“What is a Complex System?”: Notes on Ladyman, Lambert, and Weisner (Part 1)

May 19, 2015

This update is largely a pedagogical exercise in examining and extracting information regarding complexity theory, derived from James Ladyman, James Lambert, and Karoline Weisner’s paper “What is a Complex System?” As such, it can hardly be regarded as a work of original scholarship, but I hope it will be useful for future research, and the summary of their position may be enlightening for some.

Ladyman, Lambert, and Weisner (hereafter abbreviated LLW) sketch an overview of the characteristics of complex systems. While they do not present the necessary or sufficient conditions of being a complex systems, they do try to arrive at as precise of a description as possible, based upon the existing literature. They identify the major properties associated with the science as nonlinearity, feedback, spontaneous order, robustness and lack of central control, emergence, hierarchical organization, and numerosity.

  1. Nonlinearity – Systems are said to linear if the superposition principle holds. This principle states that the net result of two or more inputs at given times with a system is equal to the net result of those inputs at another time. The simple diagrammatic figure that is often used to represent this is the waveform. Nonlinear systems diverge from this neat progression in interesting and dynamical ways. LLW make special note of the divergence between microstate linearity and macro-state nonlinear dynamic systems derived from small perturbations in the microstate progression (the classic butterfly example of chaos mathematics). Despite this divergence however, linear descriptions may often be used to approximately model the conditions of macrostate entities, even if the resulting model is not strictly true. Because of this, nonlinearity is not a necessary condition for complex systems. In addition, the fact that simple systems, like a pendulum, can exhibit nonlinear dynamics, it is also not a sufficient condition. Nonetheless, they believe that nonlinear dynamics may play a role in most complex systems, in conjunction with, or as a subset of some other conditions, and so consider it a related property.
  2. Feedback – A system presents feedback when the behaviour of interacting components of the system depend upon an interaction with neighboring components at an earlier time. LLW give the example of a flock of birds, which adjusts its group organization based upon how other members of the flight change the position of their individual flight patterns. They also note colonies of ants, in which the production of higher-order behaviour and structuration, such as tunnel-building, appears as a result of the interaction of the various ants. Feedback in this system is not enough to guarantee complexity, however, because it requires a sufficiently large number of components for the behaviour to arise. An ant left by itself, will not exhibit the behaviour of a colony.
  3. Spontaneous order – LLW consider some form of ordering of a large number of uncoordinated elements to be an important characteristic of complex system. What is less certain is how to describe this order, as various means of describing the states or processes of order may all suffer some epistemic bias, and various methods may need to be employed. They do agree, however, that neither completely ordered or disordered systems can be complex, and that complex systems exhibit features of both order and disorder, with order spontaneously emerging from disorder.
  4. Robustness and lack of central control – The order of a distributed system is said to be robust if perturbations from lower levels of the system do not affect the stability of the system. Centrally controlled systems may be at more risk if the function of one or more crucial components is disrupted. Robust distributed systems have an advantage, as redundant components may compensate for the malfunction of any one part, allowing for self-correction of the system. LLW compare robust complex systems with random systems, noting that random systems may be trivially robust, in that disturbances do not affect them at all. Instead, it is the regularity of order which allows us to form some measurement of robustness.
  5. Emergence – Emergence is often described as the increasing complexity of a system. This level of generality and tautology is not especially helpful in illuminating the concept of complexity. While not always clearly defined in the history of the literature, emergence is associated with the notion of downward causation. That is, while upward causation, from lower-level micro phenomena to macro phenomena is usually uncontroversial, the supervenience of macro phenomena on micro phenomena is a more contested claim. The major contention here is with regards to the epistemological or ontological characterization of emergence, and the issue of macro-micro relations, and whether macro-level entities may be reductively characterized in terms of micro level entities. LLW do not side one-way or the other on the epistemology/ontology divide, but seem to suggest that some-kind of ontological realism must be necessary without characterizing much of reality as abstract. That is, if we take emergent entities to be purely consequences of analytic reasoning without ontological significance, they are nothing more than mirages of intelligence.
  6. Hierarchical organization – Robustness and emergence tend to imply hierarchical organization, such that once an order emerges from the interaction of parts at a lower-level and the higher level is dependent upon the robust organization of those elements composing the lower level.
  7. Numerosity – This has been much alluded to above, but more than a few, and often many elements are required to form the kind robust, hierarchical organization which compose complex emergence.

While clear overlap seems to exist amongst these properties, they still seem to lack a precise methodology which would demarcate their common interest. LLW then look to existing mathematical and physical approaches for a more abstract and scientific description. This leads them to engage with probability and information theory to look for methods to statistically measure complexity. In the next update I will attempt to extract some general features from the theories they review and show how they relate to and sharpen the focus of the features reviewed above. I will then turn to their explication of the tentative definition they provide for complexity.