Apelles and the Birth of Illusionism: Ancient lessons in painting spatial depth

[Fig. 1] Man In Armor, Rembrandt van Rijn, Oil on canvas, 54” x 41”, 1655

Apelles and the Birth of Illusionism:

Ancient lessons in painting spatial depth

[This article appears in an edited form in Lessons in Classical Painting, by Juliette Aristides.]

During the early Middle Ages surfaces were not simply painted. That is, if painters wanted to create the look of gold they didn't just create a painted facsimile, they applied real gold to the surface. They reasoned; why bother imitating one material with another? In the 14th century, for example, Cennino Cennini recommended that if you wanted to paint wool you should scuff up the surface of your panel with a wooden block so that it would feel wooly. Artists were not interested in using paint as a tool to produce the mimetic illusion of gold the way Rembrandt did years later.

With the advent of Humanism, artists of the late Middle Ages such as Rembrandt ignored their immediate predecessors and began looking instead to the time of the ancient Greeks for inspiration. They viewed it as a time when nature itself was a guiding principle, and believed that what Proclus had said two thousand years earlier was still true: “Space is nothing other than the finest light.” Painters felt that if they could relearn how to capture the elusive effects of light, they too could command space.

Rembrandt’s stunning 1665 portrait of Alexander the Great, Man in Armor [Fig. 1], may seem relatively modern to our eyes but it employs techniques that had been invented in ancient Greece some two thousand years previously by a painter called Apelles. During Apelles’ own lifetime, his fame and reputation were unrivaled, and he soon became the favorite portraitist of Alexander the Great. So it is fitting, then, that when Rembrandt paid deferential homage to Apelles’ ancient techniques, he chose as his subject the same man; the 22 year-old Macedonian conqueror of half the globe.

[Fig. 2] The mosaic from the Galla Placidia mausoleum. Created around 450 AD, this mosaic captures the transitional style between earlier naturalism and medieval symbolism. Still, certain stylized methods were carried forward, including Apelles' line, highlighted in red for clarity (the original used gold mosaic tiles).

Apelles had understood what painters of the Middle Ages seemed to have forgotten, but his lesson was deceptively simple: Value (light and dark, essentially) is the best painterly means of producing the illusion of depth. Put another way, Apelles’ big discovery was that black recedes and white advances, or, hollows are dark and ridges are light. The term highlight indelibly carries with it this sense that what is light in color is also high in relief – a notion that did not exist in concrete form before Apelles.

Apelles' addition of a white line along the leading edge of a plane pushed space forward towards the viewer. Despite being based in observation, this was the advent of a painterly convention, a visual trick, and a lesson in perception that Rembrandt would have viscerally understood. It's one that has lasted until this day, and while it may seem blindingly obvious to us now, it’s worth taking a closer look to fully appreciate what Apelles was trying to tell us [Fig. 2].

[Fig. 3] Without Apelles' highlighted edge, the “cube” (A) on the left can be read spatially in two ways, while (B) and (C) cannot.

The Line of Apelles

Without a highlighted edge (Apelles’ so-called “line”), spatial depth in paintings can be ambiguous; form can appear raised or recessed depending on how one looks at it. The addition of Apelles’ lit edge collapses this ambiguity, and establishes forms as either raised or recessed – but not both [Fig. 3].

This was a discovery that owed its origin to developments in theatrical scene paintings of ancient Greece during the Golden Age, around 500 BCE, when artists first created the illusion of raised or recessed panels on a painted backdrop known as the skene. Scenic painters knew that the gleam on a raised edge destroys any spatial ambiguity as to the direction of the three-dimensional relief that might arise from a shifting light source [Fig. 4].


Ancient Greeks saw the world differently to medieval Europeans, and it showed in their painting. Broadly speaking, while medieval artists had subjugated the world of the senses in the service of higher ideals (in the mold of Plato), subsequent Renaissance painters re-awakened to the world of Aristotle - where knowledge could be acquired by apprehending the world via the sensory apparatus; where light and surface were worthy of study.

