Measurement Science: Constructing Bridges between Reality and Knowledge

Abstract

In this paper, we propose an explanation of the crucial role of measurement in our society by describing measurement as a bridge between the empirical world and the information world. We describe measurement science as built upon this feature, and we discuss its basic motivation and scope accordingly.

Full text

Measurement Science: Constructing Bridges between Reality and Knowledge
Luca Mari and Dario Petri
In this paper, we propose an explanation of the crucial role of measurement in our society by
describing measurement as a bridge between the empirical world and the information world.
We describe measurement science as built upon this feature, and we discuss its basic
motivation and scope accordingly.
Introduction
Measurement is as old as civilization. It derives from counting, and it developed in the
ancient world mainly through trade, astronomy, building, tools, and arms production. It was
the basis for the geographical discoveries, the development of modern science, and the
growth of industrialization. The social role of measurement and measurement standards is
critical, as excellently presented in its historical perspective in [1]. Currently, measurement is
not only a key discipline for scientific investigation, but is in all domains of human activities
and endeavors to promote social evolution and prosperity. In advanced countries,
measurements are pervasive in a huge number of situations in a multitude of subjects.
Measurement is in particular a key enabler for companies to compete globally in high-tech
markets. Indeed, metrological infrastructures are an integral part of manufacturing processes
and interface with all steps of product development, assuring production efficiency as well as
product and service quality, which are both widely recognized as cornerstones of competitive
success and business sustainability. In addition, in successful trading, business organizations
employ regulatory frameworks, grounded on measurement confidence, ensuring access to
global markets that are fair, open, and without unnecessary trade barriers. Measurement plays
an increasingly important role in emerging technologies and innovations, thus enabling the
development of new products, the creation of new industries, and improvement in
productivity or in the quality of products and services. Conversely, emerging technologies
offer new advancement opportunities to existing metrology due to demands for new
instrumentation and measurement.
According to the principle that objective data are generally the basis of effective decisions
[2], the management of entire organizations employs measurement. Measurement is then a
key enabler in transportation, environmental protection, food industries, chemical industries,
pharmaceutics, medical diagnosis and treatment, as well as social and psychological sciences.
preprint of a paper published in:
IEEE Instrumentation and Measurement Magazine, 17, 6, 6-11, 2014, doi:10.1109/MIM.2014.6968922

Thus, it is not surprising that currently “an estimated 80% [of world trade] is affected by
standards and regulations” and that, according to various studies, “the cost to producers and
service providers of complying with standards can be 10% of production costs” [3].
Measurement is, of course, the basis to assess such compliance.
Unexpectedly, despite the high effectiveness of measurement for the progress of society and
its pervasive practice in human activities, the nature and extent of knowledge pertaining to
measurement are quite vague. As a result, generation of new knowledge about measurement
frequently has little regard to where it is framed in the whole picture [4]: there is disregard of
fundamental measurement concepts and presentations when teaching the discipline are
stereotypical. Use of terminology is often peculiar, idiosyncratic, and based on implicit
assumptions, and the bulk of practitioners do not make the best use of the available body of
knowledge.
Various good reasons are responsible for this situation related to the organization of the
measurement-related aspects of the scientific enterprise as shaped by historical evolution.
Galileo emphasized the importance of the experimental method from which the industrial
revolution received a decisive trigger: measurement then became the tool to obtain pure data
from empirical phenomena, a critical role usually and implicitly assumed as unproblematic.
“The results of measurement are neutral and precise; they cannot mislead” as T. S. Kuhn
synthesized [5, p.165]. That paper was a turning point; it was a reflection on the actual
function of measurement in a context where the “most prevalent notions both about the
function of measurement and about the source of its special efficacy are derived largely from
myth” [5, p.161].
However, most intellectual efforts on measurement are currently devoted to specific aspects
of highly specialized technological topics, often seemingly ignoring the necessary systemic
context that frames them. In sharp contrast, it is becoming steadily clearer that the huge range
of measurement application domains demand revising and expanding the fundamentals of
measurement, to develop a framework of general foundational concepts and principles
universally recognized as valuable and effective in every field of empirical endeavor. This is
confirmed by the fact that the problem of measurability is a key challenge in many
knowledge domains outside of natural sciences where the development of appropriate
measurement scales and processes is an actively disputed research topic [6]. A critical
presentation of the complex events around the development of measurement in social
sciences is in [7]. In addition, measurement science could and should have a crucial unifying

