On the communication of measurement results

Measurement 29 (2001) 293–305www.elsevier.com/ locate /measurement

On the communication of measurement results*Gary Price

PO Box 57, Menai NSW 2234, Australia

Received 14 February 2000; received in revised form 1 June 2000; accepted 14 June 2000

Abstract

In recent times there have been a number of suggestive attempts to formulate a semiotics of measurement in the context ofmodern theory and practice of instrumentation. All have been critically reliant on one of the most ancient theories oflanguage – the picture or model or representational theory of meaning. Modern linguistics has concluded that therepresentational model is important but only part true. In this paper, a complementary approach is suggested based on theempirical observations of James Clerk Maxwell and approaches to pragmatic linguistics involving intentional systembehaviour, which stem from a famous discussion of meaning in 1955, by H. P. Grice. Application of Gricean effectivenessconditions for the communication of measurement results yields conditions relevant to traceability and the aims ofaccreditation practices. They underscore an essentially ethical dimension to modern metrology – that, as others have put it,measurements ought to be what they purport to be. It is increasingly necessary that they also be seen to be both what theypurport to be, and fit for purpose. 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Measurement; Meaning; Units; Convention

1. Introduction: why meaning is important critically on the results of very sophisticated mea-surements. The challenge is only partly technical and

Metrology, like Janus, has two faces. One looks to involves also the clear communication to the widerthe future from the immense developments in science society of users of such measurements not onlyand technology of the past century or so. The other is measurement results, but their meaning.ancient and looks to the integral role that measure- So far as human decision and action on the basisment generally plays in the common daily affairs of of measurement is concerned, what matters is notall men and women in all organised society. Bring- meaning as understood by the ‘speaker’ – theing these two perspectives together is a significant reporter of results – but meaning as understood bychallenge to modern metrology as science and the audience – the decision maker or actor. In thattechnology becomes increasingly important to socio- respect, transparency – and especially the lack of it –economic well being. A great many important deci- assumes vital importance. Instrumentation growssions at all levels of socio-economic, industrial, almost daily more complex and less transparent.trading, medical and environmental activity depend With more and more precision, audiences know less

and less what the measurements mean on which theirdecisions depend. With less transparency goes the*Tel.: 161-29-543-2224; fax: 161-29-543-2224.

E-mail address: [email protected] (G. Price). need for the measurer and reporter to earn more

0263-2241/01/$ – see front matter 2001 Elsevier Science Ltd. All rights reserved.PI I : S0263-2241( 00 )00053-1

294 G. Price / Measurement 29 (2001) 293 –305

trust. How to do that is a major issue for modern constant multiples. The mathematical group structuremetrology. of all the ratio scales for any given quantity is

defined by the similarity group of operations, wherethe numerical values or scale or measure numbers, x9

and x of any given example of the quantity, as2. Maxwell’s factmeasured on any two such scales, are related by anequation of the form x9 5 ax, where a is a constantLet us start with a fact. I call it Maxwell’s fact. Infor any pair of such scales, representing the ratio ofany era there are a rare few genuinely original ideastheir respective units. The principle is that whateverwithout precedent which immediately become soparticular scale is used, any quantity valuetrivially obvious as to hardly ever again require(number3unit) is an invariant which does not de-conscious reference. I am going to refer to two suchpend on human convention.and Maxwell’s fact is one of them. It is a cornerstone

However, as a general proposition about theof modern metrology and it is an empirical observa-linguistic form in which measurements are actuallytion on the use of language [1], a fact of languageexpressed, ‘Maxwell’s fact’ applies equally to alluse:quantitative measurement regardless of the particularscale type employed. For example we use the sameEvery expression of a quantity consists of twoform, of number multiplied by unit, to expressfactors or components. One of these is the nametemperature in degrees celsius despite the fact thatof a known quantity of the same kind as thethe celsius scale is an interval scale with only aquantity to be expressed, which is taken as aconventionally assigned zero. In this case, we needstandard of reference. The other component is theto remember that not all the common arithmeticnumber of times the standard must be taken inoperations have a physical counterpart. We cannotorder to make up the required quantity. Thesay, for example, that one temperature is ‘twice’standard quantity is technically called the unitanother. This is because the measure number, orand the number is called the numerical value ofnumerical value is a number on the same scale asthe quantity.defined by the unit itself and which attaches nomeaning to the operation of absolute doubling ofThis is often summarised by a simple formula:temperature values. The best we can say is that one

Value of physical quantity 5 number 3 unitinterval may be twice another interval on such a

