Levels of Description: A Novel Approach to Dynamical Hierarchies (original) (raw)
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In [2], Mark Bedau et al. proposed a set of fourteen open problems in artificial life. The content of this special issue specifically addresses one of those suggested problems: How can we create a formal framework for synthesizing dynamical hierarchies at all scales? The dynamical hierarchy concept refers to a system that consists of multiple levels of organization having dynamics within and between the entities described at each of the different levels.
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We address the nature of information from a systemic structural point of view. Starting from the Natural hierarchy of living systems, we elucidate its decomposition into two partial hierarchies associated with its extant levels and inter-level regions, respectively. External observation of a hierarchical system involves the generation of approximate hyperscalar representations of these two partials, which then reintegrate to give a singular metascalar result. We relate Havel's categories of reality and Peirce's categories of experience to this result, and indicate that the ultimate result of the reintegration of hyperscalar data and context is a sign which is information.
PRE-PRINT of: Dorin, A., McCormack, J., "Self-Assembling Dynamical Hierarchies
2004
This paper addresses the open problem of assembling multilevelled hierarchical structure. It presents a model of an infinitely-levelled, self-assembling dynamical hierarchy which arises from the interaction of geometric primary elements with a fixed complexity. A formal description of the presented hierarchy is derived. This quantifies the relative compression achieved by describing the system in terms of components of different organization. The relationship between properties of representations and those of physical objects is then discussed to support the view that at each level in the hierarchy presented, the components exhibit emergent properties not possessed by those at the levels below. It is concluded that these new properties are trivial and that such infinitely-levelled structures may be constructed easily. However since the definition of the problem in the literature admits such trivial possibilities, further discussion is required to ensure "interesting" emergent properties are clearly distinguished from those that are not.
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On the modelling of dynamical hierarchies: Introduction to the workshop WDH 2002
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International Society for Systems Science - 2018 Conference Papers, 2018
A single holistic theory for how the universe is organized, and how its diversity of scales and systems coordinate and perform together, may yet be obtainable. But not within the current paradigms. We are stopped by some foundational misunderstandings within mathematics that forced the impasse we are currently at-especially the discontinuity between relativity and quantum mechanics-especially the discontinuity between physics/chemistry and biology/sociology/economics. A solution is presented, illuminating and defining mathematical relations previously ignored/unidentified. A third model that interfaces Prigogine's statistical emergence of complexity and Mandelbot's fractal (non-statistical) emergence of complexity.
Complexity and Dynamical Depth
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We argue that a critical difference distinguishing machines from organisms and computers from brains is not complexity in a structural sense, but a difference in dynamical organization that is not well accounted for by current complexity measures. We propose a measure of the complexity of a system that is largely orthogonal to computational, information theoretic, or thermodynamic conceptions of structural complexity. What we call a system's dynamical depth is a separate dimension of system complexity that measures the degree to which it exhibits discrete levels of nonlinear dynamical organization in which successive levels are distinguished by local entropy reduction and constraint generation. A system with greater dynamical depth than another consists of a greater number of such nested dynamical levels. Thus, a mechanical or linear thermodynamic system has less dynamical depth than an inorganic self-organized system, which has less dynamical depth than a living system. Including an assessment of dynamical depth can provide a more precise and systematic account of the fundamental difference between inorganic systems (low dynamical depth) and living systems (high dynamical depth), irrespective of the number of their parts and the causal relations between them.