245
As discussed in Sect. 7.2.2, improving the model of the measurand involves distinguishing between the intended property and the effective property and identifying the role of affecting properties, and improving the model of the measuring
instrument behavior involves distinguishing between the contributions of the effective property and the influence properties to the transduced property. These improvements make it possible to evaluate (a) the sensitivity of the transducer by assuming
that the effective property may be changed in a controlled way while all influence
properties are held constant, or, vice versa, (b) the selectivity of the transducer with
respect to a given influence property by assuming that the influence property may be
changed in a controlled way while the effective property and all other influence
properties are held constant.
Hence a pre-measurement, as performed through a sequence
transduction matching local scale application
→
→
as introduced in Sect. 7.3.1 produces the simplest case of measurement-related
semantic information: if two pre-measurements with the same measuring instrument produce distinct local values, and the instrument behaves sufficiently well (in
terms of its sensitivity, selectivity, etc.), then we may infer that the two corresponding measured properties are distinct.
Nevertheless, the process cannot yet be considered a measurement (which is why
the term “pre-measurement” was coined by Frigerio, Giordani, and Mari, 2010) for
at least two reasons: the generated information
(i) is reported in terms of values in the local scale, which are values of the transduced property—i.e., the instrument indication—which might not be of the
same kind as the property under measurement, and
(ii) is also about the instrument, not only the object under measurement.
A next stage is then required, in which the metrological system offers a structural
solution to these problems. Through the instrument’s calibration, local values are
mapped to public values, which (i) are of the same kind as the property under measurement and (ii) provide information independent of the instrument. Even though
we are not able to quantitatively evaluate this contribution of calibration,
7
it is clear
that information is thus increased: accordingly, calibration enhances the model of
the measuring instrument behavior, and makes it possible to report measurement
results as Basic Evaluation Equations (where, by the way, the metaphor of smoke
and fire no longer applies: the outcome of the inference is not that smoke and fire
7 The foundational work made some decades ago for establishing a quantitative basis of (semantic)
information—sometimes presented in terms of amount of content—did not lead to anything comparable to what Shannon’s entropy constitutes for the quantitative evaluation of the amount of
(syntactic) data (see, e.g., the extensive analysis by Hintikka, 1970). From this perspective it is
unfortunate that the basic mathematical entity of Shannon’s theory, −log(p(x i )), has been called
“quantity of information” instead of “quantity of data”. The usual remedy is to specify “quantity
of syntactic information”, or “quantity of statistical information”, or also “quantity of technical
information” in the lexicon adopted by Weaver, as mentioned above.
8.1 Introduction
As discussed in Sect. 7.2.2, improving the model of the measurand involves distinguishing between the intended property and the effective property and identifying the role of affecting properties, and improving the model of the measuring
instrument behavior involves distinguishing between the contributions of the effective property and the influence properties to the transduced property. These improvements make it possible to evaluate (a) the sensitivity of the transducer by assuming
that the effective property may be changed in a controlled way while all influence
properties are held constant, or, vice versa, (b) the selectivity of the transducer with
respect to a given influence property by assuming that the influence property may be
changed in a controlled way while the effective property and all other influence
properties are held constant.
Hence a pre-measurement, as performed through a sequence
transduction matching local scale application
→
→
as introduced in Sect. 7.3.1 produces the simplest case of measurement-related
semantic information: if two pre-measurements with the same measuring instrument produce distinct local values, and the instrument behaves sufficiently well (in
terms of its sensitivity, selectivity, etc.), then we may infer that the two corresponding measured properties are distinct.
Nevertheless, the process cannot yet be considered a measurement (which is why
the term “pre-measurement” was coined by Frigerio, Giordani, and Mari, 2010) for
at least two reasons: the generated information
(i) is reported in terms of values in the local scale, which are values of the transduced property—i.e., the instrument indication—which might not be of the
same kind as the property under measurement, and
(ii) is also about the instrument, not only the object under measurement.
A next stage is then required, in which the metrological system offers a structural
solution to these problems. Through the instrument’s calibration, local values are
mapped to public values, which (i) are of the same kind as the property under measurement and (ii) provide information independent of the instrument. Even though
we are not able to quantitatively evaluate this contribution of calibration,
7
it is clear
that information is thus increased: accordingly, calibration enhances the model of
the measuring instrument behavior, and makes it possible to report measurement
results as Basic Evaluation Equations (where, by the way, the metaphor of smoke
and fire no longer applies: the outcome of the inference is not that smoke and fire
7 The foundational work made some decades ago for establishing a quantitative basis of (semantic)
information—sometimes presented in terms of amount of content—did not lead to anything comparable to what Shannon’s entropy constitutes for the quantitative evaluation of the amount of
(syntactic) data (see, e.g., the extensive analysis by Hintikka, 1970). From this perspective it is
unfortunate that the basic mathematical entity of Shannon’s theory, −log(p(x i )), has been called
“quantity of information” instead of “quantity of data”. The usual remedy is to specify “quantity
of syntactic information”, or “quantity of statistical information”, or also “quantity of technical
information” in the lexicon adopted by Weaver, as mentioned above.
8.1 Introduction