Visual reasoning and the perception of forms

Abstract

Whenever a new device enables our senses to access an uncharted sensible world, our experience needs to be widened to be able to embrace it. Many animals don’t recognize themselves in mirrors. Thus, mirrors found in ancient Egyptian tombs bear witness to a device that involved a widening of human experience. While by then reflectors were commonly believed to hold the spirit of their beholder, they also provided the motivating force for use of geometry as a logical framework, rather than the form of the outer world. Euclid of Alexandria conceived of geometric constructions and their rules as the connecting link between visual world and hypothetical-deductive reasoning. Yet, he didn’t have a clue about receivers. In our view the problem of linking received information in an image format to a mathematical space cannot be solved once and for all, but rather needs to be posed and understood afresh once in a while. All the more so in an information and telecommunication era, when the techniques of acquisition and rendering of visual information have been extended well beyond the domain of optical instruments, and the language of mathematics has advanced to a different level of proficiency.