Super-linear scaling and collapse

[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.

[phantom power]

1. my first reaction to that is...

isn't {3} more or less bounded by {1,2}, which is in turn more or less bounded by {1}?

Assuming that is true, it almost seems optimistic - we get super-linear creative interactions from a sub-linear infrastructure. By the way, I think that would more or less agree with Kauffman's "4th law" of thermodynamics, where the adjacent possible (roughly speaking - the space of possible creativity) grows a lot faster than the number of agents and niches.

Also, it seems to me that we've remarked more than once here in E/E that the initial phase of any logistic curve is exponential. Any finite system saturates in that way.

[GliderGuider]

2. I agree that it's optimistic.

Any time creativity is added to the mix, we get more outputs of various sorts for the same inputs. Of course some of those outputs are inevitably energy/material-consuming, so there's a positive feedback loop driving consumption. I think the process would be slowed but not stopped by a static population.

I don't quite follow your first point. Yes, if we run out of materials or energy to satisfy growth in {1} or {2} (e.g. not enough infrastructure or food) that will act to limit population. I don't see how that would act to bound {3}, which consists essentially of the outputs of human creativity. It would be slowed, as I said above, but I don't see any guarantee that it would be stopped. Of course, if a Liebig Limit is encountered in any of them, "rien ne va plus."

[phantom power]

3. Fewer humans with less disposable time results in less creativity.

At least to the extent that creativity is a function of meme cross-pollination, which works better the more people there are, and the more time they have to exchange ideas and do things with them. People can also be creative all by themselves too.

I suspect we violently agree.

There's an "old" saying from the Roaring Internet 1990s - "whoever can waste bandwidth/computation the fastest wins" I contrast that with one of the interesting developments from Russia, where computation *was* a lot more limited: for a while, the soviet numerical analysis guys were the go-to guys for algorithms. They couldn't throw cheap computation at problems like we Americans did, and they got correspondingly better with their math and algorithms.

One of the things about creativity -- it flows in the directions where it's most rewarded. In a resource constrained environment, creative solutions to resource constraints prosper. In an environment where resources are cheap and plentiful, creativity that finds ways to use them up in new and interesting ways are rewarded instead.

I admit, I don't really know where I think I'm going with this.

[GliderGuider]

4. (Contrarian alert:) In this context I'm ambivalent about the value of creativity.

I normally think that our creativity is one of humanity's greatest glories. But when it's framed as being the driving energy behind the activity that is destroying the planet, I wince a little.

I wonder if we'd really be less happy in a world where there wasn't quite so much ever-accelerating mental and physical motion. Where it was OK for people to think, "You know, it doesn't really need to be any better than this." But that leaves me open to charges of cultural imperialism and ethnocentricity, so I shoulder my share of the white man's burden once again and shuffle off down the road looking for creative solutions to things that aren't actually "problems".

But half a mile further on I think, "Fuck that noise!", drop my burden like a hot rock, and sit down with a spliff. Moments later, much better.

[phantom power]

5. there's creativity, and then there's wisdom

I think questions having to do with "whether we ought to do things, even if we could" is more about wisdom than creativity. Buddy of mine once said, "80% of wisdom is fatigue." We've been living in a world with cheap energy. It's like being 25 years old. But middle age is coming.

Also, I have some hope that we might find a way to re-invent our concept of economic growth to be more aligned with "growth in variety and creativity." The biosphere has been in resource equilibrium for a long long time. It doesn't grow in the way we currently think of growing our economy -- by occupying more and more resources. The biosphere's notion of 'accumulating capital' is more about increasing variety, and increasing niches.

So, to hear somebody saying that their research suggests that creativity can grow faster than basic infrastructure tells me that maybe there's hope for a re-invented notion of growth after all.