Why computing with space?

Where is this fascination about UD from? Think about it a bit from a visual point of view (and mind that I am not writing about the exact, whatever it turns out to be, algorithm, but about principles). The information coming to the brain by the visual path is ridiculously small compared to the complexity of the world. Yes, when we look at something, the world takes care of the intricacies of ray-tracing for us. But what about the visual world reconstructed in our brains? There is no ray-tracing, there are no octrees, nor coordinates. Again, I repeat that despite all the very useful knowledge people have about robotic vision, this knowledge fails spectacularly to explain how we, humans, or simple creatures like flies, see.  This cartezian point of view, based on coordinatizing the exterior world and treating it like a given geographical space, is not, neuroscience tells us, how we manipulate space in the brain. Again , I repeat that algorithms, which are devices invented to solve problems, are not the right mean for trying to understand this problem, despite the amazing ideas that CS might give concerning the understanding of the world as some big system which we act upon and which it acts upon us. That is because our little grey cells (but let us not forget about those of the humble fly) don’t work by proposing themselves to solve problems. This is just another disease inflicted by the cartezian viewpoint. (I hope that at this stage you can still make the difference between mine and the average crackpot’s talking.)

If we look at the other side, the one of neuroscience, what we find? Sloppy data, compared to physics, due to the complexity of the systems studied, lack and even despise of mathematical knowledge, again compared with physics, due to the fact that these new sciences are in their infancy.

But somehow, as it has always been, somewhere there is an armchairian (word invented by Scott Aaronson), an ancient greek philosopher kind, which could get rid of the cartezian disease and see clearly  a system through the huge pile of data. My bet goes to a mathematician, but I may be biased.

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2 thoughts on “Why computing with space?”

    1. Yes, I know of course about ter Haar Romeny, scale space, Koenderink. It’s very interesting mathematically. There are also applications of sub-riemannian geometry to models of the structure of V2, initiated by Petitot. I don’t think I saw any interaction between these models, for example a scale-space model not based on the exterior euclidean space, but on the interior, intrinsic structure of V2. Just saying, I would love to work on this, but with people really in the know of biological vision, not just with mathematicians.

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