DISCUSSIONS

D E F I N I N G T H E C O N C E P T OF I N F O R M A T I O N

IN THE T H E O R Y OF M E A S U R E M E N T S

~. P. S e m e n y u k UDC 621.391.001.11:620.1.08.001.1

The foundations of the information theory of measurements and the measurement information systems were laid at the beginning of the sixties [2-5]. Many works have deal t with the development of cer ta in aspects of these theories [6-22], thus indicat ing the considerable fecundity of the new trend in the theory of measurements.

The estabiishment of any new theory is re la ted to a s ingle-valued and adequate definit ion of its basic concepts. Among such concepts of the information theory of measurements and the theory of measurement- informat ion systems figure above a l l the concept of "information" and the closely r e n t e d with i t concept of "measurement information." These concepts are now being general ly used in the works on the theory of measurements and measurement tech- niques. It is charac.teristie that the concept " information" figures in most of the formulations suggested in recent years for the latest definit ion of the basic concept of m e t r o l o g y - "measurement" [4.6-8.23]. This alone indicates the pressing necessity of specifying this concept. However, in our opinion, there are no satisfactory definitions of the concepts of " information" and "measurement information."

Definitions which are l imi ted by their interpretat ion of information as a certain in te l l igence , for instance, as:

"Information is any in te l l igence presented in the form of speech, writing, images, numbers of measured quantit ies, instructions, or signals" [2, p. 7] cannot be considered sufficiently scientif ic or fully ref lect ing the complex nature o f information.

An a t tempt to reveal the very content of information (which is lacking in the definitions of the above type) has been made in [4]: "Information specifies the content of events which change the in i t ia l uncertainty of an exper i - ment ." However, one is bound to agree with the cr i t ic ism of this defini t ion as abstract and diffused [24]. Moreover, the above definition, in our opinion, is insufficient and one-sided, since its only base consists of the ma themat i ca l theory of information, whose object is to establish only the quant i ta t ive characteris t ics of information on the basis of a s tat is t ical probabil i ty approach to it, thus de l ibera te ly digressing from analyzing the pithy nature of information. It should be noted that, in view of the l imi ted task of the information theory, C. E. Shannon, one of the founders of this scientif ic discipl ine, warned espec ia l ly against extending the appl ica t ion of its results beyond its possibilities [25, pp. 667-668]. The a t tempt to provide a general definit ion of information only on the basis of the above mathe- mat ica l theory is, in our opinion, exac t ly one of such instances. Although the authors of [4] justly point out that it is inadmissible to transplant mechanica l ly into the theory of measurements the concepts of the information theory, they could not overcome, in formulat ing the definit ion of information for the theory of measurements, the one-sided approach to information which is pecul iar precisely to the information theory. This is comple te ly understandable

historical ly, since at the t ime [4] was published the theory of information was the only scient i f ic discipline within whose framework a serious analysis of information and of the pattern of information processes was made.

A large number of works deal ing with a comprehensive analysis of the nature of information appeared in re- cent years. Various aspects of information and approaches to its understanding are now being studied in different sciences. An absolute preponderance of special investigations in the field of the quanti ta t ive characterist ics of in- formation is pecul iar to the works deal ing with measurement information. This is e loquent ly represented by the very t i t les of the works such as [11-18]. As a result of these investigations the quant i ta t ive aspect of measurement information can be considered successfully developed in adequate detai l (which of course does not e l imina te the necessity of a further development of the work in this direction). However, the study of only the quanti ta t ive char- acterist ics of measurement information cannot, in our opinion, be considered sufficient and exhaustive.

The present stage of the development of the information theory is character ized by the appearance of a new information approach to measurements. It is distinguished by a search not only for quanti tat ive, but also for qual i - ta t ive characterist ics of measurement information processes. Such characterist ics include the nature of information

Translated from Izmer i t e l ' naya Tekhnika, No. 8, pp. 88-92, August, 1968. Original ar t ic le submitted Novem- ber 31, 1967.

