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What Do the Mathematical Models Say?

Another way to probe the future is to use mathematical and computer models. They do not enable us to predict the future but they give guidance on the behaviour and evolution of our systems and our societies. We have selected two models, one of which, HANDY, was developed in a study that created a stir at the start of 2014 because it was funded by NASA, and announced – according to the exaggerated remarks of some journalists – ‘the imminent end of civilization’. The other, still valid after forty years of critiques and comparisons with real data, is the World3 model that served as a basis for the famous Meadows Report or Club of Rome Report.

An original model: HANDY

Developed by a multidisciplinary team composed of a mathematician, a sociologist and an ecologist, the HANDY model (Human and Nature Dynamics) simulates the demographic dynamics of a fictional civilization subject to biophysical constraints.1 It’s a scientific experiment that aims to gain a better understanding of the phenomenon of collapse observed in the past and to explore the changes that would prevent it in the future. The originality of this new model lies in the fact that it incorporates the parameter of economic inequalities.

HANDY is based on a system of equations conceived in the 1920s by mathematicians Alfred Lokta and Vito Volterra, and frequently used in ecology to describe interactions between populations of predators and prey. In a schematic way, when prey is abundant, the population of predators thrives and causes a drop in the number of prey, and this in turn entails a collapse in the population of predators. The cycle then begins all over again since, when there are few predators, the number of prey again increases. Thus, in the long term, we have a kind of ‘beat’ in growths and declines, two sinusoids of population.

In the HANDY model, the predator is the human population and the prey is its environment. But unlike fish or wolves, humans possess this ability to extricate themselves from a Malthusian world where the limits of resources dictate the maximum size of the population. Thanks to their ability to create organized social groups, to use technology and to be able to produce and store surpluses, humans do not systematically suffer population decline at the slightest depletion of a natural resource. Thus two additional parameters have been introduced into the equations to make the model more realistic: the total amount of accumulated wealth; and the distribution of this between a small caste of ‘elites’ and a greater number of ‘commoners’.

Three groups of scenarios have been explored. The first (a) assumes an egalitarian society in which there are no elites (elites = 0). The second (b) explores a fair society where there is an elite caste but where income from labour is distributed equitably between this caste of non-workers and the workers. Finally, the third (c) explores the possibilities of an inegalitarian society where elites appropriate the riches to the detriment of the commoners.

Before launching the simulations, the researchers vary the resource-consumption rates of each virtual society, generating four types of scenarios from the most sustainable to the most brutal: (1) populations slowly approach an equilibrium between population and environment; (2) the approach is uneven, showing an oscillatory motion before reaching an equilibrium; (3) cycles of growth and collapses; and (4) strong growth followed by an irreversible collapse.

In an egalitarian society without castes (a), when the consumption rate is not exaggerated, the society achieves an equilibrium (scenarios 1 and 2). When this rate increases, the society experiences cycles of growth and decline (3). And, finally, when consumption is sustained, the population grows before collapsing irreversibly (4). This first series of results shows that, regardless of inequalities, the rate of ‘predation’ of a society on natural resources is in itself a factor of collapse.

Now let’s add the inequality parameter. In a ‘fair’ society, i.e., one where a small part of the population does not work but the majority does work and wealth is well distributed (b), a scenario of equilibrium can be achieved only if the level of consumption is low and growth is very slow. When consumption and growth accelerate, the society can tip over into the other three scenarios (disruptions, cycles of decline or collapse).

In an inegalitarian society where elites appropriate the wealth (c), which seems to correspond rather well to the reality of our world, the model indicates that a collapse is difficult to avoid, regardless of the consumption rate. However, there is a subtle difference. At a low rate of overall consumption, as one might expect, the caste of elites begins to grow and monopolizes a large amount of the resources available to the detriment of the commoners. These latter, weakened by poverty and hunger, are no longer able to provide enough work power to maintain the society, which thus starts to decline. It is therefore not the exhaustion of resources but the exhaustion of the people which causes the collapse of an inegalitarian society that is relatively modest in its consumption of resources. In other words, the population disappears faster than nature. According to researchers, the case of the Maya, where nature recovered after the collapse of the populations, follows this type of dynamic. So even if a society is overall ‘sustainable’, the overconsumption by a small elite leads irremediably to its decline.

In the case of an inegalitarian society that consumes a great deal of resources, the result is the same but the dynamic is the opposite: nature is exhausted faster than people, which makes the collapse swift and irreversible. This was typically the case for Easter Island or Mesopotamia, where the environment was still exhausted even after the disappearance of civilizations.

In general, what HANDY shows is that intense social stratification makes it difficult to avoid a collapse of civilization. The only way to avoid this outcome would therefore be to reduce economic inequalities within a population and to put in place measures that aim to keep the demographics below a critical level.

