ABSTRACT
The aim of this paper is to understand the dynamics of the theory of order in the nineteenth century and to reveal a specific approach to mathematics, science, philosophy and decorative art in which order plays a prominent role. We will analyze the singular meaning that Poinsot assigns to the notion of order in the mathematical sciences, before describing the circulation of his writings on the order in the nineteenth century. Poinsot is one of the main sources of Cournot, who places the notions of order and form as the basis of his knowledge system. Then we will study the writings of Bourgoin who develops a combinatorics of ornaments based on the categories of order and form.
Subject(s)
Mathematics/history , History, 19th Century , History, 20th Century , Humans , Nonlinear Dynamics/history , Philosophy/history , ProbabilityABSTRACT
Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites.
Subject(s)
Art/history , Creativity , Nonlinear Dynamics/history , History, 20th Century , HumansABSTRACT
The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined.
Subject(s)
Nonlinear Dynamics/history , Psychological Theory , Psychology/history , History, 20th Century , History, 21st Century , Humans , United StatesABSTRACT
Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century, when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely, although they can be predicted to some extent, in line with the chaos theory. Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory. This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms.
Subject(s)
Mathematics , Models, Biological , Models, Theoretical , Nonlinear Dynamics/history , History, 17th CenturyABSTRACT
Even though our view of the physical world has shifted from that of determinism to randomness, randomness itself can now be exploited to retrieve a system's deterministic response.
Subject(s)
Nonlinear Dynamics , History, 19th Century , History, 20th Century , Noise , Nonlinear Dynamics/history , Sound , Trees/physiologyABSTRACT
How is it that form arises out of chaos? In attempting to deal with this primary question, time and again a "Missing Third" is posited that lies between extremes. The problem of the "Missing Third" can be traced through nearly the entire history of thought. The form it takes, the problems that arise from it, the solutions suggested for resolving it, are each representative of an age. This paper traces the issue from Plato and Parmenides in the 4th--5th centuries, B.C.; to Neoplatonism in the 3rd--5th centuries; to Locke and Descartes in the 17th century; on to Berkeley and Kant in the 18th century; Fechner and Wundt in the 19th century; to behaviorism and Gestalt psychology, Jung, early in the 20th century, ethology and cybernetics later in the 20th century, then culminates late in the 20th century, with chaos theory.
Subject(s)
Biological Science Disciplines/history , Neurosciences/history , Nonlinear Dynamics/history , Philosophy/history , Animals , History, 15th Century , History, 16th Century , History, 17th Century , History, 18th Century , History, 19th Century , History, 20th Century , History, Ancient , History, Medieval , HumansABSTRACT
La teoría del caos permite modelar y explicar el cambio; en particular los cambios abruptos, las discontinuidades que desmienten periódicamente la creencia en que Natura non facit saltum. El particular atractivo de esta teoría es que el mismo modelo que genera comportamientos estables da lugar también a conductas caóticas. En realidad, el caos es tan sólo una de las alternativas que presentan los sistemas dinámicos no lineales. Se comienza por definir qué es un sistema dinámico no lineal, qué es un atractor y, en particular, qué es un atractor caótico. Se muestra cómo un sistema estable deja de serlo y, a través de bifurcaciones sucesivas, emprende la ruta del caos. Finalmente, se analizan algunas posibles implicancias de la teoría del caos, particularmente en cuanto a la predecibilidad e impredecibilidad de los fenómenos. Se analiza la relación entre la teoría del caos y la estadística tradicional. (AU)
Subject(s)
Nonlinear Dynamics/history , Models, Theoretical , Fractals , Science/history , KnowledgeABSTRACT
La teoría del caos permite modelar y explicar el cambio; en particular los cambios abruptos, las discontinuidades que desmienten periódicamente la creencia en que Natura non facit saltum. El particular atractivo de esta teoría es que el mismo modelo que genera comportamientos estables da lugar también a conductas caóticas. En realidad, el caos es tan sólo una de las alternativas que presentan los sistemas dinámicos no lineales. Se comienza por definir qué es un sistema dinámico no lineal, qué es un atractor y, en particular, qué es un atractor caótico. Se muestra cómo un sistema estable deja de serlo y, a través de bifurcaciones sucesivas, emprende la ruta del caos. Finalmente, se analizan algunas posibles implicancias de la teoría del caos, particularmente en cuanto a la predecibilidad e impredecibilidad de los fenómenos. Se analiza la relación entre la teoría del caos y la estadística tradicional.
Subject(s)
Nonlinear Dynamics/history , Models, Theoretical , Science/history , Fractals , KnowledgeABSTRACT
A compact glance at the history and impact of mathematical models in development provides background for predicting the fate of dynamical systems modeling in developmental psychology. Dynamic models are considered and the articles by Thelen and Ulrich (1991) and van Geert (1991) are summarized. Deterministic and probabilistic models are compared and some cautions are presented along with a consideration of forms that can be attained by linear models in comparison to those well known in logistic difference models. Reactions to the research by Rabinowitz, Grant, Howe, and Walsh; Kreindler and Lumsden; and Cooney and Troyer are given, with some concluding remarks on survival of dynamical systems modeling in developmental psychology.
