Homeomorphic Topologies

Dimensions - Variable

At it’s root, a topology is the study of “place” : geographical, geometrical, topographical, architectural, environmental, social, psychological, energetic... In anatomy, topology is used to describe the relationship between biological systems such as muscles and nerves; tendons and bones... In mathematics a topology is a continuously deforming geometrical object generated by stretching, twisting and bending, but, not tearing or adhering. Think of a mobius strip (a twisting object with only one surface and one edge) or a piece of fabric held taut and a tented shape generated by pushing a finger into its surface. What kind of space is created when we plunge a conical shape into a body of water?

Two objects that share the same topological characteristics can be described as a homeomorphism; a function between two topological spaces that has a continuous function. Visualize an animated drawing of a donut morphing into a coffee cup and back again. Consider the relationship of water to wind and a wave...

The “stillpoint” is the place between two moving objects that remains in constant proportional relationship to the two objects. It is a spatial point that does not move (in relativity). Imagine a point in the space between two ballroom dancers that move in mirrored unison; or the space between a birds wing and the air it moves; or the space between a boat lulling back and forth and the body of water on which it floats.

It is this point in [shifting] time and [deforming] space that concerns me here. What is the relationship between the water and the air that moves it? Is there a space (metaphorical and/or physical) between the moving air and the water and does this place cease to move in the heart of its movement? Can there be a psychological “place” generated by understanding the inextricably intertwined connection between two or more (if not infinite) objects/systems/experiences? What is this?

Again, consider the relationship of wind on a body of water creating surface waves. These shapes are a combining of a material (water) and a force (a flow of gases: air). The wave, which seems to be “of” the water, will not exist without its counterpart, the wind. It is like the male and female components of a casting mold, coalescing, merging, yet remaining separate. Can this indicate a quality of “presence” in the human condition?                

David Teeple