Geometry & painting

Adèle (c) Samantha Groenestyn (oil on linen)

Importing mathematics into painting has some potentially grand implications. The idea makes me flush with uncontainable excitement; it smacks of Descartes (2006 [1637]: 9) and his methodical approach to knowledge, and I would echo his rationalist sentiment: ‘I was most keen on mathematics, because of its certainty and the incontrovertibility of its proofs.’ This unlikely marriage between mathematics and painting is especially dear to me because it offers something steady and dependable in terms of colour and not merely in terms of drawing; it promises to embrace the entirety of painting with its sober orderliness. This systematisation hardly destroys the poetry of painting. Rather, it allows us to sharpen our technical methods, which equips the genius (of the Kantian flavour) to paint something deeply insightful and moving. And it promises a double elegance: the sight of the painting itself, just like the sounds in music, may please us, and at the same time be grounded in delightfully crisp mathematical relationships, just like the improbable mathematical elegance of harmony in music.

These longings for order and systematisation sound rather like seventeenth-century aspirations to elevate painting to a science, or at least to a liberal art, which has much to do with shedding its humble craft status, as a trade practiced by illiterates. Painting has certainly made many efforts in this direction; it may boast of its academic status now that it is so commonly taught in universities rather than in ateliers, now that it defends itself verbally and indeed often consists more in its verbal conception and explanation than in its visual execution. But perhaps these victories are no victories at all: they strip painting of the very things that distinguish it as painting. Painting might have done better to have sought an intellectual ally in mathematics rather than in language, for there it would have found ways to describe its visual concepts succinctly and precisely.

Copy after Rodin, Burgher of Calais

This camaraderie is most apparent when it comes to colour. Colour is the rogue that has been seized by painters who want to defy philosophical discourse, and it is the uncontainable element that philosophy has used to subordinate painting. It seems to defy principles, thus it eludes philosophers, and it seems to operate largely by inspiration, superstition and magic, which seems to be attractive to painters. Across both disciplines, there is general agreement that colour is definitively not rule-amenable, while drawing is. Jacqueline Lichtenstein (1993 [1989]: 4; 62-3), in The Eloquence of Colour, traces this long-standing tension back to Plato and Aristotle, observing that ‘being material, colour has always been seen as belonging to the ontologically deficient categories of the ephemeral and the random.’ Philosophy has, she writes, thus favoured the more conceptually manageable element of painting: drawing (Lichtenstein, 1989 [1993]: 4).

If colour does not lend itself to principles, this has another, more practical, result. Philosophy aside, it means that colour cannot be taught. This lends itself to all varieties of unwelcome mysticism, that I personally would like to see chased out of the discipline of painting. It suggests that painters are ‘gifted,’ that they are conduits for ‘inspiration,’ or that they must operate by chance–all of which deny that painting is a disciplined skill that can be developed and improved and harnessed for aesthetic purposes. This is an unhappy state for painting to be in, for it grants artists license to all sorts of nonsense and self-indulgence, and abuses the viewer with all manner of ineptly executed work. In short, it encourages carelessness and invites decadence. Painting is visibly decaying before our eyes.

Copy after Rodin, Burgher of Calais

In the face of these two apparent deficiencies, I want to argue that the emphasis on drawing–both as philosophically acceptable and as practically teachable–is misplaced. Drawing certainly does lend itself to principles which can indeed be taught, and perhaps this fact is even overplayed. There are elements to drawing that cannot be taught, because each draughtswoman will adapt the learned principles to her own sensibility; she will interpret them, introducing a quality of line that no one else has. And, more broadly, the principles that are discussed and taught are not incontestable facts of existence. This is very clearly described by Panofsky’s (1991 [1927]: 37) contrast of spherical and linear perspective. Lastly, I want to raise a surprisingly little-grasped fact, one that is also popularly rejected by painters: colour is indeed amenable to principles, and there are painters who work with these principles and succeed in teaching them. Colour is very acutely described by geometry. In our infatuation with language, this straightforward ordering of colour has persisted largely unnoticed for at least two hundred years.

