Information and Life (eBook)

Foreword Information and Life by Gérard BattailDonald R. ForsdykeAuthor’s Foreword1 IntroductionPart I Information as a scientific entity2 What is information?2.1 Information in a usual meaning2.2 Features of information as a scientific entity2.3 Comments on the definitions of information2.4 An information as a nominable entity2.4.1 Naming and counting2.4.2 Defining and representing natural integers2.4.3 Concept of nominable entity2.4.4 Representatives of nominable entities need to be protected2.5 Short history of communication engineering2.6 Communication over space or over time3 Basic principles of communication engineering3.1 Physical inscription of a single symbol3.2 Physical inscription of a sequence3.2.1 Symbols and sequences3.2.2 Representing a sequence of symbols by a sequence of signals3.3 Receiving a binary symbol in the presence of noise3.4 Communicating sequences in the presence of noise: channel coding3.4.1 Channel coding is needed3.4.2 Redundancy enables channel coding4 Information theory as the science of literal communication4.1 Shannon’s paradigm and its variants4.1.1 Basic paradigm4.1.2 Variants of Shannon’s paradigm4.1.3 Functions and limits of the coding processes4.2 Quantitative measures of information4.2.1 Principle of information measurement4.2.2 Proper and mutual information4.2.3 Entropy and average mutual information4.2.4 Properties of entropy and of the mean mutual information4.2.5 Information rates; extension of a source4.2.6 Cross-entropy4.2.7 Comments on the measurement of information4.3 Source coding4.3.1 Source models4.3.2 Representation of a code by a tree, Kraft inequality4.3.3 Fundamental theorem of source coding4.3.4 Source coding by the Huffman algorithm4.3.5 Some comments about source coding5 Channel capacity and channel coding5.1 Channel models5.2 Capacity of a channel5.2.1 Defining the capacity of a channel5.2.2 Capacity of simple discrete input channels5.2.3 Capacity of the additive white Gaussian noise channel5.2.4 Kolmogorov’s ε-entropy5.3 Channel coding needs redundancy5.4 On the fundamental theorem of channel coding5.4.1 A geometrical interpretation of channel coding5.4.2 Random coding, its geometrical interpretation5.4.3 Random coding for the binary erasure channel5.4.4 Largest minimum distance of error-correcting codes5.4.5 General case: Feinstein’s lemma5.5 Error-correcting codes5.5.1 Defining an error-correcting code5.5.2 Using error-correcting codes: decoding and regeneration5.5.3 Designing error-correcting codes5.5.4 Recursive convolutional codes5.5.5 Turbocodes5.5.6 Low-density parity-check codes5.5.7 Decoding random-like codes: principles5.5.8 Decoding an LDPC code5.5.9 Decoding a turbocode5.5.10 Variants and comments5.5.11 Error-correcting codes defined by non-mathematical constraints: softcodes6 Information as a fundamental entity6.1 Algorithmic information theory6.2 Emergent information in populations6.3 Physical entropy and information6.3.1 Thermodynamics and physical entropy6.3.2 Boltzmann constant as a signal-to-noise ratio6.3.3 Exorcizing Laplace’s demon6.3.4 Information is not a physical entity6.4 Information bridges the abstract and the concretePart II Information is coextensive with life7 An introduction to the second part 1497.1 Relationship with biosemiotics7.2 Content and spirit of the second part8 Heredity as a communication problem8.1 The enduring genome8.1.1 A blatant contradiction8.1.2 An upper bound on the DNA channel capacity8.1.3 Main hypothesis: genomic error-correcting codes must exist8.1.4 Subsidiary hypothesis: nested codes8.2 Consequences meet biological reality8.2.1 Genomes are redundant8.2.2 Discrete species exist with a hierarchical taxonomy8.2.3 Nature proceeds with successive generations8.2.4 Evolution is contingent and saltationist8.2.5 Evolution trends towards increasing complexity8.2.6 Some comments about the consequence of the hypotheses8.3 A toy living world8.3.1 A toy living world in order to mimic the real world8.3.2 Permanence of a ‘genome’8.3.3 Populations of individuals within species8.3.4 An illustrative simulation8.3.5 Natural selection in the toy living world8.4 Identifying genomic error-correcting codes9 Information is specific to life9.1 Information and life are indissolubly linked9.2 Semantic feedback loops9.2.1 Semantic feedback loops and genetic mapping9.2.2 Semantic feedbacks implement Barbieri’s organic codes9.2.3 Semantic feedback loops are compatible with evolution9.2.4 Conjecture about the origin of semantic feedback loops9.3 Information as a fundamental entity9.3.1 Information is an abstract entity9.3.2 On the epistemological status of information9.4 Nature as an engineer10 Life within the physical world10.1 A poorly understood divide10.2 Maxwell’s demon in physics and in life10.3 A measurement as a means for acquiring information11 ConclusionAppendix A Tribute to ShannonA.1 Introduction A.2 His life A.3 His work: information theoryA.4 Shannon’s influenceA.5 Shannon’s legacyAppendix B Some comments about mathematicsB.1 Physical world and mathematicsB.2 On numbersB.3 Definitions and notations in the bookB.3.1 Exponentials and logarithmsB.3.2 Representing symbols and sequencesB.3.3 ProbabilitiesAppendix C A short glossary of molecular geneticsIndex.