211
starting from the preliminary process of the design and construction of the measuring instrument.
7.3.1 The design and construction of a measuring instrument
Direct measurement is enabled by the use of a measuring instrument, a device able
to interact with the property under measurement
13
and to map it to a value in the
local scale embedded in the instrument. The usual structure of a measuring instrument may be described as constituted of three functional components: (i) a transducer, (ii) a scale, and (iii) something that matches the transducer outputs with the
properties in the scale. (An exception is discussed in Sect. 7.3.3.)
The starting point of the design and construction of a measuring instrument is the
formulation of the hypothesis (and in some cases the observation) of a causal relationship between the general property of interest and another general property—the
transduced property—whose instances are in some sense more readily empirically
distinguishable. In the case of temperature this happened with the discovery of thermal expansion, i.e., the transduction effect according to which changes of the temperature of a body cause changes in its volume. In the case of a competence, like
reading comprehension ability (RCA), this is typically based on the construction of
a test whose items are specifically designed for checking that competence, where
the transduced property is then the pattern of responses produced by a reader who
responds to those items. We develop the case of temperature here, and the case of
RCA in Sect. 7.3.5.
Let us consider the example of an alcohol thermometer: it is a transducer from
temperatures Θ of objects a, Θ[a], to positions X m of the upper surface of the alcohol
column housed in the glass tube, where the index m refers to the measuring instrument, in this case a thermometer. Under a hypothesis of causality, the transduction
is modeled as a map Θ[a] → X m . Prior to its usage in a measurement, the instrument
must then be configured by etching a set of marks along the tube, corresponding to
the distinguishable positions X i
*
of the upper surface of the alcohol in the tube, in
such a way that these positions—which could be called local reference properties to
emphasize their dependence on the instrument—are mapped to values, so as to
establish a local scale, modeled as a map X i
*
→ x i from reference positions X i
*
to
values of position x i . This map, which is constructed under controlled conditions
and then is assumed to be invertible, takes into account the specific features of the
instrument, and as such differs from instrument to instrument.
13 For the sake of simplicity, in this initial presentation we do not distinguish between (i) the
intended property (that is, the measurand), i.e., the property referred to in the Basic Evaluation
Equation that reports the result of measurement, and (ii) the effective property, i.e., the property
that interacts with the measuring instrument and produces an effect on it; we call both of them the
property under measurement.
7.3 A structural model of direct measurement
starting from the preliminary process of the design and construction of the measuring instrument.
7.3.1 The design and construction of a measuring instrument
Direct measurement is enabled by the use of a measuring instrument, a device able
to interact with the property under measurement
13
and to map it to a value in the
local scale embedded in the instrument. The usual structure of a measuring instrument may be described as constituted of three functional components: (i) a transducer, (ii) a scale, and (iii) something that matches the transducer outputs with the
properties in the scale. (An exception is discussed in Sect. 7.3.3.)
The starting point of the design and construction of a measuring instrument is the
formulation of the hypothesis (and in some cases the observation) of a causal relationship between the general property of interest and another general property—the
transduced property—whose instances are in some sense more readily empirically
distinguishable. In the case of temperature this happened with the discovery of thermal expansion, i.e., the transduction effect according to which changes of the temperature of a body cause changes in its volume. In the case of a competence, like
reading comprehension ability (RCA), this is typically based on the construction of
a test whose items are specifically designed for checking that competence, where
the transduced property is then the pattern of responses produced by a reader who
responds to those items. We develop the case of temperature here, and the case of
RCA in Sect. 7.3.5.
Let us consider the example of an alcohol thermometer: it is a transducer from
temperatures Θ of objects a, Θ[a], to positions X m of the upper surface of the alcohol
column housed in the glass tube, where the index m refers to the measuring instrument, in this case a thermometer. Under a hypothesis of causality, the transduction
is modeled as a map Θ[a] → X m . Prior to its usage in a measurement, the instrument
must then be configured by etching a set of marks along the tube, corresponding to
the distinguishable positions X i
*
of the upper surface of the alcohol in the tube, in
such a way that these positions—which could be called local reference properties to
emphasize their dependence on the instrument—are mapped to values, so as to
establish a local scale, modeled as a map X i
*
→ x i from reference positions X i
*
to
values of position x i . This map, which is constructed under controlled conditions
and then is assumed to be invertible, takes into account the specific features of the
instrument, and as such differs from instrument to instrument.
13 For the sake of simplicity, in this initial presentation we do not distinguish between (i) the
intended property (that is, the measurand), i.e., the property referred to in the Basic Evaluation
Equation that reports the result of measurement, and (ii) the effective property, i.e., the property
that interacts with the measuring instrument and produces an effect on it; we call both of them the
property under measurement.
7.3 A structural model of direct measurement