This model is an original attempt at modelling complex behaviour using a relatively simple mathematical structure – perhaps even a simplistic one, since you cannot model the world in four equations. However, this work is an important heuristic tool and indeed a warning which it would be wrong to dismiss out of hand.

In his book How the Rich are Destroying the Earth,2 Hervé Kempf showed the close ties between inequality and consumption. The increase in economic disparities triggers an overall acceleration of consumption through a sociological phenomenon called ‘conspicuous consumption’, described for the first time by the sociologist Thorstein Veblen: every social class tends to do everything (and in particular to consume) so as to resemble the social class just above it. The poor strive to resemble the middle classes, and the latter seek to assume the attributes of the rich, who do everything to show that they are among the ‘seriously rich’. This phenomenon is so powerful that consumption can, in rich societies, become inseparable from the construction of personal identity. Stuck in a model of competition, the society sinks into this infernal spiral of consumption and depletion of resources.

The HANDY model is all the more relevant as our society is currently displaying all the symptoms of the inegalitarian society that consumes a great deal of resources as described in the model. Since the 1980s, inequalities have exploded. The problem is that we now have evidence that economic inequalities are very toxic to our society.

According to Joseph Stiglitz, these inequalities discourage innovation and erode the confidence of whole populations by reinforcing a feeling of frustration that undermines people’s trust in the political world and its institutions. ‘Real democracy is more than the right to vote once every two or four years. […] increasingly, and especially in the United States, it seems that the political system is more akin to “one dollar one vote” than to “one person one vote”.’3 Abstention is growing, but the stranglehold of the wealthiest (who do vote) on the way government works is increasing.

Inequalities are also toxic tor health. The feelings of anxiety, frustration, anger and injustice among those for whom such abundance lies beyond their grasp have a considerable impact on crime rate, life expectancy, psychiatric illnesses, child mortality, alcohol consumption, obesity rates, academic achievement and corporate violence. This finding has been remarkably well described, documented and costed by epidemiologists Richard Wilkinson and Kate Pickett in their bestseller The Spirit Level.4 By comparing data from 23 industrialized countries (taking data from the United Nations and the World Bank), they discover that many of the health indicators of a country worsen not when its GDP drops but when the level of economic inequality rises. In other words, not only is economic inequality toxic to a society but equality is good for everyone, even for the rich!

Inequalities also generate economic and political instability. The two most important financial crises of the last hundred years – the Great Depression of 1929 and the stock market crash of 2008 – were both preceded by a sharp rise in inequality. According to the economic and financial journalist Stewart Lansley, the concentration of capital in the hands of a small elite caste leads not only to deflation but also to speculative bubbles, i.e., to a decline in economic resilience and therefore to intensified risks of financial collapse.5 Repeated shocks erode confidence and especially growth in GDP, which only increases the disparities between classes. Worse, economic inequalities are also amplified by the adverse effects of climate change as these hit the poorest people and countries the hardest.6 This negative spiral of inequalities cannot fail but lead finally to self-destruction.

For economist Thomas Piketty, it is the very structure of capitalism, its ‘DNA’, which favours the growth of inequalities.7 In a large-scale historical analysis based on available tax records since the eighteenth century, he and his team demolish the conventional wisdom that the revenues generated by GDP growth benefit the entire population of a country. In reality, wealth is concentrated inexorably in the hands of a small caste of rentiers when the return on capital (r) is higher than economic growth (g). This is simply a mechanical process. The only way to avoid this pitfall is to set up powerful national and international institutions to redistribute income fairly. But for such outbreaks of democracy to occur, we need extraordinary conditions. However, over the twentieth century, these conditions were met only after the disasters of the two world wars and the Great Depression of the 1930s. The financial world needs to be on its knees, sufficiently weakened for it to be controlled by powerful institutions. And this is all the more difficult as these institutions have prospered, thanks to the periods of rapid growth that have followed conflicts (with reconstruction as a stimulus) – a situation that we do not find today.

From this perspective, the ‘Thirty Glorious Years’ of growth and welfare in France (1945–75) were a ‘historical aberration’,8 and the return of inequality since the 1980s seems therefore to be just a return to normal. In the United States, for example, the level of inequality recently went back up to what it was in 1929.9

What is most disturbing about this narrative is that we are now observing the inexorable return of inequality, despite the evidence of its corrosive effects on societies and despite the lessons of history. Could it be an inevitable destiny? Are we perhaps doomed to wait for the next war or, failing that, a collapse of civilization? Why are the elites doing nothing, even though it is obvious that they too will suffer from these two catastrophic outcomes?

