- ''.;■ Lieber 



steps. The first consists of a definition of equilibrium, in which force is the 

 aspect of nature to which the word equilibrium in the definition refers. The 

 second uses this definition to express the universal law which asserts that equi- 

 librium so defined is constantly maintained in nature, i.e., everywhere and at 

 all times. 



The existence in nature of hierarchies of uniformity which, as in the par- 

 ticular case of equilibrium, are all directly revealed in experience by forces, 

 leads here naturally to the identification of a universal law that although free of 

 contingencies in its assertion, nevertheless conditions aspects of nature which 

 are contingent upon the evolution in space and time of distinct hierarchies of 

 uniformity. The law does not in this case constantly refer to a particular hier- 

 archy, but reports a universal proposition that governs a process of evolution 

 which is contingent upon the emergence in space and time of the various hier- 

 archies of uniformity. The usual laws of mechanics which are indeed embraced 

 by this general law, are a very special case of it, insofar as the particular 

 hierarchy of uniformity in terms of which they are expressed is always constant 

 and therefore not contingent. This is precisely the reason why the established 

 laws of mechanics are inherently and completely devoid of contingency in all 

 aspects, and consequently of historical thrust, causality, stability criteria, and 

 evolution. This is, of course, also true for all of the equivalent formulations of 

 the laws of classical mechanics, and in particular for their formulation in terms 

 of the principle of least action. I refer here particularly to the principle of 

 least action because of its power and unifying role in physical theory. The 

 power of this principle in the formulation given to it by Hamilton, is seen by the 

 fact that not only the classical mechanics of particles and rigid bodies, but also 

 elasticity and hydrodynamics, electromagnetism and all modern field theories 

 connected with ultimate particles (electron, proton, and neutron) can be formu- 

 lated with its help. All of the theories formulated with its help therefore share 

 with Newton's laws of classical mechanics the important feature of being devoid 

 of historical commitment, causality, and inherent stability criteria. In other 

 words, all of these theories are free of historical content, and consequently es- 

 sentially devoid of an evolutionary principle. 



On A General Stability Principle 



We have shown earlier that the formulation of the laws of classical mechan- 

 ics may be conceived in two essentially distinct steps. The first is a definition 

 of equilibrium, and in the second the proposition is made that equilibrium as 

 defined by the first step holds constantly everywhere, and for all time. The no- 

 tions of stability and equilibrium were both developed by observing and examin- 

 ing critically the phenomenological behavior of classical mechanical systems. 

 As was explained in the case of equilibrium, a general operational definition 

 based on forces was established on the basis of experience, and then used in the 

 formulation of the known laws of mechanics, which inherently report nothing 

 about stability for reasons already described. Whereas the notion of stability 

 has been described by many definitions, these have led to various stability cri- 

 teria which are statements of convention rather than of a general law that refers 

 to stability in the same way as the laws of mechanics refer to equilibrium. I 

 shall now endeavor to formulate a statement of a general stability law which will 



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