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Systèmes complexes [page consultée le 2000-10-22]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ [page consultée le 2000-10-22]


Michael J. Jacobson
Allison~LoBue Group, LLC

Kenneth Brecher
Department of Astronomy
Boston University

Marshall Clemens

Win Farrell
PricewaterhouseCoopers Consulting

Jim Kaput
Department of Mathematics
University of Massachusetts-Dartmouth

Uri Wilensky
Center for Connected Learning and Computer Based Modeling
Tufts University


Session Chair: Michael J. Jacobson

This paper provides an overview of issues related to learning about complex systems and the application of complexity concepts and approaches that were considered as part of presentations at the Education in Complex Systems session given during the Second International Conference on Complex Systems. There are at least two main challenges related to the sciences of complex and dynamical systems for education and training broadly construed to encompass schools and the workplace. The challenge for science education is obvious. The scientific literacy of the next century may well require that students in school develop a deep understanding of new cross-disciplinary concepts and new ways of doing science that are related to complexity and complex systems. Unfortunately, given that students frequently have difficulty understanding the scientific knowledge from before the twentieth century, helping students learn ideas and concepts related to complex and dynamical systems may prove to be even more difficult. Further, there are important cognitive, learning, and curricular issues that to date have not been systematically considered.

The second major challenge relates to the application of scientific findings, intellectual perspectives, and modeling techniques based on complex and dynamical systems research to problems and issues in the "real world." Senior executives in business and industry, policy makers in government, and the general public may need to make important technological, economic, and social decisions for which knowledge about complex systems is relevant, yet about which they have had no formal training. Further, there is reason to believe that many complex systems ideas and concepts are not only cognitively demanding, but also counter intuitive, and thus may prove difficult for both students and adults in non-scientific and even scientific fields to learn. And lacking a solid understanding of these ideas, there is the danger that relevant scientific knowledge based on complex and dynamical systems research may not be appropriately applied to technical, economic, and social problems and issues. The presentations given as part of this session considered these, and other important issues, related to learning and applying knowledge from this emerging field of scientific inquiry.

Real Complexity For Real People

Presenter: Win Farrell

Win Farrell observed in his talk that there has been much intellectual debate recently about whether the sciences of complexity represent a metaphor for thinking about the way “the world works," or represent something more than a metaphor--a context for thinking about difficult and important problems. Several years have passed since "toy" complex systems models have been demonstrated to business executives who have real-world responsibilities. While instructive, these “toy” models have also served as a starting point to evaluate whether real complex systems models of the world, populated with real data from business data warehouses, can serve as predictive models that can be trusted.

Important features--reality, suitable predictive power, instruction, and context--are all brought into focus with the contemporary high-powered complexity models that are starting to be used by the business community. Although features such as these are the perceived advantages driving executives to resort to complexity models, the field's novelty raises important issues such as a model's testability and veracity. Consequently, the all-important trust that many executives have in complexity models is still below the level of trust in other modeling techniques that rely on more conventional "top down" systems thinking. Corporate executives' and managers' trust in these complexity models, just as they have in the traditional top-down judgment and decision making models to which they accustomed, however, is presumably the critical aspect to the success and permanence of complexity models in the real world. Farrell conjectured that in order for complexity models to flourish, the establishment of real-world users' comfort and trust in bottom-up, complexity-based models must be similar to that of the incumbent top-down models. Is it only a matter of time, or the revelation of some "moment of truth," when complexity models consistently outperform traditional top-down alternatives? Moreover, if this flash of insight is not achieved, is the metaphorical utility of complexity enough to sustain interest beyond the notion of complexity as "just another passing fad?" These questions remain to be answered.

