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RobKohr — Wed, 12 Jul 2006 17:29:48 GMT

RobKohr:

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RobKohr — Mon, 06 Feb 2006 17:59:00 GMT

RobKohr:

Gödel, Escher, Bach - An Eternal Golden Braid

This wiki is for conversations and thoughts on the book. Below is a list of chapters of the book where you can enter your own thoughts about each section.

=[[PART I: GEB]]=
==[[INTRODUCTION: A MUSICO-LOGICAL OFFERING]]==
*[[Author]]
*[[Bach]]
*[[Canons and Fugues]]
*[[An Endlessly Rising Canon]]
*[[Escher]]
*[[Gödel]]
*[[Mathematical Logic: A Synopsis]]
*[[Banishing Strange Loops]]
*[[Consistency, Completeness, Hilbert's Program]]
*[[Babbage, Computers, Artificial Intelligence...]]
*[[...and Bach]]
*[[Gödel Escher Bach]]
*[[Three-Part Invention]]
==[[CHAPTER 1: THE MU-PUZZLE]]==
*[[Formal Systems]]
*[[Theorems, Axioms, Rules]]
*[[Inside and Outside the System]]
*[[Jumping out of the System]]
*[[M-Mode, I-Mode, U-Mode]]
*[[Decision Procedures]]
*[[Two-Part Invention]]
==[[CHAPTER 2: MEANING AND FORM IN MATHEMATICS]]==
*[[The pq-System]]
*[[The Decision Procedure]]
*[[Bottom-up vs. Top-down]]
*[[Isomorphisms Induce Meaning]]
*[[Meaningless and Meaningful Interpretations]]
*[[Active vs. Passive Meanings]]
*[[Double-Entendre!]]
*[[Formal Systems and Reality]]
*[[Mathematics and Symbol Manipulation]]
*[[The Basic Laws of Arithmetic]]
*[[Ideal Numbers]]
*[[Euclid's Proof]]
*[[Getting Around Infinity]]
*[[Sonata for Unaccompanied Achilles]]
==[[CHAPTER 3: FIGURE AND GROUND]]==
*[[Primes vs. Composites]]
*[[The tq-System]]
*[[Capturing Compositeness]]
*[[Illegally Characterizing Primes]]
*[[Figure and Ground]]
*[[Figure and Ground in Music]]
*[[Recursively Enumerable Sets vs. Recursive Sets]]
*[[Primes as Figure Rather than Ground]]
*[[Contracrostipunctus]]
==[[CHAPTER 4: CONSISTENCY, COMPLETENESS, AND GEOMETRY]]==
*[[Implicit and Explicit Meaning]]
*[[Explicit Meaning of the Contracrostipunctus]]
*[[Implicit Meanings of the Contracrostipunctus]]
*[[Mapping Between the Contracrostipunctus and Gödel's Theorem]]
*[[The Art of the Fugue]]
*[[Problems Caused by Gödel's Result]]
*[[The Modified pq-System and Inconsistency]]
*[[Regaining Consistency]]
*[[The History of Euclidean Geometry]]
*[[The Many Faces of Noneuclid]]
*[[Undefined Terms]]
*[[The Possibility of Multiple Interpretations]]
*[[Varieties of Consistency]]
*[[Hypothetical Worlds and Consistency]]
*[[Embedding of One Formal System in Another]]
*[[Layers of Stability in Visual Perception]]
*[[Is Mathematics the Same in Every Conceivable World?]]
*[[Is Number Theory the Same in All Conceivable Worlds?]]
*[[Completeness]]
*[[How an Interpretation May Make or Break Completeness]]
*[[Incompleteness of Formalized Number Theory]]
*[[Little Harmonic Labyrinth]]
==[[CHAPTER 5: RECURSIVE STRUCTURES AND PROCESSES]]==
*[[What Is Recursion?]]
