. - Lieber 



I shall now introduce the observations and ideas which led me to the con- 

 ception of the principle of maximum uniformity in which force is conceived as 

 the fundamental physical aspect of nonuniformity. The identification of a natural 

 law is not an exercise in formal logic, nor is what its propositions assert, prov- 

 able. General propositions about nature are testable only by experience —by 

 what they predict and explain of it. In the present case the principle of maxi- 

 mum uniformity was discerned by fully generalizing explicit global information 

 which was obtained as a theorem for a class of dynamical systems, by suitably 

 modifying and using Gauss's and Hertz's formulations of the principles of clas- 

 sical mechanics (2). This information pertains to a global, positive, definite 

 scalar measure of the internal forces generated at each instant within such a 

 system. The modifications of the Gauss-Hertz variational principles of me- 

 chanics which render this general information explicit and without quadrature, 

 consist of ascribing to force the dominant role in mechanics, and of identifying 

 all forces in nature with an ontological-geometrical basis for the production of 

 stringent geometrical constraints, which were in Refs. 2, 6, and 9 originally 

 conceived to emerge from the impenetrability of matter understood as a prop- 

 erty of position. This information, which bears directly on the fundamental 

 problem of continuum mechanics, has not been made explicit, and as far as I 

 see cannot be made explicit by Newtonian mechanics in which the only represen- 

 tation given to force in its propositions is vectorial. This means that in the sig- 

 nificant sense of information -rendering, the various formulations of the princi- 

 ples of mechanics are only conditionally equivalent. This development led me 

 inexorably to the concept of 'Categories of Information,' in terms of which 

 questions concerning the equivalence and none qui valence of various formulations 

 of the principles of mechanics can be rationally examined and resolved. This 

 led to identification of eleven distinct yet related categories of information, by 

 examples derived from familiar as well as more sophisticated aspects of expe- 

 rience. Once cited, these examples invoke consensus (1). 



The global information so explicitly obtained as a theorem on the distribu- 

 tion of internal forces, asserts that a positive, definite scalar measure of all 

 the internal forces is instantaneously less for the actual motion, than it is for 

 any other motion which satisfies the initial conditions and the geometrical con- 

 straints (as well as the external forces) which are instantaneously impressed 

 upon the dynamical system. This theorem was established for a particular 

 (nontrivial) class of dynamical systems. For this class, the scalar measure of 

 the internal forces can be directly interpreted as a global measure of nonuni- 

 formity in momentum space. 



The principle of maximum uniformity as it pertains to classical mechanics 

 and classical continuum mechanics was obtained by (a) interpreting the infor- 

 mation obtained from the above theorem as a particular aspect of a general law 

 which holds in all mechanical systems, and (b) introducing the concept of condi- 

 tionally stringent geometrical constraints and relating these to material prop- 

 erties through which they are implemented in nature. This brings the principle 

 of maximum uniformity into correspondence with the thermodynamical aspects 

 of the equations for the constitution of various materials, and relates the idea of 

 conditionally stringent geometrical constraints to uncertainties in the initial 

 conditions from which historical commitment, causality, and a general stability 

 principle naturally emerge. 



464 