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and noise, their interrelat ionship and interchangeabi l i ty , the relationship of measurement information to the in i t ia l uncertainty, the conditions of obtaining and the existing structures of measurement information, its content, value, reproducibi l i ty , the role of measurement information in shaping various levels of scient i f ic knowledge, etc. There- fore, the information theory of measurements cannot be considered only as the appl ica t ion of the concept and mathe- mat ica l apparatus of the information theory (cybernetics) to the theory of measurements. In connection with the general information approach to measurements i t is also necessary to examine, for instance, the problems which are now being developed and are common to both measurement techniques and engineering psychology [26,27].

It should be noted tha t the formation of an information approach to measurements is not something isolated in the general scientif ic development of recent years. This process can be understood only as a part of the persis- tentIy developing, extending and deepening general information approach to the problems of real i ty, as its extension to the field of measurements, and its specific definit ion under conditions of the part icular problems in the theory of measurements. The first impetus in the formation of a general information approach to the problems of rea l i ty was provided by cybernetics. However, the scient i f ic possibil i t ies of this approach were so great that in a short t ime it grew out of the framework of cybernetics and became a general scient i f ic phenomenon. As a part of this process the concept of information grew out of the framework of the information theory and, in our opinion, has become a general scient i f ic criterion.

It is important to stress that in the formation of a modern scient if ic concept of information, precisely owing to its general scient i f ic significance, a special part has to be p layed by philosophy which general izes the achievements of various sciences and is the methodology of science. Although in recent years many philosophical works appeared on the problem of information, there does not exist an exhaustive analysis of measurement information in part icular.

The object of the present a r t ic le consists of analyzing the recent ly suggested basic concept of information from the point of view of its app l i cab i l i ty to the theory of measurements and of developing on this basis sufficient-

ly comprehensive and convincing definitions of the concepts of " information" and "measurement information."

The problem of the interrelationship of information and matter is of overwhelming interest and importance. Some of the investigators consider that . information is one of the manifestations, aspects of matter side by side with

its mate r ia l and energy aspects [28,29, p. 45]. In this connect ion the wel l -known proposition of N. Wiener that ". . . . information is information and not mat ter or energy" [30, p. 166]* has been sometimes c r i t i c ized [28].

Other investigators consider information a nonmater ia l phenomenon [81-34]. Without suggesting a fundamen- ta l solution of this dispute (the seriousness and extent of this problem requires special investigations), i t is possible to note a fact which is indisputable for a l l mater ia l is t scientists that information does not exist outside mater ia l processes, it is inseparably related to mat ter and movement, to physical carriers. It is precisely the organic inse- parable relationship of information to mat ter which makes the obtaining of measured information by means of instru- ments possible. Measurements are a imed at obtaining data of a given kind only about physical (and not ideal) ob- jects. Thus, the recognit ion of an indissoluble bond between information and matter is important by the fact that i t discloses the theore t ica l possibi l i ty of using the concept of " information" in the theory of measurements.

At present two basical ly different approaches to the concept of " information N are widely used in science. The

first approach which conceives of informat ionas a negentropy, a measure of ordering, organizat ion of the mater ia l sys- tem as opposed to entropy (a measure of chaos, disorder, and disorganization of the system) is based on the fact that the ma themat i ca l expression for information is equal to that for entropy with a reversed sign [32,85-88]. Thus, the understandable information is an internal property of a mater ia l system in itself, apart from its relationships to other mater ia l objects. Somet imes i t is known as structural information [38] and sometimes as s ta t is t ical informa- tion [89]. This concept is approached by the suggestion of considering information as "... a measure of nonuniformi-

ty in the distribution of matter and energy in space and t ime, a measure of variations which accompany al l the processes existing in the world ~ [40]. The second approach always relates information to the relationship of at least two mate r ia l systems consisting of the source and the detector of information [28,88,41,42]. As distinct from the

structural information, this concept is sometimes ca l led re la t ive information [38].

*In this connect ion i t is interesting to note the remark expressed to the author of this a r t ic le by Professor P. V. No-

vitskii. In his opinion the c i t e d proposition is an inaccurate translat ion into Russian of N. Wiener 's book. On the basis of its context the above passage should read: ~Information is information and not a substance or energy." Al- though this opinion can be disputed, it is perfect ly reasonable, since the English word "mat ter" which is used in the original is polysemous and can be translated into Russian as "mat ter" or nsubstance."

