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Laurent Perrinet - Team InViBe
Institut de Neurosciences de la Timone UMR 7289
Aix Marseille Université, CNRS, 13385 cedex 5, Marseille, France



<Laurent DOT Perrinet AT univ-amu  DOT fr>


Institut de Neurosciences de la Timone (UMR 7289)
Aix Marseille Université, CNRS
Faculté de Médecine - Bâtiment Neurosciences
27, Bd Jean Moulin
13385 Marseille Cedex 05


+33.491 324 044



<Laurent DOT Perrinet AT gmail DOT com>


+33 6 19 47 81 20

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Figure 1: Band-pass motion stimuli for perception and action tasks. (a) In the space representing temporal against spatial frequency, each line going through the origin corresponds to stimuli moving at the same speed. A simple drifting grating is a single point in this space. Our moving texture stimuli had their energy distributed within an ellipse elongated along a given speed line, keeping constant the mean spatial and temporal frequencies. The spatio-temporal bandwidth was manipulated by co-varying Bsf and Btf as illustrated by the (x,y,t) examples. Human performance was measured for two different tasks, run in parallel blocks. (b) For ocular tracking, motion stimuli were presented for a short duration (200ms) in the wake of a centering saccade to control both attention and fixation states. (c) For speed discrimination, test and reference stimuli were presented successively for the same duration and subjects were instructed to indicate whether the test stimulus was perceived as slower or faster than reference.

"Think of the image of the world in a convex mirror. ... A well-made convex mirror of moderate aperture represents the objects in front of it as apparently solid and in fixed positions behind its surface. But the images of the distant horizon and of the sun in the sky lie behind the mirror at a limited distance, equal to its focal length. Between these and the surface of the mirror are found the images of all the other objects before it, but the images are diminished and flattened in proportion to the distance of their objects from the mirror. ... Yet every straight line or plane in the outer world is represented by a straight line or plane in the image. The image of a man measuring with a rule a straight line from the mirror, would contract more and more the farther he went, but with his shrunken rule the man in the image would count out exactly the same results as in the outer world, all lines of sight in the mirror would be represented by straight lines of sight in the mirror. In short, I do not see how men in the mirror are to discover that their bodies are not rigid solids and their experiences good examples of the correctness of Euclidean axioms. But if they could look out upon our world as we look into theirs without overstepping the boundary, they must declare it to be a picture in a spherical mirror, and would speak of us just as we speak of them; and if two inhabitants of the different worlds could communicate with one another, neither, as far as I can see, would be able to convince the other that he had the true, the other the distorted, relation. Indeed I cannot see that such a question would have any meaning at all, so long as mechanical considerations are not mixed up with it." — Hermann von Helmholtz In 'On the Origin and Significance of Geometrical Axioms," Popular Scientific Lectures< Second Series (1881), 57-59. In Robert Moritz, Memorabilia Mathematica (1914), 357-358.

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