Some reflections onSome reflections onwhat is measurement - and what it is notwhat is measurement - and what it is not

Luca MariLuca MariUniversità Cattaneo – LIUC, ItalyUniversità Cattaneo – LIUC, Italy

Warwick Business SchoolWarwick Business School21 July 201521 July 2015

AbstractAbstractThe concept of measurement is central to both physical and social sciences, as it is The concept of measurement is central to both physical and social sciences, as it is intimately related to the experimental acquisition and validation of knowledge. intimately related to the experimental acquisition and validation of knowledge. However, measurement is commonly considered a critical but only instrumental However, measurement is commonly considered a critical but only instrumental process, which provides “the correct assignment of numbers to physical variables” process, which provides “the correct assignment of numbers to physical variables” (Chang, Cartwright 2008) and that connects “reason to Nature” (Margenau 1958). (Chang, Cartwright 2008) and that connects “reason to Nature” (Margenau 1958). Regrettably, despite its long history, measurement is laden with stereotypes rooted Regrettably, despite its long history, measurement is laden with stereotypes rooted in outdated conceptions of the physical world, which hinder its theoretical in outdated conceptions of the physical world, which hinder its theoretical advancement and practical contribution. Moreover, the adoption of measurement in advancement and practical contribution. Moreover, the adoption of measurement in very diverse fields has resulted in context-dependent, ambiguous terminology (e.g., very diverse fields has resulted in context-dependent, ambiguous terminology (e.g., “quantity”, “accuracy”, “scale”) that makes interdisciplinary communication and “quantity”, “accuracy”, “scale”) that makes interdisciplinary communication and collaboration on measurement related topics difficult.collaboration on measurement related topics difficult.

This seminar will start by presenting a brief history of measurement and will then This seminar will start by presenting a brief history of measurement and will then discuss the following: discuss the following: ● what is measurement and why is it so important?what is measurement and why is it so important?● how is measurement different from opinion and generic evaluation?how is measurement different from opinion and generic evaluation?● how can we decide whether measurement results are acceptable? how can we decide whether measurement results are acceptable? ● what are the effects of measurement on what is being measured?what are the effects of measurement on what is being measured?● can measurement be defined and used in the same way for both physical and can measurement be defined and used in the same way for both physical and

non-physical properties?non-physical properties?

Luca Mari (M.Sc. in physics; Ph.D. in measurement science) is full Luca Mari (M.Sc. in physics; Ph.D. in measurement science) is full professor of measurement science at the Cattaneo University – LIUC, professor of measurement science at the Cattaneo University – LIUC, Castellanza (VA), Italy, where he teaches courses on measurement Castellanza (VA), Italy, where he teaches courses on measurement science, statistical data analysis, system theory.science, statistical data analysis, system theory.

He is currentlyHe is currently the cha the chairman of the TC1 (Terminology) and the secretary irman of the TC1 (Terminology) and the secretary of the TC25 (Quantities and Units) of the International Electrotechnical of the TC25 (Quantities and Units) of the International Electrotechnical Commission (IEC), and an IEC expert in the WG2 (VIM) of the Joint Commission (IEC), and an IEC expert in the WG2 (VIM) of the Joint Committee for Guides in Metrology (JCGM). He has been the chairman Committee for Guides in Metrology (JCGM). He has been the chairman of the TC7 (Measurement Science) of the International Measurement of the TC7 (Measurement Science) of the International Measurement Confederation (IMEKO). He is the author or coauthor of several Confederation (IMEKO). He is the author or coauthor of several scientific papers published in international journals and international scientific papers published in international journals and international conference proceedings. His research interests include measurement conference proceedings. His research interests include measurement science and system theory.science and system theory.

My profileMy profile

D.Petri, LM, P.Carbone, D.Petri, LM, P.Carbone, A structured methodology for measurement developmentA structured methodology for measurement development, , IEEE Trans. Instr. IEEE Trans. Instr. MeasMeas., 2015., 2015

LM, LM, Evolution of 30 years of the International Vocabulary of Metrology (VIM)Evolution of 30 years of the International Vocabulary of Metrology (VIM), , MetrologiaMetrologia, 2015, 2015

LM, D.Petri, LM, D.Petri, Measurement science: constructing bridges between reality and knowledgeMeasurement science: constructing bridges between reality and knowledge, , IEEE Instr. IEEE Instr. Meas. Mag.Meas. Mag., 2014, 2014