Lichtenstein (1993 [1989]: 142) notes that ‘ever since society has set a hierarchy among human activities, their relation to language has been the ultimate criterion for the establishment of a division, both social and philosophical, between the noble arts and the servile trades.’ Because of this, she explains, painting has sought to prove itself by ‘literary credentials;’ in order to do this, it has been expected to ‘satisfy both theoretical and pedagogical objectives,’ as we have already considered (Lichtenstein 1993 [1989]: 142; 151). Since she accepts that colour defies principles, she looks to rhetoric to redeem the intellectual status of painting, a fascinating move that demands more attention elsewhere, but we may here respond with our geometry of colour.

Copy after Rodin, Burgher of Calais

A fascinating little tract by Philipp Otto Runge appeared in the early 1800s. His Farbenkugel, or ‘colour sphere,’ is a mathematically pure way of conceptualising colour. It conceives of the relations between all colours three-dimensionally. He begins with a flat triangle that represents the three unmixed colours of red, yellow and blue. Each line is bisected to indicate that, mathematically, the secondary colours are the halfway points between each of these: orange, green and purple. These six points are extended out to the edges of a circle, which is then pierced by a perpendicular axis at whose poles stand white and black. The mid-point of this pole is, mathematically, a mid-tone grey. As colours move directly across the horizontal axis, they are neutralised by their mathematical opposite, entirely cancelling each other out as grey at the mid-point–yellow becomes, not more purplish, but more grey, as it moves towards purple, its opposite. Green and red exist in the same relation, and orange and blue. The knowledge of these relationships means a painter in fact need not use a black paint to recreate these relationships in paint: grey is not the absence of colour, but the annihilation of one colour in its mathematical opposite–‘alle einander auf derselben Gerade gegenüberliegenden Farben [sind] als Kräfte anzunehmen, welche einander entgegenstehen und sich durch ihre Vermischung zerstören in Grau’ (‘all colours that lay across from each other on the same line are to be assumed opposing forces that, upon mixing, annihilate each other in grey’) (Runge, 1810: 28). The rest of the sphere is filled out by every conceivable mixed colour and in every level of lightness and darkness, vividness and neutrality. The whole thing is most easily grasped visually, and this is the advantage of geometry.

(After Philipp Otto Runge)

It is a very beautiful model, one developed concomitantly with discussions with Goethe, and a living idea still used and taught by artists who appreciate the more rugged borders of three-dimensional colour-space. But more than this, the emphasis on relationships allows a shift in thinking: rather than considering colours as absolutes, bound to precise recipes of two-parts cadmium yellow to one-part prussian blue, they may instead be managed and manipulated as a complex but entirely rational web of relationships. This means, in fact, an emancipation from the types of dogmas that more mystically-inclined painters tend to bark at other painters: it means a shift from objectively defining colours to subjectively experiencing them. It allows a painter to recreate her perceptual experience of seeing colours; it allows for the fact that a certain mixture can appear pink or green, depending on the context it is set in. It marks a dramatic difference between painters who ask ‘what colour this really is,’ and those who ask how they perceive it. The second mindset affords far greater flexibility and dexterity with colour. And it can be taught.

(From Philipp Otto Runge, Farbenkugel)

This kind of dexterity is important because ultimately, while we might define our concept of colour in a pure mathematical way, paint itself does not respond to such precise geometrical divisions, and does not correspond so precisely to light. The painter must cope with two additional overlays to her mathematical concept of colour: the chemistry of paint and how the mixtures are achieved by actual pigments of vastly different physical properties, and the physics of light and the fact that her eyes take in a much broader gamut of colours than her paint is capable of mixing. A swift and nimble understanding of the relationships as geometric proportions is a solid conceptual ground that can be modified empirically as the painter’s experience with using paint and approximating it to what she sees grows. Runge (1810: 62) notes this as an aside to Goethe in one of his letters: ‘Ich kann mich hier nicht über die Praktik ausbreiten, weil es erstlich zu weitläufig wäre,’ (‘I cannot expand upon the practice here, firstly because it would ramble on too long,’) but he mentions that the artist requires ‘den nötigen chemischen wie mathematischen Kenntnissen’ (‘the necessary chemical alongside the mathematical knowledge.’)

