Synthesized answer
The passages suggest that existing definitions of complexity often focus on information-theoretic objects like messages or strings [1, 2]. These definitions can be related to the length of the shortest computer program that can generate a given string [5]. This perspective might describe a system based on its information content or the compressibility of its representation.
In contrast, dynamical complexity offers a physical interpretation of these mathematical advancements, focusing on the "dynamical features" of a physical system [1, 2]. It is described as a fact about the "pattern-richness of the system’s location in the configuration space defined by fundamental physics" [3]. Equivalently, it's about "how many predictively useful ways the system can be carved up" [3]. This means dynamical complexity is a fact about how a system behaves, specifically concerning the number of perspectives that can be adopted to predict its future changes [4]. The passages do not provide a simple, non-climatic example to illustrate this difference directly.
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
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…
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…
ad of me is just that the system containing me can be usefully carved up in more ways than the system containing my cat. My brain is more complex than my cat’s brain in virtue of there being more ways to compress systems containing my brain such that the time-evolution of those states can be reliably predicted than there are ways to compress systems containing my cat’s brain such that the same is true. The global climate today is more complex than was the global climate 1 billion years ago in virtue of there being more ways to usefully carve up the climate system today than there were 1…
mplex systems look like; whatever complexity is, a box of gas at perfect thermodynamic equilibrium sure doesn’t have it. This observation has led a number of information theorists and computer scientists to look for a refinement on the naïve information-theoretic account. A number of authors have been independently successful in this attempt, and have produced a successor theory called “effective complexity.” Let’s get a brief sense of the formalism behind this view (and how it resolves the problem of treating random strings as highly complex), and then examine how it relates to the account…
More questions about this book
- The text introduces "Dynamical complexity" as a concept designed to bridge mathematical complexity theory with a general account of science. If you were explaining this concept to someone with no background, what specific problem does "dynamical complexity" aim to solve that existing definitions of complexity, primarily developed for information-theoretic objects, fail to address for physical and social systems?
- 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?
- 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?