7. STATISTICAL PROPERTIES OF THE EPIGENETIC SYSTEM 123 



theory of neural function and the learning process in higher organisms. The 

 fundamental oscillators which he assumes to underlie the temporal organization 

 of neural activity are closed loops of neurones which produce reverberatory 

 cycles of firing or discharge. His analysis suggests that many of the charac- 

 teristic features of the learning process can be understood in terms of the 

 interaction of these non-linear neural oscillators which are coupled together 

 through shared neurons. The main argument in Pringle's paper, and the most 

 significant one for our present study, is that there is a close parallel between the 

 fundamental forces producing temporal organization in systems composed of 

 many interacting non-linear oscillators and those operating in evolving 

 populations which are subject to the Darwinian principles of competition and 

 selection. Thus his suggestion is that such a population of interacting oscilla- 

 tors will "evolve" in the sense that under the influence of random disturb- 

 ances the system will move from states of less to states of greater complexity, 

 and that the selective principle operating on these states is one of maximum 

 adaptive value. The argument, which is ingenious and convincing, is couched 

 in terms of the prey-predator language which was used above to describe the 

 interaction of non-linear oscillators. The parallels between the dynamic be- 

 haviour of a system of coupled oscillators and the evolution of natural popula- 

 tions of organisms thus become evident, and the introduction of Darwinian 

 notions to describe the "evolution" of the oscillatory system follows as an 

 important extension of these ideas to a completely new situation. 



Whether or not Pringle's assumptions about the fundamental oscillatory 

 structure of neural nets is correct, his analysis of the temporal behaviour which 

 may be expected to occur in oscillators remains of very great interest and im- 

 portance. All his arguments can immediately be applied to the system of 

 oscillators which is the subject of the present monograph, with important 

 suggestions for the organizational principles underlying the time-ordering of 

 physiological events in cells. The adaptive significance of temporal coordina- 

 tion in physiological activities has been discussed by Halberg (1960), in a paper 

 which presents a great deal of experimental evidence for the importance to the 

 organism of the right event occurring at the right time. Most of the processes 

 which he discusses are organized on a circadian or daily regime, and it is clear 

 that the phenomenon of entrainment is of great importance in ordering phy- 

 siological activities adaptively in relation to the hght-dark, dry-humid, warm- 

 cold, and other environmental cycles which have a 24 h period. 



However, Halberg correctly emphasizes that synchronous entrainment of 

 rhythm cannot be used to explain the occurrence of an ordered time-structure 

 with constant or nearly constant differences in phase between constituent 

 physiological processes. As well as entrainment, producing synchrony, there 

 must be other forces operating between physiological oscillators, such as a 

 tendency to establish stable antiphase relations. On the basis of the forces 

 acting between oscillatory components, it may be possible to find some general 

 principle of optimization for the oscillatory behaviour of cellular control- 

 systems by proceeding along the lines already explored by Pringle, using the 

 parallels with Darwinian theory to suggest how adaptive processes might 



