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.




One does not find one’s people wherever one goes. Kindred spirits are harder to find, even among those with common interests. The minds that encircle me—those rare few among the many who draw, paint and write—immediately evinced to me a particular harsh quality, a certain incisiveness of thought, a terrible dismembering inquisitiveness, and an undeniable probity in their search for solid principles, for secure footing. These minds apply their powers to questions in ethics, in quantum mechanics, in political theory, in painting, and in every field they shun the mysticism that sparkles around the unstable ground of chance. For as Baudelaire (1972: 65) would have it: ‘There is no such thing as chance in art any more than in mechanics. A happy idea is no more than the consequence of sound reasoning.’

We were thus irresistibly drawn together by a common inquiring impulse. We formed each other in that especially malleable phase of life, reflecting each other’s ideas and words back at each other, finding common concepts and developing consistent vocabulary. Our ideas were strengthened by this validation, deepened by the many viewpoints, tested and stretched out and proven. We constructed our own language, our own way of speaking about these matters, seizing upon terms from those we looked up to, from books, sometimes importing terms from parallel concepts in our complementary fields. And this language is of supreme importance to people like us: because we demand precision. We preference the specific over the mystical and the vague. Our inclination to pull things apart demands a precise vocabulary in order to speak about the patterns we discover, to organise them and to piece them back together. Our approach might well be considered analytic, since we push onwards by first pulling apart and inspecting the parts, carefully piecing them back together. And when I finally found painters who operated this way, I latched onto them fiercely. Painting profits from this near-scientific precision, though most people would prefer to cast art in with magic. Our precision only turns up more profound questions.


For anyone can throw paint around and delight in improbable new constellations of colour. We revelled in this in purest glee in childhood: ‘The child sees everything as a novelty, the child is always “drunk,”’ Baudelaire (1972: 398) observes, and while this vague dizzy delight is essential, it is by no means sufficient. Our compulsion to understand harnesses this childlike drunkenness and directs it wilfully and powerfully. ‘Genius is no more than childhood recaptured at will, childhood equipped now with man’s physical means to express itself, and with the analytical mind that enables it to bring order into the sum of experience, involuntarily amassed’ (Baudelaire 1972: 398).

Order! How unromantic! Such a cold and diffident regime to impose upon art! Yet why should it be so? The painters I look up to continually show me that there is a way through the nonsensical mess if one pays attention and works systematically, and their work grows in depth and facility day by day, in embarrassing contrast to the stagnation of those who deny it. Richard Wagner’s musical abilities were mistrusted for ‘the very breadth of his faculties and his high critical intelligence,’ (Baudelaire 1972: 340). ‘“A man who reasons so much about his art cannot produce beautiful works naturally,”’ it was complained (Baudelaire 1972: 340). But it is this blind trust in nature that thwarts the intelligent production of art.


This notion of working ‘naturally’ denies that art, too, is work, that it must be learned, trained, cultivated, challenged and advanced. It longs for the subtle result, the piece lightly breathed into existence, the confident strides of an effortless creator. But these are the very refinements that only come with dedicated and focused work. The untrained hand is clumsy. We should not forget that nature, while she surges on with profuse energy, delights in wild, self-devouring frenzy more than subtlety and harmony. ‘Review,’ challenges Baudelaire (1972: 425), ‘analyse everything that is natural, all the actions and desires of absolutely natural man: you will find nothing that is not horrible. Everything that is beautiful and noble is the product of reason and calculation.’ The artist tames nature, moulds nature imperceptibly, crafts mesmerising variations upon it that captivate us precisely because they are tailored to us, rather than wild. ‘Things seen are born again on the paper, natural and more than natural, beautiful and better than beautiful’ (Baudelaire 1972: 402). A sensitive and intentional distillation of nature takes place as the raw materials of nature ‘are classified, ordered, harmonised, and undergo that deliberate idealisation’ by the skilled artist (Baudelaire 1972: 402).

The order we seek to impose is thus not entirely removed from nature. It is rooted in nature, it grows out of a desire to understand nature, and this understanding breeds knowledgeable work. Understanding of muscles and bones brings greater sensitivity to the supple movements of a living, straining body subject to forces. An artist can grow ever more attuned to motion and action, and can make quicker and more economical decisions of how to represent this, favouring eloquent overlaps of tendons here, underlining a weight-bearing limb there, gently bringing out a swelling muscle in preference to a less critical bump, wrapping folds of compressed flesh in sympathy with the stoop and twist of the figure. Order does not extinguish the life of nature. On the contrary: it seeks out the essential life-breathing elements, it searches for the harmony between them, it emphasises unity that would otherwise be lost in the cacophony of overstimulating nature, it reconstructs the world according to highly attentive hierarchies (form over tone, perhaps, and elegance of line over faithfulness to contours, light secondary to volume, atmosphere over crisp exactitude, grouping of shapes of colour rather than fidelity to the infinitude of colour). These choices are wherein the art lies. An artist contemplates the limitless world, re-forms it and returns it to us in a more pleasing arrangement.


