It will not quite have the significance of Nixon in China – I can't see an opera about it – but President Obama's visit there does have huge significance.

In 1972, when President Nixon went there, it was the leader of the world's largest economy opening up the relationship with the leaders of the world's most populous country. Now it is the leader of the world's largest economy meeting the leaders of the second largest economy, for China is currently passing Japan in the economic league table to take the number two spot. If, in another 37 years' time, the president of the US visits China, it will be the leader of the world's second largest economy visiting the world's largest one.

That is the context that overshadows this meeting: the stark fact that over the next generation the baton of economic leadership is being passed from one giant to another. It is as important as the shift of power that took place from Europe to the US in the last century.

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All the debate in Beijing about trading relationships, climate change, human rights, intellectual property and so on – the whole caboodle – has to be seen in this context. For the time being the Chinese economy remains much smaller than that of the US. But soon it won't be. China knows that, and more thoughtful people in the West know it too. But in the US, and also Europe, we have hardly begun to think through the consequences of this shift of power: not just what it will mean for geopolitics or economics but also what it will for our whole western societies. It is such a breathtaking transition that the reaction of many people will be one of denial; that it can't happen. So perhaps the first question to be tackled is whether China's advance really is durable or whether there will be some bump that will deflect its course.

The most helpful framework for looking at the progress of the Chinese economy is the work of the investment bank Goldman Sachs. For the past eight years it has been modelling the growth of the main emerging economies and contrasting it with the performance of the main developed ones. It coined the clever acronym of the "BRICs", to describe the four largest emerging economies, Brazil, Russia, India and China. As it has turned out, China has actually been growing even faster than early versions of the model predicted, with the result that it has been passing the big Western economies even earlier than expected. The latest projections suggest that China will pass the US in 2027; the earlier versions suggested some time in the 2040s. A long-term proposition has become a possibility within 20 years.

Economic models are only economic models and we have had enough experience of economists getting things wrong in the past couple of years to take all growth projections with a certain scepticism. Remember too the way, a generation ago, many people thought the Japanese economy would come to dominate the world. Nevertheless the BRIC model has been a good intellectual anchor and it would be silly not to take its projections extremely seriously. My own view is that it is the best place to start from when thinking about the rise, not just of China, but of India and the rest of the developing world.

If you want to list the possible blocks to growth that China faces, you can bang on quite a while. They include a squeeze on energy and raw material supplies; environmental challenges, particularly over water; the ageing of the population and eventually the shrinking of the workforce; the dependence on foreign export markets including the US; the need to import technologies; and of course all the questions about the viability of an authoritarian political system continuing to coexist with an increasingly liberal economic one.

My feeling is that you have to acknowledge that the challenges are enormous and that any linear projections of anything should be distrusted. Nevertheless, you have to postulate some almost unthinkable catastrophe to believe that the country's progress will be completely blocked. Growth will inevitably slow from its heady 10 per cent a year or more as the population ages, but the Goldman model takes this into account. We should surely accept its advance as probable and indeed desirable. Growth may not be quite as fast as Goldman suggests, though it may actually turn out to be even faster, but the broad direction is pretty much set.

If that is right, China's advance will go far beyond the economic sphere. There are already some obvious political consequences, such as its role in shaping economic development in Africa. Chinese investment there is putting in far more infrastructure than all Western aid put together. But the thing that is perhaps hardest to get our head round is the extent to which Chinese ideas about society will start to influence our own.

We have in the West an inbuilt presumption that the way we organise our societies is, if not optimal, at least a rough model for the rest of the world. But that is in some measure an authority based on economic power. Our self-confidence in the values of our economic system was much increased by the collapse of the alternative version developed in the Soviet Union and the conversion of China towards some sort of market economy. But if we experience stagnation and China experiences growth then we will inevitably do some rethinking about the way we run things.

That re-thinking will surely spread beyond narrow economics. I am not saying that Mr Obama's successors will have to listen patiently to criticism from Chinese leaders about America's approach to human rights. What I am saying is that as we move to a more balanced world in the sphere of economics we will move in parallel to a more balanced world in the spheres of politics and society. The more that mainland China moves towards the Hong Kong model – Hong Kong, for example, is ranked at the top of the economic freedom league tables – the more we may feel we need to learn.

We should surely welcome that. We in the West have been too arrogant for too long. We don't have to buy every aspect of the Chinese model, or the Indian model, or the many other emerging economies models, to respect them and seek to learn from them.

h.mcrae@independent.co.uk