217
ferred option is instead to embed the information produced by the calibration
directly in the instrument, for example by writing the public values directly on the
instrument scale in place of the indication values, as is common for many thermometers. Of course, this substitution does not imply any structural change in the model
we have just presented.
Thanks to the calibration map, pre-measurement finally upgrades to (direct)
measurement: the instrument-related map of pre-measurement Θ[a] → x i can be
composed with the calibration map x i ↔ θ j , together producing a map Θ[a] → θ j ,
which corresponds to a Basic Evaluation Equation and therefore to the expected
outcome of a measurement (again, in the simple case in which uncertainties are not
taken into account). This structure is depicted in Fig. 7.10 which is a summary version of the more explicit structure in Fig. 7.11, in which the role of the public scale
in the creation of the calibration map is also shown.
7.3.3 An alternative implementation
As the diagram in Fig. 7.11 shows, in measurements like the ones performed by
means of an alcohol thermometer the properties under measurement and the reference properties in the public scale are not compared directly: as a consequence, for
the instrument map and the calibration map to be correctly composed, the instrument must not significantly change its behavior over time or across environments.
These two conditions were characterized (in Sect. 3.2.1) in terms of instrument
stability and selectivity, respectively (if these conditions do not hold, the instrument
may be in need of recalibration or repair). Under the condition that the instrument
behaves in a sufficiently stable and selective way, the sequence shown in Fig. 7.10 of
transduction matching local scale application calibration
→
→
→
m mapping
provides an operational implementation of a direct measurement.
An alternative implementation of direct measurement is possible if the instrument allows the direct comparison of the property under measurement and the public reference properties, as in the case of the measurement of weight by means of a
two-pan balance,
17
in which the property under measurement, i.e., the weight of the
object under measurement, is directly compared with some standard masses.
18
This
process may be modeled as matching the property under measurement to the refer17 We are using the contrast of direct and indirect in two distinct ways. Given the distinction
between direct and indirect measurement, the reference is here to a difference about operational
implementations of direct measurement, which may be performed by indirectly or directly comparing the measured property and the reference properties in the public scale. In summary, a direct
measurement can be performed through an indirect (as usual) or a direct comparison.
18 This case is quite rare in the human sciences, due to the already mentioned rarity of reference
objects.
7.3 A structural model of direct measurement
ferred option is instead to embed the information produced by the calibration
directly in the instrument, for example by writing the public values directly on the
instrument scale in place of the indication values, as is common for many thermometers. Of course, this substitution does not imply any structural change in the model
we have just presented.
Thanks to the calibration map, pre-measurement finally upgrades to (direct)
measurement: the instrument-related map of pre-measurement Θ[a] → x i can be
composed with the calibration map x i ↔ θ j , together producing a map Θ[a] → θ j ,
which corresponds to a Basic Evaluation Equation and therefore to the expected
outcome of a measurement (again, in the simple case in which uncertainties are not
taken into account). This structure is depicted in Fig. 7.10 which is a summary version of the more explicit structure in Fig. 7.11, in which the role of the public scale
in the creation of the calibration map is also shown.
7.3.3 An alternative implementation
As the diagram in Fig. 7.11 shows, in measurements like the ones performed by
means of an alcohol thermometer the properties under measurement and the reference properties in the public scale are not compared directly: as a consequence, for
the instrument map and the calibration map to be correctly composed, the instrument must not significantly change its behavior over time or across environments.
These two conditions were characterized (in Sect. 3.2.1) in terms of instrument
stability and selectivity, respectively (if these conditions do not hold, the instrument
may be in need of recalibration or repair). Under the condition that the instrument
behaves in a sufficiently stable and selective way, the sequence shown in Fig. 7.10 of
transduction matching local scale application calibration
→
→
→
m mapping
provides an operational implementation of a direct measurement.
An alternative implementation of direct measurement is possible if the instrument allows the direct comparison of the property under measurement and the public reference properties, as in the case of the measurement of weight by means of a
two-pan balance,
17
in which the property under measurement, i.e., the weight of the
object under measurement, is directly compared with some standard masses.
18
This
process may be modeled as matching the property under measurement to the refer17 We are using the contrast of direct and indirect in two distinct ways. Given the distinction
between direct and indirect measurement, the reference is here to a difference about operational
implementations of direct measurement, which may be performed by indirectly or directly comparing the measured property and the reference properties in the public scale. In summary, a direct
measurement can be performed through an indirect (as usual) or a direct comparison.
18 This case is quite rare in the human sciences, due to the already mentioned rarity of reference
objects.
7.3 A structural model of direct measurement