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?
Copyright 1995-2023 Living Capital Metrics Last updated 10 January 2023.
