One conceptual diculty that sometimes a!icts discussions of the role of modeling techniques is the conation between the computer program and the theory. Some authors have gone as far as claiming that \Theories can be stated as computer programs" (Simon, 1992, p 152). In contrast, we consider that it is crucial to insist on the distinction and complementarity between the simulation system and the accompanying theoretical gloss. Computer simulations complement rather than replace verbal descriptions. A clear statement of this complementarity appeared in Palmer & Kimchi (1986), who argue against the notion that the computer program as such constitutes a psychological theory, and insist on the importance of the accompanying description:
a running simulation is only an IP information processing] theory by virtue of the fact that it too can be described by a ow diagram plus mini-mapping theories of its components (p. 57).
Their major argument is that a computer program can be described at various levels of speci cation, and that it may be dicult, without a verbal account, to decide which levels of description are psychologically relevant. This is the problem of mapping hypothetical constructs in the model onto their psychological counter-parts. There is also, however, a related but distinct diculty, which we call the redescription problem. Modelers must specify the properties and characteristics
underlying the model's functioning at a level of abstractness that permits useful and appropriate generalizations.
4.5.1. The mapping problem
The rst point may seem obvious. A model is a metaphor, and a metaphor is illumi-nating only as far as one clari es the relevant features that the metaphorical object shares with the target system, or better, the relevant level(s) of analysis at which a correspondence may be established between the two systems. Yet, in practice, expliciting and understanding the relationship between a simulation model and the corresponding human process is far from trivial. A major cause of this diculty is that both human cognitive processes and computer programs are complex objects that allow for a multiplicity of levels of description.
One well-known reference on the issue of description levels is a well-known pro-posal by David Marr (1982) that identi es three levels of analysis of information processing tasks. The three levels correspond to the computational description of the system (the input-output mapping that the system realizes), its algorithmic description (the algorithm used to perform the mapping) and its hardware imple-mentation. Marr's discussion makes it clear that all three levels may contribute to the understanding of the observed phenomena: some being explicable through hardware properties (afterimages), others (the Necker cube) requiring consideration of both hardware properties and algorithmic description. Furthermore, the notion of algorithmic description masks the fact (known to everyone who has engaged in any sort of computer programming project) that an algorithm can be described with various grains, independently of the hardware speci cations (cf. Palmer and Kinchi's notion of recursivedecomposition).
Given the multiplicityof potential algorithmicdescriptions, a simulationmodel at the algorithmic level could in principle be constructed to match the real function at many dierent levels, from the most abstract level of the input-output mapping (as happens, for instance, if a regression technique was used to derive a mathematical function), to the nest-grained level of elementary processes, with all intermedi-ate possibilities (such as, for instance, in Massaro's, 1989a, Fuzzy Logical Model of Perception, which assumes three stages of perceptual processing|evaluation of per-ceptual features, integration and decision|but restrict the simulationto an abstract mathematical description of the integration and decision operations). Concerning evaluation, it seems obvious that a (hypothetical) simulationmodel in which the cor-respondence goes down to the most elementary level is better, in scope and power, than a model restricted to the most abstract level of mapping. Nevertheless, this does not mean that starting at the most detailed level is the best research strategy.
As Marr suggested, it may be easier to start from a broad abstract characterization of the function, and gradually focus the microscope.
These issues pertain not only to symbolic approaches to modeling, but also to the arti cial neural networks framework. Willshaw (1995) describes a formal technique through which sets of symbolic and subsymbolic algorithms may be organized hier-archically in terms of their level of abstraction and implementation, and concludes
that \symbolic and subsymbolic algorithms are not neatly divided into two distinct classes, with the one being at a 'higher' level than the other" (p. 16).
4.5.2. The description problem
The problem of redescription|extracting an appropriate description of the model functioning from simulation results and knowledge of its design to allow useful generalizations|may appear more acute if one adopts the gardener's approach, though in no way would we argue that it is speci c to that strategy. As we have repeatedly stated, any reasonably complex model may at some point produce un-expected behavior. Indeed, our recent results with trace illustrate one case in which the behavior of the system did not correspond to the description given by its designers. It is the job of the designers (or, for that matter, of any serious user of the model) to explore the details of the system performance, the way it changes with variations of the stimulus set, or parameter values, and to provide principled and accurate accounts of how and why the system behaves the way it does.
The gardener's approach may, with much know-how and perhaps a bit of luck, lead to an outcome that matches the empirical observations. Still, that is only the beginning of the hard work. Simulations are not explanations. If we do not understand the simulationprocess any more than we understand the real one, having a running simulation of a given function is of little help. To borrow from a judicious analogy introduced by Forster (1994), this would be no more helpful than having a next-door neighbor capable of predicting, without explaining how, the outcome of any experiment that we might design and run. To some extent, the problem is similar to the use of statistical data- tting techniques: A mathematical equation may provide a descriptively and predictively adequate account of some regularity, but not an explicit description of the process that produces the regularity itself, and this strongly restricts possible generalizations.
