|Peter Lewin|
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 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.
-------------------------------
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.