3, this has the explicit form \sum_i 1/(e^{2l_i}-1) = -\chi(S)/4.Comment: 6 pages; version 2 incorporates referee's comment