From Chapter 4 …
Presently, I am again bringing my attention to my eyes as they stereoview the Klein bottle. I direct my awareness to the place where the Klein bottle intersects itself. If this is the gateway to the “fourth dimension,” if this is where subjectivity enters the picture, and if the subjectivity in question is not some abstraction but is concretized as the viewer’s own subjectivity, then the region of self-penetration must function as a kind of mirror. Regarding the movement of the Kleinian signifier back into itself not as something happening “out there” in an object that is merely external to me, but as a movement back in here, it is as if these eyes of mine that view the self-intersection are viewing themselves—as if, in proprioceptively stereoviewing the Klein bottle’s reentry into itself, I enter the hole this creates to perceive my own eyes engaged in the act of viewing. Of course, ordinary mirroring takes place in ordinary space so that, when looking at my eyes in the glass, they appear as objects detached from this viewing subject. The Kleinian mirror is different. With its involvement of alchemy’s added psychophysical dimension, the mirroring should indeed close the gap between the viewing subject “in here” and the object viewed “out there,” since—in the Kleinian vessel—inside and outside flow together as one.