Statistical Mechanics and the Foundations of Thermodynamics (1928)

Question

If "dynamical complexity" provides a "physical interpretation of the formal tools of mathematical complexity theory," what specific insights might this offer for understanding fundamental concepts like "theories, explanation, and lawhood" within the philosophy of science?

Synthesized answer

Dynamical complexity offers a physical interpretation of the formal tools of mathematical complexity theory, serving as a framework for understanding fundamental philosophical concepts in science such as theories, explanation, and lawhood [1]. It provides a way to bridge the gap between abstract mathematical formalisms and the study of physical and social systems [1].

This approach helps in understanding how scientists identify new ways to describe the world, making different patterns in how the world changes over time salient [4]. Dynamical complexity captures how fruitful and difficult scientific inquiry into a system's behavior is likely to be [4]. It takes into account the multiplicity of ways physical systems can be described and relates the abstraction described by mathematicians to the actual practice of scientists [3]. The passages do not elaborate on the *specific* insights dynamical complexity offers for understanding theories, explanation, and lawhood, but rather state that it can be *used* as a framework for these considerations [1].

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…
Passage [4]
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…
Passage [205]
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…
Passage [194]
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…
Passage [196]
ic quantum mechanics, for instance, still hasn’t been answered to the satisfaction of either philosophers or physicists. Philosophical attention to the measurement problem in the mid-20 century led directly to the overthrow of the Copenhagen Interpretation, and (more recently) to work on decoherence and einselection (e.g. Zurek [2003]). For an accessible survey of some of the ways in which philosophical thinking has contributed to physics in the 20 century, see Maudlin (2007). For examples of excellent current work in these areas, see Wallace (2011) and (2009), as well as Albert (2000). ↑…
Passage [368]

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