Such systems equip us with knowledge, and thus confidence, and in the case of colour, adequately describe and organise the material reality of paint and at the same time accommodate our subjective, perceptual experience of it. Runge (1810: 42; 61) hopes that these pure insights will permit more definite expression; he thinks that being secure in the mental connections of the elements is the only means of setting a painter’s mind at ease, in the face of such superstition and chance. It would be well at this point to remind ourselves not to take the implications of these principles too far, and thus to return to Panofsky.

Copy after Claudel, Vertumne et Pomone

For the principles of vanishing-point perspective, the mainstay of principled drawing, are, indeed, a construction devised during the Renaissance, as Panofsky (1991 [1927]: 27) notes early on. It provides us with a mathematical space that is actually at odds with our perceptual experience of space, but that does not undermine its usefulness to us. Panofsky (1991 [1927]: 29-30) contrasts the visibly rigid ‘structure of an infinite, unchanging and homogenous space–in short, a purely mathematical space’ with ‘the structure of psychophysiological space.’ Our working concept of perspective demands that space conforms entirely to reason, that it is ‘infinite, unchanging and homogeneous’ (Panofsky (1991 [1927]: 28-9); but that demands certain assumptions that deny our experience of it: firstly, ‘that we see with a single and immobile eye,’ and secondly, that a flat plane adequately reproduces our curved optical image–two ‘rather bold abstractions’ from our perceptual experience.

‘In a sense,’ write Panofsky (1991 [1927]: 31), ‘perspective transforms psychophysiological space into mathematical space.’ And there is indeed nothing wrong with that if we recognise it as such, and do not take our theoretical underpinnings too far, thus over-emphasising the theoretical validity of drawing over colour.

Copy after Claudel, Vertumne et Pomone

Beginning with (helpfully visual) geometric principles, we can thus devise rigorous and teachable theoretical systems for both of the equally important parts of painting, for drawing and for colour, describing them in pure, abstracted, mathematical terms, whose constancy is beautiful in and of itself. We can reclaim the liberal art of painting, award it some intellectual prestige, and even ground it in scientific principles that draw on chemistry and physics as well. Descartes’ project might not prove so alien in the murky and superstitious realm of painting.

Copy after Rodin, The sculptor and his muse

Lichtenstein, Jacqueline. 1993 [1989]. The Eloquence of Colour: Rhetoric and Painting in the French Classical Age. Translated by Emily McVarish. Berkeley: University of California.

Panofsky, Erwin. 1991 [1927]. Perspective as Symbolic Form. Translated by Christopher S. Wood. New York: Zone.

Runge, Philipp Otto. 1810. Farbenkugel: Konstruktion Des Verhältnisses Aller Mischungen Der Farben Zueinander Und Ihrer Vollständigen Affinität. Köln: Tropen.

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On naturalism

Pantzergasse, Winter (c) 2016 Samantha Groenestyn (oil on linen)

Pantzergasse, Winter (c) 2016 Samantha Groenestyn (oil on linen)

When I paint, I am ever torn between two conflicting intentions. I am driven towards what we might call naturalism, the honest representation of things as they appear to me in the natural world, but I am constantly diverted by the lusciousness of paint and by my own systems of manipulating that substance that I have cobbled together from things learned and things discovered. As I stand before my canvas, I anticipate how convincingly naturalistic my finished painting will be, but my brain immediately sets to work in undermining that intention by ordering what I see into a complex system of relationships. In short, I cannot paint what I see, because paint promises the possibility of depicting things in more suggestive ways, and because it also imposes certain physical limits, within which I try to condense my understanding of what I see.

This leads me to survey my work with dismay: my paintings positively glow with an unearthly artificiality. The objects and people that populate them are glaringly constructed, and set under a contrived light, though observed from life. I see a more naturalistic painting and I despair at my own artifice.