This is not to say that there is one mould of beauty, for each artist structures her work according to a different system. And not only that, but we each grapple with the time in which we live. Baudelaire (1972: 403) writes of the two halves of art. One is ‘the eternal and the immovable,’ an antiquity alive and present in every age, but this eternal element does not give itself up so freely, and it is this that the artist must distill from the world. It is embedded in every present, and so in each age it takes on a different guise, it cloaks itself in ‘the transient, the fleeting, the contingent’—this is the other half of art (Baudelaire 1972: 403). The real artist, then, ought not renounce her time; she is tasked with extracting from it ‘the poetry that resides in its historical envelope, to distill the eternal from the transitory’ (Baudelaire 1972: 402).

And what precedes such skill is a certain penetrating type of mind. One must, from one’s earliest childhood, be ruthlessly critical. ‘For a poet not to have a critic within him is impossible,’ states Baudelaire (1972: 340), pitying poets dependent solely on instinct. For our ability to improve depends on our selectivity, on our Urteilskraft, on our powers of judgement. Our eye is not easily satisfied, not out of misanthropy but because one taste of something grand has forever raised our standards. We know what is within human reach, and cannot be content with less. We must be ‘poet and critic rolled into one’ (Baudelaire 1972: 340), or we will fail to make a true estimate of our own work, and fail to discover how to amend it.


If there is one thing Baudelaire has really opened my eyes to, it is this: we must not hold back. While our private critiques have bolstered our position, honed our work and sharpened our faculties, we have worked long and hard enough to stand firmly and speak confidently and clearly. And vigorously. What we say might sting, it might win us enemies, it might ring with insult, we might (like Edgar Allan Poe) become known for ‘a hundred other passages where mockery rains down, thick as shot and shell, and yet remains nonchalant and haughty’ (Baudelaire, 1972: 191). But the strength of our insights demand equally forceful delivery. Baudelaire (1972: 51) spurs us on:

‘Once armed with a reliable criterion, drawn from nature, the critic must do his duty with passion; for critic though he may be, he is a man nonetheless, and passion draws men of like temperaments together and raises reason to new heights.’

So my unapologetic intellectual compatriots subject the world to all manner of analysis, inspect it, dissect it, meditate upon it. They put it back together with fearful insight and dexterity. They bolster their cloudy intuitions with concepts they can name. And, when the occasion demands, they rain down their judgements with precision and conviction. Though mountains and oceans separate us, the common threads of our thoughts stretch like glittering webs across the world, fine but strong, and everywhere we rest we plant the seeds of our ideas. We teach, we challenge, we initiate discussion, we loan books, we drop our words, we work, and small ripples begin to spread across the world.


Baudelaire, Charles-Pierre. 1972 [1842-1860]. Selected writings on art and artists. Trans. P. E. Charvet. Penguin: Harmondsworth, England.


In order of appearance in my orbit:

Thoughtful Wander
Conrad Ohnuki
An Island in Theoryspace
R W Daffurn
Scott Breton




The decision (c) Samantha Groenestyn (oil on linen)

The decision (c) Samantha Groenestyn (oil on linen)

In his eminently readable paper, ‘How I see philosophy’ (collected in the book of the same name), Friedrich Waismann urges us on to the dizzying thrill of the questions that originally brought our buzzing, inquisitive minds to philosophy. His plea perhaps grows increasingly relevant as philosophy becomes more analytically constrained, as the scientific project and its quest for order and explanation and proof creeps into all spheres of our lives, as ordinary people demand answers that ring with the clarity of science. Waismann makes a plea for the fog, for the roving unrest it stirs in us, for the rabbit holes it leads us down and the impassioned discussions it gives rise to. ‘The genius of the philosopher,’ asserts Waismann (1968: 16) ‘shows itself nowhere more strikingly than in the new kind of question he brings into the world. What distinguishes him and gives him his place is the passion of questioning.’ And yet further: ‘There is nothing like clear thinking to protect one from making discoveries’ (Waismann, 1968: 16).


This is not to decry reason and to rally behind an unthinking mental anarchy. Quite the opposite. It is to stimulate original thought, to pursue reason wherever she may lead, away from convention if she must, out of habits, disrupting prejudices (Waismann, 1968: 32). It is to remember why we started–we and our compatriots in thought, all the way back to Plato–quite simply: wonder (Waismann, 1968: 3). Waismann (1968: 16) urges us, as we flounder in the heady haze of brain-breaking wonderment, to take heart that ‘some of the greatest discoveries have even emerged from a sort of primordial fog.’ The ‘clarity neurosis’ will not furnish us with solutions, but only with the appearance of them. Clarity is reassuring, it gives us no reason to challenge the well-worn groove we circle around in, and for that very reason it extinguishes our creative spark before it gets a chance to warm up.