*[[Pushing, Popping, and Stacks]]
*[[Stacks in Music]]
*[[Recursion in Language]]
*[[Recursive Transition Networks]]
*[[Bottoming Out" and Heterarchies"]]
*[[Expanding Nodes]]
*[[Diagram G and Recursive Sequences]]
*[[A Chaotic Sequence]]
*[[Two Striking Recursive Graphs]]
*[[Recursion at the Lowest Level of Matter]]
*[[Copies and Sameness]]
*[[Programming and Recursion: Modularity, Loops, Procedures]]
*[[Recursion in Chess Programs]]
*[[Recursion and Unpredictability]]
*[[Canon by Intervallic Augmentation]]
==[[CHAPTER 6: THE LOCATION OF MEANING]]==
*[[When is One Thing Not Always the Same?]]
*[[Information-Bearers and Information-Revealers]]
*[[Genotype and Phenotype]]
*[[Exotic and Prosaic Isomorphisms]]
*[[Jukeboxes and Triggers]]
*[[DNA and the Necessity of Chemical Context]]
*[[An Unlikely UFO]]
*[[Levels of Understanding of a Message]]
*[[Imaginary Spacescape]]
*[[The Heroic Decipherers]]
*[[Three Layers of Any Message]]
*[[Schrödinger's Aperiodic Crystals]]
*[[Languages for the Three Levels]]
*[[The Jukebox" Theory of Meaning"]]
*[[Against the Jukebox Theory]]
*[[Meaning Is Intrinsic If Intelligence is Natural]]
*[[Earth Chauvinism]]
*[[Two Plaques in Space]]
*[[Bach vs. Cage Again]]
*[[How Universal Is DNA's Message?]]
*[[Chromatic Fantasy, and Feud]]
==[[CHAPTER 7: THE PROPOSITIONAL CALCULUS]]==
*[[Words and Symbols]]
*[[Alphabet and First Rule of the Propositional Calculus]]
*[[Well-Formed Strings]]
*[[More Rules of Inference]]
*[[The Fantasy Rule]]
*[[Recursion and the Fantasy Rule]]
*[[The Converse of the Fantasy Rule]]
*[[The Intended Interpretation of the Symbols]]
*[[Rounding Out the List of Rules]]
*[[Justifying the Rules]]
*[[Playing Around with the System]]
*[[Semi-Interpretations]]
*[[Ganto's Ax]]
*[[Is There a Decision Procedure for Theorems?]]
*[[Do We Know the System Is Consistent?]]
*[[The Carroll Dialogue Again]]
*[[Shortcuts and Derived Rules]]
*[[Formalizing Higher Levels]]
*[[Reflections on the Strengths and Weaknesses of the System]]
*[[Proofs vs. Derivations]]
*[[The Handling of Contradictions]]
*[[Crab Canon]]
==[[CHAPTER 8: TYPOGRAPHICAL NUMBER THEORY]]==
*[[The Crab Canon and Indirect Self-Reference]]
*[[What We Want to Be Able to Express in TNT]]
*[[Numerals]]
*[[Variables and Terms]]
*[[Atoms and Propositional Symbols]]
*[[Free Variables and Quantifiers]]
*[[Translating Our Sample Sentences]]
*[[Tricks of the Trade]]
*[[Translation Puzzles for You]]
*[[How to Distinguish True from False?]]
*[[The Rules of Well-Formedness]]
*[[A Few More Translation Exercises]]
*[[A Nontypographical System]]
*[[The Five Axioms and First Rules of TNT]]
*[[The Five Peano Postulates]]
*[[New Rules of TNT: Specification and Generalization]]
*[[The Existential Quantifier]]
*[[Rules of Equality and Successorship]]
*[[Illegal Shortcuts]]
*[[Why Specification and Generalization Are Restricted]]
*[[Something Is Missing]]
*[[[w]-Incomplete Systems and Undecidable Strings]]
*[[Non-Euclidean TNT]]
*[[[w]-Inconsistency Is Not the Same as Inconsistency]]
*[[The Last Rule]]
*[[A Long Derivation]]
*[[Tension and Resolution in TNT]]
*[[Formal Reasoning vs. Informal Reasoning]]
*[[Number Theorists Go out of Business]]
*[[Hilbert's Program]]
*[[A Mu Offering]]
==[[CHAPTER 9: MUMON AND GÖDEL]]==
*[[What is Zen?]]