and enabling role in the current mainstream efforts aimed at promoting the convergence of
distinct disciplines underlying new broad fields of investigation. Unfortunately,
multidisciplinary research on the foundations of measurement are very limited and rare,
despite the fact that there is much more room for improvement in this field than in the
investigation of highly specialized topics. Referring to this ubiquitous application scenario,
this paper proposes some viewpoints and key issues on the motivation and the scope of
measurement science.
What is Measurement Science?
The International Vocabulary of Metrology (VIM) defines metrology as the “science of
measurement and its application” [8, 2.2]. That measurement is pervasively applied is not
under discussion, but is there, properly speaking, a science of measurement? Or is
measurement such a cross-disciplinary activity, from fundamental physics to psychology, that
there are no actual commonalities or characterizing features identifiable for it? The point is
not of neglecting the importance of measurement, whose effectiveness for experimental
sciences is unanimously recognized and the only doubt remains whether measurement is
merely a tool for them, even though a pivotal one, or a definitional element, as claimed by N.
R. Campbell, who stated that physics “might almost be described as the science of
measurement” [9, p.267]. Rather, the issue we underscore here is about the nature and the
disciplinary autonomy of the body of knowledge devoted to measurement.
Paradoxically, this doubt mainly arises in the context of physical measurement. Social
sciences, lacking the well-established theoretical foundation that physics grants, have been
eager to adopt and adapt measurement-related concepts and to give them a structural
justification, thus generating a relevant literature around measurement scales (at least since
[10]), measurement models (e.g., [11] and [12]), and finally measurement theory as such [13].
Physicists and engineers are sometimes unaware of this literature, for the generally good
reason that the methods elaborated in social measurement – inclusively known as
psychometrics [6] – are not so useful whenever measurement is a process whose
experimental component includes a physical transducer. Hence, the paradox exists: physical
measurement is much more effective than social measurement (or assessment: one questions
even the measurability of non-physical properties and the issue has generated a long-standing
debate [14], [15]). However, in recent decades, social scientists developed a reflection on
foundations of measurement from which physicists and engineers could find something of
interest.

Were measurement science an autonomous science, it should be possible to exhibit its
contents. What are they? The list of investigation fields of relevance for research in
measurement is inherently multi-disciplinary: from solid-state physics and electronics, to
systems theory and control theory, to signal theory and statistics, but also, information theory
and computer science, biology and nanotechnologies, philosophy of science and ontology. In
perspective, the supposition is that even political science and ethics will be progressively
interested in measurement and its social implications. Is there a distinctive, common ground
for a science of measurement in the diversity of these topics? In addition, even if it is
accepted as a science, how would it be classified in reference to Popper’s problem of
demarcation [16]; as an experimental (as physics and chemistry) or a formal (as mathematics
and logic) science? That is, does it generate experimentally falsifiable statements or theorems
derivable from suitably chosen axioms? (Fig.1).
The answer to these questions is not univocal, although the value of specialization in
academia and industry, so strongly emphasized in our epoch, would plausibly lead to the
conclusion that measurement science is just a more or less fashionable term to denote an
indistinct, fuzzy area of knowledge. A provocative opinion in this direction comes from the
following quotation, attributed to E. Fermi: “There are two possible outcomes: if the result
confirms the hypothesis, then you’ve made a measurement; if the result is contrary to the
hypothesis, then you’ve made a discovery.”
An objection could be that metrology is instead the niche area of super-high precision
activities related to the definition of quantity units, their realization in primary standards and
their key comparisons [17] as performed by National Metrology Institutes [18]. In fact, some
contexts reverse the VIM definition and consider metrology this specific part of the broader
body of knowledge devoted to measurement. Or, stating it another way, metrology might be
characterized not by content, but by its emphasis on the organizational issues arising from
that so peculiar sociotechnical infrastructure that is the metrological system. By focusing on
measurement standards and traceability chains of calibrations aimed to guarantee the
metrological traceability of measurement results and, more globally, the sustainability and the
reliability of the international technical accreditation or certification systems, metrology is
superposed to legal metrology.Measurement science would be then mainly a matter of
emphasis. A researcher working on a physical effect is operating as a physicist. Then, in the
role of a metrologist (s)he exploits the effect to design and build a transducer, (s)he studies
the sensitivity, the resolution, the repeatability, etc., of the device, and finally (s)he calibrates
the measuring instrument based on that transducer.