Representations and Complex Systems

Presenter: Marshall Clemens

In the talk by Marshall Clemens, he asserted that the importance of the field of complex systems lay not just in the applicability of the complex systems concepts across the many scientific disciplines they transcend-as interesting and important as those applications may be-but in the fact that the field transcends these disciplines at all. Complexity's transcendent ability suggests that it might form a set of truly general concepts applicable across a wide range of domains, and thus should be of great value to all students no matter what field they may eventually specialize in. Complex systems theory has the potential to be the first truly viable candidate for a scientifically based “liberal arts” curriculum. Both the power and difficulty of such a knowledge backbone lies in its abstraction. Such high-level concepts are necessarily abstract and abstract concepts are often the most difficult to acquire and apply. Abstractions must be built, bottom up, from specific examples, grounded, top-down, in numerous instances, and fleshed-out in verbal, visual, tactile, and auditory representations. This is the challenge of teaching complexity: mediating between the concrete and abstract using all available modalities.

The unique nature of complexity science-its newness, transdisciplinary roots, and conceptual complexity-has made it difficult to synthesize into a concise yet complete educational package. Clemens argued that visual representations, in addition to verbal and mathematical ones, are an essential component in integrating and understanding complexity concepts. Following the account of human understanding pioneered by George Lakoff and Mark Johnson-that at its core, human knowledge is based largely on image-schema and their metaphorical extensions-Clemens proposed that image-schematic constructs are essential to grasping many complexity concepts. And, conversely, if one lacks the correct image construct, or an appropriate visual analogy, understanding will be partial or erroneous. In the task of integrating these concepts into a unified picture of complexity science, here again, but for a different set of reasons, visual-diagrammatic representations are essential. When the body of knowledge to be integrated becomes conceptually complex (i.e., when it exceeds the capacity of our working memory of 7+-2 concepts or relations) external representations become a practical necessity. Among external representations, diagrams-because of their unique abstractive, mnemonic, and relational affordances-are particularly well suited to the task of knowledge synthesis. Diagrams can explicitly show conceptual relationships hidden in verbal or mathematical arguments, and can help mediate between the concrete and abstract by linking general concepts to specific examples. The balance of Clemens' presentation discussed ways to design complex systems visual representations, such as shown in Figure 1, based on his recent work in this area.

Figure 1. Example of a visual representation of core complex systems concepts.

Justifying and Visualizing Complexity

Presenter: Uri Wilensky

Wilensky presented an outline of a four-year computational modeling project sponsored by the National Science Foundation. The project, entitled "Making Sense of Complex Phenomena through Building Object-based Parallel Models" ( "", is developing modeling languages (such as StarLogoT) and tools for the study of complex systems and is studying students building models with these tools. In this presentation, Wilensky described research by his student Kenneth Reisman and himself in which students used the StarLogoT modeling language to explore the relations between different biological levels. (Note: For a more complete discussion of this research, see their paper elsewhere in the ICCS Proceedings.) In their research, students used the StarLogoT language to model the micro-rules that underlie the emergence of a phenomenon, and then observed the aggregate dynamics that resulted (see Figure 2). Two situations were discussed in the presentation in which this approach had been employed with students.

Figure 2. StarLogoT multi-agent model of a wolf-sheep-grass ecosystem.

On Growth and Form, the Random Universe, Patterns in Nature, and the Dance of Chance: Helping Students Learn How Order Comes Out of Chaos

Presenter: Kenneth Brecher

Kenneth Brecher discussed a series of NSF supported projects conducted during the 1990's by a collaborative team of university scientists, education specialists, and high school teachers that set out to explore how students might learn about a variety of complex systems. These projects had three main goals: (a) to bring forefront research topics into the classroom in order to provide students with the opportunity of dealing with current, rather than centuries old, ideas; (b) to test how new technologies, particularly computers, could best be used in education, particularly in the realm of simulations, but also in data gathering and analysis; and (c) to combine computer simulations with hands-on experiments to provide an inquiry based environment in which students construct their own knowledge effectively.

In the course of these projects, software was written with simple underlying rules that lead to the formation of complex patterns. Diffusion limited aggregation, percolation, and other current topics in complex systems could then be explored by students themselves. In addition, simple biological, chemical, and physical experiments were developed which showed how complex, but apparently ordered, patterns form from random physical processes. Techniques for determining the fractal dimensions of resulting patterns were also developed. Students were then placed in a position to compare theoretical models they could control with real physical phenomena that they themselves generated and measured.