Waismann does not champion confusion. Rather, he sees philosophy as having a different aim than science (Waismann, 1968: 34). He reflects on a tradition grounded in Descartes and Spinoza, in which precise definitions, like quanta of knowledge, stack up—Lego-like—into tight axioms, by which we can deductively prove that the finite and infinite substances and all their attributes are none other than God himself, Q.E.D. (Spinoza, 1677). Such a logical project is admirable in its ambition, noble in its intentions. And Descartes (1997 [1637]: 7), after all, would not force his method on us (‘Es ist also nicht meine Absicht, hier die Methode zu lehren, die jeder befolgen muß, um seinen Verstand richtig zu leiten, sondern nur aufzuzeigen, wie ich versucht habe, den meinen zu leiten’—‘It is not my intention here to teach the methods that everyone must follow in order to correctly guide his reason, rather to demonstrate how I have tried to guide my own’). No, Waismann (1968: 20) does not seek confusion, but he does call for a change of outlook, defiantly declaring in the face of all this elegant reasoning that ‘insight cannot be lodged in a theorem.’

Franz von Stuck - Amazone

Franz von Stuck, Amazone (copy after sculpture)

Insight! When we had hoped for answers and airtight proofs, Waismann leads us back to the questions in order redefine the essence and purpose of philosophy. And the essential feature, he (Waismann, 1968: 32) argues, is vision. A philosopher is not a builder of systems, but an agile thinker who cannot help but challenge our accepted modes of thought. She takes nothing for granted, and takes everything in with the same open-eyed amazement as a child, with the same persistent ‘why’ dogging every new piece of knowledge she encounters. She keeps a level head in that primordial fog, and, says Waismann (1968: 10), if she reframes the troubling question she might just ‘dissolve’ rather than ‘solve’ it. But this, he adds, would be a meagre and negative task for philosophy, to simply dispel fogs. No, the positive task for philosophy, he (Waismann, 1968: 21) argues, ‘what is essential in philosophy, is the breaking through to a deeper insight.’ And the purpose, far from satisfying us, is to keep us ruffled and amazed: ‘to open our eyes’ (Waismann, 1968: 21).

Rubens - Venusfest

Rubens, Venusfest

What Waismann calls for is an attentive outlook that is willing to look at things sideways, to chew them over backwards, and to act in a creative manner. A search for answers already makes a fatal assumption. I am reminded of the notoriously inquisitive physicist, Dr Jacques Pienaar, who guilelessly prefaces his papers with such opening statements as, ‘In order to solve the problem of quantum gravity, we first need to pose the problem.’ This is the hallmark of the born philosopher: ‘the passion of questioning’ is in his blood. He navigates the fog not in order to obscure, not in order to destroy, but because of an insatiable sense of wonder backed up by the courage to cast a discerning eye over all intellectual territory. Emerson’s (1847: ‘Self-reliance’) words echo in Waismann’s: ‘Whoso would be a man must be a nonconformist. He who would gather immortal palms must not be hindered by the name of goodness, but must explore if it be goodness. Nothing is at last sacred but the integrity of your own mind.’


What is compelling about Waismann’s view is that is recaptures the philosophical spirit, it reminds us why we started. It reassures us in our hours of solitude, when we are trapped deep in a problem—a snare which we nonetheless find energising. It reassures us when, at our desks, in our libraries, we struggle to formulate our nascent insights into accepted parlance. It reassures us that we are on the right course, so long as we are asking the questions that stir us the most: ‘You don’t choose a puzzle, you are shocked into it’ (Waismann, 1968: 37). It rings in tune with our restless, roving minds.

‘The heart’s unrest is not to be stilled by logic.’

(Waismann, 1968: 13).


Descartes, René. 1997 [1637]. Von der Methode des richtigen Vernunftsgebrauchs und der wissenschaftlichen Forschung. Übs.: Lüder Gäbe. Felix Meiner: Hamburg.

Emerson, Ralph Waldo. 1847. Essays: First Series.

Pienaar, Jacques L. 2016. The Relativity Principle in Quantum Mechanics.

Spinoza, Baruch de. [1677]. Ethica, ordine geometrico demonstrata. („Ethik, nach geometrischer Methode dargestellt“).

Waismann, Friedrich. 1968. How I See Philosophy. Ed. R Harré. Macmillan: London.



Solution (Dr Jacques Pienaar) © Samantha Groenestyn

Solution (Dr Jacques Pienaar) © Samantha Groenestyn

If I could kindle your enthusiasm about just one thing, it would be paint. If I use overly impassioned language when describing paintings, it’s not to be floridly arty—it’s not to transfigure paintings into words, and thus do away with the picture. I only want to show you how to be caught up in what you see, to guide you with a language you already understand. I want to show you a way in, and expose my own thoughts so you might feel confident in your own.

