Perspectivo Scientifico or, Where the Rays Convene, I Fix a Point

Go to the pillar separating the medieval section of the museum from the gallery of Renaissance paintings and stop. If you listen carefullyvery carefullyyou can hear a quiet gasp as the medieval painter, after a hundred years of trial and error (give or take a few), finally grasps the notion of perspective and stumbles into enlightenment.

But we. We gasp when we finally stumble and see that we don’t really have true perspective.

When I was in high school, I had a gigantic acacia tree pressing against the windowpanes of my second-story, corner bedroom. In January the tree would pop into flower, like kernels of corn in a pale green pan. They grew and grew until there was no more green to see. Just fragrant, joyful yellow outside my sanctuary.

But it was a dirty tree. The dried flowers tumbled to the ground in handfuls and stuck like fuzz to the bottoms of your shoes. The thin, brown seed pods twisted, split and shattered their seed on the ground. And then hundreds of tiny delicate trees sprang up like weeds.

“It’s got to go,” my mother said. “I can’t take the mess. And it blocks the view.” One day it was gone.

In the morning the sun rose up over the freeway, cleared the roofs of the neighboring houses and the telephone wires and came blaring into the room. My mother pushed the bedroom door.

“Now, isn’t all this sunshine nice?” she declared.

I crossed my eyes at her and growled. My tree was gone: another reason to leave.

European painting of the medieval period is characterized by flatness. Everything that needs revealing is on the painting’s surface. Past events are portrayed in hazes of activity on the sky while the present moment of the painting looms large on the middle ground of the panel. Future conditionals cringe below the dark line of terra firma.

This two-dimensional schematic for painting suits the hierarchy of the medieval church: The world is flat, God is above, Purgatory and Hell below, and there are only two possible endings to a man’s life. Like childhood, it is a simplicity that serves well. But unlike the Byzantine, its flatness is striving to go somewhere. Striving for a new alignment with the stars and the sky, a new horizon.

In college, supposedly, Americans broaden their horizons. Get exposed to new points of view. Learn to be independent thinkers. In fact, maybe all that happens is the tree is cut down so that we can look out the window for the first time. And then, depending on our personalities and families, we head back to our familiar horizons and to a chosen course, or we fall for the allure of the distant horizon.

After college I gathered my little money and went off to visit relatives living on the distant horizons. I imposed on addresses, smelled the strange smells in their kitchens, slept under strange blankets and did my best to utter strange words. Finally I ran out of addresses and the Joni Mitchell tape I played in my head was getting faint. Someone said, “Go visit my cousin in West Berlin.” I packed my camera and notebook and was on the train the next day.

I ended up in a bullet-ridden, crumbling, 18th century plastered building on a gray cobblestone street, deadly in winter. The toilet was in a cubicle on the landing halfway down the stairway (or up, depending on where your apartment was). When I moved to an apartment with its own toilet, I had the view of a dark, inner third courtyard of a factory, cluttered with ash cans and cats, and one perennially dying tree.

I moved again and got my own cat. My fifth-floor balcony looked down at a blanket-sized patch of garden with a dusty broken brick wall. On the other side of the wall were the deserted wilds of a wide strip of abandoned S-Bahn terrain. There was a large gap in the fence and I took long walks there. In the afternoons I explained the present participle. At night I got high on Pilsner and schnapps and discussions of the social construction of reality. One day I fell asleep in the middle of a private lesson. Mortified, I went home to figure out on whose horizon I’d been.

In the afternoon of the 14th century the medieval painter sits back from his work and realizes that what he is painting is not what he is seeing. That there is a material world with its own horizons and natural laws. He decides to impose a grid of orthogonals on the surface of his painting, as if to make a doorway through which he can pass into the three-dimensional space he senses beyond. He uses the fiat plane of his grid to attenuate objects. But the effect is not right. The horizon has too many points and the side angles extend in too many directions. Things are still floating and he is still learning to see.

I was in graduate school, working on my future, convinced I would never go back to Europe, taking a huge bite of my sprout-and-cream-cheese sandwich when an acquaintance of a fellow student walked up. He gave me a coincidental smile while he talked to the fellow student, and then he left. But we ran into each other again and again until the coincidental smiles became smiles of complicity and the acquaintance of an acquaintance became a point of reference. Life can be that way.

He was, it turned out, visiting from his tiny, picturesquely wealthy, pastorally beautiful, European country. And it would soon be time to go back. I couldn’t fathom life without him any more than I could fathom it with him. He, on the other hand, had a plan. So I dumped mine and we married.

But I was sure I was returning to a familiar horizon, just with more perspective. We found a very modern apartment and moved in. This time I had a modern view, a dishwasher and a bathroom-and-a-half.

I went shopping every day with a willow basket slung over my arm and did my wash on Mondays. I learned to put the fork in my left hand and the knife in my right and to shake hands or kiss cheeks whenever I met someone I knew. I ate steak de cheval and overcooked vegetables. I learned to take chrysanthemums and heather to the graves on All Saints’ Day. And finally I learned to push a baby carriage, make ratatouille for lunch and ignore the view out my modern kitchen window.

