International Journal of General Systems

1974, Vol. 1, pp. 41-60

 

HUMAN KNOWLEDGE

The Role of Models, Metaphors, and Analogy

 

DANIELLE MIHRAM and G. ARTHUR MIHRAM

 

Haverford College, Haverford, Pennsylvania and University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A.

(Received February 11, 1972; in final form October 31, 1972; Manuscript originally prepared and typed in the summer of 1971.)

 

 

pp. 41-43

 

[Abstract]

The paper presents an operational description of the procedure by which simulation models are constructed, verified, and then validated by systemic scientists so as to provide credible and substantiated mimicries of the pertinent attributes of complex, general systems. The operational procedure is shown to equate in a step-by-step fashion with the cybernetics of the well-established, more classical, scientific method, including its reliance an preciseness, logical rectitude, and predictive capability.

Modelling is demonstrated as the essence of science, particularly in the context of the definition of science as a search for the explanation of naturally occurring phenomena and especially so if the communication of the scientist's explanation is subjected to the controls of grammatical and logical verification and of subsequent validation testing by the scientific community. In a historical perspective, the primary classes of scientific models (physical, mathematical, and simular) are each viewed in terms of their acceptability and credibility as representations of the nature surrounding Man.

Over an extended time frame, the metaphorical contributions of the men of letters are presented in terms of their literal presentation, their grammatical and logical rectification, and their acceptance by society as valid, or confirmed, hypotheses of the nature of the perceivable universe. This metaphorical process is also equated, in an isomorphic fashion, with the cybernetic model describing the scientific method.

The reliance, of both scientific models and literal metaphors, upon observations of the perceivable universe is demonstrated to be based upon the human requirement for analogy to the conduct of his individual behaviour. The use of, as well as the distinction between, the simile and the metaphor become of the essence in communicating these analogical findings. The established (i.e., the verified and confirmed) inter-connexions among extant and evolving models and metaphors become thereby contributions to human knowledge.

 

INDEX TERMS Analogy, cybernetics and feedback, epistemology, hypothetico-deductive method, metaphorical process, modelling process, scientific hypothesis, simile, simulation, verification and validation

 

 

1 INTRODUCTION

 

Subsequent to this introductory section, an extended taxonomy of the models available to the systemic scientist is presented in a context which explores the purposes and goals of scientific models. Three fundamental categories of models are introduced: the material, the literal, and the hybrid (material-symbolic). Each fundamental category is itself subcategorized, examples of each are given, and distinctions among the subcategories are delineated.

Attention is focused in Section 3 on the most flexible model category (viz., the literal, or symbolic, models) in order to describe an operational definition of the simulation model, itself shown to be the most general category of symbolic models that are capable of facile manipulation for experimental purposes. In this context, the Simulation methodology is presented in Section 4 as a coherent modelling process, a cybernetic feedback structure which incorporates verification and validation activities and which is deemed applicable as well to all scientific (hypothetico-deductive) modelling activities. The cybernetic process applicable to credible simulation modelling is shown to correspond isomorphically to the well-established scientific method.

 

The importance of the metaphor to the man of letters is then examined in the ensuing section. It is demonstrated that the construction of, as well as the academic acceptance of, the metaphor in the humanities is indeed isomorphic to the procedure of communication and control by which the scientific model becomes an acceptable and credible segment of accumulated human knowledge.

Indeed, the dynamic process of the accumulation and evolution of human knowledge is shown in Section 6 to be representable by the fundamental modelling process employed by the systemic scientist. The role of both the metaphor and the model in the acquisition of human knowledge is thus made quite apparent by means of an operational definition of the acquisition process.

In conclusion, the quest for knowledge, by means of scientific model-building and the construction of metaphors, is shown to be founded on the fundamental notion of analogy, itself an extension of the intrinsic inquisitiveness which is so essential to adaptive, evolving, animal species. Man is therefore revealed as the model-building species, and human knowledge is seen as an evolving, dynamic process of successively improved models and metaphors, each evolutional gain relying on validation and verification procedures that are appropriate to the particular model or metaphor at hand.

 

 

2 A TAXONOMY OF MODELS

 

The initial categorization of models, as they are employed in science, was accomplished by Rosenblueth and Wiener (99) and was constituted by two broad categories:

(a) Material Models - the representation of a complex system by one that is assumed to be simpler and that is assumed to have properties similar to those of the original, complex system; and

(b) Formal Models - symbolic (i.e., mathematical) assertions in logical terms of an idealized, relatively simple, situation sharing the structural properties of the original factual system.

Subsequently, in the context of operational research, Churchman, Ackoff, and Arnoff (27) bifurcated the Rosenblueth/ Wiener material category into iconic (material models which pictorially or visually represent certain aspects of a system) and analogue (material models which employ one set of their own properties to represent some other set of properties that the system being studied possesses), yet applied the term symbolic to models of the Rosenblueth/ Wiener formal category.

 

Sayre and Crosson (103) seeking a format for the modelling of mind, noted an essential distinction among the formal models being employed by systemic scientists (i. e., operational researchers, systems and industrial engineers, and management scientists). As a result, they suggested a bifurcation of the Rosenblueth/ Wiener formal category into:

(a) formalizations - symbolic models in which both the components of the modelled system and their inter-connections are represented by symbols that can be manipulated according to the provisions of a well-defined formal discipline, such as algebra, mathematical logic, calculus, or numerical analysis; and,

(b) simulations - symbolic (or literal) models whose representations are conveyed by symbols not all of which are manipulated in accordance with the rules of formal disciplines. Though re-defining the Rosenblueth/ Wiener material models as replications, Sayre and Crosson appreciated the fact that the algorithmic, or procedural, representation of the simulation model should be distinguished from the strictly mathematical representation provided by the formalized model.

