There’s been a bit of a buzz lately about a working paper by Safa Motesharrei, Jorge Rivas and Eugenia Kalnay about doom, utter destruction, and the apocalypse.

Motesharrei et al. describe a theoretical model – Human and Nature Dynamics, or HANDY, for short – that simulates the rise and fall of societies. It’s not a complicated model, really. All it has is four main equations, two of them describing the population of two classes of people, ‘commoners’ and ‘elites’, one describing ‘nature’, and one to describe the accumulation of ‘wealth’. And, or so people say, it predicts that we shall all perish soon!

I don’t want to go into too much detail here, but these are the equations (in the same order as above):

Looks simple enough, doesn’t it? The *α _{C}*,

*α*,

_{E}*C*and

_{C}*C*

_{E }all depend on

*ω*,

*x*and

_{C}*x*as well. Basically,

_{E }*α*‘s

*denote death rates,*

*β*‘s denote birth rates,

*x*‘s stand for the population of commoners and elites,

*C*‘s are their respective consumption, and

*ω*is accumulated wealth (somewhat of a strange notion of wealth, but more on that below).

*y*is the stock of natural resources,

*γy(λ – y)*is a regeneration term (where

*γ*is a regeneration factor and

*λ*is the maximum possible amount of natural resources – nature’s ‘capacity’), and

*-δ*is a depletion term (where

*x*y_{C}*δ*is the rate of depletion per worker). You should note here that

*δ*is also society’s production.

*x*y_{C}There’s also some inequality in the model, because elites consume more than commoners:

Where *s* is a minimum (‘subsistence’) wage, *ω _{th}* is the minimum level of wealth society needs to feed all its members, and

*κ*≥1 measures inequality in salaries (i.e. elites get

*κ*times more money). If any one of those consumption terms ends up being smaller than one, that group experiences a higher death rate. That’s bad.

The punchline of all this is that, given certain parameter values, this model simulates society’s collapse, either because all commoners starve to death and thus production stops (had I mentioned that only commoners produce in this model? Elites have positions in management, but they don’t really do anything substantial), and everybody dies, or because all of nature is used up, and everybody dies. Usually over time horizons of up to 1000 years.

Now, I’m all for mathematical modelling, and this is kind of a neat model, and it’s very good at producing neat little curves. And quite a few people seem to think that this is kind of a mathematical proof that inequality (a bigger *κ* will tend to kill you) and unsustainable use of natural resources (a bigger *δ* will also tend to kill you) will bring about our collective doom.

I think there are some good points to be made about how much inequality is justifiable, but also how much inequality we need to have an efficient economic system; I recommend reading John Rawls. There are also good points to be made about the value of preserving nature, the benefits of a medium-term shift towards more renewable energy sources, climate change, and a lot more things of that persuasion. But I don’t think this model does an awesome job at getting those points across.

For one thing, it’s very much underspecified. Aren’t there any other factors besides inequality and use of natural resources that could influence what happens to a society? What about the political system? What about social mobility (of which, in this model, there is none: you’re born a commoner, you’ll die a commoner)? And what exactly is a ‘society’, exactly? The authors talk about some examples of collapse, like the Roman Empire. So is a society today a nation state? Or ‘the West’? Or the whole world? If I can ruin somebody else’s stock of natural resources without hurting my own, does that still hurt me?

Also, some variables are rather strangely defined. For one thing, why do only commoners produce ‘wealth’? And why do the elites not contribute anything valuable to society? All they do is consume things that commoners have to produce, and at a higher rate at that. Is management really completely worthless? What about the arts, or science? And what is this ‘wealth’, anyway? It’s this strange, durable consumption good that people need to live, but can store pretty much indefinitely (in some scenarios, the commoners all die out, but elites still have a couple of decades left living off of society’s wealth stock. Is it all canned food?! Also, wouldn’t even the high and mighty elites eventually take to farming, if only to save their hide?). Plus, birth rates are constant. Over a thousand years. Seems like quite the assumption. Plus, the authors never really defend their choice of parameter values. It’s not like they estimate what the ‘correct’ values of those would be for today’s world. Or if they do, they don’t say so.

Motesharrei et al. actually acknowledge a lot of this stuff, and say that they’re working on including more of it in future versions of the model. And I’m very much looking forward to seeing that. But in the meantime, it seems to me that a lot of people just see a bunch of equations, and thus assume that this model must be making a very strong point about inequality and sustainability. Really though, it’s just a theoretical model, no more or less so than if it were completely verbal. There’s absolutely nothing empirical about it. I think a lot of the hype so far is math bias, rather than genuine appreciation of the model (which needs more work).

So I’m looking forward to the next revision of this paper, and to seeing the improvements it brings. But until then, please hold off on the ‘math has proven that we shall all die soon’-craze.

umbrownThis reminds me of the Dan Brown novel Inferno. I don’t want to give any spoilers but those who have read it will understand.

This is all interesting to think about and there may be some policy implications on family size and population growth if taken seriously, but I think that their models overestimate the fragility of human society.