*[[Zen Master Mumon]]
*[[Zen's Struggle Against Dualism]]
*[[Ism, The Un-Mode, and Unmon]]
*[[Zen and Tumbolia]]
*[[Escher and Zen]]
*[[Hemiolia and Escher]]
*[[Indra's Net]]
*[[Mumon on MU]]
*[[From Mumon to the MU-puzzle]]
*[[Mumon Shows Us How to Solve the MU-puzzle]]
*[[Gödel-Numbering the MIU-System]]
*[[Seeing Things Both Typographically and Arithmetically]]
*[[MIU-Producible Numbers]]
*[[Answering Questions about Producible Numbers by Consulting TNT]]
*[[The Dual Nature of MUMON]]
*[[Codes and Implicit Meaning]]
*[[The Boomerang: Gödel-Numbering TNT]]
*[[TNT-Numbers: A Recursively Enumerable Set of Numbers]]
*[[TNT Tries to Swallow Itself]]
*[[G: A String Which Talks about Itself in Code]]
*[[G's Existence Is What Causes TNT's Incompleteness]]
*[[Mumon Has the Last Word]]==
=[[PART II: EGB]]=
*[[Prelude...]]
==[[CHAPTER 10: LEVELS OF DESCRIPTION, AND COMPUTER SYSTEMS]]==
*[[Levels of Description]]
*[[Chunking and Chess Skill]]
*[[Similar Levels]]
*[[Computer Systems]]
*[[Instructions and Data]]
*[[Machine Language vs. Assembly language]]
*[[Programs That Translate Programs]]
*[[Higher-Level Languages, Compilers, and Interpreters]]
*[[Bootstrapping]]
*[[Levels on Which to Describe Running Programs]]
*[[Microprogramming and Operating Systems]]
*[[Cushioning the User and Protecting the System]]
*[[Are Computers Super-Flexible or Super-Rigid?]]
*[[Second-Guessing the Programmer]]
*[[AI Advanced Are Language Advances]]
*[[The Paranoid and the Operating System]]
*[[The Border between Software and Hardware]]
*[[Intermediate Levels and the Weather]]
*[[From Tornados to Quarks]]
*[[Superconductivity: A Paradox" of Renormalization"]]
*[[Sealing-off]]
*[[The Trade-off between Chunking and Determinism]]
*[[Computers Can Only Do What You Tell Them to Do]]
*[[Two Types of System]]
*[[Epiphenomena]]
*[[Mind vs. Brain]]
*[[...Ant Fugue]]
==[[CHAPTER 11: BRAINS AND THOUGHTS]]==
*[[New Perspectives on Thought]]
*[[Intensionality and Extensionality]]
*[[The Brain's Ants]]
*[[Larger Structures in the Brain]]
*[[Mappings between Brains]]
*[[Localization of Brain Processes: An Enigma]]
*[[Specificity in Visual Processing]]
*[[A Grandmother Cell"?"]]
*[[Funneling into Neural Modules]]
*[[Modules Which Mediate Thought Processes]]
*[[Active Symbols]]
*[[Classes and Instances]]
*[[The Prototype Principle]]
*[[The Splitting-off of Instance from Classes]]
*[[The Difficulty of Disentangling Symbols from Each Other]]
*[[Symbols -- Software or Hardware?]]
*[[Liftability of Intelligence]]
*[[Can One Symbol Be Isolated?]]
*[[The Symbols of Insects]]
*[[Class Symbols and Imaginary Worlds]]
*[[Intuitive Laws of Physics]]
*[[Procedural and Declarative Knowledge]]
*[[Visual Imagery]]
*[[English French German Suite]]
==[[CHAPTER 12: MINDS AND THOUGHTS]]==
*[[Can Minds Be Mapped onto Each Other?]]
