THE LETTER 01 (Summer 1994) pages 136-148
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.
This is very different to the representation of space that is to be found, for example, in the Book of Kells, because space is represented there as a weaving, a fabric. Why is it so different from the Euclidean way of thinking? If the surface is represented by a weaving then what, at a certain moment, disappears and goes outside, returns again. In a weaving or texture there is no cutting, and what has been repressed returns. But in the case of the circle, what has been put outside must remain outside, and we will have to be very vigilant so that what has been put out does not come back in. …