Complexity Explorer Santa Fe Institute


Dynamics of Complex Systems

Abstract: "'Complex' is a word of the times, as in the often-quoted “growing complexity of life.” Science has begun to try to understand complexity in nature , a counterpoint to the traditional scientific objective of understanding the fundamental simplicity of laws of nature. It is believed ,however, that even in the study of complexity there exist simple and therefore comprehensible laws . The field of study of complex systems holds that the dynamics of complex systems are founded on universal principles that may be used to describe disparate problems ranging from particle physics to the economics of societies . A corollary is that transferring ideas and results from investigators in hitherto disparate areas will cross-fertilize and lead to important new results. In this text we introduce several of the problems of science that embody the concept of complex dynamical systems. Each is an active area of research that is at the forefront of science. Our presentation does not try to provide a comprehensive review of the research literature available in each area. Instead we use each problem as an opportunity for discussing fundamental issues that are shared among all areas and therefore can be said to unify the study of complex systems. We do not expect it to be possible to provide a succinct definition of a complex system. Instead, we give examples of such systems and provide the elements of a definition. It is helpful to begin by describing some of the attributes that characterize complex systems. Complex systems contain a large number of mutually interacting parts. Even a few interacting objects can behave in complex ways. However, the complex systems that we are interested in have more than just a few parts.And yet there is generally a limit to the number of parts that we are interested in. If there are too many parts, even if these parts are strongly interacting, the properties of the system become the domain of conventional thermodynamics—a uniform material. Thus far we have defined complex systems as being within the mesoscopic domain— containing more than a few, and less than too many parts.However, the mesoscopic regime describes any physical system on a particular length scale,and this is too broad a definition for our purposes. Another characteristic of most complex dynamical systems is that they are in some sense purposive.This means that the dynamics of the system has a definable objective or function. There often is some sense in which the systems are engineered.We address this topic directly when we discuss and contrast self-organization and organization by design. A central goal of this text is to develop models and modeling techniques that are useful when applied to all complex systems. For this we will adopt both analytic tools and computer simulation. Among the analytic techniques are statistical mechanics and stochastic dynamics.Among the computer simulation techniques are cellular automata and Monte Carlo. Since analytic treatments do not yield complete theories of complex systems, computer simulations play a key role in our understanding of how these systems work. The human brain is an important example of a complex system formed out of its component neurons. Computers might similarly be understood as complex interacting systems of transistors.Our brains are well suited for understanding complex systems, but not for simulating them. Why are computers better suited to simulations of complex systems? One could point to the need for precision that is the traditional domain of the computer. However, a better reason would be the difficulty the brain has in keeping track of many and arbitrary interacting objects or events---we can typically remember seven independent pieces of information at once. The reasons for this are an important part of the design of the brain that make it powerful for other purposes. The architecture of the brain will be discussed beginning in Chapter 2. The study of the dynamics of complex systems creates a host o f new interdisciplinary fields. It not only breaks down barriers between physics, chemistry and biology, but also between these disciplines and the so-called soft sciences of psychology, sociology, economics,and anthropology.As this breakdown occurs it becomes necessary to introduce or adopt a new vocabulary. Included in this new vocabulary are words that have been considered taboo in one area while being extensively used in another. These must be adopted and adapted to make them part of the interdisciplinary discourse. One example is the word “mind.” While the field of biology studies the brain,the field of psychology considers the mind.However, as the study of neural networks progresses,it is anticipated that the function of the neural network will become identified with the concept of mind. Another area in which science has traditionally been mute is in the concept of meaning or purpose. The field of science traditionally has no concept of values or valuation. Its objective is to describe natural phenomena without assigning positive or negative connotation to the description. However, the description of complex systems requires a notion of purpose, since the systems are generally purposive. Within the context of purpose there may be a concept of value and valuation. If, as we will attempt to do, we address society or civilization as a complex system and identify its purpose, then value and valuation may also become a concept that attains scientific significance . There are even further possibilities of identifying value, since the very concept of complexity allows us to identify value with complexity through its difficulty of replacement. As is usual with any scientific advance, there are both dangers and opportunities with such developments. Finally, it is curious that the origin and fate of the universe has become an accepted subject of scientific discourse—cosmology and the big bang theory—while the fate of humankind is generally the subject of religion and science fiction. There are exceptions to this rule, particularly surrounding the field of ecology—limits to population growth, global warming—however, this is only a limited selection of topics that could be addressed. Overcoming this limitation may be only a matter of having the appropriate tools. Developing the tools to address questions about the dynamics of human civilization is appropriate within the study of complex systems. It should also be recognized that as science expands to address these issues, science itself will change as it redefines and changes other fields. Different fields are often distinguished more by the type of questions they ask than the systems they study. A significant effort has been made in this text to articulate questions, though not always to provide complete answers, since questions that define the field of complex systems will inspire more progress than answers at this early stage in the development of the field."

Y. Bar-Yam
mesoscopic; cellular automata; Monte Carlo simulation

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