6/14 AN INTRODUCTION TO CYBERNETICS 



6/14. The deliberate refusal to attempt all possible distinctions, 

 and the deliberate restriction of the study of a dynamic system to 

 some homomorphism of the whole, become justified, and in fact 

 almost unavoidable, when the experimenter is confronted with the 

 system of biological origin. 



We usually assumed, in the earher chapters, that the observer 

 knew, at each moment, just what state the system was in. It was 

 assumed, in other words, that at every moment his information 

 about the system was complete. There comes a stage, however, as 

 the system becomes larger and larger, when the reception of all 

 the information is impossible by reason of its sheer bulk. Either 

 the recording channels cannot carry all the information, or the 

 observer, presented with it all, is overwhelmed. When this occurs, 

 what is he to do ? The answer is clear : he must give up any ambition 

 to know the whole system. His aim must be to achieve a partial 

 knowledge that, though partial over the whole, is none the less 

 complete within itself, and is sufficient for his ultimate practical 

 purpose. 



These facts emphasise an important matter of principle in the 

 study of the very large system. Faced with such a system, the 

 observer must be cautious in referring to "the system", for the term 

 will probably be ambiguous, perhaps highly so. '"The system" may 

 refer to the whole system quite apart from any observer to study it — 

 the thing as it is in itself; or it may refer to the set of variables (or 

 states) with which some given observer is concerned. Though the 

 former sounds more imposing philosophically, the practical worker 

 inevitably finds the second more important. Then the second 

 meaning can itself be ambiguous if the particular observer is not 

 specified, for the system may be any one of the many sub-machines 

 provided by homomorphism. Why all these meanings should be 

 distinguished is because different sub-machines can have different 

 properties; so that although both sub-machines may be abstracted 

 from the same real "thing", a statement that is true of one may be 

 false of another. 



It follows that there can be no such thing as the (unique) behaviour 

 of a very large system, apart from a given observer. For there can 

 legitimately be as many sub-machines as observers, and therefore 

 as many behaviours, which may actually be so different as to be 

 incompatible if they occurred in one system. Thus the 5-state 

 system with kinematic graph 



has two basins, and always ends in a cycle. The homomorphic 



106 



