6/4 DESIGN FOR A BRAIN 



primary operations applied to the two-variable system mentioned 



above, x is the angular deviation from the vertical, in degrees ; 



y is the angular velocity, in degrees per second ; the time is in 



seconds. 



The first two Lines show that the lines of behaviour following 



the state x = 14, y = 129 are equal, so the system, as far as 



it has been tested, is absolute. 

 The line of behaviour is shown 

 solid in Figure 6/3/1. In these 



Iqq. swings the length of the pendulum 



was 40 cm. This parameter was 

 then changed to 60 cm. and two 

 further lines of behaviour were 

 observed. On these two, the lines 

 of behaviour following the state 

 x = 21, y = 121 are equal, so the 



Figure 6/3/1. s y stem is a S ain absolute - The 



line of behaviour is shown dotted 



in the same figure. But the change of parameter- value has caused 



the line of behaviour from x = 0, y = 147 to change. 



The relationship which the parameter bears to the two variables 



is therefore as follows : 



(1) So long as the parameter is constant, the system of x and 

 y is absolute and has a definite field. 



(2) After the parameter changes from one constant value to 

 another, the system of x and y becomes again absolute, and has a 

 definite field, but this field is not the same as the previous one. 



The relation is general. A change in the value of an effective 

 parameter changes the line of behaviour from each state. From 

 this follows at once : a change in the value of an effective parameter 

 changes the field. 



The converse proposition is also true. Suppose we form a 

 system's field and find it to be absolute. If our control of its 

 surroundings has not been complete, and we test it later and find 

 it to be again absolute but to have a changed field, then we may 

 deduce, by S. 22/5, that some parameter must, in the interval, 

 have changed from one constant value to another constant value. 



6/4. The importance of distinguishing between change of a 

 variable and change of a parameter, that is, between change of 



74 



