Defining and Modeling Complex Adaptive Systems

Almost all the critical problems of our time are problems of control and almost all of them concern complex adaptive systems. If we want to know more about our bodies, it is not just to increase knowledge but so that we can control our health. If we want to know more about our economies, it is so that we can control the process of economic development. But my argument, that all systems need a little disorder, is not universal. For one, the argument does not hold for simple systems.

What Is A Complex Adaptive System?

The first question that then needs to be answered is: What is a complex adaptive system? David Krakauer defines complex systems as “systems that don’t yield compact forms of representation”1. In other words a complex system cannot be described by a simple set of equations. Why would this be the case? As Krakauer notes, it is the “adaptive” nature of these systems that leads to this intractability. Agents within the system respond to each set of environmental conditions within a complex adaptive system with a different set of responses and the number of such environments and their corresponding agent responses that need to be accounted for to construct an accurate model of the system is simply too large. But is this simply a problem of impracticality? Could we, at least in theory, construct a model that takes into account all possible environmental conditions and all possible agent behaviours? Although some scientists may argue that such an approach is theoretically possible, there is ample evidence that the critical “adaptive” component of some complex adaptive systems may in fact be unmodelable. There is no better example of this than the problems faced by the economist Hyman Minsky in formalising many of his most important ideas.

Limits Of Formal Modelling Techniques: Hyman Minsky’s Insights

Hyman Minsky’s core insight, that “stability is destabilising”2 is simple enough to explain. Long periods of economic and financial stability encourage a shift from conservative financing (“hedge finance”) to more speculative financing strategies (“Ponzi finance”) and an increase in systemic leverage. The fragile economic system is then prone to be tipped over into a recession by even an ordinary shock. At least in theory, this is an eminently modelable process. But Minsky’s insights go far beyond this description of the business cycle. Minsky was a strong advocate of strong action by the central bank and the government to stabilise the business cycle. But he was also well aware of the long-term damage inflicted by such a regime where all disturbances were snuffed out at source – the build-up of financial “innovation” designed to take advantage of this implicit protection and subvert the regulatory framework, the descent into crony capitalism and the growing fragility of a private-investment driven economy3. This understanding that was also reflected in his fundamental reform proposals4. Minsky also appreciated that the short-run cycle from hedge finance to Ponzi finance does not repeat itself in the same manner across business cycles. The long-arc of stabilised cycles is itself a disequilibrium process (a sort of disequilibrium super-cycle) where performance in each cycle deteriorates compared to the last one. An increasing amount of stabilisation needs to be applied in each cycle in order to achieve poorer results compared to the previous cycle.

It is this long-run adaptation by firms, banks and other agents within the economy that is so resistant to being modelled in a formal manner. This problem was identified by Duncan Foley5 who observed that a model that can “represent change only as the quantitative variation of a given set of variables” cannot capture the essence of the adaptive process which is the generation of novelty, “the emergence of qualitatively new phenomena”. This is not a problem that can be solved simply by adding new “regimes” to the model and the problem is not just that any realistic model rapidly becomes unwieldy. There is a much deeper and more profound problem. For example, how can any quantitative representation of this process account for financial products that have not yet been invented? How can a quantitative model in 1990 account for the role of the yet-to-be-invented CDO in fuelling the financial crisis of 2008? And even more importantly, how can any such model account for the ability of firms, banks and other agents to generate such “innovation”?

Simple Systems vs Complex Systems

When analysed against the criteria of whether all possible environments and their corresponding agent responses can be specified in advance, there are many systems we seek to control that are not complex in nature. One of the most vivid examples comes from the field of war. Although conventional, hierarchical command-and-control warfare is not effective in complex environments such as jungles, mountains and urban settings, it is still effective in executing clear missions in simple environments such as the desert6. Another example comes from the field of computing where the modern computing environment faces many of the same control issues precisely because it has transformed from its prior monolithic, relatively simple form into an interdependent and networked collection of adaptive components7. In fact, complex adaptive systems can often be identified by observing the critical role that disorderly processes play in maintaining system resilience. For example, the disorderly and often unpredictable nature of flooding is a vital factor in maintaining the productivity and resilience of many complex river-floodplain systems. But the same rarely holds for simpler systems such as small temperate streams8.

Misidentifying A Complex System As A Simple System

Although some systems are clearly not as complex as others are, system managers must be careful not to misidentify a complex system as a simple system. A common error is to ignore factors at higher hierarchical levels of the system that subvert control efforts at lower levels. Many systems that are relatively simple when viewed in isolation become complex when viewed within the context of a larger system. Desert terrains may represent a simple battlefield but even simple victories on the battlefield can be negated by the unintended consequences on the larger socio-political system9. Even the simplest technological system often exhibits complex behaviour when viewed within the context of the social and organisational system within which it resides.

