THE BLACK BOX 



6/15 



sub-machine (with states /■ and s) given by the transformation 



h j k I in 



I ^ y ' ^ 



r s 



has graph s * r, with one basin and no cycle. Both statements are 

 equally true, and are compatible because they refer to different 

 systems (as defined in S.3/11). 



The point of view taken here is that science (as represented by the 

 observer's discoveries) is not immediately concerned with discovering 

 what the system "really" is, but with co-ordinating the various 

 observers' discoveries, each of which is only a portion, or an aspect, 

 of the whole truth. 



Were the engineer to treat bridgebuilding by a consideration of 

 every atom he would find the task impossible by its very size. He 

 therefore ignores the fact that his girders and blocks are really 

 composite, made of atoms, and treats them as his units. As it 

 happens, the nature of girders permits this simplification, and the 

 engineer's work becomes a practical possibility. It will be seen 

 therefore that the method of studying very large systems by studying 

 only carefully selected aspects of them is simply what is always 

 done in practice. Here we intend to follow the process more 

 rigorously and consciously. 



6/15. The lattice. The various simplifications of a machine have 

 exact relations to one another. Thus, the six forms of the system 

 of Ex. 6/13/2 are: 



(1) a, b, c, d 



(2) a + b, c, d 



(3) a, b, c -{- d 



(4) a + b, c + d 



(5) a,b + c-^d 



(6) a + b + c + d 



where, e.g. "a -\- b" means that a and b are no longer distinguished. 

 Now (4) can be obtained from (3) by a merging of a and b. But 

 (5) cannot be obtained from (4) by a simple merging; for (5) uses a 

 distinction between a and b that has been lost in (4). Thus it is 

 soon verified that simphfication can give: 



