____________________________________________________________________________http://www.paper.edu.cn 1 The Comparison among the Schools of Science of Complexity Xuefeng Song John N. Warfield School of Business Administration The School of Public Policy China University of Mining & Technology George Mason University Xuzhou, Jiangsu, 221008, P. R. China Fairfax, VA22032, USA ABSTRACT These questions have the same answer: So many complex phenomena have emerged from “Nobody knows”. Some of them don’t even seem economic and social systems that traditional like scientific issues at all. Yet, when you look at economics and management science can do nothing little a closer, they actually have quite a lot in about them. For resolving the problems under the common. For instance, every one of these questions environment of complexity, scientists have been refers to a system involving complexity. Many trying to search the routine of coping with complex independent agents are interacting with each other problems since the 1970s. As the result of their in a great many ways. Moreover these systems are efforts, five schools of science of complexity can be self-organizing and adaptive. They actively try to identified. So in this paper, the five schools are turn whatever happens to their advantage. Every compared systematically. The thoughts and theories one of these complex, self-organizing, adaptive of the schools are analyzed respectively. Finally, the systems possesses a kind of dynamism that makes developed and applied foregrounds of the schools them qualitatively different from static objects such of complexity are prospected. as computer chips or snowflakes, which are merely Keywords: Science of Complexity, Chaos, complicated. Complex systems are more Adaptive Systems, Emergence spontaneous, more disorderly, more alive than that. Moreover every complex system is structurally 1. Introduction nonlinear rather than linear. Wide ranges of complex phenomena have The Complexity of Organization Behavior emerged from the life of organizations time after implies that “without changing our pattern of time and all over the world. Many people may thought, we will not be able to solve the problems remember the following issues. The Queen’s we created with our current patterns of thought banker, Barings was brought down by Nick Lesson (Einstein)” in a very short time; The New York stock market The origin of physical science of crashed more than 500 points on a single Monday complexity can be dated back to the 19th century. in October, 1987; The Soviet Union came apart The physicist Sadi Carnot and other researchers quickly in 1991; In most East Asia countries, realized it was both tedious and impractical to financial systems emerged into crisis one by one describe every interaction taking place in physical during 1997 to 1998. systems. Why did these organizations fall down so fast? Based on Newtonian concepts, system Why could none forecast these phenomena’s predictions became the law of thermodynamics. coming? What are the mechanisms of these Their existence could explain the increase in organizations’ evolution? temperature and pressure when gas molecules are heated in a container. But at the same time, 1 Supported by NSFC (No. 79970115) 中国科技论文在线___________________________________________________________________________http://www.paper.edu.cn thermodynamics did not provide a complete 2.2 Chaos Theory description of the most complex interactions as, for It was a meteorologist Edward Lorenz, who example, in the case of gas molecules strongly first perceived chaos as such, back in 1960, while attracted to one another. working on the problem of weather predication. He Subsequently, Henri Poincare (1854-1912) intended to model the weather’s behavior using a realized that if a system consisted of a few parts set of twelve equations in a computer set up. This that interacted strongly, it could exhibit led him to identify what came to be known as the unpredictable behavior. This concept is at the origin butterfly effect, which later became the emblem of of chaos theory. chaos theory. Lorenz started to work on a simpler There have been many attempts to solve system that had sensitive dependence on initial nonlinear dynamics problems so far. And as the conditions. Initially he took twelve equations for results of the evolution of Science of Complexity in convection. the 19th and 20th century, five schools of thought One of pioneers in the field was a biologist, about complexity shown in table 1-1 have Robert May, who became concerned with a developed. problem which occurs with the prediction of biological populations. He found the line broke in Table 1-1. Schools of the Science of Complexity two as soon as the growth rate passed 3, meaning Name of School Inventors that instead of settling down to a single population, 1. System Dynamics Jay Forrester it would jump between two different ones from a year to another. Raising the value of the growth rate 2. Chaos Theory Groups in many a little more caused it to jump between four Locations different values. And as the parameter rose further 3. Adaptive Systems Santa Fe Institute the line bifurcated or doubled again. Bifurcation Theory came faster and faster until chaos appeared 4. Structure-Based John N. Warfield suddenly. After a certain value of growth rate is Science of passed it becomes impossible to predict the Complexity population, which implies a kind of chaos. 