After he wrote his famous equation, George Price cut his own throat with nail clippers.
Image: via New Scientist
January 6, 1975. A young Israeli immigrant pushes open the door of his north London squat to find the dead body of a homeless man. George Price had cut the carotid artery out of his own throat with a pair of nail scissors.
It was a bloody end for a troubled man who believed he had been chosen by God to reveal a secret about the true nature of love. His revelations may not have been divine, but they were inspired—and ended up contributing significantly to our understanding of evolutionary biology.
Price's journey from quirky Harvard dropout to delusional outcast was fueled by a desire to write his name into scientific history. After carrying out covert research on the effects of atomic radiation at the Manhattan project in the 1940s, he began working in cancer research and then into the newly emerging computer industry in the 60s. He claimed he came up with the idea of computer-aided design before having it stolen by his employers at IBM.
"There was something in George that was really frantically searching for greatness," said Oren Harman, author of The Price of Altruism, a biography about Price. "At one point before he moved to England, he was communicating with four separate Nobel laureates in four separate fields of research and with each of them he was trying to convince he had made some breakthrough that would make his name. Everyone was aware of his obvious intelligence but there was also something about his intellect which was like a diamond in the rough that hadn't been polished."
Price left his native New York in 1967, dissatisfied with the lack of scientific prestige he'd attained by his mid 40s. He left a steady job at IBM, too bitter to watch as an invention he felt was his took off in the hands of his colleagues. He left his wife and two young daughters.
The scientist was also partially paralysed due to a botched operation to remove a tumour from his thyroid. The surgery was carried out by an old friend who was a doctor, and left him needing to take vital medication in order to survive.
He arrived in London at the height of the summer of love. He would make his name in the course of a brief few years.
Price lived a very solitary life in London. He had never been particularly social, but he was now completely alone in a foreign city.
Perhaps it was thoughts of his abandoned family that drew Price to Bill Hamilton's work on kin selection, the idea that evolution can favour the survival of one's relatives over one's own reproductive success under certain circumstances.
Hamilton is now widely recognised as one of the greatest minds in evolutionary biology and perhaps the most influential since Darwin, but at the time he was relatively unknown. He had only just published the first of his defining papers when Price became interested in his work.
He showed, in essence, that when we think we are behaving lovingly, we are actually working on a carefully calibrated scale of self-interest
As with many of Price's previous academic pursuits, such as working in cancer research developing techniques of fluorescence microscopy, he had no previous involvement in the field.
"He became interested in the problem of the evolution of the family precisely as he was taking in the meaning of having abandoned his own family," Harman said.
Hamilton's kin selection theory offers an explanation for how altruism evolves within the extended family. Drive your sister to the airport and you are ensuring half your genes go safely on holiday, but it's probably not worth getting up at 4 AM for your cousin. Hamilton's rule (rB>C) elegantly describes how a behavioural interaction could evolve, so long as the benefit (B) to the recipient, weighted by their degree of relatedness (r), is larger than the cost (C) to the actor. This explains why bees sting—the cost of sacrificing their own life is smaller than the benefit of protecting the hive.
This was a landmark in the understanding of evolutionary biology. It suddenly became apparent that our genes weren't as loyally devoted as we thought. In fact they would quite happily see us dead as long as their replicas survived within the bodies of others. Richard Dawkins later popularized this idea in The Selfish Gene, describing humans as "robot vehicles blindly programmed to preserve the selfish molecules known as genes."
Price recognized limitations to Hamilton's rule; it didn't always work and it could only be used to explain certain behavioural traits. Its beauty is in its simplicity, but Price wasn't a simple man. He derived his own equation to describe not only kin selection, but evolutionary change in general.
"He went to the late opening libraries in London, came across Hamilton's paper and ultimately wrote an equation," Harman said. "Which he then took with him physically, off the street, walked up to the professor of biostatistics office at UCL [University College London], introduced himself and said 'My name is George Price, here's my equation, what do you have to say about this?' and he was very quickly given the keys to his own office and a fellowship was set up for him."
THE PRICE EQUATION
The Price Equation (wΔz=Cov(wi,zi)+E(wi,zi)) is a complete description of the relationship between a trait (z) and its relative fitness (w). The covariance part of Price's equation (Cov(wi,zi)) is a mathematical description of simple Darwinian logic. Covariance is a measure of association, so if you you have a trait which is positively associated with fitness it will increase in frequency. This is just a mathematical translation of the expression "survival of the fittest."
Things start getting interesting when we look at the expectation part of the equation (E(wi,zi)). This accounts for any factor that disrupts the process of natural selection (the covariance part of the equation). For example, one of these factors could be selfish genes acting in a way that is damaging to the individual.
"The best the natural process can do is a kind of second hand kindness, a selflessness which is not really selfless but rather very much selfish."
The equation allows us to explore the effects of natural selection from different perspectives. For instance, do entire populations compete with one another in the same way the individuals compete? Or, do selfish genes behave similarly to selfish people?
