The Geometry Of Thought

I often draw inspiration and insight from normal, everyday experiences.

I think it is because there is nothing really new under the sun, there are simply new ways to look at old realities. Every now and again there is also a kind of serendipity or synchronicity where something entirely practical and ordinary suddenly reveals itself as something much larger. That happened to me last week while we were packing the trucks for our move, and like many things that ultimately become meaningful, it did not seem especially important at the time.

Like most people preparing for a long-distance move, we approached the process methodically. We focused first on getting the boxed goods and larger pieces of furniture loaded because that seemed like the logical priority. At first everything appeared to be going according to plan. The trailers were swallowing enormous amounts of material and because most of what we were loading consisted of boxes, totes, dressers, cabinets and other rectangular objects, the available space was being used with remarkable efficiency. It was only around the halfway point of loading the second trailer that reality quietly announced itself to us. Despite all our planning, some of our stuff was not going to fit.

The reason turned out to be surprisingly simple once I stepped back and thought about it. A trailer is essentially an elongated cube, more properly called a cuboid, and cuboids naturally accommodate other cuboids with extraordinary efficiency. Boxes, dressers, chests and rectangular furniture cooperate geometrically. They stack wall to wall and floor to ceiling with minimal wasted space because their shapes complement the structure containing them. Eventually we reached the point where all we had remaining were the awkward items, the things I began mentally calling the “space eaters.” Tables with non-removable legs, dining chairs, upholstered chairs and oddly shaped household items consumed large amounts of cubic volume while leaving tremendous amounts of unusable vertical space above and around them. The problem was not really the quantity of material we had left to load. The problem was the geometry of the material itself and the inability of those asymmetrical shapes to efficiently occupy the available space.

At the end of the second day, we walked away exhausted and a little panicked, assuming the answer would simply involve obtaining more capacity. We discussed renting a U-Haul truck for the overflow and having my youngest son drive it with us to Tennessee before flying him back afterward. It was not a disastrous solution, merely an expensive and inconvenient one, and because we were mentally buried inside the process itself, it seemed like the obvious answer. Sometime during the night my brain continued working on the problem in the background, and in the wee hours of the morning a different solution suddenly emerged. Looking back, it was probably something others would have recognized much earlier, but I had become so focused on loading objects that I failed to fully understand the nature of the problem itself. The issue was not insufficient volume. The issue was inefficient geometry.

Once I recognized that distinction, the answer became almost embarrassingly straightforward. The goal was not to find more space but to recover the wasted vertical space we already possessed by creating cuboid spaces for non-cuboid objects. One of the few tools still available to me happened to be something we had fully expected to leave behind if we could not solve the problem at all: a set of heavy-duty storage racks we had purchased years earlier from Home Depot for organizing boxes and totes in our basement storage room. I assembled those racks directly inside the trailer, ratchet-strapped them together and secured them against the trailer walls. The shelving crossbars essentially created suspended cuboid compartments that allowed awkward and asymmetrical objects to occupy organized spaces without requiring direct stacking. In effect, I created geometry that compensated for the absence of geometry in the objects themselves.

Long story short, it worked. It saved us from renting another truck, buying another plane ticket and wasting additional money paying for cubic trailer space that still would not have been efficiently utilized because additional space alone would not have solved the underlying problem. What stayed with me afterward, however, was not simply the satisfaction of solving a practical moving issue, but the realization that human beings engage in this exact same process constantly in our thinking and reasoning. We are perpetually confronted by asymmetrical, irregular and non-cuboid information that does not naturally fit inside the mental structures we already possess. Life presents us with contradictions, competing motivations, uncomfortable truths, historical complexities and realities that resist neat categorization. Most of reality is not naturally stackable.

What we do, consciously or unconsciously, is construct conceptual shelving systems to manage it all. Ideologies, philosophies, political identities, religious frameworks, moral systems and even personal routines often function as mental cuboids into which we attempt to organize asymmetrical reality. These structures help us recover wasted cognitive space and impose enough order on complexity to make the world psychologically manageable. Sometimes those structures are enormously useful and even necessary. Sometimes they become intellectual prisons, and sometimes people become so emotionally attached to the structure itself that they begin trying to force reality to conform to the framework rather than altering the framework to better accommodate reality. That, it seems to me, is where much of human conflict originates. Many people would rather accuse the chairs of being defective than admit their storage system is inadequate.

What struck me most about the experience is that the solution only appeared once I stopped concentrating exclusively on the objects and began thinking differently about the nature of the space itself. That distinction feels important well beyond the confines of a moving trailer. An ideologue attempts to force every irregular fact into a preexisting conceptual structure no matter how poorly it fits. A wiser person recognizes that sometimes the structure itself must be reconsidered, redesigned or expanded to better accommodate reality as it exists. Increasingly, modern society feels full of people angrily attempting to cram asymmetrical reality into rigid ideological cuboids while treating anything that refuses to stack neatly as dangerous or illegitimate.

Reality does not care about our preferred geometries. Every trailer fills up sooner or later, and eventually every conceptual framework encounters information that refuses to cooperate. At that point we either redesign the shelves, pay dearly for another truck, or discover too late that some of our most important things have been left behind.