Studies on the Motion of Viscous Flows— II 



essentially of this character. The principle of maximum uniformity will be 

 considered in a larger context and in much more detail from the biological view 

 in a later volume concerned with the constants of nature and biological theory, 

 categories of information, and aspects of evolution, and in which it will assume 

 a unifying role. 



Stability, according to the present definition, is a characteristic of the in- 

 stantaneous state of a system, just as is equilibrium; moreover, the stability so 

 defined has both local and global aspects, which again correspond to the case of 

 equilibrium. The instantaneously stable state is defined as the force configura- 

 tions belonging to the highest hierarchy of uniformity which instantaneously sat- 

 isfies all the conditions cited above in the statement of the principle of maximum 

 uniformity. According to this definition, instantaneous global stability is defined 

 as the collection of instantaneous locally stable force configurations. The defi- 

 nitions given here for hierarchies of uniformity and for stability are descriptive, 

 pictorial, and conceptual, not analytic or quantitative in a mathematical sense. 

 For this purpose it is natural to consider continuously extended material do- 

 mains, in which the forces joining an element to the universe are characterized 

 by a stress tensor. The principle of maximum uniformity and the general sta- 

 bility law that derives from it will be in part formulated in more analytical 

 (terminology) language in another volume, in which it is planned to treat this 

 subject in a more comprehensive manner, particularly its biological ramifica- 

 tions. 



The principle of maximum uniformity is manifested in the domain of clas- 

 sical mechanics, as required by the principle of universal correspondence, by 

 the evolution in time at different locations of various and distinct /orce configu- 

 rations. Each of these force configurations belongs to the hierarchies of uni- 

 formity, and has in common a particular member of the hierarchy, which is 

 defined here by the equilibrium of forces. The progressive evolution in time of 

 the hierarchies of uniformity is revealed in all experience, and therefore in the 

 classical domain in particular, by the progressive evolution of different force 

 configurations, each of which may also be interpreted as a hierarchy of order. 

 As noted earlier, all forces are understood here to give direct expression in 

 experience to the universals, which are reflected by the Dimensional Universal 

 Constants, and consequently to what is referred to in Ref. 7 as the domain of the 

 domain of the universals. By this way of thinking, the operation in nature of the 

 principle of maximum uniformity and the conception of its operation demand the 

 existence, and the consideration of the relation between, and interaction of, the 

 domain of the universals and what I call in Ref. 7, the domain of the observables. 

 This, of course, applies equally to the operation in nature of the universal sta- 

 bility law manifested in every domain of experience, and which derives, as do 

 the conventional laws of mechanics, from the principle of maximum uniformity. 



The principle of maximum uniformity and the universal stability law attend- 

 ant upon it, have been made operational within the realm of classical mechan- 

 ics, i.e., have been exercised computationally in this realm by the development 

 of an algorithm, by modelling certain aspects of the domain of universals by a 

 potential theory. This model allows the formal description of the interaction 

 between viscous flow fields which belong to the domain of the observables, and 

 an ideal domain characterized by the potential theory from which according to 



473 



