Related papers: Chaos at Fifty
A half century ago, Lorenz found the "butterfly effect" of chaotic dynamic systems and made his famous claim that long-term prediction of chaos is impossible. However, the meaning of the "long-term" in his claim is not very clear. In this…
This is an outline of my Gibbs Lecture to the American Mathematical Society in January 1994; it is essentially a sign-posted guide to a still-developing literature.
Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this…
Lorenz attractors are important objects in the modern theory of chaos. The reason from one side is that they are met in various natural applications (fluid dynamics, mechanics, laser dynamics, etc.). At the same time, Lorenz attractors are…
Although implicit in the discovery of the Schwarzschild solution 40 years earlier, the issues raised by the theory of what are now known as black holes were so unsettling to physicists of Einstein's generation that the subject remained in a…
The study of complex systems has attracted widespread attention from researchers in the fields of natural sciences, social sciences, and engineering. Prediction is one of the central issues in this field. Although most related studies have…
It is traditionally believed that the macroscopic randomness has nothing to do with the micro-level uncertainty. Besides, the sensitive dependence on initial condition (SDIC) of Lorenz chaos has never been considered together with the…
We describe some highlights in the theory of chaos, that started with Poincare (1899). Generic systems have both ordered and chaotic domains. Chaos appears mainly near un- stable periodic orbits. Large chaotic domains are due to resonance…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…
The problematic relationship between science and philosophy has, since the beginning of modernity, divided the world into two separate domains: nature and human. Some of today's schools of philosophy and epistemological inquiry have…
In this short report the first attempt of a new approach to the still mysterious phenomenon of the life, and its peak, the human being, is presented from the view point of the natural sciences, i.e. of the physics in the broad sense of the…
In 1960 Edward Lorenz (1917-2008) published a pioneering work on the `maximum simplification' of the barotropic vorticity equation. He derived a coupled three-mode system and interpreted it as the minimum core of large-scale fluid mechanics…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
A source of unpredictability is equivalent to a source of information: unpredictability means not knowing which of a set of alternatives is the actual one; determining the actual alternative yields information. The degree of…
We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
Twenty-five years ago, Dunkelmann and Radons (1994) proposed that neural networks should self-organize to a critical state. In models, criticality offers a number of computational advantages. Thus this hypothesis, and in particular the…
Every society has a story rooted in its most ancient traditions, of how the earth and sky originated. Most of these stories attribute the origin of all things to a Creator - whether God, Element or Idea. We first recall that in the Western…
The dynamics of the classical Lorenz system is well studied in $1963$ by E. N. Lorenz. Later on, there have been an extensive studies on the classical Lorenz system with the complex variables and the discrete time Lorenz system with real…
Independent of Maxwell, in 1867 the Danish physicist L. V. Lorenz proposed a theory in which he identified light with electrical oscillations propagating in a very poor conductor. Lorenz's electrodynamic theory of light, which formally was…