1. General Systems Theory Dan Youberg Michael Harris

2. Introduction General Systems Theory Originally proposed by Ludwig von Bertalanffy. Suggested that a system is characterized by the interactions of its components and non-linearity of those systems. o A common element of all systems is that knowing one part of a system enables us to know something about another part. Systems can either be controlled (cybernetic) or uncontrolled. According to Kuhn's model a decision is to move a system towards equilibrium.

3. Studying Systems General Systems Theory Cross-Sectional Developmental Deals with the interactions between two systems Deals with the changes in a system over time

4. Evaluating Systems General Systems Theory Holist Approach Reductionist Approach Functionalist Approach All three recognize the existence of sub-systems operating within a larger system.

5. Chaos Theory

6. “Chaos is a name for any order that produces confusion in our minds.” George Santayana

7. Chaos Theory General Systems Theory Attempts to explain and model seemingly random components of a system What is Chaotic System? o Must have the following three properties  Must be sensitive to initial conditions  Must be topologically mixing  Its periodic orbits must be dense. Chaotic systems can have both stable and unstable components

8. Phase Space Chaos Theory Proposed by mathematician Stephen Smale in 1980 Set of all possible initial conditions for a dynamical system o The dimension of the phase space is the number of initial conditions required to uniquely specify a trajectory (i.e. the number of variables in the dynamical system) Each point in a phase space represents the state of a dynamic system at an instant in time.

9. Poincare Map Chaos Theory Developed as a way of understanding three dimensional systems by taking a series of two dimensional "slices" relative to a line through the origin and overlaid on top of each other Distinct patterns emerge by combining these sections Imply that order is not an absolute and can only be understood relative to an observer o Nature of a system is a matter of perception and/or beliefs.

10. Poincare Map vs. Phase Space Graph

11. Mandelbrot Chaos Theory Discovered that the apparent random noise bursts were actually following a regular cycle Pointed out that chaos theory models a rough, pitted world Proposed that the concept of dimension itself can only be stated relative to an observer Introduced the word fractal as a way to visualize infinity o Implies a quality of self-similarity

12. Types Of Non-linear Systems Chaos Theory Intransitive systems o Have two or more stable states, after one of the states is achieved the system will remain in that state until something changes in the environment Almost intransitive systems o Have two or more stable states but does not require any input from the environment

13. Conclusion Chaos Theory An important conclusion discovered from chaos theory is that a relatively small, but well timed/placed jolt can send a whole system into chaos Systems operating in a chaotic environment are continually being challenged to maintain their purpose and structure Small structures can adapt to change more efficiently than larger ones. Primary chaos theory teaches us about the nature of change in our organizations and social institutions.

14. Fuzzy Logic

15. “The difference between science and the fuzzy subjects is that science requires reasoning while those other subjects merely require scholarship” Robert A. Heinlein

16. Fuzzy Logic General Systems Theory Proposed by Jan Lukasiewicz in 1920 as a postulate to Cantor's universe of discourse The main problem that fuzzy logic tries to explain is how we categorize things Added a third logical value (possible) o This allowed a numerical value to be used to represent the degree of truthfulness Judgment and context are used to assign values to a membership

17. “As complexity rises precise statements lose meaning and meaningful statements lose precision” Lofty Sade

18. Fuzzy Logic vs. Probability Fuzzy Logic Probability Remains the same as the amount of information increases Deals with truths Change with increasing information Deals with the likelihood that something happens

19. Example Problem A 100 ml glass contains 30 ml of water. Two states: Empty and Full One could say the glass is 0.7 empty and 0.3 full However by fuzzy logic, the definition of full may be 50 ml or more of water in the glass. o This value is up to the designer or observer and may vary.

20. Classification of Categories Fuzzy Logic Proposed by Eleanor Rosch in 1975 Found that certain words are better examples of a class than others. Classification Categories o Superordinate (abstract categories) o Basic (concrete images) o Subordinate (subcategories)

21. Future

22. “The tongue cannot taste itself, the mind cannot know itself, and the system cannot model itself” Willian Thompson From "Evil and World Order" (1976)

23. Questions?

24. References General Systems Theory Hasseblatt, Boris: A First Course in Dynamics: With a Panorama of Recent Developments. Cambridge University Press, 2003. Gleick, J.: Chaos: Making a New Science. Sphere Books Ltd, London, 1987 Lorenz, Edward: Climatic Determinism. National Center for Atmospheric Research, 1968. Skyttner, Lars: General Systems Theory: Problems, Perspectives, Practice (2nd Edition). World Scientific Publishing Co. Pte. Ltd, Singapore, 2005. Walonick, David: General Systems Theory. 1993. "Crayola Crayon Chronology". Crayola LLC. http://www.crayola.com/colorcensus/history/chronology.cfm. "Crayola Crayon Chronology" http://www.crayola.com/colorcensus/history/chronology.cfm