Visual space is the experience of space by an aware observer. It is the subjective counterpart of the space of physical objects. There is a long history in philosophy, and later psychology of writings describing visual space, and its relationship to the space of physical objects. A partial list would include René Descartes, Immanuel Kant, Hermann von Helmholtz, William James, to name just a few.
Object space and visual space
Space of physical objects The location and shape of physical objects can be accurately described with the tools of geometry. For practical purposes the space we occupy is Euclidean. It is three-dimensional and measurable using tools such as rulers. It can be quantified using co-ordinate systems like the Cartesian x,y,z, or polar coordinates with angles of elevation, azimuth and distance from an arbitrary origin.
Space of visual percepts Percepts, the counterparts in the aware observer's conscious experience of objects in physical space, constitute an ordered ensemble or, as Ernst Cassirer explained, Visual space can not be measured with rulers. Historically philosophers used introspection and reasoning to describe it. With the development of Psychophysics, beginning with Gustav Fechner, there has been an effort to develop suitable experimental procedures which allow objective descriptions of visual space, including geometric descriptions, to be developed and tested. An example illustrates the relationship between the concepts of object and visual space. Two straight lines are presented to an observer who is asked to set them so that they appear parallel. When this has been done, the lines are parallel in visual space. A comparison is then possible with the actual measured layout of the lines in physical space. Good precision can be achieved using these and other psychophysical procedures in human observers or behavioral ones in trained animals.
Visual space and the visual field The visual field, the area or extent of physical space that is being imaged on the retina, should be distinguished from the perceptual space in which visual percepts are located, which we call visual space. Confusion is caused by the use of Sehraum in the German literature for both. There is no doubt that Ewald Hering and his followers meant visual space in their writings.
Formal, physical and perceptual spaces
The fundamental distinction was made by Rudolf Carnap between three kinds of space which he called formal, physical and perceptual. Mathematicians, for example, deal with ordered structures, ensembles of elements for which rules of logico-deductive relationships hold, limited solely by being not self-contradictory. These are the formal spaces. According to Carnap, studying physical space means examining the relationship between empirically determined objects. Finally, there is the realm of what students of Kant know as Anschauungen, immediate sensory experiences, often translated as "apperceptions", which belong to perceptual spaces.
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