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The designation by the same term of two basical ly different concepts is inadmissible (at least within the range of the same science). A s ingle-va lued concept is required. Therefore, i t appears necessary to distinguish between the concept of nnegentropy" (the first approach) is6] and " information n (the second approach) [82], although many authors consider them to be ident ical . We shall base our reasoning on the fact that negentropy (an objec t ive ly ex- isting measuring of ordering and organizat ion of matter) represents only a possibili ty of obtaining measurement in- formation which becomes a rea l i ty in the presence of a t least two interact ing physical systems consisting of the measured object and the measuring instrument [15] (the third interact ing system in the major i ty of cases consists of a human operator).

Since information is always related to the interact ion of a t least two mate r ia l objects, i t is indisputably cor- rect to re la te information to the philosophical category of-reflection [8,4,88]. However, there exist different points of view on the essence of this relationship.

Certain authors identify information with ref lect ion [48]. This point of view accepts the so-ca l led e lementary information whose detector consists of any nonorganic object i rrespective of the degree of its organizat ion [42]. Sometimes it is suggested to consider information as a ref lect ion in the consciousness of people of the objec t ive sources resulting from relationships in the ac tua l world [84]. In our opinion, the investigators who stress the close relationship between information and reflection, but deny their ~dentity, are right [28,44,45]. In fact, if these con-

cepts were ident ical , there would be no sense in using two different terms. In what then does information differ from reflect ion?

In certain works it is suggested to consider information as a type of reflection, namely ordered re f l ec t ion and

consider noise and inteference as unordered reflections [10,82,46]. Such a concept is fruitful to a certain extent. However, in our opinion, the ordering of reflections is possible outside information processes. It should be considered more correct to interpret information as an aspect of ref lect ion side by side with its mater ia l energy aspect [44,47]. Such an interpretat ion is fully app l icab le to the measurement information.

In recognizing the undoubted relationship between the measurement and ref lect ion processes, cer tain specif ic

features of reflections in obtaining measurement information should be noted. First, the ref lect ion of the measured object by the instrument is specific. It is par t ia l only from the point of view of obtaining a quanti ta t ive character - ist ic of the measured parameter , thus ref lect ing from an infini te set of an object ' s properties a single one. Normally i t is the question of only a most obvious reflection, that of a measured object in a measuring instrument. For in-

stance, the ref lect ion of a measured object ' s temperature in a mercury thermometer is represented by a change in the volume of mercury. But this ref lect ion is insufficient for measurements. It must be preceded in t ime by the re-

f lect ion of a mate r ia l measurement unit in the instrument. An indispensible condit ion of the measurement process consists of comparing with the instrument the results of the two reflections. Despite the difference in t ime between the two reflections, such a comparison is possible owing to the fact that the result of the first one is f ixed physical ly in the instrument (in measurement techniques this process is known as the instrument 's cal ibrat ion). In the major i ty of cases yet another act of ref lect ion is necessary for measurements, this consists of the ref lect ion of the measuring instrument in the consciousness of a human operator (by means of his sensing organs). This again is not a ref lect ion of the entire instrument, but a ref lect ion of some of its components (for instance, its scale and pointer) and only of

some of their properties (for instance, the position of the pointer with respect to the fixed marks of the scale). Such is the mechanism in obtaining measurement information by using a single instrument. However, if in termedia te links are required for measurements (transducers, measurement converters; and secondary instruments) the chain of reflections is increased accordingly.

Thus, in determining the measurement information with respect to reflections, i t is necessary to note the com- plex relationship between their aggregate concepts. On the one hand fneasurement information is only a part of the entire measured object ' s information which in turn is only one of the aspects of reflection. On the other hand measurement information cannot be obtained from a single reflection. It is the result of synthesizing a whole chain of such reflections. In this process the quantity of e lementary reflections acquires a new property by forming an in- formation transmitt ing channel.

