DISTURBED SYSTEMS AND HABITUATION 13/4 



selection where, although it is recognised that mutations and re- 

 combinations of defective viability can occur, yet as the processes 

 of evolution are viewed over an increasing range of time, so 

 do these defectively adapted individuals sink into insignificance. 

 Statistical mechanics, too, uses the same principle, for it excludes 

 an event by proving that its occurrence is not impossible but 

 infrequent. Sometimes we shall not be able to distinguish even 

 the transient from the permanent, but only the lesser from the 

 greater persistence. Nevertheless, the distinction may be im- 

 portant, especially if the small difference acts repeatedly and 

 cumulatively ; for what is feeble on a single action may be over- 

 whelming on incessant repetition. 



It will be suggested later (S. 16/6) that the animal's behaviour 

 depends not on one system but on many, so that what counts is 

 not the peculiarity of one particular field but the average proper- 

 ties of many. In the discussion we shall therefore notice the 

 average properties and the tendencies rather than the individual 

 peculiarities of the various fields. 



Effects of small random disturbances 



13/3. A disturbance may affect variables or parameters. If it 

 affects the variables, the system will undergo a sudden change of 

 state ; in the phase-space the representative point would be 

 displaced suddenly from one line of behaviour to another. If 

 it affects a parameter, there will occur a sudden change of field : 

 the representative point will be affected only mediately. 



13/4. We shall now examine the effect on an ultrastable system 

 of small, occasional, and random disturbances applied to the 

 variables. I assume at first that the displacements are distributed 

 in all directions in the phase-space. 



A displacement may make the representative point meet a 

 critical state it would not otherwise have met ; then the dis- 

 placement destroys the field. The three fields of Figure 13/4/1 

 show some of the consequences. In fields A and C the undis- 

 turbed representative points will go to, and remain at, the resting 

 states. When they are there, a leftwards displacement sufficient 

 to cause the representative point of A to encounter the critical 

 states may be insufficient if applied to C ; so Cs field may survive 



145 