This presentation displayed some of the products of this research and development efforts. It discussed some of the lessons learned in working with over 150 teachers during the development stages of the project. The presentation also described results from the classroom, particularly changes in the role of teachers and students; presented anecdotal stories concerning changes in students' understanding and attitude towards modern scientific research and the origin of complexity in nature. Materials from this project may be found at the following Web site:  ""

"Schoolifying" The Mathematical Side Of Complexity And Dynamical Systems: Conceptual And Curricular Integration

Presenter: Jim Kaput

Jim Kaput posed several questions and issues that must be addressed in order to incorporate Complexity and Dynamical Systems into core curriculum for mainstream students. For example: What does it mean to go beyond the pretty pictures? The answer involves both finding ways to make the ideas about complex and dynamical systems learnable, and finding ways to integrate and/or transform the relevant curricula now in place. Other issues include how to link with existing curricula, and the development of new curricula. On the mathematical side, education dealing with complexity and dynamical systems knowledge will need to integrate with the existing relevant school curricula involving notions of rate and ratio, periodicity, composition/iteration, randomness and probability, and so on. Also, there are topics that are usually associated with "high end" school curricula such as connections between rates and totals of varying quantities for different types of variation (e.g., linear, polynomial, exponential, logistic), limits, and continuity and approximation. In addition, ways must be found to deal with topics such as closeness, sensitivity, dimensionality, and so on that are not part of school curricula, as well as skills such as visualization, scaling, and "clever testing" of multivariate situations that are not part of explicit curricula at any level.

Working out answers to questions and issues such as these is likely to be a generation-long task, although the Kaput indicated he was predisposed to be highly optimistic regarding "learnability" issues. Indeed, Kaput asserted that many of the traditionally "hard" topics of science and mathematics may become more learnable within the rich and integrated approaches afforded by combinations of highly visual, student-controllable simulations, meaningful physical and social settings that tap into students' naturally occurring linguistic, kinesthetic, perceptual and cognitive sense-making powers, and local learning objectives that build on their interests and felt needs. The explorable modeling and simulation worlds that are now becoming available could be immensely more accessible and interesting to mainstream students than the highly idealized universe of classical science that was only available in the language of formal algebra-and which was put at the end of a long series of prerequisites that acted to filter out all but a tiny minority of students.
Kaput concluded his presentation by discussing selected conceptual and curricular issues in more detail based upon research with his colleagues Ricardo Nemirovsky, Walter Stroup, Jeremy Roschelle, and Helen Doerr as part of the ongoing NSF funded SimCalc Project. He expressed hope that projects such as the SimCalc Project may help lay the base for the next level of curricular innovation required to "schoolify" Complexity and Dynamical Systems.


The presentations in this session discussed a variety of issues related to the integration or use of complex systems knowledge in education and business. In particular, this work suggests that merely presenting or providing complex systems content to business executives or students-whether as concepts or as multi-agent modeling techniques-may not be enough. For example, Farrell observed that business executives may not have trust in complex systems modeling techniques since they are based on different assumptions than conventional top-down modeling approaches. Kaput poses a related question in education when he asks what does it mean to go beyond the “pretty pictures.” Given the conceptual demands and counter-intuitive nature of many complex systems concepts and perspectives, helping adults in business or students in school to develop “trust” and understanding of complex systems conceptual and modeling approaches may prove to be significant challenges.

Fortunately, the education oriented presentations in this symposium discussed innovative representational, pedagogical, and learning approaches that show promise for meeting these challenges. These presentations discussed several ways that students may use powerful computer visualizations and modeling software as part of constructive science and mathematical learning experiences that often bring students into direct contact with cutting edge scientific issues and knowledge. Of course, much more work is necessary to expand and generalize approaches such as these for more widespread integration into the science and social science curricula our students are involved with. Still, the challenges and the work to be done notwithstanding, the importance of the projects described in these presentations should not be underestimated. They are showing us glimpses of the future of science, mathematics, and social science learning and of ways to use advanced knowledge in the “real world.” These are very exciting glimpses.