Geometry, Vector, Action

Descartes' innovative Geometry is probably best commemorated by the eponymous Cartesian Plane, though unlike most versions of the latter, he uses only one axis.  Still, even one axis signifies the essential break from Euclidean Geometry.  For, any axis on these grids is a foundation of all the figures that appears in them, and is constituted by three basic components--a point of origin, a line originating in the point, and a direction.  In other words, the structural foundation of Cartesian Geometry combines two of the elements of Euclidean Geometry--the Point and the Line, and adds a third--Direction.  Thus, the foundation of the new Geometry is the Vector, in which Space is essentially oriented, even if the figures that appear in it are not.  So, the Philosopher who best appreciates how Geometry is a Form of Experience is not Kant, but Bergson, for whom the Subject of Experience is a center of Action.  Perspectivism is close, but, as a theory of Perception, inverts the fundamental direction of the orientation, i. e. from centripetal to centrifugal.  Likewise, it is only the later development of Polar Coordinates that highlights the fundamental break of Cartesian Geometry from its Euclidean ancestor--the institution of the Vector as its foundational element, thus signifying action and construction, rather than a fixed object of contemplation.