with the world around them, whether religion or boat building or hammering a nail into a piece of wood. The impact of cooperation on culture is huge and, for me, the central reason why life is so beguiling and beautiful.
QUEST FOR THE EVOLUTION
OF COOPERATION
Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
—Bertrand Russell, Study of Mathematics
My overall approach to reveal and understand the mechanisms of cooperation is easy to explain, even if my detailed workings might appear mysterious. I like to take informal ideas, instincts, even impressions of life and render them into a mathematical form. Mathematics allows me to chisel down into messy, complicated issues and—with judgment and a little luck—reveal simplicity and grandeur beneath. At the heart of a successful mathematical model is a law of nature, an expression of truth that is capable of generating awe in the same way as Michelangelo’s extraordinary sculptures, whose power to amaze comes from the truth they capture about physical beauty.
Legend has it that when asked how he had created David, his masterpiece, Michelangelo explained that he simply took away everything from the block of marble that was not David. A mathematician, when confronted by the awesome complexity of nature, also has to hack away at a wealth of observations and ideas until the very essence of the problem becomes clear, along with a mathematical idea of unparalleled beauty. Just as Michelangelo wanted his figures to break free from the stone that imprisoned them, so I want mathematical models to take on a life beyond my expectations, and work in circumstances other than those in which they were conceived.
Michelangelo sought inspiration from the human form, notably the male nude, and also from ideas such as Neoplatonism, a philosophy that regards the body as a vessel for a soul that longs to return to God. Over the few centuries that science has been trying to make sense of nature, the inspiration for mathematical representations of the world has changed. At first, the focus was more on understanding the physical world. Think of how Sir Isaac Newton used mathematics to make sense of motion, from the movement of the planets around the sun to the paths of arrows on their way to a target. To the amazement of many, Newton showed that bodies on Earth and in the majestic heavens were governed by one and the same force—gravity—even though planets are gripped in an orbit while objects like arrows and apples drop to the ground.
Today, the models of our cosmos are also concerned with biology and society. Among the eddies and ripples of that great river of ideas that has flowed down the generations to shape the ways in which scientists model these living aspects of the world are the powerful currents generated by Charles Darwin (1809–1882), who devised a unifying view of life’s origins, a revolutionary insight that is still sending out shock waves today.
Darwin worked slowly and methodically, using his remarkable ability to make sense of painstaking studies he had conducted over decades, to conclude that all contemporary species have a common ancestry. He showed that the process of natural selection was the major mechanism of change in living things. Because reproduction is not a perfect form of replication, there is variation and with this diversity comes the potential to evolve. But equally, as the game of Chinese Whispers (also known as Gossip or Telephone) illustrates, without a way of selecting changes that are meaningful—a sentence that makes sense—the result is at best misleading and at worst a chaotic babble. Darwin came up with the idea that a trait will persist over many generations only if it confers an evolutionary advantage, and that powerful idea is now a basic tenet of science.
Darwin’s message is simple and yet it helps to generate boundless complexity. There exists, within each and every creature, some information that can be passed from one generation to the next. Across a population, there is variation in this information. Because when there are limited resources and more individuals are born than can live or breed, there develops a struggle to stay alive and, just as important, to find a mate. In that struggle to survive, those individuals who bear certain traits (kinds of information) fail and are overtaken by others who are better suited to their environs. Such inherited differences in the ability to pass genes down the generations—natural selection—mean that advantageous forms become more common as the generations succeed. Only one thing counts: survival long enough to reproduce.
Darwin’s theory to explain the diverse and ever-changing nature of life has been buttressed by an ever-increasing wealth of data accumulated by biologists. As time goes by, the action of selection in a given environment means that important differences can emerge during the course of evolution. As new variations accumulate, a lineage may become so different that it can no longer exchange genes with others that were once its kin. In this way, a new species is born. Intriguingly, although we now call this mechanism “evolution,” the word itself does not appear in The Origin of Species.
Darwin himself was convinced that selection was ruled by conflict. He wrote endlessly about the “struggle for existence” all around us in nature. His theme took on a life of its own as it was taken up and embellished with gusto by many others. Nature is “red in tooth and claw,” as Tennyson famously put it when recalling the death of a friend. The catchy term “survival of the fittest” was coined in 1864 by the philosopher Herbert Spencer, a champion of the free market, and this signaled the introduction of Darwinian thinking into the political arena too.
Natural selection is after all about competition, dog-eat-dog and winner takes all. But Darwin was of course talking about the species that was the best adapted to an environment, not necessarily the strongest. Still, one newspaper concluded that Darwin’s work showed that “might is right & therefore that Napoleon is right & every cheating tradesman is also right.” Darwin’s thinking was increasingly abused to justify the likes of racism and genocide, to explain why white colonialists triumphed over “inferior” native races, to breed “superior” humans and so on. These abuses are, in a twisted and depressing way, a testament to the power of his ideas.
But, as I have already stressed, competition is far from being the whole story. We help each other. Sometimes we help strangers too. We do it on a global scale with charities such as Oxfam, which helps people in more than seventy countries, and the Bill & Melinda Gates Foundation, which supports work in more than one hundred nations. We do it elaborately, with expensive celebrity-laden fund-raising dinners in smart venues. We are also charitable to animals. Why? This may look like an evolutionary loose end. In fact it is absolutely central to the story of life.
When cast in an evolutionary form, the Prisoner’s Dilemma shows us that competition and hence conflict are always present, just as yin always comes with yang. Darwin and most of those who have followed in his giant footsteps have talked about mutation and selection. But we need a third ingredient, cooperation, to create complex entities, from cells to societies. I have accumulated a wide range of evidence to show that competition can sometimes lead to cooperation. By understanding this, we can explain how cells, and multicellular organisms such as people, evolved, and why they act in the complicated ways that they do in societies. Cooperation is the architect of living complexity.
To appreciate this, we first need to put evolution itself on a firmer foundation. Concepts such as mutation, selection, and fitness only become precise when bolted down in a mathematical form. Darwin himself did not do this, a shortcoming that he was only too aware of. In his autobiography, he confessed his own inability to do sums: “I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics; for men thus endowed seem to have an extra sense.” He seemed aware that more rigor was required to flesh out the implications of his radical ideas about life. He regarded his mind “as a machine
