THE MACHINE WITH INPUT 4/12 



arbitrariness in the distribution of the immediate effects over the 

 phase space. Often, however, the distribution shows continuity, so 

 that over some appreciable region, the variable u, say, has an 

 immediate effect on y while over the same region x has none. When 

 this occurs, a diagram can often usefully be drawn showing these 

 relations as they hold over the region (which may sometimes be the 

 whole phase-space). An arrow is drawn from u to y if and only if 

 u has an immediate effect on y. Such a diagram will be called the 

 diagram of immediate effects. 



Such diagrams are already of common occurrence. They are 

 often used in physiology to show how a related set of variables (such 

 as blood pressure, pulse rate, secretion of adrenaline, and activity 

 at the carotid sinus) act on one another. In the design of computing 

 machines and servomechanisms they are known as "control-flow 

 charts". They are also used in some large businesses to show the 

 relations of control and information existing between the various 

 departments. 



The arrow used in such a diagram is, of course, profoundly 

 different in meaning from the arrow used to show change in a 

 transition (S.2/2). In the latter case it means simply that one state 

 changes to another; but the arrow in the diagram of immediate 

 effects has a much more complex meaning. In this case, an arrow 

 from A to B says that if, over a series of tests, A has a variety of 

 different values — B and all other conditions starting with the same 

 value throughout — then the values that B changes to over the series 

 will also be found to show variety. We shall see later (S.8/1 1) that 

 this is simply to say that a channel of communication goes from A 

 to B. 



When a transducer is given, either in algebraic or real material 

 form, we can examine the immediate effects within the system and 

 thus deduce something of its internal organisation and structure. 

 In this study we must distinguish carefully between "immediate" 

 and "ultimate" effects. In the test given above, the effect of x on y 

 was considered over a single step only, and this restriction is neces- 

 sary in the basic theory, x was found to have no immediate effect 

 on ;^ ; it may however happen that x has an immediate effect 

 on u and that u has an immediate effect on y; then x does have some 

 effect on v, shown after a delay of one extra step. Such an effect, 

 and those that work through even longer chains of variables and 

 with longer delay, will be referred to as ultimate effects. A diagram 

 of ultimate effects can be constructed by drawing an arrow from A 

 to B if and only if A has an ultimate effect on B. The two diagrams 

 are simply related, for the diagram of immediate effects, if altered 



57 



