The Letter, Issue 1, Summer 1994, Pages 136 - 148
PARANOIA[*]
Charles Melman
Paranoia is above all linked to our representation of space, because spontaneously our representation of space is Euclidean, which has been the natural geometry for centuries. We continue to think according to the rules of this geometry, and there has been an effort made by rationalism to assimilate the rules of thinking to the rules of this geometry. But this Euclidean geometry is based on the existence of closed figures, that is, an isolation of what is inside from what is outside. Here is an absolute boundary between the inside and outside (the circle) which is the basis for paranoia.
People have questioned themselves for a long time about the materiality of the line, and that is why geometricians say that it is a line without thickness. But in so far as it separates the inside from the outside, we can say that it is a cut or a cutting. What gives meaning to the Euclidean surface is this cutting. Lacan has this very surprising formula: he says that the surface is the cut.