All of these interpretations have both conceptual and historical justifications, but we believe
that they still depict only a part, and not the most fundamental one, of the whole story. Not
only is measurement becoming a connecting glue of our sociotechnical systems, but also
measurement science is its conceptual ground. In what follows, we develop and argue this
thesis.
Reliably Connecting Worlds
We can characterize measurement science fundamentally in respect to the mentioned problem
of demarcation. Some disciplines like physics aim at the knowledge of aspects of the
empirical world and some others like mathematics at the development of formal structures.
Physics aims at producing theories of the empirical world that pass rigorous experimental
tests and, because the theories pass the tests, physics considers the theories at least partially
and temporarily true. Mathematics aims at producing theories that allow consistent
demonstrability of interesting (in some sense of the word) theorems. However, despite this
difference, or maybe exactly because of it, physics exploits mathematics as a tool to properly
represent information and perform inference from it (consider the paradigmatic role of
mathematics in physics). Mathematics looks for inspiration and experimental application in
the context of physics (as in the case of the several sub-disciplines of applied mathematics,
such as statistics and control theory). Hence, demarcation depicts two remarkably distinct
realms – let us metaphorically consider them islands – which we call:
empirical island and information island, if the emphasis is on the nature of the
inhabitants (the distinction in atoms vs. bits is suggestive but misleading, because it
does not catch the social and psychological phenomena belonging to the empirical
island), and
island of experimental methods and island of formal methods, if the emphasis is on
exploration methods.
While the islands are distinct for inhabitants and exploration methods, bridges connect them:
achievement of the goal of better knowing the whole world is by building and crossing
bridges to and from the other island.
In the current understanding of human knowledge, refining the image further is possible by
admitting the existence of an asymmetry:
while the explorers of the information island might never desire to cross bridges (let
us call them pure mathematicians or something like that; of course, they must exploit
physical means to communicate their discoveries, but this is a practical, not a

scientific, issue),
in the exploration of the empirical island, the information contents and the formal
methods have been proved more and more effective, as the status of physics witnesses
as the most mathematized of all experimental sciences.
A Different Viewpoint?
Is this metaphor of two islands too sharp a separation? Do we not live in one world and so is
there a distinction only on methods to know and intervene on it?
This is a venerable position that philosophers call monism (for a discussion on this concept,
see [19]). It states, “everything is X, where X is (depending on the author) matter, spirit,
number, perception, etc.” While the present paper is surely not the right context to enter into
such a complex discussion, if we just assume that:
energy and information are fundamental entities, and
they are not reducible to each other because energy is conserved and information is not,
then the metaphor of the two islands becomes at least plausible.
An interesting and provocative viewpoint of the information island is
Physical reality is a disaster. It is way too complicated, and nothing is
at all what is appears to be. [In physical reality] nothing can truly be
measured. [...] Any measurement made in this universe is necessarily
a rough approximation. [...] Mathematical reality, on the other hand,
is imaginary. It can be as simple and pretty as I want it to be. I get to
have all those perfect things I cannot have in real life. I will never
hold a circle in my hand, but I can hold one in my mind. And I can
measure it.” [20].
In fact, purely empirical data are considered inaccessible [5], and the island explored by
physics, chemistry, biology, ... (but also psychology, sociology, economy, ...) can only be
known, and then described, by creating maps of it. But since maps are entities that belong to
the other island, bridges are unavoidable, because they connect “the realm of things we say as
distinguished from the realm of things we do” [21, p.226], and experimental sciences are
aimed at producing things that can be said (and tested, and taught, and applied, etc.).
Measurement is then a privileged tool for building such bridges, and measurement science

