16/2 DESIGN FOR A BRAIN 



16/2. The multistable system is itself ultrastable. The pro- 

 position may be established by considering the class of ' all 

 ultrastable systems '. Such a class will include every system 

 not incompatible with the definition of S. 8/6. It will, for 

 instance, contain systems whose main variables are all full-func- 

 tions, systems some of whose main variables are part-functions, 

 and systems whose main variables are all part-functions (S. 11/8). 

 Further, the class will include both those whose step-functions 

 are wide in their immediate effects and those whose step-functions 

 act directly on only a few main variables. The class will there- 

 fore include those systems defined as ' multistable '. 



From this fact it follows that all the properties possessed gener- 

 ally by the ultrastable system will be possessed by the multi- 

 stable. In particular, the multistable system will reject all 

 unstable fields of its main variables but will retain the first 

 occurring stable field. In other words, the multistable system 

 will ' adapt ' just as will any other ultrastable system. 



On the other hand, the faults discussed in Chapter 11 were 

 due to the fact that the systems considered before that chapter 

 had main variables which were all full-functions. Now that the 

 main variables have become all part-functions we shall find, in 

 this and the next two chapters, that the faults have been reduced 

 or eliminated. 



16/3. In a multistable system, if no step-function changes in 

 value, the main variables, being all part-functions, will form a 

 system identical with that discussed in S. 14/15. In particular, 

 it will show dispersion : two lines of behaviour will make active 

 two sets of variables ; the two sets will usually not be identical, 

 and may perhaps have no common member. 



16/4. It is now possible to deduce the conditions that must 

 hold if a system, multistable or not, is to be able to acquire a 

 second adaptation without losing a first. 



We may view the process in two ways, which are really equi- 

 valent. First, I will suppose that we have an ultrastable system 

 which can be connected to either of two environments (as Units 

 3 and 4 of the homeostat, representing the adapting system, 

 might be joined to either Unit 1 or Unit 2, representing the 

 two environments). Suppose that the system has been joined 



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