# Abstract Graham White 16th January 2014

## Gibson, Grothendieck, Husserl

Gibson, in his "ecological theory of perception", takes as fundamental the idea of temporally extended episodes of visual perception, and bases his theory of perception on that, rather than on the idea of temporally isolated perceptual states. Given such an episode, Gibson claims that the fundamental operation of the perceptual apparatus is to find "invariants". I explain why these cannot be invariants in the standard mathematical sense, but that there is a mathematical formulation which will handle them very well. I then describe how the mathematician Grothendieck, in the years after the second world war, had very similar intuitions: in particular, his "context principle" is similar to, but more general than, Gibson's choice of temporally extended perceptual episodes as basic. I then argue that a plausible link between these two figures can be found in Husserl: Grothendieck was influenced by the sort of mathematics that Husserl studied in his PhD, whereas Gibson (via Gestalt psychology) was influenced by Husserl.

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