1/3 AN INTRODUCTION TO CYBERNETICS 



1/3. Cybernetics stands to the real machine — electronic, mechani- 

 cal, neural, or economic — much as geometry stands to a real object 

 in our terrestrial space. There was a time when "geometry" 

 meant such relationships as could be demonstrated on three- 

 dimensional objects or in two-dimensional diagrams. The forms 

 provided by the earth — animal, vegetable, and mineral — were larger 

 in number and richer in properties than could be provided by ele- 

 mentary geometry. In those days a form which was suggested by 

 geometry but which could not be demonstrated in ordinary space 

 was suspect or inacceptable. Ordinary space dominated geometry. 



Today the position is quite different. Geometry exists in its own 

 right, and by its own strength. It can now treat accurately and 

 coherently a range of forms and spaces that far exceeds anything 

 that terrestrial space can provide. Today it is geometry that con- 

 tains the terrestrial forms, and not vice versa, for the terrestrial 

 forms are merely special cases in an all-embracing geometry. 



The gain achieved by geometry's development hardly needs to be 

 pointed out. Geometry now acts as a framework on which all 

 terrestrial forms can find their natural place, with the relations 

 between the various forms readily appreciable. With this increased 

 understanding goes a correspondingly increased power of control. 



Cybernetics is similar in its relation to the actual machine. It 

 takes as its subject-matter the domain of "all possible machines", 

 and is only secondarily interested if informed that some of them have 

 not yet been made, either by Man or by Nature. What cybernetics 

 offers is the framework on which all individual machines may be 

 ordered, related and understood. 



1/4. Cybernetics, then, is indifferent to the criticism that some of 

 the machines it considers are not represented among the machines 

 found among us. In this it follows the path already followed with 

 obvious success by mathematical physics. This science has long 

 given prominence to the study of systems that are well known to be 

 non-existent — springs without mass, particles that have mass but no 

 volume, gases that behave perfectly, and so on. To say that these 

 entities do not exist is true; but their non-existence does not mean 

 that mathematical physics is mere fantasy; nor does it make the 

 physicist throw away his treatise on the Theory of the Massless 

 Spring, for this theory is invaluable to him in his practical work. 

 The fact is that the massless spring, though it has no physical 

 representation, has certain properties that make it of the highest 

 importance to him if he is to understand a system even as simple 

 as a watch. 



