Let’s try a quick experiment.
Take a peek through the windows of the box below.
Now imagine the hidden object and try to draw it. Probably, if we compared all the drawings, we would find that they are all different from one another, and from the actual object as well.
But what do those windows really offer us? Authentic, yet partial, visions.
Since I started studying geometry, I’ve always been fascinated by orthogonal projections.
In the transition from three dimensions to two, something very curious happens: a single object can be faithfully represented by completely different, apparently unrelated images.
For example, the contrast between a rectangle and a circle does not contradict the fact that they represent the same cylinder, viewed from the front and from above: it’s a visual riddle!
Interestingly enough, our visual representations of most things are linked to particular viewpoints. For example, the most recognizable image of a human being is usually the frontal view. Or think of a chair: how would you imagine it? Almost certainly not from above, nor from below…
In Western culture, the “typical” way to visually represent an object is often through a certain perspective. This has a lot to do with a cultural tradition deeply influenced by Renaissance art and architectural environments built around straight lines.
We are so used to reading images through perspective that our brains do it automatically. Yet, this is only one of many ways to represent reality, no more valid than any other.
Perhaps the same is true of our opinions and ideas – our cognitive points of view?
In Foundations and Applications of Logotherapy, psychiatrist Viktor Frankl uses the metaphor of orthogonal projections to explain the complementarity of different disciplines for investigating a given object: these perspectives do not exclude one another, but together they can offer a closer approximation of the object’s “truth” by integrating their specific qualities.
He writes:
What is said about vision also applies to knowledge. We live in an age of specialists: people who no longer see the forest of truth because of the trees of individual facts. Of course, we cannot turn back the wheel of history, and society cannot do without specialists.
But is it really true that the danger lies in a lack of universality? Or is it perhaps hidden in the claim to totality? What is truly dangerous is the attempt by an expert — for example, a biologist — to explain human beings solely in biological terms.
Our personal experiences, background, and history also act as lenses that shape what we see.
Being responsible means taking a stand without becoming rigid, and without mistaking a part for the whole. Understanding our own perspective can help us avoid being trapped by it. And orthographic projections can offer a tool to play with all of this.
Cover photo by Laura Berloni 🙏