THE MACHINE WITH INPUT 4/19 



states, rather than the more usual variables, that it requires no 

 explicit mention of the system's number of pans; and theorems once 

 proved true are true for systems of all sizes (provided, of course, that 

 the systems conform to the suppositions made in the argument). 



What remains valid is, of course, the truth of the mathematical 

 deductions about the mathematically defined things. What may 

 change, as the system becomes very large, is the apphcability of these 

 theorems to some real material system. The applicability, however, 

 can be discussed only in relation to particular cases. For the 

 moment, therefore, we can notice that size by itself does not invali- 

 date the reasonings that have been used so far. 



4/19. Random coupling. Suppose now that the observer faces a 

 system thai, for him, is very large. How is he to proceed? Many 

 questions arise, too many to be treated here in detail, so I shall 

 select only a few topics, letting them serve as pattern for the rest. 

 (See S.6/19 and Chapter 13.) First, how is the system to be 

 specified ? 



By definition, the observer can specify it only incompletely. This 

 is synonymous with saying that he must specify it "statistically", 

 for statistics is the art of saying things that refer only to some aspect 

 or portion of the whole, the whole truth being too bulky for direct 

 use. If it has too many parts for their specification individually, 

 they must be specified by a manageable number of rules, each of 

 which apphes to many parts. The parts specified by one rule need 

 not be identical; generahty can be retained by assuming that each 

 rule specifies a set statistically. This means that the rule specifies a 

 distribution of parts and a way in which it shall be sampled. The 

 particular details of the individual outcome are thus determined not 

 by the observer but by the process of sampling (as two people might 

 leave a decision to the spin of a coin). 



The same method must be used for specification of the coupling. 

 If the specification for coupling is not complete it must in some way 

 be supplemented, for ultimately some individual and single coupling 

 must actually occur between the parts. Thus the couphng must 

 contain a "random" element. What does this mean? 



To make the discussion definite, suppose an experimenter has 

 before him a large number of identical boxes, electrical in nature, 

 each with three input and three output terminals. He wishes to 

 form an extensive network, coupled "at random", to see what its 

 properties will be. He takes up some connecting wires and then 

 realises that to say "couple them at random" is quite insufficient as 

 a definition of the way of coupling; all sorts of "couplings at 



63 



