Dynamic networks – or complex systems – are very different to the systems studied in Chaos Theory. They contain a number of constituent parts (“agents”) that interact with and adapt to each other over time. Perhaps the most important feature of complex systems, which is a key differentiator from chaotic systems, is the concept of emergence. Emergence “breaks” the idea of determinism because it means the outcome of some interaction can be inherently unpredictable. In large systems, macro features often emerge that cannot be traced back to any particular event or agent.
To understand the concept of emergence further, we can look at water. We know the qualities of oxygen atoms and we know the qualities of hydrogen atoms, so presumably we can determine the qualities of H20, water? Actually we cannot. Really, however freakishly this might sound, we cannot. It turns out that we are familiar with the qualities of water only because we have observed them empirically. The properties of water are emergent. If any reader wished to delve further in to this, I would recommend Stuart Kauffman’s book Re-Inventing the Sacred. In this book, Kauffman wrote that
“it is something of a quiet scandal that physicists have largely given up trying to reason ‘upward’ from the ultimate physical laws to larger-scale events in the universe”
The reason for the inability to reason ‘upwards’ from hydrogen and oxygen to water is because the properties of water are emergent and therefore indeterminable from the properties of the constituent atoms.First of all, I’ve read Kauffman’s book and would personally recommend it to anyone interested in physics, complexity and/or emergence. Second, the difference between chaos and complexity, although it may appear subtle, highlights a critical concern for the study and modeling of complex systems. The macro economy is one of these complex systems in which “the outcome of some interaction can be inherently unpredictable.”
Peter Lewin moves this discussion into the realm of economic modeling with his (Complex?) Thoughts on Heterogeneity and Complexity; Quality and Quantity (my emphasis):
Returning to the theme of the relationship between quantity and quality, quantitative modeling works when both the independent and dependent variables are meaningful, identifiable quantifiable categories that can be causally related. The model ‘works’ then in the sense of providing quantitative predictions. The inputs and outputs can be described in quantitative terms. But, when the outcome of the process described by the model is a new (novel) category of things, no such quantitative prediction is possible. Ambiguity in the type and number of categories in any system destroys the ability to meaningfully describe that system exclusively in terms of quantities. We have a sense then of the effects of heterogeneity. Variation applies to quantitative range. Heterogeneity (variety) applies to qualitative (categorical) range. Diversity incorporates both, but they are significantly different. Heterogeneity may not be necessary for complexity, but heterogeneity does militate in its favor. For example, compound interaction between quantitative variables (categories) can be an important characteristic of complex systems, but complex systems are likely to result from substantial heterogeneity, especially where heterogeneity is open-ended, in the sense that the set of all possible categories of things is unknown and unknowable.
Heterogeneity rules out aggregation, which, in turn, rules out quantitative prediction and control, but certainly does not rule out the type of ‘pattern prediction’ of which Hayek spoke. In fact, erroneously treating heterogeneous capital as though it were a quantifiable magnitude has led to misunderstandings and policy-errors, such as the those associated with the connection between investment and interest rates - errors that could have been avoided with a better understanding of capital heterogeneity and its effects. The capital-structure is complex, but it is intelligible. We can understand and describe in qualitative (abstract) terms how it works and render judgment on economic policies that affect it. And, as a result of Hayek’s insights into complex phenomena, we have an enhanced appreciation of what is involved.Economics is slowly moving in the direction of recognizing that heterogeneity not only exists in the real world, but is critical to understanding how the system works. Unfortunately, we are not yet at the point where most economists accept the inherent inability to quantitatively forecast macroeconomic outcomes and render accurate policy proposals from those conclusions. Many physicists now accept the consequences of and are incorporating complexity into models of various systems. Economics and economic policy would benefit greatly from moving in the same direction.