[Fig. 4] In the left panel, the image reads as small raised rectangles, while on the right, it looks as though the rectangles are recessed and it’s the background grid that’s raised. They are however the same image; the one on the right is just flipped upside down. It’s an illusion caused by the fact that we evolved to orient ourselves by the sun, and it’s much less likely that the sun is shining from below than it is for the rectangles to have gone from raised to recessed, so we believe the latter. 

[Fig. 4a] Above, the lessons of Figs. 3 and 4 have been combined into a rendering of the capital letter E. In (A), the letter can be read spatially as either recessed grooves lit from below or raised relief lit from above. In (B), the application of Apelles’ white line forces us to read the letter as raised relief, lit from the top left.

Not surprisingly, this intellectual precedent had cultural significance in the ancient world stretching back even further than the Greeks. “In Old Kingdom Egyptian tombs, the figure of the deceased had to be recognizable so the Ka could find its proper habitation,” said the American historian Daniel Boorstin, explaining the cultural focus on verisimilitude that clearly informed artistic production in Hellenized Egypt [Fig. 5]. Apelles was the product of a culture that valued observational reality, and when this method of inquiry was rediscovered in the 16th century, so was he.

If we compare the ancient Egyptian paintings known as the Fayum mummy portraits (named after their place of discovery) with Rembrandt’s Portrait of a Bearded Man [Fig. 6] painted almost two thousand years later, we can see very little difference. The lighting is practically identical – from the accentuated bright spot on the tip of the nose and the sparkle of light in the eye to the hint of reflected light on the right edge of the cheek.

And then of course, there is Apelles’ line running down the bridge of the nose. Rembrandt knew, as had the Greeks, that placing your brightest values next to your darkest draws our attention. The human eye is inescapably drawn to high contrast. In a field of white sheep, it's hard not to stare at the black one. Echoing Apelles, Rembrant merely exaggerated the transition from light to dark into what was to become his signature style; a schizophrenic drama of bright illumination on the one hand and brooding darkness on the other.

[Fig. 6] Fayum mummy portrait, C. 100 BCE (left) Portrait of a Bearded Man with Wide Brimmed Hat (detail), Rembrandt Van Rijn, 1633  (right)

Contrast as a Cue to Spatial Depth

Not only does the addition of highlights naturally draw our attention, it contains valuable information regarding spatial depth. Physiologically speaking, if the visual data received by the eye are either highly contrasted, have concentrated detail (or both, as in the eyes and nose in Figs. 5 and 6), we interpret them as being closer to us than data that have less contrast and less detail.

There is an unavoidable psychological response to fine-painted detail at play here. Humans discern spatial information from surface texture such that when our eyes make small jumps (called saccades) from point to point while looking at a rough surface, our brain picks up the message that that surface is near to us. Rough texture is a depth cue understood by the brain to signify proximity. Thus, objects with sharp light-to-dark transitions or strong background contrast are interpreted by the brain as being close to us, while objects with smooth light-to-dark transitions or weak background contrast are interpreted as being far away. No doubt, there was an evolutionary advantage to being immediately able to tell whether that charging wildebeest was near or far. Depth cues manipulated by artists trace a psychological lineage all the way back to early hominids hunting the plains and avoiding danger [Fig. 7].

[Fig. 7] Here, Munsell’s value scale (1-9) has been superimposed in rows upon a graduated background. Known as the Bartleson-Brenneman effect, values along the red diagonal axis appear to be further away because they contrast less with the background, while values along the green axis appear closer because they contrast more with the background.

Value Constancy

Furthermore, we interpret our world not through absolutes of value, but via relative differences. A white floor tile seen in an interior by Vermeer, for example, can be instantly recognized as "white" by the brain despite being nowhere near the white end of Munsell's value chart in terms of its actual value [Fig. 7a].

Form and space are interpreted not through absolutes of value but through the relationship of one value to another. What's more, even in a darkened room we can still read depth and form despite all the values being dark and relatively similar in an absolute sense [Fig. 8]. In a room that's almost completely dark we can still spot that white floor tile, reminding us that perception happens in the mind and not the eye.

The actual value of the floor tile outlined in red (A), when plotted against Munsell's value chart, is surprisingly dark despite us knowing that it is "white."

