Edge of Chaos

To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization? 

Keywords: Complex adaptive systems (CAS); Complexity theory; Biocybernetics; Biosemiotics; Emergence; Non linear dynamics; Self-organization; Symbolic dynamics analysis; Systems theory.

Complexity,” “self-organization,” and “emergence” are terms used extensively in life-origin literature. Yet precise and quantitative definitions of these terms are sorely lacking. “Emergence at the edge of chaos” invites vivid imagination of spontaneous creativity. Unfortunately, the phrase lacks scientific substance and explanatory mechanism. We explore the meaning, role, and relationship of complexity at the edge of chaos along with self-organization. We examine their relevance to life-origin processes. The high degree of order and pattern found in “necessity” (the regularities of nature described by the “laws” of physics) greatly reduce the uncertainty and information retaining potential of spontaneously-ordered physical matrices. No as-of-yet undiscovered law, therefore, will be able to explain the high information content of even the simplest prescriptive genome. Maximum complexity corresponds to randomness when defined from a Kolmogorov perspective. No empirical evidence exists of randomness (maximum complexity) generating a halting computational program. Neither order nor complexity is the key to function. Complexity demonstrates no ability to compute. Genetic cybernetics inspired Turing’s, von Neumann’s, and Wiener’s development of computer science. Genetic cybernetics cannot be explained by the chance and necessity of physicodynamics. Genetic algorithmic control is fundamentally formal, not physical. But like other expressions of formality, it can be instantiated into a physical matrix of retention and channel transmission using dynamically-inert configurable switches. Neither parsimonious law nor complexity can program the efficacious decision-node logic-gate settings of algorithmic organization observed in all known living organisms.

The text describes the ability of school’s function on the edge of chaos. For this purpose, applied is the concept of institutions on the edge of chaos by S.L. Brown and K.M. Eisenhardt. Such a thinking about the school’s functioning, although it seems optimal, doesn’t be possible yet. Schools in Poland are not ready for such a radical change yet.

Our ability to adapt to the relentless change of modern society and to transform how we see the world are essential to our survival in these complex times. However, we are rapidly losing that race as increasing complexity overtakes our ability to build our adaptive and transformative capacity. Transformative learning and systems literacy are essential components to turning that tide. This paper gives an overview of transformative learning theory and applies a systems and complexity framework to that process to create a foundation for transformative change. It covers the concepts of the disorienting dilemma, critical reflection, dialogue, and meaning making at the edge of chaos.

The text describes the ability of school’s function on the edge of chaos. For this purpose, applied is the concept of institutions on the edge of chaos by S.L. Brown and K.M. Eisenhardt. Such a thinking about the school’s functioning, although it seems optimal, doesn’t be possible yet. Schools in Poland are not ready for such a radical change yet.

A dynamical system description of the transition process in shear flows with no linear instability starts with knowledge of exact coherent solutions, among them traveling waves (TWs) and relative periodic orbits (RPOs). We describe a numerical method to find such solutions in pipe flow and apply it in the vicinity of a Hopf bifurcation from a TW which looks to be especially relevant for transition. The dominant structural feature of the RPO solution is the presence of weakly modulated streaks. This RPO, like the TW from which it bifurcates, sits on the laminar-turbulent boundary separating initial conditions which lead to turbulence from those which immediately relaminarize.

We propose a general strategy for determining the minimal finite amplitude disturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At and above this threshold, the optimising search naturally seeks out disturbances that trigger turbulence by the end of the period, and convergence is then practically impossible. The first disturbance found to trigger turbulence as the amplitude is increased identifies the `minimal seed' for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold.  This seems at least approximately true for our choice of energy growth functional and the pipe flow geometry chosen here.

Uno de los problemas importantes que tiene la gestion de la innovacion es que a menudo los encargados de la toma de decisiones tienen perspectivas e intereses divergentes que se anteponen a los procesos de cambio necesarios para introducir novedades al mercado. Esta razon, sumada a la velocidad del mercado, los problemas de competitividad y los cambios en el comportamiento de los consumidores, crea un panorama complejo e incierto que paraliza la busqueda de nuevas oportunidades. Este trabajo presenta la aplicacion de los enfoques de competencia en el borde del caos de Brown y Eisenhardt (1998), y reglas simples de Sull y Eisenhardt (2015), para abordar la complejidad que encierra la ejecucion de la estrategia y la necesidad de generacion de una dinamica de crecimiento en la empresa Bonem S.A. Con el fin de sortear los retos y dificultades que amenazan la sostenibilidad de la empresa, se realizo una intervencion empleando la metodologia de investigacion-accion (IA) que permite aborda...

In this theoretical paper, we introduce and describe a model, and demonstrate its origins from the disciplines of Enterprise Architecture, cybernetics and systems theory. We use cybernetic thinking to develop a 'Co-evolution Path Model' that describes how enterprises as complex systems co-evolve with their complex environments. The model re-interprets Stafford Beer's Viable System Model, and also uses the theorem of the 'good regulator' of Conant and Ashby, exemplifying how various complexity management theories could be synthesised into a cybernetic theory of Enterprise Architecture, using concepts from the generalisation of EA frameworks.

Linear transient growth analysis is commonly used to suggest the structure of disturbances which are particularly efficient in triggering transition to turbulence in shear flows. We demonstrate that the addition of nonlinearity to the analysis can substantially change the prediction made in pipe flow from simple two-dimensional streamwise rolls to a spanwise and cross-stream localized three-dimensional state. This new nonlinear optimal is demonstrably more efficient in triggering turbulence than the linear optimal indicating that there are better ways to design perturbations to achieve transition.

This book has origin in dialogues amongst academic research and everyday professional practice. It aims at creating bridge between theory and practice, to facilitate travel from academic side of the bridge to practice side and vice versa. School of Applied Psychology at Zurich University took initiative in this direction and organized a conference in Sept. 2014 with the aim of adding international perspective by inviting scholars from India, China, Netherlands, Israel, Germany and Switzerland. This book is a collection of some conference presentations, highlighting the variety of theory-practice-discussions we encountered so far. The dialogues must continue. Book will be useful to those who would like to join some of the fundamental questions about knowledge and wisdom in social life.

This book has origin in dialogues amongst academic research and everyday professional practice. It aims at creating bridge between theory and practice, to facilitate travel from academic side of the bridge to practice side and vice versa. School of Applied Psychology at Zurich University took initiative in this direction and organized a conference in Sept. 2014 with the aim of adding international perspective by inviting scholars from India, China, Netherlands, Israel, Germany and Switzerland. This book is a collection of some conference presentations, highlighting the variety of theory-practice-discussions we encountered so far. The dialogues must continue. Book will be useful to those who would like to join some of the fundamental questions about knowledge and wisdom in social life.

New families of three-dimensional nonlinear traveling waves are discovered in pipe flow. In contrast with known waves [H. Faisst and B. Eckhardt, Phys. Rev. Lett. 91, 224502 (2003); H. Wedin and R. R. Kerswell, J. Fluid Mech. 508, 333 (2004)], they possess no discrete rotational symmetry and exist at a significantly lower Reynolds numbers (Re). First to appear is a mirror-symmetric traveling wave which is born in a saddle node bifurcation at Re=773. As Re increases, “asymmetric” modes arise through a symmetry-breaking bifurcation. These look to be a minimal coherent unit consisting of one slow streak sandwiched between two fast streaks located preferentially to one side of the pipe. Helical and nonhelical rotating waves are also found, emphasizing the richness of phase space even at these very low Reynolds numbers.