The Point

Abstract

The world is geometry, a finite universe that obeys geometrical and mechanical laws. In the world geometry, the spider follows nature’s laws of mechanics and spins its web in polygonal and circular forms, the beaver builds dams according to geometrical principles, the bird makes its nest based on the figure of the circle, and bees shape their honeycombs in hexagons. There is a natural mechanics, Swedenborg writes in Principia rerum naturalium (1734), in which the senses are shaped in harmony with the elementary mechanics of the world. Geometry applies to everything that is finite and bounded, but there are things that are not geometrical or mechanical: the infinite, providence, love. This chapter focuses on the point, the mathematical and natural point. Swedenborg conceives the world as one large geometry in motion, where mathematical points outline the parts of the machine, the perfect geometrical figures. The world geometry rests on a number of metaphors, that matter is geometry, that mechanics is geometry in motion, that a point is a spot. It also concerns the hypostatization of geometry, making the abstract real. It was believed that geometry is found in the world, not only in our imagination of it. It is the world of the geometrical spider.