An Introduction to Models

Systems Analysis Model Simul , 2003, Vol. 43, No. 1, pp. 111–120 AN INTRODUCTION TO MODELS GRANINO A. KORN* Electrical and Computer Engineering Department, University of Arizona (Received 3 August 2002) We survey the origins, development, and applications of models and modeling and discuss their dramatic use- fulness and possible dangers. We go on to present a nontechnical introduction to some basic abstract models used in mathematics, statistics, and syste ms engine ering. We stron gly empha size the differ enc e betwe en models and thi ngs modeled and tou ch on the role of mod elin g in play, art , operations analys is, and modern physics. Keywords: Model; Prediction; Control; Decision; Homomorphism; Isomorphism 1. MODELS In the Beginning Human survival requires decision-making in a world perceived as an overwhelming welter of different sense impressions. Of necessity, our decisions can be based only on selected features of this enormously complicated ‘‘real’’ environment. Next, any sort of communication – even among animals – requires a consensus on sounds or gestures to be associated with selected features of significant sense inputs (e.g. ‘‘food!’’ or ‘‘enemies in sight!’’). Experience normally lets us assume that these sense imp ressions are more or less si milar for differe nt indi vid uals. Thought s, sou nds , and ges tures abs tracte d fro m important sense impres sions for m the fir st simple models. At this primitive level, humans are not conscious of modeling. Nevertheless, important decisions – flight, say, or attack – do begin to be based on models rather than just on simple reflexes. Model Construction Consci ousl y or not, one constructs each model in terms of clas ses of obj ects that abstract sele cte d, curren tly signif ican t fea tures of the rea l wor ld. Spe cif ically, eac h class of model objects is defined by abstracted relations between objects. Game animals, *E-mail: [email protected] ISSN 0232-9298 print: ISSN 1029-4902 online 2003 Taylor & Francis Ltd DOI: 10.1080/0232929031000116371

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An Introduction to Models