This phenomenon is called value constancy: it’s our innate tendency to group and hold the perception of an object despite changes in visual data. Thus understood, representational painting is no longer the strict transcription of optical data but becomes, according to historian Ernst Gombrich, a “system of notification;” a set of agreed-upon conventions that may have little to do with observational reality - we paint what we know, not necessarily what we see. Apelles knew this better than any Middle Age painter.

Equally, Rembrandt knew that he didn’t have to pepper his whole canvas with strong blacks and whites in order to render form. He knew that by manipulating value constancy, contrast and value, he could create a more convincing illusion of spatial depth and surface texture (such as gold) than by simply applying real gold to canvas. Understanding the way the mind perceives the world is the key to Rembrandt’s metallic sheen in Man in Armor, and he valued it among his most prized magic tricks.

It's important to note here that learning by observing reality does not mean painting what you see in front of you. This seems counterintuitive at first, but what was important about Apelles' discovery was not that it conformed to what the eye sees, it's that it conformed to how the mind perceives. Aristotle, as the father of the scientific method, knew that insights into human perception came from direct observation of nature. It's up to the representational artist to learn how to manipulate this psychology into illusionism.

Talk of "mimesis" and "observation" may fool us into thinking that we are learning how to see the truth of the world. The greatest illusion of the artist is to convince the viewer that she is seeing reality. All of this is nothing but painterly smoke and mirrors. Tricks of the trade. All that we in the West are seeing when we look at a Rembrandt, for example, is a set of Western cultural conventions; artistic norms that may have a basis in shared psychology but are temporally and culturally rooted. Indeed, there's nothing less realistic about the Art of the Middle Ages than that of the Renaissance, or any other time for that matter.

[Fig. 8] This classic illusion demonstrates “value constancy." Even with all the lights turned down (or in shadow, as above) we can still recognize a “white” square on the floor, although in absolute terms the square is far from white: A and B are the same value.

Metallic Sheen

Rembrandt's ability to capture the effect of metallic sheen was a hard-won technical victory in what was, at the time, a march towards mimesis - the ability to capture the optical effects of light bouncing off the material substance of the world around us - and it owed much to Apelles. Indeed, there is a direct line from the ancient Greek's early innovations that carries all the way through the Renaissance to inform representational painters to this day. But when it came to rendering metal in paint, Rembrandt took Apelles' lesson one step further.

Rendering highlights is not the same as rendering reflection. With the further inclusion of specular highlights to the effects of modeling, much information about the nature of the surface texture can be suggested. Metallic surfaces (particularly curved surfaces such as Alexander the Great's armor or the lip of a goblet) tend to reflect the intensity of the light source – usually the sun. With the exception of bronze and gold, these metallic surfaces reflect little if any local color.

Unfortunately for the painter, white pigment has an upper limit as far as its ability to depict specular highlights – it simply will never be as bright as the sun – so Rembrandt had to cheat when painting his armor. He knew that if he simply painted everything else darker, then his lights would automatically look lighter. Because we intuitively know what we’re looking at thanks to the gestalt principle of value constancy, he knew that he could artificially lower the observed values of the overall scene without compromising spatial depth, and that even on a darkened canvas we’d still be able to read form and surface texture. The only way to make your specular highlights seem as bright as the sun is to darken everything else.

This trick would simultaneously enable him to create a higher relative jump in value to his specular highlights – a necessity when it comes to painting metallic sheen [Fig. 9]. This observation holds true when we consider Man in Armor: precisely because the overall value is relatively dark and indistinct, we know that we are looking at the shiniest metal when we see the bright reflection on Alexander’s helmet and breastplate.

Perhaps, in the end, old people are not simply bad at computers and unpredictable in traffic. Maybe they do have something to teach us.

[Fig. 9] The Rape of Prosperine, (detail) Rembrandt van Rijn. In order for Rembrandt to depict specular light on metal he lowered his surrounding values, enabling the highlights to pop. His specular highlight (f) is almost 4 value points from its next closest value, perceptually implying that we are looking at metallic sheen. And yet, notably, when plotted against the Munsell value chart, it’s clear that even his highest highlights (f) are still relatively low-key (7 on the Munsell chart). Rembrandt still has room to spare at the top end of the value chart if he needed it.

