rhizomes.06 spring 2003

Points (Lucretian Codes)
Ondrej Galuska


[1] ... the point. the point thereof. the meaning of introducing points into painting, points not unlike those in geometry, having no extension, by themselves imperceptible, and yet different for being points of intensity, of colour. not quite abstraction. atomisation. in fact no abstraction without atomisation. the opposite of Platonism. the greatest simulacra made of the smallest atoms.

[2] Points and atoms are what can only be thought but also what must be thought as the basis of everything. One cannot perceive points and atoms. One only perceives their blend, shapes and shades (simulacra). What Seurat understood better than other Neo-Impressionists is that atoms must be simple. They themselves cannot be compound. He thus did not blend his colours. The colours blend themselves on the level of the perceptible, just as atoms do, according to certain laws. However the existence of such laws does not imply that there has to be any sort of resemblance between the atomic and the perceptible levels. The contrary holds. And this is the point where pointillism makes both collage and abstract art possible. The point that means the split between what is expressed and what expresses, between the conditioned and the condition, between shapes and shades and points and atoms.

[3] Because if collage is a recontextualisation, it presupposes the necessity of the primary existence of elements whose context (though endowing them with meaning-perceptibility) is secondary. The rights of the atom. A different grammar. A language of words stemming from letters which do not resemble them. A language that is the only thing we can hear, knowing it is not its own condition, nor is it conditioned from above, but that it is an outgrowth, an epiphenomenon, of the imperceptible bubbling depths. For not even letters are the real atoms. And if abstract art is a freeing of the signifying from the signified or of that which expresses from the expressed, it is primarily a search for the true atoms, the emancipation of the atom.

[4] Is "painting in one dimension" more realistic? As in today's computer graphics, where you get a clearer picture by increasing the number of pixels? (And indeed we live in a pointillist world today.) Yet many of Seurat's contemporaries complained of his paintings being fuzzy. No, realism and materialism are two different things. Atoms are real. But they are imperceptible. We only see shapes and shades. But those are but simulacra. Real and Not-there or There and Not-real. No in-between. Is it the aim of abstract art to make the Real perceptible as well? If so, it is a vain project and pointillism is the more sophisticated of the two. Even more sophisticated for being fuzzy. Being the predecessor of op-art in which the effect, or the work itself, is created in the perceiver, pointillism points out (by its fuzziness) the logic of perception. We can only perceive on the basis of something which we cannot perceive. We do not perceive the basis, the point. If we did, we would not make anything out anyway, there would be no shapes or shades. In other words, if we are to see something it is necessary that what we see be not real. Enough to make one go dotty...

[5] The traditional technique of painting is platonic and realistic. Platonism and realism do not exclude one another. In Platonism what we see is not real, but it bears a direct resemblance to what is real. What is real is the condition of what is perceived, just as in materialism, but this condition is in fact thought on the basis of what we see. The real and the perceptible are alike. Lines and shapes in the traditional painting resemble what is to be painted. And what is to be painted, the real, conditions the drawing; it leads the lines and shapes. The painting is already finished even before it is started. Because of their resemblance there does not even arise the difference between what expresses and what is expressed. The difference is there, however, and Plato knew it well. It manifests itself in the changeability of the perceptible and the stability of the real. Yet in painting this changeability of the perceptible is reduced, which led some commentators to claim that paintings portray ideas. Anyway, it takes pointillist materialism to introduce the split into the painting. Again, a split that cannot be perceived, but is felt, or sensed through the intensity of the shades of colours and the fuzziness of the simulacra.

[6] A traditional problem arises for such an interpretation. If there are only points and atoms, and no ideas or teleology, how is it possible that the atoms fit into regular shapes and recognisable figures? At this point we will probably be inclined to revise or at least complicate purely atomistic principles. After all, the painter knows what he wants to paint. (Although what does this knowing amount to if the painting takes more than two years to finish and consists of over three million dots? Dotty. Seriously.) But let us forget about the painter. The traditional answer to the atom-thing problem is that there is an infinity of worlds in which what we see as regular is sheer chaos and that even our world on a different temporal scale is nothing truly stable. This world-painting is after all a chance combination. Which brings us the other way around to Swift. The difference is that we have the finished work and we wonder how it could have appeared through chance alone. This might be where abstract art decides it does not want to take the chances.

