Forces of Nature. Andrew Cohen

become streamlined to allow the manatee to swim at up to 12 km/hour. The manatee can dive deep, for up to twenty minutes at a time, but being an air-breathing mammal it must surface for air eventually. Its time under water is maximised by slowing down its heartbeat and metabolic rate, reducing the need for oxygen; but this is where biology comes into conflict with physics. A low metabolic rate means limited heat production, and water is an extremely good conductor of heat away from the body, so there is a danger of becoming too cold. The compromise solutions discovered, naturally, by natural selection, are to get bigger, which reduces the surface-area-to-volume ratio and therefore decreases the rate of heat loss per unit volume, and to get spherical (see illustration, here).

      This graph shows how the surface area decreases for rounder shapes and the surface-area-to-volume ratio decreases as the volume increases.

      This is a beautiful example of a naturally occurring shape reflecting a deeper mathematical reality. The sphere is the three-dimensional shape with the lowest surface-area-to-volume ratio. If you want to generate lots of heat by having a large volume, but lose as little through your surface as possible, you’ll be spherical – and the manatee is the most spherical mammal on Earth. What a wonderful thing to be – unless you are an astronomer. The astronomer Fritz Zwicky is credited with calling a group of his colleagues Spherical Bastards, because they are bastards, whichever way you look at them. Which brings us nicely back to the subject of symmetry. If a physicist designed a manatee it would be spherically symmetric. Symmetrical shapes such as planets tend to be the result of the action of symmetrical laws of Nature, unless there are reasons for the symmetry to be broken. There are no perfectly symmetric large organisms in biology. Why?

Symmetry and symmetry breaking in biology

      Leonardo da Vinci’s ‘Vitruvian Man’ is perhaps the most famous drawing of the human form in history. It depicts a man in two superimposed positions within a circle and a square. The proportions are carefully calculated in an attempt to represent the underlying perfection of Man and to link him directly to the Universe. Da Vinci was inspired by one of the great classical works, De architectura, written by the Roman architect Vitruvius. The relationship of the human form to a circle and square reflects ancient ideas – dating back to Plato, Pythagoras and earlier mystic traditions – which attempted to forge a link between Nature and geometry. Kepler’s early work on the motion of the planets was firmly rooted in this tradition, and he only jettisoned the idea that the motion of the planets could be described in terms of the perfect ‘Platonic’ solids when the data forced him to conclude that planets actually move in elliptical orbits rather than circular ones. It is interesting to reflect on the fact that the explanation for the motion of the planets is more elegant and beautiful than Kepler’s hoped-for geometrical perfection. As we’ve seen, the motion of all the planets and moons in the Solar System, and indeed every solar system in the Universe, can be described by the application of Newton’s laws of motion and Universal Gravitation; a profound simplification that would surely have appealed to Kepler, and to Plato before him, because Newton’s laws do embody a ‘perfect’ spherical symmetry, which is hidden but still evident in the structures it creates.