THE DETERMINATE MACHINE 



3/1 



Appearsx^ 



/ 



Courts/" 



Female < 



Follows 



\ 



Enters nest\^ 



Spawns 





Zigzag dance 

 Leads 



Shows nest entrance 



Trembles 



Fertilises 



Male 



He thus describes a typical trajectory. 



Further examples are hardly necessary, for the various branches 

 of science to which cybernetics is applied will provide an abun- 

 dance, and each reader should supply examples to suit his own 

 speciality. 



By relating machine and transformation we enter the discipline 

 that relates the behaviours of real physical systems to the properties 

 of symbolic expressions, written with pen on paper. The whole 

 subject of "mathematical physics" is a part of this discipline. The 

 methods used in this book are however somewhat broader in scope, 

 for mathematical physics tends to treat chiefly systems that are 

 continuous and linear (S.3/7). The restriction makes its methods 

 hardly applicable to biological subjects, for in biology the systems 

 are almost always non-Hnear, often non-continuous, and in many 

 cases not even metrical, i.e. expressible in number. The exercises 

 below (S.3/4) are arranged as a sequence, to show the gradation 

 from the very general methods used in this book to those commonly 

 used in mathematical physics. The exercises are also important as 

 illustrations of the correspondences between transformations and 

 real systems. 



To summarise: Every machine or dynamic system has many 

 distinguishable states. If it is a determinate machine, fixing its 

 circumstances and the state it is at will determine, i.e. make unique, 

 the state it next moves to. These transitions of state correspond 

 to those of a transformation on operands, each state corresponding 

 to a particular operand. Each state that the machine next moves to 

 corresponds to that operand's transform. The successive powers 

 of the transformation correspond, in the machine, to allowing 

 double, treble, etc., the unit time-interval to elapse before recording 

 the next state. And since a determinate machine cannot go to two 

 states at once, the corresponding transformation must be single- 

 valued. 



27 



