Synthesized answer
Dynamical complexity, as a framework for thinking about "theories, explanation, and lawhood" [1], could deepen philosophical understanding of **theories** by offering a physical interpretation of the formal tools of mathematical complexity theory. This interpretation takes into account the multiplicity of ways physical systems can be described [3], and relates the abstraction described by Gell-Mann to the actual practice of scientists [3]. Theories, within this framework, might be understood in terms of how they carve up the world to make different patterns in how systems change over time salient [4]. The fruitfulness and difficulty of scientific inquiry into a given system's behavior could be captured by dynamical complexity [4].
However, the passages do not elaborate on how dynamical complexity specifically reshapes philosophical understanding of theories, beyond suggesting it provides a conceptual tool and a way to relate abstract mathematical frameworks to scientific practice. The passages focus more on defining dynamical complexity and its connection to identifying patterns in changing systems [4] and its application to understanding complex systems [5].
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
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…
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…
or effective complexity, we can perfectly coherently talk about summing all the useful ways given our goals and values . The value of this sum will change as we make new scientific discoveries—as we discover new patterns in the world that are worth paying attention to—but this again just serves to emphasize the point from Chapter One : the world is messy, and science is hard. Complexity theory is part of the scientific project, and so inherits all the difficulties and messiness from the rest of the project. Dynamical complexity, in other words, offers a natural physical interpretation for the…
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…
verall. Chapters Two and Three taken together are primarily a contribution to the foundations of complex-systems theory. Building on the account of science from Chapter One , I argue that the traditional bifurcation of science into physical and social sciences is, at least sometimes, misleading. I suggest that we should also see some scientific problems in terms of a distinction that cuts across the physical/social science division: the distinction between complex-systems sciences and simple-systems sciences. After reviewing some of the attempts to define "complexity" in the (relatively…
More questions about this book
- The text suggests existing definitions of complexity are not "entirely satisfactory" for physical and social systems. How does Lawhead's "Dynamical complexity" aim to bridge the gap between mathematical complexity theory and these real-world systems, and what makes its "physical interpretation" crucial for this endeavor?
- Lawhead calls climatology a "paradigmatic complex systems science." Beyond simply stating its multidisciplinary nature, what specific attributes of climatology, as described, make it an *ideal* case study for understanding the "dynamical features" and the "interaction of many different components operating at many different temporal and spatial scales" characteristic of complex systems in general?
- Given that "How do we know that we can trust science?" is a "paradigmatic foundational question" for complex systems, how might Lawhead's concept of 'Dynamical complexity' offer a novel approach or framework for understanding and addressing the basis of scientific trust, especially in light of how these systems change over time?
- The excerpt notes that climate model families are "significantly more diverse" than in most other sciences. How does this diversity, coupled with the difficulties in answering the foundational question "what makes a system complex?", directly influence the "methodological questions" of how climate science constructs, trusts, and improves its models?