can be thought of as the architecture of peculiarly reliable bridges, able to guarantee high
quality maps of (portions of) the empirical island. However, where do these guarantees come
from?
From the point of view of the information island, measurement results might be odd maps;
hybrid mixtures of native entities, such as numbers, and more or less explicit references to
entities belonging to the other island, called measurement standards, now literally widespread
all around the world. In addition, entities like 1.234 kg have absolutely nothing in them
sufficient to provide the mentioned guarantees of reliability. They can be easily created, e.g.,
by “guessing that the mass of this object is 1.234 kg” (a “things we say,” indeed). That is,
quantitative statements might be necessary in high quality maps (although ordinal scales of
measurement make this claim questionable), but they are surely not sufficient, given that
guesses, opinions, forecasts, judgments by experience, etc. can be stated in quantitative terms
while nevertheless remaining arbitrary bad maps. Measurement science is not the science of
quantity: measurement might be a, but surely not the, “process of assigning numbers to
represent qualities” [9, p.267].
Hence, measurement results are high quality maps, thanks not to some intrinsic features of
them, but because they are created by crossing high quality bridges. This is, in fact, a
characterizing feature of measurement, and, therefore, of measurement science. In a
pragmatic view, measurement can be defined [22], [23] as a process expected to be able to
produce:
information specific to the measurand, i.e., a given property of the object under
measurement, then independent of any other property of the object or the surrounding
environment (that is why sensitivity and selectivity of measuring instruments are so
important). It is a condition about the appropriate attribution of information to its claimed
object, and hence, a requirement of objectivity of information; and
information that is interpretable in the same way by different subjects in different places
and times because it is expressed in a form independent of the specific context and only
refers to entities which are universally accessible. (This is clearly the case of 1.234 kg,
thanks to the definition of the kilogram measurement unit and the existence of effective
traceability chains connecting daily usages and the realizations of the unit’s definition.) It
is a condition about the appropriate reconstruction of information by different subjects
and hence, a requirement of inter-subjectivity of information.

Uncertainty as Quantification of Connection Reliability
The analysis of the concrete feasibility of objective and inter-subjective information
processes shows that they are not yes-no features.
There are certain human activities, which have apparently perfect sharpness. The
realm of mathematics and of logic is such a realm, par excellence. Here we have
yes-no sharpness – two numbers are either equal to each other or they are not; a
certain point either lies on a given line or it does not; there is only one straight
line connecting any two points. Now, it is a matter of observation that this yes-no
sharpness is found only in the realm of things we say, as distinguished from the
realm of things we do [21, p.226].
As a critical consequence, measurements and their results, which are maps of things we do,
cannot be yes-no sharp: their goal is to be objective and inter-subjective; however, they
cannot be completely. For sure, the basic target of measurement science is to develop
empirical and formal tools for obtaining high quality maps. But, perfectly objective and inter-
subjective information is, generally, impossible to obtain for both epistemic and pragmatic
reasons: it would require gathering an infinite quantity of information by means of an infinite
quantity of resources. This leads to the conclusion that the two pillars of objectivity and inter-
subjectivity that construct the measurement science bridge lean on soft ground (Fig.2).
Hence,
… when reporting the result of a measurement, it is obligatory that some
quantitative indication of the quality of the result be given so that those
who use it can assess its reliability [24, 0.1].
Until a relatively recent past, the existence of this soft ground was justified for purely
experimental reasons. Metrologists assumed that quantities had intrinsic true values, that
measurement could only estimate due to experimental errors. This is the conceptual basis of
the distinction between systematic and random errors, which gave origin to the theory of
errors and several more or less explicitly derived estimation and filtering techniques
(techniques often grounded on further hypotheses, such as the linearity of the underlying
phenomenon and its time stationarity, a precondition for repeatability of measurement and
then statistical sampling). Accordingly, metrologists envisioned at least parts of the empirical
island as having a true map although they did not know the map, only because the bridge for
reaching the information island is not stable enough.

