A new look on the process of observation

2. Outline of the proposal

After some necessary remarks on the process of observation, a ‘theoretical backbone’, a formalism for the description of cognitive processes and cognitive systems will be developed. This formal- ism is based on five classes of characteristic opera- tors, such that at least a significant majority of all cognitive processes can be represented by suitable combinations thereof Section 4. It will be found that the algebras A and A formed by these oper- ators have astonishing similarities with the opera- tor algebras used in quantum theory Section 5. It is proposed here to describe physical pro- cesses as processes of interpretation – e.g. a parti- cle interprets a surrounding field by following a specific curved path derived from that field. Thus the term ‘interpretation’ will become rather com- prehensive, including both physical and cognitive processes, and hence can be a promising candi- date for the basis of a uniform description re- quested here.

3. A new look on the process of observation

3 . 1 . The process of obser6ation as a sequence of se6eral steps The term ‘observation’ will be used here in a broad sense including e.g. “ any kind of measurement of a single variable or of a set of variables in experimental sciences “ the scientific analysis of a work of art e.g. in order to give an interpretation or to classify it as genuine or fake “ observations in the social sciences. Any process of observation can be understood as an ordered sequence of several consecutive phases. In special cases, one or another of these phases may be less important; it may even remain unnoticed at a first glance, or appear as non-exis- tent. But for the sake of a general and compre- hensive theory and in order to refute some frequent misunderstandings, see Section 3.2 the following sequence of steps should be kept in mind. We must make a distinction between the initia- tor of an observation and the obser6er as such. Both can be identical, but this is not the general case. The observer can be a human individual like an anthropologist exploring a foreign cul- ture, a team, or a technical device like an inter- planetary probe; following a proposal due to Matsuno 1985, 1989, we can also include physi- cal probes, like atoms, molecules, rays, waves, etc., entering a physical object under investigation. Now, a process of observations can be charac- terized by the following phases: 1. The initiator decides what is to be observed and how this shall be done, simultaneously defining the context, e.g. the purpose of the observation, the relative importance of differ- ent features, etc. definition phase. 2. If necessary, technical preparations are done preparation phase. 3. The observation as such is performed: there is an internal state change within the observer, which, depending on the context, can be de- scribed as registration, learning, insight, etc. 4. The results — possibly after preprocessing as in the case of an interplanetary probe or after a reformulation as an understandable report 2 — are transmitted to the initiator of the observation. 5. The initiator receives and interprets the results. Of particular interest here is the fact that the role of the decision phase no. 1 is frequently underestimated or ignored for a possible mathe- matical tool see the Appendix. 3 . 2 . The specific role of perspecti6e notions Perspecti6e notions are terms which — beyond the well-known context-dependence of any mean- ing of words — require an explicit statement of the context. A simple example is the term ‘classifi- cation’: e.g. the chemical elements can be classified according to their atomic weights, spe- cific weights, electrochemical or radioactive prop- 2 For the ‘recordreport antagonism’, the observer’s neces- sity to formulate a report such that it will get a chance of being understood, see Gernert 1998. erties, etc. The tasks to classify a single object or to subdivide a given set can be accomplished only after the purpose of the classification or the rele- vant criteria have been disclosed. Of course, that indispensable context is often self-understood among the persons involved, but just this fact brings about an additional complication to be discussed below. The following remarks on per- spective notions, although of interest by them- selves, are a necessary preparation for the main part of this paper. Four essential perspective notions or pairs of such notions 1. meaning and interpretation, 2. complexity, 3. pragmatic information, 4. similaritydissimilarity can be represented by the four corners of a regu- lar tetrahedron in three-dimensional space, or by a plane drawing as in Fig. 1. The six lines con- necting the corners are to show that each of the four entries is interrelated with each other 3 . The meaning of a word, a sentence, a symbol, etc., as well as the process of interpretation and its outcome, depend on the situation, the historical and social context, and the purpose of the analy- sis. Without any doubt, the complexity of a struc- ture will depend among other things on the individual education and training; what seems to be very complex to a newcomer may be simple for an expert. Just as demonstrated above by the example of classification, the similarity or dissimi- larity of two objects or two structures can by defined only after exposing the purpose or the relevant criteria — within a given set, two objects can be similar or less similar according to their size, shape, appearance, function, etc. The concept of pragmatic information claims that information can be understood only as an impact upon or an alteration within a receiving system brought about by the arrival of a message: information begins when the channel has ended. For the argumentation in detail, the history of this concept, and a possible quantification only a reference can be given Gernert, 1996. What is of interest here is the fact that ‘pragmatic informa- tion’ is a perspective notion, too. The same in- coming message may be considered highly important under one perspective, but irrelevant under a different view. If a message is regarded under the aspects of telecommunication engineer- ing, then we are back to the classical Shannon – Weaver theory with its possible extensions and ramifications, but the same message can also be judged under aesthetical, pedagogic, or economic aspects, etc. Exactly the same situation is found with respect to obser6ation. In the general case, the definition phase Section 3.1 cannot be ignored or circum- vented; the necessary context must be specified and taken into consideration. The term ‘observa- tion’ also includes measurement, which can be regarded as a special case of observation. The situation in which the context is self-evident can be exemplified as follows. If somebody in a labo- ratory is told to ‘measure the temperature’ then the location and the time are clear, as well as Fig. 1. Four eminent perspective notions and their relation- ships. 3 The relations between complexity and meaning are studied in Grassberger 1989 and in Atmanspacher et al. 1992, those between complexity and information in Atmanspacher 1997. For the connections between similarity and pragmatic infor- mation, and between these two concepts and the rest of the diagram see Gernert 1996. further circumstances, like the required precision, the available instruments, and the style of docu- mentation. As a consequence, the predominance of situations like that leads to the illusion of a ‘single-step measurement’: it is broadly assumed that only the name of one variable or observable must be said and then everything is clear. By way of contrast, there are situations in which the definition phase, the identification of the context can no longer be skipped and, further- more, will require some labour and a methodical procedure. If, for instance, the similarity or dis- similarity between two structures from a given set is to be quantified, this will require the formula- tion of a suitable graph grammar that generates at least all the structures under consideration Gern- ert, 1996. As soon as such a graph grammar has been specified, the requested similarity measure is clear. Now, the crucial point is that a graph grammar with the required properties always ex- ists, but it is not uniquely defined. The necessity to select exactly one graph grammar from the multitude of all suitable ones just stands for the compulsory specification of the context, like the goal pursued by that individual measurement of similarity. A characteristic feature of perspective notions is the necessity of a two-step proceeding, such that a definition phase precedes. A mathematical treat- ment is possible, but this is distinguished from the customary style: a measure will no more be sup- plied by a single formula, nor by several formulas, but by a proceeding in which, in addition, a mathematical structure must and can be set up that accounts just for the peculiarity of the per- spective notion. The above-mentioned illusion of a single-step measurement, the expectation that problem data simply can be inserted into a couple of formulas, turns out to be a widespread tacit assumption 4 . It seems plausible that just this tacit assumption is one of the causes why the concept of pragmatic information is accepted in such a reluctant and hesitating manner.

4. A systematic description of cognitive processes