Instead of modelling the traits and fitness of individuals, we could model the traits and fitness of a set of groups. The covariance part of the equation (Cov(wi,zi)) now describes the selective pressures occurring between competing groups and the expectation part (E(wi,zi)) describes the factors disrupting those selective pressures. This allows us to model how the behaviour of selfish individuals compromises the fitness of the group much like the behaviour of selfish genes affecting the fitness of the individual.
The Price equation explained how all behavioural traits have evolved because they are beneficial to some entity within the biological hierarchy: be it the social group, the family, the individual, or the single gene. He showed, in essence, that when we think we are behaving lovingly, we are actually working on a carefully calibrated scale of self-interest.
Price began attracting the attention of some of the biggest names in evolutionary biology. He and Bill Hamilton were beginning to form a formidable working relationship and close friendship. But his behaviour was becoming extremely erratic.
"I'VE GOT HOTLINE TO JESUS"
Having been an outspoken atheist and ultra-rationalist his entire life, Price suddenly converted to evangelical Christianity. He spent days obsessively reading the Bible, searching for hidden codes. Jesus came to him in a vision, he claimed, to say he had been chosen by God to share his equation and its implications with mankind.
Now believing his destiny to be in the hands of a higher force his actions became increasingly fatalistic. Price believed he was obeying direct commands from God. He declared himself a "slave" and stopped taking his thyroid medication in order to let God decide whether he lived or died.
Price was finally beginning to gain some academic recognition
"He thought he had been chosen by a deity to reveal these things to humanity," Harman said. "He tried to convince Hamilton to help him find codes in the Bible because he thought he and Hamilton had a similar type of intelligence, a similar kind of penetration. But Hamilton of course was an atheist, a nonbeliever and loved George very much but thought he was completely crazy."
"I think he reached a conclusion that if you could formalize the evolution of trait such as altruism, what it meant is that altruism is never what you think it is," Harman said. "There is that famous quote, 'you scratch an altruist and watch an egoist bleed.' Basically what George thought the equation meant was that since you can explain formally how a trait like altruism evolves, what it means is that the trait is always to the advantage of whatever level in the biological hierarchy that it is evolving within. So the best the natural process can do is a kind of second hand kindness, a selflessness which is not really selfless but rather very much selfish."
One colleague at UCL recalls him marching down the corridor shouting "I've got a hotline to Jesus." But despite his psychological irregularity, he was already turning his mind to new ideas about the evolution of sociality.
Price had previously been immersed in Cold War politics through working on the Manhattan project, and by the 1950s he was writing hawkish magazine articles warning of the menace of communism and the need to win the arms race. In 1957 he published an article, titled "Arguing the Case for Being Panicky," describing how the USA would soon be part of the USSR unless they were well aware and prepared for the Soviet threat. His reasoning was based on the strategic decision making process known as game theory.
After establishing himself in the field of evolutionary biology, Price turned his interests back to the political and economic arguments of the Cold War and started working on the Nash equilibrium.
EVOLUTION AND GAME THEORY
"Individual ambition serves the common good" so said the father of modern economics, Adam Smith. What he meant is everybody ruthlessly pursuing their own objectives results in the most positive collective outcome. But John Nash saw things differently. Whilst studying for his Ph.D. at Princeton University toward the end of the 1940s, he recognized flaws in Smith's theories. Nash realized that the best decisions people could make were based on the actions of others. When everybody is acting in a way that is maximally beneficial to the group as well as themselves, we have Nash equilibrium.
In the Nash biopic, A Beautiful Mind, they give the example of everybody trying to pursue the most attractive girl at a bar; everybody blocks the other's attempts. By the time they have given up on the beautiful girl, her friends aren't up for second place. But he says if they all go for the slightly less attractive girls from the beginning, "we don't get in each other's way and we don't insult any of the girls. It's the only way we win. It's the only way we all get laid."
Almost 25 years after Nash produced his Ph.D thesis on game theory, Price picked up on the Nash equilibrium and started working with another acclaimed evolutionary biologist, John Maynard Smith.
"I think George felt that at one point science wasn't enough, that people had to change the world and he was going to do it."
In November 1973, Price and Maynard Smith coauthored a landmark paper called "The Logic of Animal Conflict" introducing the idea of the evolutionary stable strategy, or ESS. An ESS occurs when an entire population adopts a behavioural strategy which no mutant strategy can successfully invade. Just like the Nash equilibrium, this occurs when every individual is making the best decision for themselves based on the decisions made by every other player.
The evolutionary stable strategy explained why, for instance, male reindeer have vast unwieldy antlers that are more decorative than dangerous. It shows that ultimately it benefits the individual if the males can engage in skirmishes but not full-blown combat. This mechanism of damage limitation is an example of an evolutionarily stable strategy.
