Husserl (1907) carries out an analysis of the properties of visual space that counts as an example of the “analytic approach” to the geometry of perceptual space (cf. Wagner, 2006: Ch. 4). Instead of assuming the axioms of one geometry (see the hierarchy of geometries in Suppes, 1977: 403) to derive the properties of phenomenal space and test them, Husserl tries to specify its coordinate systems. His approach is “direct” because the coordinate systems emerge through the analysis of the observable connection and variation of the appearances that are presented to a naive subject when she perceives things as she or the objects freely move in the environment. Indeed, the characteristic of Husserl’s analysis is the tenet that the structures of visual space are specified by their correspondence with the possible movements of perceivers and objects. It is essential to remark, however, that this correspondence has a functional meaning, because movements do not determine the content of appearances and accordingly the latter are not used by subjects as mere consequences of the former (as in the sensory-motor theories, see Philipona et al., 2003).
Husserl claims that visual space is describable as an infinite manifold of positions and that it can emerge from the finite visual field by means of the perceivers’ possible movements. Indeed, the visual field presents a continuous and connected system of positions in which forms, colors and textures are extended. It has outer and inner boundaries. The former are the borders that always move with the field. The latter are the pieces of the field that can be distinguished by the qualitative discontinuities of forms or colors, the edge segmentation and the partition of objects (although field pieces do not need to correspond to the objects’ parts). Each piece is the place of a part or feature of appearances. Each appearance or part thereof makes a piece of the field distinguishable from the others. Therefore, since each piece is decomposable into an inner and an outer part, pieces of the field and parts of perceived objects delimit one another.
The visual field is the ordering system of appearances. Movement of a defined kind induces a change of appearances and of their position in the visual field. Each kind of possible movement is related to the order of the field as a whole. Each region of the visual field becomes accessible only through a definite type of movement. The possible movements form distinct manifolds whose dimension is the number of the independent variables of locomotion needed to describe univocally the change of position. Thus a type of movement has a coordinate system and the movement that is realized is one of the admitted transformations of the coordinate system. At the same time, the changes of appearances require that these pass smoothly and orderly over the positions they fill in the field. However, the visual field is finite; hence, the possibility of movement is rendered by the order of the transformations that induce such changes.
The correspondence between every type of movement and the whole ordered visual field together with the coordination of movements with appearances determine the functional role that the movement has for the emergence of the spatial properties of things and finally of visual space. The series of appearances coordinated to the movements cannot be arbitrary. For each movement there are appearances whose features of form and color undergo a specifiable change. Each movement can be substituted with another in order to make other coordinated appearances occur. Thus one appearance cannot be arbitrarily substituted with any other and for a transformation perceivers become acquainted with its inversion. Accordingly, the appearances are connected in series spreading across the ordered field or pass into one another as a function of possible movements. Thus the movements induce transformations of both the visual field onto itself and of the manifold of appearances onto itself. Therefore the spatial properties of perceivable things and of visual space are the phenomenal result of the changes of indefinitely mobile appearances that fill qualitatively the visual field. The coordinate systems of the movements that make the spatial properties of things and space emerge from the appearances themselves are the following.
The coordinate system of oculomotor movements is a bounded plane with a null point, corresponding to the normal position of the eye (straight ahead), and the axes up-down and left-right as the directions along which appearances vary. The eye movements extend the visual field and the appearances undergo a cyclic change of position, because each appearance enters or exits along the center-periphery direction. The visual field is stable because its smooth variation always occurs from the borders. Since it provides a stable system of order, the variable appearances may acquire a first form of invariance through position changes. For instance, two appearances undergoing the same change of ordered positions preserve their distance and are perceived as a pair. Thus other perceptual groupings may arise: pairs of appearances that have an integral change with one another form a configuration; sequences of configurations emerge as the varying aspects of something common.
The coordinate system of head-trunk movements is described as a finite cylindrical plane with a null point fixed by the normal position of the eye and the head. It is unbounded along the closed line of head rotation in the left-right direction, while it is bounded along the vertical line of head elevation in the up-down direction. If the movements of the trunk are also taken into account, the following transformations are allowed:
- rotation of the visual field, for which appearances preserve a one-to-one correspondence;
- dilation: appearances, which are expanded and contracted, preserve the similitude to one another so that
- appearances, which remain invariant through dilation, are segregated from those that vary;
- segregated invariant appearances become the aspects of something at a varying distance;
- displacement through translation or rotation with occlusion: an appearance slides smoothly and overlaps another one that ends with being partially or totally occluded; the features of the occluded appearance disappear and may re-appear cyclically, and this cycle allows perceptual completion.
Occlusion is a first form of depth, although it does not give determinate perceptual clues on the spatial structure of the things to which appearances belong. These clues occur by means of other transformations like:
- deformation: the qualitative features and extent displayed by appearances are deformed in a homogeneous or heterogeneous manner so that homogeneous deformation selects appearances that belong to the same object, while heterogeneous deformation segregates them from those that do not because they are not deformed or are deformed differently;
- “turning” or rotation and deformation along the perceived object axis: appearances change the tilt, slant and orientation, giving rise to one or more distinct sequences in which they vary along a determinate direction; (5.1) appearances that occlude one another but may be successively displayed always along the same direction of change belong to one another as well as to the same perceivable object.
This transformation does not preserve the coordinates. Therefore, Husserl claims that it is sufficient to make the self-enclosed surfaces of perceivable things appear and to endow them with clues on three-dimensionality and depth.
If, rather than movements of single body sub-systems, locomotion is allowed, the coordinate system is describable as a bounded but mobile space with a transposable null point that coincides with each position at rest that perceivers may reach through their movement. Therefore, all points become equivalent because the movement to reach them is periodical and invertible. The horizon is continuously displaced at each movement and emerges as something that can be preserved only as a boundary at the limit. The appearances of things, which occur as locomotion is carried out, undergo changes that imply transformations of the coordinates and make the determinate three-dimensionality of things finally perceivable. If these transformations are such as to compensate the ever-occurring displacement of the visual horizon, the perception of an infinite space can take place.
Husserl’s theory shares the common assumption of phenomenology that phenomenal space is something that is only abstractly separable from the structure of the appearances, although clearly this does not mean that it is not also perceived with a relative independence of things and of their qualities. It is interesting because it outlines a theory of the geometry and kinematics of appearances themselves to account for visual space as the perceptual result of transformations induced on the independent content of appearances. Structures and properties of visual space emerge from the invariance of features and the connection between appearances through a closed system of transformations of an ordered system of positions onto itself through the manifold of possible movements.
As regards geometry, unlike Brentano Husserl describes visual space as something that can be set into correspondence with the Euclidean space only through locomotion, namely with the form of perceptual space that comes last in the logical order of phenomenological analysis, while the preceding forms admit a description in terms of Riemannian space (1907: 311, 318-321, 335f., 371f.).
Source: Calì Carmelo (2017), Phenomenology of Perception: Theories and Experimental Evidence, Brill.
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