TRANSMISSION OF VARIETY 8/14 



be used repeatedly later: given long enough, any transducer can 

 transmit any amount of variety. 



An important aspect of this theorem is its extreme generality. 

 What sort of a machine it is that is acting as intermediate transducer, 

 as channel, is quite irrelevant: it may be a tapping-key that has 

 only the two states "open" and "closed", or an electric potential 

 that can take many values, or a whole neural ganglion, or a news- 

 paper — all are ruled by the theorem. With its aid, quantitative 

 accuracy can be given to the intuitive feeling that some restriction 

 in the rate of communication is imphed if the communication has 

 to take place through a small intermediate transducer, such as 

 when the information from retina to visual cortex has to pass through 

 the lateral geniculate body, or when information about the move- 

 ments of a predator have to be passed to the herd through a solitary 

 scout. 



£.v. 1 : An absolute system, of three parts, Q, R and S, has states {q,r,s) and 

 transformation 



q: ,123456789 

 ^': ^466565888 

 , _ r 0, if ^ + /■ is even, 

 \ 1,„ „ „ odd. 

 s' = 2s — r. 



Q thus dominates R, and R dominates S. What is R's capacity as a 

 channel ? 



Ex.2: (Continued.) Nine replicates were started at the initial states (1,0,0), 

 (2,0,0), . . ., (9,0,0), so that only Q had any initial variety, (i) How did the 

 variety of the Q's change over the first five steps? (ii) How did that of 

 the R's ? (iii) That of the 5's ? 



Ex. 3: (Continued.) Had the answer to Ex..2(iii) been given as "5':1, 1,4,5,5", 

 why would it have been obviously wrong, without calculation of the actual 

 trajectories ? 



8/14. The exercise just given will have shown that when Q, R and 

 S form a chain, 5* can gain in variety step by step from R even though 

 R can gain no more variety after the first step (S.8/12). The reason 

 is that the output of R, taken step by step as a sequence, forms a 

 vector (S.9/9), and the variety in a vector can exceed that in a com- 

 ponent. And if the number of components in a vector can be 

 increased without limit then the variety in the vector can also be 

 increased without limit, even though that in each component remains 

 bounded. Thus a sequence of ten coin-spins can have variety up to 

 1024 values, though each component is restricted to two. Similarly 

 /?'s values, though restricted in the exercises to two, can provide a 

 sequence that has variety of more than two. As the process of 



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