6/6 AN INTRODUCTION TO CYBERNETICS 



Ex. 7: Two Black Boxes are of identical external appearance, and each has a 

 single input a and a single output x, each a numerical variable. They were 

 labelled I and II, and their canonical representations were found to be 



I: a;' = X + 1 - a 



II: A-' = (1 + a)x - 2 + a. 



Unfortunately the labels "I" and "11" have since become detached and it is 

 now not known which is which. Suggest a simple test that will re-identify 

 them. 



6/6. Inaccessible states. Examination of the transformations 



shows that the state g, once past in the protocol, cannot be made to 

 re-appear by any manipulations of the input. The transitions from 

 g thus cannot be explored further or tested repeatedly. This fact, 

 that certain states of the Box cannot be returned to at will, is very 

 common in practice. Such states will be called inaccessible. 



In its most dramatic form it occurs when the investigation of a 

 new type of enemy mine leads to an explosion^ — ^which can be des- 

 cribed more abstractly by saying that the system has passed from a 

 state to which no manipulation at the input can make the system 

 return. Essentially the same phenomenon occurs when experiments 

 are conducted on an organism that learns; for as time goes on it 

 leaves its "unsophisticated" initial state, and no simple manipulation 

 can get it back to this state. In such experiments, however, the 

 psychologist is usually investigating not the particular individual 

 but the particular species, so he can restore the initial state by the 

 simple operation of taking a new individual. 



Thus the experimenter, if the system is determinate, must either 

 restrict himself to the investigation of a set of states that is both 

 closed and freely accessible, such as /, h, j in the example, or he 

 must add more states to his input so that more transformations 

 become available and thus, perhaps, give a transition to g. 



6/7. Deducing connexions. It is now clear that something of the 

 connexions within a Black Box can be obtained by deduction. For 

 direct manipulation and observation gives the protocol, this (if 

 the system is determinate) gives the canonical representation, and 

 this gives the diagram of immediate effects (one for each input state) 

 (S.4/13). But we must go cautiously. 

 It must be noticed that in a real system the "diagram of internal 



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