11/6 AN INTRODUCTION TO CYBERNETICS 



elements as small as possible (ignoring for the moment any idea of a 

 target). He marks an element in the first row. In the second row 

 he must change to a new column if he is not to increase the variety 

 by adding a new, different, element; for in the initially selected 

 column the elements are all different, by hypothesis. To keep the 

 variety down to one element he must change to a new column at 

 each row. (This is the best he can do; it may be that change from 

 column to column is not sufficient to keep the variety down to one 

 element, but this is irrelevant, for we are interested only in what is 

 the least possible variety, assuming that everything falls as favourably 

 as possible). So if R has n moves available (three in the example), 

 at the /7-th row all the columns are used, so one of the columns 

 must be used again for the next row, and a new outcome must be 

 allowed into the set of outcomes. Thus in Table 11/5/1, selection 

 of the A:'s in the first three rows will enable the variety to be kept to 

 one element, but at the fourth row a second element must be allowed 

 into the set of outcomes. 



In general: If no two elements in the same column are equal, and 

 if a set of outcomes is selected by R, one from each row, and if the 

 table has r rows and c columns, then the variety in the selected set 

 of outcomes cannot be fewer than rjc. 



THE LAW OF REQUISITE VARIETY 



11/6. We can now look at this game (still with the restriction that 

 no element may be repeated in a column) from a slightly different 

 point of view. If i?'s move is unvarying, so that he produces the 

 same move, whatever i)'s move, then the variety in the outcomes will 

 be as large as the variety in D's moves. D now is, as it were, exerting 

 full control over the outcomes. 



If next R uses, or has available, two moves, then the variety of 

 the outcomes can be reduced to a half (but not lower). If R has 

 three moves, it can be reduced to a third (but not lower); and so on. 

 Thus if the variety in the outcomes is to be reduced to some assigned 

 number, or assigned fraction of Z)'s variety, i?'s variety must be 

 increased to at least the appropriate minimum. Only variety in R's 

 moves can force down the variety in the outcomes. 



11/7. If the varieties are measured logarithmically (as is almost 

 always convenient), and if the same conditions hold, then the theorem 

 takes a very simple form. Let V^ be the variety of D, Vj^ that of R, 

 and Vq that of the outcome (all measured logarithmically). Then 



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