Let us speculate that the psychotic subject has a form of vision that we call parallel vision, and that this is a question of conception not fact (anatomic, optic, or otherwise). The psychotic subject is not without unity or coherence but it is not the unity imposed upon the subject by the linguistic environment in which most subjects dwell (what Lacan calls the symbolic order). Language binds the subject into a single point of perception and thought. The coherence of the psychotic subject is the coherence of parallel lines. S/he slides along the striations of a layered space. S/he sees one thing many times when the neurotic sees many things once. It is more objective, in the way that the elevation and the axonometric drawing are more objective than the perspective drawing. In the elevation and the axon, the lines of construction are parallel; the world appears from all or no points of view. There is no projection and no points of projection; the world is simply stamped onto the drawing paper the way a penny is pressed into clay. By contrast, in the perspective drawing, the world appears from a point of view. It is the model of a certain form of inter-subjectivity. It is inter-subjective because it is cross-checkable with other subjects, and so constitutes the space of the shared external world.
The psychotic subject is typically regarded as disorganised and detached from the shared world of others. In Freudian and Lacanian analysis, this is regarded as a fundamental loss. In the paper ‘Neurosis and Psychosis’ (1923), Freud describes the psychotic subject’s delusion as a ‘patch’ placed over the ‘rent’ where the ego would have been attached to the external world. For Lacan, the external world is the inter-subjective world shared by many subjects, may subjectivities joined together by a shared linguistic or symbolic environment. Lacan describes the psychotic subject’s disengagement with the joined up world of others as a loss of symbolic authority: the name of the father, i.e., the symbolic father, authorises the symbolic world for the subject. In the case of the psychotic, it was never assimilated in the subject’s development. In Lacan’s paper ‘On a Question Prior to any Possible Treatment of Psychosis’ (1958), it is foreclosed to the subject (note the real estate terminology).
Perspective is a model for a certain form of organised vision, in which all angles within the cone of vision come to a single point. It enjoys the elevated status in western thought as the formula for reality, because it colludes so closely with the egos view of itself and its relation to the world. In philosophy, perspective is often associated with concepts of the self. The internal world of Descartes’ Cogito is pictured as a single point of self defining doubt vis-à-vis an extended triangulated external world. Because this cone of vision is an analogue of the way optics works, perspective is also regarded as reality. Moreover, the perspective model of eye (point of projection) – window (picture plane) – city (world) provides an easily understood geometric model for the relation between the interior of the subject’s psyche and exterior worlds of shared space.
Psychotics see perfectly well, although without the agency of the symbolic father; it is how they relate themselves to the shared world of others that is different; they are not attached to the world the way we are; nor do they join it up the way we do. We can reflect this in a diagram for vision in which the perspective cone of vision is foreclosed to the subject, leaving him/her in a parallel world.