In the spirit of Plato, a new generation of science mavericks is seeking to find a mathematical understanding of nature, from the number of petals in a flower to the shape of spots on a peacock. Ian Stewart explains why we should take their flaky theory seriouslyby Ian Stewart / February 20, 1996 / Leave a comment
Human beings have been aware of patterns in nature for as long as they have been human. Without such an awareness, human culture cannot function. Agriculture is impossible without an understanding of the seasons; even before agriculture, hunting depended upon animal life cycles and patterns as simple as the trajectory of a thrown rock. Humans have discovered that one of the most effective tools for grasping nature’s patterns is mathematics.
Some physicists think that the universe is made of mathematics. Even if this is an exaggeration, there is no doubt that the universe often behaves as if mathematics is a central component of it. It is a message that goes back well before Plato, with his celebrated image of the real world as the shadow on a wall, cast by an ideal mathematical world that we glimpse only imperfectly. It was Pythagorean philosophy which maintained that all is number. Later thinkers added geometry as well; Johannes Kepler discovered that the orbit of Mars is an ellipse, a curve that featured prominently in the geometry of Euclid. It was this geometric pattern which led Isaac Newton to formulate the law of gravity. In so doing, he introduced new mathematical tools such as calculus and dynamics, and his “System of the World” was so successful that it became a model for succeeding generations.
But models change, and today we are starting to glimpse a new vision of mathematics in nature, one that is more flexible and adaptable than the numerology of Pythagoras or the rigid geometry of Euclid. This vision is providing a mathematical understanding of nature’s processes as well as its structures.
hidden within the Newtonian paradise was a philosophical time bomb; it has just exploded. For centuries science made a plausible assumption: that the key to understanding nature is to find the simple laws which underpin it. Once the laws are known, all else follows. Not so. Thanks to various scientific mavericks, we now know that simple laws can give rise to behaviour of endless complexity-and conversely, that highly complex systems often exhibit well defined, but apparently acausal, patterns.
One area that stands to benefit from this new knowledge is biology. There are many biological phenomena that we do not understand in depth. One is the evolution of organised structure in the living world; another, our main focus here, is the occurrence of mathematical form in an organism.