On page 145 of his book, The Mathematics of Measurement: A Critical History, John Roche quotes Charles de La Condamine (1701-1774), who, in 1747, wrote:
‘It is quite evident that the diversity of weights and measures of different countries, and frequently in the same province, are a source of embarrassment in commerce, in the study of physics, in history, and even in politics itself; the unknown names of foreign measures, the laziness or difficulty in relating them to our own give rise to confusion in our ideas and leave us in ignorance of facts which could be useful to us.’
Roche (1998, p. 145) then explains what de La Condamine is driving at, saying:
“For reasons of international communication and of civic justice, for reasons of stability over time and for accuracy and reliability, the creation of exact, reproducible and well maintained international standards, especially of length and mass, became an increasing concern of the natural philosophers of the seventeenth and eighteenth centuries. This movement, cooperating with a corresponding impulse in governing circles for the reform of weights and measures for the benefit of society and trade, culminated in late eighteenth century France in the metric system. It established not only an exact, rational and international system of measuring length, area, volume and mass, but introduced a similar standard for temperature within the scientific community. It stimulated a wider concern within science to establish all scientific units with equal rigour, basing them wherever possible on the newly established metric units (and on the older exact units of time and angular measurement), because of their accuracy, stability and international availability. This process gradually brought about a profound change in the notation and interpretation of the mathematical formalism of physics: it brought about, for the first time in the history of the mathematical sciences, a true union of mathematics and measurement.”
As it was in the seventeenth and eighteenth centuries for physics, so it has also been in the twentieth and twenty-first for the psychosocial sciences. The creation of exact, reproducible and well maintained international standards is a matter of increasing concern today for the roles they will play in education, health care, the work place, business intelligence, and the economy at large.
As the economic crises persist and perhaps worsen, demand for common product definitions and for interpretable, meaningful measures of impacts and outcomes in education, health care, social services, environmental management, etc. will reach a crescendo. We need an exact, rational and international system of measuring literacy, numeracy, health, motivations, quality of life, community cohesion, and environmental quality, and we needed it fifty years ago. We need to reinvigorate and revive a wider concern across the sciences to establish all scientific units with equal rigor, and to have all measures used in research and practice based wherever possible on consensus standard metrics valued for their accuracy, stability and availability. We need to replicate in the psychosocial sciences the profound change in the notation and interpretation of the mathematical formalism of physics that occurred in the eighteenth and nineteenth centuries. We need to extend the true union of mathematics and measurement from physics to the psychosocial sciences.
Previous posts in this blog speak to the persistent invariance and objectivity exhibited by many of the constructs measured using ability tests, attitude surveys, performance assessments, etc. A question previously raised in this blog concerning the reproductive logic of living meaning deserves more attention, and can be productively explored in terms of complex adaptive functionality.
In a hierarchy of reasons why mathematically rigorous measurement is valuable, few are closer to the top of the list than facilitating the spontaneous self-organization of networks of agents and actors (Latour, 1987). The conception, gestation, birthing, and nurturing of complex adaptive systems constitute a reproductive logic for sociocultural traditions. Scientific traditions, in particular, form mature self-identities via a mutually implied subject-object relation absorbed into the flow of a dialectical give and take, just as economic systems do.
Complex adaptive systems establish the reproductive viability of their offspring and the coherence of an ecological web of meaningful relationships by means of this dialectic. Taylor (2003, pp. 166-8) describes the five moments in the formation and operation of complex adaptive systems, which must be able
- to identify regularities and patterns in the flow of matter, energy, and information (MEI) in the environment (business, social, economic, natural, etc.);
- to produce condensed schematic representations of these regularities so they can be identified as the same if they are repeated;
- to form reproductively interchangeable variants of these representations;
- to succeed reproductively by means of the accuracy and reliability of the representations’ predictions of regularities in the MEI data flow; and
- adaptively modify and reorganize representations by means of informational feedback from the environment.