How to Paint the Figure in Trompe l'Oeil

Here is a detail from the finished painting, enlarged because I used very small brushes.

You can use any background you like. I used an old faux-painted limestone sample I had lying around, but you could just as easily do this on faux bois to imitate the look of carved wood. The only stipulation I'd make is that to get the best effect, your background should be no darker than mid-range on the value scale.

In the next image, you can see the brushes I used. One small pointy one, and another splayed out and busted one. When doing shadows, I'd paint with Mr. Pointy then stipple and soften with the busted one. I'm not very fussy about materials or brushes. When I was young, I used to read all those manuals and study hard to learn the "secret" materials that would give me the edge. The only secret, I learned, is your eyes.

Step 1

 If you look closely in Step 1, you can just make out the pencil lines I used to establish the basic design. I took a photo of a bas relief panel at the Met as my reference. This is actually the first time I've used a photograph of actual relief as reference material. Mostly, I'm either inventing relief or copying another trompe l'oeil painter's work (who probably also invented the relief). This was a great chance for me to exercise Rule # 1 in illusionistic painting: Paint what you see, not what you know. 

It's all too easy to fall back on what we "know" about Form rather than simply using the evidence presented before our eyes. "Shadows are dark; highlights are white; reflected light goes here; etc." These are all learned rather than observed truths. [Painters use old tricks such as flipping their image upside down, or examining their work in a mirror, to escape the natural tendency to paint what we think we see.]

Step 2

Step 2 shows the completed shadows. There are no highlights at all here. You can see that the effect is 99% complete already. We could easily leave it like this, and call it a day.

I build the shadows very slowly using Ultramarine and Raw Umber acrylic paint, mixed with a little matte varnish (which dries quickly so I can keep working) as a medium.

The shadows are built up in layers. I never try to establish the darkest dark in the first pass. It's much more tentative then that. I build up darks in translucent glazes, always erring on the lighter side. I tend to work back and forth all over the image, as opposed to finishing each area completely as I go.

Step 3

Step 3 is my first pass at highlights. They might be hard to detect on your screen, as they are very subtle, but they are there. I used an opaque white, mixed with yellow and a little purple. I've heard that some people like to shift the hue of their highlights in opposition to the background color in order to make them pop more. [In other words, if the background hue is yellow (as with mine), they might shift their highlights into purple so that they jump out at you.] I don't do this. I use a lighter value of the background.

Use highlights very sparingly! As subtle as mine might look to you, when I look at the opening detail image of this post, the highlights jump out at me as being too strong and brushy. The image looks like it's been dusted with snow.  The shadows are soft and muted, as they should be, but the highlights are harsh, overused and overly delineated. We want to avoid this at all costs. (It was too late for me).

Step 4

 In Step 4, the only difference is that I carefully glazed the chest, top of the head, and the right knee with a second highlight. I decided that those three areas should be a little more prominent than they were.

It will be easier to see the differences between stages if you view these images in slideshow mode, and scroll between them.

Step 5

 Step 5 might be hard to see, but I think it made a difference. Since all my highlights were already laid down, the only way I could make the relief pop a little more was by darkening the background. I explained the reasoning behind this in a separate post about relative value, here.

I certainly didn't want to add any more highlights, as mine were already too bright. Instead, I used a very washy ultramarine/raw umber glaze and stippled it all around the top right corner, outside the main figure.

I also used a glazed version of my highlight color and subtly lightened the bottom left corner (again, outside the figure only).

Finished.

To give you an idea of how light/dark my values are, here is a chart that shows you (below)...

Along the top you see 3 swatches of color. These represent averaged tones taken directly from the finished piece. Directly underneath them, you see 3 grey values (A, B, and C). These are the same colors from the top line desaturated so as to see value only. Below that, I plotted A, B, and C against the Munsell value chart. You can see that the entirety of my painting occupies roughly three value steps on the Munsell chart (from 6 to 9). No white, and nothing at all on the lower half of the chart.

Some more detail photos...

I bet you a million dollars you fail this color test

The human eye is as good a camera as can be made from a scrap of meat and a dash of jelly, but our ever-distrustful brain works hard to overrule our eyes at every turn. "Grass is green," our brain tells us. Our eyes see something else, myriad shades across a spectrum, but they are mute. It's our brains that do all the talking. 

