Planning Documents for a National Initiative on Complex Systems in K-16 Education

Eric Jakobsson & Working Group 1 Collaborators

(Part of Planning Documents for a National Initiative on Complex Systems in K-16 Education)

Our current educational model is based on the compartmentalization of knowledge. This has been a powerful tool, but in today's world more and more knowledge is spilling over the boundaries of the compartments we have constructed, for example across the boundaries between biology, chemistry, and physics. The Internet has provided essentially universal access to all this knowledge, albeit in a form that can be intimidating and confusing as well as enlightening and empowering. Today's students, the citizens and leaders of the new millennium NEED tools to organize, understand, act on, and add to, the exploding body of human knowledge in an increasingly interconnected world.

We believe that a useful tool and SOURCE OF organizing principles that can contribute to dealing with the knowledge environment of the new millennium is the body of knowledge we have acquired about the structure and behavior of complex systems. Understanding complex systems is critical for both scientists and non-scientists. For scientists and engineers, the understanding of complex systems is critical for the ability to APPLY knowledge and techniques ACROSS contexts, for example to APPLY physics knowledge to a biological context. As science and technology have become so fast-moving and changing, this ability has become more important, as an individual scientist and engineer can now expect to be called on to deal with vastly different problems at various stages of his or her career. Indeed, the interactions between science and technology have become more complex, and the boundary between basic and applied science less clear than ever before.

Especially in biology but also in other areas, new technologies are now so rapidly incorporated into methodologies for scientific research, and new scientific discoveries are so rapidly incorporated into technology, that the distinction between bioengineering and basic biology is not at all clear. In any case, it is clear that modern biology and bioengineering depend critically on new advances in physics, chemistry, other areas of engineering, and computer science, so a tremendous amount of science and engineering is now done across traditional disciplinary boundaries. For all people, understanding the world as interlocked complex systems (social systems, job markets, financial markets, political systems, schools AND SCHOOL SYSTEMS, ecological systems, universities, etc.) is critical for making decisions in their lives as individuals and as citizens.

Indeed, people need to understand that not only do they deal with the realities of complex systems, but in fact they deal with models of those systems whether they are conscious of that fact or not. For example, governments and businesses make financial decisions based on economic models that attempt to tell them the likely consequences of those decisions. In turn, all citizens, consumers, and workers deal with the actual consequences of those model-based decisions. When individuals make economic, career, and other life decisions, those decisions must be based on some model (sometimes not explicitly formulated, but a model nevertheless) that presents the likely consequences of their individual actions. For example, planning for one's old age and possible retirement is based on a model that is parameterized by assumptions about one's individual earnings, possible changes in the value of money, and what money will earn if it is set aside for later use by various investment means. Even the most emotionally charged things that people do, such as courtship and interacting with family members, are based to some extent on models of interpersonal dynamics; i.e., an array of assumptions that attempt to predict how people will respond to various actions. Understanding how models work, and what they can and can not do, is an enormous benefit in all aspects of life, not just for people pursuing such quantitative professions as science, technology, business, and economics.

Perhaps the most intuitively understandable, as well as one of the most important, attributes of complex systems is feedback, and the related concepts of positive feedback, negative feedback, and adaptive feedback. Everybody understands that individuals and social systems modify their behavior under the influence of various pressures. These modifications usually are adaptive, and tend to help the individual or the system to cope--this is adaptive feedback. But sometimes some large perturbation moves the individual or the system across some threshold to a new state--or to some serious damage or even destruction (generally the result of a "vicious cycle", in common parlance). While many people understand these issues intuitively, many do not understand that there are useful quantitative models of this type of dynamics, and what the value of these models might be. The importance, the generality, and the common intuitive understanding of the concept of feedback may make the presentation of it an excellent avenue to introduction of systems as a matter of general interest.

What Are Some Fundamentals Of Complex Systems Worth Learning?

Complex systems are sets of interconnected elements whose collective behavior arises in a non-obvious way (and often counterintuitive and surprising way) from the properties of the individual elements and their interconnections. Knowledge of complex systems rests on three foundations: Experiment and observation in the real world; use of computation for modeling and information search and analysis; and underlying theory about the properties of nonlinear systems.