I feel so strongly about the physicality of painting. Every day I paint, and far from confining itself to a neat, two-dimensional substrate, paint subdivides and multiplies and sticks to everything. In my haste I smear it on my hands, I lean into it and get it on my clothes. The stuff has a mind of its own; like amoebic eighties horror film monsters it exists in three-dimensional space. With patience and determination, the painter tames it and uses it to describe something. This is why much contemporary painting disappoints me so much. Paint has lost its body. It has become a hesitant filler. It is so often reduced to a broad medium for covering an expanse in sloppy colour, as though with the click of the fill-bucket button.

Kunst Handwerk

My eyes are ravaged by it everywhere: just enough paint is used to block in a shape, a thin scratchy film, cheap bleached white canvas and its prickly texture shouting through it, proclaiming its cheapness. No wonder painting is so unpopular, when cheap paint smeared thin as vegemite across cheap canvases presents such a shamelessly insipid surface.


Robert Nelson cautions against the ‘fetishisation of paint,’ but a little over-enthusiasm might be needed to correct this scourge of painterly apathy. Painting can be more than colouring-in: paint, as German so poetically (in its beautifully literal way) reminds us, is farbe—it is colour itself. Nelson (2010: 39) argues, ‘Paint as colour is less interesting than colour as paint, because paint gives to the very concept of colour a willfully mutating character.’ Rather than thinking of paint as the filler that wedges between the lines of your drawing, you might embrace paint as ‘mobilised colour’ (2010: 42).


Yes! Far from stretching like a skin over empty space, paint—embodied colour—can sprout from a surface, can clamber over itself, undulate, amalgamate. Colour as paint is nothing like a grid of pixels, an expanse with no depth. Paint allows us to move colour around almost as if it were clay. Of course, we are still constructing a two-dimensional illusion, and I am not arguing that one ought to paint in relief. But we ought not forget that we have a real substance in our hands and that its expressive properties are every bit as physical and substantial as clay. This is our advantage, as painters, over digital painting and photography. The quickening of our surface is what sets us apart from our sister arts. And it is the reason paintings need to be seen in the flesh, and why their pixelated reduction to disembodied colour is so dissatisfying.


John Dewey draws an interesting comparison between physics and the arts which perhaps makes a good analogy for Nelson’s conception of ‘mobilised colour.’ Nelson describes paint by way of its fluid application rather than by its dried and polished result. ‘Paint,’ he writes (2010: 39), ‘which first arrives on the palette in distinct colours, is nevertheless contrived in analogous viscosities so that each colour slips into its neighbouring colour and becomes another colour entirely (or other colours, prolifically mutating), often imperfectly dragging two or more discrete colours into a kind of staggered spectral section.’ For the artist, paint exists not only as a clever arrangement of colours, but it exists as colours struggling with each other in time, dancing about each other, harmonising, violating each other. Paint exists as colour-in-application: as colour in time. And this is Dewey’s contention: we are misled when we separate space from time in the arts, just as physicists were forced to wrap their heads around the concept of space-time. ‘For the extension and volume of an object, its spatial properties cannot be directly experienced—or perceived—in a mathematical instant,’ he (1934: 183) explains, ‘nor can temporal properties of events be experienced save as some energy displays itself in an extensive way.’

Physics roof



None is more conscious of this than the artist herself, and it is something I am eager to convey to people who like to look at paintings. Perhaps it is something people make some attempt to come to terms with when they ask such questions as, ‘how long did this take to paint?’ But rather than quantifying a painting (and probably attempting to see if the price matches the labour), recognising the marriage of time and space in painting will bring a richness of understanding to a picture. A colour spans some distance. But paint, pulled by the vigorous action of a stroke and grooved with the bristles of the brush, is distance over time.

v = d/t

Dewey elaborates (1934: 183-4):

‘The separation of temporal and spatial in the fine arts was always inept. As Croce has said, we are specifically (or separately) conscious of temporal sequence in music and poetry, and of spatial co-existence in architecture and painting, only when we pass from perception to analytic reflection. The supposition that we directly hear musical tones to be in time and directly see colours as being in space, reads into an immediate experience a later interpretation of it due to reflection. We see intervals and directions in pictures and we hear distances and volumes in music. If movement alone were perceived in music and rest alone in painting, music would be wholly without structure and pictures nothing but dry bones. …

Any section of the music and any cross-section of it has precisely the balance and symmetry, in chords and harmonies, as a painting, statue or building. A melody is a chord deployed in time.’

In fact, Dewey insinuates, we sort of already experience the arts as both temporal and spatial. It is only when we try to describe them that we build these artificial distinctions. The painter knows it when she drags a loaded brush across a canvas, and the pianist knows it when he visualises a chord as the shape of his hand or as a numerically arranged hieroglyph on a stave. And the viewer and the listener taste it when they are absorbed into the aesthetic experience, or else something likely rings false to them.