[7] ...the truth in pointillism. "The hypokeimenon, that underneath, hides another underneath." [1] If painting points somewhere beyond itself, to a referent or an object, pointillist painting starts pointing inwards as well, to the other Not-there. And this pointing is pretty much infinite, it occurs within every geometrical point on the canvas; the painting is infinitely punctured. A double vertigo: infinite atoms, infinitely small, and infinite simulacra, big-screen pictures. Not that this pointing does not already appear in impressionism and its use of colours. What is new about pointillism is the new grammar, which becomes essential to collage and op-art. But what distinguishes pointillism from these later art movements and styles (save for collage perhaps) is the simultaneous retaining of the other pointing, of the objective simulacrum. The images of gods.


[8] Now to get to the point. It is not true that everything starts with a point. The big bang blunder. Everything starts from an infinity of points, which amounts to saying that nothing really ever starts. Nor ends for that matter -- the moral of materialism. Once again it will be objected that the painter necessarily begins with a single point. Yet after three million dots (also a de facto argument, always philosophically ignorable) who could remember which was the first? And if one did, how would this point serve as a beginning with precedence over all the other altogether same points? But let us forget about the painter's time.

[9] Now, three different but analogous kinds of point can be distinguished; three points which serve as the atoms of their respective fields: a geometrical point, a metaphysical point, and a painted point.

  1. "Definitions: 1. A point is that which has no part." [2] Euclid indeed begins with the point. With a point, to be precise, because in geometrical space every point is the same. One point cannot be distinguished from another precisely because it is a point, i.e. it has no parts. It has not even a single part (if that is imaginable), it has no extension, the implication of which being that any area of space contains an infinity of points. Euclid in a way combines ancient atomism and Pythagorean fascination with number and order. His Elements are a construction of a world which seeks to be absolutely coherent (ceasing thereby to be philosophical). Geometrical point has no extension and no quality. Nothing can really be said about it, which is its definition. Except that it is a point. Always infinite points. Never the point.
  2. Monads are metaphysical points. They have no extension, because they are metaphysical, but that does not mean that they contain nothing. They in fact "incorporate" the whole universe. Each monad is a mirror of the world from its own perspective, with its own particular clarity. For Leibniz then, there is an infinity of monads, each of which is different and yet the same. There is an infinity of possible worlds. And this world contains an infinity of worlds which in their turn contain other infinities and so on. Infinities of infinities. The ancient atomists claimed that there are infinite worlds too as there are infinite atoms. These worlds, however, are only contiguous. Leibniz puts worlds into worlds where atomists stop with the atom, the indivisible. Not that monads are divisible or contained within one other. But some may be said to be superior and some to be inferior (always relatively, of course). This is possible only because there are differences between monads, not of extension, but of expression and its clarity. No such difference is possible among geometrical points.
  3. A painted point. Undoubtedly something very different from the preceding ones. And maybe something much harder to conceptualise ("nonconceptual concept of noncontradiction"). [3] A painted point is first of all something material. It will thus necessarily have some qualities like colour and texture. It will have intensity. It will be visible: directly or indirectly. But rendering the point material does not seem to make it easier to analyze.

[10] Kandinsky shows how multiform this strange (formless) object can be. "The dimensions and the form of the point may change causing the relative resonance of the abstract point to change as well." [4] The painted point for Kandinsky combines the qualities of the geometrical and metaphysical points. It is maximum economy and silence. At the same time it is an inner tension and a message. It is "a small world in itself" [5] with weak or no bonds to its surroundings (much like the monad). Its tension is always centripetal. The point is the originary element of painting, even though no elements are pure or basic, free of complication (a very Leibnizian point). The difference between traditional objectival painting and abstract painting is that within the former the resonance of this element is suppressed and shrouded by objectness, while in the latter it is allowed to function freely.

[11] Deleuze points out that Kandinsky is in fact more of a Cartesian for whom the point is something firm, set in motion only by an exterior force. For Paul Klee, on the other hand, the point is the genetic element of the active, spontaneous line. "Inflection is the authentic atom, the elastic point. [...] ...the point as a "nonconceptual concept of noncontradiction" moves along an inflection. It is the point of inflection itself, where the tangent crosses the curve. That is the point-fold. [...] ...no exact and unmixed figure can exist." [6] Klee's elastic point is different from Kandinsky's, but there are more affinities for them to be purely juxtaposed. Kandinsky's point is not completely firm in that it contains ambiguity, tension and resonance. It has an inner movement. It is just as true for Kandinsky as for Klee that no pure and unmixed figure can exist. And they both think of the point in terms of the spiritual. For Kandinsky the point is a small world in itself, for Klee it is "a site of cosmogenesis". [7]

