Saturday, August 25, 2012

(Complex?) Thoughts on Heterogeneity and Complexity; Quality and Quantity

Considering the concept of heterogeneity throws light on the relationship between quantity and quality.
All observation and explanation proceeds on the basis of classification (categorization). Phenomena are grouped into categories according to our perception of their essential similarity (homogeneity). The elements of any category (class) might be different in some respects, but in all respects that ‘matter’ to us they are identical. Items within a particular category can be counted, quantified. The ability to quantify is crucially dependent on being able to count items in this manner. The number and type of categories (variables) is known and fixed. Thus, the arrival of a new category cannot be accommodated within a scheme of simple quantitative variation and must be considered to be a change in quality. Qualitative differences are categorical differences.
All quantitative modeling proceeds on the basis of the assumption that the individual elements of any given quantifiable variable are identical (homogeneous) and are different in some important respect from those of another variable. Variables are essentially distinguishable categories. In addition the elements of a quantifiable category do not interact with each other – else they could not be simply counted. Each element is an independent, identical instance of the class. (Most obvious is the case of ‘identical randomly distributed variables’). This does not preclude the elements themselves being complex – being the result of lower-level interactions, like identical molecules or biological cells, which are incredibly complex phenomena.
We may think of this in terms of structure. Structure implies connections/interactions. A structure is composed of heterogeneous items that are more than simply a list of those items. There is a sense of how the heterogeneous items work together to ‘produce’ something. (We see here how a capital-structure is both a metaphor for and a particular case of the phenomenon of complex structures in the world.) A structure is an ‘order’ in Hayek’s sense, in which it is possible to know something about the whole by observing the types and the ways in which they are related, without having to observe a totality of the elements. Structures are relational. Elements are defined not only by their individual characteristics but also by the manner in which they relate to other elements. These interactions are, in effect, additional variables.
Thus, though the elements of a quantifiable category may be unstructured, these elements may be composed of structured sub-elements. This is the basis of the phenomenon of modularity. Self-contained (possibly complex) modules may be quantified. This dramatically simplifies the organization of complex phenomena, as has been noted in a fast growing literature on the subject. Modularity is a ubiquitous phenomenon in both nature and in social organizations. It is an indispensable principle of hierarchically structured complex systems. The benefits of modularity in social settings include the facilitation of adjustment to change, and of product design, and the reaping of large economies in the use and management of knowledge (see for example work by Baldwin and Clark 2000, Langlois 2002, 2012) and it is clearly an aspect, perhaps the key aspect, of Lachmannian capital-structures. Capital-goods themselves are modules, which are creatively grouped into capital-combinations which constitute the modules of the (non-quantifiable) capital-structure.
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 betweenquantitative 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.
Baldwin, C. Y and K. B. Clark (2000), Design Rules (Cambridge, Mass.: MIT Press).
Langlois, Richard N. (2002), ‘Modularity in Technology and Organization,’ in Entrepreneurship and the Firm: Austrian Perspectives on Economic Organization, N. J. Foss and P. G. Klein, 24-47. Aldershot: Edward Elgar,.
Langlois, Richard N. (2012), ‘The Austrian Theory of the Firm: Retrospect and Prospect,’ Review of Austrian Economics, forthcoming.