As the 14th century is drawing to a close, the painters say, “Well, if we can’t get this attenuation part right, at least we can create the illusion of perspective.” They want to imitate the diffusion of light as it recedes toward the horizon on an early spring evening when the sky is smoldering with blue and black rain clouds over the golden-green fields. Atmospheric perspective requires complex color mixing. But there is a problem: The tempera paint is drying too quickly. Adding more egg yolk doesn’t help. Oil paint needs to be discovered.

Jan van Eyck, alive in 1390 and dead by 1440, has been credited with the invention of oil paint. I’m sure it was a propitious moment of coincidence, the kind that mark all important changes in point of view. Probably his wife (for all painters were men in those days) brusquely set down the oil lamp one night, angry that it was she who had the flu and still had to put all the children to bed. The oil sloshed irritably onto his palette, brilliant with splotches of tempera drying quicker than he could get it onto his panel. “Watch what you’re doing, woman!” he cried, but she was gone. The oil slid serpentinely around the eggy patches and caught bits of the scattered pigment dust, and held them suspended. Fascinated, he forgot about his wife with the flu and his children.

In my new country, I met a beautiful but—as it turned out— always unhappy friend. Even though two towns separated us, we were neighbors because we were surrounded by a strange language. One day I visited her. She was in the hospital again, doing tests, but I never quite got what was wrong.

This time her room was on the 12th floor, with an expansive view of a broad winter flatland. On it, in the curve of a river wending along a forest-topped sandstone cliff, stretched the red-tiled roofs of a brown and gray European town. Cathedral towers reached up, marking the long bar of snow-covered Alps forming the horizon.

“What a view,” I sighed, my eyes lingering on the horizon the way they linger over desserts.

“I don’t want a view,” she sighed weakly,” I want someone to save me.” I looked at her wan face. “I’m sorry,” I said, “I don’t even know how to save myself.”

I said goodbye, picked up the kids and went home to my European efficiency kitchen. The carrots I’d bought at the market that morning were still wrapped in newspaper by the sink, the epitome of European charm. I turned and looked out the window.

I saw a flat gray apartment building behind an empty playground (the mothers didn’t come out till after nap time). A pine tree leaned weakly over the desolate sandbox. An old woman, bundled in a thick coat and stockings, pulled a shopping trolley into the high-rise. The pale sun squeezed through a passing hole in the trundling clouds as if it were stubbornly heading out regardless of the weather.

The next morning I looked at my husband in surprise and announced, “I’m going home.”

My husband stared at me, his thick slice of bread spread with currant jam in midair to his mouth.

“Why?” he asked, stupefied.

“It’s the view,” I said, shaking my head. ‘I just can’t stand the view.”

Every view implies a vanishing point. A vanishing point, at its most abstract, is nothing more than points converging at infinity on an ideal horizon, one that we have created for ourselves. Mathematically speaking, it is the fixed point that forms the axis of two or more coordinates. Picturesquely, it is a hole that pierces the horizon. The piercing that gives it perspective.

Our painter, sitting on the threshold of the Renaissance in his dirty smock, stares piercingly out his atelier window. He does not yet quite know what is missing in his painting. He senses the narrowing of energy straining toward the horizon, he has made a grid, his passageway, but he is still not satisfied. His view keeps shifting. Until he suddenly realizes the absolute importance of himself that one spot in the world where he is sitting and looking, mixing pigments and thinking about God and the world.

I flew home with just the children. The children said, “This isn’t home.”

“Enjoy it,” I answered. “It’ll give you a new point of view.” But I wasn’t feeling very much at home in a place I was used to calling home. I looked around for the horizon. A steady stream of cars threaded its tangled way over the hills and choked the view. Friends dashed in and out, leaving hurried messages of no importance. Houses spread across every hill and ridge. Homeless lined some streets, while jostling jeeps studded every parking lot. Had it been so long? In the stores I studied rows of labels and in the end bought only one box of cereal, one bag of bagels and one jar of peanut butter.

I went to the bookstores. I wandered the malls. I had long telephone conversations with kind friends and wrote long letters to my husband. Negotiation, whether with other people or with oneself, is a tricky thing. It requires a certain flexibility, and yet an unfailing sense of where one is in the world. It requires patience and understanding.

The grid, the point of reference, the oil paint, the horizon and the morning of the 15th century. The sky is taking on new dimensions; the world is opening up. The life hereafter is slinking back under the pews of the cathedral and minds are travelling.

In Florence, Filipo Bruneüeschi is fascinated by the idea of representing mathematical relationships in space. He convinces his friend Donatello, the painter, to go with him to Rome to do some measuring. Every day for a whole year he measures while Donatello paints. By the time he returns to Florence, he’s figured out the architecture of proportion and relation. With certainty, he publishes “Construzione Legittima,” but linear perspective remains abstract.

This is not enough,” thinks Leon Battista Alberti as he sits on his vine-covered terrace one afternoon in 1435. “We have enough intelligence to deal with this insight in a concrete way.” He takes up his metal pen nib and homemade ink and begins to write: The view we see is constructed of a pyramid of light. The base of the pyramid is the surface we see, while the apex of the pyramid, where all rays of light convene, rests within us. “Tost haec unicum punctum” … To find true perspective, I choose a single point where the rays of light meet for me, and I fix that point.