Selbstbildnis

But I do not despair for long, because I quickly turn to questioning naturalism itself. And on this point I am persuaded by two claims from Ernst Gombrich. In Art and Illusion, he argues that ‘all representations are grounded on schemata which the artist learns to use’ (Gombrich, 1959: 264). And very quickly thereafter, he points out that the very ‘stimulus … is of infinite ambiguity’ (Gombrich, 1959: 264-5). ‘Naturalism’ is something of a misleading idea because it disguises how variable nature and our own visual experience of it is. At the very least, we might demand that the term be broad enough to admit many types of representation that aim at capturing something honest about the natural world. But one breed of naturalism tends to prevail as the most correct or ‘realistic’ in our modern eyes: the kind that makes us mistake paintings for photographs. We have permitted photography to become the unerring benchmark for ‘reality’ in the visual realm. Photography conditions our experience of sight.

Photography, it must be pointed out (for it is often forgotten), lets us down on many accounts. It fails to match the rich spectrum of colours our eye is able to enjoy, or to exhibit such a fine sensibility towards tonal gradations; it is not binocular, and does not have the luxury of flitting around a scene just as our ever-active eyes devour it, composing a view out of collected fragments. A photograph, an arbitrary slice of time, is often precisely the ‘wrong’ slice that we feel does not represent us, caught blinking or speaking or chewing. Focal lengths distort perspective, bending our physical constitution. As a measure for ‘reality,’ photography makes a fairly poor standard, and probably a worse one for coming so close and deserting us when we least expect it. If we are ignorant of its shortcomings, our conception of ‘reality’ is itself swallowed up by photography.

Selbstbildnis 2

I do not want to attempt to define reality, for this is an immense task I should not like to claim responsibility for. But I want to suggest that our own vision is more remarkable than photography. When we judge the success of any representation, painted or otherwise, we might remark how near to our own complex visual experience it comes. And we might bear in mind that sight is one thing, and representations are quite another, and the camera, let us not forget, offers but another mode of representation.

And as Gombrich argues, every representation is founded on schemata. Painting that orients itself via photography imports the schemata of photography into painting. The schemata of photography are not simply felt in the work of artists who copy photographs. They permeate the work of many who work ‘from life,’ who directly observe the world, but whose strategy in painting is to organise what they see just as a camera would. They crush dark tones together, even ones that are not actually shadows. They blanch and flatten light areas, uninterested in the undulating forms of the voluminous object before them. They impose a high tonal contrast—very dark against very light—to great dramatic effect, but utterly without nuance. Softness and blur takes on the uniform flavour of the lens, unlike the scattered haze that bleary or myopic eyes encounter. But when refining a surface they disguise lack of structural understanding with microscopic precision: paying painful attention to the blemishes and creases and stray hairs that are prized as ‘detail.’ ‘The artist’s starting point will determine the final product,’ cautions Gombrich (1959: 92); ‘The schema on which a representation is based will continue to show through the ultimate elaboration.’

self-portrait-2

Put differently: choose your influences, guide your aesthetic. A painter is constantly growing and adjusting her schemata according to what she pays attention to. It was at this point in my reflections that I realised my paintings are bound to become jubilantly vivid and muscular: I feed on a steady visual diet of Baroque paintings. What I relish are full forms, highly energised compositions, three-dimensional rhythms flowing in and around each other, electrified but systematic application of light in its confrontation with colour. Rubens hands down his schemata which celebrate the writhing, swelling, interlocking qualities of the natural world, basked in vivifying light.

