244
everything that generates the transduced property is kept within the black box and
no assumptions are given about the input of the process (i.e., the effective property
and the influence properties), then the transduced property, and therefore the indication value obtained via matching and scale application, is measurement data.
Indeed, in this case the basic (syntactic) understanding of data as support for selection of differences applies, and in particular whenever a transducer invariably produces one and the same transduced property (i.e., its output is constant), thus in a
condition of “no freedom of choice” in Weaver’s words, we may safely conclude
that it is unable to produce data. The local scale as such is in fact what measurement
data is about: nothing more than that can be obtained by measurements performed
by the instrument in this case, and entropy, in Shannon’s sense, provides a means for
its characterization.
6
However, the assumed conditions make the system so simple that it is basically
useless. Even the low-level features of measuring instruments introduced in Sect.
3.2.1, i.e., sensitivity and selectivity, cannot be evaluated if the only condition is the
observability of the transduced property, and nothing is hypothesized about the
cause of the observed effect. For example, the observation of smoke (as differentiated from non-smoke) as pure data is still not sufficient to infer the presence of fire.
Measurement data becomes semantic information only when at least a primitive
version of both a model of the measurand and a model of the measuring instrument
behavior is adopted (about these models and their relations see Sect. 7.2):
• The simplest version of a model of the measurand assumes that the property
intended to be measured exists and the object under measurement carries an
instance of it, with no further specifications.
• The simplest version of a model of the measuring instrument behavior assumes
that the transducer is sensitive to the property intended to be measured and connects it causally to the transduced property, with no further specifications.
The fact that via these two models the property under measurement is embedded in
a nomic network—though possibly a very simple one that connects the property
under measurement only to the transduced property—shows that the adoption of
these two models is definitely not a trivial move: rather, it is, conceptually and
sometimes also operationally, a huge leap. Only on this basis does the transduced
property convey semantic information on the property under measurement, and
smoke becomes a sign of fire.
6 For any given set X = {x i } equipped with a probability distribution such that p(x i ) is the probability
of selection of x i (so that ∑ p(x i ) = 1), the quantity of information—which should then be more
specifically called “quantity of syntactic information” or “quantity of data”—conveyed by the
selection of x i is –log(p(x i )). Accordingly, Shannon’s entropy, −∑ p(x i ) log(p(x i )), can be interpreted as the average “amount of freedom” in the selection of elements from X. The maximum
freedom is when the probability distribution is uniform, and therefore it does not add any constraints to the definition of the set; as mentioned above, the minimum freedom—zero entropy, no
freedom at all—is when one element is certain, and therefore all other ones are impossible. From
the semiotic perspective we are discussing, this is a purely syntactic characterization: only data is
involved, with no references to the property under measurement as its possible meaning.
8 Conclusion
everything that generates the transduced property is kept within the black box and
no assumptions are given about the input of the process (i.e., the effective property
and the influence properties), then the transduced property, and therefore the indication value obtained via matching and scale application, is measurement data.
Indeed, in this case the basic (syntactic) understanding of data as support for selection of differences applies, and in particular whenever a transducer invariably produces one and the same transduced property (i.e., its output is constant), thus in a
condition of “no freedom of choice” in Weaver’s words, we may safely conclude
that it is unable to produce data. The local scale as such is in fact what measurement
data is about: nothing more than that can be obtained by measurements performed
by the instrument in this case, and entropy, in Shannon’s sense, provides a means for
its characterization.
6
However, the assumed conditions make the system so simple that it is basically
useless. Even the low-level features of measuring instruments introduced in Sect.
3.2.1, i.e., sensitivity and selectivity, cannot be evaluated if the only condition is the
observability of the transduced property, and nothing is hypothesized about the
cause of the observed effect. For example, the observation of smoke (as differentiated from non-smoke) as pure data is still not sufficient to infer the presence of fire.
Measurement data becomes semantic information only when at least a primitive
version of both a model of the measurand and a model of the measuring instrument
behavior is adopted (about these models and their relations see Sect. 7.2):
• The simplest version of a model of the measurand assumes that the property
intended to be measured exists and the object under measurement carries an
instance of it, with no further specifications.
• The simplest version of a model of the measuring instrument behavior assumes
that the transducer is sensitive to the property intended to be measured and connects it causally to the transduced property, with no further specifications.
The fact that via these two models the property under measurement is embedded in
a nomic network—though possibly a very simple one that connects the property
under measurement only to the transduced property—shows that the adoption of
these two models is definitely not a trivial move: rather, it is, conceptually and
sometimes also operationally, a huge leap. Only on this basis does the transduced
property convey semantic information on the property under measurement, and
smoke becomes a sign of fire.
6 For any given set X = {x i } equipped with a probability distribution such that p(x i ) is the probability
of selection of x i (so that ∑ p(x i ) = 1), the quantity of information—which should then be more
specifically called “quantity of syntactic information” or “quantity of data”—conveyed by the
selection of x i is –log(p(x i )). Accordingly, Shannon’s entropy, −∑ p(x i ) log(p(x i )), can be interpreted as the average “amount of freedom” in the selection of elements from X. The maximum
freedom is when the probability distribution is uniform, and therefore it does not add any constraints to the definition of the set; as mentioned above, the minimum freedom—zero entropy, no
freedom at all—is when one element is certain, and therefore all other ones are impossible. From
the semiotic perspective we are discussing, this is a purely syntactic characterization: only data is
involved, with no references to the property under measurement as its possible meaning.
8 Conclusion