In short, it’s not hard to find anecdotes that seem to contradict a guiding principle behind much of Pinker’s work – which is that science and human reason are, slowly but unmistakably, making the world a better place.

Repeatedly during our conversation, I seek to puncture the silver-haired professor’s quietly relentless optimism. If the ongoing tolls of war and violence can’t do it, what about the prevalence in America of unscientific beliefs about the origins of life? Or the devastating potential impacts of climate change, paired with the news – also released in the week we meet – that 23 per cent of Americans don’t believe it’s happening, up seven percentage points in just eight months?

I try. But it proves far from easy.

At first glance Pinker’s implacable optimism, though in keeping with his sunny demeanour and stereotypically Canadian friendliness, presents a puzzle. His stellar career – which includes two Pulitzer Prize nominations for his books How the Mind Works (1997) and The Blank Slate: The modern denial of human nature (2002) – has been defined, above all, by support for the fraught notion of human nature: the contention that genetic predispositions account in hugely significant ways for how we think, feel and act, why we behave towards others as we do, and why we excel in certain areas rather than others.

This has frequently drawn Pinker into controversy – as in 2005, when he offered a defence of Larry Summers, then Harvard’s President, who had suggested that the under-representation of women in science and maths careers might be down to innate sex differences.

“The possibility that men and women might differ for reasons other than socialisation, expectations, hidden biases and barriers is very close to an absolute taboo,” Pinker tells me. He faults books such as Lean In, by Facebook’s chief operating officer, Sheryl Sandberg, for not entertaining the notion that men and women might not have “identical life desires”. But he also insists that taking the possibility of such differences seriously need not lend any justification to policies or prejudices that exclude women from positions of expertise or power.

“Even if there are sex differences, they’re differences in the means of two overlapping populations, so for any [stereotypically female] trait you care to name, there’ll be many men who are more extreme than most women, and vice versa. So as a matter of both efficiency and of fairness, you should treat every individual as an individual, and not prejudge them.”

It is generally assumed that anyone who takes human nature seriously will be a fatalist, and probably politically conservative. If we’re pre-wired to be how we are, the reasoning goes, we might as well accept it and give up on hopes of any change. One way of interpreting Pinker’s most recent book, The Better Angels of Our Nature, is as an 800-page doorstopper of a riposte to this idea. Not only can we change, but when it comes to arguably the most important measure of improvement – the violence we inflict on each other – we actually have changed, to an almost incredible degree.

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“I had very often come across the objection that if human nature exists – including some ugly motives like revenge, dominance, greed and lust – then that would imply it’s pointless to try to improve the human condition, because humans are innately depraved,” says the 59-year-old, whose distinctive appearance – today he is sporting black cowboy boots – frequently gets him stopped in the street. “Or there’s an alternative objection: that we ought to improve our lot, and therefore, it cannot be the case that human nature exists.”

Pinker puts all this down to “a fear that acknowledging human nature would subvert any attempt to improve the human condition”. Better Angels argues that this is a misunderstanding of what human nature means. It shouldn’t be identified with a certain set of behaviours; rather, we have a complex variety of predispositions, violent and peaceful, that can be activated in different ways by different environments. The book’s title, drawn from Abraham Lincoln’s first inaugural address, is “a poetic allusion to the parts of human nature that can overcome the nastier parts,” he explains.

But Better Angels is notable above all for the sheer weight of evidence it amasses, culled from forensic archaeology, government statistics, town records, and studies by ‘atrocitologists’ of historical genocides and other mass killings. The book demonstrates that homicides, calculated as a proportion of the world’s population at any given point, have plummeted; when you look at the numbers this way, World War II wasn’t the worst single atrocity in history, but more like the tenth.

Pinker dwells, in sometimes unnerving detail, on horrifying methods of torture once considered routine. “The Heretic’s Fork had a pair of sharp spikes at each end,” he writes, in what is definitely not the most appalling passage. “One end was propped under the victim’s jaw and the other at the base of his neck, so that as his muscles became exhausted he would impale himself in both places.”

“Human nature or no human nature,” Pinker says, “it’s just a brute fact that we don’t throw virgins into volcanoes any more. We don’t execute people for shoplifting a cabbage. And we used to.”

He offers a multi-pronged explanation for this decline, from the rise of the state and of cities, to literacy, trade and democracy. Whether this constitutes an across-the-board endorsement of scientific rationality may be debated. (“Like other latter-day partisans of ‘Enlightenment values’,” the critic John Gray wrote, “Pinker prefers to ignore the fact that many Enlightenment thinkers have been doctrinally anti-liberal, while quite a few have favoured the large-scale use of political violence”.) But it’s hard to question the basic finding that your chances of meeting a sticky end, all else being equal, are vastly lower in 2014 than they were in 1014.

If Pinker’s message has proved hard for some to swallow, that may be because our standards are improving even faster than our actual behaviour, giving the misleading impression that things are getting worse. “Hate attacks on Muslims are deplorable, and they ought to be combated, and it reflects well that we’re concerned when they do occur,” Pinker says. “But by the standards of past pogroms and ethnic cleansings, they’re in the noise: this is not a phenomenon of the same magnitude as the ethnic expulsions of decades past.”

We’ve even witnessed the emergence of whole new categories of condemnable acts. Take bullying, says Pinker: “The President of the United States gave a speech denouncing bullying! When I was a child, this would have been worthy of satire.” As we continue to construct a social environment that activates more and more of our peaceable dispositions, and fewer and fewer of our aggressive ones, the remaining instances of bad behaviour stick out like ever-sorer thumbs.

What’s more, evolutionary psychology, one of Pinker’s several specialisms, can explain why. For reasons that long ago made excellent sense, our brains are adapted to focus on bad news over good, vivid threats over vague ones, and recent horrors over historically distant atrocities. Our elevated levels of anxiety about the future might actually be a sign of reason’s triumph.

“It could be interpreted as a sign of our growing up,” Pinker says. “We worry about more things, because we know that there are more things to worry about. Every time we go to a restaurant, we worry we might be ingesting saturated fats, or carcinogens. For my parents’ generation, the main concern about food was: ‘Does it taste delicious?’”