P.Micheli, LM, P.Micheli, LM, The theory and practice of performance measurementThe theory and practice of performance measurement, , Manag. Accounting ResearchManag. Accounting Research, , 20142014

LM, M.Wilson, LM, M.Wilson, An introduction to the Rasch measurement approach for metrologistsAn introduction to the Rasch measurement approach for metrologists, , MeasurementMeasurement, , 20142014

A.Frigerio, A.Giordani, LM, A.Frigerio, A.Giordani, LM, On representing information: a characterization of the analog/digital On representing information: a characterization of the analog/digital distinctiondistinction, , DialecticaDialectica, 2013, 2013

LM, LM, A quest for the definition of measurementA quest for the definition of measurement, , MeasurementMeasurement, 2013, 2013

LM, A.Giordani, LM, A.Giordani, Quantity and quantity valueQuantity and quantity value, , MetrologiaMetrologia, 2012, 2012

LM, P.Carbone, D.Petri, LM, P.Carbone, D.Petri, Measurement fundamentals: a pragmatic viewMeasurement fundamentals: a pragmatic view, , IEEE Trans. Instr. Meas.IEEE Trans. Instr. Meas., 2012, 2012

A.Giordani, LM, A.Giordani, LM, Measurement, models, uncertaintyMeasurement, models, uncertainty, , IEEE Trans. Instr. Meas.IEEE Trans. Instr. Meas., 2012, 2012

A.Giordani, LM, A.Giordani, LM, Property evaluation typesProperty evaluation types, , MeasurementMeasurement, 2012, 2012

V.Lazzarotti, R.Manzini, LM, V.Lazzarotti, R.Manzini, LM, A model for R&D performance measurementA model for R&D performance measurement, , Int. J. Production Int. J. Production EconomicsEconomics, 2011, 2011

A.Frigerio, A.Giordani, LM, A.Frigerio, A.Giordani, LM, Outline of a general model of measurementOutline of a general model of measurement, , SyntheseSynthese, 2010, 2010

D.Macii, LM, D.Petri, D.Macii, LM, D.Petri, Comparison of measured quantity value estimators in nonlinear modelsComparison of measured quantity value estimators in nonlinear models , , IEEE IEEE Trans. Instr. Meas.Trans. Instr. Meas., 2010, 2010

Some of my recent publicationsSome of my recent publications

A customary opinionA customary opinion

Consequence:Consequence:

never argue with an engineernever argue with an engineerif you are interested inif you are interested in

fundamental problems of measurementfundamental problems of measurement

quantum quantum physicsphysics

social social sciencessciencesengineeringengineering

number of open number of open fundamental problems fundamental problems

of measurementof measurement

Correct?

Correct?

A basic questionA basic question

What is the differenceWhat is the differencebetween measurement and opinion?between measurement and opinion?

Lexical note:Lexical note:● ““measurement”: the process (a measurement”: the process (a nomen actionisnomen actionis))● ““measurement result”: the result (a measurement result”: the result (a nomen rei actaenomen rei actae))

The different interpretationsThe different interpretationson the scientific role of measurementon the scientific role of measurement

shed some lightshed some lighton the different interpretationson the different interpretations

of what measurement isof what measurement is

«Our most prevalent notionsboth about the function of measurement

and about the source of its special efficacyare derived largely from myth»

[Kuhn 1961]

According to the Euclid’s Elements, Book V,According to the Euclid’s Elements, Book V,

– – sometimes intended as “the earliest contribution to the sometimes intended as “the earliest contribution to the philosophy of measurement available in the historical philosophy of measurement available in the historical record” record” [Michell 2005][Michell 2005] – –

«a magnitude is a part of a(nother) magnitude, the lesser of «a magnitude is a part of a(nother) magnitude, the lesser of the greater, when it the greater, when it measuresmeasures the greater» the greater»

The traditional interpretationThe traditional interpretationof the role of measurementof the role of measurement

Measurement is a (the?) toolto obtain quantitative information

«[Newton’s mechanics] was a deductive science, exactly like «[Newton’s mechanics] was a deductive science, exactly like geometry. Yet Newton himself asserted that he had wrested geometry. Yet Newton himself asserted that he had wrested its functional principles from experience by its functional principles from experience by inductioninduction. In . In other words, Newton asserted that other words, Newton asserted that the truth of his theory the truth of his theory could be logically derived from the truth of certain could be logically derived from the truth of certain observation-statementsobservation-statements.».»

