4/6 AN INTRODUCTION TO CYBERNETICS 



To talk about the transient, as distinct from the repetitive part 

 that follows, it is convenient to be able to mark, unambiguously, 

 its end. If the transformation is discrete, the following method 

 gives its length rigorously: Let the sequence of states go on till 

 repetition becomes evident, thus 



ABCDCDCDCDC.orHEFGGGGGGG... 



Then, coming in from the right, make the mark "1" as soon as the 

 sequence departs from the cycle, thus 



ABiCDCDCDCDC.orHEFiGGGGGGG... 



Next add the mark "2", to the right of 1, to include one complete 

 cycle, thus 



ABiCD2CDCDCDC...orHEFiG2GGGGGGG... 



Then the transient is defined as the sequence of states from the 

 initial state to the mark 2 : A B C D , or H E F G. 



Rigorous form can now be given to the intuitive impression that 

 complex systems can produce, in constant conditions, more complex 

 forms of behaviour than can the simple. By drawing an arbitrary 

 kinematic graph on N states it is easy to satisfy oneself that if a 

 closed single-valued transformation with A'^ operands is apphed 

 repeatedly, then the length of transient cannot exceed N states. 



Ex. 1 : What property must the graph have if the onset of a recurrence is to be 



postponed as long as possible ? 

 Ex. 2: What is the transient of the system of Ex. 3/6/6, started from the state 



(8,5)? 



COUPLING SYSTEMS 



4/6. A fundamental property of machines is that they can be 

 coupled. Two or more whole machines can be coupled to form 

 one machine; and any one machine can be regarded as formed by 

 the coupling of its parts, which can themselves be thought of as 

 small, sub-, machines. The coupling is of profound importance 

 in science, for when the experimenter runs an experiment he is 

 coupling himself temporarily to the system that he is studying. To 

 what does this process, the joining of machine to machine or of 

 part to part, correspond in the symbolic form of transformations ? 

 Of what does the operation of "coupling" consist ? 



Before proceeding to the answer we must notice that there is 

 more than one answer. One way is to force them roughly together, 



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