The timescale of neural firing is nested within the timescale of cognition, which is nested within the timescale of behavior over learning and development. As a representative example, consider mathematical equivalence problems with addends on both sides of the equal sign (e.g., 3 + 4 + 6 = 3 + __). The thermodynamics sources are not the traditional ones; rather they are modeled after recent chaos theories (Gleick, 1987). Dynamic systems theories conceptualize development as change within a complex system that involves interactions of multiple factors at different levels and on different timescales (e.g., Smith & Thelen, 2003; From: Advances in Child Development and Behavior, 2019, Barbara M. Newman, Philip R. Newman, in Theories of Adolescent Development, 2020. The last foundational concept is the nesting of timescales. The interest in them here is that they differ from one another in their assumptions about the structure–function relation, although they otherwise have much in common. Control parameters may include factors at different levels and on different timescales. Harry Beilin, in Advances in Child Development and Behavior, 1994, Dynamic system theories share with neuroscience theories the adoption of models from outside of psychology itself. This metaphor is useful in understanding the “dynamic cascade” of development (Thelen & Smith, 2006, p. 263). It had been assumed for a long time that determinism implied predictability or if the behavior of a system was completely determined, for example by differential equation, then the behavior of the solutions of that system could be predicted for-ever after. Systems are historical, which means that their organization in an attractor state in the moment biases them to revisit those attractor states at a future point in time (Spencer & Perone, 2008). Generalized Ratio Control of Discrete-Time Systems. Approaches to measurement include case studies, mathematical simulation models, social network analysis, and state space grids. In a linear system the phase space is the N-dimensional Euclidean space, so any point in phase space can be represented by a vector with N numbers. The phase line 19 2.4. Chief among the contributions of dynamic systems theory is a set of concepts facilitating examination of overall patterns of change. From a dynamical systems perspective, the human movement system is a highly intricate network of co-dependent sub-systems Does God play dice? What appears to happen is that the children start to relate the three variables of height, width, and quantity, as mentioned before. 1.2 Nonlinear Dynamical Systems Theory Nonlinear dynamics has profoundly changed how scientist view the world. Its intellectual roots are traced to mathematics, astronomy, physics, meteorology, and biology. Further, within any set of possible behavior patterns, some patterns are more likely to emerge than others. In its contem porary form ula-tion, the theory g row s d irectly from advances in under-stand ing com plex and nonlinear system s in physics and m athem atics, but it also follow s a long and rich trad i-tion of system s th in k ing in biology and psychology. Then there is the way an object appears to people (the percept), such as whether they see it as white or blue. The mountain stream metaphor is useful in conceptualizing these ideas: current weather patterns that influence how quickly (or slowly) the mountain snow melts to create the stream, the molecular composition of the water and how this impacts the pace and flow of the current, and the mountain’s vegetation and its impact on evaporative processes. That is, they realize that when you take both height and width into account, quantity remains constant, or is “conserved.” Here the three variables are brought into a new integration, which creates a new form of stability. Historical geological factors that act over periods of time also help to shape present-day patterns. Copyright © 2021 Elsevier B.V. or its licensors or contributors. New York: Guilford Press. The contributions to behavior in the moment include a person's body, age, mental state, emotional state, social context, personal history, and more. As we illustrate in subsequent sections, however, we contend that multicausality can inform research design, implementation, and interpretation through the questions we ask with our studies, the way in which we gather information, and how we extrapolate from our results. Dynamic systems can show how a complex, self-regulating system can emerge from the interaction of a few variables, and offer natural interpretations of concepts such as equilibration and self-regulation which are at the core of the theories of both Piaget and Vygotsky. Kauffman, S. (1995). G.S. S. Perone, V.R. Dynamic systems theory addresses the process of change and development, rather than developmental outcomes; in dynamic systems terms, there is no end point of development (Thelen & Ulrich, 1991). T he This approach: Dreams and Memory Consolidation longer-term developmental transformations framework for studying how systems as valuable research tools specific. Consists of generating simulations of the interactions of multiple factors in processes of strategy change, Tyson R.. In Advances in Child development and behavior, 2008 via massive quantities of real-time processes that occur multiple. 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