36
Even in this introductory stage a few words are appropriate to provide an explanation of this peculiarity. The mixed nature of measurement, partly empirical and
partly informational, as mentioned in Sect. 2.2.1, originates from a process whose
high-level, functional structure may be described as follows, in the structurally simplest case of what may be called a direct measurement (a short term for “measurement based on a direct method”) (Giordani & Mari, 2019).
24
1. Transduction. An empirical device—let us call it a measuring instrument
25
—is
put in interaction with the object under measurement with respect to a property
of the object, to which it is sensitive. The device operates as a transducer: as a
result of the interaction, the device changes its state, by transducing the measured property to another property, usually called an instrument indication or
“reading”. For example (a) the spring of a dynamometer, as is traditionally found
in a bathroom scale, is intended to be a measuring instrument which transduces
the applied weight force (the property being measured) to a spring elongation
(the indication), or (b) a paper sheet with the printed text of a test comprising
several multiple-choice items is intended to be a measuring instrument which
transduces the reading comprehension ability of an individual to a response in
the form of a pattern of marks on the printed checkboxes (the indication). Hence
this stage is entirely empirical.
2. Instrument-scale application. A measuring instrument is designed so as to make
it possible to associate distinguishable indications with distinct information entities (typically but not necessarily numbers), which may be then called indication
values, through a mapping that is usually called a scale. For example (a) the
elongation of the spring is mapped to a value of length in a given unit, or (b) the
pattern of marks on the printed checkboxes is mapped to a set of scored responses.
Hence this stage is partly empirical and partly informational.
3. Calibration function computation. The measurand and the indication are not,
generally, properties of the same kind: hence indication values are generally not
accepted as suitable means to convey information about the measurand. (In our
examples, it would imply reporting information about a force by means of a
24 In Sect. 3.2 we make the presentation more realistic by introducing measurement error/uncertainty; in Chap. 7 we present this as the basic structure of a direct method of measurement, and
refine it in order to better identify its components.
25 The VIM has different definitions for measuring instrument, a “device used for making measurements, alone or in conjunction with one or more supplementary devices” (JCGM, 2012: 3.1), and
measuring system, a “set of one or more measuring instruments and often other devices, including
any reagent and supply, assembled and adapted to give information used to generate measured
quantity values within specified intervals for quantities of specified kinds” (JCGM, 2012: 3.2). The
difference is subtle: Is a balance a measuring instrument? Its graduated scale? One of its pans? A
screw in it? In order to maintain a distinction with measurement system—as introduced in Sect.
2.2.2—we will use one term, “measuring instrument”, for both. Hence a measurement system is an
overall entity that includes both empirical and informational components, while a measuring
instrument is an empirical component of a measurement system.
2 Fundamental concepts in measurement
Even in this introductory stage a few words are appropriate to provide an explanation of this peculiarity. The mixed nature of measurement, partly empirical and
partly informational, as mentioned in Sect. 2.2.1, originates from a process whose
high-level, functional structure may be described as follows, in the structurally simplest case of what may be called a direct measurement (a short term for “measurement based on a direct method”) (Giordani & Mari, 2019).
24
1. Transduction. An empirical device—let us call it a measuring instrument
25
—is
put in interaction with the object under measurement with respect to a property
of the object, to which it is sensitive. The device operates as a transducer: as a
result of the interaction, the device changes its state, by transducing the measured property to another property, usually called an instrument indication or
“reading”. For example (a) the spring of a dynamometer, as is traditionally found
in a bathroom scale, is intended to be a measuring instrument which transduces
the applied weight force (the property being measured) to a spring elongation
(the indication), or (b) a paper sheet with the printed text of a test comprising
several multiple-choice items is intended to be a measuring instrument which
transduces the reading comprehension ability of an individual to a response in
the form of a pattern of marks on the printed checkboxes (the indication). Hence
this stage is entirely empirical.
2. Instrument-scale application. A measuring instrument is designed so as to make
it possible to associate distinguishable indications with distinct information entities (typically but not necessarily numbers), which may be then called indication
values, through a mapping that is usually called a scale. For example (a) the
elongation of the spring is mapped to a value of length in a given unit, or (b) the
pattern of marks on the printed checkboxes is mapped to a set of scored responses.
Hence this stage is partly empirical and partly informational.
3. Calibration function computation. The measurand and the indication are not,
generally, properties of the same kind: hence indication values are generally not
accepted as suitable means to convey information about the measurand. (In our
examples, it would imply reporting information about a force by means of a
24 In Sect. 3.2 we make the presentation more realistic by introducing measurement error/uncertainty; in Chap. 7 we present this as the basic structure of a direct method of measurement, and
refine it in order to better identify its components.
25 The VIM has different definitions for measuring instrument, a “device used for making measurements, alone or in conjunction with one or more supplementary devices” (JCGM, 2012: 3.1), and
measuring system, a “set of one or more measuring instruments and often other devices, including
any reagent and supply, assembled and adapted to give information used to generate measured
quantity values within specified intervals for quantities of specified kinds” (JCGM, 2012: 3.2). The
difference is subtle: Is a balance a measuring instrument? Its graduated scale? One of its pans? A
screw in it? In order to maintain a distinction with measurement system—as introduced in Sect.
2.2.2—we will use one term, “measuring instrument”, for both. Hence a measurement system is an
overall entity that includes both empirical and informational components, while a measuring
instrument is an empirical component of a measurement system.
2 Fundamental concepts in measurement