Paul Laffoley
(b. 1940, Cambridge, Massachusetts)

Temporality: The Great Within of the Universe
1974
Oil, Acrylic, Ink, Lettering on Canvas
73 1/2 x 73 1/2 in.

Subject: The Nature of Temporality

Symbol Evocation: The Geometry of Change

Comments: Most of the geometries (earth measures) that attempt to model the reaction of human consciousness to nature only deal effectively with spatiality. No aspect of temporality was ever properly described by a geometry until the mid-Nineteenth Century, and we are only now beginning to be able to more fully express the nature of temporality by geometry. Before the Nineteenth Century, the line or the circle was used to depict Time, both in the West and East. Eternity was essentially left a geometric blank, and any dimensions of temporality below Time were simply not considered. Occasionally someone might have used a spiral to attempt to join the intuitions of the line and the circle, but overall the rigidity of these spatially-based forms of geometry have always found temporality--in essence, the concept of change--too elusive, even for calculus.

By 1850, a new branch of mathematics had surfaced known as topology, concerned with those properties of geometric configuration (point sets) that are unaltered by elastic deformations (such as stretching or twisting); points are homeomorphic, remaining the same regardless of changes in configuration. Since points were all that remained of classical geometry in topology, temporality finally had its geometry. A point is unperceivable and inconceivable, thus it can represent an instant of time.

I have used topology's most complex form named after its inventor, the mathematician Felix Klein (1849-1925). A Klein bottle is a seven-sided convex topological surface that appears to enclose space but in reality has no inside or outside. Since it does not model space in the conventional sense, I have found that it can map temporal notions of change like Goethe's Zeitgeist (time spirit), the Kairos (the teleology of the moment of crisis) and other aspects of temporality which I am continuing to research.