Rectangle Vision

It’s probably not a good idea to look directly at the rectangles.

If you get into this mode – Rectangle Vision – you wake up in the morning on your rectangle. You lift your head off of its rectangle and toss aside the rectangles wrapped around you, still holding your body’s warmth. You pull a string to lift the sheet of rectangles covering the rectangle in the wall and let the light stream in. You pick up your rectangle to check the time, and perhaps touch a rectangle inside of it, to see all the latest rectangles to make you mad.

You step through a rectangle to leave the bedroom, step through another to wash (perhaps using a cuboid of soap), dry your skin and hair with a rectangle, and check out your reflection in the rectangle. Make your way to the kitchen and open up the rectangle that shields the cold things; perhaps open another rectangle to warm something up. Take it from the counter rectangle and eat it on the table rectangle, sitting on a rectangular platform. Wipe your face with a rectangle. Leave the house through the rectangular portal, making sure you carry your necessary rectangles for identification, payment, work, and entertainment. Then you really enter the land of rectangles: the walls, the steps, the parking spaces, the sidewalk blocks, the signs, the crosswalks, the vents and gratings, all the windows, and every discarded wrapper of a rectangular eyeglass wipe.

Where did all these rectangles come from? There are few rectangles in nature; those that do form (e.g., tessellated pavements) are objects of wonder and mystery, precisely because rectilinear forms present to us as the work of man. This is why the rectangular cuboid monolith in 2001: A Space Odyssey is so evocative: without saying so, it’s understood that a regular cuboid like this is the work of intelligence like ours.

Somehow, rectangles managed to enter our brains, seemingly out of nowhere, and then escape our brains to become the primary form of our world. Perhaps it’s a product of pathological Rectangle Vision, but rectangles and rectilinearity seem to me to be as much a part of special human consciousness as projected self-awareness. My questions are these: what were the first rectangles? How did rectilinearity enter our consciousness? How did they get everywhere? And what do they mean, if anything?

Dawn of the Rectangles

I had some hypotheses about the origin of rectangles in human culture. One was farming: the linearity of farming (sowing seeds or plowing along straight lines) goes back at least seven or eight thousand years. The linearity of the farming, combined with the relatively planar nature of the surface of the earth, and again combined with conceptions of individual property, would naturally lead to rectangular farms.

Another candidate was weaving. Weaving goes back perhaps 27,000 years, and the nature of woven fabric is inherently rectangular. Mathematician Ralph Abraham traces the development of geometric forms in wall paintings and tile tessellations to earlier woven geometric forms; perhaps this was the origin of rectangular geometry as well?

Nope.

The paintings in the Lascaux caves (dated to around 17,000 years ago) are mostly naturalistic animal figures; there are also hand stencils and other non-rectilinear forms. I didn’t expect to see this guy:

Rectangle at Lascaux cave

Here’s some rectangles inscribed on a lion head sculpture, dated to around 35,000 years ago, in Vogelherd Cave in Germany:

Lion Head Sculpture, Vogelherd Cave, Germany. Photo by Rainer Halama.

But the oldest human-created rectangle I’m aware of is described by Christopher S. Henshilwooda, Francesco d’Errico, and Ian Watts, found in the Blombos Cave in South Africa. They located pieces of ochre inscribed with lines forming rectangles; the oldest (below) is dated to between 98,000 and 100,000 years ago.

The authors note that “when the incisions were freshly made, they would have stood out as vivid red against a dark background.” Here rectangles emerge from the planar face of the rock, and parallel lines inscribed upon it. (In some cases, the rock face was smoothed prior to the engraving.)

A hundred thousand years, is how old the first known rectangle is.

It may not be meaningful, but Henshilwood et al. found a slightly earlier engraving in which there are inscribed lines, but they aren’t quite parallel. They look to me like stems of an aquatic plant growing upward and outward in a natural way:

Is it possible that in those few thousand years between when the two artifacts were created, the makers of the inscribed stones were developing the capacity to perceive and recreate parallel linearity? Maybe. It’s probably just chance.

Tiling and Close Packing

It’s interesting that the first rectangle isn’t all on its own. It emerges specifically in a tiling of rectangular shapes, a sort of proto-frieze (this becomes even more apparent with the later Blombos pieces and the Vogelherd lion’s head, above). And it may be that the main point of rectangular shapes is that they tile easily with each other in two and three dimensions: cuboid rooms and rectangular lots, cuboid cereal boxes and shipping containers, yoga mats and parking spaces.