See the blue tiles on the top side of the big Rubik's cube on the left, above? Ok; how about the yellow tiles on top of the right Rubik's cube above? They are the same color. You're not seeing blue on the left, nor are you seeing yellow on the right. What your eyes are actually seeing is the same color. It's your brain that has created a difference. If there was ever proof that seeing happens in your brain and not in your eyes, this is it.

The test was to see them both as the same, and you failed. So I'll be spending my million dollars on cocaine and nose jobs, in that order.

Harry Chapin ruined family car-trips across the world with "Flowers are Red..."

but he certainly made an impact. I still remember all the damn words. [video link]

What on earth is going on in our brains? Diane Ackerman explains in A Natural History of the Senses. "We are not really cameras. Our eyes do not just measure wavelengths of light. As Edwin Land, inventor of the Polaroid Land Camera and instant photography, deduced, we judge colors by the company they keep. We compare them to one another, and revise according to the time of day, light source, memory." 

Beau Lotto, founder of Lottolab, a hybrid art space and scientific laboratory, investigates the crossover between what our eyes apprehend and what our brain perceives when it comes to color. Watch his fascinating TED talk here, if you haven't already seen it. He's produced some incredible graphics that fool the eye so completely that I had to check in Photoshop using the eye-dropper tool to make sure I wasn't losing my mind (including the three color tests reproduced here).

In the Image above for example, how would you feel if I told you that the x-shaped piece at the center of both of these building block contraptions is the same color? On the left it looks blue, and on the right it looks yellow, but all of that is happening in your head based on assumptions your brain is making about the environment surrounding each x-shaped piece. In fact, they are both standard 50% grey, and not a "color" at all. Bring that image into Photoshop and check if you don't believe me.

Lotto explains in his TED talk that the perceptual function of color, not surprisingly, has a basis in evolution. It's a point with which Ackerman agrees in her book. "Every college student at one time or another has asked what it means to know something," she says, "and whether there are simple perceptual truths that people share. We watch color television because our ancestors had eyes cued to the ripening of fruit; and they also had to be wary of poisonous plants and animals (which tend to be brightly colored)."

At dusk, we still see a blue mailbox or a red car, but they are everything but. "Even though it's sunset and the quantity, quality, and brightness of light have all diminished, we still perceive the blue mailbox as blue, the red car as red." Conceptual categories like Red and Blue lump disparate phenomena together, such as a flower "hit by glare, rinsed with artificial light, saturated with pigment, or gently bathed in moonlight."

"Otherwise, our ancestors wouldn't have been able to find food at sunset or on overcast days. The eye works with ratios of color, not with absolutes. Land was not a biologist, but a keen observer of how we observe, and his theory of color constancy, proposed in 1963, continues to make sense. 

The brown tile on the top and the orange tile on the side are in fact the same color.

In the end, perhaps the words we use to describe colors have more to do with the idiosyncrasies of the particular culture in which we are raised than a relationship to what's actually out there. "Not all languages name all colors. Japanese only recently included a word for blue," continues Ackerman. "In past ages, aoi was an umbrella word that stood for the range of colors from green and blue to violet. Primitive languages first develop words for black and white, then add red, then yellow and green; many lump blue and green together, and some don't bother distinguishing between other colors of the spectrum. 

"Because ancient Greek had very few color words, a lot of brisk scholarly debate has centered around what Homer meant by such metaphors as the "wine-dark sea" Welsh uses the word glas to describe the color of a mountain lake, which might in fact be blue, gray, or green. In Swahili, nyakundu could mean brown, yellow, or red. The Jalé tribespeople of New Guinea, having no word for green, are content to refer to a leaf as dark or light. 

"Though English sports a fair range of words to distinguish blue from green (including azure, aqua, teal, navy, emerald, indigo, olive), we frequently argue about whether a color really should be considered blue or green, and mainly resort to similes such as grass green, or pea green. The color language of English truly stumbles when it comes to life's processes."

