CHAPTER 2 



Dynamic Systems 



2/1. In the previous chapter we have repeatedly used the con- 

 cepts of a system, of parts in a whole, of the system's behaviour, 

 and of its changes of behaviour. These concepts are fundamental 

 and must be properly defined. Accurate definition at this stage 

 is of the highest importance, for any vagueness here will infect 

 all the subsequent discussion; and as we shall have to enter the 

 realm where the physical and the psychological meet, a realm 

 where the experience of centuries has found innumerable possi- 

 bilities of confusion, we shall have to proceed with unusual caution. 



That some caution is necessary can be readily shown. We have, 

 for instance, repeatedly used the concept of a ' change of 

 behaviour ', as when the kitten stopped dabbing at the red-hot 

 coal and avoided it. Yet behaviour is itself a sequence of changes 

 (e.g. as the paw moves from point to point). Can we distinguish 

 clearly those changes that constitute behaviour from those changes 

 that are from behaviour to behaviour ? It is questions such as 

 these which emphasize the necessity for clarity and a secure 

 foundation. (The subject has been considered more extensively 

 in /. to C, Part I; the shorter version given here should be sufficient 

 for our purpose in this book.) 



We start by assuming that we have before us some dynamic 

 system, i.e. something that may change with time. We wish to 

 study it. It will be referred to as the ' machine ', but the word 

 must be understood in the widest possible sense, for no restriction 

 is implied at the moment other than that it should be objective. 



2/2. As we shall be more concerned in this chapter with prin- 

 ciples than with practice, we shall be concerned chiefly with 

 constructing a method for the study of this unknown machine. 

 When the method is constructed, it must satisfy the demands 

 implied by the axioms of S. 1/10-15: 



(1) The method must be precisely defined, and in operational 

 form; 



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