How does Lawhead's concept of "dynamical complexity" specifically address the limitations of existing complexity definitions by providing a "physical interpretation" for physical and social systems, rather than just "information-theoretic objects"?

From the book

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…

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…

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…

semble is high in effective complexity. This resolves the central criticism of the algorithmic information content (i.e. Shannon) approach to defining complexity, and seems to accord better with our intuitions about what should and should not count as complex. What, then, is the relationship between effective complexity and dynamical complexity? Moreover, if effective complexity is the right way to formalize the intuitions behind complexity, why is this the case? What’s the physical root of this formalism? To answer these questions, let’s look at one of the very few papers yet written that…