When is a process of observation completely described? Outline of the proposal

BioSystems 54 2000 165 – 180 Towards a closed description of observation processes Dieter Gernert Department of Economics, Technical Uni6ersity of Munich, Arcisstrasse 21 , D- 80333 Munich, Germany Received 24 May 1999; received in revised form 26 October 1999; accepted 5 November 1999 Abstract A closed description of observation processes must necessarily include the observer, too. In order to find a basis for such a unified description, an operator algebra is developed which enables a formal description of at least a significant majority of cognitive processes. It is found that this operator algebra, which is a noncommutative semiring of a type already known in literature, has astonishing similarities with the usual operator algebras in quantum theory. Combined with a method for the formal treatment of perspective notions, the representation scheme proposed here may open a chance for a unified description of a process itself together with the relevant cognitive processes on the observer’s side. By the description of parallel-processing systems on the same basis an operational definition of ‘internal time’ becomes possible. © 2000 Elsevier Science Ireland Ltd. All rights reserved. Keywords : Observation; Measurement; Unified description; Operator algebra; Quantum theory; Cognitive process; Perspective notion; Semantics www.elsevier.comlocatebiosystems 1. When is a process of observation completely described? ‘‘Any description of the world that someone advocates as being complete… must ‘close the circle’: it must include an account of how we come by that description. In particular, any phys- ical theory that claims such completeness must account for our experience as observers.’’ But- terfield, 1995 The crucial role of the observer in quantum physics is generally accepted, and there is an abundant literature just on this topic. Prob- lems immediately arise when an ‘inclusion of the observer’ is understood in a strict sense, because this will inevitably imply a study and formal description of processes beyond the usual scope of physics. ‘‘Consciousness exists, but it resists definition.’’ Flanagan, 1995 This quotation gives a cue to stop for a moment searching for a perfect defin- ition of terms like ‘consciousness’, ‘mind’, ‘men- tal’, etc. Rather, an attempt will be made here to supply a basis for a unifying description 1 through a ‘change of perspective’, which will not only help circumventing that trouble with definitions, but, hopefully, will also bring about some new insight. 1 The ‘problem of two languages’ and the necessity of a ‘unified description’ are particularly emphasized by Lau- rikainen 1988. 0303-264700 - see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 3 0 3 - 2 6 4 7 9 9 0 0 0 7 2 - 6

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