Gödel’s Theorem and Economic Resilience

Logic is the anatomy of thought.

John Locke

Kurt Gödel was one of the last century’s preeminent mathematicians and philosophers. He is most famous for proving that for any system of logic, there are meaningful questions that can be asked, but that cannot be answered within that logical system.

It is easy to dismiss this as academic navel-gazing, but there are real-world examples of this. One of the over-riding issues of our times is the quest for social “justice.” But what is justice? Some say that government should take from those who have more and give to those who have less, and that is justice. But others (J D Vance and Wendell Berry) point out that this creates dependence and eventually is destructive. I can ask questions about justice, but can’t definitively answer them.

If I killed a man a thousand years ago in England, justice then would demand that I pay a wergild to the person’s family or lord to recompense them for their loss. Today, I would most likely either languish in prison (essentially a ward of the state) or be executed – the family of my victim would be uncompensated. Which “justice” is more just?

If we pass on to a higher plane, perhaps we’ll know. And, generally, that is one way to answer the unanswerable questions – move to a higher level framework. In the physical sciences, one of the great unresolved questions of the 19th century was – is light a particle or a wave? Newtonian physics said light was particulate, but couldn’t explain why light sometimes acted as a wave. It was only when quantum mechanics was developed (with Newtonian physics as a special case) that the question was finally answered with a resounding “Yes. Light is both particle and wave.” Quantum mechanics became that “higher plane” to explain light’s behavior; a new “logic” that subsumed Newtonian physics as a special case.

In the social sciences we have a similar situation – we can ask if a community or a community system (e.g., its economy) is resilient, but we can’t really answer that a priori within the logic of what we know. We have to develop the logic for that “higher plane” if we are to be able to predict resilience.

Shade Shutters, in a recent article,* has given us a glimpse of what that higher plane might be. He and his co-workers developed a quantitative measure for the economic structures of 938 urban areas. Rather than looking at this as a static property, they looked at the change of the economic structure over the period 2001-2017. Their primary interest was in finding a relationship between the evolution of an area’s economy and the economy’s performance during and after the Great Recession (GR). They chose the area’s per capita GDP as their performance measure.

They identified six clusters that were archetypes of an area’s economic evolution:

  • The economies in Cluster 1 were relatively stable prior to the GR, changed rapidly during the Recession, and then stopped changing, i.e., achieved a stable “New Normal.”
  • The economies in Cluster 6 behaved similarly, except that they had been significantly changing even before the GR.
  • The economies in Cluster 2 significantly changed prior to the Recession, and then essentially were stable.
  • The economies in Cluster 3 changed leading up to and in the early part of the Recession and then slowly evolved back to a prior configuration.
  • The economies in Cluster 4 had an almost constant rate of change in structure; there was little discernible influence of the GR on their makeup. I am tempted to think of them as the continuously adapting economies.
  • The economies in Cluster 5 had virtually no change before, during or after the Recession. In response to my query, Shutters indicated that these all seemed to be “micropolitan” – small urban centers.

Looking at the performance of each cluster, the economies in Cluster 4 (continuously adapting) were the only ones to show a net growth from the start of the GR through its recovery. All of the others lost ground in terms of their net change in per capita GCP. Somewhat surprisingly (to me), Cluster 5 – the unchanging one – did not perform the worst; the worst performing were the economies in Cluster 3, which had drifted back into their pre-Recession makeup.

Like all good research, Shutters’ work leads to lots of questions.

  • Besides the structural evolution of their economies, is there any other common thread that seems to key the best-performing archetype, or any of them? Geography, presence or absence of a dominant employer, prevalence of a certain type of industry, or trends. I would anticipate that communities with an “eds and meds” economy would tend to be more a Cluster 5, for example.
  • Cluster 3 is an anomaly to me – a sort of “Back to the Future” evolution. The figure seems to imply either that the Cluster’s evolution prior to the Great Recession was to an unstable state or that there was growth up to and into the Great Recession which was then chopped off. In a subsequent note, Shutters indicated that the evolution of Cluster 3 economies might reflect a temporary condition due to unemployment changing the apparent structure and then a recovery to the Old Normal.
  • A community’s economy is a more-or-less decentralized system. Its structural evolution reflects decisions made independently by scores of entrepreneurs and business owners. If the Invisible Hand was ever at work, it certainly has to be here.  Are these results applicable to other community systems, especially other decentralized ones (e.g., social systems)?
  • We tend to look at internal factors that cause a system to evolve in a certain way. But, in general, systems evolve in response to changes in their environment (everything that’s not a part of the system). The continuously adapting economies may simply be in an environment that is changing slowly enough that they can “keep up.”

Shutters has not yet reached that higher plane that will allow us to truly understand what makes a community resilient. But I believe his work points us toward that higher plane. Several years ago, I told a parable of foresters looking at fallen trees to try to understand the causes of their fall. I concluded the tale

[the foresters] are standing in the midst of a forest in which the trees are each bending to the wind and the other elements and then straightening when the wind or the rain or the snow dies down. And we as foresters are really most interested in what keeps the trees standing, not what makes them fall. So it should be with community recovery and resilience. Resilience does not arise from demonstrated weakness but rather from the exertion of strength. Thus, we need to know and understand the strengths of each community, how those strengths are exerted, and how we can nurture those strengths so that they become even stronger.

Shutters, as a wise forester, is focusing on recovery, not vulnerability. He is honed in on an economy’s dynamic character, not its static attributes. And by doing that, he is pointing to a path that I believe will lead to a greater understanding of what makes a community resilient. And if we achieve that understanding, the next – greater – challenge will be transform our communities so that they can adapt to their changing environments.


* Shutters, Shade T., S. S. Kandala, F. Wei, and A. P. Kinzig. “Resilience of Urban Economic Structures Following the Great Recession.” Sustainability 13, no. 2374 (2021).

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3 thoughts on “Gödel’s Theorem and Economic Resilience

  1. According to Walter Brueggemann, economic theorist in 1989, “Justice is to sort out what belongs to whom, and to return it to them. Such an understanding implies that there is a right distribution of goods and access to the sources of life. There are certain entitlements that cannot be mocked. Yet through the uneven workings of the historical
    process, some come to have access to or control of what belongs to others. If we control what belongs to others long enough, we come to think of it as rightly ours, and to forget it belonged to someone else.” Therefore, if the the perpetrator of the offense of injustice, cannot return the “offended” to whole, the only measure that can be responsibly taken is “accountability.”

    Shade Shutters’ six clusters conveniently began quantitative measures for the economic structures of 938 “urban areas” restricted to the relatively recent period of 2001-2017. His methodoloy, was developed in abstraction from the history that created the conditions existing in these Black and Brown communities in 2001 — the inability to receive quality education; own land; the theft of land from freed slaves; provide testimony in court; develop credit, redlining, jim crow, anti-Mexican laws — ensured that people in his clusters are predominantly responsible for their own plight. A community’s economy is NOT a decentralized system, but rather a subset of the broader economic system that cannot and does not act separately from the larger forces acting upon it. (He appears to deny physics.)

    None of us acts independently of the system or the “container” in which we exist. Urban areas have no “separate system.” I hope Shuters, et al, comfortably feel absolved of any guilt they feel from the white privilege they benefit from.

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