13/4 



THE SYSTEM WITH LOCAL STABILITIES 



only because it is typical of the set. With the population as his 

 sample space (derived from the two primary sample spaces) he 

 may then legitimately speak of the probability of the system 

 showing a certain event, or having a certain property. 



If to this specification we add the restriction that the original 

 parts are rich in states of equilibrium (e.g. as in S. 12/15), we get a 

 type of system that will be referred to frequently in what follows. 

 For lack of a better name I shall call it a polystable system. 

 Briefly, it is any system whose parts have many equilibria and 

 that has been formed by taking parts at random and joining them 

 at random (provided that these words are understood in the exact 

 sense given above). 



Definitions can only be justified ultimately, however, by their 

 works. The remainder of the book will demonstrate something 

 of the properties of this interesting type of system, a key-system 

 in the strategy of S. 2/17. 



13/3. In such demonstrations we shall not be discussing one 

 particular system, specified in all detail: we shall be discussing a 

 set. When a set is discussed we must be careful to keep an 

 important distinction in mind, and we must make the distinction 

 arbitrarily: (1) are we discussing what can happen? — a question 

 which focuses attention on the extreme possibilities, and therefore 

 on the rare and exceptional; or (2) are we discussing what usually 

 happens? — which focuses attention on the central mass of cases, 

 and therefore on the common and ordinary. Both questions have 

 their uses ; but as the answers are often quite different, we must be 

 careful not to confuse them. 



13/4. A property shown by all state-determined systems, and 

 one that will be important later is the following. In a state- 

 determined system, if a subsystem has been constant and then 

 commences to show changes in its variables, we can deduce that 



A B 



\^ 



C 



173 