[Popper 1962][Popper 1962]

The traditional interpretationThe traditional interpretationof the scientific role of measurementof the scientific role of measurement

Measurement is a (the?) toolto obtain true observation-statements

truetrue values of values of quantitiesquantities

«Theories cannot be logically derived from observations. They can, «Theories cannot be logically derived from observations. They can, however, clash with observations: they can contradict observations. however, clash with observations: they can contradict observations. This fact makes it possible to infer from observations that a theory This fact makes it possible to infer from observations that a theory is false. is false. The possibility of refuting theories by observations is The possibility of refuting theories by observations is the basis of all empirical teststhe basis of all empirical tests.».»

[Popper 1962][Popper 1962]

FalsificationismFalsificationism

«The results in the table seem «The results in the table seem to function as a test of theory. If to function as a test of theory. If corresponding numbers in the corresponding numbers in the two columns agree, the theory is two columns agree, the theory is acceptable; if they do not, the acceptable; if they do not, the theory must be modified or theory must be modified or rejected.»rejected.»

[Kuhn 1961][Kuhn 1961]

This position does not imply a re-interpretation

of the scientific role of measurement

FalsificationismFalsificationism

Given the emphasis on theories and their epistemic role, Given the emphasis on theories and their epistemic role, falsificationism seems to be less interested in “observations”:falsificationism seems to be less interested in “observations”:

measurement results can be still taken for granted...measurement results can be still taken for granted...

ConstructivismConstructivism

«Seeing is a “theory-laden” undertaking: «Seeing is a “theory-laden” undertaking: observation of observation of xx is is shaped by prior knowledge of shaped by prior knowledge of xx»»

[Hanson 1958][Hanson 1958]

... so that «pure or neutral observation-languages» do not exist... so that «pure or neutral observation-languages» do not exist[Kuhn 1962][Kuhn 1962]

«Although conception without perception is merely «Although conception without perception is merely emptyempty, , perception without conception is perception without conception is blindblind (totally inoperative). [...] (totally inoperative). [...]

With false hope of a firm foundation gone, with the world displaced With false hope of a firm foundation gone, with the world displaced by worlds that are but versions, with substance dissolved into by worlds that are but versions, with substance dissolved into function, and with function, and with the given acknowledged as takenthe given acknowledged as taken, we face , we face the questions how worlds are made, tested, and known.»the questions how worlds are made, tested, and known.»

[Goodman 1978][Goodman 1978]

If «anything holds» (including cheating about experimental results) If «anything holds» (including cheating about experimental results) [Feyerabend 1975][Feyerabend 1975], what does it remain of the claimed “special efficacy” , what does it remain of the claimed “special efficacy” of measurement?of measurement?

How is measurement different from opinion, judgment by experience, guess, … then?

ConstructivismConstructivism

… … maybe it is because quantification,maybe it is because quantification,as in Euclidean geometry?as in Euclidean geometry?

Measurement is not quantificationMeasurement is not quantificationEuclid’s Elements:Euclid’s Elements:

«a «a magnitudemagnitudeis a part of a(nother)is a part of a(nother)

magnitudemagnitude,,the lesser of the greater,the lesser of the greater,

when it when it measuresmeasures the greater» the greater»

«a «a numbernumberis a part of a(nother)is a part of a(nother)

numbernumber,,the lesser of the greater,the lesser of the greater,

when it when it measuresmeasures the greater» the greater»

and in fact, throughout the Elements, ‘measurement’ is never used, since «in the geometrical constructions employed in the Elements empirical proofs by means of measurement are strictly forbidden»

(from the introductory notes of [Euclid])

Do not consider “measure” and “measurement” as synonymous!

see also [Bunge 1973]

Measurement DOES remain different from opinion:but how?

claim: measurement claim: measurement ≠≠ opinion opinion

why?why?

traditional position:traditional position:

truthtruth quantificationquantification

falsificationismfalsificationism

constructivismconstructivism

??????

The default position for PHYSICAL properties is, more or less:The default position for PHYSICAL properties is, more or less:

measurement is a process performedmeasurement is a process performedby a properly designed, setup, and operated measuring instrument, by a properly designed, setup, and operated measuring instrument,

based on a sensor able to interactbased on a sensor able to interactwith the property under measurementwith the property under measurement

Trying to recover measurement...Trying to recover measurement...