[12] However fascinating and insightful these theories are, there is yet another way to draw the point. After all, Kandinsky operates with a point that is directly visible. He mentions its growing and its becoming a plane, but he omits its approximating the geometrical point, its disappearing. The urge of the point for infinite smallness. Infinite density of matter. Klee, on the other hand, seems to dispense with the materiality of the point completely. That is due to his overall transcendentalism. "Today we reveal the reality that is behind visible things, thus expressing the belief that the visible world is merely an isolated case in relation to the universe and that there are many more other, latent realities..." [8] What is meant here by the unseen reality is no doubt something spiritual, even more immaterial than the visible world. Both Kandinsky and Klee feel that it is the spiritual aspect of art that needs to be emphasized and explored, while it just might be art's materiality that is the greater mystery. And indeed this may be a general phenomenon accompanying modernism: the more art explores its material aspects, the more the artist attempts to give it a spiritual explanation and justification.

[13] So, to summarise. the geometrical point and the monad are without extension and they are invisible. So is perhaps Klee's point, which is the analogon of the monad (at least in Deleuze's interpretation). The geometrical point has no qualities, which is not true of any of the other points. All the other points envelope or express worlds of infinities. That means that there may be differences of intensity between particular instances of these points. Kandinsky's point is nevertheless similar to the geometrical point in that it is static (in opposition to the dynamic line) and has a firm position on the plane. It would be hard to speak of a spatial organisation of Leibniz's or Klee's points. As far as their mobility is concerned, they are more like the atoms than Kandinsky's point and the geometrical point. As far as their (and Kandinsky's point's) infinite content is concerned, they are less like the atoms than the geometrical point (though atoms are also inwardly differentiated). And as far as the immateriality of them all is concerned, they are not like the atoms at all (though monads may still be called the atoms of Leibniz's universe, etc.).

[14] So there is yet another way to draw the point, which is closer to the ancient conception of the atom. The atoms are material but invisible. They are indivisible but differentiated. And they are the basis and condition of what is seen, of simulacra, which do not resemble them. The pointillist point is such an atom. Unlike Kandinsky's point it is invisible (or visible only indirectly through simulacra). Unlike Klee's point it is material ("scientific", even). Its infinity and its differentiation is only that of intensity (pure colour), not that of content. It is the condition of the visible, itself invisible (when we look at the picture -- which is what we are supposed to do -- we don't see the points; when we look at the points we do not see the picture). The pointillist painting is a (re)invention of Lucretius' aesthetics. The rebirth of the atom. The point.


[15] After all, it is not the pointillists' goal to go crazy over the dot, just as Lucretius' main concern is not with physics but with ethics. The main concern is to paint a picture -- to learn of the nature of simulacra; the main goal is to intensify the shades of colours -- to bring peace to the worrying soul. "It is this passion for beautiful colours which makes us paint as we do...and not the love of the 'dot', as foolish people say." [9] Seurat's technique adopted by Paul Signac reflected the fact that colours create different effects when they blend on the canvas than when they blend in the viewer's eye. Seurat and Signac would then experiment with scientifically juxtaposed small dots of pure colour, which were meant to combine only visually. Other pointillists would use blended colours for their dots as well, but Seurat seemed to attach particular importance to the purity of colours (an inspiration for Mondrian perhaps). Signac then expresses a great aversion towards the mixing of colours on the canvas. "I attach more and more importance to the purity of the brushstroke - I try to give it maximum purity and intensity. Any defiling sleight of hand or smearing disgusts me. When one can paint with jewels, why use [manure]? Each time that my brushstroke happens to come up against another, not yet dry, and this mixture produces a dirty tone, I feel great physical disgust!" [10] A convinced atomist.

[16] Felix Fénéon testifies to the effect this method of painting had in Signac's work. "His colourings spread out in spacious waves, tone down, meet, fuse and form a polychromatic design similar to a linear arabesque. To express these harmonies and oppositions, he uses only pure colours. Arranging these on his palette in the order of the spectrum, the painter mixes only contiguous colours, thus as far as possible obtaining the colours of the prism, adding white to graduate their tone scale. He juxtaposes these dabs of paint on the canvas, their interplay corresponding to local colour, light and varying shadows. The eye will perceive them mixed optically. The variation of colouring is assured by this juxtaposition of elements, its freshness by their purity and a brilliant lustre by the optical blending, because unlike a mixture of pigments, optical mixing tends to brightness." [11]

[17] It is clear now that the pointillists are aware of the split between the visible and the real. These two spheres are completely different and disparate. What appears as a brilliant shade of a plane on the level of the simulacra is but an aggregate of monochrome dots on the atomic level. The lightness of the images is directly opposed to the scientific, laborious technique of pointillism. The more so for what they are images of, following the impressionist tradition.