Belvedere storm

Belvedere, Vienna


Perhaps, then, trusty English has something to offer us that German cannot. For the word ‘painting’ describes a process, a happening, an event. And this is Nelson’s (2010: 40) point, which clarifies Dewey’s: ‘The medium intrinsically narrates the events of the process.’

And this is why I live in hope that painters will express something bordering on a fetish for paint in their work. That their disturbing obsession with it might infect the viewer. For painting, as Nelson (2010: 39; 40) so satisfyingly insinuates, is very sexy: ‘Paint, … certainly, you can keep it neat, but the substance is made for creamy interaction. In any intercourse with another wet colour, the paint visibly mutates by the muscular caress of the brush. … As one colour works its way into another—according to the slewed interpenetration just mentioned—traces of the process are left visible, because the pre-existing strokes remain manifest even as the dramatic stage in which fresh impulses have collided.’

And perhaps Nelson (2010: 42) is right to insist that paint as mobilised colour, as colour through time, with its ‘inestimable expressive potential’ is more than ‘pretty extravagance’ or ‘material fetish,’ and rather something so lofty as ‘an existential resource.’ But I’m not above admitting to a little predilection for paint bordering on the prurient.



Dewey, John. 1934. Art as experience. Minton, Malch & Company: New York.

Nelson, Robert. 2010. The visual language of painting: An aesthetic analysis of representational technique. Australian Scholarly Publishing: Melbourne.


Keine Grenzen

Heather © Samantha Groenestyn, oil on linen

Heather © Samantha Groenestyn, oil on linen

For two months I’ve adopted Scotland, once more, as my home, learning the rugged streets of Glasgow, adopting the frank and fearless tongue of the Scots. Having studied at the University of Edinburgh several years ago I feel intellectually cocooned by this place, a small weave in the strong intellectual fabric of this proud nation, whose independence I near witnessed. The Scottish intellectual heritage is a formidable one, and I’ve lately been enthralled by some research into the specifically Scottish flavour of much Enlightenment thinking and, just as importantly, action.

Aye ready

I’ve been reading of the vibrant, open and liberal mental environment of Scotland in the eighteenth century in Alexander Broadie’s neat little history The Scottish Enlightenment. Certain fortuitous developments, argues Broadie, made Scotland fertile intellectual ground in the wake of the darker middle ages. One was certainly that Scottish thinkers had the impertinence to question things and to think for themselves rather than bowing to authorities like state and church (or Kirk). This mental independence exhibits something of a disrespect for authority. But such openness went both ways, with these authorities in turn being open-minded and tolerant enough to permit such boldness. ‘Intellectual progress appears not to be possible except in an intellectual climate in which people are not overly respectful of authorities,’ Broadie (2001: 18) suggests. Wilful Scotland, impassioned and staunchly maintaining an identity apart from England, has this quality in spades.


Importantly, this independent thought was not the response of individuals working in isolation in reaction to established authorities and entrenched modes of thought. Broadie (2001: 78) lays great stress on the ‘communal thinking, thinking with and through others’ of the ‘social phenomenon’ of the Enlightenment. I’m reminded of the reported lively exchange of the Viennese Salons much later, the merging of scientific and artistic minds, the concurrent burgeoning ideas of psychology. In the salons of Vienna, as in the clubs of Scotland, significant developments in philosophy, science, art and politics were birthed through the sweet communion of minds—minds very different, perhaps, in their private obsessions, but formed of the same stuff, the same inquisitiveness and drive. The Scottish Dugald Stewart (in Broadie, 2001: 110) noted that ‘In many cases … the sciences reflect light on each other; and the general acquisitions which we have made in other pursuits, may furnish us with useful helps for the farther prosecution of our own.’ And in the many and vibrantly diverse ‘Enlightenment clubs and societies,’ Broadie informs us, ‘men of disparate and wide-ranging accomplishment set off intellectual sparks in each other, and exemplified the Enlightenment ideal that people should think for themselves but not by themselves.’


Freed from the shackles of dogmatic thinking, and drawn to each other for the flint of inspiration, Enlightenment thinkers came together in ‘an international Republic of Letters,’ a written exchange of ideas that transcended borders and nationalities in a true cosmopolitan spirit (Broadie, 2001: 78). And as I shift from city to city, exchanging ideas with my compatriots of all nationalities, absorbing new sensations and nesting in new pockets of this vast earth, if only for a week, a month, or two, borders dissolve and I feel myself a citizen of a broader nation. I proudly state with David Hume, ‘I am a Citizen of the World’ (in Broadie, 2001: 95). And are our minds not freer than flesh? Our ideas travel even to places we may not, and we must send them there, and welcome back the responses.

