THE MULTISTABLE SYSTEM 16/5 



to environment a, has adapted to it, and has thus reached a 

 terminal field. To record this ' first adaptation ', we disturb a 

 slightly in various ways and record the system's responses. Give 

 the variables activated in these responses the generic label A. 

 Next, remove a, join on environment /?, and allow ultrastability 

 to establish a ' second adaptation '. Give the generic label S 

 to all step-functions that were changed by this process. Finally, 

 remove fi, restore a, and again test the system's responses to 

 small disturbances applied to a ; compare these responses with 

 those first recorded to see whether the first adaptation has been 

 retained or lost. For the responses to he unchanged — -for the first 

 adaptation to be retained — it is necessary and sufficient that during 

 the responses there should be a wall of null-functions between the 

 variables A and the step-functions S. The condition is necessary, 

 for if an S is not so separated from an A, then at least one A's 

 behaviour will be changed. It is also sufficient, for if the wall 

 of constancies is present, then by S. 14/8 the A's are independent 

 of the S's, and the *S"s changes will not affect the A's responses. 



(The other way of viewing the process is to allow a parameter 

 P to affect the ultrastable system, the two environments being 

 represented by two values P' and P". The ' disturbance from a ' 

 becomes a transient variation in the value of P. The reader 

 can verify that this view leads to the same conclusion.) 



The necessary wall of constancies can be obtained in more 

 than one way. Thus, if the system really consisted of two 

 permanently unconnected parts, one of which was joined to a 

 and the other to {3, then the addition of a second adaptation 

 would be possible ; so the present discussion includes the case 

 of the iterated ultrastable systems. More interesting now is 

 the possibility that the constancies have been provided by part- 

 functions, for this enables the connections to be temporary and 

 conditional. The multistable system is certainly not incapable 

 of so acquiring a second adaptation. The facts that set A will 

 often be only a fraction of the whole, that part-functions are 

 ubiquitous, and that all step-functions are only local in their 

 effects makes the separation of A and S readily possible. 



16/5. As a further step towards understanding the multistable 

 system, suppose that we are observing two of the subsystems, 

 that their main variables are directly linked so that changes of 



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