2/2 AN INTRODUCTION TO CYBERNETICS 



then easy to see the form that the changes will take if the points 

 were to become infinitely numerous and close together. 



In fact, however, by keeping the discussion to the case of the finite 

 difference we lose nothing. For having established with certainty 

 what happens when the differences have a particular size we can 

 consider the case when they are rather smaller. When this case is 

 known with certainty we can consider what happens when they are 

 smaller still. We can progress in this way, each step being well 

 established, until we perceive the trend ; then we can say what is the 

 limit as the difference tends to zero. This, in fact, is the method 

 that the mathematician always does use if he wants to be really sure 

 of what happens when the changes are continuous. 



Thus, consideration of the case in which all differences are finite 

 loses nothing; it gives a clear and simple foundation; and it can 

 always be converted to the continuous form if that is desired. 



The subject is taken up again in S.3/3. 



2/2. Next, a few words that will have to be used repeatedly. 

 Consider the simple example in which, under the influence of sun- 

 shine, pale skin changes to dark skin. Something, the pale skin, 

 is acted on by a factor, the sunshine, and is changed to dark skin. 

 That which is acted on, the pale skin, will be called the operand, 

 the factor will be called the operator, and what the operand is 

 changed to will be called the transform. The change that occurs, 

 which we can represent unambiguously by 



pale skin -^ dark skin 

 is the transition. 



The transition is specified by the two states and the indication of 

 which changed to which. 



TRANSFORMATION 



2/3. The single transition is, however, too simple. Experience has 

 shown that if the concept of "change" is to be useful it must be 

 enlarged to the case in which the operator can act on more than one 

 operand, inducing a characteristic transition in each. Thus the 

 operator "exposure to sunshine" will induce a number of transitions, 

 among which are: 



cold soil -> warm soil 

 unexposed photographic plate -^ exposed plate 



coloured pigment -^ bleached pigment 



Such a set of transitions, on a set of operands, is a transformation. 



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