China and America: After you Cool War: The Future of Global Competition. By Noah Feldman. Random House; 201 pages; $26. Buy from Amazon.com DURING the cold war the world was divided into two camps, each one bristling with missiles and bent on the other's destruction. A miscalculation, many feared, could annihilate mankind. As was clear from last week's friendly meeting between Barack Obama and Xi Jinping (pictured), the leaders of America and China, today's rivalry between these two nations is quite different. Unlike the Soviet Union, China does not dream of fomenting a global revolution. Though nominally communist, its ruling party has no real ideology besides a determination to remain in charge. So the tension between the world's biggest powers is less dangerous today than it was a generation ago. A "Cool War" has replaced the old cold one, says Noah Feldman, a Harvard academic. This is a timely book. Throughout history, rising powers have come to blows with waning ones: think of Germany in 1914 or Japan in the 1930s. Some suppose that a rising China is doomed to clash violently with America. Not necessarily so, says Mr Feldman. Both sides have too much to lose. Economically, they are more intimately entwined than any previous pair of rivals. The old Soviet block barely traded with the West. China not only trades with America on a stupendous scale but also holds much of its debt. A trade embargo would cripple China's economy. That would undermine the Communist Party's main claim to legitimacy: that China has prospered under its rule. And that in turn would threaten the party's precious grip on power. So it "would simply be irrational" for China and America to go to war, Mr Feldman writes. Alas, just because something is irrational does not mean it will not happen. The Communist Party's other claim to legitimacy is that it embodies Chinese nationalism. As growth slows and the Chinese people tire of being robbed by corrupt officials, Beijing may feel tempted to crank up the aggression in its backyard. Taiwan is the scariest flashpoint. China claims the island; America has vowed to defend it. For America to abandon Taiwan altogether would signal that it is no longer the sole superpower. Its Asian allies would no longer trust its security umbrella. They would have no choice but to find some accommodation with China. China does not need to match America's military strength. All it needs is to be powerful enough to deter the United States from fighting it over Taiwan. Controversially, Mr Feldman thinks the tipping point is close. And if Taiwan decides that it cannot count on America, he thinks it may have to negotiate the best deal it can get: perhaps something like Hong Kong's (in which the former British colony bowed to Beijing's rule while keeping old freedoms). China's ambitions are largely pragmatic. It seeks regional sway and global access to markets and minerals. It covets African oil, but cares little how Africa is governed. The destabilising ideology in the cool war comes from the West, reckons Mr Feldman. Since China's rulers are unelected, many Westerners believe them to be "fundamentally illegitimate." Think of it from the Chinese leaders" point of view, he urges. They must sit down with negotiating partners who would like to see their regime crumble. "This is not a good starting point for mutual trust or respect," he warns. True enough, but trust and respect must be earned. Mr Feldman sees a future of economic co-operation and geostrategic rivalry. In their different ways, the two powers are racing to recruit allies. China offers trade without lectures on human rights. Many regimes prefer this to American moralising. The trouble is that the ones which find China most attractive, such as Iran, North Korea and Sudan, are hardly the most attractive allies. America still has a big advantage when dealing with democracies. Mr Feldman is sharp, logical and as cool as his book's title. A law professor with a doctorate in Islamic thought, fluent in Hebrew and Arabic, he helped draft Iraq's post-war constitution. That process may have left him sceptical of democracy's universal appeal. He predicts that China's unelected regime - and with it, the cool war - will last longer than is generally expected in the West. Perhaps. But the cold war showed that autocracies are brittle. When the end comes, it can come suddenly.