3/1 AN INTRODUCTION TO CYBERNETICS 



brass in the wheels, the oil on the pivots, the properties of steel, the 

 interactions between atoms of iron, and so on with no definite limit. 

 As we said in S.2/3, the "operator" is often poorly defined and some- 

 what arbitrary — a concept of little scientific use. The transformation, 

 however, is perfectly well defined, for it refers only to the facts of 

 the changes, not to more or less hypothetical reasons for them. 



A series of changes as regular as those of the clock are not readily 

 found in the biological world, but the regular courses of some diseases 

 show something of the same features. Thus in the days before the 

 sulphonamides, the lung in lobar pneumonia passed typically 

 through the series of states: Infection— ^ consolidations red 

 hepatisation -> grey hepatisation -^ resolution -> health. Such a 

 series of states corresponds to a transformation that is well defined, 

 though not numerical. 



Next consider an iron casting that has been heated so that its 

 various parts are at various but determinate temperatures. If its 

 circumstances are fixed, these temperatures will change in a deter- 

 minate way with time. The casting's state at any one moment will 

 be a set of temperatures (a vector, S.3/5), and the passage from state 

 to state, iSo -> 5*1 -^ 5'2 — > . . ., will correspond to the operation of a 

 transformation, converting operand Sq successively to T{S^, 

 TKSo), THSo), . . ., etc. 



A more complex example, emphasising that transformations do 

 not have to be numerical to be well defined, is given by certain forms 

 of reflex animal behaviour. Thus the male and female three- 

 spined stickleback form, with certain parts of their environment, a 

 determinate dynamic system. Tinbergen (in his Study of Instinct) 

 describes the system's successive states as follows: "Each reaction 

 of either male or female is released by the preceding reaction of the 

 partner. Each arrow (in the diagram below) represents a causal 

 relation that by means of dummy tests has actually been proved to 

 exist. The male's first reaction, the zigzag dance, is dependent on a 

 visual stimulus from the female, in which the sign stimuli "swollen 

 abdomen" and the special movements play a part. The female 

 reacts to the red colour of the male and to his zigzag dance by swim- 

 ming right towards him. This movement induces the male to turn 

 round and to swim rapidly to the nest. This, in turn, entices the 

 female to follow him, thereby stimulating the male to point its head 

 into the entrance. His behaviour now releases the female's next 

 reaction: she enters the nest. . , . This again releases the quivering 

 reaction in the male which induces spawning. The presence of 

 fresh eggs in the nest makes the male fertilise them." Tinbergen 

 summarises the succession of states as follows: 



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