People of Armenian descent learned early.

To describe the violence done to them around 1915, the young 20th century had to find a new word. Theirs was the first example of the use of the French word, genocide: 1.5 million lives, tiny or aged, intellectual or peasant, removed from the planet.

But those were early days. Another cliché interrogated by Richard Bessel is that things had barely got going in 1915, that by the time humankind finished with the century 100 million had perished. It's an ugly round number; a best guess; a rough way of saying, time and again, that the 20th was the most depraved of Christian centuries. It was, in the words of Charles Maier, an epoch of "moral atrocity".

That sounds hard to dispute. Armenia, the Shoah, Cambodia, Rwanda: what - comes the question - will we not do? Statistics flood over us. But Bessel is subtle. There is, for one thing, the self-advertising claim of a Harvard guy and psychologist, Steven Pinker, who insists that the 20th century wasn't so bad, that it was probably "the most peaceful moment of our species' time on earth".

Again: hard to dispute. Hard to dispute, that is, if you happen to be white, male, European or American, born after 1945, not classed as an economic asset or a foodstuff, and teaching at Harvard. If all that is true, these have certainly been the best of times. It is patently better to be a suburbanite chap grumbling now over the morning commute than a woman amid the Thirty Years' War.

Pinker isn't crass, though. He wants to say that, despite the headlines, humanity is, slowly, finding its way. Those who hand us our "economic solutions" thanks to the economic failures of capitalism are, perhaps understandably, keen to agree. They like those Planglossian answers. Bessel prefers more intriguing questions.

Why does violence now trouble us so? Why do we no longer treat a good hanging or a bit of animal torture as an afternoon's entertainment for the family? If we are safer than ever before, in the white northern world, why do we panic at even the verbal expression of the implied threat of potential violence? Are we luxuriating in special pleading, or beginning - at last - to understand ourselves a bit better?

Bessel writes of a "contemporary sensitivity to violence". For him, that's the puzzle, a useful puzzle: the old bestiality alongside a modern, near-Socratic wonder at the nature of the beast. As the author observes, the study of violence has itself become an academic "growth area" in recent years. When peoples were rampaging across continents and laying waste to other peoples, the subject was not much discussed, and never taught. But then, human rights were not much discussed by the old hordes.

Like most of what matters, it flows from the Enlightenment. The idea that you can have a right not to end in a bloody mess in a ditch is, historically, novel. The idea that you can have rights of any description is recent enough. Today, a phrase such as "economic violence" is not disputed. The idea that violence can be done to a woman just with words is not - or not often - argued over. And all of this is new.

The fact that we can even talk properly about what violence means is one of those "Enlightenment values" that causes American conservatives to reach for the assault rifle. But Bessel is right: we have a discourse now based on the broad agreement that a discourse is possible. So what, actually, are we talking about? Our western awareness of what violence ordains - our "sensitivity" - does not explain fear. Just "Barbarians are coming and I don't want to die"?

Violence: A Modern Obsession is a rich book. A lot is packed into 300 pages. What emerges is painfully clear. First, that the 20th century was indeed stupendous in its hellishness. It astonished those who began with Victorian educations. It made them step back and wonder, much as Bessel wonders, over the nature of the talking ape. "Progress", that human boast, was held in doubt as the immense, industrialised slaughters swept the globe.

But the white, north hemisphere folk got rich. They acquired the delusion that all the old nightmares were buried in the cellar called "history". If their lives could be so transformed, so distant from all that grandparents endured, what was violence if not a threat to sanity? The Hitler War was fought, in essence, to do away with lunacy, to ensure stability, to guarantee rights.

Women wanted those. Bessel is especially good when describing how the understanding of violence has developed through waves of feminism and the challenge to what men, left to their own devices, will do. A male reviewer describing a book written by a man can only wonder, after that phrase, what violence still means. Bessel does not contend that we are at the end of this story.

We are telling the story, however. "The media" also count in this. Violence, in all its senses, is something we talk about endlessly now in ways the species has never talked before. The marvel of Bessel's book is that it makes you wonder about your reality. Why does violence trouble us so?

Because we have, like a class attentive to its own failures, paid attention and learned from Rwanda or Armenia? Because we have an uneasy knowledge that it could all happen again? Or because the species has a dire habit of committing acts it cannot acknowledge, far less understand?

Bessel, with his grounding in recent German history, has not written a polemic. Only mildly does he reprove those who claim to know how things tend. Instead, his dazzling book says (I paraphrase) this: "We have become self-aware. The 20th century has reminded us of what we can be. We know it. What do we do with that knowledge?"

People of Armenian or Rwandan descent might say that it is too late to matter. Studies of violence and the evolving studies of the histories of violence didn't help them. Having achieved its Enlightenment, Europe still sent its gunboats and its slavers. US Strategic Air Command still, for decades, carried the motto "Peace is our Profession". But if we cannot think, we cease to justify "sapiens" in the job description.

There's an oddity, however. The animal that grows more "sensitive" to violence has not ceased to be violent. First, it hides behind the euphemisms of human collateral "damage". Then it takes refuge in technology, from strategic bombing to drone killing. It runs from the scene. But within the insulation of machines and verbiage people lust as merrily as ever for more blood, more death, more violence.

If Bessel's book does its job - and it surely will - you will think a little more about what violence truly means, how it happens in our world. and why it yet survives. If the volume fails in that, it was probably written with you in mind. The question is paradoxical: if we think more about our violence, is our violence less likely? We might not be the right species to answer the question.

Violence - A Modern Obsession by Richard Bessel is published by Simon & Schuster, priced £20