Important differences exist in modern science regarding the nature and the degree of organizat ion of the ma- ter ia l objects which carry information (there is no disagreement on the sources of information; i t is recognized or inferred that they can consist of any mater ia l object). Some of the investigators consider that an information de tec- tor may consist of a mater ia l object of any nature and degree of organiza t ion [88,37,41,42,48,49]. According to this point of view it is suggested to divide the entire possible information into three categories consisting of e l emen- tary (nonorganic detector), b io logica l (organic detector), and logica l or semant ic information (the detector possesses a n internal model of the external world [29] or is capable of reasoning as a human being [42]).

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Other authors think that i t is impossible to consider inorganic objects as detectors of information, with the except ion of those which have been made spec i f ica l ly for this purpose by man [28,81,44,45]. Sometimes the concept of infor- mat ion is interpreted to a considerable extent as being indispensibly re la ted to the conscious ac t iv i ty of man [84,36]. In other words the information detector is then considered to consist only of a mater ia l system whose highest organi- za t ional l ink is represented by a human brain. From the point of view of modern science as a whole the recognit ion only of information re la ted to the conscious percept ion of man is, in our opinion, insufficient and too narrow. An obviously more correct and thoughtful definit ion admits information detectors as natural and man-made physical systems with a degree of organizat ion sufficient to perceive information for the purpose of its subsequent storage, processing, and ut i l izat ion.

The concept of measurement information has any meaning only in connection with the conscious ac t iv i ty of

man. By using the above-men t ioned classif ication, the measurement information should obviously be referred to the third category as a logica l or semant ic information. In our opinion, a t tempts to interpret measurement informa- tion as e lementary , on the basis that its primary detector (measuring instrument) is inorganic by its very nature, are impossible, since the very existence of the instrument is indissolubly re la ted to the conscious ac t iv i ty of man. It has been known for a long t ime and it is not contested that the function of measuring instruments is the continuation and development of the human sensing organs. This relationship is once more stressed in one of the definitions in

which information is understood to be ". . . every in te l l igence on the processes and conditions of any nature which can be perceived by human sensing organs or instruments ~ [50].

In the light of the defini t ion suggested above, are measuring instruments information detectors.* Often infor- mation processes in inorganic nature are l imi ted to cybernet ic machines. In our opinion, measuring instruments shoutd be def ini te ly recognized as information detectors, although in a general case some of the above-ment ioned

functions are lacking in them (storage, processing, and ut i l iza t ion of information). However, they al l possess the first function, which is bas ica l ly necessary for a l l the succeeding ones and consist of detect ing the information for its subsequent ut i l izat ion, i .e. , a function from whose name the word ~detector" is derived. The specific properties of a measuring instrument as an information detector consist of its pecul iar combinat ion of two effect ive objectives. The instrument detects information for its u t i l iza t ion as determined by the instrument 's designer. The physical ob- jects which not only de tec t information, but also ensure the further stages o f storing and processing, constitute the information system distinct from the detectors. The informat ion system combines the functions of a detector, a store, and a converter of information. A measuring device can be both a type of information system and its part, i .e . , only a detector of information [4]. The highest stage of an information system consists of its controll ing device which, in addi t ion to the above mentioned functions, also uti l izes the information for control purposes. Cybernet ic machines belong precisely to this type of system. The gradual compl ica t ion of functions (and, therefore, of struc-

ture, of commerc ia l information devices produced by man and ranging from an information detector to a control system have an obvious his tor ical analogy in the form of a gradual compl ica t ion in the evolut ionary process of func-

tions and structures of the natural information devices consisting of receptors and nervous systems.

Information has been recent ly interpreted as a diversity of physical systems and the information content as the amount of diversi ty [37,41,48,49,51,52]. We can agree that this is a widest possible conception and i t does not con- t radict any of the approaches to the problem [41]. "Any mention of information is unjustif iable unless there is di- versity, a cer tain mul t ip l ic i ty of possibilities. Therefore, the possibil i ty of choosing is an indispensible condit ion for obtaining information" [4]. The effectiveness of this conception consists in the fact that it can be used for classifying various types of information in any field of knowledge as a division of sets into subsets of various classes

of diversity [41].

