1730 Paragraph 28
If multiplicities are defined and transformed by the borderline that determines in each instance their number of dimensions, we can conceive of the possibility of laying them out on a plane, the borderlines succeeding one another, forming a broken line. It is only in appearance that a plane of this kind "reduces" the number of dimensions; for it gathers in all the dimensions to the extent that flat multiplicities—which nonetheless have an increasing or decreasing number of dimensions—are inscribed upon it….
Far from reducing the multiplicities' number of dimensions to two, the plane of consistency cuts across them all, intersects them in order to bring into coexistence any number of multiplicities, with any number of dimensions. The plane of consistency is the intersection of all concrete forms. Therefore all becomings are written like sorcerers' drawings on this plane of consistency, which is the ultimate Door providing a way out for them. This is the only criterion to prevent them from bogging down, or veering into the void. The only question is: Does a given becoming reach that point? Can a given multiplicity flatten and conserve all its dimensions in this way, like a pressed flower that remains just as alive dry?...
Everything becomes imperceptible, everything is becoming-imperceptible on the plane of consistency, which is nevertheless precisely where the imperceptible is seen and heard. It is the Planomenon, or the Rhizosphere, the Criterium (and still other names, as the number of dimensions increases). At n dimensions, it is called the Hypersphere, the Mechanosphere. It is the abstract Figure, or rather, since it has no form itself, the abstract Machine of which each concrete assemblage is a multiplicity, a becoming, a segment, a vibration. And the abstract machine is the intersection of them all.









