Is altruism simply self-interest in disguise? And can a mathematical equation hope to answer the question?

In 1968, an academic almost unknown in the UK walked into University College London and presented its staff with an equation so remarkable, that they offered him an honorary position and the keys to his own office.

His name was George Price, and his equation addressed a problem that has vexed scientists since Charles Darwin published On The Origin of Species more than a century earlier. If we are selfish creatures, engaged in a battle for survival, why do we display altruism? Why do we show kindness to others even at a cost to ourselves?

Price's equation explained how altruism could thrive, even amongst groups of selfish people.

The maths of altruism George Price, 1922-75 Born in the US, moved to London in 1967

Specialised in selfish gene theory, socio-biology, evolutionary psychology and altruism

Jewish born-again Christian who spent his final years ministering to the poor

"He perfected an existing mathematical equation that shows how altruism can prosper among basically selfish animals - even humans" - the Independent WD 'Bill' Hamilton, 1936-2000 Born in Cairo to New Zealand parents, brought up in rural Kent

Naturalist and population geneticist

Specialised in sexual selection and parasite-host interactions

"All his major works [drew] on mathematical structures... He covered pages in algebra, and often drew scribbled diagrams to help his line of thought" - Guardian obituary

It built on the work of a number of other scientists, arguably beginning with JBS Haldane, a British biologist who developed a theory in the early 1950s. When asked if he would sacrifice his own life to save that of another, he said that he would, but only under certain conditions. "I would lay down my life for two brothers, or eight cousins."

Haldane's reasoning was a simplistic explanation of a theory that has come to dominate evolutionary biology - that of "kin selection".

Since he would share 50% of each brother's genetic makeup, and 12.5% of each cousin's, his genes would survive even if he were to die.

It took until the early 1960s for another scientist, William Donald Hamilton, to popularise the theory. He wrote a simple equation to explain that an organism would demonstrate self-sacrificing behaviour if it would enhance the reproductive chances of those it was closely related to.

In 1967 Price arrived in London from the United States, where he had been a scientist and journalist, but with no background in the field of evolutionary biology.

He discovered Hamilton's theory in a public library and thought he could improve upon it. Working in seclusion, he rewrote the equation in a simpler but more wide-reaching way. It explained the relationship between different generations of a population, and could be used to show how the prevalence of particular traits would change over time.

Although it was a fairly simple statement, it had never been expressed in clear mathematical terms, and the staff at the University College London recognised his insight as wildly original.

Image caption The Price equation

A debate about the scientific roots of altruism still rages to this day, but kin selection remains a hugely influential theory, and Price's contribution is held in high regard by many.

George killed himself due to his interpretation of the equation Oren Harman

"It underpins a lot of modern evolutionary biology research," says Andy Gardner, an evolutionary biologist at Oxford University, who uses the Price Equation in much of his work.

Oren Harman, who wrote Price's biography in 2010, says the view is shared by plenty of people in the field.

"Although there are those who fail to see the precise use of the equation, others think of it as the most simple and brilliant description of the dynamics of natural selection."

But Price began to find the implications of his work very difficult to deal with, according to Harman. If altruism was simply an attempt to ensure the survival of one's own genes, could it be considered altruism at all?

Lee Dugatkin, professor of Biology at the University of Louisville, thinks it was this thought that triggered a major change in Price. "That was what got him going," he says. "He was so depressed when he found out that Hamilton was right."

In the summer of 1970, Price became a devout Christian and embarked on a radical project - giving himself over to the service of others.

"He was going to go out to try and show that human beings are the only species that can beat out their own nature. And he was going to do that by becoming a pure selfless altruist," says Harman.

Price began giving money to homeless people, and invited many of them to live with him in his flat near Oxford Circus. His increasingly erratic behaviour left him penniless. He left his flat and eventually moved into a squat in Kentish Town.

It is not universally agreed that Price's equation triggered his downfall - he was undoubtedly suffering from some form of mental illness as well. And in the winter of 1975, Price took his own life.

For Harman, the two are inextricably linked. "I think the fact that George killed himself due to his interpretation of the equation really focuses the problem to the utmost degree."

Price's story is laced with tragedy, but need his scientific work imply a dark, depressing view of human nature?

Samir Okasha, professor of the philosophy of science at Bristol University, thinks not. "The idea that what evolutionary theory shows is that altruism is self-interest in disguise is, to my mind, a questionable thing to say."

Behaviour in some animal species is indeed genetically determined, he says, but with humans "that certainly isn't the case". He argues that culture sets us apart from animals in that respect, and points to the huge variance in social norms in different countries, and over short periods of time.

"We have seen rather dramatic change over, say, a 300-year period, which cannot be explained by genetics," he says.

Harman also disagrees with Price's interpretation of his own work. "It is not a necessary logical conclusion. It was his own conclusion, the conclusion of a troubled mind, but it's what led him to a terrible realisation that there is no true kindness in the world.

"If we want to understand behaviour, biology is part of it - it has to be by definition. But that's never an entire and complete explanation for the complexity and grandeur of the human condition."

Gardner thinks it is always possible to think of people as attempting to protect and reproduce their own genetic material. "But that's not necessarily always selfish," he says. "There's room for altruism in that logic."

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