7/7 DESIGN FOR A BRAIN 



spread tendency for systems to show changes of step-function 

 form if their variables are driven far from some usual value. 

 Later (S. 10/2) it will be suggested that the nervous system is not 

 exceptional in this respect. 



Systems containing full- and null-functions 

 7/7. We shall now consider the properties shown by absolute 

 systems that contain step-functions. But the discussion will be 

 clearer and simpler if we first examine some simpler systems. 



Suppose we have an absolute system composed wholly of full- 

 functions and we ignore one of the variables. Every experimenter 

 knows only too well what happens : the behaviour of the system 

 becomes unpredictable. Every experimenter has spent time 

 trying to make unpredictable experiments predictable ; he does 

 it by identifying the unknown variable. The unknown variable 

 may be scientifically trivial, like a loose screw, or important, like 

 a co-enzyme in a metabolic system ; but in either case, he cannot 

 establish a definite form of behaviour until he has identified and 

 either controlled or observed the unknown variable. To ignore a 

 /wZZ-function in an absolute system is to render the remainder non- 

 absolute, so that no characteristic form of behaviour can be 

 established. 



On the other hand, an absolute system which includes null- 

 functions may have the null-functions removed from it, or other 

 null-functions added to it, and the new system will still be absolute. 

 (The alteration is done, of course, not by interfering physically 

 with the 4 machine ', but by changing the list of variables.) Thus, if 

 the two-variable system of the pendulum (S. 6/3) is absolute, and 

 if the length of the pendulum stays constant once it is adjusted, 

 then the system composed of the three variables : 



(1) length of pendulum 



(2) angular deviation 



(3) angular velocity) 



is also absolute. A formal proof is given in S. 21/4, but it follows 

 readily from the definitions. (The reader should first verify that 

 every null-function is itself an absolute system.) Conversely, if 

 three variables A, B, N, are found to form an absolute system, 

 and N is a null-function, then the system composed of A and B 

 is absolute. 



Unlike the full-function, then, the null-function may be 



86 