 

Not addressing this distinction, Springer, Herlihy, and Beggs (106) retained the Churchman/ Ackoff/ Arnoff bifurcation of material models (iconic and analogue), yet classified as symbolic models two types:

(a) mathematical - apparently correspondent to the Rosenblueth/ Wiener formal variety; and,

(b) verbal - descriptive models expressed in terms of natural language.

 

These categorization schemes have been summarized and extended by Mihram, (79, 80) noting that a fundamental distinetion among material models can be made; viz., that material models may be either –

a) replicas, those material models which retain all three space-dimensional aspects of the modelled; or

(b) quasi-replicas, those material models which, like a map, contain dimensional exclusions.

Thus, physical models can be classified as either replicas, quasi-replicas, or analogue models, though the third category implies a definite shift of medium in moving from the original system to the model.

 

Viewed from this perspective, all types of symbolic (literal) models constitute also a change of medium from the represented system in that each category (description, simulation, and formalization) is expressed in an appropriate language (respectively: natural, operational or computer programming, and mathematical). Thus, there would appear to be two primary classifications of models:

physical and literal,

with three pertinent sub-categories in each case (replicas, quasi-replicas, and analogue; and, description, simulation, and formalization, respectively). (80)

 

A third primary category is now also evident. Calling these hybrid models, we would include:

(a) models implemented on hybrid computing devices (requiring, therefore, both a physical (analogue) model, and a programmed (literal) model);

(b) operational gaming models, such as those decision processes mimed by human participants in conjunction with simulation models on digital computers (See, e. g., Shubik (104, 105) and Raser (96)): and,

(c) board games, such as Monopoly, which require a descriptive set of rules and human participants.

 

Basic cross-classifications of all these model categories are provided by each of the rather self-explanatory antonymous pairs: deterministic vs. stochastic; and, static vs. dynamic. A detailed list of exemplary models of each cross-categorized type has been provided elsewhere. (80) For the purposes of immediate reference, however, an abbreviated tabulation of exemplary model types is provided in Table I.

 

TABLE I

A taxonomy of models

 

Category	Exemplary models
PHYSICAL MODELS
Replicas	Biological twins; earthen relief maps
Quasi-replicas	Silhouettes; planetarium shows
Analogue	White noise generators; statues
SYMBOLIC MODELS
Descriptions	Textbook; metaphorical essay
Simulations	Operational, procedural description
Formalizations	Differential equation; Poisson distribution
HYBRID MODELS
Analogue-sirnular	Hybrid computer model of river flow and storage
Replica-descriptive	War gaming exercise
Replica-simular	Operational, computerised, gaming model
Others	Board games, such as Monopoly

 

 

For the most part, the remainder of the present paper investigates the class of literal models, primarily because of their great generality and their richness of expression, but also because of the insight which they provide into the modelling process, in particular, and into the accumulation of human knowledge, in general. In particular, emphasis shall be placed initially on the modelling process as it applies to the class of dynamic, stochastic simulation models because

a) dynamic models are more general than static ones;

b) deterministic models are special cases of the stochastic variety;

c) among literal models, the simular variety is an operational, procedural description of the system of interest and is readily tractable for experimentation purposes; and,

d) in a certain sense, the class contains as a subset the purely formalized models since simular models contain symbols not all of which are, yet many of which can be, manipulated formally.

 

For the present, however, it is noteworthy that the many varieties of models span much of the creative activity of man. Certain model types (viz., sub-categories of physical models) are more easily identified with artists, sculptors, architects, and the classical engineer, whereas others (viz., sub-categories of literal models) are more readily associated with the biologist, the systemic scientist, the classical scientist, and the mathematician. Subsequent to the ensuing discussion of the modelling process, as deemed applicable to the construction and the justification of large-scale, dynamic, stochastic representations of the simular variety, a clearer indication of the commonality of models to the creative aspect of man is developed.

 

 

REFERENCES

 

99. A. Rosenblueth and N. Wiener, "The role of models in science." Philo. Sci., 12, 1945, pp. 316-321

27. C. W. Churchman, R. L. Ackoff, and E. L. Arnoff, Introduction to Operations Research, John Wiley, New York, 1957.

103. K. M. Sayre and F. J. Crosson (editors), The Modeling of Mind. Simon and Schuster, New York (1963), 1968.

106. C. H. Springer, R. E. Herlihy, and R. I. Beggs, Advanced Methods and Models. R. D. Irwin, Home wood, Illinois, 1965.

79. G. A. Mihram, Simulation: Statistical Foundations and Methodology. Academic Press, New York, 1972.

80. G. A. Mihram, "The modelling process." I. E. E. E. Transactions on Systems, Man, and Cybernetics, SMC-2, 1972, pp. 621-629.

104. M. Shubik, "Bibliography on simulation, gaming, artificial intelligence, and allied topics." J. Am. Stat. Assoc., 55, 1960, pp. 736-751.

105. M. Shubik, "Simulation of socio-economic systems." General Systems, 12, 1967, pp. 149-175.

96. J. R. Raser, Simulation and Society: An Exploration of Scientific Gaming. Allyn-Bacon, Boston, 1969.