The world comes down to bits. Everything, the universe in all its variety, can be reduced to elementary particles. They are too small to be perceptible, but not infinitely small: there's a point where you can divide things no further. And while these basic particles aren't all identical, there is only a limited number of types. In different compounds and proportions, they generate all the entities and qualities of the known cosmos.
This is the doctrine of Atomism. It has modern scientific versions, but it originated from the pre-Socratic Greek philosophers. It is also alarming. It seems to threaten the physical solidity of the world, and of our conceptual framework. Matter crumbles. Nature is infinitely mutable. Nothing, except the atoms themselves, has a fixed form or substance or identity. As the physicist Arthur Eddington put it, in an atomistic universe the ground gives way beneath our feet. "To step on it is like stepping on a swarm of flies."
People who look at pictures should understand this idea, and its anxieties, only too well. Most of our images are atomistic. However solidly real they appear, they're made up out of - and can break down into - tiny particles.
Put a reasonably powerful magnifying glass to any printed photograph, and its seamless surface disintegrates into dots. Full colour comes down to dots of four colours, in varying mixtures. Monochrome is just black dots, with greys a matter of their density. Computer images, likewise, can be easily magnified into their constituent pixels, a grid of tiny identical squares, though here the range of available hues and tones is much wider.
It's not only the newer image technologies. Traditional printing techniques are equally particle-based. Their smoothly shaded look is generated by a fine-grained "stippling" of single dots or a woven "hatching" of single lines. You find the effect in paintings, too. The loaf of bread in Vermeer's Milkmaid turns on nearer inspection into "granules of light". And the Pointillism of Seurat revels in the possibilities of atomisation. The image is a field of largish, same-sized and distinct brushstrokes of pure colour. It can dissolve and resolve before your eyes.
All of these pictures contain a potential point of disillusion, when the eye looks too closely, and the imaginary world you were gazing at suddenly separates out into its constituent atoms, into its swarm of flies. It's a moment of disappointment and revelation, as the illusion is undermined, and analysed into its bare ingredients.
But even in Seurat, the distinction between the picture and the pictorial atoms remains clear. You can see what the image is. And when you come closer, you can identify the elements that it's made up from - a field of dots of paint. There are these two levels, these two ways of looking at the picture, and you know when you've made the switch between them. Not every picture lets you feel so sure.
Take Piet Mondrian's Composition in Line. This monochrome abstraction is a painting about atomisation. It lies firmly in the tradition of the atomised picture. It has the two levels of perception. There's no image, but there is a shape, lying against a background. And there is the cloud or swarm or gathering of black particles, out of which this shape materialises. Of course you don't need to look very closely to make out these individual particles. They're always present to the eye. And what gives this abstract painting its life and movement, is that it keeps the relationship between picture and pixels in constant play.
The picture is a perfect square. That at least is certain. Within it lies a round area. But that's not so certain, because it's not a perfect round, and it's not perfectly centred, and it's not all in view. The area spreads beyond the edges of the picture, so how precisely we should read its shape is doubtful. Part of the problem, of course, is that the round area doesn't have a firm edge or body. It is a formation of separate, congregated elements - a scattering of black bars on the white ground.
What are these elements? Another uncertainty. At first glance they look so formulaic, you may suppose there's a strict repertoire of units and permutations. Perhaps the round area is entirely composed of regular pluses and minuses? Well, no, it's not. The bars are all straight, yes, and either vertical or horizontal. Some lie in isolation. Others are in combinations - equals signs, miscellaneous crosses and T-junctions, more complex composites. There seems to be a ban on pure L-junctions, and on enclosed oblongs.
But beyond those rules - no curves, no diagonals, no Ls or enclosures - there aren't any specifications. Bar-lengths vary a lot. Some are so short as to be little squares. Widths vary, too. No composite has more than six bars, but would seven be out of the question? You sense there are some limits - the bars can't be too long, they can't all join up into a single web - but they're undefined. The picture is made of elements, but you can't tell precisely what they are.
Nor can you tell precisely what it is that they make up. The uneven densities in the field of bars give a hint of light and shade. They suggest a swelling 3Dform.Near the top of the picture, where the space clears, doesn't that create a kind of highlight? And isn't there a crescent of shadow within the lower circumference? This round could be a ball, no? But when you stand back - the normal test, to see how an image coalesces - it doesn't become a ball. Mondrian has put in too many other little clearings, here and there, disrupting any sense of consistent modelling. Try to extract a solid globe out of this swarm of bars and they keep falling back into a flat shape.
The individual bars are so visible they themselves are likely to become the protagonists of the picture, quite upstaging any shape they may produce. Sure, you can see Composition in Line as primarily a round form, made up of criss-cross particles. But the so-called particles are almost too big to register as mere material - and you can also see it as primarily a host of bars that just happen to lie in a rough circle. The elements have a life of their own. The universe doesn't just break down into atoms. The atoms have taken over the universe.
Piet Mondrian (1872-1944) was the greatest master of modern abstraction. Living in solitude, and following the principle of theosophy, he rejected nature, and reduced his art to a linear grid of black on white, plus the three primary colours. These precariously calculated compositions can "move with the force of a thunderclap or the delicacy of a cat", wrote the critic David Sylvester. In his writings, Mondrian took the idea of "dynamic equilibrium" beyond the field of painting, into urban living, even into international relations, and - before nuclear weapons - he envisaged the concept of Mutually Assured Destruction.