Can four equations explain the collapse of civilisations?

And the frenzy began. In two days, Ahmed’s article was tweeted 6500 times and shared 100,000 times on Facebook. The mainstream press ran headlines like these:

Ahmed called the paper “a highly credible wake-up call to governments, corporations and business — and consumers — to recognize that ‘business as usual’ cannot be sustained, and that policy and structural changes are required immediately”.[1]

The first person to say so was Nafeez Ahmed, a self-described “investigative journalist and international security scholar” whose blog is hosted by the UK Guardian . On March 14 he described an unpublished “NASA-sponsored study” that, he said, showed that “global industrial civilisation could collapse in coming decades due to unsustainable resource exploitation and increasingly unequal wealth distribution”.

March 31, 2014 -- Climate & Capitalism , posted at Links International Journal of Socialist Renewal with permission -- If hundreds of newspaper and online reports are to be believed, scientists at NASA’s Goddard Space Agency have proven that Western civilisation will collapse unless we radically reduce inequality and shift to renewable resources.

So the authors of “Human and Nature Dynamics” can only be termed ambitious for attempting to identify “a mechanism that is not specific to a particular time period of human history, nor a particular culture, technology, or natural disaster” – and even more ambitious for claiming not just that they have succeeded, but that they can express that mechanism in just four equations : two for population, one for “nature” and one for accumulated wealth.

Others have tried to do that. Arnold Toynbee’s A Study of History , a massive 12-volume work published between 1934 and 1961, claimed to have identified common factors in the fall of 26 major world civilisations. Others have focused on fewer cases: Edward Gibbon filled six large volumes in an effort to explain just one, in The Decline and Fall of the Roman Empire .

The paper’s ambitious goal is to propose a mathematical model that explains why societies in general collapse. After listing several dozen complex societies that no longer exist – from the ancient Egyptian, Mesopotamian and Chinese empires to the Mayan civilisation in Central America and Cahokia in the Mississippi valley – they write that “although many different causes have been offered to explain individual collapses, it is still necessary to develop a more general explanation”.

We’re told that the paper has been accepted by an academic journal, but it hasn’t been published yet. Two somewhat different drafts have been circulated on the net: my comments refer to the more recent version, dated March 19, 2014. I’ll refer to it as “the paper” or by the abbreviated title “Human and Nature Dynamics”.[3]

Unfortunately, far from being “a highly credible wake-up call”, this much-hyped article adds nothing to our understanding of the causes and solutions of the global environmental crisis. The inclusion of egalitarian proposals should not blind environmental activists to its fundamental flaws.

Normally I’d ignore a paper like this: many graduate students write papers, some get published, and most are quickly forgotten. But this one has been widely publicised, so it requires review, if only to understand its argument. After all, if the authors really have proved that Western civilisation is on the brink of collapse that only greater equality and a shift to renewables can prevent, ecosocialists should be eager to publicise it!

If the original blog post had made that clear, the study wouldn’t have attracted much attention – as the headlines show, it was the supposed NASA connection that drew media interest.

The paper is signed by three US academics. Lead author Safa Motesharrei is a PhD candidate in mathematics and public policy at the University of Maryland; his co-authors, Eugenia Kalnay and Jorge Rivas, are professors at the University of Maryland and the University of Minnesota, respectively. The only connection to NASA anyone has identified is a general research grant NASA gave to Professor Kalnay’s department.

On March 20, NASA publicly denied that it had “solicited, directed or reviewed” the paper, calling it “an independent study by the university researchers utilising research tools developed for a separate NASA activity”.[2]

Most reporters simply quoted Ahmed’s blog, not bothering to read the original study. Liberal and leftish writers did so enthusiastically, while right-wingers fulminated at NASA’s anti-capitalist collectivism. If they had done their jobs and gone to the source, we might have been spared a lot of scare headlines, unwarranted praise and outraged denunciations.

They accomplish that astonishing feat by accepting, without reservation, the Malthusian claim that the decline of past societies – which they call “collapse”, a term they don’t define – was caused by population growth and/or mass consumption of limited resources. They identify several sources for that view, most notably Jared Diamond’s Collapse: How Societies Choose to Fail (Viking 2005) and William Catton’s Overshoot: The Ecological Basis of Revolutionary Change (University of Illinois Press, 1980).

They seem unaware that the views of their preferred authors are, to say the least, controversial. Jared Diamond’s arguments, for example, were thoroughly debunked by experts on each of the societies he described, in the excellent anthology Questioning Collapse.[4]

The authors call their four equation model “HANDY”, short for “Human and Nature DYnamics”. It is based on the so-called predator-prey model created by mathematicians Alfred Lotka and Vito Volterra in the 1920s to show how interaction between competing species can affect population. It says, for example, that if there are many rabbits but only a few wolves in an area, the wolf population will rise because food is plentiful, and the rabbit population will fall because they are being eaten. Eventually there will be too many wolves and too few rabbits, so most of the wolves will starve to death. With fewer predators remaining, the rabbit population will increase, and the cycle repeats – lots of rabbits, then lots of wolves, then ...

That sounds reasonable, but, as population ecologist Daniel Botkin writes, both laboratory experiments and real world observations have shown that “predator and prey do not oscillate as would a Lotka-Volterra set”.[5] That suggests Motesharrei and his co-authors are trying to explain 50 centuries of history using formulas that don’t accurately describe a closed system containing just two kinds of animals.

Botkin’s book is not listed in the bibliography, and there is no indication that the authors are aware that their fundamental formula may not be valid. They simply adopt it and declare: “We can think of the human population as the ‘predator,’ while nature (the natural resources of the surrounding environment) can be taken as the ‘prey,’ depleted by humans”, and proceed.

But nature isn’t a thing you can count, so how do you put it into an equation? The authors finesse that problem by replacing it with an imaginary currency they call eco-Dollars, undifferentiated units that somehow reduce nature’s variety and complexity to a single number. They don’t explain how that could conceivably be done in the real world.

To their credit, the authors recognise that human societies are more complex than the simplistic predator-prey equations allow, so they have modified them to incorporate accumulated wealth (saved eco-Dollars) and social inequality. These additions make the model more complex, but they don’t fundamentally change it. With humans as “predators” and eco-Dollars as “prey” the formulas produce an oscillation: when lots of eco-Dollars are available, the human population rises; when the eco-Dollars are depleted, the human population falls. Accumulated wealth can delay the population decline and elite overconsumption can accelerate it, but the pattern remains.

Thought experiments

Having reduced the complexity of human-nature interaction to four equations, the authors devote most of their paper to “thought experiments” about scenarios that they say represent “three distinct types of societies”. In the Egalitarian scenario, everyone consumes and works equally. In the Equitable scenario, everyone consumes equally, but some do not work, so workers must work harder. In the Unequal scenario, non-working elites consume 10 to 100 times as much as commoners, who do all the work.

For each case they calculate a “carrying capacity” – the maximum number of people that a given number of “eco-Dollars” can support indefinitely. Although they list Joel Cohen’s authoritative work on this subject in their bibliography, they don’t mention his conclusion that “the question ‘How many people can the earth support?’ has no single numerical answer, now or ever”.[6]