I have been reflecting on different forms of growth ‘dynamics’. I can think of three types, but there may be more.

- Sigmoidal, or S-curve, growth: growth starts slowly, accelerates for a while before decelerating to a zero growth rate. This growth dynamic explains why trees do not grow to the sky.
- Exponential: the growth rate is consistently positive up until the point of collapse. An example would be the growth of a colony of bacteria in a petri dish. There is a technical wrinkle concerning whether the point of collapse occurs in finite time (a problem for us) or in infinite time (we can ignore).
- Chaos: the classic example here is the growth in the rabbit population on an island, with unpredictable booms and crashes.

The common thread across all three is access to resources. Growth stops when the resources can’t be extracted from the environment fast enough. In the case of exponential growth, collapse comes when all available resources have been harvested.

This leads me to think about ‘sustainability’. In the context I have just developed, sustainability becomes the art of extracting resources from the environment at exactly the rate at which they are replenished. Therefore I conclude that, over the very long term, the only sustainable growth rate is 0% per annum. This is not how we appear to be wired – we seem to be wired for growth – so how do we explain this mismatch? Two different strands of thought occur to me.

First, there is history. For the vast majority of human history global GDP growth is estimated to have been between 0% pa and 0.05%pa, and then around 1750 it exploded exponentially. This growth pattern would fit either the sigmoidal or exponential dynamics reviewed above. Arguably the former is the ‘more sustainable’ option – and it is possible to make the case that we could currently be in the deceleration phase. If global GDP is truly exponential, then reasoning by analogy would suggest that positive growth can be sustained until the resources run out, at which point it collapses. In this latter case we would need to define the time frame over which we were concerned about ‘sustainability’ and if the collapse is likely beyond this, then it is outside our frame of reckoning.

The second strand of thought is inspired by Eric Beinhocker’s The origin of wealth. This book makes the case that wealth is knowledge – so more knowledge equals more wealth. Assuming this to be true, wealth will increase indefinitely if knowledge increases indefinitely. The indefinite increase of knowledge seems plausible, given that the more discoveries we make the more recombinations of them can be made, to yield yet further discoveries. There are two caveats in my mind. Again from history, the lesson from the destruction of Arab centres of learning shows that knowledge (and wealth) can be destroyed – even if that is harder to imagine now that knowledge exists in digital form. Second, for me, the problem of resource limits still needs to be solved. For knowledge and wealth to increase indefinitely it seems to me that both have to be free of any resource constraints – and that is hard for me to imagine.

To conclude, I am settling on a belief that over the very long run the only sustainable growth rate is 0%pa. Given my belief in complex adaptive systems, a steady state seems remotely likely. More likely would be a chaotic pattern of positive and negative growth rates. And, of course, it is possible that such an outcome is decades – or perhaps centuries – away; which somewhat devalues this line of thinking.

Tim Hodgson