[18] One cannot really say what the pointillist atom is like, or what it does. It is imperceptible. One can in a way only speculate about what it must be like and what it must do (as Lucretius does). It is the vertigo of fuzziness which forces us to acknowledge the split and introduce the notion of the atom, which must be simple, real, material, infinitely small and distant yet intensive and indivisible. This is not the point of Kandinsky, nor that of Klee. But it is the point from which they must have departed, the point from which it is possible to depart in many ways, regardless of what is gained or lost.

[19] Abstract art owes this to pointillism: it has discovered the split and the two autonomous spheres. "The difference between traditional objectival painting and abstract painting is that within the former the resonance of this element [the point] is suppressed and shrouded by objectness, while in the latter it is allowed to function freely." [12] Abstract art frees the atom from its subordination to the organizing simulacra. It renders it visible and spiritual. It thereby loses the atom. "That underneath hides another underneath."

[20] (Mondrian's abstract work may be thought of in terms of the search for the atomic. What he in fact strives for is the eternal and the infinite. The atomic tulip. "Intense involvement with living things is involvement with death. [...] 'Let us recognize the fact once and for all: the natural appearance, natural form, natural colour, natural rhythm, natural relations most often express the tragic . . . We must free ourselves from our attachment to the external, for only then do we transcend the tragic, and are enabled consciously to contemplate the repose which is within all things.' [...] Attachment had to be transferred from natural objects to things not subject to death." [13] A speech that could have been taken straight out of Lucretius. The repose within simulacra: the eternal atom. "Mondrian wanted the infinite, and shape is finite." [14] That is also why cubism is an altogether different project and why Mondrian felt greater allegiance to Seurat than to Braque.)

[21] Collage is a fascination with detachable elements. At the same time it works with elements of larger scale than atoms. It combines simulacra. And if the world is the context of particular elements and recontextualisation means the changing of a world, then collage is the pluralisation of worlds. Furthermore, since the elements which it uses are themselves certain contexts, collage means the putting of worlds into worlds. Collage is therefore the true Leibnizian art (and James Joyce is the true Leibnizian writer), going beyond Leibniz in that it explores the plurality of possible worlds.

[22] Op-art is perhaps the one style that takes pointillism to a higher level. What was after all missing from the pointillist atomism was movement. Both the atoms and the simulacra were static. Op-art also operates with the difference between the material aspect of the artwork and the effect triggered by it in the viewer. The real and the perceptible are disparate. That is the principle of atomism. But op-art breathes life into this atomism when it introduces movement into the effect of the artwork. (And if we were ancient philosophers we would no doubt say that it introduces movement into its atoms as well, because it is a question of what the condition must be like if we know what the conditioned is like.)

[23] ... so what is the point? The pointillist artists seemed to be concerned with colour and perception theories more than with any philosophical grounding of their method. Nevertheless, it appears that their greatest (though perhaps unacknowledged) contribution to later modernism lies in something that may be described on the basis of materialist philosophy. While emphasizing shades of colours of images the pointillists give new autonomy and power to raw paint (pure colour without a shape or with a minimal shape). They thus open new possibilities for what is to be painted and how it is to be painted. The pointillists draw a line between traditional painting and what is to become of art in the twentieth century. And they themselves occupy this thin line, themselves being a unique point in the history of art. Which is the point we were trying to make.



[1] Jacques Derrida: Restitutions of the Truth in Pointing; in A Derrida Reader (Columbia University Press, 1991) p. 308.

[2] Euclid's Elements; Britannica 1952.

[3] Paul Klee; cited in Deleuze's The Fold (Minnesota 1993), p. 14.

[4] Translated from: Wassily Kandinsky: Bod, linie, plocha (Triáda 2000), p. 24.

[5] Ibid. p. 27.

[6] Deleuze: op. cit. p. 14.

[7] Ibid. p. 15.

[8] www.artchive.com.

[9] « www.si.umich.edu/Chico/Emerson/Seurat».

[10] Ibid.

[11] «painting.about.com/library».

[12] Kandinsky: op. cit. p. 46.

[13] «www.artchive.com».

[14] Ibid.