Every Quadrilateral is Not a Parallelogram

Sometimes a vacation is just a vacation, though that is rarely true in my experience. Our own personal challenges and issues tend to play out during travel in ways that might not arise at home, by virtue of putting ourselves into a new or unaccustomed environment.  For me, the discomfort this can elicit is one of the draws of traveling–it is a clue that I have chance to work through a problem, or learn something new about myself.

Last summer, on a tour of the Frank Lloyd Wright-designed Kentuck Knob in Pennsylvania, the guide added the verbal flourish “some say rhombus, I say parallelogram” to his description of the kitchen’s design elements. While the two figures are not interchangeable in the way he meant, his comment stuck with me for some reason and led my brain on a convoluted exploration of relationships among geometry, physics, travel, and psychotherapy. Stick with me, I’m pretty sure I can tie this together.

At first, I found myself preoccupied with the inaccuracy of the guide’s statement (a rhombus is a parallelogram that also is an equilateral quadrilateral, meaning all four sides are the same length; however a parallelogram, while always a quadrilateral, needn’t be equilateral). Gradually my thoughts migrated to quadrilaterals more generally, which are not always parallelograms. A complex quadrilateral can include intersecting lines, like so:

complex quad

No matter the shape a quadrilateral takes, and whether it is simple, complex, and/or a parallelogram, the interior angles always add up to 360°. Here’s where we pull travel (and physics!) back into the conversation. Just like every quadrilateral has four sides, every journey exists in four dimensions: length, width, depth, and time.  There is a literal aspect to all of them, but metaphor is so much more fun–the mileage we travel literally, versus the internal distance we traverse. Our journeys are perceived and experienced in 3-dimensional space, but all the while there is magic happening in the fourth dimension: time. When we travel there are often dramatic illustrations of the differences between who we were in the past and who we are in the present (especially when we return to places we inhabited in our youth); however, we are also actively navigating (consciously or unconsciously) the differences between who we are in the present and who we will be in the future as a result of what we learn on the journey.

What is the mechanism for this magic? The 360° perspective we get when we travel; the chance to transcend everyday life and observe a new landscape with fresh and childlike eyes. This is partly why I rarely travel to the same places more than once–I like the experience of observing a place completely afresh, because of the process it awakens. My senses are heightened by the newness and I am extra-alert to chances I may never get again. As I push myself to take those chances, my awareness of my intrapersonal dynamics or issues is rarely overt–usually that gets sorted out afterward (sometimes immediately, sometimes years later, or sometimes perhaps not at all).

Ah, psychotherapy. The parallel process theory of psychotherapy supervision posits that the dynamics at play in a therapy relationship will inevitably play out in the relationship between therapist and supervisor as well. If observed and interpreted properly, this process can be used to benefit the therapy client and grow the therapist’s self-knowledge and skills. Something very similar happens when we travel: the dynamics of our home lives play out in how we interact with gate agents, our fellow travelers, and the residents of the places we visit.  Patterns are inevitable, and if we are open to them there is a wealth of self-knowledge to be had. Interestingly, despite the parallel nature of the process, it is driven and nurtured by all the points at which we choose to intersect–with the people we meet on the road, the natural environments we encounter, the experiences we face without fear.

Those points of intersection might form the basis for dozens of complex quadrilaterals in a single journey, yet none of them would be a parallelogram. At the same time, though, they somehow form a massive parallelogram every time, if we can only see the forest for the trees.



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