Concept and Use of Models (Parts 1 and 2). Revision

Abstract

Abstract : An attempt is made to present a unified view of modeling. Beginning with the earliest concept of model a brief history of the subject is presented for the period beginning from prehistoric times into the twentieth century. The evolution of the concept of model is discussed in some detail and a taxonomy of the subject is suggested. Special attention is given to the relationship between the concept of model and the prevailing ideas of space, time, and matter. The role of dimensional analysis is reviewed and its relationship to modeling examined at length. Specific types of models which constitute the taxonomy are defined and illustrated with numerous examples. The idea of a Newtonian model is introduced and then extended to cover many physical cases. The new concept of disclosive model and its role is defined and illustrated. Its historical origin is reviewed. Its value in the evolution of generalized modeling is examined at length. In Part II the treatment of the concept model has been greatly extended. In Part I we presented a brief history of the subject from the earliest days of man to the latter part of the twentieth century. Also, a tentative classification of models was suggested. It consisted of what we called the iconic, the analogic, the similitudinous, the Newtonian, the extended Newtonian, and the disclosive models. The latter category was suggested for the first time to our knowledge. In Part II we have explored somewhat at length our understanding of the concept of disclosive model and its ramifications. Also, we found it necessary to distinguish between the use of model in mathematics and mathematical modeling, as applied in the various scientific areas. An important viewpoint is presented in connection with what we call adjectival modifiers.