Black and white. For many, what come to mind are the stark extremes these absolutes conjure up. Wrong and right, evil and good and the other dichotomies that divide the world.

I am not one of these people. Things are never resolved quite so neatly for me. Humans fall inconveniently short of being complete saints or villains, their actions inhabiting the murky area between right and wrong. (This is what makes characters in good novels so interesting.) What black and white suggest to me is grey. Absolute purity is very rarely stumbled across – look closer and you’ll see at least a trace of the other colour mixed in. A range of grey is the natural scale to use – whether one is evaluating emotion or intention or consequence.

This leads to an interesting duality in the way people negotiate the world. There are those who think in black and white terms, for whom these simplified states are sufficient for most categorisation and analysis. The rest need a broader palette to assign values, regarding black and white as the two extremes of an all-prevalent grey. (Think Bush for the first, Obama for the second.) While the second approach has the potential for greater sensitivity, one could argue that the first, which needs only two colours, is more succinct.

Looking beyond the idea of black and white as metaphor, one can ask the question: how do these considerations play out in the physical world we live in? Is the universe as we know it a black and white system, or is it intrinsically grey? Do we need a whole range of intermediate values to describe it, or are two extremes sufficient?

To understand the question better, let’s first take a closer look at the colour grey itself. Recall, from art class, that the way to produce it is to mix together colours from the black and white paint tubes. (One can actually combine any two complementary colours to get grey tones – adding traces of blue or yellow gives it a cool or warm cast.) For the case of screen images (such as on computer terminals and televisions), a true B&W (or binary) image, which involves only pure black or pure white pixels, is rarely employed. Instead, what is commonly used is greyscale, where a number from 0 (pure black) to 100 (pure white) determines the shade of grey for each of the pixels that make up the image.

The above suggests that as far as imaging (as opposed to text) goes, a range of greys might be indispensable. However, it turns out that the greyscale idea fails completely when it comes to printing, for the simple reason that the only ink used is black. Instead, the greys observed on the page are a result of the halftone process, where the pixels are, perforce, coloured pure black and it is their size, rather than their intensity, that is varied. When viewed from a sufficient distance, the brain combines these tiny dots together so that one sees various shades of grey. Which brings us to a curious realisation: at a sufficiently high resolution, only black and white remain – grey ceases to exist on the printed page.

The French painter Seurat was one of the first to realise this unconscious mental synthesis, exploiting it in the artistic movement called pointillism. His paintings were composed of individual dots and dashes of colours rather than continuous brushstrokes. He was able to create various colours by juxtaposing together dabs of pure component colour, rather than mixing the pigments together (this also allowed him to enhance or degrade the luminosity of areas of his canvas). His contribution has often been called the precursor of pixilation.

In addition to his paintings, Seurat was a master craftsman when it came to drawing, producing a body of work that significantly advanced the state of the art. Using only black conté crayons and nothing else, he was able to create enormously complex effects of light and shadow, of tone and luminosity. Interestingly enough, his technique to create grey was not restricted to the dots and dashes he used in the medium of paint. He also varied the intensity with which he pressed down on the crayon, letting the texture of the white paper show through to create a stippled effect.

What Seurat’s pointillism and the halftone process demonstrate is that monochromatic images can be generated quite effectively using only black and white, without resorting to intermediate greys. On the other hand, these greys are an essential component of traditionally painted as well as computer screen images. The difference in philosophy is closely related to the choice between digital and analog, between discrete and continuous (the continuously varying grey being simulated by the discrete dots in black). As any number of advances in audio, video and computer technology have demonstrated, analog processes can be successfully approximated by digital ones, at least to the satisfaction of most humans. Even though the applications (digital cameras, CDs…) have only entered our lives in the past few decades, the theoretical underpinnings have been around for centuries – much of mathematics, for instance, is concerned with the approximation of the continuous by the discrete, and vice versa (this includes the whole field of calculus).

Rephrasing the question about the universe being B&W or grey in this context, what we really seem to be asking is whether it is discrete or continuous in nature. Time, Einstein’s fourth dimension, is surely continuous, as are (at least conceptually) the first three dimensions of space. But what about matter? Surely the decomposition into molecules and atoms and subatomic particles prove its intrinsic nature to be discrete?

And yet, the double-slit experiment, one of the cornerstones of quantum physics, shows how unreliable our intuition can be. A screen with two slits is placed in the path of a single photon and instead of going through one or the other slit, the photon behaves as if it is simultaneously going through both of them, thus establishing its wave (rather than particle) nature. Matter, it follows, can be both digital and analog, discrete and continuous, depending on the circumstances. Black and white dichotomy or a model built on grey – the universe seems to be simultaneously validating both perspectives.

Manil Suri, author of The Death of Vishnu and The Age of Shiva, is a mathematics professor at the University of Maryland Baltimore County.

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