234 WORLD BUILDING 



has, so to speak, been carried round the circuit will be 

 the relation AP with which we originally started. 



We have now two relations AP, AP' radiating from 

 the first relatum, their difference being connected with 

 a certain circuit in the world AEFA. The loose ends of 

 the relations P and P have their monomarks, and we 

 can take the difference of the monomarks (i.e. the 

 difference of the identification numbers comprised in 

 them) as the code expression for the change introduced 

 by carrying AP round the circuit. As we vary the circuit 

 and the original relation, so the change PP' varies; and 

 the next step is to find a mathematical formula express- 

 ing this dependence. There are virtually four things to 

 connect, the circuit counting double since, for example, 

 a rectangular circuit would be described by specifying 

 two sides. Each of them has to be specified by four 

 identification numbers (either monomarks or derived 

 from monomarks) ; consequently, to allow for all com- 

 binations, the required mathematical formula contains 

 4 4 or 256 numerical coefficients. These coefficients give 

 a numerical measure of the structure surrounding the 

 initial relatum. 



This completes the first part of our task to introduce 

 numerical measure of structure into the basal material. 

 The method is not so artificial as it appears at first sight. 

 Unless we shirk the problem by putting the desired 

 physical properties of the world directly into the original 

 relations and relata, we must derive them from the 

 structural interlocking of the relations; and such 

 interlocking is naturally traced by following circuits 

 among the relations. The axiom of comparability of 

 contiguous relations only discriminates between like 

 and unlike, and does not initially afford any means 

 of classifying various decrees and kinds of unlikeness; 



