THE BLACK BOX 6/20 



the Newtonian theory has, in principle, solved all gravitational 

 problems, yet its application to three bodies is most complex, and 

 its application to half a dozen is prohibitively laborious. Yet 

 astrophysicists want to ask questions about the behaviour of star 

 clusters with 20,000 members! What is to be done? 



Experience has shown that in such cases the scientist must be 

 very careful about what questions he asks. He must ask for what 

 he really wants to know, and not for what he thinks he wants. Thus 

 the beginner will say simply that he wants to know what the cluster 

 will do, i.e. he wants the trajectories of the components. If this 

 knowledge, however, could be given to him, it would take the form 

 of many volumes filled with numerical tables, and he would then 

 reahse that he did not really want all that. In fact, it usually 

 happens that the significant question is something simple, such as 

 "will the cluster contract to a ball, or will it spread out into a disc?" 



The physicists, led originally by Poincare, have now a well 

 developed method for dealing with such matters — that of topology. 

 By its means, unambiguous answers can be given to simple questions, 

 so that the intricacies that would overwhelm the observer are never 

 encountered. 



A similar method, applied to complicated differential equations, 

 enables the main important features of the solutions to be deduced 

 in cases where the full solutions would be unmanageably complicated. 

 This is the so-called "stabihty" theory of these equations. 



What is important for us here is that these methods exist. They 

 suggest that if a Black Box (such as a brain) has far too many 

 variables for a study in every detail to be practical then it should 

 be possible for the cybernetically-minded psychologist to devise a 

 "topological" approach that shall enable him to get what informa- 

 tion he really wants (not what he thinks he wants!) without his 

 being overwhelmed with useless detail. Lewin attempted such a 

 psychology; but in the '30s topology was not yet developed to be a 

 useful tool. In the '50s, however, it is much better developed, 

 especially in the form published under the pseudonym of Nicholas 

 Bourbaki, by the French School. At last we have before us the 

 possibility of a psychology that shall be at once rigorous and 

 practical. 



THE INCOMPLETELY OBSERVABLE BOX 



6/20. So far, in this chapter, we have assumed that the observer 

 of the Black Box has the necessary means for observing all that 

 pertains to the Box's state, so that he is Uke a Ship's Engineer (S.6/2) 



8 113 



