7/24 AN INTRODUCTION TO CYBERNETICS 



We may, in fact, not really be considering one machine, however 

 much we speak in the singular (S.7/3), but may really be considering 

 a set of replicates, as one might speak of "the Model T Ford", or 

 "the anterior horn cell", or "the white rat". When this is so we can 

 consider all the replicates together, one in one state and one in 

 another; thus we get a set of states for one transformation to act on. 



A set of states can also arise even if the machine is unique. For 

 we may wish to consider not only what it may do at one time from 

 one state but also what it may do at another time from another 

 state. So its various possible behaviours at a set of times are 

 naturally related to a set of states as operands. 



Finally, a set may be created by the fiat of a theoretician who, not 

 knowing which state a particular machine is at, wants to trace out 

 the consequences of all the possibilities. The set now is not the 

 set of what does exist, but the set of what may exist (so far as the 

 theoretician is concerned). This method is typically cybernetic, for 

 it considers the actual in relation to the wider set of the possible 

 or the conceivable (S.1/3). 



7/24. Decay of variety. Having, for one of these reasons, a set 

 of states and one single-valued transformation, we can now, using 

 the result of S.7/22, predict that as time progresses the variety in the 

 set camiot increase and will usually diminish. 



This fact may be seen from several points of view. 



In the first place it gives precision to the often made remark that 

 any system, left to itself, runs to some equilibrium. Usually the 

 remark is based on a vague appeal to experience, but this is un- 

 satisfactory, for the conditions are not properly defined. Sometimes 

 the second law of thermodynamics is appealed to, but this is often 

 irrelevant to the systems discussed here (S.1/2). The new formula- 

 tion shows just what is essential. 



In the second place it shows that if an observer has an absolute 

 system, whose transformation he knows but whose states cannot, 

 for any reason, be observed, then as time goes on his uncertainty 

 about its state can only diminish. For initially it might be at any 

 one of all its states, and as time goes on so does the number of its 

 possible states diminish. Thus, in the extreme case in which it has 

 only one basin and a state of equilibrium, he can, if initially 

 uncertain, ultimately say with certainty, without making any further 

 observation, at which state it is. 



The diminution can be seen from yet another point of view. If 

 the variety in the possible states is associated with information, so 

 that the machine's being at some particular state conveys some 



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