To answer this question, let’s go back for a moment to the HANDY model. It is particularly interesting to note that in both scenarios of the collapse of inegalitarian societies (famine among the commoners or a collapse of nature), the elites, cushioned by their wealth, do not suffer immediately from the first effects of the decline. They do not feel the effects of a disaster until long after the majority of the population or long after irreversible destruction of ecosystems – in other words, too late. ‘This buffer of wealth allows Elites to continue “business as usual” despite the impending catastrophe’.10

Moreover, while some members of society are sounding the alarm to indicate that the system is heading towards an imminent collapse and advocating structural social change, the elites and their supporters are blinded by the long and seemingly sustainable period that precedes a collapse and take this as an excuse to do nothing.

These two mechanisms (the buffer effect of wealth and the excuse of a past of abundance), added to the innumerable causes of lock-in that prevent sociotechnical transitions from occurring (see chapter 4), seem to explain why the collapses observed in history have been permitted to take place by elites who seemed unaware of the catastrophic trajectory of their society. According to the developers of the HANDY model, in the case of the Roman Empire and the Maya, this is particularly obvious.

Today, as most poor countries and the majority of people in rich countries suffer from astonishing levels of inequality and the destruction of their living conditions, ever more piercing cries of alarm rise into the media sky. But those who find this annoying inveigh against ‘catastrophism’, while others shoot the messengers, and nobody really cares. Since the 1970s and the famous Meadows Report up to the latest report from the IPCC, including the synthesis documents of the WWF, the United Nations and the FAO, the message is clearly the same, apart from just one detail: the verbs are no longer conjugated in the future tense but in the present.

A robust model: World3

The World3 model is more than forty years old. It has been described in the bestseller (over twelve million copies sold worldwide) The Limits to Growth, better known as the ‘report to the Club of Rome’.11 However, the main message of this last text has been very poorly understood all this time, both by those who think they agree with it and by those who disagree. What it said was: if we start from the principle that there are physical limits to our world (this is a basic assumption), then a widespread collapse of our thermo-industrial civilization will most likely take place during the first half of the twenty-first century.

In the late 1960s, the Club of Rome12 asked researchers at the Massachusetts Institute of Technology to study the long-term evolution of the ‘world’ system. They included Jay Forrester, professor of systems dynamics, and his students, including Dennis and Donella Meadows. These were the early days of computer science, and they decided to design a systemic computer model (World3) to describe the interactions between the world’s main parameters, the six most important of which were population, industrial production, service production, food production, pollution levels and non-renewable resources. Then they fed it into a computer.

The goal of the game was to introduce the real data of the world into the model and press ‘Enter’ to simulate the behaviour of this world-system over a hundred and fifty years. The first result, called the ‘standard run’ and viewed as the business-as-usual scenario, highlighted how our system was extremely unstable, and described a widespread collapse in the twenty-first century (see Figure 8.1). Between 2015 and 2025, the economy and agricultural production start to fall apart, and they collapse completely before the end of the century at a pace faster than the exponential growth that followed the Second World War. From 2030, the human population begins to decrease ‘uncontrollably’, finally sinking to about half of its maximum at the end of the century, about four billion people (these figures are approximate -they just give orders of magnitude).

Figure 8.1 Meadows model, ‘standard run’, updated by Graham M. Turner.

Note: In bold, real data; dotted lines, the model.

Source: after Graham M. Turner, ‘On the cusp of global collapse? Updated comparison of The Limits to Growth with historical data’, GAIA-Ecological Perspectives for Science and Society 21(2), 2012: 116–24.

Surprised by this result, the researchers then simulated ‘solutions’ in the form of as many scenarios as humankind could apply to try to make the system stable. What would happen if we developed efficient technologies? If we discovered new resources? If we stabilized population or industrial production? If we increased agricultural yields or if we brought pollution under control? The researchers then changed the parameters of the model and tested all of this in two or three clicks. Enter. Enter. Enter. Unfortunately, almost all the alternative scenarios led to collapses, some more catastrophic than others. The only way to make our ‘world’ stable – to end up with a ‘sustainable’ civilization – was to implement all of these measures simultaneously and to start as soon as the 1980s!

In the 1990s, an update of the report showed that these limits (and ‘boundaries’, in the meaning of the term as discussed in chapter 3) did indeed exist and that our civilization was approaching the limits and going beyond the boundaries.13

Even more definitively, the update showed that nothing had been done since 1972 to avoid the business-as-usual scenario.14 On the contrary, since 1963, global industrial production had doubled every twenty-four years! In 2008, and then in 2012, an Australian scientist, Graham Turner, decided to compare the actual data over these last forty years with different scenarios to find out which one was closest to reality.15 What was the result? Our world clearly behaved in accordance with the business-as-usual scenario – in other words, the worst scenario. And Turner concluded, ‘This is a very clear alarm bell. We are not on a sustainable path.’