De Pittura” travels quickly through Italy and Germany, to Flanders and Holland. It is met with excitement, astonishment and joy. The secret of true perspective is so simple: You need a fixed point of reference (the viewer or yourself, a horizon and a point on the horizon toward which imaginary lines extend beyond the painting into infinity.

It seems obvious, now, from where we sit in history; every schoolchild learns to draw perspective. But back then it took over a hundred years to figure out the necessity of using the self as a systematic reference point.

One day I took my children to the beach. While they climbed a rock I stared at the low, sparkling-green wall of the Pacific. I pressed my bare feet hard against the cool sand. I breathed deeply, thinking about orthogonals and wondering if square miles of openness could constitute a grid. Sunlight glittered in tiny points across the water until one in particular, right on the edge of the horizon, where the ocean reaches the sky, caught my eye.

I stared at it so hard that it suddenly pierced the horizon and I sailed on past miles of islands to continents of land filled with billions of people, all living and breathing and doing the million different things that they do in their millions of different ways. Millions of straggly roosters crowed while millions of dogs of every color barked at the edge of many jungles.

A seagull landed three feet away and eyed me crossly. I was obviously disturbing his view. I looked back at the sea. I understood—the view is not what is in front of our eyes, but the architecture we give to that view. I had left home without knowing where my reference point was, had put up a grid without knowing where my vanishing point was. Why should I blame someone else for my ignorance of perspective?

Without perspective, where do we go in life, I ask myself, sipping the last of my California Zinfandel as I sit on the enormous yellow flowered sofa I bought last week. I look out the window. I like this new house. My husband has chosen well: It has many windows.

A pristine glide of pasture slides down to a wide, sheltering tile roof on an old Swiss farmhouse before slipping gracefully up beyond the dark green woods (where mist rises on November days), past the tiny steepled village on its way up the foothill, and on to the perfectly formed silhouette of the Alps. Snow-covered Alps. Breathlessly cold and crisp on a clear day.

They rear up into the sky and part. When I look out the window, I can see Hannibal and his elephants floating over the pass. Back march Swiss merchant soldiers. Up struggle factory workers. Back grind trucks loaded with Mercedes and BMWs. Light quivers behind the glacial slopes. Warm fragrant winds, heavy with salty moisture, waft up and are sometimes caught by the cold fists of the north, and then they cry. But when they pass through, the frigid northern farmland swells and blossoms. Why hadn’t I seen this before? Was I too busy blaming?

A hundred years after Alberti, Albrecht Dürer erected free-standing screens in front of objects and pulled strings taut between them and his drawing paper in order to show true scientific perspective. He did not call it art; he called it science. Another hundred years and Abraham Bosse, taken by the idea of mathematics in the service of vision and art, proposes an even simpler, portable method for seeing perspective. The visual pyramida kind of hand-held box like a slide viewerallows potential perspecteurs to wander at will. Whenever they wish, they can stop, hold the visual pyramid up to their eye. The sides of the pyramid form a natural glide to the apex, the point toward which lines convene. Wherever I go, I can fix a point. Such clear constraints provide the basis for a new kind of liberty.

Perspective pointed the way for the camera obscura, a simple, closed box with a hole that allowed only a selection of reflected light to enter. It must have been the painters great-great grandson who, tired of the easel and looking at his own thumb stretched out against the horizon, said, “I need a more objective point of view.” But imagine, without pinning down one’s own point of view, the camera would not have been possible.

“So, how’s your view,” I ask my always beautiful friend. She’s over having lunch, but it doesn’t please her, I can tell. I have forgotten how to cook.

“Everything is the same,” she says, pushing back her chair. Her eyes roll sardonically. “I can’t take it anymore,” she whispers. “See you later,” she says as she goes out the door. I know now what she is going to do. She can afford the quick fix.

“Wait!” I want to shout. “Don’t go! Try this pyramida perspectiva! It makes things easier. Post haec unicum punctum!”

If half of life is chosen, and half is accidental, is the horizon the line between the two? But she’s already left and, in fact, there is no scientific device to help us find perspective in this post-modern life.

I return to my sofa with a sigh. Behind the granite blue and white mountains stretched across the horizon like a birthday-card streamer, I see clouds pushing up from the south. I can live with this view. I have chosen it. And perhaps it has chosen me. It changes every day—a misplaced word, a meaningful gesture—but I know where I am.

And there, between two peaks, where I have made the point that pierces my horizon, I draw lines of convergence.

Selection and relation. Perspectivo scientifico.

Birds take flight, The clouds 
drain from the sky I and the 
mountain sit together until only 
the mountain remains.

purloined and adapted from Li Po

1. “de Pictura” L.B, Alberti, 1435; Book I, section 7.

About the Author

Susan L. Rose

Susan L. Rose is a writer, editor and translator working near Fribourg, Switzerland. Her most recent work is an adventure novel for middle-grade readers.

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