7/13 THE ULTRASTABLE SYSTEM 



Here, however, a difficulty arises. The attempt to follow, 

 conceptually and imaginatively, the actual events in the whole 

 system, as environment poses problems to the essential variables 

 (by threatening to drive them outside their normal limits), as 

 the values in S determine a particular way of behaving in R, as 

 R behaves in that way, interacting with the environment at every 

 moment, as the outcome falls on the essential variables, as S is 

 (or perhaps is not) changed, as R behaves in a new way — all this 

 is apt to be exceedingly complex and difficult to grasp conceptually 

 if the variables in environment, R, and S all change continuously, 

 i.e. by infinitesimal steps. 



Experience has shown that the whole system, and its psycho- 

 logical and physiological implications, are much easier to grasp 

 and understand if we study the particular case in which the 

 variables in environment and R all vary continuously, while 

 those in S vary discretely (i.e. by finite jumps, occurring at finite 

 intervals). Evidence will be given, in S. 9/4, suggesting that 

 such discrete variables are in fact likely sometimes to be of real 

 importance in the subject; for the time, however, let us regard 

 them as merely selected by us for our easier apprehension. 



Step-functions 



7/13. Sometimes the behaviour of a variable (or parameter) can 

 be described without reference to the cause of the behaviour: if 

 we say a variable or system is a 4 simple harmonic oscillator ' 

 the meaning of the phrase is well understood. In this book we 

 shall be more interested in the extent to which a variable displays 

 constancy. Four types may be distinguished, and are illustrated 

 in Figure 7/13/1. (A) The full-function has no finite interval of 

 constancy ; many common physical variables are of this type : the 

 height of the barometer, for instance. (B) The part-function has 

 finite intervals of change and finite intervals of constancy; it 

 will be considered more fully in S. 12/18. (C) The step-function 

 has finite intervals of constancy separated by instantaneous jumps. 

 And, to complete the set, we need (D) the null- function, which 

 shows no change over the whole period of observation. The four 

 types obviously include all the possibilities, except for mixed 

 forms. The variables of Figure 2/12/1 will be found to be part-, 

 full-, step-, and step-functions respectively. 



87 



