400 Geographical Analysis

2. Losca, AUGUST. Die raumliche Ordnung der Wirtschuft. Translated by W. H. Woglom and W. F. Slolper as The Economics of Location. New Haven, Conn. : Yale University Press (1954).

3. NOURSE, HUGH 0. Regional Economics. New York: McGraw-Hill (1968). 4 4 . VALAVANIS, STEFAN. “Losch on Location,” American Economic Review, 45

(1955), 637-44.

Simplicity Isn’t That Simple

Stephen Gale*

William Bunge [b] has recently put forward some rather interesting arguments for the inclusion of “simplicity” as a guiding principle for geographic research. I find his arguments, couched in a rather hetero- dox interpretation of form and process [4] (which, Bunge notes, is derived from Schaefer’s sentence, “patterns are morphological laws” [9]), difficult to follow. I cannot help but feel that some very important points of clarification are missing. The suggestion [b, p. 3891 that theoretical simplicity is the same as “placing interacting objects of specified dimension as near to each other as possible” emphasizes this lack of clarity all the more, since the operational variants of this statement are, at best, ambiguous.

In Bunge’s view, I suppose that I am faced with a simple dichotomy: do I accept the simplicity of the “nearness effect,’! or do I condemn the principle of parsimony in science? This presents quite a dilemma, but one which may be cleared up, to some extent, by noting that there seem to be two separate points implied within the dichotomy: First, that simplicity in geography-locational simplicity-is a function only of geometric properties such as “nearness.” And, second, that the rejection of simplicity, on any grounds (geometric or otherwise), necessitates the rejection of parsimony. The first argu- ment is, of course, distinct from the second and has been treated at some length by Blaut [ I ] , Eichenbaum and Gale [4], and Olsson [7]. The second issue is of a general nature and requires more detailed discussion. In this regard, perhaps a comparison of several of William Bunge’s views with those of the philosopher-physicist Mario Bunge 14 might help to resolve the problem.

1. Metaphysical simplicity. Underlying William Bunge’s implicit definition of simplicity seems to be the almost fundamentalist notion

* The support of the Social Science Research Council, Research Training Fellowship, is gratefully acknowledged. I would also like to thank Dr. Gunnar Olsson for his helpful comments.

Stephen Gale i s presently a postdoctoral fellow at the University of California, Berkeley.

Research Notes and Comments 407

that scientific laws can be reduced to very simple forms. The analogy is to the Newtonian paradigm of a law. Through the prodigious effort of pure reason, Bunge assumes that these human behavioral universals will be revealed. As exemplified in the works of both Levi-Strauss and Chomsky, there exists some evidence in support of this argument. General Systems Theory also seems to follow this line of reasoning. At the same time, however, it can be seen that the idea that “nature is simple” is a metaphysic or an hypothesis and is not in any sense a proven conclusion. The arguments for its validity may, in fact, be roughly compared to those asserted for the existence of Divine Order.

2. Aspirational simplicity. The metaphysical arguments for scien- tific simplicity make use Of the abstract notions of reason and faith, uniformity and causality, and of analogies to the physical sciences. Perhaps of more interest in a practical vein is the relationship be- tween simplicity and the level of inference which is being sought. Obviously, what is simple at one level of aspiration, or in relation to one set of problems, might be quite complicated on another level of aspiration. The “nearness principle” might well be a reasonable law if one only considers the location of the cities of a nation state or the rivers of a watershed. But given present knowledge, this same principle seem inapplicable when extended to such problem as the settlement of ethnic neighborhoods, consumer shopping behavior, or the design of children’s parks. To speak about nearness in these latter contexts implies such diflicult transformation problems that it no longer makes sense to use it as a simplifying and unifying notion. In short, what is simple for one purpose is not necessarily simple for any other [7].

3. Operatimal simplicity. Perhaps the most forceful part of William Bunge’s discussion focuses on what might be called operational simplicity. It is here that the argument also becomes most obscure. Clearly, most scientists would find it difficult to argue that a com- plicated path was necessarily the best. And it would appear that this same observation is of equal importance in the choice of theories and models. But this is not necessarily the complete picture. As an illustration, let us consider two different ways of specifying an opera- tional model of human migration. First, we may choose a model so as to make its syntactical properties simple-say, something on the order of the gravity model. Here we have a formulation (usually a simple regression model) in which interaction is expressed solely as a function of distance; as such, it is amenable to the ordinary checks for completeness, consistency, and accuracy. But as Huff [6] and others [6] have pointed out, the simple version of the gravity model is inadequate as a picture of short distance movements; the linear function in the logarithms does not usually provide a reasonable fit, and the univariate distance relationship leaves much to be desired in terms of the interpretation of the structure. In general, syntactic

402 Geographical Analysis

simplicity would seem to preclude some of the needs of semantic simplicity. In this latter case, quite different designs phenomena become important. Here the concern is with simplicity in interpreta- tion rather than with notational or logical simplicity; with the ac- curacy of the correspondence rules rather than the parsimony of the mathematics [7].

An attempt to formulate a semantically-oriented model-a dy- namic contingency table design-has recently been presented elsewhere [S]. The emphasis of that model was on the interpretability of the parameters and the generation of new hypotheses rather than on strict deduction. But the crucial point is once again that syntactic and semantic simplicity are often incompatible. For instance, the simple regression model fails as an accurate and complete picture of intraurban population movements because the transformations of the distance variable are inevitably quite complex; this, in turn, precludes ampliative generalizations. The dynamic contingency table may, on the other hand, be too detailed where only gross predictions are required. In effect, it once again comes down to a question of aspiration: Accuracy is needed in some investigations, and here one set of models is simple; notational parsimony is required for other problems and the set of models required here may be entirely diferent. The conclusion must therefore be that there is just no unique char- acterization of simplicity. Very simply, I think it would serve us well to agree with Mario Bunge that simplicity is not as simple as William Bunge would have us believe.

LITERATURE CITED

1. BLAUT, J. M. “Space and Process,” The Professional Geographer, 13 (1961),

2. BUNQE, W. “Simplicity,” Geographical Analysis, 1 (1969), 388-91. 3. BUNQE, M. The Myth of Simplicity. Englewood Cliffs, N.J.: Prentice Hall,

1963. 4. EICHENBAUM, J. and S. GALE. “Form, Function, and Process: A Methodo-

logical Inquiry.” Mimeographed. Economic Geography (forthcoming). 5. GALE, S. “Probability and Interaction: A Stochastic Approach to Intra-

regional Mobility.” Ph.D. dissertation, University of Michigan, 1969. 6. HUFF, D. L. “A Note on the Limitations of Intraurban Gravity Models,”

Land Economics, 38 (1962), 64-66. 7. OLSSON, G. “Inference Problems in Locational Analysis,” in Behavioral

Problems i n Geo raphy: A Symposium, ed. K. R. Cox and R. G. Golledge. Evanston: Nortiwestern University Press, 1969. Pp. 14-34.

8. OLSSON, G. and S. GALE. “Spatial Theory and Human Behavior,” Papers and Proceedings of the Regional Science Association, 21 (1969).

9. SCHAEFER, F. K. “Exceptionalism in Geography: A Methodological Exami- nation,” Annals of the Association of American Geographers, 43 (1953), 226-49.

1-7.