Geoffrey West on Scaling Rules

Physicists really like simplicity and elegance. And, as a result, they have a wonderful knack for coming up with interesting ways that show how things that appear to be different are really the same.

(Warning: obscure sociology reference impending.) Simmel would love them. (Explanation of obscure reference: Simmel, the progenitor of formal sociology and what has subsequently become network analysis, was treated poorly by the German academic establishment -- in part because his lectures were so popular. Those lectures typically took the following structure: Look at thing A, Look at thing B, Look at thing C. Surprise A, B and C are really the same thing!)

That is the same general approach that West takes as part of this Yahoo Labs Big Thinker presentation exploring the scaling rules of cities, businesses and other things only discovered when you watch!

Unfortunately, the viewer doesn't display time, so I can't identify precisely where to find the interesting bits, ..... but somewhere between a fifth and a quarter into the talk you find this slide which is attached to an interesting observation:

a) there is a systematic relationship between the size of a biological organism and the amount of energy that it requires that b) remains the same over the entire 27 orders of magnitude of biological phenomenon (i.e., from below the cellular level to the blue whale). An increase in size of the system by 4 orders of magnitude requires only 3 orders of magnitude increase in energy input.

At about the 1/4 point, after talking about a number of other scaling relationships, Wests suggests that it is networks that underpin these relationships and the existence of the mathematical relations is a product of natural selection (which has optimized the design and selected for the most efficient) and the mathematics of network processes.

At about the 1/3 point, he notes that similar scaling processes occur not only when looking between species, but also when conceptualizing networks made up of the same object. Thus, the same principals that hold for a single tree also hold for the forest as a whole. Thus, for example when looking at all the different trees in a forest, there is a consistent relationship between the diameter of the trunk of a particular type of tree and the number of trees of that type in the forest.

He then turns to a discussion of growth -- based on the idea that incoming metabolized energy serves two functions a) the maintenance of existing cells and b) the growth of new cells. The first half of the talk, dealing with biological systems, is summarized in the following slide:

The central point is that the relationships are found in biology because natural selection has operated on the systems and selected for those which are optimized. Thus, the question for the second half of the talk becomes whether or not social systems show the same patterns. If they do, then they are likely sustainable. If they don't, problems are likely.



This slide, around the half way mark, summarizes the results of his empirical findings -- that social organization scales in terms of three different types of relationship rather than the single one characterizing biological systems.





And here, in contrast to biological processes that scale at a less than linear rate, we see the consequences of that aspect of social process that scales at a greater than linear rate. Thus, where biological systems that are large go slower than those that are small, social systems that are large operate at a pace that is faster than those that are small.

At this point, around 2/3 of the way through, it gets really interesting. In contrast to interpreting the exponential growth in terms of the standard Limits to Growth argument, West notes that you can 'reset' the initial conditions and, hence, modify the curve, through the process of social innovation. But, drum roll for the long awaited punchline,to do this and keep the system operating requires it to be 'reset' on a more and more rapid basis. In other words, there is a need not just for new innovation, but for more rapid and more fundamental innovation, as the system grows. This structure, like trying to run on a treadmill that is continuously accelerating and from which you will ultimately fall off, is unsustainable.

West closes with a discussion of corporations and the tension between infrastructure (governed by biological type scaling laws that are less than linear) and innovation (governed by scaling laws greater than one) and why companies, in contrast to cities, tend to die out.

There are lots of interesting parallels between West's argument and those of Tad Homer-Dixon and his notion of the ingenuity gap. Homer-Dixon argues that the fundamental problem we face is that the requirement for ingenuity is rising faster than our ability to supply it and, hence, there exists an ingenuity gap. I've always conceptualized the main driver behind the increased requirement as the increasing complexity, scale and fundamental nature of the problems we face. Or, in panarchy terms, the co-creation of increasingly higher-level (slower, larger scale) adaptive cycles. West provides a slightly different explanation for the increased requirement for ingenuity -- tracing it to the increasingly rapid need to 'reset' the growth curve.