6/7 PARAMETERS 



(The exact nature of the operation of joining is shown most 

 clearly in the mathematical form (S. 21/9) for there one can see 

 what is essential and what irrelevant. A detailed treatment has 

 been given in /. to C, S. 4/6; here we can discuss it less rigorously.) 



To join two systems, A and B say, so that A affects B, A must 

 affect 2?'s conditions. In other words, the values of some of B's 

 parameters (perhaps one only) must become functions of (de- 

 pendent on) the values of A's variables. Thus, if B is a developing 

 egg in an incubator and A is the height of the barometer, then 

 A could be i joined ' so as to affect B if the temperature (or other 

 suitable parameter) were made sensitive to the pressure. 



In this example there is no obvious way of making the develop- 

 ment of the egg affect the height of the barometer, so the joining 

 of B to A can hardly be done. In most cases, however, joinings 

 are possible in either direction. If both are made, then feedback 

 has been set up between the two systems. 



In very simple cases, the behaviour of the whole formed by 

 joining parts can be traced step by step by logical or mathematical 

 deduction. Each part can be thought of as having its own phase- 

 space, filled by a field ; which field it is will depend on the position 

 of the other part's representative point. Each representative 

 point now undergoes a transition, guided by its own field, whose 

 form depends on the position of the other. So step by step, each 

 goes forward guided by the other and also guiding it. (The process 

 has been traced in detail in /. to C, S. 4/7.) 



This picture is too complicated for any imaginative grasp of 

 how two actual systems will behave; the details must be worked 

 out by some other method. What is important is that the nature 

 of the process is conceptually quite free from vagueness or ambi- 

 guity; so it may properly be included in a rigorous theory of 

 dynamic systems. 



Parameter and stability 



6/7. We now reach the main point of the chapter. Because 

 a change of parameter-value changes the field, and because a 

 system's stability depends on its field, a change of parameter- 

 value will in general change a system's stability in some way. 



A simple example is given by a mixture of hydrogen, nitrogen, 

 and ammonia, which combine or dissociate until the concentrations 



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