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Models are ubiquitous across disciplines, but the model as a means of conveying knowledge and abstracting reality is little studied. Scholars in different disciplines may use a variety of divergent types of models and each understands his or her world through a prismatic view provided by the specialized model used. If each field focuses only on its own variety of model and each model has shortcomings, we're still missing the big picture. The authors propose a taxonomy that may be used to classify the universe of models as used in numerous scientific and non-scientific disciplines. Such a framework can enable scholars to better communicate with their counterparts in other disciplines and to adapt the models of other disciplines to their own, thereby gaining a better understanding of their own specialized areas of study.
Introduction
The past decade has witnessed a convergence of technology more fantastic than science fiction. This is primarily due to widespread digitization and to the Internet, which can be seen as digitization plus telephony. Some of the results of this trend are: telephone companies provide cable, and cable companies provide telephone service; companies that produce printers are now in the camera business; long distance telephone calls use a broadband internet connection; photographs are transmitted via e-mail using a cellular telephone; several companies are competing for video-on-demand; computer manufacturers are in the music business; and many more. Convergence is even evidenced on the user side, in consumption convergence (6), meaning that consumers may be using several media simultaneously, e.g., computer, internet, music, newspapers, telephone, camera, etc., and in consumers who produce "mash-ups" using several forms of media.
The purpose of this paper is to investigate the use of models across disciplines, to try to create a framework in which diverse areas of scientific endeavor are represented specifically due to that discipline's use of a model. The authors feel that such a framework will go a long way towards providing a structure for further interdisciplinary scholarly work, a way for scholars from different areas of study to establish common language and thereby develop new paradigms for research in this age of disciplinary convergence.
Convergence of Disciplines
Just as technological innovations are converging across product categories, and as product distinctions and corporate mission statements have become rapidly dated, so too scientific disciplines have been converging as well. Indeed, many of the most important discoveries of this century were made possible by individuals whose interests and training extended beyond narrow disciplinary boundaries. It is interesting to note, for example, that the technology for developing the laser existed for several decades before the first working laser was demonstrated in 1960. Part of the technology needed for developing lasers was well known in the electrical engineering field, that of oscillating amplifiers used in radio (light amplification). The quantum mechanical aspects of laser technology were well known in atomic physics, and were developed in the 1920's by Albert Einstein (stimulated emission of radiation). The laser could not, however, be perfected until individuals who knew the two fields could combine the two technologies. Much technology works this way and it is therefore, in many cases, important for individuals to have knowledge of two or more fields. Increasingly, we find that the distinctions between individual disciplines are blurring and are due more to historical traditions than to substantive differences.
Johnson-Laird (7) points out that sometimes the same concept or methodology is examined by researchers from many diverse disciplines. For instance, decision making (logicians, statisticians, economists, psychologists) and parsing (mathematical linguists, psychologists, computer scientists). The past decade--even two decades--has seen a plethora of new inter- and multi-disciplinary studies (10). What are the implications for education? Kolodny [11, pp. 40-41] asserts that interdisciplinary programs are crucial for students educated in the 21st century, and that the antiquated way of organizing colleges--by departments--will have to "evolve into collaborative and flexible units." Perkins (13) feels that academic subjects are "artificial partitions with historic roots of limited contemporary significance." Duderstadt (4) suggests that the university of the future will be very different from today's institution. One major change will be that the future university will be divisionless, i.e., there will be many more interdisciplinary programs. There will also be "a far more intimate relationship between basic academic disciplines and the professions." Duderstadt (3) asks us to consider "whether the concept of the disciplinary specialist is relevant to a future in which the most interesting and significant problems will require 'big think' rather than 'small think.' Indeed, the very survival of the university itself may require that it become a 'learning organization.' The learning organization is characterized, among other traits, by its flexibility and free flow of knowledge. This is expressed, in the context of a university, as significant cross-disciplinary synergies both inside and outside the school (16).
Students seem to have come up with their own solution: majoring in one, two, three, four, or even five fields. Lewin (12) notes that the number of multiple majors is increasing at most universities. He cites the following interesting statistics: At Georgetown University, the number of double majors grew from 14% of the class in 1996 to 23% in 2002; at Washington University, the number of double majors rose from 28% in 1997 to 42% in 2002. Weber (14) states that about 25% to 35% of students at major graduate schools of business are now pursuing double majors (e.g., JD/MBA, MD/ MBA, MPP/MPA, ME/MBA, and MSW/MBA to name a few). The purpose is to make oneself more marketable in a difficult job market.
The Role of Models
With the convergence of disciplines it becomes important to look at the way we handle information--studying, analyzing, managing, reducing, employing, etc.--in various diverse areas of study. How do scholars wrap their minds around vast quantities of information in diverse formats? Is it even possible? If we can find common ground in the way information is handled in the process of acquiring knowledge in disparate fields of human endeavor, perhaps it will be a first step towards this goal.
Every field of human endeavor requires us to process data into information. In any modeling effort, abstraction and structure are important universal features. These two related concepts are involved in the reduction and management of complexity. Perhaps the best or, at least, the most parsimonious, definition of model is that it is a representation of a real-world entity but not the "real thing" itself. This definition, necessarily vague, encompasses just about any type of model in the spectrum, from physical models, like the full-scale mock-ups used to train airplane pilots, to the heuristic models of today's expert systems. Abstraction models reality or, at the very least, a chosen view of reality in which irrelevant objects or properties are ignored in favor of streamlining the model, thus making the model simpler conceptually and easier to study, manipulate, and implement.
The general model governing abstraction is the so-called black box model [e.g. 1], adopted from the engineering disciplines to many diverse areas. In this model, a set of inputs is mapped to a set of outputs or results by means of a transform. To use the transform, once it has been built, one need not know how it works; only that it does work. For example, we do not need to understand much about electricity to know that when we flip the light switch (input), the bulb will light up (output).
All abstraction uses the concept of information hiding. When models are well designed, they are relatively independent. They communicate with each other only through well defined interfaces. A "user" system does not require access to all the implementation details of the "used." This unnecessary information may be hidden from the user, protecting the integrity of individual systems and reducing the confusion that comes along with too much information.
Abstraction also allows one to ignore the tedious details (at least temporarily) involved in building a system, and concentrate on the larger picture. Abstraction is the major concept used in bottom up design: the construction of a large program by building layers upon layers of abstraction. Abstraction comes in many forms. Every field has its own specialized model, from the concrete to the abstract, from the real (say, a fashion model) to the simulated models of virtual reality.
Modeling refers to the various techniques we use to understand our world. The process of modeling includes analysis, abstraction, simplification, and approximation. Assumptions are made and tested. Simplicity, efficiency considerations, and the goals of the modeling effort are the prime determinants of the type of model to be employed; sometimes, a combination of modeling techniques is indicated.
Methodology
In an early attempt at creating a family tree of models in different disciplines, Friedman's (9) objective was to indicate the relative position of system simulation models--these are (usually) large, complex computer programs that represent a dynamic, probabilistic system composed of people, machinery, computers, processes, etc.--in the modeling "family tree" as indicated in Exhibit 1.
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If disciplines that are so different from each other are still similar enough to support the myriad and multiple convergences we observe every day, then there must be a way to expand this tree so that it includes many other areas, e.g., natural sciences, philosophy, psychology, etc.
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