6/9 



AN INTRODUCTION TO CYBERNETICS 



output) of the one machine into those of the other can convert 

 the one representation to the other. 

 Thus, in the example given, apply the one-one transformation P 



S € g h j k 



P:\ 



,5 



a 



a 



b d 



to A^'s table, applying it to the borders as well as to the body. The 

 result is 



This is essentially the same as M. Thus, c and ;8 in the border 



Fig. 6/9/2 



give d in both. The isomorphism thus corresponds to the definition. 

 (The isomorphism can be seen more clearly if first the rows are 

 interchanged, to 



and then the columns interchanged, to 



but this re-arrangement is merely for visual convenience.) 



When the states are defined by vectors the process is essentially 

 unchanged. Suppose R and S are two absolute systems: 



x' = .V + V' { u' = —u — V 



y' = A" — V \v' = —u -^ V 



98 



R: 