This is maybe ok, but does not apply for NON-PHYSICAL propertiesThis is maybe ok, but does not apply for NON-PHYSICAL properties

Here appear the so-called “representational theories of measurement”Here appear the so-called “representational theories of measurement”

Measurement is any process producing information that preserves Measurement is any process producing information that preserves empirical relations (“measurement as morphic representation”)empirical relations (“measurement as morphic representation”)

(see, e.g., the monumental [Krantz et al 1971, 1989, 1990])(see, e.g., the monumental [Krantz et al 1971, 1989, 1990])

This is a reasonable necessary condition, but hardly sufficientThis is a reasonable necessary condition, but hardly sufficient

(it neglects things such as measurement standards, instrument (it neglects things such as measurement standards, instrument calibration, metrological traceability, ...)calibration, metrological traceability, ...)

Representational theoriesRepresentational theoriesof measurementof measurement

What is measurement then?What is measurement then?

algebraic algebraic conditionsconditions

experimental experimental conditionsconditions

nono yesyes

nono

yesyes 2. Galileo2. Galileo4. ???4. ???

1. Euclid1. Euclid3. Stevens3. Stevens

Measurement is a process that delivers information, as values of Measurement is a process that delivers information, as values of properties, that is:properties, that is:

● specifically related to the measurand and not to some other specifically related to the measurand and not to some other properties of the object under measurement or the empirical properties of the object under measurement or the empirical environment, which includes also the subject who is measuring environment, which includes also the subject who is measuring → it is a → it is a condition of object-relatednesscondition of object-relatedness,,

i.e., of i.e., of objectivityobjectivity

● univocally interpretable by different users in different places and univocally interpretable by different users in different places and times, thus implying that a measurement result has to be times, thus implying that a measurement result has to be unambiguous and unambiguously expressedunambiguous and unambiguously expressed→ it is a → it is a condition of subject-transparencycondition of subject-transparency,,

i.e., of i.e., of intersubjectivityintersubjectivity(see, e.g., [Mari et al 2012])(see, e.g., [Mari et al 2012])

A proposalA proposal

When measuring a physical property, these conditions are When measuring a physical property, these conditions are guaranteed by the measurement system itself:guaranteed by the measurement system itself:

● the output of the measuring instrument ideally depends only on the output of the measuring instrument ideally depends only on the property under measurement, and it is independent of all the property under measurement, and it is independent of all other properties of the empirical environmentother properties of the empirical environment→ → this confers objectivity to the provided informationthis confers objectivity to the provided information

● the measuring instrument is calibrated against a measurement the measuring instrument is calibrated against a measurement standard, thus making measurement results traceable so that standard, thus making measurement results traceable so that different measuring instruments calibrated within the same different measuring instruments calibrated within the same metrological system provide compatible informationmetrological system provide compatible information→ → this confers intersubjectivity to the provided information this confers intersubjectivity to the provided information

MeasurementMeasurementand measuring systemsand measuring systems

intersubjectivity contextintersubjectivity context

objectivity contextobjectivity context

environmentenvironment

system undersystem undermeasurementmeasurement

measurandmeasurand

other propertiesother properties

other propertiesother properties

measuring systemmeasuring systemmeasurement measurement

resultresult

measurementmeasurementstandardstandard

measurement measurement unitunit

The structure of measurementThe structure of measurement

Realistic situationRealistic situation

environmentenvironment

system undersystem undermeasurementmeasurement

measurandmeasurand

other propertiesother properties

other propertiesother properties

measuring systemmeasuring systemmeasurement measurement

resultresult

measurementmeasurementstandardstandard

measurement measurement unitunit

An issueAn issue

For physical quantities there is a long, well-established tradition For physical quantities there is a long, well-established tradition about how to design, set up, and operate this system in order to about how to design, set up, and operate this system in order to maintain non-objectivities and non-intersubjectivities at an maintain non-objectivities and non-intersubjectivities at an acceptable degreeacceptable degree

What about non-physical quantities?

environmentenvironment

system undersystem undermeasurementmeasurement

measurandmeasurand

other propertiesother properties

other propertiesother properties

measuring systemmeasuring systemmeasurement measurement

resultresult

measurementmeasurementstandardstandard

measurement measurement unitunit

A R&D programmeA R&D programme

algebraic algebraic conditionsconditions

experimental experimental conditionsconditions

nono yesyes

nono

yesyes ...

how to structurally obtain

objectivity and intersubjectivity

even without physical sensors?

