6/15 AN INTRODUCTION TO CYBERNETICS 



The various simplifications are thus related as in the diagram, in 

 which a descending line connects the simpler form (below) with the 

 form from which it can be directly obtained (above): 



1 



2 3 



This diagram is of a type known as a lattice — a structure much 

 studied in modern mathematics. What is of interest in this Intro- 

 duction is that this ordering makes precise many ideas about 

 systems, ideas that have hitherto been considered only intuitively. 



Every lattice has a single element at the top (like 1) and a single 

 element at the bottom (like 6). When the lattice represents the 

 possible simplifications of a machine, the element at the top 

 corresponds to the machine with every state distinguished; it corres- 

 ponds to the knowledge of the experimenter who takes note of every 

 distinction available in its states. The element at the bottom 

 corresponds to a machine with every state merged; if this state is 

 called Z the machine has as transformation only 



Z 



This transformation is closed, so something persists (S.10/4), and 

 the observer who sees only at this level of discrimination can say 

 of the machine : "it persists", and can say no more. This persistance 

 is, of course, the most rudimentary property of a machine, distin- 

 guishing it from the merely evanescent. (The importance of 

 "closure", emphasised in the early chapters, can now be appreciated 

 — it corresponds to the intuitive idea that, to be a machine, an 

 entity must at least persist.) 



Between these extremes lie the various simplifications, in their 

 natural and exact order. Near the top lie those that differ from the 

 full truth only in some trifling matter. Those that lie near the bottom 

 are the simplifications of the grossest type. Near the bottom hes 

 such a simplification as would reduce a whole economic system 



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