And thus, when I paint, I bring other concerns to my easel than the artist who corrects himself by the standards of photography. Uninterested in a snapshot moment, I wade into the confusing and rich task of melting together a multiplicity of moments. A painting takes time to make, and my eyes take time to wander over my subject, drinking in every shifting property and letting them settle into a sustained, unified impression. I continually consider the whole, the way the elements relate to and influence each other. I use line to investigate visually pleasing trails, and I use drawing to animate nature. I orchestrate the elements into a cohesive composition, uninterested in a ‘found’ image, but determined to take responsibility for the construction of this image from the very first.

hands-ink

I make tonal decisions—how closely to group my dark tones, while preserving a logical gradation; separating shadows from halftones so I can meaningfully describe the way light plays over the surfaces. I consider the gamut of colours available to me in my paint choices—how a cadmium yellow and a pale rose red can stretch it further than a yellow ochre and a deep transparent red. I know that no matter what, paint does not have the reach of light, and it is not possible to match the full range that I see. So I establish my limits, reserving the highest chroma available to me for where I most need it, and correspondingly dulling the rest. I impose a logical system of neutralising colour with the falloff of light, conceptualising the relationships between colours as a three-dimensional space that I can move through with increasing fluency. When I vary yellow, I factor in the way purple neutralises it, and what that would mean in my picture, and I consider the ‘vertical’ shift I want to make in tone and in chroma as I transition from one colour to another.

hands-ryan

I think about the brush in my hand, how stiff or springy its bristles are, how splayed, how neat and flexible, and I invoke textures by the movement of my hand. Those textures hang in relation to one another, I must reserve certain techniques for smooth objects compared to coarse ones. And everything must fit into the system dictated by the quality of the light: whether it is diffuse, grey natural light, or blue unclouded daylight, or orange-yellow artificial light, or something else. ‘Every artist has to know and construct a schema before he can adjust it to the needs of portrayal,’ Gombrich (1959: 99) is right to insist. And my schema, derived from many places, but notably not from photography, is reasonably sophisticated.

hands-ink-2

 

 

Painting the ever-shifting natural world demands visual acuity, but also a mental acuity. For as painters, we do not merely observe and transcribe, but we organise what we see. When we paint, we establish relationships, and the character of those relationships—of light to dark, of vividness to neutrality, of smoothness to coarseness to softness to brittleness—directs the quality of the painting. Painting is not, as Gombrich (1959: 78) argues, ‘a faithful record of a visual experience but the faithful construction of a relational model.’ All painters construct relational models; it is only a question of what the model is based on, and how well the painter understands that model.

self-portrait-7

And the crucial point is whether a painter is passive or active. Because an artist worthy of our attention and respect does not work mindlessly, or randomly, or uncritically. She tests every new observation, and wrestles with it until she finds a way to work it into her system. She pushes her system to do more and more, to cope with greater ambiguity, to suggest more with less, to reflect the shimmering richness of the natural world. To do that, she will probably have to move away from the sufficient but sorely limited laws of the lens, to embrace the sticky willfulness of paint and to try to subdue the chaos in new ways, even if they are unsuccessful at first. ‘[The artist] is the man who has learned to look critically, to probe his perceptions by trying alternative interpretations both in play and in earnest,’ (Gombrich 1969: 265).

My paintings are a head-on struggle between what I see and the beautifully restricted medium in which I work. They document the hard-won schemata that I continue to grow as I bounce between the natural world and the teachings of other artists living and dead. ‘Naturalism’ in painting should never be fettered to the camera, for photography is only another means of representation, with other limits that painting can be blissfully free of. We are mistaken to find a painting more ‘realistic’ the more its relationships match those we are familiar with through photography, because, as Gombrich (1959: 75) puts it, ‘there is no neutral naturalism.’ Paint offers so many subtle and lively possibilities that approach the rich and nuanced experience of sight in ways that photography never will.

Selbstbildnis

 

Gombrich, E. H. 1959. Art and Illusion. Phaidon: London.

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Adventures in colour space

Praha © Samantha Groenestyn

A huge motivation for my recent sojourn to Sydney was the opportunity to take a five day workshop with David Briggs, a teacher at the Julian Ashton Art School. David kindly ran the workshop at his studio by the beach, meaning I ate my lunch gazing into refreshing seascapes each day, and gorged myself on cakes from the Hungarian bakery below his apartment every afternoon.