If rectangular tiling is so great, why isn’t it used in nature? Organisms tend to tile in spirals (composite flowers) or hexagons (emerging from an attempt to tile circles, as in beehives and plant stalks). Rivers become curvier and less linear over time; any curves in the river are dug out further by the action of the water, which flows faster on the outside of a curve. You won’t see any rectangles in national parks, other than a sign or two, and the ones you bring with you (and you had better carry them out).

Plants (and animals) do respect the linearity of gravity; many plants grow directly upward in order to distribute loads properly and maximize sunlight. But when plants try their hardest to do rectilinearity, it comes out like this:

Onion cells, E. B. Wilson, 1900

Somehow rectilinearity doesn’t emerge from bottom-up processes. In the onion, there is nothing holding the quasi-rectangular cells to a rectangular geometry; they squish around however, and end up in irregular shapes. Rectilinearity emerges from lines: painted dividers for parking spaces, walls, threads on looms, etc. Parallel lines are the hallmark of legibility in the James C. Scott sense. Rectilinearity must be imposed. Generally, human brains must impose it.

When tiling is used for aesthetic beauty, as in Anatolian architecture, circular geometries are preferred to rectangular. Physicist Peter Lu has argued that special regular (but non-rectangular) tiling shapes called Girih tiles were used to create the spectacular geometric effects. Somehow, hiding the legibility seems to be important for beauty, as if there were a tradeoff between legibility and an arrangement whose order is mysterious.

Monolith Vision

One of my favorite independent scholars, Rob Ager, has a theory that the movie 2001: A Space Odyssey is Kubrick’s attempt to induce Rectangle Vision in the viewer. The rectangular cuboid monolith, he says, obviously represents the screen on which the viewer is viewing the movie. (In fact, he argues that within the logic of the movie, the monolith is not an alien artifact at all, but a sort of hoax produced by humans.)

The Industrial Revolution was an explosion in rectilinearity. Its factories, products, and shipping networks imposed the rectangle on the world on a scale never before seen. But the most important rectangle of our age is the one that you’re reading this through. How many rectangles can you see right now?

Again, I don’t know if it’s a particularly good idea to walk around being aware of the rectangles. Following Heidegger and John Dewey, we’re mostly aware of the form of our tools, such as their rectilinearity, if they break down (e.g. if they become “bricked”). Perhaps it’s best to continue interacting with them as invisible portals through with we access cold food, outside, the internet, etc., and body-extension territories such as parking spaces, rooms, yoga mats, etc. But there may be times when we want to see legibility itself. For that, there’s Rectangle Vision.

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About Sarah Perry

Sarah Perry is a ribbonfarm contributing editor and the author of Every Cradle is a Grave. She also blogs at The View from Hell.
Her primary interests are in the area of ritual and social behavior. Follow her on Twitter

Comments

  1. Oh come on, those cross hashes aren’t rectangles per se. The Lascaux one is legit though.

    What about subatomic structures. You do get face-centered and body-centered cubics in crystals.

  2. Now write about the color blue :)

  3. Interestingly, the 60s counterculture was explicitly anti-rectangle, reflected in their embrace of the geodesic dome (circles and triangles) and use of “square” to label the mainstream. Partly justified from Native American writings:

    After the heyoka ceremony, I came to live here where I am now between Wounded Knee Creek and Grass Creek. Others came too, and we made these little gray houses of logs that you see, and they are square. It is a bad way to live, for there can be no power in a square. You have noticed that everything an Indian does is in a circle, and that is because the Power of the World always works in circles, and everything tries to be round. In the old days when we were a strong and happy people, all our power came to us from the sacred hoop of the nation, and so long as the hoop was unbroken, the people flourished. The flowering tree was the living center of the hoop, and the circle of the four quarters nourished it…But the Wasichus have put us in these square boxes. Our power is gone and we are dying, for the power is not in us any more. You can look at our boys and see how it is with us. When we were living by the power of the circle in the way we should, boys were men at twelve or thirteen years of ago. But now it takes them very much longer to mature.

  4. Metacelsus says:

    Did someone say Crucifix Glitch?

  5. Ravi Daithankar says:

    I think you are missing the point by looking at a rectangle as the unit. While rectangles themselves may not be seen to occur commonly in nature, all they really are, is a sort of purist rendition of an ordinary quadrilateral; one that follows a particular sense of order. If you took a slightly more fractal view, you’d see plenty of instances in nature that tend toward rectangles: a special case of four intersecting lines. In nature, function trumps aesthetic. The functionality of the rectangle lies in its predictability and order. That’s why, in your example of farming, someone all those thousands of years ago must have decided to plant seeds in some sense of order or pattern rather than just throwing them randomly in every direction. The natural and the most basic manifestation of order is a line. And when you have 4 of them, they tend toward a rectangle. I would wager that nobody ever set out creating a rectangle. The rectangle or something close to a rectangle merely happened. Imagine you were the first guy trying to build a shelter from the wind or the rain. The primary functional requirement would be to have something that could be erected on the ground. Since the surface of the earth for all practical purposes was obviously a flat plane, the logical and instinctive thing to do would be to erect a “wall” that complimented this plane for maximal stability. Throw in a couple of other basic requirements like maximal coverage, being a compliment to a roof etc., and voila, you have your first iteration of the rectangle. Not a rectangle, but something that resembles it quite a bit.

