197
The idea that a measurement is direct
2
if it does not involve properties other than the
measurand is also accepted by the Guide to the expression of uncertainty in measurement (GUM), which notes that “in most cases, a measurand Y is not measured
directly, but is determined from N other quantities X 1 , X 2 , …, X N through a functional relationship f, Y = f(X 1 , X 2 , …, X N )” (JCGM, 2008: 4.1.1; emphasis added). On
this matter, it has been pointed out that (Bich, 2008: p. 272; emphasis added)
even the simplest, seemingly direct measurements […] fall into this categorization. For
example, the indication of a bathroom balance, which is expressed in divisions of the scale,
is not the measurand Y (which is the mass of the person in kilograms), but simply one of the
input quantities, say, X 1 . The measurand is obtained from the indication X 1 , perhaps repeated
two or three times, and a series of corrections X 2 , X 3 , …, X N (the zero and the span of the
scale, and perhaps its linearity, or the deviation of the local acceleration due to gravity from
that of the place in which the balance was manufactured and adjusted).
The consequence is then straightforward: since “even the simplest model will be
incomplete if corrections to the indications of the instruments used in direct measurements are not taken into account […] no measurement can strictly be considered to be ‘direct’” (Lira, 2002: p. 50; emphasis added).
Something peculiar can be observed in this sequence of apparently coherent
steps: it started by emphasizing that the foundational role of measurement is guaranteed by fundamental, or direct, measurement, and ended with the admission that,
in practice, no measurement can be, in this sense, direct! This shift might have been
driven by the acknowledgment that even in the simplest measurements some computational activity is required, as part of the modeling of the empirical process that
takes place in the interaction between the object under measurement and the measuring instrument in the given experimental context. Significantly, the functional
relationship f mentioned above is described by the GUM as a model of measurement
(JCGM, 2008: 4.1.2), thus with the understanding that “observations are never
interpreted independently of some abstract model of the […] system” (Cook, 1994:
p. 4), because “observation of x is shaped by prior knowledge of x” (Hanson, 1958:
p. 19), i.e., all observations are unavoidably “theory laden”.
Let us take for granted then that, even for measurement, “pure empirical data” is
not accessible, for two reasons: first, because measurement is not a purely empirical
process, given that at least some background model is always and unavoidably
(though sometimes only implicitly) present, and, second, because any measurement
includes a computational stage (see Sect. 2.3 for a preliminary justification of this
claim). Thus, we must ask: Has this crisis of foundationalism in measurement (Mari,
2005) put an end to the very distinction between direct and indirect methods of
measurement?
The issue is not settled simply by acknowledging the unavoidable presence of the
functional relationship f, as used by the GUM and then ratified by the VIM, which
defines as a “mathematical relation among all quantities
2 About direct and indirect methods of measurement, see also the discussion by Boumans (2007:
Sect. 9.3).
7.2 Direct and indirect measurement
The idea that a measurement is direct
2
if it does not involve properties other than the
measurand is also accepted by the Guide to the expression of uncertainty in measurement (GUM), which notes that “in most cases, a measurand Y is not measured
directly, but is determined from N other quantities X 1 , X 2 , …, X N through a functional relationship f, Y = f(X 1 , X 2 , …, X N )” (JCGM, 2008: 4.1.1; emphasis added). On
this matter, it has been pointed out that (Bich, 2008: p. 272; emphasis added)
even the simplest, seemingly direct measurements […] fall into this categorization. For
example, the indication of a bathroom balance, which is expressed in divisions of the scale,
is not the measurand Y (which is the mass of the person in kilograms), but simply one of the
input quantities, say, X 1 . The measurand is obtained from the indication X 1 , perhaps repeated
two or three times, and a series of corrections X 2 , X 3 , …, X N (the zero and the span of the
scale, and perhaps its linearity, or the deviation of the local acceleration due to gravity from
that of the place in which the balance was manufactured and adjusted).
The consequence is then straightforward: since “even the simplest model will be
incomplete if corrections to the indications of the instruments used in direct measurements are not taken into account […] no measurement can strictly be considered to be ‘direct’” (Lira, 2002: p. 50; emphasis added).
Something peculiar can be observed in this sequence of apparently coherent
steps: it started by emphasizing that the foundational role of measurement is guaranteed by fundamental, or direct, measurement, and ended with the admission that,
in practice, no measurement can be, in this sense, direct! This shift might have been
driven by the acknowledgment that even in the simplest measurements some computational activity is required, as part of the modeling of the empirical process that
takes place in the interaction between the object under measurement and the measuring instrument in the given experimental context. Significantly, the functional
relationship f mentioned above is described by the GUM as a model of measurement
(JCGM, 2008: 4.1.2), thus with the understanding that “observations are never
interpreted independently of some abstract model of the […] system” (Cook, 1994:
p. 4), because “observation of x is shaped by prior knowledge of x” (Hanson, 1958:
p. 19), i.e., all observations are unavoidably “theory laden”.
Let us take for granted then that, even for measurement, “pure empirical data” is
not accessible, for two reasons: first, because measurement is not a purely empirical
process, given that at least some background model is always and unavoidably
(though sometimes only implicitly) present, and, second, because any measurement
includes a computational stage (see Sect. 2.3 for a preliminary justification of this
claim). Thus, we must ask: Has this crisis of foundationalism in measurement (Mari,
2005) put an end to the very distinction between direct and indirect methods of
measurement?
The issue is not settled simply by acknowledging the unavoidable presence of the
functional relationship f, as used by the GUM and then ratified by the VIM, which
defines
2 About direct and indirect methods of measurement, see also the discussion by Boumans (2007:
Sect. 9.3).
7.2 Direct and indirect measurement