Many different but converging reasons have made this understanding more and more alien to
our culture, even though still implicitly widespread among some metrologists.
Are Models Unavoidable?
J. L. Borges beautifully argued about the relations between the world and its models in his
short tale On Rigor in Science:
In that Empire, the Art of Cartography attained such Perfection that
the map of a single Province occupied the entirety of a City, and the
map of the Empire, the entirety of a Province. In time, those
Unconscionable Maps no longer satisfied, and the Cartographers Guilds
struck a Map of the Empire whose size was that of the Empire, and which
coincided point for point with it. The following Generations, who were
not so fond of the Study of Cartography as their Forebears had been, saw
that that vast Map was Useless, and not without some Pitilessness was it,
that they delivered it up to the Inclemencies of Sun and Winters. In the
Deserts of the West, still today, there are Tattered Ruins of that Map,
inhabited by Animals and Beggars; in all the Land there is no other Relic
of the Disciplines of Geography [25].
The synthesis is that maps cannot be the territory [26], and this is not due to some flaws of
the bridges connecting the two islands, but to the essential differences of such islands: the
only true map would not be a map anymore, but the territory itself.
This has nothing to do with cultural relativism, as instead is sometimes mistakenly supposed.
Measurement scientists are usually, and wisely, at least moderately realist and recognize as
unproblematic that their instruments actually interact with parts of the territory, i.e., objects
and their quantities, whose existence is independent of maps (i.e., models; we are omitting
here any consideration of quantum measurement). On the other hand, the results of such
interactions have to be maps (i.e., information entities) and not empirical objects. (The astute
reader might look at the consequences of “a scheme for entirely abolishing all words
whatsoever” in Gulliver’s report of his visit to “the grand academy of Lagado” [27, part 3
chapter 5]). Hence, measurands (i.e., the quantities to which measurement results are
attributed) are not intended by the VIM as “quantities subject to measurement” anymore [28,

2.6]. Appropriately, the new definition is “quantities intended to be measured” [8, 2.3], where
the presence of these intentions emphasizes the pragmatic knowledge-based nature of
measurement and surely does not hinder realism, as clearly pointed out by M. Bunge. “An
interpretive hypothesis, such as ‘e is the electron charge’, involves the assumption that there
are certain physical objects, e.g., electrons, that is, certain things out there, independent of the
mind. […] But this is an assumption that may turn to be false. Therefore one speaks of the
hypothetical or intended referent of a theory — in the philosophical not the psychological
sense of the word. Nonetheless a physical theory does talk, even though hypothetically, of
real entities: total fictions are left to literature.” [29, p.58]. This is plausibly the most
fundamental reason why the quality of the information conveyed by measurement is currently
stated not in terms of measurement errors, i.e., differences with (generally unknowable) true
values but of measurement uncertainty, formalizing the degree of belief attributed to the
gathered information on the measurand [24], [30] – [33]. Measurement uncertainty is then an
encompassing entity. It may take into account errors if identified, and, for some reason, not
corrected, and more generally, encompass several different causes that prevent the complete
objectivity and inter-subjectivity of measurement.
Conclusions
Measurement plays a fundamental role in sustaining a fair, efficient, and evolving society.
However, despite its crucial importance, there is only a vague definition of the nature and
extent of basic knowledge pertaining to measurement science, and there is not enough
analysis or understanding of its multi-disciplinary fundamentals.
There can be many good historical reasons for this situation: mainly, those related to the
problem of demarcation, as metrology shares features of both experimental and formal
sciences and, therefore, it is neither a purely empirical nor a purely formal body of
knowledge. In fact, while paradigmatically natural sciences build maps of the empirical
island and mathematics studies how to build maps that populate the formal island,
measurement science operates in between. This is its apparent weakness: considering bridges
just as tools to make connections. However, this is also its strength; experimental sciences
and their impact on practical human activities need such connections. Thus, we need a
sharper definition and a deeper understanding of the measurement body of knowledge for an
essential basis of multidisciplinary research and for the benefit of our society.
Acknowledgement
The authors are grateful to Mr. Damiano Zanchetta for allowing the use of his figures in this