The most important c lassif icat ion of the possible information consists obviously of its division into qual i ta t ive and quant i ta t ive information. Qual i ta t ive information reflects the definiteness of an object inseparable from its very existence as a given object and it is expressed in defini te logica l conclusions [58]. Quant i ta t ive information reflects the objec t ive ly existing ~... definiteness of quant i ta t ive ly s imilar phenomena, or the qual i ty of its space- t ime aspect from the point of view of its existence in space and t ime" [58]. The subset of qual i ta t ive information comprises measurement information as a special diversity class obtained by means of special (measuring) instruments

and system [3].

According to the form of the relationship between the source and the detector, the information can be contin- uous (analog) or discrete [42]. Several works note that discrete information and the quant izat ion re la ted to it are

important both in a general way [40,54] and with respect to measurements [2,11,18,22,55]. In a general case the

form in which Ne measured information is presented depends on the par t icular features of the information detector.

Man can only perceive a numerica l system for expressing quant i ta t ive characterist ics. It is precisely owing to this

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feature of human perception that discrete information has obtained such importance and the numerica l form is often specified as an indispensible condit ion for expressing quant i ta t ive information (including measurement information) [3]. The la t ter proposition cannot be accepted as str ict ly correct, since certain detectors (analog machines) are capable of reproducing measurement information in a purely analog form without convert ing i t into a numer ica l form.

In discussing the part icular features of measurement information as a whole i t should be noted first that i t does not contain an absolute quanti ta t ive character is t ic of the measured objects but only one of the many possible quant i ta t ive characterist ics of a given type which is represented by its two aspects comprising the measured parame- ter and the unit of measurement. (It is obvious that the qual i ta t ive character is t ic obtained by combining heterogen- eous parameters and measurement units is not measurement information and is valueless.) Second, one of the ma- ter ia l conditions for obtaining measurement information consists precisely of using a special (measuring) instrument (or system). It is important to stress this, since there exist other types of instruments which do not measure but pur- sue other aims, for instance, of raising the power of our sensing organs (microscopes, telescopes, acoust ica l instru- ments) or rect i fying their def ic iencies (spectacles, hearing aids). In addi t ion to the above there exist whole groups of instruments consisting of signaling and regulat ing devices whose measurement functions do not constitute their f inal object ive, but only an in te rmedia te stage without which their basic a im cannot be at tained. The measurement function in these instruments is always performed by a separate unit or stage which in a cer ta in sense (from the point df view of obtaining measurement information) can be considered as an independent measuring instrument, although

it is not always separated structurally and its measurement results are not represented in a d igi ta l form, remaining purely analog.

Various cri teria are possible for dividing the measurement information into subsets. Such a cri ter ion consists above a l l of the measured parameter ( temperature, pressure, level ,-f low, t ime, etc.). According to its relationship

to t ime the measured information can be transitory (unrecorded) or f ixable (recorded) [z~2]. A further subdivision of the recorded information can be made with respect to its recording medium (tape chart, disc diagram, punched tape,

photographic paper, e tc . ) or to its recording method (continuous recording with ink, recording with points, punching tapes, e tc . ) [2]. Information can also be classified according co the re la t ive position of the source and the detector as f irst-hand (direct) and indirect information [3,42]. Single-point and mult ipoint information is obtained by classi- fying it according to the number of measured points [3]. Final ly i t may be of some interest in pract ice to classify measurement information according to the auxi l iary energy which is used in obtaining it and is related to the pr inci- ple of measurement. In this case e lec t r i ca l measuring methods are of part icular importance [3,8,55].

The concept of information as a diversity is re la ted to a probabi l i ty approach which arises in the ma themat i - ca l theory of information. Among other approaches i t is expedient and necessary, since i t reflects an important

property of information, which is not s imply a select ion of one possibili ty among many, but a select ion with a given degree of probabi l i ty [54,56]. In the theory of measurements the probabi l i ty approach has a specif ic feature. The probabi l i ty of information has been provided with a definite and fixed relationship to one of tile most important characterist ics of instruments, their precision class [17]. In addi t ion to systemati c errors, the precision class includes the entire aggregate of random errors, which can be excluded by s tat is t ical processing of a number of measurement results. Therefore, repeated measurements are useful, since they increase the precision of measurement (they raise the degree of probabi l i ty of the obtained information), i .e . , they contain a cer tain addi t ional information about the measured quantity, whereas from the point of view of the information theory repeated measurements do not provide addit ional information [7].