River Kelvin

As I’ve seen some universities grow perplexingly protective of their knowledge, closing their libraries and seminars to outsiders, I’ve seen others welcome me, if curious of my presence; I’ve seen discontented academics ponder the possibility of alternative free academic journals, investigate open access publishingargue for legislators to back public access to research and freely publish their ideas on hugely popular blogs, impatient of the increasingly outmoded notions of copyright and intellectual property. Our scientist colleagues are working openly, collaboratively, discussing their ideas even before publishing, giving us a clear indication that they chase real intellectual progress above success as it is traditionally measured. The international Republic of Letters is revived in this renewed ‘general acknowledgement of our right to put our ideas into the public domain’ (Broadie, 2001: 78).


So let us seize this task as our right! Let us not feel bordered by our institutions or lack thereof, our fields, or our passports. The world might be tightening its border security, shunting hopeful Australians between the Continent and the British Isles and back again, undermining the stability of our physical existences. Despite our European heritage we are denied the freer movement of the generation or two before us, despite our British head of state we are denied permission to live and work on the civilised side of the world. Despite the significant contributions of our Australian forebears—artists permitted the luxury of extended life and education in Paris, London, Florence—we are expected to lick the crumbs of three-month stints and produce impressive bodies of work on a strict time limit.


Nonetheless, our physical circumstances need not dictate our intellectual contribution. Our citizenship in the borderless intellectual republic depends solely on our ‘active participation in discussions and debates conducted in the public arena’ (Broadie, 2001: 95). Adam Ferguson, another celebrated Scottish thinker, urged ordinary citizens to lead an active life, equating a passive existence with being forcefully restrained. Ferguson (in Broadie, 2001: 89) offers a warning somewhat prophetic of present-day Australia, arguing that the smothering of all action in an effort to stamp out undesirable action stifles a nation’s brilliance:

…if a rigorous policy, applied to enslave, not to restrain from crimes, has an actual tendency to corrupt the manners, and to extinguish the spirit of nations; if its severities be applied to terminate the agitations of a free people, not to remedy their corruptions; if forms be often applauded as salutary, because they tend merely to silence the voice of mankind, or be condemned as pernicious, because they allow this voice to be heard; we may expect that many of the boasted improvements of civil society, will be mere devices to lay the political spirit at rest, and will chain up the active virtues more than the restless disorders of men.

And might not this fearful outlook extend to our modern preoccupation with borders, our growing and blinding nationalism? If we are made criminals for seeking to move amongst our intellectual compatriots, for attempting to settle in an existing society that is culturally rich and not an isolated backwater, might not many important achievements be denied our generation? Are we not destroying the intellectual climate necessary for progress other than the commercial?


Our ideas might be unsettling and our movements unpredictable, but this very irreverence for the established modes of thought and action is, if eighteenth-century Scotland demonstrates anything, key to dramatic intellectual progress. Such golden ages exploded into being where ‘geniuses and … other immensely creative people … were living in each other’s intellectual pockets (as well, often, as in each other’s houses)’ (Broadie, 2001: 219). And yet our borderless minds need not threaten cultural identities or national stability, for rather than being thought strictly anti-nationalist, we might perhaps more aptly be considered post-nationalist, something broader and more humanist that encompasses but moves beyond our homelands. As Hume was both a rightfully proud Scot and gladly a citizen of the world, our arbitrary home soil can only ‘be strengthened morally by the presence in it of citizens who attach a high value to rationality and civil liberty’ (Broadie, 2001: 96).

Leaf crunching


Broadie, Alexander. 2001. The Scottish Enlightenment. Birlinn: Edinburgh.


The squirrel

Hyndland house © Samantha Groenestyn, oil on canvas

Hyndland house © Samantha Groenestyn, oil on canvas


Sometimes it would be really excellent to have access to an art education, but sometimes you have to find a way to educate yourself. At times like this, the answer might come from Jack White, via a squirrel. ‘Take all your problems and rip ’em apart’: isolate, master, and finally, integrate.

Venus and Adonis ( / Jack White) by Abraham Janssens

Venus and Adonis ( / Jack White) by Abraham Janssens

Taking a class means you have a structure imposed on you, regularity and routine, and are fed ideas in a logical sequence. But in the event that you are not enrolled in a class, you can still find plenty to chew on, and with enough discipline you can create a solid routine. The important things are to be excited, to follow the trail and to be persistent. Travel affords one the perfect opportunity to get outside and work from nature, eyeballs twitching from all the spectacular new stimuli. But nature is hard: full of bugs, dogs, shrieking children, nosy people, trees, changing light and other painterly woes. One works with an urgency that can be shaken in the private peacefulness of the studio, but at the same time one finds the details mounting, crowding out the picture, looking rushed and untended to. I, for one, include too much, and struggle to keep the main design at the fore of my decisions.

