6/19 AN INTRODUCTION TO CYBERNETICS 



the parts. Biological systems are thus particularly likely to show 

 the difference. We must therefore be on guard against expecting 

 the properties of the whole to reproduce the properties of the parts, 

 and vice versa. 



The examples of ammonium chloride and sugar mentioned above 

 are simple examples, but more complex cases occur. Consider, for 

 instance, the concept of "localisation" of some function in a system. 

 It may well happen that the view taken when the matter is examined 

 in the small is quite different from that taken in the large. Thus 

 suppose it is asked whether the brewing industry in England is 

 localised. The Exciseman, knowing of every building in his district 

 whether it is or is not part of the brewing trade, will say that brewing 

 is undoubtedly "locahsed". On the other hand, the map-maker of 

 England, being unable to mark any particular county as being the 

 seat of brewing, will say that it is not localised. Each, of course, is 

 correct. What allows the contradiction is that when the range of 

 size is great, what is true at one end of the scale may be false at the 

 other. 



Another example showing how contradictory may be the proper- 

 ties in the small and the large is given by an ordinary piece of elastic. 

 For years physical chemists searched for what made the molecule 

 contractile. They have since discovered that they were making 

 exactly the mistake that this section is attempting to prevent. It is 

 now known that the rubber molecule has no inherent contractility: 

 stretch one out and let it go, and nothing happens! Why then does 

 rubber contract? The point is that "stretching rubber" is not 

 "stretching one . . ."; the molecules, when there are more than one, 

 jostle each other and thereby force the majority to take lengths less 

 than their maxima. The result is that a shortening occurs, just as 

 if, on a crowded beach, a rope fifty feet long is drawn out straight: 

 after a few minutes the ends will be less than fifty feet apart! 



Further examples are hardly necessary, for the point to be made 

 is the merely negative one that in a large system there is no a priori 

 necessity for the properties of the whole to be a simple copy of those 

 of the parts. (S.7/3 adds some further examples.) 



6/19. As the system becomes larger, so does the fundamental 

 method of study (S.6/3) become more laborious in application. 

 Eventually the amount of labour necessary becomes prohibitive. 

 What then is the observer to do ? The question is of great import- 

 ance in the biological sciences, whether zoological or sociological, 

 for the size and complexity of the systems is great indeed. 

 The same difficulty has occurred in other sciences. Thus although 



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