*[[Comparing Different Semantic Networks]]
*[[Translations of Jabberwocky]]
*[[ASU's]]
*[[A Surprise Reversal]]
*[[Centrality and Universality]]
*[[How Much Do Language and Culture Channel Thought?]]
*[[Trips and Itineraries in ASU's]]
*[[Possible, Potential, and Preposterous Pathways]]
*[[Different Styles of Translating Novels]]
*[[High-Level Comparisons between Programs]]
*[[High-Level Comparisons between Brains]]
*[[Potential Beliefs, Potential Symbols]]
*[[Where is the Sense of Self?]]
*[[Subsystems]]
*[[Subsystems and Shared Code]]
*[[The Self-Symbol and Consciousness]]
*[[Our First Encounter with Lucas]]
*[[Aria with Diverse Variations]]
==[[CHAPTER 13: BlooP AND FlooP AND GlooP]]==
*[[Self-Awareness and Chaos]]
*[[Representability and Refrigerators]]
*[[Ganto's Ax in Metamathmatics]]
*[[Finding Order by Choosing the Right Filter]]
*[[Primordial Steps of the Language BlooP]]
*[[Loops and Upper Bounds]]
*[[Conventions of BlooP]]
*[[IF-Statements and Branching]]
*[[Automatic Chunking]]
*[[BlooP Tests]]
*[[BlooP Programs Contain Chains of Procedures]]
*[[Suggested Exercises]]
*[[Expressibility and Representability]]
*[[Primitive Recursive Predicates Are Represented in TNT]]
*[[Are There Functions Which Are Not Primitive Recursive?]]
*[[Pool B, Index Numbers, and Blue Programs]]
*[[The Diagonal Method]]
*[[Cantor's Original Diagonal Argument]]
*[[What Does a Diagonal Argument Prove?]]
*[[The Insidious Repeatability of the Diagonal Argument]]
*[[From BlooP to FlooP]]
*[[Terminating and Nonterminating FlooP Programs]]
*[[Turing's Trickery]]
*[[A Termination Tester Would Be Magical]]
*[[Pool F, Index Numbers, and Green Programs]]
*[[The Termination Tester Gives Us Red Programs]]
*[[GlooP...]]
*[[...Is a Myth]]
*[[The Church-Turing Thesis]]
*[[Terminology: General and Partial Recursive]]
*[[The Power of TNT]]
*[[Air on G's String]]
==[[CHAPTER 14: ON FORMALLY UNDECIDABLE PROPOSITIONS OF TNT AND RELATED SYSTEMS]]==
*[[The Two Ideas of the Oyster]]
*[[The First Idea: Proof-Pairs]]
*[[Proof-Pair-ness Is Primitive Recursive...]]
*[[...And Is Therefore Represented in TNT]]
*[[The Power of Proof-Pairs]]
*[[Substitution Leads to the Second Idea]]
*[[Arithmoquining]]
*[[The Last Straw]]
*[[TNT Says Uncle!]]
*[[Yields Nontheoremhood When Arithmoquined]]
*[[Gödel's Second Theorem]]
*[[TNT Is [w]-Incomplete]]
*[[Two Different Ways to Plug Up the Hole]]
*[[Supernatural Numbers]]
*[[Supernatural Theorems Have Infinitely Long Derivations]]
*[[Supernatural Addition and Multiplication]]
*[[Supernaturals Are Useful...]]
*[[...But Are They Real?]]
*[[Bifurcations in Geometry, and Physicists]]
*[[Bifurcations in Number Theory, and Bankers]]
*[[Bifurcations in Number Theory, and Metamathematicians]]
*[[Hilbert's Tenth Problem and the Tortoise]]
*[[Birthday Cantatatata...]]
