for the way in which he had injected the rigor of math into biology to reveal the underlying order in the living world. He had studied whether stability is the cause of the diversity of ecosystems, or whether it is the other way round (it turns out that populating an ecosystem with a diverse range of living things does not automatically mean stability). He charted the relationships between insects and their parasites. Using mathematical models, Bob had revealed how connections between species could lead to fluctuations in the number of individuals. In this way Bob had introduced chaos into biology—revealing how apparently random and complex behavior is ordered by simple underlying rules (I am writing this at home while sitting at the very same desk at which Bob made this discovery—a gift from him to help furnish my first house).
Karl did not rate my chances of moving to Oxford very highly, so I had also applied to Berkeley and Göttingen. My future life, career, and everything now depended on insubstantial aerograms. As these air mail letters winged their way around the world my predicament was both romantic and sad. I was about to marry Ursula and our time in Vienna was drawing to a close. The melancholy of leaving home was tempered by the excitement of a new adventure. Neither of us knew where on the planet we would end up.
Initially, Karl’s judgment seemed spot on. Bob rejected me, saying he did not have a group. Nor did he work much with postdoctoral students. I wrote to him again, pointing out that I might bring along my own funding, an Erwin Schrödinger Fellowship. By this time, Karl was lobbying Bob too. Eventually, to my delight, he agreed. At last the next step in my career was clear—up to a point. I had absolutely no idea what to expect at Oxford.
Ursula and I got married in Vienna the month before our move. We said our goodbyes after the service and went home to our respective parents until the time came to catch a train for what would turn out to be a nine-year honeymoon, starting in 1989. The day of departure saw us laden with seven suitcases and two bikes. It was cold and windy. A battleship grey sky threatened a torrential downpour. Our families saw us off that night from the Westbahnhof in Vienna. A friend stiffly stood before me and formally shook my hand. “Don’t embarrass us,” he joked. As the train pulled out into the darkness, my new wife cried.
The next day, once the cross-Channel ferry had set us down, I caught my first glimpse of Britain. It was not William Blake’s green and pleasant land. The soil was cracked and dry. The grass and foliage were brown and the country was in the grip of a drought. Reservoirs were drained and there were hosepipe bans and fines for anyone found washing a car. In Plymouth, flower beds were being showered with treated sewage effluent. In one British zoo, dirty water from the penguin pool was being sprinkled on parched putting greens. As our train waited, a fire was put out on the tracks ahead.
My expectations took a sharp departure from reality once again, when I eventually walked into my new place of work, the Zoology Department at the University of Oxford, an unlovely concrete pile on South Parks Road. There were posters showing birds and other animals. But there was not an equation or diagram in sight. Was I in the right place? I was. And I would discover that I was lucky to be there. There was little in the way of formalities. Unlike the hierarchical Austrian academic system, which discourages lowly students from bothering busy Herr Professors, I found myself having an informal chat over a cup of coffee or afternoon tea with many influential figures, from the great Bill Hamilton, who did pioneering work on cooperation, to Sir Richard Southwood, Richard Dawkins, Paul Harvey, and John (later, Lord) Krebs. This was a wonderful, heady intellectual atmosphere. I fell in love with the place.
Bob May would sometimes play soccer with everybody—all the students and professors were as obsessed by games as I was. This was a worry, given that he was so intensely competitive. In the British tradition, winning was beside the point and taking soccer too seriously was frowned upon. But not when it came to this wiry, quick Australian. Fortunately for the rest of us, he was somewhat ineffective. Appropriately enough, the goddess of randomness did smile on him from time to time, however. During one early encounter, when the score was seven all and I was the goalkeeper, Bob kicked the ball past me in the very last minute of the game. Jubilant, Bob screamed: “Martin, this was excellent for your career!”
He and I are so different, the odd couple. He is a compact, frizzy haired wisecracker who has little sympathy for religion. I tower over him, a balding Catholic with a Schwarzenegger-like English accent that is a gift when it comes to recording the message on telephone answering machines (“I’m away at the moment but I’ll be back!”). Bob is endowed with a heady blend of traits: a passion for precision, an equal love of profanity, and a hilarious disdain for his peers (“A biologist is someone who wanted to be a scientist but was not good enough to be a physicist”). We were united by our love of games, from the mathematical to the physical, and we both wanted to win. He was bemused when I told him that, remarkably enough, my German lacks an everyday word for “competitive.”
Our rapport had an energizing effect on my work. For my first project, I followed up an idea that first came to me at a high-powered gathering organized by the German Nobel laureate Manfred Eigen in Klosters, Switzerland. During a talk there by Bill Haseltine on the human immunodeficiency virus, HIV, I realized that the body of an AIDS victim must harbor a swarm of closely related replicating viruses. This reminded me of my work with Peter Schuster in mathematical biology. One day, I thought to myself, I would like to develop a mathematical model of virus infections. But my respect at that time for the difficulty of solving problems was almost paralyzing.
I was fortunate that Bob had already studied the virus with a colleague, Roy Anderson. Together, they had charted how the virus spreads between people. But I wanted to take this approach in a new direction. I wanted to model what happens inside a person who is unfortunate enough to have been infected with the virus. That would require explaining how the virus spreads between cells in the face of attacks from the body’s immune system. To find out how HIV fares in the human body, I would have to use a brand of mathematics similar to that used in my tournaments with Karl.
I discovered that I could explain the puzzlingly long delay between HIV infection and AIDS and why this period can vary so greatly between patients—it could show up in less than two years in one person and yet lurk for more than a decade in another. What was remarkable was that I could draw my conclusions from existing data without the need for new experiments on animals or trials on patients. All I needed was a ready supply of computer number crunching power to explore the way that the virus breeds and mutates inside the body.
Bob was so thrilled by this result that he insisted that I show my findings to Roy Anderson, who was by then working at Imperial College London. He too was amazed. After I published the first results in the journal AIDS in 1990, an extended version of my theory and clinical data came out in the prestigious journal Science the year after. I worked, too, on hepatitis B virus with Barry Blumberg, master of Balliol College, who won the Nobel Prize for discovering the virus and making a vaccine. This kind of research helped to establish the field that is now known as virus dynamics, where mathematical models chart out the progress of virus infections within infected hosts.
SOARING EAGLES, DIVING STRATEGIES
Karl and I had so many games left to play, with so many variants and so many potential outcomes. In 1992, our work on Generous Tit for Tat was published in the British journal Nature, which shares with the American journal Science the distinction of being the journal that scientists want to appear in most of all. Karl and I had plenty of new ideas when it came to extending our work. My second summer at Oxford, I once again returned to Austria to resume our explorations of the Prisoner’s Dilemma.
Previously, Karl and I had calculated the strategies that emerge when the decision of a player only depended on the opponent’s last move. But, of course, this only gives a partial picture of what can happen. We now wanted to look at strategies that also take into account the player’s own moves. Let me give you an example to show exactly what I mean by this. Put yourself in the position
