THE BLACK BOX 6/5 



One way is to alter the set of inputs and outputs — to take more 

 variables into account — and then to see if the new system (equivalent 

 to a new Box, S.3/11) is determinate. Thus a chemist may find 

 that a system's behaviour is at first not determinate, but that when 

 the presence of traces of chloride is taken into account it becomes 

 determinate. A great deal of research consists of such searches for 

 a suitable set of variables. 



A second way is to abandon the attempt to find strict determinacy 

 and to look for statistical determinacy, i.e. determinacy in averages, 

 etc. The experimenter, with extensive records available, then studies 

 them in long sections, to see whether, if the details are not pre- 

 dictable from step to step, the averages (or similar statistics) are 

 predictable from section to section. He may find that the records 

 show the statistical determinateness of the Markov chain; (but 

 discussion of this will be left to Chapter 9, for until then we shall be 

 concerned only with machines that are determinate from step to 

 step). 



To summarise : once the protocol has been obtained, the system's 

 determinateness can be tested, and (if found determinate) its 

 canonical representation can be deduced. 



Ex. 1 : Deduce the kinematic graph for input at « directly from the protocol of 



the system of S.6/3. 

 Ex. 2 : (Continued.) and for input at p. 

 Ex. 3 : A system with only one input state gave the following sequence of states 



as output: 



DGAHCLHCLHCF C... 



Is it absolute? 

 Ex. 4: A system has two variables, .v and y, each of which can take the values 

 0, 1 or 2. The input can take two values, a or /3. The protocol gave : 



Is it a machine with input? 

 Ex. 5: (Continued.) What is its transformation if the input is held at a? 



Ex. 6: If a machine has m input-states and n output-states, what is the least 

 number of steps of observation sufficient for its complete study? 



91 



