And makes me poor indeed.
—Shakespeare, Othello
During our hike in the Vienna woods, Karl and I had discovered another mechanism for the evolution of cooperation, one that relied on reputation. In direct reciprocity, all I can do is to learn from repeated encounters with the same person. As a result, my behavior depends on what you have done to me. But for indirect reciprocity, there are repeated interactions in a group. Now my behavior toward you also depends on what you have done to others.
This idea is now abundant in e-commerce, where there are many applications. The web abounds with ways to score the behavior of people, for example. Even when you encounter a stranger, you can benefit from someone else’s experience with him or her. Now, when buying a camera online, you consider the seller’s reputation as closely as the price. Subscribers to eBay auctions are asked to state, after every transaction, whether they were satisfied with their partner or not. Their partner’s score can accordingly increase or decrease by one point. The ratings of eBay members, accumulated over twelve months, are also public knowledge. This crude form of assessment seems to suffice for the purpose of reputation building and seems to be reasonable proof against being manipulated.
As a result, I can benefit from the experience of others when dealing with you by paying close attention to your reputation. If you have been unreliable, then I will be wary. However, if you have been generous, I am more likely to work with you. In this way indirect reciprocity is a powerful promoter of cooperation. David Haig, an evolutionary biologist at Harvard, sums this up elegantly: “For direct reciprocity you need a face. For indirect reciprocity you need a name.”
And for a name you need language, a convenient label to distinguish one person from another in the great game of life. Thus for indirect reciprocity to work, we need a way to communicate with each other, to discuss our hopes and our fears, and to learn from the experiences of others. I believe that the demand for social cooperation via indirect reciprocity has, more than anything else, propelled the evolution of human language. And to possess a faculty as complex as human language, you need an impressive brain. My stroll with Karl had taken us a long way from direct reciprocity to reveal a vast new panorama of cooperation.
Spatial Games— Chessboard of Life
The chess-board is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us.
—Thomas Huxley
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
—John von Neumann
Where there’s life, there are lumps, clumps, and colonies. Bacteria grow in films. Slime molds aggregate in three-dimensional shapes, similar to Mexican hats. Bisons gather in herds. Ants work in colonies. Apes form troops. There are sleuths of bears, murders of crows, pods of whales, and gaggles of geese. And, of course, populations of people form structures too. We are organized in villages, towns, and cities. We gather in the workplace, at schools, and in theaters and pubs. We have mobs and crowds and posses and throngs.
When I started to work on ways reciprocity can solve the Prisoner’s Dilemma, I wondered if population structure could offer another way to solve the Dilemma. Remember that the calculations of the past two chapters were based on a simple assumption: the players in the Dilemma were in a well-mixed population, where every player has an equal chance of meeting every other player. In these uniform populations we found that defectors always outcompete cooperators. But, of course, all real populations have some structure. What difference does this make? Could population structure affect the outcome of the simple Prisoner’s Dilemma? Could there be structures that make cooperators triumph over defectors?
The very fact that people decide to live in the same patch, rather than dotted around at random, has to do with cooperation. Why? Some believe, for example, that the first communities evolved as a result of success in agriculture: surplus food from farming enabled people to settle down and specialize, from butcher to baker to candlestick maker. Others link it to ancient belief systems and religions. At Göbekli Tepe in Turkey (“Hill with a potbelly”), for example, is a sanctuary with limestone pillars that were carved and erected by hunter-gatherers more than eleven thousand years ago. That remarkable discovery would suggest that temples planted the seeds of cities.
Perhaps cities were born of the struggle for existence: in his book Whole Earth Discipline, Stewart Brand suggests that the very first urban invention was the defendable wall, followed by rectangular buildings that could pack people efficiently inside that wall. The Cambridge archaeologist Colin Renfrew argues that the first communities came with the birth of the modern mind. That is when the effects of new intellectual software kicked in, allowing our ancestors to work together in a more settled way. However, I would discover from my computer simulations that you do not need any brainpower at all to benefit from forming a huddle.
THE GOD GAME
One can trace the efforts to link life and geography—in the guise of what are called spatial automata—to a study by the great John von Neumann, who believed that biological organisms could be thought of as information-processing systems. The fact that it is now possible to write and synthesize the genetic code of a living thing in the laboratory, like a glorified computer program, shows how right he was. He puzzled over the difference between the trivial kind of reproduction that enables crystals to grow in a test tube, for example, and the clever kind that enables creatures to breed. To explore the difference, von Neumann wanted to design a machine that was complex enough to reproduce itself.
To this end, he devised a “self-reproducing automaton,” a robot that was afloat on a sea of its own components, just as living things on Earth thrive and abound among the chemical building blocks of life. He built on the work of Alan Turing, the English mathematician who had laid the logical foundations of computing with the idea of the “universal Turing machine,” which offered a splendid abstract device to explore the theoretical limits of mathematics.
Von Neumann showed that there also exists a universal automaton, an abstract simulation of a physical universal assembler. Logical errors within the automaton could be viewed as mutations, allowing the possibility of more complex varieties of automaton to emerge; in an environment with finite resources, selection pressure—survival of the fittest—would lead to Darwinian evolution. But there was no mathematically rigorous way to analyze his creation, let alone the means to build one.
The mathematician Stanislaw Ulam gave von Neumann advice on how to make his self-reproducing machine simpler. He put forward a way that Neumann’s “machines” could be built of pure logic. Ulam suggested replacing the floating automaton with what he christened “tessellation robots.” This quaint term refers to the growth of crystals, which occurs by the buildup of unit blocks, or “tessera.” Today Ulam’s tessellation robot is called a “cellular automaton” and consists of an abstract array of cells programmed to execute rules en masse. This collection of cells—like squares on a chessboard—carries out computations in unison and can be viewed as a kind of organism, running on pure logic, though the cells in question have little to do with the real thing.
Each cell in the array is in a particular “state” at a given time. A state might be a certain color, say red, green, or blue, a numeric value, or simply