Where ‘equals’ means ‘is expressed, modeled, or scale. Time is another example of a quantity com-represented by’. monly expressed in terms of interval scales. Interval

This is arguably the most basic equation in all of scales form the group structure of the linear group ofmodern measurement. operations, where x9 5 ax 1 b, and where b is also a

It is perhaps worth noting that Maxwell himself, constant for any pair of such scales, reflecting theand many subsequent workers, applied this proposi- conventional assignment of the zero or origin. Ratiotion only to what came to be called ratio scales of scales may be regarded as the case where b50.measurement and which possess a non-conventional It is simply a fact of common language use thator natural zero (or origin), the unit defining the we express quantitative measurement results as ainterval between zero and one. Stevens [2] later number multiplied by a unit and this is so whetherdeveloped the basis for much of the modern under- ratio or interval scales are involved. The difference isstanding of measurement scales, distinguishing be- in the meaning that may be attached to the unit andtween nominal, ordinal, interval and ratio scales. whether in so defining the scale, a conventional or aRatio scales have the immensely useful property that natural zero is specified.they model the ordinary sequence of rational num- Similarly we assign ordered numbers to chemicalbers and thus all the common arithmetic operations elements on the even more basic ordinal scale of thehave a physically possible analogue and different periodic table of the elements but always rememberunits for the same quantity are simply related as that there are no elements of atomic number zero or

G. Price / Measurement 29 (2001) 293 –305 295

2.5. Another example of an ordinal scale is any ing and decoding steps. It is this syntactic theory,sequential numbering of pages in a book. However, concerned with the accuracy with which symbolsthere would be some disagreement among metrolog- may be transmitted which is at the heart of modernists as to whether ‘measurement’ on an ordinal scale information technologies and their myriad applica-is really quantitative measurement (or even measure- tions to measurement instrumentation. It says veryment at all). Stevens, who subscribed to a general little about the content of whatever symbols may bedefinition of measurement as the assignment of transmitted. The output of a roomful of monkeysnumbers to things according to rules so as to with typewriters is indistinguishable from Hamlet sorepresent facts about them, argued not only that the far as the amount of information is concerned. Howuse of ordinal scales was an example of measure- those symbols convey a meaning and how thatment, but that the even more trivial operation of meaning affects the behaviour of the recipients isidentifying a measurand on a nominal scale, where unaddressed by the syntactic theory of information.numbers are simply used as names for classes, could Weaver himself, in a note to the Mathematicalbe regarded as a measurement of sorts. However, theory, emphasised the three separate but interactingStevens also acknowledged that there could be no levels of communication: the technical (the subjectquarrel of substance or principle with those who of the Mathematical theory); the semantic (how doobject to the attribution to such a process of the the symbols convey a meaning); and the pragmatic‘dignity implied by the term measurement’. (how does the meaning affect behaviour of the

recipients). In more recent times, the last two topicshave often been discussed under the title of semiotics

3. Information and measurement [5].

Maxwell’s fact tells us how we express measure-ment results but it doesn’t tell us what they mean. 4. Meaning and measurementInformation theory doesn’t tell us what they meaneither and this basis of modern instrumentation is a Lord Kelvin, in his famous dictum reminded us oftheory only of the transmission, conservation and the creative, epistemological aspect of measurement.correction of physical symbols. To describe physical systems is to have a meagre

In the 1920s Sir Ronald Fisher in his classical kind of knowledge, but when we measure, ourwork on statistical methods and experimental infer- knowledge is of an entirely different order. Some-ence proposed a measure of the amount of infor- thing new comes into being, accessible to the humanmation that may be extracted from a physical system, understanding.given the unavoidable errors (today we would prefer Recently, originating particularly in suggestionsto call them uncertainties). Fisher’s proposal [3] was by Finkelstein [6] and Finkelstein and Leaning [7],essentially a linear function of an experimental the first steps have been taken towards a comprehen-selection of a state from the possible states of the sive theory of instrumentation and measurement [8–system. 14]. The practical import of this program should not

The theory of information with which we are be underestimated. In many areas there is still thetoday familiar is a logarithmic measure yielding a epistemological gulf remarked on by Finkelstein [15]metric formally similar to the thermodynamic ex- between the general theory of measurement and thepression for negative entropy, but the essential idea understandings possessed by those who design andremains: the selection of a message from an array of engineer instruments. This is particularly noticeablepossibilities. It received its mature expression in the in the important area of chemical measurementsinfluential Mathematical theory of Communication which in the past few decades has undergone whatby Shannon and Weaver [4]. It is not a theory of has been termed the fourth big scientific revolutionmeaning but a theory of the encoding, transmission [16] – the instrumental revolution. At the same time,and decoding of physical symbols, given noise in the as part of this very process, the social, industrial,system and corrective feedback between the encod- economic, trading, medical and environmental im-


portance of such measurements has expanded represent. Indeed, subsequent to Wittgenstein’s par-dramatically. ticularly clear statement of a picture theory of

