Intro
Preface
Contents
Part I Natural Systems as Information Processors
1 The Concept of Information
1.1 Some History
1.2 The "Three Dimensions" of Information
1.3 From Boltzmann's Entropy to Shannon's Information
1.4 Sign: Entropy and Negentropy: Actual Versus Potential Information
1.5 Hierarchical Structures
1.6 Properties of Shannon's Definition of Information
1.6.1 An Extremum Property
1.6.2 Equal Probabilities Imply Maximum Entropy
1.6.3 Information Content of Tree Structures

1.7 Joint, Conditional, Mutual Information, Bayes' Law, Correlations and Redundancy
1.8 Information in Continuous Physical Quantities
2 Simple Applications
2.1 Logics
2.1.1 Propositional Logics
2.1.2 Boolean Algebra and Electronic Implementations
2.1.3 Set Theory
2.1.4 Inference Chains
2.2 The Genetic Code
2.2.1 Syntax
2.2.2 Semantics, The Central Dogma
2.2.3 Pragmatics and Discussion
2.2.4 Genetic Information in Phylogenesis
2.3 Fourier Transform
2.3.1 Discrete Symmetries in Fourier Transformation
2.3.2 Sampling
2.3.3 Uncertainty Relations

2.3.4 Fast Fourier Transformation
3 Epistemological Aspects
3.1 Causality
3.1.1 Causality from Topology: Markov Chains and Bayesian Networks
3.1.2 Causality from Information Flow: Transfer Information
3.1.3 Causality in Continuous Time: Kolmogorov-Sinai Entropy
3.1.4 Records and Memory
3.1.5 Causality and Special Relativity Theory
3.1.6 Finality
3.2 Prediction
3.2.1 Prediction, Anticipation, Simulation
3.2.2 Prediction from Within: Self-Fulfilling and Self-Destroying Prophecy
3.2.3 Self-Reference and Information-Theoretical Limits of Self-Prediction

3.3 Learning and Adaption
3.3.1 Detectors of Correlation and Causality
3.3.2 Predictors in Society
3.3.3 Darwin's Demons: Anticipatory Systems and Entropy Flow in Ontogeny and Phylogeny
4 Information and Randomness
4.1 Quantifying Randomness
4.2 Randomness According to Structure: Redundancy, Data Compression, and Scientific Induction
4.2.1 Induction
4.2.2 Pattern Recognition and Algorithmic Complexity
4.3 Gödel's Theorem and Incompleteness
4.3.1 Formal Systems
4.3.2 Gödel's Incompleteness Theorem and Provability of Randomness

4.3.3 Interpretations and Consequences of Gödel's Incompleteness Theorem
5 Information in Classical Hamiltonian Dynamics
5.1 Review of Hamiltonian Dynamics and Symplectic Geometry
5.2 Hamiltonian Dynamics of Continuous Density Distributions
5.3 Information Density, Information Flow, and Conservation of Information in Hamiltonian Systems
5.4 Conservation of Information Without Energy Conservation: Harmonic Oscillator Driven at Resonance
5.5 Information Processing in Chaotic Hamiltonian Systems: Bernoulli Shift and Baker Map