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Capital is abstract meaning brought to life in two phases characterizing the development of transferable representations, such as titles, deeds, and other legal, financical, and scientific instruments. In the first phase, something significant is conceived. That is, meaning is created experientially or experimentally by establishing the abstract existence of something capable of standing rigorously independent of the written, geometrical, metaphorical, historical, numerical, or dramatic figures carrying it. When a figure of any kind functions as a symbol, any instance of it is then potentially interpretable as significant in a specific respect.

Once so conceived, the new form of life must be gestationally nurtured by progressively determining the limits of the environment required to sustain it. A sense of these limits is typically obtained via metrological ruggedness tests (Wermimont, 1978), wherein the conditions under which the invariant additivity, divisibility, and mobility of the numeric or other symbolic figures instrumental to capital representations come to be understood. In the human sciences, such ruggedness tests have taken the form of multiple independent experimental investigations of the fit of data to mathematical models of fundamental measurement (Fisher, 1997, 2000, 2004). In this initial phase of capital formation, the form of life acts consistently as an agent compelling agreement among investigators as to its independent real existence (Wise, 1995).



For this potential to be made actual, for what has been conceived and gestated to be born as an independent form of life, the second, maturational, phase of development must take place. In this phase, the symbol is mobilized via a standardized inscription device within a network or ecological niche prepared to recognize and accept it as a common currency mediating the exchange of its particular value. This kind of cross-laboratory coordination of instruments, samples, operators, number systems, etc. is typically obtained by metrological round-robin trials (Mandel, 1978). In this second phase are determined the various conventions through which a particular form of capital will be recognized for what is. Where the consistent display of invariant properties characterizes the first phase of capital formation, in the second phase the former agent of agreement is transformed into a product of agreement (Wise, 1995).

A law of living capital can be stated formally in the mathematical form that virtually all the laws of physics assume, a multiplication or division of measures (or an addition or subtraction, after taking the natural logarithm of the measures) (Andrich, 1988, pp. 19-20). Rasch (1960), for instance, found that his study of reading tests led to the discovery that the natural logarithm of the odds of a correct response from a particular student on a particular item was equal to the difference between the student n’s overall correct response odds B and the item i’s overall incorrect response odds D (Wright & Stone, 1979):

ln(Pni/(1-Pni)) = Bn - Di

By dropping the natural logarithm, converting the Bn - Di subtraction to the non-log equivalent division, replacing Pni/(1-Pni) with Ani, and expressing the relation in the form of a division of measures, we get

Ani = Bn / Di ,

which, Rasch (1960, pp. 110-5) observed, has exactly the same form as Maxwell’s 1876 analysis of the concepts of acceleration, mass and force in Newton’s theory of motion:

Ani = Fn / Mi ,

which represents the relation of the mass M of the object i to the force F exerted by instrument n that results in the acceleration A.

Rasch (1960, p. 115) concludes that

Where this law can be applied it provides a principle of measurement on a ratio scale of both stimulus parameters and object parameters, the conceptual status of which is comparable to that of measuring mass and force. Thus, ... the reading accuracy of a child ... can be measured with the same kind of objectivity as we may tell its weight.

The law then requires a simultaneously-effected mutual convergence and separation of 1) figures serving as the media instrumental to meaningful qualitative relations and 2) observations hypothesized to represent those relations. Rasch describes how to implement what is in effect a mathematical definition of capital by making a distinction between the abstract parameters estimated (the meaning) and the concrete observations recorded as data (the written figures):

On the basis of [one of the equations in the model] we may estimate the item parameters independently of the personal parameters, the latter having been replaced by something observable, namely, by the individual total number of correct answers. Furthermore, on the basis of [the next equation] we may estimate the personal parameters without knowing the item parameters, which have been replaced by the total number of correct answers per item. Finally, [the third equation] allows for checks on the model [another equation], which are independent of all the parameters, relying only on the observations (Rasch 1961, p. 325; 1980, p. 122).

To satisfy the requirements of this separability theorem, hash marks on a ruler that appear evenly spaced must consistently correspond with apparently evenly-spaced differences observed in some relevant range of objects extended in space, and vice versa. The convergence effected between any one instrument and any one set of things measured must then be generalizable in the sense that the same qualitative relations must be found to hold 1) when the instrument is applied to a new sample, and 2) between any other instruments of the given type and any other samples from the same population of objects. Studies of this kind of invariance are the object of metrological ruggedness tests in the natural sciences and engineering.

Similar requirements must be posed and met in the human, social, and environmental sciences for their respective forms of capital to be brought to life. Examination, survey, and assessment questions must also be required to take up consistent and invariant orders and spacings along measurement continua in association with appropriately varying observations of human, social, or natural capital phenomena. Though such a requirement may seem too rigid an obstacle for many instruments to overcome, it is met fairly routinely in the context of probabilistic models that allow for, and estimate, small amounts of error in the calibrations and measures (Bond & Fox, 2001; Fisher & Wright, 1994; Smith & Smith, 2004).

Theoretical explanations for the behaviors of items across instruments and respondent samples has advanced in the cases of a few variables to the point that the differences between predicted and observed calibrations are quite small (Carpenter, Just, & Shell, 1990; Dawson, 2002; Embretson, 1998; Green & Kluever, 1992; Stenner, Burdick, Sanford, & Burdick, 2006). Though the value of this achievement is not widely appreciated, it would seem foundational to an effective metrological paradigm for currently intangible forms of capital.

That is, the most flexible, valid, and reliable measurement can be obtained only when a form of capital is understood well enough that measures of it can be calibrated from theory. If we had to calibrate electrical cable, thermometers, batteries, and all other kinds of measuring devices in the course of their manufacture, the vast majority of the consumer products we take for granted would probably be too expensive to purchase. In that kind of economy, capital resources would be effectively dead because they would remain tied to the concrete particulars comprising them.

These resources in fact enrich our lives because mathematical theories make it possible to manufacture electrical cable, for instance, in a manner that requires only intermittent and limited testing of its properties as assurance that it will perform as expected. A standard length of cable manufactured of a standard composite alloy at a certain diameter will routinely resist the flow of electrical current by a standard unit. In so doing, the cable serves as a transferable representation of the Ohm, and facilitates the distribution, application, and sale of capital energy resources.

How might similar economies of living capital be created for other kinds of human, social, and natural resources, given that decades of measurement research have firmly established the validity of Rasch’s epistemological claim that data fitting his models supports measurement as objective as the measurement of weight?
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Living Capital Metrics
Last updated 10 January 2023.
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Measures for Managing Living Capital