The model has not only resisted the innumerable and vehement criticisms aimed at it from the start but has even been corroborated by forty years’ worth of facts. The main result of the Meadows Report is not that it predicts the future accurately, advocates ‘zero growth’ or announces that petrol will run out by 2000, as its detractors claimed. It simply warns us of the extreme instability of our system (as it generates exponentials). The model shows remarkably clearly how all crises are interconnected, as well as demonstrating the power of systemic thinking. We cannot be content with ‘solving’ just one problem, for example peak oil, or birth control, or pollution, as this would change almost nothing about the outcome. They must be tackled simultaneously.

After the 2004 version, the optimist on the team, Donella Meadows, liked to say that maybe there was a little window of opportunity not to be missed. The model indicated that three conditions would have to be met in order to maintain the economy and the population in equilibrium, given the Earth’s carrying capacity.

Condition 1. If we can rapidly stabilize the population (an average of two children per family), then the population would reach 7.5 billion by 2040 (or 0.5 billion less than expected), which would make it possible to postpone for a few years a global collapse of the economy and the population. But that would not be enough. ‘So we cannot prevent the collapse if we merely stabilize the world’s population’; we need a second lever.

Condition 2. If we manage to stabilize global industrial production at 10 per cent above what it was in 2000 and redistribute the fruits of this production fairly, we would postpone the outcome by another few years. But that still would not be enough to avoid it because pollution levels would continue to rise and to jeopardize the regenerative capacities of ecosystems. So we need a third lever.

Condition 3. If greater technological efficiency is achieved, i.e., the levels of pollution and soil erosion are decreased while agricultural yields are increased, then the world could stabilize and allow a population of just below eight billion inhabitants to enjoy a good standard of living (close to the one we know) at the end of the twenty-first century. This scenario of equilibrium is possible only if the measures are implemented very quickly. But these results date back to 2004 … It is impossible to advance any precise date but what is certain is that each year that goes by significantly reduces our room for manoeuvre.

The window of opportunity we might have used to avoid a global collapse is closing. So, on his European tour in 2011–12, Dennis Meadows, more pessimistic than ever, repeated in interviews and in an article he wrote for the Momentum Institute: ‘It’s too late for sustainable development, you have to prepare for shocks and urgently build small resilient systems.’16

So? What does your intuition suggest? 2020? 2030? 2100?

Notes

  1. 1. S. Motesharrei et al., ‘Human and nature dynamics (HANDY): Modeling inequality and use of resources in the collapse or sustainability of societies’, Ecological Economics 101, 2014: 90–102.
  2. 2. Hervé Kempf, How the Rich are Destroying the Earth (Foxhole, Dartington: Green Books, 2008).
  3. 3. Joseph Stiglitz, The Price of Inequality. How Today’s Divided Society Endangers Our Future (New York: W. W. Norton and Company, 2012), p. 14.
  4. 4. Richard Wilkinson and Kate Pickett, The Spirit Level: Why More Equal Societies Almost Always Do Better (London: Allen Lane, 2009).
  5. 5. Stewart Lansley, The Cost of Inequality: Three Decades of the Super-Rich and the Economy (London: Gibson Square Books, 2011).
  6. 6. C. B. Field et al., ‘Climate change 2014: Impacts, adaptation, and vulnerability’, Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC), 2014.
  7. 7. Thomas Piketty, Capital in the Twenty-First Century, trans. Arthur Goldhammer (Boston, MA: Harvard University Press, 2014).
  8. 8. See E. Marshall, ‘Tax man’s gloomy message: The rich will get richer’, Science 344(6186), 2014: 826–7.
  9. 9. E. Saez and G. Zucman, ‘Wealth inequality in the United States since 1913: Evidence from capitalized income Tax Data’, Working Paper, National Bureau of Economic Research, 2014, http://www.nber.org/papers/w20625.
  10. 10. Motesharrei et al., ‘Human and nature dynamics (HANDY)’, p. 100.
  11. 11. Donella Meadows et al., Limits to Growth: The 30-Year Update (White River Junction VT: Chelsea Green Publishing, 1992).
  12. 12. A group bringing together scientists, economists, national and international civil servants as well as industrialists from fifty-three countries.
  13. 13. Meadows et al., Beyond the Limits: Global Collapse or a Sustainable Future (New York: Earthscan Publications, 1992).
  14. 14. Meadows et al., Limits to Growth.
  15. 15. G. M. Turner, ‘A comparison of The Limits to Growth with 30 years of reality’, Global Environmental Change 18(3), 2008: 397–411; G. M. Turner, ‘On the cusp of global collapse? Updated comparison of The Limits to Growth with historical data’, GAIA-Ecological Perspectives for Science and Society 21(2), 2012: 116–24.
  16. 16. As well as the interviews published in Le Monde, Libération, Imagine and Terra Eco, see his article ‘Il est trop tard pour le développement durable’, in Agnès Sinaï’ (ed.), Penser la décroissance. Politiques de l’Anthropocène (Paris: Les Presses de Sciences-Po, ‘Nouveaux Débats’, 2013), pp. 195–210.