CHAPTER 6 



Parameters 



6/1. So far, we have discussed the changes shown by the vari- 

 ables of a state-determined system, and have ignored the fact that 

 all its changes occur on a background, or on a foundation, of 

 constancies. Thus, a particular simple pendulum provides two 

 variables which are known (S. 2/15) to be such that, if we are 

 given a particular state of the system, we can predict correctly 

 its ensuing behaviour ; what has not been stated explicitly is that 

 this is true only if the length of the' string remains constant. The 

 background, and these constancies, must now be considered. 



Every system is formed by selecting some variables out of the 

 totality of possible variables. ' Forming a system ' means dividing 

 the variables of the universe into two classes: those within the 

 system and those without. These two types of variable are in 

 no way different in their intrinsic physical nature, but they stand 

 in very different relations to the system. 



6/2. Given a system, a variable not included in it is a parameter. 

 The word variable will, from now on, be reserved for one within 

 the system. 



In general, given a system, the parameters will differ in their 

 closeness of relation to it. Some will have a direct relation to it : 

 change of their value would affect the system to a major degree; 

 such is the parameter ' length of pendulum ' in its relation to the 

 two-variable system of the previous section. Some are less closely 

 related to it, their changes producing only a slight effect on it; 

 such is the parameter 4 viscosity of the air ' in relation to the same 

 system. And finally, for completeness, may be mentioned the 

 infinite number of parameters that are without detectable effect 

 on the system; such are the brightness of the light shining on 

 the pendulum, the events in an adjacent room, and the events in 

 the distant nebulae. Those without detectable effect may be 

 ignored; but the relationship of an effective parameter to a 

 system must be clearly understood. 



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