THE BLACK BOX 6/21 



Observer One can see, like us, the values of both A and Z. He 

 studies the various combinations that may lead to the appearance 

 of B, and he reports that B appears whenever the whole shows a 

 state with Z at y and the input at a. Thus, given that the input 

 is at a, he relates the occurrence of B to whether Z is at j now. 



Observer Two is handicapped — he can see only / and A, not Z. 

 He will find that knowledge of ^'s state and of /'s state is not suffi- 

 cient to enable him to predict reliably whether B will be shown; 

 (for sometimes Z will be at y and sometimes at some other state). 

 If however Two turns his attention to earlier events at / he finds he 

 can predict 5's appearance accurately. For if / has in succession 

 the values /u., a then behaviour B will appear, and not otherwise. 

 Thus, given that the input is at a, he relates the occurrence of B 

 to whether / did have the value ju. earlier. 



Thus Two, being unable to observe Z directly, can none the less 

 make the whole predictable by taking into account earlier values of 

 what he can observe. The reason is, the existence of the corres- 

 pondence: 



/ at ju, earlier <-^Z a.t y now 

 / not at fi earlier <-^ Z not at y now. 



As this correspondence is one-one, information about /'s state a step 

 earlier and information about Z's state now are equivalent, and each 

 can substitute for the other; for to know one is to know the other. 



If One and Two are quarrelsome, they can now fall into a dispute. 

 One can maintain that the system shows no "memory", i.e. its 

 behaviour requires no reference to the past, because the appearance of 

 behaviour B can be fully accounted for by the system's present state 

 (at 7, A and Z). Two can deny this, and can point out that the 

 system of I and A can be shown as determinate only when past 

 values of /are taken into account, i.e. when some form of "memory" 

 is appealed to. 



Clearly, we need not take sides. One and Two are talking of 

 different systems (of / -f ^ + Z or of 7 -f A), so it is not surprising 

 that they can make differing statements. What we must notice here 

 is that Two is using the appeal to "memory" as a substitute for his 

 inability to observe Z. 



Thus we obtain the general rule : If a determinate system is only 

 partly observable, and thereby becomes (for that observer) not 

 predictable, the observer may be able to restore predictability by 

 taking the system's past history into account, i.e. by assuming the 

 existence within it of some form of ''memory''. 



The argument is clearly general, and can be applied equally well 



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