Art and the Geometry of Visual Space

This chapter considers the geometric structure of visual space and the way it has been artistically depicted. This structure is hard to quantify using scientific methods and has not been precisely defined, in part because it is highly variable and subjective. But artists have often sought to record their visual experience and in doing so have rendered the structure of visual space in the objective form of paintings and drawings. Where audiences respond favourably to these artworks, it is in part because they recognise in them aspects of their own visual experience. Artworks, then, can serve as a source of data from which we derive evidence about the nature of visual space, and this in turn can inform scientific investigation of its geometry. It has been argued that linear perspective—a projective geometry discovered by artists and architects in fifteenth-century Italy—is the most accurate way to depict visual space. But although often trained in the techniques of linear perspective, artists have rarely applied its rules rigorously, and have instead developed various forms of ‘natural perspective’ that, it can be argued, are more effective at depicting visual space and so operate more effectively as works of art.