==[[CHAPTER 15: JUMPING OUT OF THE SYSTEM]]==
*[[A More Powerful Formal System]]
*[[The Gödel Method Reapplied]]
*[[Multifurcation]]
*[[Essential Incompleteness]]
*[[The Passion According to Lucas]]
*[[Jumping Up a Dimension]]
*[[The Limits of Intelligent Systems]]
*[[There Is No Recursive Rule for Naming Ordinals]]
*[[Other Refutations of Lucas]]
*[[Self-Transcendence -- A Modern Myth]]
*[[Advertisement and Framing Devices]]
*[[Simplicio, Salviati, Sagredo: Why Three?]]
*[[Zen and Stepping Out]]
*[[Edifying Thoughts of a Tobacco Smoker]]
==[[CHAPTER 16: SELF-REF AND SELF-REP]]==
*[[Implicitly and Explicitly Self-Referential Sentences]]
*[[A Self-Reproducing Program]]
*[[What Is a Copy?]]
*[[A Self-Reproducing Song]]
*[[Epimenides Straddles the Channel]]
*[[A Program That Prints Out Its Own Gödel Number]]
*[[Gödelian Self-Reference]]
*[[A Self-Rep by Augmentation]]
*[[A Kimian Self-Rep]]
*[[What Is the Original?]]
*[[Typogenetics]]
*[[Strands, Bases, Enzymes]]
*[[Copy Mode and Double Strands]]
*[[Amino Acids]]
*[[Translation and the Typogenetic Code]]
*[[Tertiary Structure of Enzymes]]
*[[Punctuation, Genes, and Ribosomes]]
*[[Puzzle: A Typogenetical Self-Rep]]
*[[The Central Dogma of Typogenetics]]
*[[Strange Loops, TNT, and Real Genetics]]
*[[DNA and Nucleotides]]
*[[Messenger RNA and Ribosomes]]
*[[Amino Acids]]
*[[Ribosomes and Tape Recorders]]
*[[The Genetic Code]]
*[[Tertiary Structure]]
*[[Reductionistic Explanation of Protein Function]]
*[[Transfer RNA and Ribosomes]]
*[[Punctuation and the Reading Frame]]
*[[Recap]]
*[[Levels of Structure and Meaning in Proteins and Music]]
*[[Polyribosomes and Two-Tiered Canons]]
*[[Which Came First -- The Ribosome or the Protein?]]
*[[Protein Function]]
*[[Need for a Sufficiently Strong Support System]]
*[[How DNA Self-Replicates]]
*[[Comparison of DNA's Self-Rep Method with Quining]]
*[[Levels of Meaning of DNA]]
*[[The Central Dogmap]]
*[[Strange Loops in the Central Dogmap]]
*[[The Central Dogmap and the Contracrostipunctus]]
*[[E. Coli vs. T4]]
*[[A Molecular Trojan Horse]]
*[[Recognition, Disguises, Labeling]]
*[[Henkin Sentences and Viruses]]
*[[Implicit vs. Explicit Henkin Sentences]]
*[[Henkin Sentences and Self-Assembly]]
*[[Two Outstanding Problems: Differentiation and Morphogenesis]]
*[[Feedback and Feedforward]]
*[[Repressors and Inducers]]
*[[Feedback and Strange Loops Compared]]
*[[Two Simple Examples of Differentiation]]
*[[Level Mixing in the Cell]]
*[[The Origin of Life]]
*[[The Magnificrab, Indeed]]
==[[CHAPTER 17: CHURCH, TURING, TARSKI, AND OTHERS]]==
*[[Formal and Informal Systems]]
*[[Intuition and the Magnificent Crab]]
*[[The Church-Turing Thesis]]
*[[The Public-Processes Version]]
*[[Srinivasa Ramanujan]]
*[[Idiots Savants]]
*[[The Isomorphism Version of the Church-Turing Thesis]]
*[[Representation of Knowledge about the Real World]]
*[[Processes That Are Not So Skimmable]]
*[[Articles of Reductionistic Faith]]
*[[Partial Progress in AI and Brain Simulation?]]
