6/22 AN INTRODUCTION TO CYBERNETICS 



if the special, earlier, event (/x) occurred not one step earlier, but 

 many. Thus in general, if earlier events E^, E2, ■ ■ -, Ek leave traces 

 Ti, T2, • ■ ; T^ respectively, which persist; and if later the remainder 

 of the system produces behaviours Bi, B2, . . ., B^. corresponding to 

 the value of T, then the various behaviours may be related to, or 

 explained by, either 



(1) the present value of T, in which case there is no need for the 

 invocation of any "memory", or 



(2) the past value of E, in which case the observer is compelled 

 to postulate some form of "memory" in the system. 



Thus the possession of ''memory" is not a wholly objective property of 

 a system — it is a relation between a system and an observer; and the 

 property will alter with variations in the channel of communication 

 between them. 



Thus to invoke "memory" in a system as an explanation of its 

 behaviour is equivalent to declaring that one cannot observe the 

 system completely. The properties of "memory" are not those of 

 the simple "thing" but the more subtle "coding". 



*Ex. 1 : Prove the statement (Design . . S. 19/22) that in an absolute system we 

 can avoid direct reference to some of the variables provided we use deri- 

 vatives of the remaining variables to replace them. 



*Ex. 2 : Prove the same statement about equations in finite differences. 



*Ex. 3 : Show that if the system has n degrees of freedom we must, in general, 

 always have at least // observations, each of the type "at time if variable Xf 

 had value Xi' if the subsequent behaviour is to be predictable. 



6/22. A clear example showing how the presence of "memory" is 

 related to the observability of a part is given by the digital calculator 

 with a magnetic tape. Suppose, for simplicity, that at a certain 

 moment the calculator will produce a 1 or a 2 according to whether 

 the tape, at a certain point, is magnetised + or — , respectively; the 

 act of magnetisation occurred, say, ten minutes ago, and whether 

 it was magnetised + or — depended on whether the operator did or 

 did not, respectively, close a switch. There is thus the corres- 

 pondence: 



switch closed <-^ + «-> 1 



switch open <- > - <-^ 2 



An observer who can see the magnetic tape now can argue that 

 any reference to the past is unnecessary, for he can account for the 

 machine's behaviour (i.e. whether it will produce a 1 or a 2) by its 

 state now, by examining what the tape carries now. Thus to know 



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