Throughout the contemporary program for under- language a whole new field of mathematical logicstanding modern instrumentation and measurement emerged, concerned with the connections betweenthe problem of meaning and measurement has been formal languages and their interpretations, calledbroached. Recently for example a proposal was made model theory, developed by Tarski [20] and elabo-for a semiotics of measurement [17,18]. In all of that rated by Suppes and Zinnes [21] and Pfanzagl et al.important literature, there exists a ubiquitous theory [22] as a basis for a formal theory of measurement.of meaning. Very often it is quite explicit, but even A fragment of model theory is of course, none otherwhen it is not, it is very much taken for granted. than the quantity calculus, which is the basis of the

International System (SI) of units [23].There is something profoundly true and important

5. The picture theory of meaning about the picture theory of meaning, especially whenapplied to physical science, mathematics and logic. I

The received theory of meaning is variously called do not want to suggest that it is wrong. Far from it.the picture, or representation, or model theory. It is a Yet there is also something profoundly dissatisfyingtheory with impeccable provenance and an illustra- about it. It is at least incomplete and not the wholetive example of its expression is Wittgenstein’s story. This is nicely illustrated in an anecdoteepoch making Tractatus Logico-Philosophicus which sometimes told about Wittgenstein.transformed logic and influenced modern thinking in As is well known, after the Tractatus, Wittgensteinfields as diverse as mathematics, linguistics, the felt that he had dissolved all the substantial puzzlesphysical and social sciences and psychology. It is of philosophy, abandoned Cambridge and took upsometimes forgotten that the young Wittgenstein was school teaching. Later he and others had secondsteeped in the culture of classical mechanics, thoughts. There is a story that he had his trip toprofoundly influenced by Hertz and Boltzmann and Damascus on a train journey with the Italianstudied under Rutherford. Here he is on classical economist Piero Sraffa. Wittgenstein was explainingmechanics [19]: the Tractatus to the economist who made a familiar

Italian gesture in which the palm of the hand isLet us imagine a white surface with irregular passed under the chin. It signifies something betweenblack spots on it. We then say that whatever kind mild contempt and ‘why are you bothering me withof picture these make, I can always approximate this?’ It stopped Wittgenstein dead in his tracks, notas closely as I wish to the description of it by because of any imagined slight, but because here wascovering the surface with a sufficiently fine an example of perfectly good communication ofsquare mesh, and then saying of every square meaning which did not appear to involve any picturewhether it is black or white. making at all. The story is seminal. Thenceforth the

question was not ‘What pictures do we pass betweenThe picture theory of meaning holds that there is a each other?’ but ‘What do we do with them, what ismapping or correspondence between our descriptions their use?’and what they describe. Our propositions are models Another straw in the wind for the picture theoryor representations of what they are about and that is was the theory of the quantum and the Bohr orhow they acquire their meaning and how we com- Copenhagen interpretation of this magnificently suc-municate it – we pass on to others a picture by cessful theory of physics. Even today, most physicslinguistic means, a representation or linguistic model textbooks in their first paragraphs sternly enjoin theof what is meant which is decoded by the audience. student to abjure their instinct for picture making.

It is a theory of language that is very amenable, Quantum theory does not construct pictures. Thereeven trivially self-evident, to the scientific temper of are only equations and measurement informationmind. Theories in the physical sciences often are created by our experimental intervention. So long asmodels, which stand in correspondence to what they the equations cohere with the measurements when-


ever they are made, all is well and no further enquiry even less so with the psychological states of theiris possible into what the physical system might be participants.like between the disturbing measurements. There is If we are dealing with more complex systems,no picture to be had. Our measurements are more such as motor cars, clocks or chess playing com-like artifacts of our interaction than representations puters, we find it more useful to adopt the designof an undisturbed world. stance, in which we regard the system as if it were

designed to achieve some purpose. Thus, we do notneed to learn mechanics in order to drive a car. Welearn there are various things like the accelerator,

6. Intentional system theory brake etc, which are designed to do various otherthings. Only when the car breaks down need we

