-■- - Lieber 



the algorithm, they emerge by what is analogous to a process of evolution. This 

 has produced mathematical representations of viscous flow fields that evidently 

 satisfy the fundamental partial differential equations of classical hydrodynamics 

 and realistic boundary conditions. 



The interaction between the domain of the universals and the observable 

 domain brings necessarily under consideration multiple scales and the realiza- 

 tion that they assume an essential role, especially their interrelationship, in the 

 interaction between these domains. From the standpoint of classical mechanics, 

 for example, such scales may be identified with temperature fluctuations in a 

 heat bath which are related to the universal Boltzmann constant, and with the 

 production of inelastic deformations in a solid subjected to forces impressed by 

 the universe from the outside. These considerations, as well as the relation- 

 ships between the principle of maximum uniformity, the stability law, the role 

 of the constants of nature as the foundation of natural law and the development 

 of biological theory; and the connection between these, and the existence in na- 

 ture of Categories and Hierarchies of Information, all will be comprehensively 

 examined together in a later volume more specifically directed at their ulti- 

 mate biological aspects. 



CONCERNING DEVELOPMENT OF HIERARCHIES OF 

 UNIFORMITY IN CONTINUA ENDOWED WITH 

 RHEOLOGICAL CHARACTERISTICS 



In this section we will describe the spatial and temporal development of 

 hierarchies of uniformity in classical continua, as a process, by presenting a 

 procedure which gives operational expression to the principle of maximum uni- 

 formity through an algorithm in which potential theory assumes the fundamental 

 role. This procedure and the algorithm which formally describes it have al- 

 ready been effectively used in the construction of analytical representations of 

 viscous flow fields which satisfy the Navier -Stokes equation and which emerge 

 from realistic boundary conditions. This procedure evidently has very broad 

 applications, and consequently can be applied to physical continua endowed with 

 various linear as well as nonlinear constitutive properties, provided they have 

 rheological features. 



In all such cases uniformity, or its counterpart nonuniformity, is directly 

 manifested and in experience, in its various hierarchies, by stress fields, which 

 are understood here to correspond to force fields, as considered previously in 

 conjunction with particle mechanics. Accordingly, the same fundamental role 

 and meaning is ascribed here to stress, as I have done earlier to force, in the 

 case of particle mechanics. In other words, stress directly posits to experience 

 both the uniform as well as the nonuniform universal connections that exist be- 

 tween an element of a continuously extended material domain and the entire uni- 

 verse to which it belongs. 



Just as force has been shown above to dominate the propositions of classi- 

 cal mechanics, so correspondingly, stress dominates the laws that condition 

 natural phenomena which transpire in continuously extended material domains. 



474 



