The σ profile is presented as a tool to analyze the organization of systems at different scales, and how this organization changes in time. Describing structures at different scales as goal‐oriented agents, one can define σ ∈ [0,1] (satisfaction) as the degree to which the goals of each agent at each scale have been met. σ reflects the organization degree at that scale. The σ profile of a system shows the satisfaction at different scales, with the possibility to study their (...) dependencies and evolution. It can also be used to extend game theoretic models. The description of a general tendency on the evolution of complexity and cooperation naturally follows from the σ profile. Experiments on a virtual ecosystem are used as illustration. (shrink)

Entropy is one of the physical bases for the fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using the fractal dimension, we can describe urban growth and form and characterize spatial complexity. A number of fractal models and measurements have been proposed for urban studies. However, the precondition for fractal dimension application is to find scaling relations in cities. In the absence of the scaling property, we can make use of the entropy function and measurements. (...) This paper is devoted to researching how to describe urban growth by using spatial entropy. By analogy with fractal dimension growth models of cities, a pair of entropy increase models can be derived, and a set of entropy-based measurements can be constructed to describe urban growing process and patterns. First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. Second, a series of indexes based on spatial entropy are used to characterize urban form. Furthermore, multifractal dimension spectra are generalized to spatial entropy spectra. Conclusions are drawn as follows. Entropy and fractal dimension have both intersection and different spheres of application to urban research. Thus, for a given spatial measurement scale, fractal dimension can often be replaced by spatial entropy for simplicity. The models and measurements presented in this work are significant for integrating entropy and fractal dimension into the same framework of urban spatial analysis and understanding spatial complexity of cities. (shrink)

Contemporary complexity theory has been instrumental in providing novel rigorous definitions for some classic philosophical concepts, including emergence. In an attempt to provide an account of emergence that is consistent with complexity and dynamical systems theory, several authors have turned to the notion of constraints on state transitions. Drawing on complexity theory directly, this paper builds on those accounts, further developing the constraint-based interpretation of emergence and arguing that such accounts recover many of the features of more traditional accounts. We (...) show that the constraint-based account of emergence also leads naturally into a meaningful definition of self-organization, another concept that has received increasing attention recently. Along the way, we distinguish between order and organization, two concepts which are frequently conflated. Finally, we consider possibilities for future research in the philosophy of complex systems, as well as applications of the distinctions made in this paper. (shrink)

Climatology is a paradigmatic complex systems science. Understanding the global climate involves tackling problems in physics, chemistry, economics, and many other disciplines. I argue that complex systems like the global climate are characterized by certain dynamical features that explain how those systems change over time. A complex system's dynamics are shaped by the interaction of many different components operating at many different temporal and spatial scales. Examining the multidisciplinary and holistic methods of climatology can help us better understand the nature (...) of complex systems in general. -/- Questions surrounding climate science can be divided into three rough categories: foundational, methodological, and evaluative questions. "How do we know that we can trust science?" is a paradigmatic foundational question (and a surprisingly difficult one to answer). Because the global climate is so complex, questions like "what makes a system complex?" also fall into this category. There are a number of existing definitions of `complexity,' and while all of them capture some aspects of what makes intuitively complex systems distinctive, none is entirely satisfactory. Most existing accounts of complexity have been developed to work with information-theoretic objects (signals, for instance) rather than the physical and social systems studied by scientists. -/- Dynamical complexity, a concept articulated in detail in the first third of the dissertation, is designed to bridge the gap between the mathematics of contemporary complexity theory (in particular the formalism of "effective complexity" developed by Gell-Mann and Lloyd [2003]) and a more general account of the structure of science generally. Dynamical complexity provides a physical interpretation of the formal tools of mathematical complexity theory, and thus can be used as a framework for thinking about general problems in the philosophy of science, including theories, explanation, and lawhood. -/- Methodological questions include questions about how climate science constructs its models, on what basis we trust those models, and how we might improve those models. In order to answer questions about climate modeling, it's important to understand what climate models look like and how they are constructed. Climate model families are significantly more diverse than are the model families of most other sciences (even sciences that study other complex systems). Existing climate models range from basic models that can be solved on paper to staggeringly complicated models that can only be analyzed using the most advanced supercomputers in the world. I introduce some of the central concepts in climatology by demonstrating how one of the most basic climate models might be constructed. I begin with the assumption that the Earth is a simple featureless blackbody which receives energy from the sun and releases it into space, and show how to model that assumption formally. I then gradually add other factors (e.g. albedo and the greenhouse effect) to the model, and show how each addition brings the model's prediction closer to agreement with observation. After constructing this basic model, I describe the so-called "complexity hierarchy" of the rest of climate models, and argue that the sense of "complexity" used in the climate modeling community is related to dynamical complexity. -/- With a clear understanding of the basics of climate modeling in hand, I then argue that foundational issues discussed early in the dissertation suggest that computation plays an irrevocably central role in climate modeling. "Science by simulation" is essential given the complexity of the global climate, but features of the climate system--the presence of non-linearities, feedback loops, and chaotic dynamics--put principled limits on the effectiveness of computational models. This tension is at the root of the staggering pluralism of the climate model hierarchy, and suggests that such pluralism is here to stay, rather than an artifact of our ignorance. Rather than attempting to converge on a single "best fit" climate model, we ought to embrace the diversity of climate models, and view each as a specialized tool designed to predict and explain a rather narrow range of phenomena. Understanding the climate system as a whole requires examining a number of different models, and correlating their outputs. This is the most significant methodological challenge of climatology. -/- Climatology's role contemporary political discourse raises an unusually high number of evaluative questions for a physical science. The two leading approaches to crafting policy surrounding climate change center on mitigation (i.e. stopping the changes from occurring) and adaptation (making post hoc changes to ameliorate the harm caused by those changes). Crafting an effective socio-political response to the threat of anthropogenic climate change, however, requires us to integrate multiple perspectives and values: the proper response will be just as diverse and pluralistic as the climate models themselves, and will incorporate aspects of both approaches. I conclude by offering some concrete recommendations about how to integrate this value pluralism into our socio-political decision making framework. (shrink)