Another common problem is that systems that appear to be minimally adaptive in the short run may be strongly adaptive in the long run often with catastrophic consequences for the control effort. An excellent example is the program to control the river Rhine during the early part of the 19th century. In response to persistent floods, the Rhine was narrowed and straightened with its embankments raised and its arteries cut off. It took one and a half centuries for the adaptive transformation in the system to manifest itself as systemic fragility when the Rhine experienced four ‘100-year floods’ in 12 years between 1983 and 199410.


  1. Introduction To Complexity: Lecture 1.6.  ↩

  2. Stabilizing an Unstable Economy. The section on Minsky is drawn largely from an earlier post of mine titled ‘The Resilience Approach vs Minsky/Bagehot: When and Where to Intervene’.  ↩

  3. From pages 163-165 of Minsky’s book ‘John Maynard Keynes’:
    “The success of a high-private-investment strategy depends upon the continued growth of relative needs to validate private investment. It also requires that policy be directed to maintain and increase the quasi-rents earned by capital – i.e.,rentier and entrepreneurial income. But such high and increasing quasi-rents are particularly conducive to speculation, especially as these profits are presumably guaranteed by policy. The result is experimentation with liability structures that not only hypothecate increasing proportions of cash receipts but that also depend upon continuous refinancing of asset positions. A high-investment, high-profit strategy for full employment – even with the underpinning of an active fiscal policy and an aware Federal Reserve system – leads to an increasingly unstable financial system, and an increasingly unstable economic performance. Within a short span of time, the policy problem cycles among preventing a deep depression, getting a stagnant economy moving again, reining in an inflation, and offsetting a credit squeeze or crunch…….
    In a sense, the measures undertaken to prevent unemployment and sustain output “fix” the game that is economic life; if such a system is to survive, there must be a consensus that the game has not been unfairly fixed…….
    As high investment and high profits depend upon and induce speculation with respect to liability structures, the expansions become increasingly difficult to control; the choice seems to become whether to accomodate to an increasing inflation or to induce a debt-deflation process that can lead to a serious depression……
    The high-investment, high-profits policy synthesis is associated with giant firms and giant financial institutions, for such an organization of finance and industry seemingly makes large-scale external finance easier to achieve. However, enterprises on the scale of the American giant firms tend to become stagnant and inefficient. A policy strategy that emphasizes high consumption, constraints upon income inequality, and limitations upon permissible liability structures, if wedded to an industrial-organization strategy that limits the power of institutionalized giant firms, should be more conducive to individual initiative and individual enterprise than is the current synthesis.
    As it is now, without controls on how investment is to be financed and without a high-consumption, low private-investment strategy, sustained full employment apparently leads to treadmill affluence, accelerating inflation, and recurring threats of financial crisis.” ↩

  4. Just like Keynes, Minsky understood completely the dynamic of stabilisation and its long-term strategic implications. Given the malformation of private investment by the interventions needed to preserve the financial system, Keynes preferred the socialisation of investment and Minsky a shift to a high-consumption, low-investment system. But the conventional wisdom, which takes Minsky’s tactical advice on stabilisation and ignores his strategic advice on the need to abandon the private-investment led model of growth, is incoherent.  ↩

  5. ‘Hyman Minsky and the Dilemmas of Contemporary Economic Method’ by Duncan Foley (1998). I cannot recommend this paper highly enough. ↩

  6. ‘Complexity of Military Conflict: Multiscale Complex Systems Analysis of Littoral Warfare’ by Yaneer Bar-Yam (2003).  ↩

  7. See, for example, ‘Cloud is complex—deal with it’ by James Urquhart.  ↩

  8. http://en.wikipedia.org/wiki/Flood_pulse_concept ↩

  9. For example, witness the unintended consequences of the intervention in Libya on countries such as Mali and Algeria. ↩

  10. ‘The Rhine: an eco-biography, 1815-2000’ by Marc Cioc (2009) ↩

Comments

  1. zaphod62 :

    Thanks for this great series. Very lucid!

    You may be interested in this, by Eugene Wigner (“The irrelevancy of so many circumstances which could play a role in [regularities in nature] has also been called an invariance. However, this invariance is of a different character from the preceding one since it cannot be formulated as a general principle. The exploration of the conditions which do, and which do not, influence a phenomenon is part of the early experimental exploration of a field. It is the skill and ingenuity of the experimenter which show him phenomena which depend on a relatively narrow set of relatively easily realizable and reproducible conditions.” http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html) and a book by secularist Stuart Kauffman where he says “we cannot follow Newton’s mandate in the evolution of he biosphere for the very deep reason that we do not know all the relevant variables beforehand.” p. 133 (also see pp 12 ff) http://books.google.ca/books?id=xpUalZ8vnVYC&printsec=frontcover#v=onepage&q&f=false as combined they support the case you are making. Clearly not all phenomena meet the law of nature model in the reductionist sense where one can determine the relevant variables beforehand as not all phenomena depend on an easily reproducible set of conditions (of the type used in reproducible experiments and machine designs.)

  2. Ashwin :

    Thanks – I am familiar with Stuart Kauffman’s work but the Wigner link is new to me.

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