Bridging Psychology and Mathematics: Can the Brain Understand the Brain?

September 2004 | Volume 2 | Issue 9 | e297 " It was not only diffi cult for him to understand that the generic term dog embraced so many unlike specimens of differing sizes and different forms; he was disturbed by the fact that a dog at three-fourteen (seen in profi le) should have the same name as the dog at three-fi fteen (seen from the front).…Without effort, he had learned English, French, Portuguese, Latin. I suspect, nevertheless, that he was not very capable of thought. To think is to forget a difference, to generalize, to abstract. In the overly replete world of Funes there were nothing but details, almost contiguous details. " —Jorge Luis Borges, " Funes the Memorius " W e are told scientists are divided into experimentalists and theoreticians. The dialectic description of the dynamics of science, with one tribe gathering data and collecting evidence and another tribe providing form to these observations, has striking examples that argue for the importance of synthesis. The 16th century revolution, which settled the way in which we see the sky today, is probably one of the best examples of how comparatively ineffective each of these tribes can be in isolation. Tycho Brahe, the exquisite observer, who built, calibrated, and refi ned instruments to see in the sky what no one else could, collected the evidence to prove a theory that Copernicus had already stated years before (in a book he dedicated to the Pope). It was only many years later that Galileo established the bridge between theory and observation; he understood the data in terms of the theory and thereby cemented the revolution. Copernicus's statements, showed Galileo, were not only fi gments of his imagination; they were an adequate description of the universe as he and Brahe had observed it. Since my fi rst steps in biology, after a prompt departure from physics and mathematics, I have looked for such encounters between theory and experiment. I began studying the visual system and the series of fundamental works by Atneave (1954), Barlow (1960), and Atick (1992) on the relationship between our visual world and the way the brain processes it. Their research was based on a simple hypothesis: (1) the images that we see are highly redundant and (2) the optic nerve is a limited channel, thus the retina has to compress information. Compression, redundancy? How do such concepts relate to …