The limited applicability and relevance of the equilibrium models that were borrowed from the natural sciences in the early twentieth century are of increasing concern to economists. The probabilistic and chaotic behaviors of markets, consumers, and producers are actually better described as nonequilibrium, self-organizing, living systems than as mechanical equilibrium systems.
In a hierarchy of reasons why mathematically rigorous measurement is valuable, few would be closer to the top of the list than facilitating the spontaneous self-organization of networks of cooperating, independent agents and actors. The conception, gestation, birthing, and nurturing of complex adaptive systems offer a reproductive logic for sociocultural traditions. Scientific traditions most explicitly form mature self-identities via a mutually implied subject-object relation absorbed into the flow of a mathematical dialectic.
Complex adaptive systems establish the reproductive viability of their offspring and organize themselves coherently in an ecological web of meaningful relationships by means of this dialectic. In the course of their histories, the various sciences have functioned as complex adaptive systems capitalizing on the mathematical subject-object unity. Networks of scientists form communities governed (mathematically disciplined) by the reference standards of technologically-embodied measurement systems (Latour, Science in action, Cambridge University Press, 1987). Rasch’s probabilistic conjoint models for fundamental measurement are poised to extend this functionality into the human sciences.
Each of the five moments in the formation and operation of complex adaptive systems (Taylor, The moment of complexity, University of Chicago Press, 2003, pp. 166-8) describes a capacity of fundamental measurement systems, in general, and of measurement systems based in Rasch’s family of models, in particular:
1) data flow regularities are captured in initial instrument calibrations; 2)
condensed local schematic representations are formed when an
instrument’s calibrations are anchored at repeatedly observed,
invariant values; 3) interchangeable nonlocally distributed
versions of these invariances are created by means of instrument
equating, item banking, and selective, tailored, adaptive instrument
administration; 4) measures read off inaccurate and unreliable
instruments do not support successful reproduction of the data flow
regularity, but accurate and reliable instruments calibrated in a
shared common unit provide a reference standard metric that enhances
communication and the shared identity of the research community; and 5)
consistently inconsistent anomalous observations provide feedback
suggesting new possibilities for as yet unrecognized data flow
Actor/agent network theory has emerged from social and historical
studies of the shared and competing moral, economic, political, and
mathematical values disseminated by scientists and technicians in a
variety of successful and failed areas of research (Latour,
Reassembling the social: an introduction to actor-network theory,
Oxford University Press, 2005). The resulting descriptive epistemology
has not yet been translated into an optimally practical program for
reproducing successful research programs. Might it be the case,
however, that deliberately crafted metasystems of complex adaptive
research systems are universally founded in « the true union of
mathematics and measurement » (Roche, The mathematics of measurement,
London, The Athlone Press, 1998)?
it even be possible that complex adaptive systems are necessarily and
inherently constituted of such a union, even if, in nature, the
mathematical character of the data flows and calibrations remains
virtual? Though few, if any, have framed the situation in these terms,
these and other questions are being explored, explicitly and
implicitly, by hundreds of researchers in dozens of fields as they
employ Rasch’s unidimensional models for measurement in their
This research is inevitably leading to the repeated disclosure of the same constructs measured in linearly comparable versions of the same metrics. As time goes on, the commensurability of the research results will lead to the realization that the common languages of reference standard, universal uniform metrics.
But must this process happen to us and only in its own time? Or might we seize the opportunity and make it happen for us in our own time? The latter would seem to be human destiny.
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