Making models of systems is key for understanding their behavior. In introducing students to modeling , we must be sure to present both the power and limitations of the entire modeling approach, and of the particular models that we present to the students and empower them to make. All models are imperfect—but even imperfect models are very useful in understanding the world. Indeed, the imperfections in models are of critical importance in guiding our future work, because it is in understanding the bases for the imperfections that we see what we do not yet know, and where our next explorations should be aimed. Making models can also help students to think better, and to develop better habits of mind. By putting assumptions into a model, students can subject their assumptions to a process of testing—the results from the modeling can either falsify or tend to validate the assumptions. By going through this process, students can learn the difference between assertion, argument, understanding, and other modes of thinking and discourse.

Several different types of computational modeling styles and techniques should be introduced in appropriate context—calculus-based differential equations, difference models, random-walk or stochastic models, and active-agent models (cellular automata, etc.)

At all stages of learning about systems, computational models need to be compared to what happens in the real world. In order to facilitate this, the computational environment that empowers modeling should also be integrated with information sources on the World Wide Web. The Web should be understood and used as a complex system of information transfer, and personal and institutional interaction, and a medium in which modeling is done.

As a consequence of being exposed to these concepts, students will learn that effects do not usually have single causes, and that causes may be either direct (primary) or indirect (secondary). They will develop a feeling for the power and the limitations of systems modeling and information analysis as applied to understanding real-world complex systems. This will be as important for scientists and engineers as for less technical people. As important as it is to teach people about systems, it is equally important to educate against excessive hubris on the part of those who do have some technical knowledge of complex systems.

We need to think clearly and teach clearly about attributes of complex systems that are universal, as compared to ways that each system is unique and must be understood on its own terms. One of the most important attributes of systems is structure. Systems are structured in such a way that some parts of systems are specialized, and systems can naturally be divided into different levels of organization, that should be modeled at different levels of detail. An important component of understanding systems is the ability to take model systems apart into their component parts and levels to see how the parts behave, and how to connect the parts and levels to understand the overall system dynamics and structure. To the average citizen, perhaps one of the most transparent examples of the importance of structure in complex systems thinking is the space program, where it is obvious that one must consider equally the behavior of individual components and the dynamics of how those components interact with each other.

Other general attributes of systems that students need to understand include: randomness, deterministic chaos, thresholds, and periodicity. They need to understand the concepts of feedback in general and adaptive feedback in particular. Students need to understand that systems evolve. The fact that real-world systems are open to exchange of information, matter, and energy with the rest of the world has consequences that students need to understand. Students need to learn how all of these aspects of systems emerge from the properties of the system components and their interconnections, and what aspects of particular systems govern the behavior of those systems.

Helping Students Learn About Complex Systems—Some Tentative Notes

Students need experience with observable and controllable complex systems from their early years onward. Hence schools and classrooms should be populated with a wide variety of artifacts that can help in the understanding of complex systems and their properties. Such objects include: Rubik's cubes, toy systems such as terraria and aquaria, complex pendulums, color-coded chemical reactions, gyrosopes, Petri dish experiments, etc. Appropriate computational tools should also be present, in the context of information about the real-world systems that the computational models are designed to describe. Kids need alternative pathways to learn about complex systems.

We should develop exercises in systems that have immediate relevance to students' lives—their personal interactions, body composition change with diet and exercise, garbage generation and recycling, traffic jams, elections, etc. We should use participatory simulation in which the students are "system variables". Biological systems such as the human body, insect societies, ecological systems, etc., are natural entries.

We need to provide time for reflection on the activities—"what did it mean?" For example, "What underlying mechanisms might give rise to the observed behavior?" "How sensitive is the outcome to changes in the model's parameters or structure or assumed environment?"

We need to develop appropriate tools for testing and assessment in the area of learning about complex systems.

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Video of Yaneer Bar-Yam's seminar on Complex Systems Principles and Education: Focusing on Universal Principles and Individual Differences



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