In the second half of the twentieth century we revert to the physical stance. Similarly, no one cancame to understand more about natural languages, beat a chess-playing computer by following thesuch as English as it is used and in distinction with physical explanation of all its workings. Rather, wethe formal languages of mathematics. Many of these assume it has been designed to win at chess follow-developments come under the general heading of ing the rules of chess and we act accordingly (andpragmatics, the study of the use of language in usually get beaten anyway).context and the context dependence of many aspects When we adopt the intentional stance we view theof linguistic interpretation. One theme, introduced by system, like ourselves, as having intentions – needs,Austin [24] was that language is a kind of per- beliefs, desires, cravings, understandings, etc and weformance, a series of locutionary acts, which we do interact with it on the basis of that hypothesis. Therein order to do other things. We promise, persuade, can be many levels of intentionality. For example,cajole, threaten, explain, describe, declare, theorise, we explain the tendency of bacteria to move towardsquestion, count, calculate, report – all things we do nutrients or plants to grow towards light by sayingwith words. The elaboration of this idea is some- they may be seen as if they were first ordertimes called ‘speech act theory’ [25] intentional systems seeking to satisfy a basic need.

Another theme, related to speech act theory, was We even say sometimes that electrons seek thethe theory of conversation, sometimes called the lowest available energy state. If your dog is simplytheory of implicature and associated with the work of happy to see you then that is first order behaviour butGrice [26]. Both of these themes and the evolution of if your dog recognises that you are angry and forpragmatics were reviewed in Searle [27]. Dennett example cowers when you shout, then that is second[28] summarised an important, intriguing and some- order behaviour. Second order intentional systemstimes controversial aspect of these developments that act as if they recognise and react to other intentionalhe called ‘the intentional stance’. systems. Third order intentional systems act as if

When we need to explain or deal practically with they intended to change the intentional state of otherpeople, things or events we adopt one of three systems, such as when your dog tries to make youdifferent explanatory stances: the physical stance, the believe that it is angry by, for example, baring itsdesign stance, or the intentional stance. teeth and snarling. It would be a fourth order and

If we need to explain the motion of the planets, we worryingly intelligent dog that understood that it wasadopt the physical stance. That is, we regard the trying to make you believe that it was angry. A fifthsystem as a physical system governed by the laws of order dog might know that you were intending tophysics as we know them and invoking that explana- make it believe that you didn’t believe it – thistion is sufficient. Using the physical stance we might would be a very scary dog and not a wise choice ofobserve a plummeting stockbroker and point to pet for small children. And so on.initial conditions, the law of gravity and the ap- There is theoretically no limit to the number ofparatus of mechanics in explanation. However, the intentional levels and shades of persuasion or subter-physical stance is less useful in dealing with socio- fuge or double or triple taking but (as Dennetteconomic events such as stock market crashes and himself wondered) I suspect that you wonder


whether I realise how hard it is for you to be sure not on duty partook of the rum rations. The teetotal-that you understand whether I mean to be saying ling Captain, who was on duty, noted in the log thatthat you can recognise that I believe you to want me ‘tonight, the First Mate is drunk’. When the Firstto explain that most of us can keep track of only five Mate later duly took his watch on the bridge, he wasor six orders of intentionality at most. chastened to find this log entry and in his turn

For us humans there is something intrinsically carefully wrote that ‘tonight, the Captain is sober’.interesting about fourth order intentional behaviours. Literally, the First Mate’s log entry is undeniablyWe tend to recognise something of the self-reflec- true, but its intentional meaning is quite otherwise.tiveness that characterises our own mental life. The implication, which the owners would naturally

Adopting the intentional stance is to regard the draw on reading it, is that this was an exceptionalsystem you are interacting with as a rational system, state of affairs meriting special remark – putting thenot unlike yourself and you try to look at things from First Mate’s transgression in a more favourable light.its point of view. This was the basis of the other So far as scientific communication is concerned,genuinely original and unprecedented idea. one of the founders of the modern theory of in-

formation, Warren Weaver captured a little of thespirit of the Gricean approach when he proposed to

7. Intentional meaning the modern scientist struggling with communicationproblems the concept of communicative accuracy

In 1957 H.P. Grice [29] gave an account of [30]. It rests on the fact that the effective accuracy ofspeaker meaning in all language-like communication: a communication depends primarily on the interpre-

When a speaker S performs some language-like tation given to it by the audience and Weaveract X for the attention of some audience A, then S suggested two conditions for communicative accura-means that P if the following conditions are satisfied: cy:

1. S intends A to think that P First, taking into account what the audience does2. S intends A to recognise this intention and does not already know, it must take the3. S intends to succeed at (1) by means of success at audience closer to a correct understanding . . .

