This workshop will present an introduction to fractals and chaos and their applications in a way that even those with a limited background in mathematics can understand. Fractals are things that have pieces that are ever-smaller copies of the bigger pieces. A tree is fractal. It has ever-finer branches that are smaller copies of the larger branches. Fractals can be used to better understand the structure and function of proteins, cells, the heart, and the brain. Chaos means simple systems that do surprisingly complex things. Chaos can be used to better understand the surprising things that molecules, cells, and people do.
The topics covered will include : (1) Fractals: Introduction, Self-Similarity, Scaling, Dimension, Statistical Properties, (2) Chaos: Introduction, Phase Space, Sensitivity to Initial Conditions, Bifurcations, Analyzing Data, and Control of Chaos. The presentation will be based on the book, Fractals and Chaos Simplified for the Life Sciences, by L. S. Liebovitch, Oxford University Press, 1998 and the CD-ROM The Mathematics and Science of Fractals by L. S. Liebovitch and L. A. Shehadeh, Deco Bytes Education (www.decobytes.com).
This workshop explains how hypotheses concerning catastrophe models, chaos, and related attractor dynamics can be tested statistically using SPSS or similar statistical software. The analytic techniques involve the polynomial extensions of the general linear model and nonlinear regression. Examples from published works on topics such as mental fatigue, leadership, population growth, personnel selection and performance, and economic inflation will be considered among other topics. This workshop is intended for participants who are familiar with the general linear statistical model and who are now ready to move forward.
The workshop is organized into six themes: (1) The statistical properties of measurements in a nonlinear process. (2) The properties of exponential distributions, power law distributions, and the interpretation thereof. (3) Catastrophe models for discontinuous change processes, which are extensions of the general linear model. (4) The properties of nonlinear regression and how it can be used to specify and test any nonlinear hypothesis, including how to find a Lyapunov exponent and a fractal dimension. (5) The exponential series for continuous change processes, such as attractor dynamics, oscillations, and the presence of chaos. (6) As time permits, the foregoing principles will be extended to cover static representations of dynamical processes and linkage (or slaving effects) in self-organizing systems. The goal in each module is to provide participants with a step by step procedure for accomplishing their analytic objectives.
John Winthrop Link and Jo Lee Loveland Link and their firm, VOLVOX, Inc., have sustained interest in applying concepts of chaos and complexity to social systems since the Links first became intrigued, together, about the world of emerging "new sciences." For the past 20 years, the Links have had opportunities to examine and explore those concepts up close in practice with real-world organizations - large complex government systems, mission-critical defense systems, emerging Information Technology initiatives in large-scale Net-Centric web-based knowledge management, intelligence community efforts to bring information sharing to high velocity while struggling to maintain security, etc. "Management of complex change" takes on new meaning in efforts with cross-enterprise integration of previously disconnected, uncoordinated, and often (sometimes covertly) competitive organizations.
Embracing complex systems paradox themselves, the Links have worked on efforts ranging from visionary social change to creating defense policy recommendations for the Office of the Secretary of Defense. John Link is an M.S. graduate of the George Mason University Conflict Management program, and has facilitated the most challenging multi-enterprise, multi-technology enterprises to collaborative action. John has a special interest in expansion of systems for human intelligence (HUMINT), non-lethal weapons, and effects-based operations, areas, which incorporate peacekeeping and nation-building efforts as well as military and information technologies. Jo Lee has advanced professional education in Applied Behavior Science/Organizational Behavior and Change through the Mid-Atlantic Association of Training and Consulting, and has worked with risk management and technology adoption projects as a Visiting Scientist for Carnegie Mellon University's Software Engineering Institute (CMU SEI). Jo Lee's focus is on using anthropological methodologies and change narratives to enhance organizational emergence and adaptation.
Their original learning laboratory, CHAOS, Inc. is available for presentation in organizations and cross-enterprise initiatives, and has been presented in educational as well as corporate and government environments. A certification process is available for those interested in becoming authorized CHAOS, Inc. presenters. For further information, contact: John Winthrop Link & Jo Lee Loveland Link, P. O. Box 610, Middletown Virginia 22645 - Phone: 540-465-1491 - email@example.com & firstname.lastname@example.org
CHAOS, Inc. is an original improvisational game that applies chaos and complexity insights to real-world social/ organizational systems. Together with participants, we co-create and enter an environment of collaborative learning and exploration.
CHAOS, Inc. was first designed by John and Jo Lee Loveland Link in 1991 as a research tool to evolve and test hypotheses on emerging "new science" concepts in actual organizations. Presented periodically ever since its inception, now CHAOS, Inc. is of growing interest by organizational leaders and members as they become more chaos/complexity savvy - or at least curious.
CHAOS, Inc. participants enter a well-defined simulated "company," and begin work. The "company" then is subjected to events and pressures typical in contemporary organizations - i.e., never the same twice. Participants face multiple dilemmas. Mid-way in the exercise, "company" members have an opportunity for organizational redesign. All are challenged and invited to reinvent their organization. Then, in a "work restart," participants can test their new strategies, assets, approaches, and learning that may be leveraged "back home."
Unlike most workshops or training -- but just like real-world organizations (one participant said: "What's really hard about this exercise for me is it's just like my real job!) - CHAOS, Inc. is a true experiential laboratory, designed for everyone from beginners through those with more advanced understanding. Again, just as in real life, we learn from one another. People from different levels of knowledge and experience create dynamic creative friction - and we are all made richer by the mix.
Highly dynamic and evolving, CHAOS Inc. produces every time outcomes and insights that are intriguing, diverse, and mirror emerging dynamics. We hope that you will come to play, explore, experiment, and learn with us!