Spirals in Time: The Secret Life and Curious Afterlife of Seashells by Helen Scales

companies are getting in on the act, razing them to the ground for the limestone inside. These are imperilled arks of biodiversity that few people have heard of. Year on year, hundreds of species are going extinct, most of them before they are discovered, when the hills they once lived on are taken away.
    Compared to Clements and Liew’s bizarre find in the Malaysian hills, most shells are far less erratic in the way they grow, and indeed they are often quite predictable. For centuries, many great minds have contemplated the elegant sculptures and patterning of shells and wondered what might govern their construction. They have hunted for clues to explain the amazing realities and tempting possibilities of shells; they have probed ideas of what makes a shell work and which shapes may ultimately never show up; and they imagined that if they could find ways of drawing shells, if they could mimic what nature has been doing for eons, it would not only bring them closer to understanding how molluscs make their intricate homes, but they might also catch a glimpse of the origins of beauty itself. What many generations of mathematicians, artists, biologists and palaeontologists have found is unexpected and elegant: toconstruct an elaborate seashell – and decorate it – requires only a handful of rules.

    Of all shell shapes, one of the simplest and most pleasing is the spiral of the chambered nautilus. The internal twist of these ocean-wanderers is revealed when their empty shells are sliced in two, from top to bottom. Trace the outer edge of a nautilus shell and you’ll see that it spins inwards in a very particular way. This graceful curve was among the first shapes in nature to be granted its own mathematical formula.
    In the seventeenth century, French philosopher René Descartes composed a simple piece of mathematics for drawing a shape called the logarithmic spiral. Unlike an Archimedean spiral, which has whorls that are always spaced the same width apart, like a coiled snake, the gaps between successive whorls on a logarithmic spiral get increasingly wide. Logarithmic spirals flare open as they get bigger, just like a nautilus shell.
    A chambered nautilus shell cut in two, revealing its logarithmic spiral.

    It was the cleric and mathematician Reverend Henry Moseley who, in 1838, first pointed out that many coiled shells are versions of the logarithmic spiral. Take a photograph of a nautilus shell cut in two, overlay the outline of a logarithmic spiral and, given the right dimensions, it should be a good fit.
    These expanding spirals pop up all over the natural world; you can spot them in patterns of seeds in a sunflower, in spiralling galaxies, in the bands of rain and thunderstorms that swirl around the eye of a tropical cyclone, and in the path taken by a doomed moth as it flies mesmerised towards a candle. All these spirals are subtly different; what unites them is the fact that they all get bigger at a constant rate. In other words, the gaps between successive coils get wider by the same amount each time the spiral makes a complete turn around its central point. This means that no matter how big the spiral becomes, its overall shape doesn’t change – and that is one of the key rules for making a seashell.
    The way molluscs make shells is reminiscent of the ancient practice of coiling pottery. For thousands of years, people around the world have rolled strips of clay between their hands and coiled them into simple pots. In a similar way, a mollusc creates its shell as a hollow tube. The mantle (the fleshy cloak that spreads across a mollusc’s body) lays down new shell only at this open end, known as the aperture. It does so by first secreting a scaffold of protein, which is then shored up with calcium carbonate in one of two varieties (and sometimes both): aragonite or calcite, the latter being a more stable form. The main building blocks for the shell are carbonate ions, consumed in the mollusc’s diet or