199
possible amendment of the IEC definition that eliminates this circularity could be as
follows:
(provisional characterization I) a measurement method is direct if the measuring instrument
is designed to empirically interact with properties of the same kind as the measurand
where the adjective “direct” refers to such a condition of direct interaction.
5
It is also
worth noting that Ellis acknowledged the importance of this typology and called it
“associative measurement”, though, in contrast to the proposal we advance here, he
considered it a form of non-fundamental and therefore indirect measurement
(1968: p. 90).
Many measurements are direct in this sense: basically, whenever the core empirical process is a transduction from a property of the same kind as the measurand to
another property (which in current physical applications is typically an electric
quantity), as implemented in a sensor. Examples of direct measurement would then
include both the measurement of temperature by means of an alcohol thermometer—where the thermometer interacts with the object under measurement and transduces its temperature into a position of the upper surface of the alcohol in the glass
tube (temperature has well-known characteristics today, yet has a long and complex
measurement history; e.g., Chang, 2007)—and the measurement of reading comprehension ability by means of a test—where the items in the test interact with the
reader and transduce his or her reading ability into a pattern of item responses.
However, we consider this characterization to be provisional because it provides
at most a necessary but not sufficient condition for a method to be direct. In fact, it
turns out that a measurement could be indirect—according to the usual way the
adjective is used as attributed to measurement methods—even if the property with
which the measuring instrument interacts and the measurand are of the same kind.
The philosophical tradition gives us a nice example of this. When visiting some
Egyptian priests, Thales asked them about the height of the Great Pyramid and,
since they were unable to answer the question, he devised a procedure to get the
information by himself. Thales measured the length of the shadow cast by the
Pyramid and compared it with the length of the shadow cast by a vertical rod of
known length, so that he could use his theorem on the proportionality of the sides of
similar triangles to infer the Pyramid’s height. If asked to assess this case, we would
5 The distinction between direct measurements and processes of evaluation which are not direct is
sometimes accepted as unproblematic. For example, consider this quotation from John Taylor
(1997: p. 45): “Most physical quantities usually cannot be measured in a single direct measurement but are instead found in two distinct steps. First, we measure one or more quantities that can
be measured directly and from which the quantity of interest can be calculated. Second, we use the
measured values of these quantities to calculate the quantity of interest itself. For example, to find
the area of a rectangle, you actually measure its length l and height h and then calculate its area A
as A = lh. Similarly, the most obvious way to find the velocity v of an object is to measure the
distance traveled, d, and the time taken, t, and then to calculate v as v = d/t” (all emphases added).
Interestingly, the process of indirect evaluation is not even called a measurement here, as if only
direct measurements were measurements, in opposition to Lira’s conclusion mentioned above (“no
measurement can strictly be considered to be ‘direct’”).
7.2 Direct and indirect measurement
possible amendment of the IEC definition that eliminates this circularity could be as
follows:
(provisional characterization I) a measurement method is direct if the measuring instrument
is designed to empirically interact with properties of the same kind as the measurand
where the adjective “direct” refers to such a condition of direct interaction.
5
It is also
worth noting that Ellis acknowledged the importance of this typology and called it
“associative measurement”, though, in contrast to the proposal we advance here, he
considered it a form of non-fundamental and therefore indirect measurement
(1968: p. 90).
Many measurements are direct in this sense: basically, whenever the core empirical process is a transduction from a property of the same kind as the measurand to
another property (which in current physical applications is typically an electric
quantity), as implemented in a sensor. Examples of direct measurement would then
include both the measurement of temperature by means of an alcohol thermometer—where the thermometer interacts with the object under measurement and transduces its temperature into a position of the upper surface of the alcohol in the glass
tube (temperature has well-known characteristics today, yet has a long and complex
measurement history; e.g., Chang, 2007)—and the measurement of reading comprehension ability by means of a test—where the items in the test interact with the
reader and transduce his or her reading ability into a pattern of item responses.
However, we consider this characterization to be provisional because it provides
at most a necessary but not sufficient condition for a method to be direct. In fact, it
turns out that a measurement could be indirect—according to the usual way the
adjective is used as attributed to measurement methods—even if the property with
which the measuring instrument interacts and the measurand are of the same kind.
The philosophical tradition gives us a nice example of this. When visiting some
Egyptian priests, Thales asked them about the height of the Great Pyramid and,
since they were unable to answer the question, he devised a procedure to get the
information by himself. Thales measured the length of the shadow cast by the
Pyramid and compared it with the length of the shadow cast by a vertical rod of
known length, so that he could use his theorem on the proportionality of the sides of
similar triangles to infer the Pyramid’s height. If asked to assess this case, we would
5 The distinction between direct measurements and processes of evaluation which are not direct is
sometimes accepted as unproblematic. For example, consider this quotation from John Taylor
(1997: p. 45): “Most physical quantities usually cannot be measured in a single direct measurement but are instead found in two distinct steps. First, we measure one or more quantities that can
be measured directly and from which the quantity of interest can be calculated. Second, we use the
measured values of these quantities to calculate the quantity of interest itself. For example, to find
the area of a rectangle, you actually measure its length l and height h and then calculate its area A
as A = lh. Similarly, the most obvious way to find the velocity v of an object is to measure the
distance traveled, d, and the time taken, t, and then to calculate v as v = d/t” (all emphases added).
Interestingly, the process of indirect evaluation is not even called a measurement here, as if only
direct measurements were measurements, in opposition to Lira’s conclusion mentioned above (“no
measurement can strictly be considered to be ‘direct’”).
7.2 Direct and indirect measurement