(2) Second, its inaccuracies (as judged at a moresophisticated level) must not mislead . . .

In other words we rely on the recognition of our Both of these criteria must be applied from theintention to communicate and we use that very point of view of the audience, not from the morerecognition to get our message across. Language-like informed and properly more critical point of viewcommunication presupposes the intentional stance: of an expert.the speaker assumes the audience is an intentionalsystem and the aim is to get the audience to Weaver concluded his editorial in Science with tworecognise that the speaker is also an intentional examples, both of which as it happens operationallysystem. The way this is done is central to getting the mean the same thing from the point of view of theaudience to reason towards the intended meaning. picture theory of meaning: two men coming home

The Gricean framework for understanding com- from work greet their wives. One says, ‘My dear,munication proposes an interaction between speaker when I look into your face, time stands still’. Theand audience. The audience is active in working out other remarks, ‘My dear, your face would stop ameaning, quite unlike the picture theory, which clock’. The difference between representationalviews the audience as a passive decoder. meaning and intentional meaning could not be

Large vessels at sea maintain a log on the bridge starker.in which the officer in control at the time may make Grice presented a suggestive framework for inten-observations, which are scrutinised by the owners in tion dependent communication but it is important nottheir assessment of the efficiency of vessel and crew. to claim too much for it. It is a proposal, a startingOn one such occasion the ship’s First Mate whilst point and not a grand theory. We need to ask how


well it fits particular language acts. How well does measurement results. One of the trivial results ofthis framework fit the communication of measure- Lewis’s analysis is that if conventional signaling isment results? One way to address that question is to involved, then we are always dealing with an exam-examine the role of convention in communication. ple of Gricean communication by getting our inten-

tions recognised. This is because linguistic conven-tions are a kind of communicative handshake: to use

8. Convention a convention is to signal a desire to communicateand if successful at this, also to indicate for the

Language use depends on the existence of conven- audience the mutual understandings which wouldtions. A dictionary is basically a compendium of enable the audience to infer the intended meanings.conventional word meanings but there are many Thus, we have an undeniable syllogism:other conventions on which we depend, such assentence construction, grammar, punctuation etc. We • Units are involved in the communication ofare familiar with many other signaling conventions measurement results (Maxwell’s Fact)too. You drive towards the traffic lights and they turn • Units are conventional in naturered. That conventionally means ‘stop’ and in re- • Whenever conventions are involved in language-sponse, you do indeed stop. like behaviour, then Gricean communication is

We take it for granted that systems of measure- being attemptedment units are conventional in nature. But what • Therefore, the communication of measurementexactly does it mean? Lewis [31] has brilliantly results is an example of Gricean communicationanalysed the nature of convention. Conventions arebasically a means to coordinate actions within apopulation. They are a type of behavioural regularity, 9. Discussion: quantities, units and etalonswhich is mutually known, expected, preferred andmaintained to the benefit of all in the population. In The foregoing arguments indicate that particularlanguage use, they coordinate speaker and audience attention needs to be given to the nature of units inunderstanding. communicating measurements and this requires us to

A behavioural regularity R within a population in consider the relations between quantities, units andrelevantly recurrent situations is a convention if (and etalons. Modern metrology was founded on theonly if): notion of physical quantity as a primary concept and

the origin of this idea is what I have labeled1. There are alternatives to R (e.g. in Australia we ‘Maxwell’s Fact’. Being a logically primitive con-

drive on the left hand side of the road but we cept, it is not surprising that all attempts to provide acould equally have chosen to drive on the right) general definition of ‘physical quantity’ turn out to

2. Everyone conforms to R (we play our part and be circular. It is not possible to point to anything indrive on the left) nature and to say unambiguously that it is a quantity,

3. Everyone expects everyone else to conform to R in the same way that it is also not possible to point to(we expect everyone else to play their part and anything and say that it is a number. However,drive on the left) particular physical quantities (such as mass, length,

4. Everyone prefers to conform to R, rather than any time etc) are capable of operational definition inof the alternatives on condition that everyone else terms of the group of operations that may be usedconforms to it. (we prefer to drive on the left hand consistently to measure them, where ‘group’ has aside only so long as everyone else does too) meaning closely analogous to the mathematical use

5. We all like the result (accidents are thus avoided) of that term. Quantities are therefore essentiallyconceptual constructs, but with empirical applica-

