Super-linear scaling and collapse [View all]

[GliderGuider]

I'm currently digesting theoretical physicist Geoffrey West's two papers on scaling factors - one on scaling in biological organisms, the other on scaling in cities. He has discovered that all biological organisms obey sub-linear scaling laws (laws in which the scaling exponent is less than one) that result in bounded growth - essentially they describe sigmoid curves.

However, for cities he has discovered that there are three classes of scaling factors:

1. Sub-linear scaling (with exponents less than 1) that comes from economies of scale, as in electrical or water distribution networks or road systems. These represent the city's shared infrastructure.
   
2. Linear scaling (with exponents approximately equal to 1) that comes from individual or household consumption, such as domestic water and electricity, and food requirements.
   
3. Super-linear scaling (with exponents greater than 1) that comes from human creative activities.

Super-linear scaling factors lead to the open, unbounded acceleration of the related activity. I think these factors hold the key to our collapse-prone future. West mentions factors like the numbers of new patents, the number of R&D institutions and total electrical consumption as factors that scale faster than population levels. Essentially while sub-linear scaling involves negative feedbacks that limit growth rates, super-linear scaling causes positive feedbacks or "gestalt effects" in which the output of the whole group is greater than the summed output of the individual members would have been.

As a follow-on from this insight, I've used global population as a representation of a single city growing over time. This model allows me to find factors that grow faster than the population itself. So far I've found (as expected, I must admit) that total primary energy consumption and especially CO2 emissions scale super-linearly - with exponents of 1.10 and 1.22 respectively since 1965. My next look will be at non-energy-related waste products.

This line of inquiry seems to point to a deeper issue at work in civilization, one that stems from the enhanced creative abilities of ever larger numbers of human intellects working together. I don't quite know what this means yet, but I suspect it's not an auspicious sign. We may not be able to reduce our activity levels while our numbers keep rising.

Activity levels that rise even faster than our population will eventually cause us to hit limits. All activity requires energy and materials to support it, whether directly or indirectly, and similarly, all activity produces waste. My concern is that efficiency improvements will not be able to keep pace with the acceleration of our activities - and all of it is driven by rising population. As each new person is added to the planet, they add one more brain to our creative planetary gestalt.

Once our increasing need for energy and materials hits its first serious "Liebig's Law of the Minimum" limit, all bets are off. In a complex dynamical system like human civilization, the likely result of hitting such a limit is a rupture followed by eventual collapse.