In many works information is represented as communicat ions, data, or in te l l igence about something [2,3,31, 33,36,38,41-48,50,51,54,56] and less often as a process in t ransmit t ing. in te l l igence [42]. Sometimes these two ap- proaches are synthesized into: "Information is in te l l igence about something considered in the process of its trans- mission" [57]. It has a l ready been stated above that the concept of information as in te l l igence is not sufficient (i t does not reveal the content of the phenomenon). However, among other approaches i t is correct and necessary. It is not by acc ident that the origin of the word "information ~ is re la ted to the above concept [58]. Such an under- standing of information, and in part icular of measurement information, is important because i t corresponds to prac- tice. It is sufficient to enumerate several processes re la ted to information in technology (input, output, reading,

readout, recording, registering, coding, decoding, search, transmission, processing, selection, distortion, reception, accumula t ion , storage, reproduction, conversion, exchange, col lect ion, and organizat ion of information) in order to become convinced that not a single one of these operations contradicts the above concept. Considerations of prac- t i ca l advisabi l i ty and convenience of appl ica t ion of a term with a given meaning should receive part icular at tention, since ". . . . the point of view of pract ice and l ife should be the primary and basic point of view .... " [1, p. 145].

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Therefore, the cri t icism of such a concept of information for its a l leged tautology, without at the same t ime point- ing out that it has a cer tain value [32], appears to us to be one-sided.

The above analysis of various approaches has led us to suggest for the concepts of " information" and "meas- ured information" the following definitions which, in our opinion, combine v a h a b l e aspects of the basic concepts.

Information is an aspect of ref lect ion distinct from its mater ia l energy factor and perceived by physical sys- tems with a degree of organizat ion sufficiently high for the storage, processing, and further u t i l i za t ion of informa- tion, an aspect which is expressed in ordered in te l l igence about the degree of probabil i ty of a given event out of a possible var ie ty of events of a given type.

Measured information is an ordered in te l l igence on the degree of probabil i ty of a given quanti tat ive character - istic appearing in a possible var ie ty of such characterist ics of a given type, an in te l l igence obtained in an analog or discrete form with special (measuring) instruments or systems by an exper imenta l comparison of two physical objects or processes, one of which is taken as a unit of measurement.

In conclusion the author wishes to express his grati tude to Prof. B. G. Kublanov, D. P. and Professor P. N. No- vitskii DSc. (Eng) for their c r i t i ca l observations and valuable advice.

1,

2.

3. 4. 5.

6. q.

8. 9.

10.

11. 12. 13. 14. 15. 16.

17. 18.

19. 20, 21. 22, 23. 24. 25. 26. 27. 28.

29. 30. 31. 32.

33. 34. 35.

36, 37.

38,

V. I.

F.E . K.B. K.B.

E .G.

P .V. P .V.

E .G. E.F,

B.G.

V . I . V . I . V . I . S .M. P .V. P .V,

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Cybernetics [Russian translation], Progress, Moscow (1966). 50. V.M. Glushkov, Introduction to Cybernetics [in Russian], Izd. AN UkrSSR, Kiev (1964). 51. W. Ross Ashby, Introduction to Cybernetics [Russian translation], ILL, Moscow (1959). 52. I. Zeman, Cognition and Information. Gnoseological Problems of Cybernetics [Russian translation], Progress,

Moscow (1966). 53. Philosophical Encyclopedia [in Russian], Vol. 2, Moscow (1962)i 54. Great Soviet Encyclopedia [in Russian], (2nd ed.), Vol. 51. 55. A.M. Damskii and G. I. Kavalerov, Izmeritel. Tekh., No. 1 (1962). 56. A. Ya. Moroz, " Concept of information and its measurement, ~ in Co11.: Methodological Problems of the

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