Leaving aside for the time being whether or not a world without borders is desirable (and I think it is), is it possible?

A hundred years ago, almost no-one in the world had a passport. Just like today, most people never crossed a national border, but those that did rarely needed any paperwork.

The Russian and Ottoman empires issued ‘passports’ solely for purposes of internal control. Tudor England did the same, as Bridget Anderson documents in ‘Controlling the Unsettled Poor’. Passports as we know them today only began to be regularly issued by the European powers during World War I.

So passports are less than a hundred years old. And in a hundred years’ time, when – if I’m lucky enough to have grandchildren – my grandchildren will be old, passports could very well be gone.

My interpretation of recent world population projections, along with evidence that economic inequalities between nation states are falling, suggest to me that our current obsession with border controls could seem as quirky and sad to future generations as, say, the racist demand that black people sit at the back of the bus – or in another bus entirely – seems to us today.

The idea of Fortress Europe is bolstered by stories of ever-growing numbers of needy non-Europeans, each desperate to crawl in under the electric fence or vault over the barbed wire. Alarmist press coverage of the United Nations Population Fund prediction that by 31 October 2011, the population of the world will have reached 7 billion (en route to many more), has already begun. But I and others argue there is an alternative scenario – one in which the population of the world peaks, and then begins to drop, which is one of the many reasons why I should not assume I will see grandchildren; my children may have so few or so late that I never do.

Between 1926 and 1960, the year in which the contraceptive pill was first widely used, world population increased from 2 to 3 billion, and 25 years later, in 1999, it reached 6 billion, suggesting that population growth was accelerating despite the availability of contraception.

But behind these numbers, across more than half the globe, fertility had fallen below replacement level. In Vanessa Baird’s recently published No-Nonsense Guide to World Population, she points out that even in Africa there are now countries where women are having on average fewer than two children over the course of their lives. Wherever women gain more literacy and a little more power, wherever parents see that their offspring’s chances of surviving to adulthood have become higher, fertility has headed down, usually quickly, towards an average of less than two children per woman. Matthew Connelly’s Fatal Misconception lays the evidence out clearly.

Demographers have been described as accountants with a charisma bypass; Vanessa’s very short and Matthew’s very long book show it’s possible to write demography with passion as well as accuracy. But in the end it all comes back to the numbers.

The latest projections published by the United Nations Population Division (UNPD) in May this year forecast 10.1 billion people by 2100. I argue in my book Fair Play (2011) that this new projection fails to take account of global ‘baby-boom’ peaks and troughs over the past sixty years. The UNPD press release came with a health warning: ‘Small variations in fertility can produce major differences in the size of populations over the long run’. I argue, based on figures which the graphs here demonstrate, that worldwide we experienced a baby-boom during the past decade that peaked in 2006. The previous boom peaked in 1986, and the one before that, in 1966. Progressively fewer children were born in the 1986 and 2006 peaks because contraception had become more popular worldwide and infant mortality was falling.

If one projects forward, following this pattern of peak and trough, then the world’s population reaches 9.3 billion in 2060, but by 2100 drops to 7.4 billion – and if the pattern holds, will continue to fall. The UNPD estimates that if women who are currently each projected to have 2.5 children just have 2, and those groups projected to have 1.5 children just have one, the drop will be even greater – to 6.2 billion in 2100. In a century there may well be fewer people in the world than there are today.

I think it is more likely that the human population never exceeds 9 billion than that it rises above 11 billion. But I have no crystal ball. If global economic inequalities were to grow rapidly, and infant mortality in poorer countries begin to rise again, then we should expect no continuing falls in fertility.

What’s the relevance of this to migration controls? Imagine for a minute what might happen if humanity doesn’t allow mass impoverishment to grow in future and infant mortality to rise again. Imagine a world in which human population (rather like oil consumption) peaks and then declines.

To try to get a grasp of how momentous these possibilities are, think back to what we know happened in Western Europe after the Black Death, that cataclysmic event between 1348 and 1351 which killed half the population in some places. The shortage of labour meant workers and peasants could command better pay and conditions - though as Bridget Anderson describes, England’s rulers did their utmost to contain this. Poor people and their labour were suddenly worth more.

Could a continuing drop in population numbers, and a corresponding drop in the numbers of workers available, lead to migration controls being weakened and then removed? I believe so.

There’s another reason to be optimistic that a future without border controls is not simply a utopian fantasy: ever since the Japanese asset bubble burst in 1991 there’s been an accumulation of evidence to suggest that while economic inequalities between individuals and within countries continue to grow worldwide, economic inequalities between countries have been falling. Glenn Firebaugh’s The New Geography of Global Income Inequality, published in 2003, was one of the first to argue that income inequality across the world peaked in the late twentieth century (after two centuries of rising continuously), and was now going down. Recent events, especially global stock market movements this summer and autumn, have strengthened his case.

It is when the richest countries on earth stop becoming even richer that the chasms between nation states stop becoming deeper. The dot com bubble of March 2000, followed by the far more significant banking crashes of 2008 onwards, are falls in the aggregate wealth claimed by the richest nations; all reduce the amount that is received in aggregate income; all narrow gaps which have not narrowed for centuries according to Angus Maddison’s global GDP series Statistics on World Population, GDP and Per Capita GDP,1-2008AD, which remains the definitive record for global trends in wealth.

Japan’s ‘lost decade’ of the 1990s may well be a precursor for what will come to be seen as the rich Western world’s ‘lost decades’; however what might also be happening, in the medium if not the short term, is a welcome readjustment from the 1980s pattern by which GDP in Africa fell, and rose only slowly in other parts of the world, while within many of the richest countries on earth it rose both absolutely and exponentially, just as inequalities within those countries also widened.

Whether world inter-country income inequalities are in fact falling is a much debated issue; many analysts on the left don’t believe capitalism can right itself like this. A simple answer depends very much on the accuracy of statistics from China, because if Chinese economists have been over-inflating production figures, then around a billion people in the middle of the world income distribution are worse off than we think; and, just as importantly, on how China will be affected by continued global recession and a dampening of demand. The possibility of absolute immiseration for the world’s poorest when food prices are rising also casts doubt on the assertion that gaps are narrowing. But the world economy, viewed in late 2011, looks very different to a decade ago. A rich country becoming poorer is no longer exceptional.

And this, in my view, has a bearing on migration. If people in country X see the prospects in countries Y and Z moving towards becoming roughly the same as in their own, the push to migrate could lose much of its force.

If inequalities between rich and poor people within countries continue to rise, we may see more internal passports, more gated communities, ID cards, and so on – but, at the same time, less perceived need to police particular national borders.

At present, the proportion of the world’s population that enjoys developed economic and social rights and can afford to travel the world on a legitimate passport is, to my mind, rather like the white population of apartheid South Africa in relation to the majority black population. Just as many white South Africans said they felt the plight of the blacks but benefited nonetheless from the privileges apartheid gave them, so today liberals in the rich world may talk about how much they care for others outside their borders, but still see those borders as essential.

Like feudalism in Britain, slavery in the United States, and apartheid in South Africa, restrictive systems of population control are all eventually overcome. But there is no progressive inevitability about world history. If the vast majority even of liberal-minded people cannot imagine a world without border controls in a hundred years’ time, then it will become harder to win that world. But as we head towards the possibility of peak population, those of us advocating for a world without borders have reasons to be optimistic.

Danny Dorling’s new book ‘Fair Play’ is published by Policy Press in October.