2/17 AN INTRODUCTION TO CYBERNETICS 



we might observe all the changes that follow the placing of a piece 

 of meat near-by. 

 Suppose, for definiteness, we have the transformation 



v.l^ •" ^ " ^ 



^ D A E D D 



If U is applied to C, then to U{C), then to U\C), then to U\C) 

 and so on,- there results the series: C, E, D, D, D, . . . and so on, 

 with D continuing for ever. If U is applied similarly to A there 

 results the series A, D, D, D, . . . with D continuing again. 



These results can be shown graphically, thereby displaying to the 

 glance results that otherwise can be apprehended only after detailed 

 study. To form the kinematic graph of a transformation, the set of 

 operands is written down, each in any convenient place, and the 

 elements joined by arrows with the rule that an arrow goes from A 

 to B if and only if A is transformed in one step to B. Thus U gives 

 the kinematic graph 



C^E^D^A<-B 



(Whether D has a re-entrant arrow attached to itself is optional 

 if no misunderstanding is likely to occur.) 



If the graph consisted of buttons (the operands) tied together 

 with string (the transitions) it could, as a network, be pulled into 

 different shapes : 



C-^E B-^A 



\ 



D or 



/ 

 B-^A D^E<-C 



and so on. These different shapes are not regarded as different 

 graphs, provided the internal connexions are identical. 



The elements that occur when C is transformed cumulatively by 

 U (the series C, E, D, D, . . .) and the states encountered by a point 

 in the kinematic graph that starts at C and moves over only one 

 arrow at a step, always moving in the direction of the arrow, are 

 obviously always in correspondence. Since we can often follow the 

 movement of a point along a line very much more easily than we 

 can compute U(C), U-{C), etc., especially if the transformation is 

 complicated, the graph is often a most convenient representation 

 of the transformation in pictorial form. The moving point will 

 be called the representative point. 



22 



