Monday, November 29, 2010

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.


  1. One take-away from this presentation is that social systems are super linear, B+1, like cities. That is, they follow a "hockey stick" curve toward extreme growth, then collapse; unless that pattern is interrupted by innovation, which then resets the growth pattern from a new baseline. But, as he said, each cycle of innovation has to go faster and faster.

    West also called social systems "cohesive, multiplicative," I think referring to their network dynamics.

  2. On second thought, exactly how does a social system reset itself to a new baseline, in order to reset the exponential growth?
    1. population mobility: migration
    2. population loss: war, pandemics, starvation
    3. population control: birth control, planned parenting
    4. social innovations that pull people into new networks and replace old networks.

    Or the other possibility is that social networks simply grow super-exponentially, without resetting. If, like Luhmann, you define the social system as communication, then communication can grow super-exponentially almost w/o limit: the Internet and all its communication networks.

    However, Albert-Laszlo Barabasi, the author of "Linked" a book on networking, describes social networks not as scales that follow a fixed linear progression (West's 0.8 law), but as "scale free" networks that follow a power law.

    "Scale free" networks develop asymetrically: they develop nodes and hubs. They are not random, but grow by forming more connections with other nodes. Some networks grow to a huge size, with many connections, and some stay small and isolated, with few connections.

    There is an element of chaos in scale-free networks that is not demonstrated in West's linear progression scales. As nodes and hubs grow in size and number of connections, they begin to dominate other nodes and hubs around them by taking over their connections. One example would be Microsoft that makes software for most the computer applications used in the world.

    But there are ways to break that dominant pattern. Upstart nodes that are highly successful at making new connections and drawing other nodes to connect with them can undermine a large hug and eventually crash it. The new upstart hubs can then take the place of the older hub. This happens with social innovation.

  3. The other take-away from West's presentation is that scales are connected with networks, and grow because of networks. But he doesn't explain how that happens in this video.

  4. West's Techonomy presentation is the same thing but its spread over 3 videos and is a much clearer statement of his theory:

    Infratructure networks (biological, urban) scale up with conservation: they are more efficient as they get larger. Efficiency=decrease in energy use by 1/4

    Social networks are super-exponential: as they scale up they need and develop more of everything. Efficiency=increase in energy use and mass by 1.5.

    Interestingly, West's theorem shows the direct relationship between social networks and energy. Information requires enormous amounts of energy, and that requirement grows super-exponentially.

    They also require constant innovation, at faster and faster speeds, to 'reset' the growth curve. Otherwise they grow exponentially and then crash--collapse.

    Chaos/innovation: creates new networks that draw populations away from older networks (hubs) to newer ones.

    Also surprising: West states that the super-exponential growth of cities (the social part, not the infrastructure) is what is threatening the sustainability of environmental systems. "Cities are the problem but they are also the solution" West says.

    But this is exactly what eco-"terrorist" Derrick Jensen says: cities are the cause of all our environmental crises. And now a physicist has proved it with the math.