Chaos and Information Processing

The following sections are included:

• Dedication

• Preface

• Contents

The relation between symbolic language (be it the genetic code, natural language or computer language) and the dynamics of “thinking”, e.g. information processing has always been — and to a great extent still remains — enigmatic. Historically, the first scientist who postulated the existence of a bilateral relationship (a functional feedback loop) between language and information processing was the linguist, Lee Benjamin Whorf…

The following sections are included:

• Introduction

• Two Elementary Examples of Dynamically Produced Information: a) Via sensitive dependence on control parameters and b) Via sensitive dependence on initial conditions

• The Invariant Measure of Maps and Flows

• Chaotic Dynamics and Markov Partitions

• An Alternative Way of Producing Information Rich Symbolic Sequences — The Quest for Spatial Asymmetry

• Zipf's Law: A Statistics Coming Out from (Real) Natural Languages

• Basic Parameters Characterizing Dissipative Chaos: Lyapunov Exponents, Entropies, (Information) Dimensionalities and Fractal or Multifractal Properties
  • The concept of Lyapunov exponents
  • The Kolmogorov entropy
  • The concept of generalized dimensions and the distribution of the fractal dimensions of singularities in the invariant measure
  • Fractals, multifractals and their connection to chaos

The following sections are included:

• Introduction

• Chaotic Dynamics in Biological Information Processing: A Heuristic Outline
  • Introduction: “mechanistic” (syntactical) vs. “biological” (semantic) processing
  • Where is information stored?
  • Communication between two “biological” processors
  • A “biological” processor possessing multiple coexisting attractors
  • Chaotic dynamics of logical paradoxes
  • Neurophysiological evidence about the role of the EEG and modelling of the role of the thalamocortical pacemaker (see also Sec. 2.2)
  • Summing up and outlook

• The Electrical Activity of the Brain — Should It be Chaotic?
  • Experimental data from EEG research
  • The model
  • Deriving the existence of an attractor and its fractal dimensionality from one-dimensional time series
  • What is a cognitive channel?
  • An example of a fractal basin boundary (separatrix)

• Application to Cognitive Processes: the “Magic Number Seven Plus-Minus Two” Revisited: (Short-Term Memory)
  • Review of experimental results
  • Information processing (generation-dissipation) and memory of a chaotic processor
  • Specific examples and relevance of the model
  • The non-uniform chaotic attractors. “Belousov-Zhabotinsky (B–Z)” attractor model
  • The role of external noise
  • Outlook

• Intermittency in Perception and Communication Processes
  • The breakdown of the “law of large numbers” in pattern recognition and random walks (“multifractal” intermittency)

• Thermodynamics of (Fractal) Curves and Patterns in the Plane

The following sections are included:

• Introduction

• The “Syntactical” Level: “Word Dynamics”

• The “Semantic” Level: Pattern Recognition

• The “Pragmatic” Level: Games of Strategy as a Modus of Communication

• Discussion and Outlook

• The “Triune” Brain of the “Faustian” Man: Uncertainty and Conflict, Noch Einmail!

• Chaos in Nonlinear Paradoxical Games
  • Paradoxical Games
  • The periodically driven model
  • Numerical results
  • Concluding remarks and outlook

• Appendix: Justification and Mathematical Modeling of Paradoxical Games

The following sections are included:

• General Appendices

• Chaotic Dynamics of Linguistic Processes at the Syntactical, Semantic and Pragmatic Levels: Zipf's Law, Pattern Recognition and Decision-Making under Uncertainty and Conflict

• Chaotic Dynamics of Generating Markov Partitions and Linguistic Sequences Mimicking Zipf's Law

• References