    Now you’d never see a perfect or near-perfect rectangle (4 right angles) in nature because there was never any great functional benefit to be achieved from the incremental effort that would have to be expended to ‘perfect’ a trapezium or a parallelogram or really any quadrilateral into a rectangle. As an analogy, that’s the reason men still have nipples. There just isn’t enough functional benefit in it for the evolutionary design cost to be incurred.

    A refined 80-piece orchestrated symphony today just represents all the incremental progress that’s accrued over time starting from the first dried out hollow stick that had the wind whistling through it nonchalantly. So do rectangles.

    • Ravi Daithankar says:

      *complement not compliment. :)

    • It strikes me that a good early example of a process that produces parallel lines is plowing; if you have an area that you plow by animal, it’s awkward to keep turning them in an outward spiralling path, much more easy to just send them in a direction following one boundary that has a relatively flat gradient, and turn back on themselves at the first sharp edge, like for example, when you begin to start going up hill.

      Plowing in this form differs from personal plowing (where it may be perfectly reasonable to start at the centre and spiral out), in that you are trying to control another animal to get the job done; quadrilaterals as a way of devoting varying levels of attention to a task; run until break point, repeat. The use of loops in code is somewhat similar, tell the computer to plow some line, then when it reaches it’s end, return on itself and continue.

      As with plant cells, you end up with loose quadrilaterals, not the strict rectangles of the modern day, that tile a landscape by being non-regular.

      Then there’s the fence I suppose, as a rectangular structure, though mostly by virtue of it’s thickness being negligible so that we view it as a rectangle, if we had been tuned by older building methods to view all walls and structures as mixes of trapezoidal and triangular prisms, perhaps we would see it as one of those instead.

      But what both the plow and the fence share is the idea of continuing with some flat process, interspersed with moments of activity, follow a boundary making a fence/plowing a line until you reach another. They allow both daydreaming and boredom.

      A perhaps even more interesting example of this particular craft dynamic is knitting, which is where I’d expect to see the most rectangles occurring in ancient culture’s work.

      Makes me wonder how this task was performed in the past, is “counting stitches” the inherent numeracy in order to jump dimensions by using from constant repeating processes, a concept of our modern technical viewpoint projected back onto the past? Or is the modern world an expansion of the world of knitting to other fields of life? I would not be at all surprised if people in the past used knitting songs rather than simple counting though, which then relates the rectangle to other repeating patterns in folk music.

      Come to the end of a line, and start again.

  6. Davis Dulin says:

    some nice pictures in theme:
    http://chaoticatmospheres.com/shapes-in-nature

  7. ItalyMich says:

    “Each person’s self is spread out among many people, simulated in all their brains at varying levels of granularity. And each person has a different “self” for each one of the people he knows, and a different self for every social context. A teenager has a very different way of behaving, speaking and thinking around his friends from the way he behaves, speaks, and thinks around his grandparents. The self at work is different from the self at home with close friends, or in bed with a spouse. And none of these are the “true self” – rather, the self exists in all these, and in the transitions between them. There can never be one single, public self; to collapse all these multiple selves together would be akin to social death.”

    One can lead an hermitic life, if he can’t suffer having to pretend, that is, superimpose masks to his one true self — which may not exist for some, many, or most, but unanswerably does for a few, specially the most introverted, people.

    Yes the ego may become one with the mask(s), but it’s not forced to do so.

    “Social death” is an apocalyptic expression. Why not “social retirement”? Or “social indifference”? Or “social estrangement”?

    “Self”, “ego”, and the various masks the ego may avail itself of (or even merge with, with no return to differentiation) aren’t to be used as the same word, denoting the same entity.

  8. Rectangles appear in the earliest urban forms of Jericho and Catal Hayuk. It’s one way of allocating fair shares of space.

  9. Davis Dulin says:

    not sure how desirable unrelated associations in comments are, but this recent slate star codex post reminds me a lot about preference falsification in weaponized sacredness:
    http://slatestarcodex.com/2017/10/23/kolmogorov-complicity-and-the-parable-of-lightning/

  10. Ever notice how everything in nature is made of tubes? Blades of grass, worms, veins, intestines, trees, esophagus, ears, nose, limbs.

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