TRANSMISSION OF VARIETY 8/10 



There results the transducer 



m^ = (ci — 2di)/d2 



m2 = d2ic2 - 2d2)l{ci - 2d{). 



If now this transducer is joined to the original transducer by 

 d^ = .x'l, fi?2 = -^'2» 'iJid to the delayers by C] = Pi, C2 = P2, then Wj 

 and /W2 will give, respectively, the values that ai and ^2 had two 

 steps earlier. 



Ex. I : Build an inverter for the transducer n' = an. 



Ex. 2: Similarly for n' = 11 — 2a + 4. 



Ex. 3 : Similarly for x' = ax — by, y' = ax + by. 



Ex. 4: Try to build an inverter for the transducer n' = n -\- a + b; why can 

 it not be done? 



*Ex. 5 : Build an inverter for the transducer 



dx\jdt = OlXlA'2 + 02 



dxzldt = (oi — l).Yi + 02x2. 



Ex. 6: Why, in the section, does M have to transform (7,3) to 4, and not to 

 —2, as the table a few lines higher might suggest? 



8/9. Size of the inverter. With the facts of the previous sections, 

 it is now possible to make some estimate of how much mechanism 

 is necessary to invert the output of some given transducer. S.8/7 

 makes clear that if the original transducer is not to lose distinctions 

 it must have at least as many output values as the input has distinct 

 values. Similarly the inverter must have at least as many, but need 

 not necessarily have more. The delayers will require little, for they 

 are simple. It seems, therefore, that if the inverter is made of 

 similar components to the original transducer then, whatever the 

 complexity or size of the original transducer, the inverter will have a 

 complexity and size of the same order. 



The importance of this observation is that one sometimes feels, 

 when thinking of the complexities in the cerebral cortex or in an 

 ecological system, that any effect transmitted through the system 

 must almost at once become so tangled as to be beyond all possible 

 unravelling. Evidently this is not so; the complications of coding 

 added by one transducer are often or usually within the decoding 

 powers of another transducer of similar size. 



TRANSMISSION FROM SYSTEM TO SYSTEM 



8/10. "'Transmitting" variety. It may be as well at this point to 

 clarify a matter on which there has been some confusion. Though 

 it is tempting to think of variety (or information) as passing through 



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