This issue has arisen in recent years in the context of the assessment of the dis-tributed arti cial neural networks framework, and the discusion has centered on Seidenberg and McClelland's (1989) model of visual word recognition and naming, and its more recent derivatives (Plaut & McClelland, 1993 Plaut et al., 1996).
Note that the issue is not whether any of these models is empirically adequate, but rather whether they provide or even lead to adequate theories of cognitive functions.
McCloskey (1991) argued that the theoretical claims formulated by Seidenberg and McClelland are vague and too general, and that the theoretical elaboration fails to describe how the network accomplishes its task, because of our limited under-standing of complex connectionist networks. Yet, such a description of processing is certainly no less appropriate or informative than any other type of model cur-rently available. As noted by Seidenberg (1993), \there is a rich theory here: it has only to be acknowledged" (p.233). Granted, the description leaves many details unspeci ed, it may be incomplete, the mechanics of the model is based on new and unfamiliar notions, it is implausible in some respects, and many aspects of its performance could be further explored. However, similar remarks could be made about any other modeling eort.
McCloskey (1991) concluded by arguing that the design (or, for that matter, the growing of) connectionist networks should be viewed more as analogous to the use of animal models than as simulations of theories of human cognitive functions.
He further stated that, just like animal models, connectionist systems are objects of study in themselves, which may aid in developing theories of cognitive systems thanks to their similarity to the human system. We would simply add that one dierence between animal models and computer models is that the availability of the former is limited and constrained by natural selection, whereas the latter are aorded through design principles and constrained by preexisting theoretical hy-potheses. From that perspective, the study of arti cial simulation systems may be the only way to examine the implications of a set of computational principles and assess their validity in accounting for human information processing.
5.
Conclusions
We started our discussion by asking some simple questions: why use computer modeling in cognitive psychology? In what ways does the exercise of computer modeling techniques modify the nature of psychological research?
We consider that a de ning characteristic of cognitive psychology is the search for a particular kind of scienti c explanations that consist in accounting for the behavioral characteristics of human performance in terms of the organization and mechanisms of mental functions. Thus, empirical regularities observed in perfor-mance are used to draw a number of conclusions regarding a hypothetical mental function, the architecture and components it requires and its probable mode of op-eration, so that the empirical observations can be reduced to logical and necessary consequences of the characteristics of that mental machinery.
In this framework, it seems to us that a useful heuristic|perhaps even the only heuristic|is to create models, that is, to produce theoretical elaborations that de-scribe the relevant characteristics of the function, and to explore how well they account for the empirical observations. The use of computer modeling is a natural and obvious extension of this endeavor. Rather than limiting themselves to a verbal description of an imaginary mechanism, designers of computer models attempt to concretize the mechanism as a computer program.
Is this modeling enterprise worth the eort? We have analyzed several types of diculties encountered in current empirical research, and have argued that com-puter modeling provides appropriate tools to confront these problems.
One basic problem stems from the great complexity of our object of study, that is, the graded and multidimensional nature of mental functions. Computer mod-eling provides a good way of dealing with this intrinsic complexity and with the dynamic nature of information processing systems. In contrast, verbal models can make only simple processing predictions and our capacity to grasp these predictions is even more limited. Very limited, indeed: those readers who have tried to present in any detail the subtleties of the dual-route model of visual word recognition to their students may know how limited our capacity to compute mentally the logical
consequences of a (very) simple architecture may be. Few of us can imagine with-out external help the combined evolution of more than two elementary dierential equations over time.
We have also argued that modeling forces researchers to elaborate more detailed and fully speci ed accounts. Although any implemented model involves many arbi-trary decisions, the \full speci cation constraint" is positive pressure that may drive scienti c progress. In fact, any arbitrary implementation choice hides a potential empirical issue: it suces that another designer suggest a dierent solution, and that the resulting models perform dierently or lead to distinct predictions.
We have also suggested that the use of modeling techniques helps delimit the space of potential explanations by enlarging the scope of theoretical accounts and also by referring to general principles of processing. By exploring the intrinsic characteristics of the model, psychologists may be led toward accounts that are more strongly motivated theoretically. Models are also concrete objects, which lend themselves to further study. Access to computational models gives psychologists collections of hypothetical devices that may be constructed, deconstructed, and manipulated at will. We have illustrated how the elaboration of computer models leads to the identi cation of new research issues, and how the exploration and the systematic study of their performance may be helpful to understand the behavioral characteristics of hypothetical processing systems.
Finally, we have claimed that to be useful from a psychological viewpoint, com-puter programs should be accompanied by an appropriate description. Jointly these make it possible to establish how the elements of the designed system map onto the real function, and how the behavioral characteristics of the system emerge from its design features. In our view, the major change that computer models introduce into psychological research is that they allow a dyadic confrontation between empirical observations and verbal models to be transformed into a triadic and interactive confrontation between data, theories and implemented simulation systems.
6.
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