Mechanisms in Dynamically Complex Systems: A New Perspective

1. MECHANISMS AND CAUSALITY IN THE SCIENCESUniversity of Kent, Canterbury, UK, September 11, 2009 Meinard Kuhlmann Institute for PhilosophyUniversity of Bremen mkuhlmann@uni-bremen.de Outline: • Main Thesis • Compositionally versus Dynamically Complex Systems • An Example: The Stochastic Multi-Agent Model of a Financial Market • From Warranted to Unwarranted Talk About Mechanisms • Towards a More Structural Notion of Mechanisms Mechanisms in Dynamically Complex Systems

2. Main Thesis • There is a whole new class of potentially mechanistic explanations in various special sciences that is not covered by the available conceptionsof mechanisms, namely:for systems with highly complex dynamical properties despite of a relatively simple composition (or where most material details of the composition are irrelevant for understanding the behaviour of the whole system). • Very simpleexample: double pendulum. • More advanced examples: phase transitions (e.g. in ferromagnets), weather, heart beat, financial markets, opinions, etc.

3. The Project • One starting point: • Talk about the discovery of ‘mechanisms’ is ubiquitous in (dynamically) complex systems research. • My questions: • Under which circumstances is such talk warranted? • If it is warranted, what are the consequences for the notion of mechanisms?

4. Why Available Conceptions of Mechanisms Fail in these Cases • Identification of parts, interactions (or ‘operations’) of these parts and their initial organisation in the whole system provides little understanding of the systems’ behaviour to be explained. • Scientists focus primarily on the dynamics of the system, which is not predictable from the knowledge of its parts, their operations and their organisation in the whole by classical analytical methods. Main points of focus instead: • (i) Careful analysis of the dynamical properties of the system. In particular: statistical analysis of time series.(Explanandum?) • (ii) Construction of models that display the extracted dynamical properties of real systems in computer simulations. (Explanans?)

5. Compositionally versus Dynamically Complex Systems (1/3) • Compositionally complex systems: • Typically linear systems obeying the principle of superposition: I.e. behaviour of compound system = summation of behaviours of its component parts.→ System behaviour predictable by identifying components, their individual input-output behaviours and the complicated initial organisation. • Complexity resides in the large number of relevant variables that characterise the component parts + detailed organisation. • Individual behaviours of the systems’ parts and the detailedwayhow these parts are organized in the compound system are decisive for the overall system behaviour: • Change the behaviour or the input of one of its parts or change relation of two parts and you will in general change the behaviour of the whole system. • Thus: in compositionally complex systems many micro details have a measurable (linear) effecton the studied behaviour of the whole system.

6. Compositionally versus Dynamically Complex Systems (2/3) • Dynamically complex systems: • Very few parameters sufficient to describe the behaviour of the whole system. • Vast majority of micro details is irrelevant: • Change of most microscopic variables and change of most interrelations of component parts have no effect on overall system behaviour. • Even incompositionally simple systems with simple (but nonlinear) rules that determine the dynamics the resulting time series can be unexpectedly complex. • E.g.: double pendulum exhibits complex chaotic behaviour, due to the non-linearity of the rules that determine its dynamics, while the compositional complexity is as low as one can think. • Thus: dynamical complexity arises from nonlinear interactions of subunits over time. • Another example:simple models for computer simulation.

7. Compositionally versus Dynamically Complex Systems (3/3) • Two cautions: • (i) Calling a system dynamically complex as opposed to compositionally complex does not mean that these systems have no components. • Rather’: the detailed nature of the components does not play an important role in the explanation. • (ii) Often, talking about compositionally versus dynamically complex systems just means to lookat one and same systemin two different ways, depending on the phenomenon one wants to explain.

8. An Example • Econophysics: • Relatively young special science between physics and economics. • Tries to analyze and explain economical phenomena by using physics. • The possibility of econophysics grounded on the insight that important properties of, e.g., financial markets can be understood if one adopts a complex systems framework. One very successful approach: • Lux, T., and M. Marchesi (1999): Scaling and criticality in a stochastic multi-agent model of a financial market, Nature 397: 498-500.

9. The Approach of Lux and Marchesi

10. Result of Computer Simulation for Lux/Marchesi-Model Time steps • Lower curve: Assumed development for fundamental value (= input of computer simulation). Probability distribution is a Gaussian (as it is for Brownian motion). • Upper curve: Result (output) of computer simulation for agent-based model of a financial market.

