12/10 AN INTRODUCTION TO CYBERNETICS 



Real objects may provide a variety of equally plausible "systems", 

 which may differ from one another grossly in those properties we are 

 interested in here; and the answer to a particular question may 

 depend grossly on which system it happens to be apphed to.) 

 (Compare S.6/22.) 



12/10. The close relation between the Markovian machine and 

 the determinate can also be shown by the existence of mixed forms. 

 Thus, suppose a rat has partly learned the maze, of nine cells, shown 

 in Fig. 12/10/1, 



Fig. 12/10/1 



in which G is the goal. For reasons that need not be detailed here, 

 the rat can get no sensory clues in cells 1, 2, 3 and 6 (Hghtly shaded), 

 so when in one of these cells it moves at random to such other cells 

 as the maze permits. Thus, if we put it repeatedly in cell 3 it goes 

 with equal probability to 2 or to 6. (I assume equal probability 

 merely for convenience.) In cells 4, 5, 7, 8 and G, however, clues 

 are available, and it moves directly from cell to cell towards G. 

 Thus, if we put it repeatedly in cell 5 it goes always to 8 and then 

 to G. Such behaviour is not grossly atypical in biological work. 

 The matrix of its transitions can be found readily enough. Thus, 

 from 1 it can go only to 2 (by the maze's construction). From 2 it 

 goes to 1, 3, or 5 with equal probabiUty. From 4 it goes only to 5. 

 From G, the only transition is to G itself. So the matrix can be 

 built up. 



Ex. : Construct a possible matrix of its transition probabilities. 



12/11. Stability. The Markovian machine will be found on 

 examination to have properties corresponding to those described 

 in Part I, though often modified in an obvious way. Thus, the 

 machine's kinematic graph is constructible ; though, as the trans- 



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