Take, for example, the received assumption that Europe's birth rate is falling and its population shrinking, year by year. Things are more complex than that. In the EU as a whole (that is, most of Europe, the major exceptions being Russia, Ukraine and Belarus) population is growing, not declining. Indeed, the latest projections take the EU population from 507 million today to a peak of 525 million by mid-century. The biggest factor affecting that change is migration, without which projections would point to decline (and for the foreseeable future, a Europe without migration is a bit of a fantasy).
But even without migration, those projections probably understate the future recovery of the birth rate in Europe. For some years now, birth rates in most European countries have been increasing, not declining. Throughout the Continent, women and men keep saying that they want on average at least two children. True, they have been saying so for the past 40 years, but the effect is now being felt in north-western Europe (including France, the Nordic countries and the UK), where birth rates are relatively close to the level needed to replace the population in the long run (equivalent to just under 2.1 children per woman).
The difference is in large part thanks to a cultural shift - with changes in public policy to match. Women today are better able to balance raising children with their desire for higher education and a career. A generation ago, as women gained access to education and employment on the same terms as men, having babies was inevitably postponed and birth rates declined. But this is being corrected through greater equality between the sexes, which is breaking down traditional domestic gender roles (albeit slowly and unevenly), leaving women better able to manage a family and a career.
The good news is that these relatively high birth rates mean an ageing population should be manageable, with some painful adjustments. Yet these adjustments are already being made, as we leave behind the obsolete notion that old age starts at 65, and now that a longer lifespan is matched with the later entitlement to pensions. Of course, rapid population growth in countries such as Britain leads to other worries: about integration, housing, infrastructure and unreformed public services.
Western countries enjoy many less tangible - but still vital - advantages over rivals in the developing world. For us, economic and social inequality is relatively modest. This helps to preserve a democratic consensus and political stability. Welfare and the rule of law, the security of property and contracts are well established. For the most part, the secular societies of the West are based ideally on notions of equal citizenship and mutual civic obligation, not on a narrow focus on duty and entitlement based on kinship or faith. A rich civil society of connections independent of the state flourishes.
Despite their enormous size and staggering economic prowess, emerging superpowers may not be ruling the world any time soon. Certainly their growing military might is amply demonstrated by their space and missile programmes, their growing defence budgets, their acquisition of the outward signs of projected power in the form, for example, of aircraft carriers. Yet they face obstacles unlike those that affect the West, or which the West has left behind.
Some of these obstacles are demographic, others more cultural or institutional, yet others are climatic. India's growing population, soon to become the biggest in the world, faces problems of resource sustainability - water, food, raw materials - made worse by its vulnerability to climate change. China also faces resource and climate problems and, with India, ranks as the worst-polluted country on Earth, which creates a significant burden on health and is a source of public unrest.
As in most predominantly agricultural societies, inequality remains very high. India's brilliant technicians send probes to Mars, but 28 per cent of the country's children attending day-care centres are malnourished and underweight - 50 per cent in the state of Bihar. The country's extraordinary democracy may function well, but Hindu nationalism and corruption are stirring public unrest.
China, meanwhile, risks falling into a low-fertility trap. Contrary to what many have said, it seems that there will be no rebound of the birth rate, even if the one-child policy were to be abandoned. In urban China, couples prefer one child and tend to only have one even when allowed two - a preference reinforced by urban conditions and cramped housing. China already faces severe levels of population ageing; continued low fertility would perpetuate it. Unlike the West, China risks becoming old before it becomes rich; others following in its footsteps risk doing likewise.
Change came slowly in Western countries; demographic maturity and economic modernisation proceeded hand in hand. But in some emerging economies, economic growth has raced ahead of social change. There, traditional patriarchal cultures typical of agricultural societies persist, as misfits, into the modern world. Sexes remain unequal, women retain responsibility for children, family and household, while outside the home they only very slowly approach equality with men. That can depress fertility rates to very low levels. Indeed, it is still a problem in southern Europe and the industrial countries of East Asia, such as Japan, Korea and Taiwan.
Worse, many emerging economies are not truly democratic and do not enjoy developed justice systems, security of property or civil society. Unlike the Soviet Union, the Chinese communist system has sustained autocracy through growing prosperity. But political stability and development is threatened by pervasive corruption. Generally, the countries of the Global South face potentially more severe effects from global climate change than those of the Global North.
Before we get carried away and trumpet our own continued triumph too loudly, we must be careful not to invent a "Death of the Rest" myth to replace the "Death of the West". No doubt many of the developing world's problems will be overcome. Autocratic governments retain some advantages in problem-solving and the creativity of many societies outside Europe is remarkable. But we need to pause, take stock, and take heart that, for demographic and broader reasons, the future balance between the "West and the Rest" is likely to be more nuanced, less sensational, less ruinous to the West, than we have been led to believe.