Escaping the Rhino box: how can we conceptualize non-Cartesian space?

Most of us in the “modern” world conceive of space using a system of abstract coordinates, the design of which is attributed to Rene Descartes. This so-called Cartesian system proposes that anything can be located in space using an x-y-z matrix, where x and y describe a horizontal plane, and z confirms a vertical point, all in relation to a 0-0-0 beginning. A measurable three-dimensional grid provides a scalable, undifferentiated chora. Today’s popular digital drawing programs—Autocad, Rhino, Sketchup, Revit—follow this logic. It is simple to visualize and universally applicable.

But its strengths are also its weaknesses. Because it is based on an abstraction, and on the underlying fabric of orthogonality, many features of the world are suppressed or eliminated. Cartesian space does not innately account for variations in landforms, natural systems, or the complex actions of humans or other living things. Most of the workings of the world we inhabit are translated through this vacant, orthogonal filter. Because we are all trapped in what I sometimes call the “Rhino box” much of our lived experience is lived in reduced form, or in translation.

When I look to the larger world for lessons, I see systems of forces acting in relation to each other: Clouds rising and rolling based temperature, humidity, and landforms. Rocks forming based on erosion, heating, and cooling. People moving to avoid an obstacle or participate in an attraction or a simple everyday movement. Trees growing as their genetic coding interacts with sunlight, available nutrients, and rainfall. Each of these occurrences can be, and often is, crudely plotted within a Cartesian mapping system. Interventions, from flood control to the design of artificial limbs, can, similarly, be proposed within this shared conceptual platform.

I wonder, though, what knowledge is excluded from consideration? By accepting this totalizing spatial logic, we often limit our bodies’ experience of movement through space, favoring this three dimensional grid (forward/backward, right/left, up/down). We ignore the knowledge provided by our larger environments, the feel of a boulderscape as we move through it, or nature’s maximum angle of incline for different kinds of soil. We may overlook the different position the sun takes each day as we rotate around it on the earth’s tilted axis, and the amazing variety of sunlight and shadow available for our delight and instruction. We ignore the knowledge of sailors and farmers, who read weather with great skill, considering the interaction of systems well beyond those neatly plotted in Cartesian space. In short, we ignore most of the world’s vast intelligence.