The Riddle of the Square

Shapes are mysterious. They are basic, rudimentary forms — simple ideas upon which we build more complex systems of understanding. They are also vast landscapes of information and meaning — doorways into mental worlds of thought, unhindered by physical limitations.

You can look at the simplest of forms — a square, a circle, a triangle — and its edges will accommodate your curiosity; they will stretch; they will become porous; their liminality will beckon you to enter and to hold them. Like the Sphinx, they may be all their edges tell you, or they may be anything else. They are riddles for the eye.

Ellsworth Kelly put it much more simply when he said that “a shape contains personality.”

Kelly was talking about just one of his Blue Panels when he said this, though his entire body of work exemplifies the idea. He is best known for painting fields of color. His contribution to modern art was, in part, a vast collection of shaped canvasses, painted in single, flat colors. Beginning his career at a time when abstract expressionism was the idea carrying modern art forward, Kelly’s work was universally iconoclastic. For many onlookers at the time, it simply wasn’t art. And though many of them had their complaints about the expressionist work of his peers, they could at least still see the artist’s hand in the work, be swept up in its motion, or even lose themselves in the physical beauty of the material itself. Kelly’s objects were made precisely to do the opposite: not to engage the viewer in the object or its maker, but to draw them in to everything beyond it. To be a riddle and an invitation.

Kelly once told a story about a man he met on an airplane. They got to talking about painting. The man shared that he often visits The Metropolitan Museum of Art to look at the paintings. “One painting really throws me,” he said. “It’s a large blue painting with nothing on it.” Kelly replied, “That’s mine. Go look at it again.” Rather than a correction, Kelly offers another riddle.

I love this story because I can tell the same one. When I was seventeen, I went with my senior art class to the same museum, and saw the same painting. We had come to tour the modern art gallery in general, but Kelly’s Blue Panel II, which is still on view in Gallery 922, became our fixation. We gathered in front of it and stared; it silently divided us. Some said it was art. Others said it was not. Its name further provoked the angst of the naysayers: “Blue Panel number two? So there are more of these things?”

The debate continued as we left the museum. It went on as we explored the city. And on still, all way home on the bus. Someone suggested we keep this going — that we get together once a week to talk about art outside of class. We named our little group The Wedge. It was a nod to Kelly’s panel and the way it had cleaved our assumed intellectual unity. The group, as far as I know, remained a fixture at my high school for a few years after we were gone but eventually faded away. But I have remained transfixed by the wedge.

As I said, Kelly made more than one Blue Panel. In what feels like an almost supernatural coincidence, one of them just happens to hang in a gallery near me at the North Carolina Museum of Art. I remember the first time I strode into the room and saw it. I stopped, dead in my tracks, as if I’d seen a ghost of my past returned in tremendous glory. The NCMA’s Blue Panel is not the same Blue Panel as the one I’d seen as a teenager at The Met. It’s bigger. It’s brighter. Its movement is less of a subtle lean to the side and more of an explosive twist. It’s my favorite of Ellsworth Kelly’s Blue Panels, and a perfect example of what is so magical about his work. I stare at his shapes and am in awe of their endless capacity. In them I see all of geometry, all of math, all surfaces, all spaces, all movement.


In no other shape is there greater mystery than the square. I wonder if that is why one of the very few single, square images that Ellsworth Kelly produced is just black. He even titled it that way: “Black,” without reference to shape or surface, leaving us all to decide what it is, or where it is, or where we are within it.

A square is a plane with four equal sides set at four right angles. Such a thing hardly exists in the world. Everything we call a square is an example that falls considerably short of the definition, provided you look closely enough. That’s because the precision of numbers doesn’t really exist in the natural world.

Plato considered numbers to be abstract. For him, they were ideas that lack physical form necessarily, because to take any form would be to lose their perfection. He also considered numbers to be eternal — perpetually existing — and therefore more real than the world in which we live. His reverence for the perfection of the abstract was almost religious. In fact, he believed that things like numbers and shapes actually existed in another space, often called now, after him, The Platonic Realm. Aristotle, his student, was more pragmatic. He considered numbers to be nothing more than an invention of the mind to aid in our understanding of nature, providing measures of amount, or distance, or duration. One can imagine the debate: One side might say, “If numbers are just a construct, then why do they describe the universe so well?” To which the other might reply, “So would anything else, if that’s what we decided to use to describe the universe!”