Tree 1

George Clausen, whose Stone pickers (1887) I was fortunate enough to encounter in the Laing in Newcastle, expressed similar pains in his lectures to the Royal Academy (published as Six Lectures on Painting; 1904: 45): ‘Everything in nature is moving—not necessarily quickly, but nothing stands still for us; this sense of life and movement must be given in a picture with the measure of detail which may be necessary, and the result reveals the artist’s mind, showing on which qualities, and in what degree, his attention was fixed.’

Tree 2

So I have happened upon an approach that lets me both practice the elements and work at the broader design. Every afternoon I head out into the world with my sketchbook and choose something to devote my attention to. Perhaps a scene will strike me, and I will sit down for an hour, two, as long as it takes, and interrogate this setting from a design perspective. These drawings are fluid, scratchy, built of simplified masses, and usually paying attention to form, reducing trees to bulbous sphere-based monstrosities, and paying careful attention to perspective in the prisms of buildings. In these drawings I’m developing a notation for three-dimensional objects, as well as forcing them into pleasing arrangements. Many of these drawings go nowhere, but some form the basis of paintings. Mostly, they reveal what the smaller problems are, and demonstrate that tackling an entire landscape all at once is too big a bite just now.

Tree 3

Other afternoons I linger in a sunny park or bunker down by a swamp and draw the trunk of a tree. These organic forms produce surprising twists, and let me explore drawing quite fluidly and more freely than when drawing the figure with its predictable anatomy. Plus, they sit still for longer, so you can while away hours investigating in as much detail as you care to, and never run out of variations. As Harold Speed (1913: 106) reminds us, ‘Nature is the great storehouse of variety; even a piece of coal will suggest more interesting rock-forms than you can invent. … And it is never advisable to waste inventive power where it is so unnecessary.’

Tree 6

For reals, this tree exists.

Mornings, I like to start with a drapery study. My kind friend Elizabeth has let me pillage her scarf drawer which means I have an endless variety of fabrics—stiff, wispy, heavy, floaty, wiry and bunched—at my disposal. It’s a nice reminder that there’s not simply drapery, but that all fabrics have their own manner of drape; that they bunch differently, fall differently and fold differently. I started out with ‘drapery sculptures,’ complex creatures to test my accuracy. But I got more excited about the puzzles of fabric, and began to explore its incarnations: table drapery, hanging drapery, folded and twisted drapery; the little pockets and cones that form in it. And besides wrapping my head around the ‘mechanics’ of this mouldable form, I found these exercises to be an invaluable means of practicing modelling. My earlier drawings are harshly seeking out the cross-contours; my later ones, even after only a few weeks, are finding a more elegant way to express the softness of the surface of my subject.

Drape 1

And here comes the exciting bit. Having broken all my problems down and gnawed away at them, varying and repeating the tasks, following my nose and trying to solve the new puzzles that arise out of them, I see just how connected they are. For a tree is a person is a drape is a composition. The ripples of the surface of the drapery find their way into my trees, and the muscularity and counter rhythms of human limbs translate into those of trees. The design-oriented sweeps through boughs—always planted firmly on the ground—resurface in the capturing of a human pose, feet rooted just as surely. And a thin piece of cloth has forms as full as any living thing, and is not simply a web of shapes dovetailing together.

Drape 2

As ever, trusty old Bammes accompanies me on my explorations, and a little such guidance never goes astray. For it’s nice to work independently, but it’s also nice to receive tested wisdom and gentle reminders: ‘If skull drawing is not practised as if it were architecture, with a perpetual ordering of primary and secondary aspects—if it is not done with awareness—it will degenerate into nothing more than clever copying and will not provide any gain in knowledge or vision’ (2010: 222).

Drape 3

Clausen empathises further (1904: 54): ‘The student’s greatest difficulty is to find himself; what it is that he really wants to express.’ He observes that we are more inclined to seek our place amongst our contemporaries, to stay attuned to current creative trends and market-driven demands. But Clausen urges the student in her ‘search for general principles:’ ‘He should try and arrive at principles, and to that end study also the work of the old artists, who have travelled the whole road; depending on nature for his inspiration, while referring to them for guidance.’ Clausen suggests a delicate balance between personal encounters and struggles with the natural world, with observation and private deduction—just as a mathematician might privately prove axioms to himself as a sure footing for further creative problem solving—and a devoted study of the masters. In this light it is not simply a dreamlike privilege to be in Europe, with daily access to world-class galleries, but a minimum requirement of the student of art. One does oneself no favours by remaining in a cultural backwater, relying only on reproductions in one’s investigations into the great work of the past. Clausen (1904: 54) argues that such study gives us a belt of tools—of insights, ideas and trains of thought—to bring to our own battles of taming nature to the canvas. ‘For we train ourselves to see and understand, by studying the work of the masters, which help us to form our judgement before nature.’