David’s workshop, Colour, Light and Vision, is so vast and deep that it is difficult to summarise. I took it because colour has always been of extreme significance to me, since I received my prized 64-box of Crayolas as a tiny person (all carefully arranged according to my own system, and all the names voraciously memorised, from periwinkle to brick red). I also took it because it promised that art could be a scientific, measurable task—rigorous and systematic, not confined to vague feelings and crazy aunts. Pigments have chemical reactions, some paints have higher tinting power than others, some are opaque to varying effect. We perceive colours differently under different lights; and in shadow, absolute change in brightness is greater in light colours. Optical illusions interfere with our perception of colours creating ‘simultaneous contrast,’ a failure of colour constancy that causes the same colour to look darker or lighter depending on the shade bordering it.

David’s studio is lined with books on colour. The man is well read, and his course thoroughly researched, and a continuing project. New books were delivered by post while I was there—old American high school art education books, old German pigment sample books. Books on Newton and Goethe, books by Munsell and Rood—these were spread across the table for our perusal, indicating the knowledge that has been tossed aside if not outright denied the modern artist. David’s mission in life seems to be to reclaim that knowledge, sort the true from the false, and to stuff any willing student full of it, in the most affable manner possible.

We began with Munsell and his A Colour Notation, a no-nonsense book from 1905 that set about giving children of all ages a thorough grasp on colour. Replacing the old red, yellow and blue primaries, Munsell began with five main colours: red, yellow, green blue and purple, shunning colours that drew their names from objects like oranges and violets. Arranging them in a type of tree diagram, some colours branched higher than others, some spanned wider, and, importantly, all branched from the solid trunk—dark at the root and light at the top, by the sun—representing tone, or value. While a tree may be drawn flat, it is really three dimensional, and it is this three-dimensionality of colour which Munsell sought to represent.

David thus demonstrates a way to map colour three-dimensionally—not as an organic tree, nor as a perfect globe, but digitally, with different and irregular gamuts for various media. Paint can only ever mix certain colours, and light can mix others. Vertically, in the centre of the colour space, we are looking at the absence of hue, and simply at the tonal scale of black through white. Hues move off in different directions, and their complements are opposite them and draw them through that greyed centre—purple will neutralise yellow, blue will neutralise red, before coming out the other side and becoming blue again. Each hue reaches its maximum chroma in a different place—yellow is at its most ‘yellow’ at a far lighter tone than blue, which fades with very little white added, and red is somewhere in between. Red under extremely bright light will look pink where yellow will still appear yellow, because of where its maximum chroma is mapped in colour space.

Yellow sphere by me

The course wasn’t entirely mind-bending theory (much as I enjoy that sort of thing!), but also a happy amount of paint mixing. We matched paint chips by approaching colour mixing in a systematic way: picking the two nearest colours to the one in question, getting them to the right tone and then mixing them in the right ratios, and neutralising them with the same-toned grey if necessary. We darkened difficult colours like yellow with black, bringing them back to the appropriate chroma by adding in a corrective colour like red. This is done purely by sight, learning to see when a yellow has turned green, but after the exercises we photographed our scales and mapped them in a lovely French colour program to test our judgements. With our colours duly mixed, we painted things: spheres demonstrating the areas of light (diffuse light, highlight, halftones and full light) and shadow. We painted still life thumbnails, correcting for the limitations of our paints: where yellow had to be the brightest, other colours had perhaps to be darkened.

(Did I mention we ate a lot of cakes? And looked at the ocean?)

Yes, a pretty intense week, but an immensely valuable one. I’d recommend David’s course in a heartbeat, and I’d take it again—not having a fixed curriculum, the course adapts to your own knowledge and experience, and if you’ve already painted the sphere, you get to try out the application of the theory on a human model ripe for painting. You can get hold of course dates and information through his website and through Julian Ashton’s. I’m still quietly mulling over the influx of information, and ready to start bringing it to my painting.

Outrageously beautiful cemetery, in which I took long, meditative afternoon walks.

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