A few years ago, I read a terrific collection of essays — It Must be Beautiful — on the great scientific equations of modern times. I loved it, but as I meandered through the book, I was struck by an unexpected poignancy. The first essays, by and large, described breakthroughs that had taken place in the laboratories of Europe. The second half was quite different. Some time in the 1920s, the balance of scientific discovery shifted inexorably to the U.S. A small book of essays held within it proof of a profound historical change.

I found myself thinking of that while reading a new book by Martin Jacques, a British journalist turned academic. Jacques’ tome is called When China Rules the World: The End of the Western World and the Birth of a New Global Order, and his thesis, which he advances with a depth of argument often missing in similar works, is made plain enough by his title. The most likely scenario for the future, Jacques writes, is that “China continues to grow stronger and ultimately emerges over the next half-century, or rather less in many respects, as the world’s leading power.” His book is an examination of how and why that will happen, and what it will mean.

Jacques is right that China’s continued development will be one of the forces that shapes the century. It is equally true, as he argues, that China will not be just any old superpower. It has its own distinctive combination of attributes: a huge population, a sense of its identity as a civilization as well as a nation state, a long-standing influence on the nations and cultures that border it, and a diaspora that impacts not just its region but the world. China’s habits of governance, Jacques argues, are not those of the Western world; its values (let us say harmony and stability, rather than liberty and justice) are not those of the West. The roles of both the state and the extended family as social mechanisms in China differ from those in modern Western societies. All of this, Jacques argues, means that the 21st century will be one of “contested modernities.” Until around 1970, he says, modernity was, with the exception of Japan, “an exclusively Western phenomenon.” But as China assumes a bigger role in global economics and politics, that is changing.

I agree with much of this. We have learned in the last 20 years that there are many ways of being modern, and that Western liberal democracy is but one of them. But that little collection of essays on the great equations reminds us that a society’s characteristics today will not necessarily shape what it will look like tomorrow. History rarely runs in straight and predictable lines. At the end of the 19th century, Germany — or perhaps more accurately, Germanic central Europe — was a technological and scientific powerhouse, its universities nurturing geniuses like Einstein, Heisenberg and Schrödinger, whose discoveries changed the way we thought of, well, everything. Then came the carnage of World War I, the rise of fascism and communism, the mass murder of European Jews and the flight of those who could escape it, often to the U.S. All of this contributed to a shift of the center of scientific progress away from Europe. Some aspects of the great European disaster might have been foreseeable in 1909, but none with any certainty. There are too many futures for them all to be known.

This is particularly apposite in the case of China, a country with not only many possible futures, but (as it were) many pasts. There is a crude but commonly held thumbnail sketch of modern Chinese history that goes something like this: Two centuries ago, European powers tried to open a hermetic society to trade; they failed until the Opium Wars forced the issue; China then entered an era of foreign domination and internal chaos, which ended with the imposition of political stability by the Communist Party in 1949; in 1978, after another round of internal unrest, China chose to modernize its economy and adopted market mechanisms to do so, with astonishing success. Cut (in the movie version of this story) to a shot of the crazy skyline of Pudong from the banks of the Huangpu in Shanghai.

This isn’t baloney, but it is hardly the whole story — as you would discover if, instead of being mesmerized by the sight of Pudong, you were to turn around and look at the solid, early 20th century buildings of the Bund, just behind you. Modernity did not come to China because Deng Xiaoping said it should. As Rana Mitter of Oxford University argues, there had been modernizing streams in Chinese society long before 1978, and had some of them taken a different course, our view of what China represents for the future would be unrecognizable from the standard text. (Just imagine what we would think if China had become a constitutional monarchy in the late Qing period. Impossible? Japan managed it.)

Chinese élites, we often forget, have had economic and cultural links with Europe for 300 years; by the 18th century, the Chinese were producing porcelain for the European market and avidly studying European art and architecture. In particular, says Mitter, the first half of the 20th century — that period when Shanghai was at its peak, but which is routinely dismissed in the thumbnail history — is “really important; the questions about their society that Chinese are asking now are very similar to the ones that they asked in the 1920s and 1930s.”

Moreover, just as there have been many Chinese yesterdays, so there are many versions of China today. It is astonishing how many predictions that China will not adopt liberal values in the future ignore the part of China that already has. For Taiwan, as Mitter says, has a deep sense of Chinese cultural identity (more so than the mainland, arguably) and yet is a “highly modern, liberal democracy.” Who knows? The island may yet turn out to be a model for China as a whole.

How China develops internally, and how it changes the wider world, will depend on an infinite number of contingencies. A crucially important one, obviously, will be how China and the U.S., the dominant global power, get along. As Barack Obama said on July 27, “the relationship between the United States and China will shape the 21st century.”

There is a lively debate in both countries as to what that relationship will look like. As Obama said, “Some in China think that America will try to contain China’s ambitions; some in America think that there is something to fear in a rising China.” Part of the difficulty in predicting the future is that China is not the only Asian power with which the U.S. has to deal. For decades, Washington is going to have to play a demanding diplomatic game in which it maintains good relations with China, with India (Secretary of State Hillary Clinton’s recent trip there was evidence of the importance the U.S. now attaches to New Delhi), and with its old ally Japan.

This will not be easy. Somehow, U.S. diplomats must help convince all three Asian nations that they can rise together, rather than descend into bitter rivalry. Japan will need special attention; its politics are becoming worryingly sclerotic, and it is beginning to feel overshadowed by China. Tokyo may soon need reassurance that Washington still takes the alliance seriously. But for all the difficulties ahead, the accompanying charts should give a glimmer of hope. The U.S. and the three Asian giants are becoming ever more closely interconnected — and not just economically. We have become familiar with the way in which trade flows between China and the U.S. have grown exponentially. But there are now some 70,000 Chinese students at universities in the U.S., and an ever growing number of American business leaders and young people who consider a spell in China an important rite of passage.

History, as always, acts as a useful damper on overconfidence. Whole shelves of studies have been written on the mutual familiarity of German and British élites in the decades before World War I — which did nothing to prevent the two nations going at each other like frenzied dogs. The point is simple: China may amaze us today, but nothing about its future is certain. Its rise, like Germany’s 100 years ago, could lead to murderous rivalries. Or it could help usher in a period in which more of humankind has more material benefits, enjoyed in peace, than has ever been known before. We can only watch, and wonder.

Michael Elliott