7/4 AN INTRODUCTION TO CYBERNETICS 



Sometimes it happens that a statement is equally true of the indi- 

 vidual and the set: "the elephant eats with its trunk", for instance. 

 But the commonness of such a double application should not make 

 us overlook the fact that some types of statement are applicable 

 only to the set (or only to the individual) and become misleading 

 and a source of confusion if applied to the other. Thus a gramme of 

 hot hydrogen iodide gas, at some particular moment, may well be 

 37 per cent ionised; yet this statement must not be applied to the 

 individual molecules, which are all either wholly ionised or not at 

 all; what is true of the set is false of the individuals. Again, the 

 Conservative M.P.s have, at the moment, a majority in Parliament; 

 the statement is meaningless if applied to an individual member. 

 Again, a tyre on a motor-car may well be travelling due west at 

 50 m.p.h. when considered as a whole; yet the portion in contact 

 with the road is motionless, that at the top is travelling due west 

 at 100 m.p.h., and in fact not a single particle in the tyre is behaving 

 as the whole is behaving. 



Again, twenty million women may well have thirty million children, 

 but only by a dangerous distortion of language can we say that Mrs. 

 Everyman has one and a half children. The statement can some- 

 times be made without confusion only because those who have to 

 take action, those who have to provide schools for the children, for 

 instance, know that the half-child is not a freak but a set of a million 

 children. 



Let us then accept it as basic that a statement about a set 

 may be either trueor false (or perhaps meaningless) if applied to the 

 elements in the set. 



Ex. : The following statements apply to "The Cat", either to the species Felis 

 chmestica or to the cat next door. Consider the applicability of each 

 statement to (i) the species, (ii) the individual: 



1 . It is a million years old, 



2. It is male, 



3. Today it is in every continent, 



4. It fights its brothers, 



5. About a half of it is female, 



6. It is closely related to the Ursidae. 



7/4. Probability. The exercise just given illustrates the confusion 

 and nonsense that can occur when a concept that belongs properly 

 to the set (or individual) is improperly applied to the other. An 

 outstanding example of this occurs when, of the whole set, some 

 fraction of the elements has a particular property. Thus, of 

 100 men in a village 82 may be married. The fraction 0-82 is 



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