All living systems, from bacteria and viruses to plants and animals to languages and cultures, are complex adaptive systems characterized by these five features.
In the history of science, technologically-embodied measurement facilitates complex adaptive systems of various kinds. That history can be used as a basis for a meta-theoretical perspective on what measurement must look like in the social and human sciences. Each of Taylor’s five moments in the formation and operation of complex adaptive systems describes a capacity of measurement systems, in that:
- data flow regularities are captured in initial, provisional instrument calibrations;
- condensed local schematic representations are formed when an instrument’s calibrations are anchored at repeatedly observed, invariant values;
- interchangeable nonlocal versions of these invariances are created by means of instrument equating, item banking, metrological networks, and selective, tailored, adaptive instrument administration;
- measures read off inaccurate and unreliable instruments will 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 reproduces the common voice and shared identity of the research community; and
- consistently inconsistent anomalous observations provide feedback suggesting new possibilities for as yet unrecognized data flow regularities that might be captured in new calibrations.
Measurement in the social sciences is in the process of extending this functionality into practical applications in business, education, health care, government, and elsewhere. Over the course of the last 50 years, measurement research and practice has already iterated many times through these five moments. In the coming years, a new critical mass will be reached in this process, systematically bringing about scale-of-magnitude improvements in the efficiency of intangible assets markets.
How? What does a “data flow regularity” look like? How is it condensed into a a schematic and used to calibrate an instrument? How are local schematics combined together in a pattern used to recognize new instances of themselves? More specifically, how might enterprise resource planning (ERP) software (such as SAP, Oracle, or PeopleSoft) simultaneously provide both the structure needed to support meaningful comparisons and the flexibility needed for good fit with the dynamic complexity of adaptive and generative self-organizing systems?
Prior work in this area proposes a dual-core, loosely coupled organization using ERP software to build social and intellectual capital, instead of using it as an IT solution addressing organizational inefficiencies (Lengnick-Hall, Lengnick-Hall, & Abdinnour-Helm, 2004). The adaptive and generative functionality (Stenner & Stone, 2003) provided by probabilistic measurement models (Rasch, 1960; Andrich, 2002, 2004; Bond & Fox, 2007; Wilson, 2005; Wright, 1977, 1999) makes it possible to model intra- and inter-organizational interoperability (Weichhart, Feiner, & Stary, 2010) at the same time that social and intellectual capital resources are augmented.
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 different successful and failed areas of research (Latour, 2005). The resulting sociohistorical descriptions ought be translated into a practical program for reproducing successful research programs. A metasystem for complex adaptive systems of research is implied in what Roche (1998) calls a “true union of mathematics and measurement.”
Complex adaptive systems are effectively constituted of such a union, even if, in nature, the mathematical character of the data flows and calibrations remains virtual. Probabilistic conjoint models for fundamental measurement are poised to extend this functionality into the human sciences. 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 unidimensional models for measurement in their investigations.
If so, might then we be on the verge of a yet another new reading and writing of Galileo’s “book of nature,” this time restoring the “loss of meaning for life” suffered in Galileo’s “fateful omission” of the means by which nature came to be understood mathematically (Husserl, 1970)? The elements of a comprehensive, mathematical, and experimental design science of living systems appear on the verge of providing a saturated solution—or better, a nonequilbrium thermodynamic solution—to some of the infamous shortcomings of modern, Enlightenment science. The unity of science may yet be a reality, though not via the reductionist program envisioned by the positivists.
Some 50 years ago, Marshall McLuhan popularized the expression, “The medium is the message.” The special value quantitative measurement in the history of science does not stem from the mere use of number. Instruments are media on which nature, human or other, inscribes legible messages. A renewal of the true union of mathematics and measurement in the context of intangible assets will lead to a new cultural, scientific, and economic renaissance. As Thomas Kuhn (1977, p. 221) wrote,
“The full and intimate quantification of any science is a consummation devoutly to be wished. Nevertheless, it is not a consummation that can effectively be sought by measuring. As in individual development, so in the scientific group, maturity comes most surely to those who know how to wait.”