paper.
References
[1] W. Kula, Measures and Men, Princeton, NJ, USA: Princeton University Press, 1986.
[2] ISO 9000:2005, Quality management systems – Fundamentals and vocabulary,
International Standardization Organization, 2005.
[3] BIPM, Evolving needs for metrology in trade, industry and society and the role of the BIPM
Kaarls Report, Bureau International des Poids et Mesures, 2007. [Online]. Available:
http://www.bipm.org/utils/en/pdf/Kaarls2007.pdf.
[4] K.R. Fowler and J. Schmalzel, “Why do we care about measurement?” IEEE Instr. and
Meas. Mag., vol. 7, no. 1, pp. 38–46, 2004.
[5] T.S. Kuhn, “The function of measurement in modern physical sciences,” Isis, vol. 52, pp.
161–193, 1961.
[6] M. Wilson, “Using the concept of a measurement system to characterize measurement
models used in psychometrics,” Measurement, vol. 46, no. 9, pp. 3766–3774, 2013.
[7] S.J. Gould, The Mismeasure of Man, New York, NY: W. W. Norton, 1981.
[8] JGCM 200:2012, International Vocabulary of Metrology – Basic and general concepts
and associated terms (VIM), Joint Committee for Guides in Metrology, 2012. [Online].
Available: http://www.bipm.org/en/publications/guides/vim.html.
[9] N.R. Campbell, Physics – The Elements, Cambridge, England, UK: Cambridge University
Press, 1920.
[10] S.S. Stevens, “On the theory of scales of measurement,” Science, vol. 103, no. 2684, pp.
677–680, 1946.
[11] L.L. Thurstone, “Attitudes can be measured,” American Journal of Sociology, vol. 33, no. 4,
pp. 529–554, 1928.
[12] L. Guttman, “A basis for scaling qualitative data,” American Sociological Review, vol. 9, pp.
139–150, 1944.
[13] D. Krantz, R.D. Luce, P. Suppes, and A. Tversky, Foundations of Measurement, New
York, NY, USA: Academic Press, 1990.
[14] J. Michell, Measurement in Psychology: A Critical History of a Methodological
Concept, Cambridge, England, UK: Cambridge University Press, 1999.
[15] G.B. Rossi, “Measurability,” Measurement, vol. 40, pp. 545–562, 2007.
[16] S. Thornton, “Karl Popper”, The Stanford Encyclopedia of Philosophy (Spring 2013
Edition), E.N. Zalta, ed., [Online]. Available:
http://plato.stanford.edu/archives/spr2013/entries/popper.
[17] The BIPM key comparison database. [Online]. Available: http://kcdb.bipm.org.