Fractal Geometry in African Villages: Lessons from an Outsider

In the 1960s, the Italian architecture firm Superstudio proposed the eradication of all architectural difference under a ubiquitous grid that they called a "Model for Total Urbanization." This is one of their posters.

"The exception proves the rule." How many times have we heard that without really understanding it? It was Cicero in ancient Rome who first said it, and what he implied was that exceptions presuppose the existence of a norm (to which they are the exception). We always look to outsiders, the exceptions to the rule, to help define ourselves as normal. Outsiders have always defined insiders. An old military adage says that you need a great enemy to create a great army. For ancient Greece, it was the Spartans and Macedonians who provided the "savage" exception that proved the superiority of the civilized Athenian polis, or city-state. For the West, a monstrous "other" occupying the rest of the world provided evidence of the dubious superiority of its own worldview.

The Western gridded "ideal city," as imagined by Fra Carnevale

In popular imagination, the exceptions to Western civilization still represent everything uncivilized, chaotic and savage in the world. When Edward Said and Claude Levi-Strauss came along in the '60s and pointed out that, hey, just because other cultures are different doesn't mean that they are devoid of their own internal logic and structure, we began to open our eyes to the fact that maybe, in the end, we had something to learn from "them." We'd gotten so blind to the veil we've fabricated as a frontier between city/country, order/chaos, insider/outsider, West/Rest, that we'd lost sight of the fact that ours is just one of many ways of being in the world, and that the veil is an illusion.

Somewhere in America

Case in point: the gridded and bordered modern city that sprang up in Europe towards the end of the Roman Empire - with its straight lines and corners retained by a circumscribing wall - quickly became the template for Western life. They were initially walled defensive positions (called Oppida), but the Romans soon became aware of their greater (in the long run) symbolic significance: The walled city is a locus of power. Those outside the walls were the medieval "wildmen," or savages beneath consideration. It established a clear - if fictional - boundary between the order of Man and the chaos of Nature.

The Universe is Euclidean, its rigid geometry tells us. The very linearity of modern cities came to represent the mythic Western advancement from barbarian to citizen, from chaos to order. The more squared-off the space, the more civilized its occupant. The barbarians lived outside the polis amid the chaos of nature, and "Nature," as Katherine Hepburn reminded Bogart in African Queen, "is what we are put in this world to rise above." Consequently, linear gridded space became the Western standard.

Hardly a coincidence that Star Trek automatons, "The Borg," occupy a cube.

By the 15th Century, Linear Perspective gained favor as a way of reifying what had already become a pervasively geometric worldview, literally set in stone by the Romans.  Perspective appealed to rich patrons because it backed up their notions of the hierarchy of social power (think majestic cathedrals with impossibly soaring trompe l'oeil ceilings inspiring awe among the plebs). Artists of Europe clamored to learn the rules of Linear Perspective as a way of codifying a "civilized" worldview, which flattered their clients by portraying them as higher-order citizens. Even if anyone had been aware of another way of seeing the world, they wouldn't have cared for it. West is best, and all that.

Every day I walk the streets of New York City, I'm aware that to get across town means zig-zagging at right angles across an artificially imposed grid that by its very inorganicness was designed to position the works of man as superior to those of nature.

What would an alternative even look like? We're so used to what we've got that it's hard to picture it, but we don't have to: When the fractal geometry of African villages was "discovered" by the West, it provided the exception that exposed the tenuousness of the norm we've come to accept. Certain villages in Africa (such as Tiébelé on the Ghanian border) have been organizing themselves for centuries according to mathematical principles that were only discovered in the West in the 1900s.

The classic Mandelbrot fractal set

Whereas the Western gridded polis denies Nature by proposing space as a system of stackable finite blocks, fractal architecture suggests an unfolding of space according to principles of organic growth. Each unit of fractal geometry relates intrinsically to its neighbor, regardless of scale. There is no frontier, no hierarchy of space as in the West.

Fractal sets are everywhere in Nature

Fractal architecture could never produce a Versailles, for example, that so self-consciously set itself apart from the populace that surrounded it. The "self-similarity" of fractal geometric modules would preclude it. Western architecture relies on the grid as an exclusionary device - you are either inside or outside the square - but fractal architecture seems to suggest that we all have the same potentiality.