Systems of measurement units also conform very tions. In keeping with that operational conception ofclearly to these requirements of convention, the final particular quantities, measurement itself is oftendesirable objective being mutual understanding of defined as an operation assigning a number to


specified objects and events in some commonly ment result is complete unless its total range ofunderstood, rule governed way so as to describe, and uncertainty with respect to its expressed units is alsoimprove our knowledge of them. specified. The estimate of the uncertainty of a

The concept of a measurement unit is every bit as measurement result reflects the necessary absence offundamental to the physical sciences as the concept any exact knowledge of a value of the measurand inof number is to arithmetic. Indeed, units (and their terms of the expressed units and this includes bothcorresponding scales) may be regarded as the means the uncertainties with which an etalon realises itswith which to apply arithmetics to physical mag- unit and the subsequent uncertainties introduced innitudes in general. Units are sometimes regarded as the comparative measurement processes themselves.of little interest by scientists and technologists on the The other side of this coin is accuracy. Accuracygrounds that they supposedly communicate no new does not mean that a measurement has been carriedinformation, but the arguments given above show to as many decimal points as possible. Accuracythat units do have a great deal to do with the means having the confidence that a measurementcommunication of meaning. Measurement units are a result gives a value within a known range ofbasic linguistic tool with which consistently to uncertainty. Another way to look at this is throughexpress and communicate quantitative knowledge of the traditional metrological concept of traceability,particular objects, events and phenomena. They are which is the means by which systematic error mayconceived as examples of a particular amount of be controlled in measurement processes – a neces-their particular quantities. Measurement units are sary condition for measurements to be what theyabstractions with a name – they are concepts defined purport to be.by convention and conceived of as quantities of the Traceability today is generally understood as asame kind as the quantity being expressed, but chain of comparisons linking a measurement to anselected by convention as a particular amount of that accepted standard, but as Bellanger [32] in hisquantity to allow the expression of other amounts of classic discussion emphasised, it is a rapidly evolv-the same kind of quantity in a consistent numerical ing concept reflecting both the pace of technologicalmanner. change in measurement practice and the increasing

Etalons are not identical to units. Units are con- significance of the decisions made on the basis of thecepts with a name, and in that regard not unlike ‘pi’, resulting measurements. Only a few decades ago‘42’ and ‘Euclidean equilateral triangle’. Etalons traceability simply meant the existence of a chain ofhowever are material objects, instruments or pro- calibration certificates with sometimes little thoughtcedures that realise a unit in a material way – they as to whether they were appropriate, whether theybring the flesh of matter to the idea (so to speak) and had been competently performed or even whether theare the practical means by which we may con- time intervals between them were appropriate. Insistently assign actual numerical values to represent 1980 Bellanger cogently argued that traceabilityquantities in particular objects, phenomena and ought to be regarded as the means to ensure mea-events. The practical, material realisation of a unit surements of accuracy adequate to their purpose.can only be achieved with a finite uncertainty, just as More recently still, the accreditation model ofany equal angled triangle drawn in the sand can only traceability has been widely adopted, involving aever approximate its Euclidean counterpart. third party peer assessment of actual technical

competence of those performing important calibra-9.1. Etalons, uncertainty and traceability tions. This not only gives assurance to the users of

measurements, but properly performed is an im-That distinction, between the defined abstraction portant means of increasing technical capabilities

(the unit) and its material realisation (the etalon) is through the interactions of assessors and otherfundamental to measurements being in physical fact, laboratories. Nicholas and White [33] conciselywhat they are symbolically purported to be in summarised these developments in their proposedlanguage. No etalon can realise its unit to less than a definition of traceability as the ability to demon-finite uncertainty. Thus, no statement of a measure- strate(my emphasis) the accuracy of a measurement


in terms of its expressed units. According to this necessary to assure interested parties that measure-definition, the traceability requirements are then a ments are fair and trustworthy.semi-public checklist to ensure all relevant factors This is very much an economic role of accredita-affecting accuracy have been taken into account and tion practice in modern metrology. Transparencyquantified as an uncertainty at a stated level of bears directly on the integrity of both measurementconfidence. systems and of markets. Fukuyama [35] has pointed

