THE MACHINE WITH INPUT 4/20 



specify a general method by which the details shall be specified by 

 some source other than himself. In the examples above, it was 

 a pack of cards that made the final decision. A final, unique 

 system can thus be arrived at provided his specification is supple- 

 mented. (The subject is developed more thoroughly in S. 13/1 8.) 



Ex. 1 : Define a method (using dice, cards, random numbers, etc.) that will 

 bring the closed single-valued transformation T: 



Si S2 Si S4 S5 Sq 



T:l 



9 7 7 7 9? 



to some particular form, so that the final particular form is selected by the 

 method and not by the reader. 



Ex. 2: (Continued.) Define a method so that the transformation shall be one- 

 one, but not otherwise restricted. 



Ex. 3: (Continued.) Define a method so that no even-numbered state shall 

 transform to an odd-numbered state. 



Ex. 4: (Continued.) Define a method so that any state shall transform only to a 

 state adjacent to it in number. 



Ex. 5: Define a method to imitate the network that would be obtained if parts 

 were coupled by the following rule: In two dimensions, with the parts 

 placed in a regular pattern thus : 





 

 



extending indefinitely in all directions in the plane, each part either has an 

 immediate effect on its neighbour directly above it or does not, with equal 

 probability; and similarly for its three neighbours to right and left and 

 below. Construct a sample network. 



4/20. Richness of connexion. The simplest system of given 

 largeness is one whose parts are all identical, mere replicates of one 

 another, and between whose parts the couplings are of zero degree 

 (e.g. Ex. 4/1/6). Such parts are in fact independent of each other, 

 which makes the whole a "system" only in a nominal sense, for it is 

 totally reducible. Nevertheless this type of system must be con- 

 sidered seriously, for it provides an important basic form from 

 which modifications can be made in various ways. Approximate 

 examples of this type of system are the gas whose atoms collide 

 only rarely, the neurons in the deeply narcotised cortex (if they can 

 be assumed to be approximately similar to one another) and a 

 species of animals when the density of population is so low that they 

 hardly ever meet or compete. In most cases the properties of this 

 basic type of system are fairly easily deducible. 



The first modification to be considered is obviously that by which 

 a small amount of coupling is allowed between the parts, so that 



5 65 