5. Indifference Postmodernists Presently, chaos theory has posed great challenges to traditional approaches to science, no wonder it has been extended to be considered the 2. Main Thoughts and Principals of the Schools science of complexity, considering the range of 2.1 System Dynamics scientific disciplines that have found points of System Dynamics (SD) was developed by Jay resemblance and complementarily in these theories. W. Forrester at the end of 1950s. System Dynamics Believers in chaos are looking for the whole, and is a theory based on the theory of feedback, have alternative set of ideas, a fresh way to proceed decision-making analysis, and simulation which has produced valuable in sights in the methodology. From the view of System Dynamics, process of understanding the world. every social and economic system is feedback system that features is determined by its inner 2.3 Adaptive Systems Theory structure. In fact, SD is a method of simulating Santa Fe Institute (SFI) was known as the complex system by its feedback structure and also research on the adaptive system theory (CAS). called management laboratory. Chen (1988, [13]) The basic thought of CAS is that complexity is researched Monetary Chaos with System Dynamics originated from the adaptive of the active agent in theory. the system, which changes itself and its 中国科技论文在线___________________________________________________________________________http://www.paper.edu.cn environment by interactive with its environment science called Structure-Based Science of and the other active agents. The revolution of CAS Complexity (SBSC) on the basis of the mentioned was just basis on this kind mechanism. The thought leaders in the history of thought. researchers in SFI developed a new methodology 2.4.2 What is Structured-Based Science of and a kind of software called SWARM basis on the Complexity (SBSC)? thought of adaptive creating complexity. Their goal (1) The Definitions and the Philosophy Thoughts is to set up the theory of dealing with complexity of SBSC by the simulation of computer. On the basis of Definition 1 Complexity is that sensation genetic algorithm, J. Holland developed CAS experienced in the human mind when, in observing model to simulate the behavior of general adaptive or considering a system, frustration arises from lack systems. of comprehension of what is being explored. 2.4 Structure-Based Science of Complexity Those who think that complexity is a 2.4.1 The Emergency of the Structure-Based property of what is being observed have to face up Science of Complexity to the challenge of trying to find, in a multitude of As one of the five schools of science of observable systems, an attribute that is shared complexity, the thought of SBSC has evolved very across all the many different types of observable slowly from thoughts of the following thought systems. Even if that could be done, the question leaders. would remain about how they could do this for • Aristotle (384-322 BC, Greece): He presented those systems that are merely being thought about, the concepts of category and the syllogism. such as systems to be designed, which do not even Both of them are important for SBSC. have any observable character. And then they • Abélard (1079-1142, France): He articulated would also have to explain why some observable the generic form of the syllogism in a single systems seem to be understood by some people, but prose proposition. not by others. Finally, it is worth noting that when • Leibniz (1646-1716, Germany): He people propose some measurement of complexity, documented the use of graphical symbols to inevitably it will involve something that people assist in the analysis and portrayal of logical have thought about or perceived with no relationships. intervening machinery, as opposed to measuring • Boole and De Morgan (1815-1864 & something like the color blue, for example, which 1806-1871): They invented a calculus of can be subjected to physical instrumentation. propositions, a language of logic, and the Definition 2 The Structured-Based Science theory of relations, the fundamental formal of Complexity consists of the following language. components: • C. S. Peirce (1839-1914, USA): He expanded Chronologies which add historical and interpreted the theory of relations, and he perspective to the context; conceived and justified the philosophy of Definitions which serve essentially as the science. suppositions or axioms upon which the science is • Harary (1921-, USA): He united several founded; branches of mathematics to produce the Laws of Complexity which advise on analytical theory of structural models. expectations to be held under normal circumstances, In order to make decisions under complex which identify hurdles that methodology must situation, John N.