A structural frameworkA structural frameworkMeasurement is a complex model-based goal-driven process Measurement is a complex model-based goal-driven process

Multiple activities performed (some implicitly) can be Multiple activities performed (some implicitly) can be organized in a structural framework inspired to both:organized in a structural framework inspired to both:● the well-known Deming cycle (Plan-Do-Check-Act) andthe well-known Deming cycle (Plan-Do-Check-Act) and● models used to represent product development processes models used to represent product development processes

in manufacturing or software engineeringin manufacturing or software engineering

In PDCA (and in FraMeD):In PDCA (and in FraMeD):● tasks are executed according to a loose tasks are executed according to a loose

ordered sequenceordered sequence● feedback is needed to refine activities feedback is needed to refine activities

until requirements are met until requirements are met

FraMeD:FraMeD:an overviewan overview

FraMeD interprets measurement FraMeD interprets measurement as a three-level hierarchically as a three-level hierarchically structured process structured process ● comprising comprising stagesstages,,● each one composed of each one composed of activitiesactivities ● performed through multiple performed through multiple taskstasks

(see [Petri et al 2015])(see [Petri et al 2015])

FraMeD:FraMeD:an overviewan overview

stages activities

planning goal setting modeling design

execution setupdata

acquisition

information extraction and

reporting

interpretation decision learning

FraMeD:FraMeD:an overviewan overview

A framework such as FraMeD is A framework such as FraMeD is useful foruseful for● discussing on concepts and discussing on concepts and

identifying conceptual or identifying conceptual or operative issues in a shared operative issues in a shared context and with a shared context and with a shared vocabularyvocabulary

● providing an analytical modeling providing an analytical modeling approach even when math is not approach even when math is not applicableapplicable

● encourage a structured encourage a structured methodology in designing and methodology in designing and performing measurementsperforming measurements

Concluding remarkConcluding remark

The empirical task of data acquisition is necessary to measurement, The empirical task of data acquisition is necessary to measurement, but measurement is much more than just an empirical taskbut measurement is much more than just an empirical task

stages activities

planning goal setting modeling design

execution setupdata

acquisition

information extraction and

reporting

interpretation decision learning

Thank youThank youfor your kind attentionfor your kind attention

Luca MariLuca Marilmari@liuc.itlmari@liuc.it

http://research.liuc.it/luca.marihttp://research.liuc.it/luca.mari

M.Bunge, On confusing ‘Measure’ with ‘Measurement’ in the methodology of behavioral M.Bunge, On confusing ‘Measure’ with ‘Measurement’ in the methodology of behavioral science, in: The methodological unity of science, M.Bunge (ed.), 1973science, in: The methodological unity of science, M.Bunge (ed.), 1973

P.Feyerabend, Against method: Outline of an anarchistic theory of knowledge, 1975P.Feyerabend, Against method: Outline of an anarchistic theory of knowledge, 1975

H.N.Goodman, Ways of worldmaking, 1978H.N.Goodman, Ways of worldmaking, 1978

N.R.Hanson, Patterns of discovery: An inquiry into the conceptual foundations of science, N.R.Hanson, Patterns of discovery: An inquiry into the conceptual foundations of science, 19581958

D.H.Krantz, R.D.Luce, P.Suppes, A.Tversky, Foundations of measurement, vols. 1-3, D.H.Krantz, R.D.Luce, P.Suppes, A.Tversky, Foundations of measurement, vols. 1-3, Academic Press, 1971, 1989, 1990Academic Press, 1971, 1989, 1990

T.S.Kuhn, The function of measurement in modern physical science, Isis, 1961T.S.Kuhn, The function of measurement in modern physical science, Isis, 1961

T.S.Kuhn, The structure of scientific revolutions, 1962T.S.Kuhn, The structure of scientific revolutions, 1962

L.Mari, P.Carbone, D.Petri, Measurement fundamentals: a pragmatic view, IEEE Trans. L.Mari, P.Carbone, D.Petri, Measurement fundamentals: a pragmatic view, IEEE Trans. Instr. Meas., 2012Instr. Meas., 2012

J.Michell, The logic of measurement: A realist overview, Measurement, 2005J.Michell, The logic of measurement: A realist overview, Measurement, 2005

D.Petri, L.Mari, P.Carbone, A structured methodology for measurement development, D.Petri, L.Mari, P.Carbone, A structured methodology for measurement development, IEEE Trans. Instr. Meas., 2015IEEE Trans. Instr. Meas., 2015

K.R.Popper, On the status of science and of metaphysics; in: Conjectures and refutations: K.R.Popper, On the status of science and of metaphysics; in: Conjectures and refutations: The growth of scientific knowledge, 1962The growth of scientific knowledge, 1962

ReferencesReferences