2/7 DYNAMIC SYSTEMS 



The operational method 



2/7. The variables being decided on, the recording apparatus 

 is now assumed to be connected and the experimenter ready to 

 start observing. We must now make clear what is assumed about 

 his powers of control over the system. 



Throughout the book we shall consider only the case in which 

 he has access to all states of the system. It is postulated that the 

 experimenter can control any variable he pleases: that he can 

 make any variable take any arbitrary value at any arbitrary 

 time. The postulate specifies nothing about the methods: it 

 demands only that certain end-results are to be available. In 

 most cases the means to be used are obvious enough. Take the 

 example of S. 2/3: an arbitrary angular deviation of the pendulum 

 can be enforced at any time by direct manipulation; an arbitrary 

 angular momentum can be enforced at any time by an appropriate 

 impulse; the cog can be disconnected and shifted, the driving- 

 weight wound up, the hand moved, and the pendulum-bob lowered. 



By repeating the control from instant to instant, the experi- 

 menter can force a variable to take any prescribed series of values. 

 The postulate, therefore, implies that any variable can be forced 

 to follow a prescribed course. 



Some systems cannot be forced, for instance the astronomical, 

 the meteorological, and those biological systems that are accessible 

 to observation but not to experiment. Yet no change is neces- 

 sary in principle : the experimenter simply waits until the desired 

 set of values occurs during the natural changes of the system, 

 and he counts that instant as if it were the instant at which the 

 system were started. Thus, though he cannot create a thunder- 

 storm, he can observe how swallows react to one simply by 

 waiting till one occurs ' spontaneously '. 



It will also be assumed (except where explicitly mentioned) that 

 he has similarly complete control over those variables that are 

 not in the system yet which have an effect on it. In the experi- 

 ment of Table 2/4/1 for instance, Pavlov had control not only of 

 the variables mentioned but also of the many variables that might 

 have affected the system's behaviour, such as the lights that 

 might have flashed, the odours that might have been applied, and 

 the noises that might have come from outside. 



The assumption that the control is complete is made because, 



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