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This Concept Map, created with IHMC CmapTools, has information related to: m1. Complexity, New dynamic states of matter may arise, states that reflect the interaction of the system with its surroundings. These new structures are termed dissipative structures to emphasize their exchange of energy, matter, and information with their surroundings autocatolysis The characteristics of living systems can be attributed to transitions induced by non-equilibrium constraints and destabilizing mechanisms similar to chemical autocatalysis. the resemblance is quite striking. This can be one of the most fundamental questions which can be raised in science., 1811 – Fourier, “the founder of Complexity”. Heat flow is proportionate to the gradient of temperature. Concept was alien to the Newtonian world. ???? The effect of heat propagation is to progressively equalize the distribution of temperature until equilibrium is reached. That this process is irreversible signaled the end of the Newtonian world of reversible processes., In complex systems, there is no simple or predictable relationship between levels of resolution; and the properties of the whole are not predictable from a knowledge its parts order parameters The most conspicuous difference between conservative and dissipative systems is in the macroscopic description of dissipative systems in which the instantaneous state is defined by collective variables (order parameters, internal to the system); temperature; concentration; pressure and convection velocity., The characteristics of living systems can be attributed to transitions induced by non-equilibrium constraints and destabilizing mechanisms similar to chemical autocatalysis. the resemblance is quite striking. This can be one of the most fundamental questions which can be raised in science. historical evolution Living beings are historical structures in that they have the ability of preserving the forms and functions acquired in the past, during the long periods of evolution., Complexity occurs in that narrow regime in the evolution of a dynamic far-from-equilibrium system as it passes from the ordered state, and just before it reaches the critical point where it goes chaotic. dissipative Complex systems are "dissipative" in that they exchange energy, matter. and information with their surroundings., Matter near equilibrium behaves in a repetitive way; in far-from-equilibrium conditions there appears a variety of possibilities for various types of dissipative structures. chance Much of our everyday experience is unexpected, seemingly beyond our control. On the other hand, we also commonly take for granted the long-term, reliable functioning of refrigerators computers and communication satellites. How is it that some aspects of our experience are regular, predictable and tamable, while others appear to be the outcomes of some cosmic game of chance? It is a remarkable and mysterious fact that at least some pieces of the universe (the explainable ones) are best described in the language of mathematics., Equations describing this structure are not invariant (i.e., they vary) under time reversal and therefore events (in dynamic systems) are irreversible. history and arrow of time One of the essential features of complex behavior is the ability to perform transitions between different states. Complexity is concerned with systems in which evolution, and therefore history, plays an important role in the observed behavior., m1. Complexity ???? Systems at rest, or at equilibrium, are static and undifferentiated (disordered or lack of order). As external forces (control parameters) add energy, mass or information to the system, it moves farther and farther from equilibrium, and progresses through several phases. At the first critical point the system develops form and structure, differentiates into ordered behavior, and then passes through a second critical point, at which time it "goes chaotic"., The theory of dynamical systems' central discovery is the prevalence of instability around the critical points underlying their formation. This means that small changes in initial conditions may lead to large amplifications of the trajectory of the system. unforeseen consequences With the appearance of Complexity science, the process of understanding the world enters a new phase with two characteristics. 1) Control of natural phenomenon begin to slip out of the grasp of observers, both because sensitivity to initial conditions severely limits the possibilities of control and prediction; and because the properties of the whole are not predictable from knowledge of the parts so that manipulation results in unforeseen consequences. 2) These properties can never- the-less be made intelligible by utilizing higher concepts that capture their essential aspects., Living beings are historical structures in that they have the ability of preserving the forms and functions acquired in the past, during the long periods of evolution. alien concept 1811 – Fourier, “the founder of Complexity”. Heat flow is proportionate to the gradient of temperature. Concept was alien to the Newtonian world., Matter near equilibrium behaves in a repetitive way; in far-from-equilibrium conditions there appears a variety of possibilities for various types of dissipative structures. physical world The idea of complexity is extending into the physical worlds and is probably a fundamental feature of nature, Ordinary physico-chemical systems can show complex behavior similar to biological systems. living systems Living systems function under conditions far-from-equilibrium. The organism receives fluxes of energy from the sun (used by plants for photosynthesis) and matter (in the form of nutrients) which it transforms into waste products which are eliminated into the environment., Dissipative structures are forced into far-from-equilibrium conditions by random fluctuations, the original structure is threatened by approaching critical moments or “bifurcations”, which change the state of the system in unknowable ways, determined strictly by chance from among several (of many) possibilities. Once the new path is taken, it remains stable until the next bifurcation occurs. interactions Complex systems involve large numbers of INTERACTING components vs. simple systems with only one or a few components, The characteristics of living systems can be attributed to transitions induced by non-equilibrium constraints and destabilizing mechanisms similar to chemical autocatalysis. the resemblance is quite striking. This can be one of the most fundamental questions which can be raised in science. inhomogeneities At the cellular level strong inhomogeneities are present. For instance the concentration of potassium K+ is in excess outside the neuron while the concentration of sodium Na+ is higher inside the neuron. Such inequalities imply high states of non-equilibrium., As systems evolves from order to complexity, they may be transformed into entirely new and unexpected forms. This is one of the fundamental new properties of far-from-equilibrium. deterministic, dissipative systems no longer reductionist In complex systems, there is no simple or predictable relationship between levels of resolution; and the properties of the whole are not predictable from a knowledge its parts, Equations describing this structure are not invariant (i.e., they vary) under time reversal and therefore events (in dynamic systems) are irreversible. agents A non-equilibrium constraint is an organizing factor not affected by intermolecular interactions. It encompasses parts of the system containing huge numbers of agents and new phenomena enjoying long range correlations are born., In far-from-equilibrium conditions a new type of order may appear. There is a new coherence among molecules. They “communicate” with each other. This type of communication is common in biology, and may be the very definition of biological systems. feature of nature The idea of complexity is extending into the physical worlds and is probably a fundamental feature of nature, Complexity emerges from processes that occur over and over again in an iterative fashion chance Dissipative structures are forced into far-from-equilibrium conditions by random fluctuations, the original structure is threatened by approaching critical moments or “bifurcations”, which change the state of the system in unknowable ways, determined strictly by chance from among several (of many) possibilities. Once the new path is taken, it remains stable until the next bifurcation occurs., Algorhythmic complexity is a sequence of data the minimum length of which is an algorhythm which would produce the same sequence as an output. iteration Iterative processes are a major source of Complexity., The theory of dynamical systems' central discovery is the prevalence of instability around the critical points underlying their formation. This means that small changes in initial conditions may lead to large amplifications of the trajectory of the system. multiple states Our world is actually one in which deterministic as well as stochastic phenomena, reversible as well as irreversible phenomena, and simple and complex exist side by side