TRANSMISSION OF VARIETY 8/16 



immediate effect on the cortex) the action has to take place through 

 a chain of systems : the sense organs, the sensory nerves, the sensory 

 nuclei, and so on; and some delay is thereby imposed. Even within 

 one such part some transfer has to take place from point to point, 

 thereby delaying its transfer to the next part. 



Conversely, if a system such as T is found on testing to transmit 

 its variety to another system only over a number of steps, then it 

 may be predicted that T, if examined in detail, will be found to 

 consist of sub-systems coupled so that not all of T's variables have 

 an immediate effect on S. 



Ex. 1 : If r consists of the sub-systems A, . . ., F joined to each other and to 

 S as shown in the diagram of immediate effects : 



how many steps are necessary for all the variety in Tto be transferred to 5? 



Ex. 2: (Continued.) How long does it take to get a "message", telling of T's 

 state, uniquely from Tto SI 



Ex. 3 : If /, with the variables w, x, y, z, dominates K, with the variable k, by 

 the transformation w' = w — y, x' = w + xz, y' = 2wy — z, z' = yz'^, 

 k' = X — Ik, how many steps are necessary for all the variety in / to be 

 transferred to AT? 



4: (Continued.) In the same system, how long would it take to get a mes- 

 sage from w to z? 



Ex 



8/16. To improve our grasp of these matters, let us next consider 

 the case of two systems joined so that there is feedback: 



U 



S.8/11 showed that Twill pass variety to U', will U, now having this 

 variety, pass it back to T and thereby increase T's variety still 

 further? 



Again the answer is given straightforwardly when we consider a 

 set of replicates. Suppose that initially the variety existed only 

 between the T's, the C/'s being all at the same state. Divide the 

 whole set into sub-sets, each sub-set consisting of those with T at a 

 particular state, so that set /, say, consists of the systems with T at 

 state r,-. Within such a subset there is now no variety in state, and 

 no variety can develop, for the whole (r,t/)-system is absolute. 

 The initial variety of the Ts, therefore, will not increase, either at 

 the first step or subsequently. In a determinate system, feedback 

 does not lead to a regenerative increase in variety. 



157 



