from cells to multicellular creatures to anthills to villages to cities. Without cooperation there can be neither construction nor complexity in evolution.
I can derive everyday insights—as well as many unexpected ones—from mathematical and evolutionary models of cooperation. While the idea that the trajectory of spears, cannonballs, and planets can be traced out by equations is familiar, I find it extraordinary that we can also use mathematics to map out the trajectory of evolution. And, of course, it is one thing to know how to foster cooperation but it is quite another to explain why an action helps us get along with each other and to what extent. The mathematical exploration of these mechanisms enables us to do this with profound understanding and with precision too. This is proof, as if we need it, that math is universal.
In the following chapters I will explain the origins of each mechanism of cooperation and interweave this train of thought with my own intellectual journey, one that began in Vienna and then continued to Oxford, Princeton, and now Harvard. En route, I have had the honor to cooperate with many brilliant scientists and mathematicians. Two of them proved particularly inspirational: Karl Sigmund and Robert May, for reasons that will become clear. I have also had to enlist the help of computer programs, students willing to play games, and various funding bodies, from foundations to philanthropists. It is a lovely and intoxicating thought that a high degree of cooperation is required to understand cooperation. And to further underline this powerful idea, this book is also a feat of cooperation between Roger Highfield and myself.
The implications of this new understanding of cooperation are profound. Previously, there were only two basic principles of evolution—mutation and selection—where the former generates genetic diversity and the latter picks the individuals that are best suited to a given environment. For us to understand the creative aspects of evolution, we must now accept that cooperation is the third principle. For selection you need mutation and, in the same way, for cooperation you need both selection and mutation. From cooperation can emerge the constructive side of evolution, from genes to organisms to language and complex social behaviors. Cooperation is the master architect of evolution.
My work has also shown that cooperation always waxes and wanes. The degree to which individuals are able to cooperate rises and falls, like the great heartbeat of nature. That is why, even though we are extraordinary cooperators, human society has been—and always will be—riven with conflict. Global human cooperation now teeters on a threshold. The accelerating wealth and industry of Earth’s increasing inhabitants—itself a triumph of cooperation—is exhausting the ability of our home planet to support us all. There’s rising pressure on each of us to compete for the planet’s dwindling resources.
Many problems that challenge us today can be traced back to a profound tension between what is good and desirable for society as a whole and what is good and desirable for an individual. That conflict can be found in global problems such as climate change, pollution, resource depletion, poverty, hunger, and overpopulation. The biggest issues of all—saving the planet and maximizing the collective lifetime of the species Homo sapiens—cannot be solved by technology alone. They require novel ways for us to work in harmony. If we are to continue to thrive, we have but one option. We now have to manage the planet as a whole. If we are to win the struggle for existence, and avoid a precipitous fall, there’s no choice but to harness this extraordinary creative force. We now have to refine and to extend our ability to cooperate. We must become familiar with the science of cooperation. Now, more than ever, the world needs SuperCooperators.
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our “creations,” are simply the notes of our observations.
—Godfrey H. Hardy,
A Mathematician’s Apology
At first, I did not appreciate the point of mathematics. I played with numbers during lessons in high school. I enjoyed solving problems. Arithmetic lessons were fun. Math was, all in all, quite interesting. But it was unclear to me what it was for. Perhaps it was a kind of mental gymnastics that had been devised—along with Latin—with the express purpose of making the children’s lives just that little bit harder.
At university I changed my mind. I had an epiphany, a spine-tingling moment when I realized that the precisely defined terms, equations, and symbols of mathematics are fundamental. I came to realize that mathematics holds the key to formulating the laws that govern the cosmos, from the grandest filaments, voids, and structures that stretch across the heavens to the peculiar behavior of the tiniest and most ubiquitous grains of matter. More important, it could say something profound about everyday life.
Mathematics is characterized by order and internal consistency as well as by numbers, shapes, and abstract relationships. Although you might feel that these concepts only inhabit the human mind, some of them are so real and absolute that they mean precisely the same thing to us as they would to a clever many-tentacled alien floating on an icy exoplanet on the far side of the universe. In fact, I would go even further than saying the ideas of mathematics are objective and concrete. The cosmos itself is mathematical: everything and anything that happens in it is the consequence of universal logic acting on universal rules.
Beyond the dimensions of space and time, mathematics inhabits a nonmaterial realm, one that is eternal, unchanging, and ever true. The empire of mathematics extends far beyond what we can see around us, beyond what we are able to perceive, and far beyond what we can imagine. There’s an unseen, perfect, and transcendental universe of possibilities out there. Even in the wake of cosmic degradation, collapse, and ruin, the inhabitants of other universes will still be there to gaze on the unending beauty of mathematics, the very syntax of nature. The truth really is out there and it can be expressed in this extraordinary language.
Some would go even further than this. They regard the mathematics that describes our cosmos as a manifestation of the thoughts of a creator. Albert Einstein once remarked: “I believe in Spinoza’s God, Who reveals Himself in the lawful harmony of the world.” For the seventeenth-century Dutch philosopher who had so impressed Einstein, God and nature were as one (deus sive natura), and the practice of doing math was tantamount to a quest for the divine. Whenever I think about this connection, I am always reminded of the last, thrilling lines of Goethe’s Faust:
All that is changeable / Is but refraction
The unattainable / Here becomes action
Human discernment / Here is passed by
Woman Eternal / Draws us on high.
My epiphany at university was that somewhere in this infinite, unimaginable ocean of truth there is a corporeal mathematics, a splash of math that you can feel, smell, and touch. This is the mathematics of the tangible, from the equations that govern the pretty patterns formed by the red petals of a rose to the laws that rule the sweeping movements of Mars, Venus, and other planets in the heavens. And of all those remarkable insights that it offers, I discovered that mathematics can capture the quintessence of everyday life, the ever-present tension that exists between conflict and cooperation.
This tension is palpable. It tugs at the emotions of participants in an internet purchase, where there is a temptation for buyers not to