I always worry that I'm writing too much in blog posts, that they're too long (because who the hell reads blog posts?), so I won't be getting into the weeds about what fractals are, except to say that they began as an outlier set of mathematical rules once considered to be useless oddities - Euclid's outsiders.

The fractal architecture of Ba-ila village, in Southern Zambia

The realization that whole communities live according to a spatial map that is entirely different to ours was an eye-opener. Watch this TED talk (and buy the book) by this fascinating mathematician who traveled Africa on a Fulbright scholarship, standing on rooftops and recording the fractal geometry he saw all around him. And next time you're sitting at a traffic light, imagine a world that has no right angles.

Ron Eglash mapped the fractal set at the heart of community life for Ba-ila villagers

Tiébelé, Ghana

How to Paint Reflections on Water

Sommarnoje, Anders Zorn
showing lengthened and broken reflections beneath the boat and pier.

The post title is a tad misleading, as it is more about seeing and understanding than painting. Why do reflections appear longer in rippled water compared to smooth water? Why do reflections not appear at all in very rough water? Is there any quantifiable way for painters to measure the correct length of reflections, besides just painting a bunch of wiggly lines?

And if you feel like a little musical accompaniment while you wrap your head around some math, try Claude Debussy's "Reflections in Water."

I'm going to let my illustrations do most of the talking in this post. I hope that they're clear enough that you will be able to understand the principles just by studying them.

Figure 1

In Figure 1 above, there is a pole [AB] standing out of the water. You can imagine looking at it along sight lines that run through an imaginary picture plane. The top of the pole intersects the picture plane (the canvas you're painting on) at point A1. The visible bottom of the pole above the water would appear on your canvas at point B1. If the surface of the water was as smooth as a mirror, the reflection of your pole on the water would be painted on your canvas extending down to point C1. Notice too that the angles x, y, and z are the same when on a perfectly flat surface.

Figure 2

If there was a concrete pier as in Figure 2, the reflections would end up looking as they do in Figure 3, below. Note the reflection of the pole in the water below. If you study Figure 2 you will understand why the reflection simply peeks out a short length below the pier reflection instead of appearing to be the full length of the pole itself.

Figure 3

Fur Traders descending the Missouri, George Caleb Bingham

In the beautiful painting by Anders Zorn that opens this post, we see that the reflection of the boat extends downwards quite a bit below where one might expect. Why? Simply because water is never as smooth as it appears in our illustrations above. Despite what Caleb Bingham might have us believe (above), water almost always has some visible movement causing ripples or waves. These waves cause the reflections to distort and extend lower on the canvas.

The reflection of a pole in rippled water [Fig. 4] would thus appear to extend in a broken line all the way down our canvas to point D1. I hope that by studying the next couple of illustrations you can understand the effect of broken water conditions upon reflections.

In addition, rougher bodies of water appear to be brighter overall than smooth bodies of water. The fascinating reason has something to do with Galileo, and can be found in a separate blogpost, here.

Figure 4

The Champion Single Sculls (Max Schmitt), by Thomas Eakins

Thomas Eakins, famously mathematical when it came to constructing his paintings, drew an illustration [Fig. 5] in one of his notebooks that shows why the reflections in rippled water appear "wiggly."

Figure 5

I've created my own version of the same phenomenon [Fig. 6], with some added notes that might help clarify what's happening.

The Quadratura of Francesco Natali

Francesco Natali created these wonderful baroque quadratura and wall frescos in a little church in Pontremoli, Italy. I'd hoped to write a lengthier post about this church, its fabulous history, and the charming work of this lesser known Italian artist, but I think you'd rather just see the photos. So here they are.

I uploaded a ton more photos of the Church on my Flickr page, here.

Remove the stone lintel in the small niche (above) and it reveals a deep crawl space used to secrete
dissidents and refugees during World War II.

Incidentally, this church weathered Allied bombardment and was even liberated by the Buffalo Soldiers, America's historic all-Black Infantry (originally Cavalry) division in World War II. They stormed the town only to free a group of jews hidden in a specially-designed crawl space disguised behind one of Natali's decorative niches in the church sacristy (photo above).