Drape 4

This idea that we distill the principles for ourselves is, to my mind, paramount. No master of any field simply reads the elementary textbooks and gets on with making bold discoveries. Many a physicist has divulged to me that they have returned again and again to the foundational principles, oiled their minds with them, looked at them from every angle, picked them apart and pieced them back together unaided, and, after a number of years working on highly abstracted concepts, have seen these principles in a new light as their specialised understanding deepens. We need the surest, securest foundation for our endeavours, and however elite and respected and coveted our school, it can never simply feed us such a foundation. We must work through the smallest of problems for ourselves, and make each discovery, have each profound epiphany, at our own hand.


And no less than the mighty Leonardo da Vinci will back us up on this. In his notebooks he admits to being no scholar, but to owing all to the mistress of experience. ‘Though I may not, like them, be able to quote other authors, I shall rely on that which is much greater and more worthy:—on experience, the mistress of their Masters. They go about puffed up and pompous, dressed and decorated with [the fruits], not of their own labours, but of those of others. And they will not allow me my own. They will scorn me as an inventor; but how much more might they—who are not inventors but vaunters and declaimers of the works of others—be blamed.’ (1888: 16-17).

Gnarly tree

In having the humility to search out general principles for ourselves, and becoming familiar with them inside and out, da Vinci argues that we will face our creative problems with clarity of mind. ‘These rules will enable you to have a free and sound judgment; since good judgment is born of clear understanding, and a clear understanding comes of reasons derived from sound rules, and sound rules are the issue of sound experience—the common mother of all the sciences and arts.’ (1888: 19) And so, artist or scientist, let’s not neglect the small puzzles, or rely on others to hand solutions to us. Let’s tear apart and then rebuild our own enduring foundations, one little acorn at a time.


You can snag most of the books cited free online!

Bammes, Gottfried. 2010. Complete guide to life drawing. Search: Kent.

Clausen, George. 1904. Six lectures on painting. Methuen: London.

Speed, Harold. 1913. The practice and science of drawing. Seeley: London.

da Vinci, Leonardo. 1888. The notebooks of Leonardo da Vinci. Trans. Jean Paul Richter.



Three (oil on linen) © Samantha Groenestyn

Three (oil on linen) © Samantha Groenestyn

I’m thinking a little more, as I’m painting, back in Brisbane, of shadows and the way they cradle and nudge the light. Not just as blank shapes, jagged voids piercing a picture, but as quiet and thoughtful terrain in their own right, and as the unshakeable support for the regions washed in light.

Nelson (p. 159) questions the modernist preference for light. ‘Things which stand out are privileged over conditions which recede,’ he writes, ‘but upon which the outstanding paradoxically depends. Shadow is relegated to the background, as though it were not integral to the image.’ He calls this modernist bias ‘photocentricity’ (p. 159), considering it the symbol of our current artistic malaise; a retina-burning dependence on flood-lit, full-chroma colours ignoring the gentle nuances of recesses folding away from the gaze, the hushed down-planes and the subdued forms shying away from the light. The quiet mystery of the dark side of the moon. Our pictures are flatter, brighter, and possibly rely more often on crisp linework to divide form from form, with shadows seeming heavy and mood-killing; overly dramatic. Modern comics, drawn on digital tablets and coloured boldly. Modern illustrations, wispy and watercoloured. The modern aesthetic is as light-obsessed as a moth.

The great eighteenth-century Western project wears the title baldly and proudly: the enlightenment extolls ‘light as intelligence and shadow as ignorance,’ (Nelson, p. 161). Shadows are dubious, guileful and deceptive. We want back-lit, fluorescent, LED brilliance, lighting our paths and shining the way forward.

In physics, one can create light by constructing electric currents and attaching filaments and such, and, in a more abstract sense, one can fill a space with light. But it is nonsensical to talk of filling a space with dark—shadow is the natural default which science allows us to manipulate. Painting equalises this bias—the painter creates shadows in just the same way as she creates light. This is the sort of super power you want to make good use of.

Campagna di Roma. Grabmal der Caecilia Metella, 1894. (c) Rudolf Bacher; Belvedere Wien.

Campagna di Roma. Grabmal der Caecilia Metella, 1894. (c) Rudolf Bacher; Belvedere Wien.

In the Lower Belvedere I found myself mesmerised by the subdued, neutral colours of Rudolf Bacher’s Campagna di Roma – Grabmal der Caecilia Metella. The girl is described with delicate modelling, her skin soft and pink, her blue dress airy in the breeze, but she rests completely in shade. Her understated colours are set starkly against the bright void of sky, the light, for once, supporting the shadow. Again, Bacher’s Redeemed, seemingly softly lit, but defiantly in shadow as evinced by the brilliant shape on the wall cast by light pouring through the window. I’ve wanted to toy with these ideas, accepting that though light is ever present, it might not reveal the truth, and it certainly doesn’t hold the secrets.


Nelson, Robert. 2010. The visual language of painting: An aesthetic analysis of representational technique. Australian Scholarly Publishing: Melbourne.