Increasingly today traceability must not only be out that trust is of great economic significance. Thebut be seen to be, and that by the self interested users costs of misunderstanding are high in terms ofof measurements who are not necessarily expert in search, transaction and disputation as well as barriersthe field of metrology in question. For example it to innovation. As transparency is reduced so the needwould be a rare medical practitioner or even rarer for independent technical interaction and oversight ispolitical decision-maker in the environmental field increased if confidence is to be maintained.who could clearly say what a mole is and how the Sophisticated electronic instrumentation tends tomeasurements on which they may depend are trace- reduce transparency, as do complicated or inferentialable to it. This is not to criticise such decision- measurement procedures, empirical correction fac-makers. The reverse is true – they have every right tors and computer dependent data handling andto expect an absolute integrity, comprehensibility modelling. All of these are characteristic of modernand transparency in the advice to them, advice that measurement. Indeed it is sometimes said that thethey in turn may need to explain to patients or the modern measurement instrument is rapidly disap-electorate. pearing up the serial port of a computer.

11. Gricean conditions for effective10. Trust and transparency

communication

Transparency has a bearing on technical proce-Grice proposed that speakers and audiences are

dure. An example is found in the now rapidlyintentional systems and to say that a speaker (S)

evolving field of metrology in chemistry. Internation-meant something (P) by uttering (X) is to say that S

al efforts to secure a common basis have resulted inintended the utterance to produce some desired effect

a definition [34] of a Primary Method of Measure-in the audience (A) by means of the recognition of

ment as:that very intention. How is this achieved – how is itthat the audience comes to think what was intended?

a method . . . whose operation can be completely In order for it to be generally sufficient to get yourdescribed and understood, for which a complete intentions recognised in order to be able to get youruncertainty budget can be written down in terms audience to believe something, there are two con-of SI units, and whose results may therefore be ditions: that the audience believes you are neither liaraccepted without reference to a standard for the nor fool. More formally:quantity being measured. (my emphasis).

1. Sincerity condition – if S intends A to believeA defining characteristic of a primary method at even that P, then S believes that P (the speaker isthe highest metrological levels for the realisation of honest)units is in fact, transparency. 2. Authority condition – if S believes that P, then P

Transparency however is generally important at all (the speaker is reliable in judgement)stations and levels of measurement traceabilitychains. It means that all interested parties are equally Taken together, sincerity plus authority amounts toinformed as to relevant variables affecting the mea- audience trust. The audience may now reason thus:surement result. Where this is not practically pos-sible, independent means, such as accreditation are • S intends me to think that P


• S is sincere and authoritative (I can trust S) cation. We see in a description like that of Penrose• Thus, if S intends me to think that P, then I can great clarity brought to bear on what is at once

believe that P transformed into a commonplace. With that ‘strange• Conclusion: P procedure’, communication is not only possible, but

highly effective, and across all fields. In fact, it isApart from the trust conditions, there are a number ubiquitous. We all do it every day for a largeof other canons for communicative effectiveness proportion of our waking hours.such as appropriateness and informative significance, Penrose’ explanation for that lovely ‘puzzle’ was abut trust has special relevance to measurement in traditional one – the Platonic answer, which historyview of the decreasing transparency in modern tells us leads to its own contradictions, but every-measurement and the increasing importance of the thing about his description is also consistent with adecisions that must be made on the basis of those ‘Gricean conversation’, in which speakers and listen-measurements. Increasingly in modern measurement, ers alternately grapple to dispel the fog and connecta chain of traceability is also a chain of relationships their own experience and conception with the newof trust. information being offered by their counterpart in the

discussion. This is the conversational model ofcommunication – that in the final analysis, meaning

12. The fog of experts is formed by the interaction of speaker and audienceas an attempted convergence of understandings

Gricean audiences can be colleagues and technical which sometimes results in clarity, sometimes inexperts too. The mathematical physicist Roger Pen- confusion but more usually something in betweenrose once described [36] how he experienced the (but a mutual advance none-the-less). Even solitaryprocess of technical communication: readers of a printed page are constantly conducting

an internal dialogue, trying to infer what the authorA common experience, when some colleague might have intended, and checking and recheckingwould try to explain some piece of mathematics to and correcting their own interpretation as they readme, would be that I should listen attentively, but on, guided in their quest by the cues and clues putalmost uncomprehending of the logical connect- down on the paper.ions between one set of words and the next. Of course, so far as measurement is concerned,However, some guessed image would form in my there is seldom the luxury of extended dialoguemind as to the ideas that he was trying to convey between the reporters and the users of measurement– formed entirely on my own terms and seemingly results. Whilst it would be clearly desirable to bothwith very little connection with the mental images (and advantageous to the user) if there were morethat had been the basis of my colleague’s own dialogue, even so, the two cardinal imperatives forunderstanding – and I would reply. Rather to my any reporter are to be concise and succinct. To aastonishment, my own comments would usually be very large degree then, the major – perhaps only –accepted as appropriate, and the conversation ‘cues and clues’ available are the uses of measure-would proceed to and fro in this way. It would be ment units. A measurement result is literally mean-clear, at the end of it, that some genuine and ingless if there is no common understanding betweenpositive communication had taken place. Yet the reporter and audience regarding the units used. Noactual sentences that each one of us would utter number can be a measurement result. A number isseemed only very infrequently to be simply a number. Only when numbers are attachedunderstood! . . . . It had often been a puzzle to me to measurement units with a statement of uncertaintyhow communication is possible at all according is there even a possibility of a measurement result.to this strange procedure . . . This might seem like a truism and triviality but it is