The paper completely revolutionised the way biologists thought about behavioural evolution, and Price was finally beginning to gain some academic recognition. Harvard's celebrated evolutionary biologist Richard Lewontin had previously been dismissive when Price had attempted to attract his attention, but he was now writing to Price admitting he had been "too stupid" to understand his work and that he hoped they would communicate in the future.
IN PURSUIT OF SELFLESS LOVE
You might have imagined George Price was dining out on his recent success, but you would be wrong. Fueled by his disturbing visions of Christ and perhaps troubled by the apparent dark heart of altruism, Price had given away most of his possessions and money to the homeless and vulnerable around Camden.
"If what science teaches us about love and giving is that it is never truly selfless love and sacrifice, then there is a problem, and so what George set out to do was to try and transcend that paradox," Harman said.
"That's what led him to the streets of London," Harman said, "and led him to the notion that what he was meant to do in life was to be a great altruist. I think he reached a point where he thought 'okay all of this giving on my part is wonderful, this is my attempt to transcend my own miraculous mathematics. But is it truly genuine? Am I giving to the homeless person because I really am a truly selfless individual?'"
"I wasn't going to marry George, but I never said yes and I never said no."
Price had turned away from obsessive Biblical study, deciding to put its teaching into practice, thereby testing the limits of his own altruism. In a letter sent to Maynard Smith in 1972, Price wrote "I am now down to exactly 15 pence... Thus I reassure myself by telling myself that God's standards of disaster will shortly be satisfied. I look forward eagerly to when the 15p will be gone." Soon enough he found himself sleeping on the streets and cleaning toilets in an office off the Euston Road.
Price eventually found shelter in Tolmer's Square near Euston Station. A stone's throw from UCL, it was a counter culture hub, a squatter's community with a collectivist ethos. The Cold War hawk was now rubbing shoulders with people who had no intention of following the script.
"It was the 70s," said Sylvia Stevens, an old friend of Price's from Tolmer's Square. "It was a time when the political and the personal were coming together. We squatted as a political act because there were lots of empty buildings and there was not enough housing. There was a guy and his wife who started a bread shop, they had a £10 note nailed to the wall with a note saying 'we don't take money.' It was like this commune and lots of different kinds of people were very tolerant of each other."
Price, now homeless, took up easily with this crowd. "George was just another one of the people who was around," Stevens recalled. "You can see if he was homeless how he would gravitate toward somewhere like Tolmer's, rather than being under the bridges or under the arches. You know, there was stimulating cultural life."
Stevens, a director and co-founder of a film production company in North London, was only 20 when she met the middle-aged Price. She remembers him as eccentric, yet endearing. She had no idea that he was even a scientist—let alone one of such stature—until she was contacted by Oren Harman just a couple of years ago while he was researching for Price's biography.
"One time he gives his shoes away, you know, then he doesn't have any shoes," she recalled. "I don't know if the person who took his shoes needed his shoes. Maybe they did, maybe they didn't. I think George felt that at one point science wasn't enough, that people had to change the world and he was going to do it."
"He was a troubled man but I always knew from the beginning he was somebody who had had another life which was probably quite high powered," Stevens said. "But, he had this idea that he was going to marry me. He always wanted us to go back to America, to live in the Midwest, have lots of kids and dogs and cats…"
When Price was found dead, he had left his parting message to Stevens. "It basically said I wasn't going to marry him… I almost hesitate to say this because it sounds too dramatic and I can't remember the exact words," she said. "But basically, he said that it was very difficult that he wanted to have this new life with me and I didn't want to have this new life, and he didn't see any purpose of going on and that was it." Suicide wasn't mentioned in the letter.
"I wasn't going to marry George, but I never said yes and I never said no," Stevens said. "It was more you felt like this person needs their fantasies and it was like 'okay yeah George c'mon, you know I'll see you tomorrow.' That sounds dismissive, but it wasn't dismissive because you didn't know half the time with George what was real and what wasn't real."
George Price died alone with no wealth or possessions, so it is unsurprising he is now buried in an unmarked grave in St Pancras Cemetery.
"Very few people followed him on his last way to his grave." Harman said. "There were maybe 10 people there on that cold January day in 1975, at least half of whom were George's last companions on the streets of London. Homeless people upon whom he had descended on like an angel almost to try and help them, who had no idea that he was a scientist of any kind—and then two of the great scientists of the age, Bill Hamilton and John Maynard Smith. And I think Hamilton and Maynard Smith were really the very small minority of important scientists who had understood George's contribution." Hamilton went so far as to say Price was "perhaps the most brilliant thinker he had ever met," according to Harman.
George Price's extraordinary work validated many conflicting views, simplifying and unifying complex ideas about the evolution of behaviour. But in the end, Price felt that science could no longer answer the questions that he was trying to ask.
Perhaps his own conclusion that we are being driven blind toward our destinies by the unseeable powers of our genes was too much for this sensitive man whose science was unhinged by his emotion.
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