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The Mathematical Theory of Information:
Table of Contents
 About Information
 The Law of Diminishing Information
 General Properties of Information
 Specific Information Measurements
 Selected Applications
 Infodynamics
 Statistical Information
 Algorithmic Information
 Continuous Systems
 Continuous Information
 Deterministic Dynamics
 Control and Communication
 Information Physics
 The Information Quantum
References
Symbols
Index
(Re)Search hints by Jan Hajek,
The Netherlands
 ABOUT
INFORMATION
 Introduction
 Information @about
 A Day at the Races
 Bits and Entropy
 Hits and Reliability
 The Sailor's Tale
 The Ideal Receiver
 The Law of Diminishing
Information
 Shannon's Noisy
Channel
 Noise and
nonlinearities
 Chains of
channels
 Bliss of
ignorance
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 THE LAW OF DIMINISHING INFORMATION
 Discrete messages
 Exhaustive sets
 Probability
 The transfer function
 Matrix notation
 Statistical independence
 Chain conditions
 The Law for discrete finite systems
 The axioms
 The Races revisited
 One observation
 Martha and Math
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 GENERAL PROPERTIES OF INFORMATION
 Classification of properties
 Irrelevant information
 Byron's law
 Theory of Games
 Utility
 Fair odds
 Reliability
 Deterministic systems
 Formal logic
 Reversibility
 Onetoone correspondence
 Information content
 Khinchin's condition
 Ford's formula
 The information function
 Joint information
 Volatility
 Additivity vs. Colligation
 Apples + Pears
 Quality of information
 Intrinsic information
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 SPECIFIC INFORMATION MEASURES
 Elements of Information
 Probabilistic information
 The absolute criterion
 Conditional information
 The semantic cont measure
 Extreme values
 Parameter space
 Convexity
 HölderJensen inequality
 Entropy encore
 The uniqueness theorem
 The ffamily
 A Medical Test
 Doublecheck
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 SELECTED APPLICATIONS
 Law lessons
 The Logic of Research
 Corroboration
 Popper's Conjecture...
 ...and its Refutation
 Beyond Bayes
 The absolute determinant
 Rank
 Capacity
 Convexity vs. Colligation
 Amount of data
 A bit uncertain
 Measure for Measure
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 INFODYNAMICS
 Dynamic systems
 Markov chains
 Rigidity
 The Pearson family
 Perron's formula
 Gerschgorin's theorem
 Regular chains
 Jordan canonical form
 Information decay
 Biased information
 The Information Society
 The Law and the law
 McTaggart's ABC
 Information geometry
 Intrinsic time
 Dissipative systems
 Deterministic time
 Thermodynamic reversibility
 Bit Brillouin
 The Gamow kitchen
 Lost ORDER
 Condensing systems
 Cause and effect
 Uniformity of nature
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 STATISTICAL INFORMATION
 Shannon's theory
 Bernoulli sets
 The law of large numbers
 Ergodicity
 MarkovBernoulli messages
 The encoding problem
 Basic Binary Bernoulli
 The duality of reliability
 Total reliability maximized
 Safety first
 Average reliability maximized
 Utility encoding
 Semantic aspects
 The Entropy story
 Coarse graining
 Gibbs' paradox
 Work for a Cause
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 ALGORITHMIC INFORMATION
 Complexity
 Squeezin' a sequence
 Algorithmic compression
 Chaitin complexity
 Infinite message sets
 The ideal computer
 Computability
 The weakness of Kraft
 Genetic information
 Algorithmic channels
 Diophantine channels
 Ciphercypher
 The Chaitin channel
 In Quest of Knowledge
 Induction and Seduction
 Coino'twotails
 Cultural constraints
 Evolution vs. Creation
 Darwin's dictum
 Anthropocentric information
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 CONTINUOUS SYSTEMS
 The probability density
 A discrete hint
 The inversion problem
 Transformed Laplace
 Kernel eigenvalues
 Triangular transfer
 Fredholm equations
 Symmetric PincherleGoursat
 The Bell of Gauss
 Jacobians
 Deterministic density
 A parabolic example
 Fuzzy sets
 Multivariables
 Uncertain probability
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 CONTINUOUS INFORMATION
 Analog signals
 Continuous entropy
 Calculus of variations
 Continuous capacity
 Transmission with tolerance
 The Law in continuous form
 Direct approach to entropy
 Reversibility criterion
 Statistics and Information Theory
 Correlation: no information measure
 Uncorrelated data
 Deterministic correlation
 Invariance: an information measure
 Accuracy
 Sensitivity
 Small sample statistics
 Information gain
 Hypotheses, hypotheses!
 Fisher information
 Galilean invariance
 A Galilean chain
 Frequency filters
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 DETERMINISTIC DYNAMICS
 The macroscopic observer
 Stability and Chaos
 The reversibility collapse
 Perturbations
 The square amplitude law
 Collapsing entropy
 Shrinking volume
 Liapunov stability
 Liapunov's method
 Liapunov and the entropy
 Chaos: Stretch'n'Fold
 Folding
 Transfinite information
 Stretching
 Topological information
 The triangular map
 Farey sequences
 Computing transformations
 Fragile indestructibility
 The teachings of Chaos
 Economic chaos
 The prophet's fallacy
 Breakdown of computer models
 Order from information loss
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 CONTROL AND COMMUNICATION
 Cybernetics
 Timeliness
 Timelag
 Process control
 Byron on control
 Optimization & control
 Control quality
 ZieglerNichols
 Shower time
 Deadbeat control
 Deming's Demon
 The Källe regulator
 The S of Malthus
 Variation and Selection
 Biological chains
 Complexity and sex
 The nature of information
 Neural correlates
 Extended Darwin
 River Time
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 INFORMATION PHYSICS
 Race in space
 Spacetime
 Einstein causality
 EinsteinPodolskyRosen
 The locality condition
 The FreedmanClauser experiment
 Bell's inequalities
 Linear consistency
 Ghost buster symmetry
 Cramer killed the cat
 Relative time
 Einstein's twins
 Relative space
 The particular relativity
 The topological interpretation
 Muon time
 Limits to light
 Advanced wave communication
 Thinner than vacuum
 The Scharnhorst effect
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 THE INFORMATION QUANTUM
 Knowledge and measurement
 The Heisenberg receiver
 The Heffner amplifier
 Schrödinger's wave equation
 A particle in a box
 Statistical Quantum Mechanics
 Quantum statistical information
 The second law of thermodynamics
 Irreversible processes
 Loschmidt's paradox
 In search of hidden order
 Order and disorder
 Phenomenologic thermodynamics
 The ideal gas thermometer
 Potential work
 Maxwell's demon
 Szilard's engine
 Kinetic equivalence
 Computation
 Objectivity!
 Epilogue
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