[18] National metrology institutes of Member States of the Metre Convention and Associate
States and Economies of the CGPM, institutes designated in the CIPM MRA, and other
institutes. [Online]. Available: http://www.bipm.org/en/practical_info/useful_links/nmi.html.
[19] J. Schaffer, “Monism”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition),
E.N. Zalta, ed., [Online]. Available: http://plato.stanford.edu/archives/spr2014/entries/monism.
[20] P. Lockhart, Measurement, Cambridge, MA, USA: Harvard Univ. Press, 2012.
[21] P.W. Bridgman, “How much rigor is possible in physics?” in: L. Henkin, P. Suppes, and
A. Tarski, eds., The Axiomatic Method, Amsterdam, Netherlands: North-Holland, 1959.
[22] P. Carbone, L. Buglione, L. Mari, and D. Petri, “A comparison between foundations of
metrology and software measurement,” IEEE Trans. Instr. Meas., vol. 57, no. 2, pp. 235–241,
2008.
[23] L. Mari, P. Carbone, and D. Petri, “Measurement fundamentals: a pragmatic view,”
IEEE Trans. Instr. Meas., vol. 61, no. 8, pp. 2107–2115, 2012.
[24] JCGM 100:2008, Evaluation of measurement data – Guide to the expression of
uncertainty in measurement (GUM, originally published in 1993), Joint Committee for guides
in Metrology, 2008, [Online]. Available:
http://www.bipm.org/en/publications/guides/gum.html.
[25] J.L. Borges, Collected Fictions, New York, NY, USA: Penguin, 1999.
[26] G. Bateson, Steps to an Ecology of Mind, Chicago, IL, USA: University of Chicago
Press, 1972.
[27] J. Swift, Gulliver’s Travels, New York, NY, USA: Penguin Classics, 2003.
[28] ISO, International Vocabulary of Basic and General Terms in Metrology (VIM), second
ed., International Standardization Organization, 1993.
[29] M. Bunge, Foundations of Physics, New York, NY, USA: Springer, 1967.
[30] A. Ferrero and S. Salicone, “Measurement uncertainty,” IEEE Instr. and Meas. Mag.,
vol. 9, no. 3, pp. 44–51, 2006.
[31] A. Ferrero and S. Salicone, “Uncertainty: only one mathematical approach to its
evaluation and expression?”, IEEE Trans. Instr. Meas., vol. 61, no. 8, pp. 2167–2178, 2012.
[32] W. Bich, “From errors to probability density functions: evolution of the concept of
measurement uncertainty,” IEEE Trans. Instr. Meas., vol. 61, no. 8, pp. 2153–2159, 2012.
[33] G. B. Rossi, “Toward an interdisciplinary probabilistic theory of measurement,” IEEE
Trans. Instr. Meas., vol. 61, no. 8, pp. 2095–2106, 2012.
BIOS:
Luca Mari
Università Carlo Cattaneo (LIUC), 21053 Castellanza, Italy, e-mail: lmari@liuc.it

Luca Mari (MS 1987; PhD 1994) is a Full Professor of measurement science with the
Cattaneo University – LIUC, where he teaches courses on measurement science, statistical
data analysis, system theory. He is currently the chairman of the TC1 (Terminology) and the
secretary of the TC25 (Quantities and units) of the International Electrotechnical Commission
(IEC), and an IEC expert in the WG2 (VIM) of the Joint Committee for Guides in Metrology
(JCGM). He has been the chairman of the TC7 (Measurement Science) of the International
Measurement Confederation (IMEKO).
Dario Petri (dario. petri@unitn.it)
University of Trento, 38123, Trento, Italy
Dario Petri is a Full Professor of measurement and electronic instrumentation at the
Department of Industrial Engineering of the University of Trento. He is currently chairing
the Italian Association of Electrical and Electronic Measurements (GMEE) and he is the Vice
President for Finance of the IEEE Instrumentation and Measurement Society. Dr. Petri is the
author of over 250 papers published in international journals or in proceedings of peer
reviewed international conferences. Dario Petri is a Fellow member of IEEE.
Figure captions;
Fig.1. Scientific knowledge: the problem of demarcation and the role of measurement (©
2014 Damiano Zanchetta, used with permission.)
Fig.2. Measurement as a bridge between the empirical island and the information island (©
2014 Damiano Zanchetta, used with permission.)
SUGGESTED HIGHLIGHTED STATEMENTS
“Introduction”:
Measurements are pervasively performed in a huge number of situations by a multitude
of subjects. They are key enablers for the progress of our society.
The nature and extent of the body of knowledge pertaining to measurement are quite
vaguely identified.
Measurement is becoming a connecting glue of our sociotechnical systems and
measurement science is its conceptual ground.

“What is measurement science?”:
Measurement is a privileged tool for building bridges between the empirical and the
information islands, or the island of experimental sciences and the island of formal
sciences
“Uncertainty as quantification of bridge reliability”:
In a pragmatic view, measurement can be defined as a both conceptual and empirical
process able to produce information with a finite level of objectivity and inter-
subjectivity.