Given that we have strong indications of how full and intimate quantification consummates a true union of mathematics and measurement, the time for waiting is now past, and the time to act has come. See prior blog posts here for suggestions on an Intangible Assets Metric System, for resources on methods and research, for other philosophical ruminations, and more. This post is based on work presented at Rasch meetings several years ago (Fisher, 2006a, 2006b).
References
Andrich, D. (2002). Understanding resistance to the data-model relationship in Rasch’s paradigm: A reflection for the next generation. Journal of Applied Measurement, 3(3), 325-59.
Andrich, D. (2004, January). Controversy and the Rasch model: A characteristic of incompatible paradigms? Medical Care, 42(1), I-7–I-16.
Bond, T., & Fox, C. (2007). Applying the Rasch model: Fundamental measurement in the human sciences, 2d edition. Mahwah, New Jersey: Lawrence Erlbaum Associates.
Fisher, W. P., Jr. (2006a, Friday, April 28). Complex adaptive functionality via measurement. Presented at the Midwest Objective Measurement Seminar, M. Lunz (Organizer), University of Illinois at Chicago.
Fisher, W. P., Jr. (2006b, June 27-9). Measurement and complex adaptive functionality. Presented at the Pacific Rim Objective Measurement Symposium, T. Bond & M. Wu (Organizers), The Hong Kong Institute of Education, Hong Kong.
Husserl, E. (1970). The crisis of European sciences and transcendental phenomenology: An introduction to phenomenological philosophy (D. Carr, Trans.). Evanston, Illinois: Northwestern University Press (Original work published 1954).
Kuhn, T. S. (1977). The function of measurement in modern physical science. In T. S. Kuhn, The essential tension: Selected studies in scientific tradition and change (pp. 178-224). Chicago: University of Chicago Press. [(Reprinted from Kuhn, T. S. (1961). Isis, 52(168), 161-193.]
Latour, B. (1987). Science in action: How to follow scientists and engineers through society. New York: Cambridge University Press.
Latour, B. (2005). Reassembling the social: An introduction to actor-network-theory. (Clarendon Lectures in Management Studies). Oxford, England: Oxford University Press.
Lengnick-Hall, C. A., Lengnick-Hall, M. L., & Abdinnour-Helm, S. (2004). The role of social and intellectual capital in achieving competitive advantage through enterprise resource planning (ERP) systems. Journal of Engineering Technology Management, 21, 307-330.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests (Reprint, with Foreword and Afterword by B. D. Wright, Chicago: University of Chicago Press, 1980). Copenhagen, Denmark: Danmarks Paedogogiske Institut.
Roche, J. (1998). The mathematics of measurement: A critical history. London: The Athlone Press.
Stenner, A. J., & Stone, M. (2003). Item specification vs. item banking. Rasch Measurement Transactions, 17(3), 929-30 [http://www.rasch.org/rmt/rmt173a.htm].
Taylor, M. C. (2003). The moment of complexity: Emerging network culture. Chicago: University of Chicago Press.
Weichhart, G., Feiner, T., & Stary, C. (2010). Implementing organisational interoperability–The SUddEN approach. Computers in Industry, 61, 152-160.
Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, New Jersey: Lawrence Erlbaum Associates.
Wright, B. D. (1977). Solving measurement problems with the Rasch model. Journal of Educational Measurement, 14(2), 97-116 [http://www.rasch.org/memo42.htm].
Wright, B. D. (1997, Winter). A history of social science measurement. Educational Measurement: Issues and Practice, 16(4), 33-45, 52 [http://www.rasch.org/memo62.htm].
Wright, B. D. (1999). Fundamental measurement for psychology. In S. E. Embretson & S. L. Hershberger (Eds.), The new rules of measurement: What every educator and psychologist should know (pp. 65-104 [http://www.rasch.org/memo64.htm]). Hillsdale, New Jersey: Lawrence Erlbaum Associates.
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