THE BLACK BOX 6/17 



with a vast number of interacting parts, going through a trade 

 cycle, to the simple form of two states: 



I i 



Boom Slump 

 i I 



Thus, the various simplifications of a dynamic system can be 

 ordered and related. 



6/16. Models. We can now see much more clearly what is meant 

 by a "model". The subject was touched on in S.6/8, where three 

 systems were found to be isomorphic and therefore capable of 

 being used as representations of each other. The subject is of 

 some importance to those who work with biological systems, for 

 in many cases the use of a model is helpful, either to help the worker 

 think about the subject or to act as a form of analogue computer. 



The model will seldom be womorphic with the biological system : 

 usually it will be a homomorphism of it. But the model itself is 

 seldom regarded in all its practical detail: usually it is only some 

 aspect of the model that is related to the biological system; thus the 

 tin mouse may be a satisfactory model of a living mouse — provided 

 one ignores the tinniness of the one and the proteinness of the other. 

 Thus what usually happens is that the two systems, biological and 

 model, are so related that a homomorphism of the one is isomorphic 

 with a homomorphism of the other. (This relation is symmetric, 

 so either may justifiably be said to be a "model" of the other.) 

 The higher the homomorphisms are on their lattices, the better or 

 more reahstic will be the model. 



At this point this Introduction must leave the subject of Homo- 

 morphisms. Enough has been said to show the foundations of the 

 subject and to indicate the main lines for its development. But 

 these developments belong to the future. 



Ex. ] : What would be the case when it was the two top-most elements of the 



two lattices that were isomorphic? 

 Ex. 2: To what degree is the Rock of Gibraltar a model of the brain? 

 Ex. 3 : To what extent can the machine 



I P Q r 

 ^ q r r 



provide models for the system of Ex. 6113121 



THE VERY LARGE BOX 



6/17. The previous sections have shown how the properties that 

 are usually ascribed to machines can also be ascribed to Black 



109 



