Synthesized answer
"Dynamical complexity" aims to bridge mathematical complexity theory with a general account of science, providing a physical interpretation of its formal tools [1]. It seeks to transform discussions of complexity that work well for information-theoretic objects, like messages, into an account that functions effectively for physical and social systems, such as climate systems [2].
The specific problem "dynamical complexity" addresses that existing definitions fail to is their focus on the static state of a system. Previous attempts have overlooked that complexity, as it concerns science, is a feature of active, changing, and evolving systems [4]. "Dynamical complexity," on the other hand, tracks facts about how systems change over time and acknowledges that this change can be tracked in numerous ways, even for a single system [4].
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From the book
formation-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…
up that project, and present a novel account of what it means for a physical system to be complex in the relevant sense. This concept, which I will call dynamical complexity , is presented as a physical interpretation of some very recent mathematical advancements in the field of information theory. The central problem that shall occupy us in the next chapter, then, is how to transform a discussion of complexity that seems to work very well for things like messages into an account that works well for things like climate systems. My hope is that dynamical complexity offers this bridge. Once…
and that moreover, the nature of complexity is such that it is likely that no single unifying definition is forthcoming. Rather, we should aim at a constellation of related notions of complexity, each of which is tailored to the different purposes toward which complexity theory might be used. I proposed the concept of dynamical complexity as best capturing the aspects of the varied proxy concepts we considered that are most relevant to scientists seeking to understand active, dynamical complex systems in the natural world (as opposed to, say, those interested in studying aspects of abstract…
ical complexity is that complexity, at least as it concerns science, is a feature of active, changing, evolving systems. Previous attempts to define complexity have overlooked this fact to one degree or another, and have tried to account for complexity primarily in terms of facts about the static state of a system. Dynamical complexity, on the other hand, tracks facts about how systems change over time, and (moreover) embraces the notion that change over time can be tracked in numerous different ways, even for a single system. If our account of science from Chapter One is right—if science is…
more general notion. 2.1 Dynamical Complexity With a more concrete goal at which to aim, then, let’s see what we can do. In this section, I will attempt to synthesize the insights in the different measures of complexity discussed above under a single banner—the banner of dynamical complexity . This is a novel account of complexity which will (I hope) allow us to make sense of both our intuitive judgments about complexity and open the door to making those judgments somewhat more precise. Ultimately, remember, our goal is to give a concept which will allow us to reliably differentiate between…
More questions about this book
- Climatology is presented as a "paradigmatic complex systems science" due to the interaction of many different components at varying temporal and spatial scales. How does this multifaceted interaction specifically challenge our ability to predict system changes over time, and in what ways does a "multidisciplinary and holistic" approach address these predictive challenges?
- The author notes that foundational questions include "How do we know that we can trust science?" when facing a complex system. If "Dynamical complexity" provides a physical interpretation of mathematical tools, how might this physical interpretation directly enhance our ability to build and justify trust in scientific models for complex systems like the climate, particularly concerning their predictions and explanations?
- The text mentions that existing definitions of 'complexity' are often developed for information-theoretic objects. How would you illustrate, using a simple, non-climatic example, the difference in understanding a system's "dynamical features" when viewed through an information-theoretic lens versus the "physical interpretation" offered by dynamical complexity?
- Considering that "Dynamical complexity provides a physical interpretation of the formal tools of mathematical complexity theory" and serves as a framework for understanding "theories, explanation, and lawhood," how might its application fundamentally alter our understanding of what constitutes a 'scientific explanation' for events or phenomena within a highly complex, multidisciplinary field like climatology?