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3.3.1 The metrological system
Measurement is a process that enables the quantity-related comparison of objects
through a process of delegation: for any two objects a and b both having a general
quantity Q (say, length or reading comprehension ability), the information that a
and b are empirically indistinguishable with respect to Q, Q[a] ≈ Q[b], can be
obtained not only through their direct comparison (e.g., by the comparison of the
extreme points of two rods, possibly mediated by a third rod, to evaluate their
lengths, or by the comparison of two individual readers by a judge, to evaluate their
reading comprehension abilities) but also by means of the independent measurement of the two quantities and the comparison of the obtained values. If the measured value of the lengths of two rods is the same, then the two rods are inferred to
have the same length; if the measured value of the reading comprehension abilities
of two individuals is the same, then the two individuals are inferred to have the same
reading comprehension ability.
Through measurement, values then operate as mediators for the comparison of
quantities of objects. The meaning of these equalities is that the chosen unit q ref is a
quantity of the same kind as Q[a] and Q[b], and Q[a] and Q[b] have the same relation with q ref , in the sense that if Q[a] = n 1 q ref and Q[b] = n 2 q ref then n 1 = n 2 . In
principle, this requires the unit q ref to be accessible for its comparison with the measurands, Q[a], Q[b], …, even if the measurements are performed in different places
and times: thus the widespread availability of the unit needs to be somehow
guaranteed.
In some cases the only practical solution is to produce and disseminate multiple
objects that realize the definition of the unit. In the tradition of physical measurement this is called a metrological system. Whenever it is possible to infer the information on the comparison to the unit from the comparison with the quantity realized
by a replicated object, a measurement result is said to be metrologically traceable
(JCGM, 2012: 2.41) to the unit. Hence, in order for one to be able to make the inference that Q[a] ≈ Q[b] from Q[a] = n q ref and Q[b] = n q ref even if the two measurements were performed in different places and times, the metrological traceability of
the two results to the same unit must be guaranteed by an effective metrological system.
The quality of metrological systems is traditionally maximized through a structural strategy of hierarchical delegation: the definition of the unit is first realized in
a primary measurement standard (JCGM, 2012: 5.4), which is then replicated in
some secondary standards that are disseminated, which in turn are replicated and
disseminated, and so on, thus generating traceability chains (JCGM, 2012: 2.42) of
standards. Mari and Sartori (2007) show that under given conditions this strategy is
both efficient and effective: the metrological system, as a network of measurement
standards and measuring instruments connected through calibrations,
• is connected by a relatively small number of calibrations (each corresponding to
an edge of the network), and therefore the system is efficient because its global
costs are relatively small,
3 Technical and cultural contexts for measurement systems
3.3.1 The metrological system
Measurement is a process that enables the quantity-related comparison of objects
through a process of delegation: for any two objects a and b both having a general
quantity Q (say, length or reading comprehension ability), the information that a
and b are empirically indistinguishable with respect to Q, Q[a] ≈ Q[b], can be
obtained not only through their direct comparison (e.g., by the comparison of the
extreme points of two rods, possibly mediated by a third rod, to evaluate their
lengths, or by the comparison of two individual readers by a judge, to evaluate their
reading comprehension abilities) but also by means of the independent measurement of the two quantities and the comparison of the obtained values. If the measured value of the lengths of two rods is the same, then the two rods are inferred to
have the same length; if the measured value of the reading comprehension abilities
of two individuals is the same, then the two individuals are inferred to have the same
reading comprehension ability.
Through measurement, values then operate as mediators for the comparison of
quantities of objects. The meaning of these equalities is that the chosen unit q ref is a
quantity of the same kind as Q[a] and Q[b], and Q[a] and Q[b] have the same relation with q ref , in the sense that if Q[a] = n 1 q ref and Q[b] = n 2 q ref then n 1 = n 2 . In
principle, this requires the unit q ref to be accessible for its comparison with the measurands, Q[a], Q[b], …, even if the measurements are performed in different places
and times: thus the widespread availability of the unit needs to be somehow
guaranteed.
In some cases the only practical solution is to produce and disseminate multiple
objects that realize the definition of the unit. In the tradition of physical measurement this is called a metrological system. Whenever it is possible to infer the information on the comparison to the unit from the comparison with the quantity realized
by a replicated object, a measurement result is said to be metrologically traceable
(JCGM, 2012: 2.41) to the unit. Hence, in order for one to be able to make the inference that Q[a] ≈ Q[b] from Q[a] = n q ref and Q[b] = n q ref even if the two measurements were performed in different places and times, the metrological traceability of
the two results to the same unit must be guaranteed by an effective metrological system.
The quality of metrological systems is traditionally maximized through a structural strategy of hierarchical delegation: the definition of the unit is first realized in
a primary measurement standard (JCGM, 2012: 5.4), which is then replicated in
some secondary standards that are disseminated, which in turn are replicated and
disseminated, and so on, thus generating traceability chains (JCGM, 2012: 2.42) of
standards. Mari and Sartori (2007) show that under given conditions this strategy is
both efficient and effective: the metrological system, as a network of measurement
standards and measuring instruments connected through calibrations,
• is connected by a relatively small number of calibrations (each corresponding to
an edge of the network), and therefore the system is efficient because its global
costs are relatively small,
3 Technical and cultural contexts for measurement systems