11. Evaluation of Results

12. From Warranted to Unwarranted Talk About Mechanisms (1/2) • Warranted Talk About Mechanisms: • Lesson from complex systems that are microscopically well-understood: • Most micro details can be irrelevant relative to one’s explanatory target. → Detailed investigations about the initial organisation of mechanisms become less important in the case of dynamically complex systems. • Instead: focus is shifted towards studying the dynamics. E.g.: Under which conditions is the dynamics robust and in which cases do instabilities occur?

13. From Warranted to Unwarranted Talk About Mechanisms (2/2) • Unwarranted Talk About Mechanisms: • If the attention is exclusively directed towards analysing the (statistical) characteristics of the dynamics: term ‘mechanism’ is no longer justified. • E.g.: sometimes talk about ‘fractal mechanisms’, although fractality is a feature that only refers to the statistics of time series. • Only warranted: the statistical characteristics indicate certain underlying mechanisms. But: • No mechanism has been identified unless at least some indication has been given about how an interaction of subunits may be involved to generate the phenomenon of interest. • Qualification ‘at least some indication’ is crucial: • Requiring more would make too many complex systems studies non-explanatory. • Even more importantly: the valuable explanatory perspective of complex systems theories would be diminished if its structural focus were given up.

14. Why still talk about Mechanisms? • Scientists themselves do so. • For dynamically complex systems just as for compositionally complex systems reference to the interactions of thesystems’ parts is essential for the explanation. • Again, both for compositionally as well as for dynamically complex systems, the resulting behaviour of the whole system must show some degree of robustness. • But: these features need to be filled in a different way.

15. Towards a More Structural Notion of Mechanisms (0/3) • Two cautions: • (i) ‘Structural’: Not meant to refer to the inner structure as opposed to the function something has.Opposite rather: material • (ii) Mechanism schemas (MDC) are also structural to some extent.But: The openness always refers to modules that fulfil a certain clearly specified function in the whole.

16. Towards a More Structural Notion of Mechanisms (1/3) • Structural explanations that rest, e.g., on basic symmetries independently of any particular ontology have a long and successful history in physics. • Example: elementary particle physics lives on considerations where symmetry principles are the cornerstones. • With the advent of the statistical mechanics of complex systems and modern computing, structural explanations spread into various fields far beyond fundamental physics. At first within physics, eventually into almost each science. • Today, the same analytical techniques, concepts, models and explanatory strategies are applied across radically different sciences such as physics, biology, economics and social science. • Apparently, the success of this transfer does not rest on a common ontology (unless one wants to reify structures, which I do not advocate).

17. Towards a More Structural Notion of Mechanisms (2/3) • In a sense these sciences have the same underlying ontology since, for instance, markets traders, human hearts and ocean waves ultimately all consist of elementary particles. • But: this common fundamental ontology is not the reason why, e.g., the same explanatory strategies can successfully be applied. • In the context of complex systems theories the reason is the observable fact that there are structural similarities in the dynamics of compound systems with completely different kinds of subunits. • These structural similarities can be classified in terms of certain dynamical patterns that can in turn be represented and discriminated in a mathematically precise and subtle way. • Today, complex systems with large numbers of nonlinearly interacting subunits have a similar significance as analytically tractable systems in the past.

18. Towards a More Structural Notion of Mechanisms (3/3) • The behaviour of complex systems is much harder to understand and to predict than the behaviour of simpler classical systems. • Nevertheless, for good reasons complex systems theorists firmly believe that—bearing in mind the much higher complexity of the subject matter—they can do more than just describe similarities of dynamical patterns. • Example 1: one can show under which conditions the statistical characteristics of dynamical patterns are robust and how these patterns arise on the basis of nonlinear interactions of subunits—subunits that need not be described more than in a rough structural way. • Example 2: in some cases it can precisely be said at which point a system may loose its stability. • This is less than in the classical cases since the further development cannot be accurately predicted, but still something explanatorily helpful can be said, e.g. for purposes of intervention.

19. Summing Up • In dynamically complex systems I am focussing on it is inappropriate to emphasize the identification of particular working parts, certain operations they perform and their initial organisation in the whole system. • The kind of nonlinear mechanisms I scrutinize work largely irrespective of the detailed individual natures of the subunits that are involved and their initial compositional as well as their detailed ‘interactive organisation’ (Bechtel) in the whole system. • Excluding investigations about dynamically complex systems misses the fact that there are different legitimate explanatory perspectives all of which provide some understanding of certain aspects of real systems. • And one of these aspects is focussed by the structural perspective of complex systems theories.

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