forgotten so often that we should perhaps suspect aPenrose is not only a perceptive mathematician, but deeper and more substantive truth behind it. Mis-also a very perceptive observer of human communi- understandings concerning units can and do cause all


sorts of mischief – as was recently shown to sometime in the last few decades. We are somewhereNASA’s embarrassment by the widely reported loss in the fourth ‘Big’ scientific revolution – the in-of an expensive Mars probe due to confusions strumental revolution. This is characterised by abetween metric and imperial units in the communica- profound rise in the importance of instrumentation intion of technical data concerning navigation and all areas, the institutions and ideas associated with itpropulsion systems. and their widespread integration into socio-economic

However, quite apart from such simple errors, the affairs generally. Among other equally significantscope for confusion over units is both subtle and areas this has been apparent in the field of chemicalwidespread throughout much of contemporary sci- measurement [16] which is today routinelyence, technology, medical practice, environmental concerned with analysis at trace levels, with analytes,management, industry and trade. Sophisticated mea- matrices, quantities, numbers and speeds of analysissurements of all kinds of chemical quantities have all unthinkable a few decades ago. This has gonebecome routine and commonplace yet there are hand-in-hand with both changing technology andmany, varying, sometimes ambiguous, sometimes social need ranging from support of high technologyinconsistent usages in just for example the field of industry to medical care to environmental manage-quantitative description of composition of mixtures ment to global production and trade to forensic need.[37,38], not to mention the use and abuse of the There are no reasons to believe that such trends in

nterms percent, parts per million and parts in 10 [39]. measurement practices will not continue and fewThere is clearly a need for metrologists to not only would wish it. Perhaps the trends towards a burgeon-talk to their audiences, but also to each other and ing social function for measurement should simplycarefully to consider the forms of information probe looked upon as emerging technological maturityvided on reports of measurement results, including but they also give renewed emphasis to a very oldexplanations of uncertainty, units and their signifi- truth – that all measurement has an end or purposecance to users and audiences. outside itself. A purposeless measurement is practi-

cally no measurement at all. It is interesting thatrecent developments in metrology in chemistry

13. Conclusion: measuring to some purpose [40,41] have been very firmly and explicitly basedon the idea that measurements must be fit for

Historians until recently distinguished three ‘Big purpose.Revolutions’ in science. Big revolutions concern the Perhaps it is time to look also at the communica-actual practice of science and are in the words of tion of their results in a similar light. The notion ofhistorian Herbert Butterfield ‘accompanied by a fitness for purpose is still a somewhat vaguelychange in our sense of the ‘texture’ of the world, in a defined one, although the term has been long in usedifferent ‘feel’ for the world.’ They embrace not just amongst those involved in practical and legal metrol-changes in concepts and theories but in practice, ogy and what used to be inadequately referred to asinstitutions and the relationships of science to the ‘weights and measures’. It involves judging not onlywider society including politics, economics and the technical aspects of measurement but also moretechnology. The first was the scientific revolution of ill defined ones such as relevance, transparency,the seventeenth century, characterised by the realisa- integrity and lack of susceptibility to fraud andtion of the importance of experiment. The second is misinformation as well as economic practicality. Noassociated with the rise of the importance of mea- longer can it be assumed that sophisticated, ‘sci-surement in the early 1800s. The third dates around entific’ measurement is conducted and communi-the end of the nineteenth century with the advent of cated amongst the colleges of science where speakersprobability and statistics and the rise of institutions and audiences share not only a generally common setfor scientific research and organised training. of interpretive concepts but also a broadly similar set

Scholars are recently putting in measured prose of aims and purposes. Science and technology arewith hard evidence what has been viscerally apparent rapidly integrating into the general affairs of mento most who have worked behind a laboratory bench and women in society at large and nowhere is this


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