Auxiliary Concepts Research Articles

Algebraic structures of degenerate systems and the indefinite metric

It is shown that the indefinite metric structures of degenerate systems as given by Strocchi and Wightman [F. Strocchi and A. S. Wightman, J. Math. Phys. 15, 2198 (1974); 17, 1930 (1976)] arise in a natural fashion from the algebraic structure of such systems, where the latter has been developed in a C*-context by Grundling and Hurst [H. B. G. S Grundling and C. A. Hurst, Commun. Math. Phys. 98, 369 (1985)]. Auxiliary concepts like gauge equivalence are examined, and the preceding general theory is specialized to the situation of linear boson fields with linear Hermitian constraints. Two examples of this situation are given—a one-dimensional scalar boson in a periodic universe and Landau gauge electromagnetism.

Smooth dendroids as inverse limits of dendrites

Smooth dendroids as inverse limits of dendrites

Management and self-management: the objective-subjective dimensions

A distinction is made between the way the Law of Requisite Variety applies to systems involving human beings and systems that do not. It is claimed that a proper interpretation of the Law for human systems involves the use of auxiliary concepts, some of which have yet to be clarified. The auxiliary concepts are implicit in the theoretical work of Beer and his associates, but become explicit in practice. Two of these concepts are agreement and participation , which are almost always tacit rather than explicit. Human systems are only viable when they involve agreement and participation, and this is not accidental but tied to the nature of variety itself. It is argued that the full development and exploration of these concepts (and others allied to them) will foreshadow a new paradigm for management science, the material basis for which now exists in current computing technology.

Psychologists' misuse of the auxiliary concepts of physics and mathematics.

Psychologists' misuse of the auxiliary concepts of physics and mathematics.