4/11 AN INTRODUCTION TO CYBERNETICS 



for x's change does not now depend on y's value; x dominates y, 

 and the action is one way only. 



On the other side stand the practical experimenters and con- 

 structors, who want to use the word to refer, when some forward 

 effect from P to R can be taken for granted, to the deliberate con- 

 duction of some effect back from 7? to P by some connexion that is 

 physically or materially evident. They object to the mathematician's 

 definition, pointing out that this would force them to say that feed- 

 back was present in the ordinary pendulum (see Ex. 3/6/14) between 

 its position and its momentum — a "feedback" that, from the prac- 

 tical point of view, is somewhat mystical. To this the mathematician 

 retorts that if feedback is to be considered present only when there 

 is an actual wire or nerve to represent it, then the theory becomes 

 chaotic and riddled with irrelevancies. 



In fact, there need be no dispute, for the exact definition of 

 "feedback" is nowhere important. The fact is that the concept of 

 "feedback", so simple and natural in certain elementary cases, 

 becomes artificial and of little use when the interconnexions between 

 the parts become more complex. When there are only two parts 

 joined so that each affects the other, the properties of the feedback 

 give important and useful information about the properties of the 

 whole. But when the parts rise to even as few as four, if every one 

 affects the other three, then twenty circuits can be traced through 

 them; and knowing the properties of all the twenty circuits does not 

 give complete information about the system. Such complex sys- 

 tems cannot be treated as an interlaced set of more or less indepen- 

 dent feedback circuits, but only as a whole. 



For understanding the general principles of dynamic systems, 

 therefore, the concept of feedback is inadequate in itself. What is 

 important is that complex systems, richly cross-connected internally, 

 have complex behaviours, and that these behaviours can be goal- 

 seeking in complex patterns. 



Ex. 1 : Trace twenty circuits in the diagram of Fig. 4/11/1 : 



Fig. 4/11/1 

 54 



