Complexity, 1997

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 unpredictability is neatly quantified by the information measure introduced by Shannon. This perspective is applied to three kinds of unpredictability in physics: the absolute unpredictability of quantum mechanics, the unpredictability of the coarse-grained future due to classical chaos, and the unpredictability of open systems. The incompatibility of the first two of these is the root of the difficulty in defining quantum chaos, whereas the unpredictability of open systems, it is suggested, can provide a unified characterization of chaos in classical and quantum dynamics.

The British Journal for the Philosophy of Science 60, 195-220, 2009

From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, this is not the case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has never before been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event, all sufficiently past events are approximately probabilistically irrelevant.

Progress in Biophysics and Molecular Biology, 2012

Determinism and unpredictability are compatible since deterministic flows can produce, if sensitive to initial conditions, unpredictable behaviors. Within this perspective, the notion of scenario to chaos transition offers a new form of predictability for the behavior of sensitive to initial condition systems under the variation of a control parameter. In this paper I first shed light on the genesis of this notion, based on a dynamical systems approach and on considerations of structural stability. I then suggest a link to the figure of epigenetic landscape, partially inspired by a dynamical systems perspective, and offering a theoretical framework to apprehend developmental noise.

1999

Abstract Basic ideas of the statistical topography of random processes and fields are presented, which are used in the analysis of coherent phenomena in simple dynamical systems. Such phenomena take place with probability one, and provide links between individual realizations and statistical characteristics of systems at large.

2011

We see that the exact equations of quantum and classical mechanics describe ideal dynamics which is reversible and result in Poincare's to returns. Real equations of physics describe observable dynamics. It is, for example, master equations of the statistical mechanics, hydrodynamic equations of viscous fluid, Boltzmann equation in thermodynamics, and the entropy increase law in the isolated systems. These laws are nonreversible and exclude Poincare's returns to an initial state. Besides these equations describe systems in terms of macroparameters or phase distribution functions of microparameters. Two reasons of such differences between ideal and observable dynamicses exist. At first, it is uncontrollable noise from the external observer. Secondly, when the observer is included into described system (introspection) the complete self-description of a state of such full system is impossible. Besides introspection is possible during finite time when the thermodynamic time arrow of the observer exists and does not change the direction. Not for all cases broken by external noise (or incomplete at introspection) ideal dynamics can be changed to predictable observable dynamics. For many systems introduction of the macroparameters that allow exhaustively describe dynamics of the system, is impossible. Their dynamics to become in principle unpredictable, sometimes even unpredictable by the probabilistic way. We will name dynamics describing such system, unpredictable dynamics. As follows from the definition of such systems, it is impossible to introduce a complete set of macroparameters for unpredictable dynamics. (Such set of macroparameters for observable dynamics allowed to predict their behavior by a complete way.) Dynamics of unpredictable systems is not described and not predicted by scientific methods. Thus, the science itself puts boundaries for its applicability. But such systems can intuitively «to understand itself» and «to predict» the own behavior or even «to communicate with each other» at intuitive level.

Classical positivist model, which truly and largely permitted the advance of modern scientific knowledge, is somehow outdated. This deterministic-like paradigm which run during the 18 th and 19 th centuries, not only based on the work of Newton but also of other distinguished scientist such as Leibniz, Euler or Lagrange as well as on the philosophical inquiries by Descartes or Comte, strongly supports what has been named as paradigm of order . It is founded on four main principles, as follows: order, reductionism, predictability and determinism. By order, one may understand that, the given causes will lead to the same known effects. Reductionism implies that the behaviour of the system can be explained by the sum of the behaviours of the parts. On the other hand, this kind of system is predictable in the sense that, once its global behaviour is defined, events in the future can be determined by introducing the correct inputs into the model. Finally, determinism implies that the process flows along orderly and predictable paths that have clear beginnings and rational ends. This way of understanding behaviour of natural (and social systems) could be summarized with the following quote of Laplace (1951):

1996

Handbook of Research on Chaos and Complexity Theory in the Social Sciences, 2016

This paper argues for the development of a metaphysics of indeterminism to complement the deterministic metaphysics of current science. Deterministic ideas are analysed to show the underlying assumptions and alternative assumptions are then proposed which allow an indeterministic view of aspects of nature.