Nevertheless, both a Platonist and an Aristotelian can agree that there is quite some distance between the perfection of geometry and the plasticity of nature. The square, again, makes for an ideal symbol. It is too perfect for nature. Observing both where we find squares and how we use them bears that out. Of all the geometric shapes, the square may be the least commonly occurring in nature. This is because most things in the natural world are molecularly asymmetrical. Mineral structures, for instance, are quite varied in their geometric correspondence. The few that are square are pyrite, galena (the mineral form of lead sulfide), and halite (rock salt). Most everywhere you look for structure in nature, though, you will find far less rigid forms. While there are a few scant natural squares — lobster eyes comprise millions of micron-length square channels; wombat poop is, oddly, cubic — circles, triangles, rhombuses, and all sorts of polygons are far more common. And most of them are warped.

When we make squares and when we don’t follows nature’s lead. I often think about how infrequently we use squares when creating spaces and structures. Our bodies, of course, determine this. A square door, for example, would be interesting to look at but impractical to use. We are taller than we are wide. A square door tall enough to give us passage would be wider and intrude upon the space in which it opened more than necessary. So doors, like many other things created by nature, for nature, in nature, are rarely square. Perfect symmetry, as it turns out, is inefficient.

I often think about that principle when, as a designer, I consider aspect ratios of imagery. Why is everything a rectangle? There is a reason why cinema screens, televisions, and monitors are wider than they are tall. A rectangular plane in landscape orientation fits our biology. Our two eyes, spaced apart on our head as they are, create a wider periphery. We can see more horizontally than vertically without moving our heads. A square screen, large enough to be absorbingly “cinematic,” would have us literally moving our heads up and down continually in order to take in the visual information it displayed. The ergonomics of wide screens are obviously superior. The visual economy of the rectangle works its way inward, from the edges of the form to its contents. As many a web designer will lament, another day, another rectangle. But it’s worth pointing out that the complaint would be the same and certainly louder, if it were another day, another square. Symmetry of form is beautiful, but it isn’t always functional.

Symmetry of system, on the other hand, can be extremely efficient, even when it doesn’t correspond to nature. Because a square is perfectly symmetrical, it can be duplicated into infinity, creating a reliably consistent structure — a grid — in all directions. Grids help us to work within and upon nature, even when within nature no grids can be found.

As a child — and to this day — I was fascinated by maps and pages of text and easily transfixed by them. I often find myself drawn to pages and screens, for instance, not by their contents but by their form. By how the information is arranged. As a child, I didn’t realize that what I was actually looking at was the grid. The form of the page became a puzzle; I was in search of the system beneath it. The grid becomes another riddle for the eye. Most things we make we do so upon a grid, though the precision of their form can never match the abstract system beneath them. There’s a tension in that, one which provides endless provocation to anyone who looks.

Ellsworth Kelly understood that. He created an installation in Boston which is an ideal illustration of the tension between the perfect symmetry and eternality of the abstract and the asymmetry and limits of nature. Within a large, open column of space within the John J. Moakley Federal Courthouse building, Kelly hung a set of colored panels. From a mezzanine, you can look out and up into the column to a point at which the arc’ed ceiling above you cuts off your view, creating the illusion that the grid of shapes goes on and up forever. When you stand in front of it, you can easily imagine them encircling you, too. It’s as if The Boston Panels were as close as Kelly could get to merging our world with The Platonic Realm.

It’s not lost on me that this has been more about forms that are not squares than those that are. For me, the square offers a glimpse of perfection that is easier to comprehend when it is bent to the will of nature. That, of course, is a paradox. Squares are not natural. But when the idea of the square — The Square, as in the Platonic ideal — wedges its way into the world, it does so in ways that bend and twist and distort so that it may be felt. That is why the work of Ellsworth Kelly, as simple, sterile, and dull as many find it, has always been the opposite for me. It is simple so that it may be complex. It is sterile so that it may be fertile. It is dull so that it may sparkle in the mind.

“Go look at it again,” he says. I suspect that the key to understanding the riddle was never the it — the Blue Panel itself — but the looking. Go look again.

Written by Christopher Butler on February 26, 2021,   In Essays

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