*[[Beauty, the Crab, and the Soul]]
*[[Irrational and Rational Can Coexist on Different Levels]]
*[[More Against Lucas]]
*[[An Underpinning of AI]]
*[[Church's Theorem]]
*[[Tarski's Theorem]]
*[[The Impossibility of the Magnificrab]]
*[[Two Types of Form]]
*[[Meaning Derives from Connections to Cognitive Structures]]
*[[Beauty, Truth, and Form]]
*[[The Neural Substrate of the Epimenides Paradox]]
*[[SHRDLU, Toy of Man's Designing]]
==[[CHAPTER 18: ARTIFICIAL INTELLIGENCE: RETROSPECTS]]==
*[[Turing]]
*[[The Turing Test]]
*[[Turing Anticipates Objections]]
*[[Parry Encounters the Doctor]]
*[[A Brief History of AI]]
*[[Mechanical Translation]]
*[[Computer Chess]]
*[[Samuel's Checker Program]]
*[[When Is a Program Original?]]
*[[Who Composes Computer Music?]]
*[[Theorem Proving and Problem Reduction]]
*[[Shandy and the Bone]]
*[[Changing the Problem Space]]
*[[The I-Mode and the M-Mode Again]]
*[[Applying AI to Mathematics]]
*[[The Crux of AI: Representation of Knowledge]]
*[[DNA and Proteins Help Give Some Perspective]]
*[[Modularity of Knowledge]]
*[[Representing Knowledge in a Logical Formalism]]
*[[Deductive vs. Analogical Awareness]]
*[[From Computer Haiku to an RTN-Grammar]]
*[[From RTN's to ATN's]]
*[[A Little Turing Test]]
*[[Images of What Thought Is]]
*[[Higher-Level Grammars...]]
*[[Grammars for Music?]]
*[[Winograd's Program SHRDLU]]
*[[The Structure of SHRDLU]]
*[[PLANNER Facilitates Problem Reduction]]
*[[Syntax and Semantics]]
*[[Contrafactus]]
==[[CHAPTER 19: ARTIFICIAL INTELLIGENCE: PROSPECTS]]==
*[[Almost" Situations and Subjunctives"]]
*[[Layers of Stability]]
*[[Frames and Nested Contexts]]
*[[Bongard Problems]]
*[[Preprocessing Selects a Mini-Vocabulary]]
*[[High-Level Descriptions]]
*[[Templates and Sameness-Detectors]]
*[[A Heterarchical Program]]
*[[The Concept Network]]
*[[Slippage and Tentativity]]
*[[Meta-Descriptions]]
*[[Flexibility is Important]]
*[[Focusing and Filtering]]
*[[Science and the World of Bongard Problems]]
*[[Connections to Other Types of Thought]]
*[[Message-Passing Languages, Frames, and Symbols]]
*[[Enzymes and AI]]
*[[Fission and Fusion]]
*[[Epigenesis of the Crab Canon]]
*[[Conceptual Skeletons and Conceptual Mapping]]
*[[Recombinant Ideas]]
*[[Abstractions, Skeletons, Analogies]]
*[[Multiple Representations]]
*[[Ports of Access]]
*[[Forced Matching]]
*[[Recap]]
*[[Creativity and Randomness]]
*[[Picking up Patterns on All Levels]]
*[[The Flexibility of Language]]
*[[Intelligence and Emotions]]
*[[AI Has Far to Go]]
*[[Ten Questions and Speculations]]
*[[Sloth Canon]]
==[[CHAPTER 20: STRANGE LOOPS, OR TANGLED HIERARCHIES]]==
*[[Can Machines Possess Originality?]]
*[[Below Every Tangled Hierarchy Lies An Inviolate Level]]
*[[A Self-Modifying Game]]
*[[The Authorship Triangle Again]]
*[[Escher's Drawing Hands]]
*[[Brain and Mind: A Neural Tangle Supporting a Symbol Tangle]]
*[[Strange Loops in Government]]
*[[Tangles Involving Science and the Occult]]
*[[The Nature of Evidence]]
*[[Seeing Oneself]]
*[[Gödel's Theorem and Other Disciplines]]
*[[Introspection and Insanity: A Gödelian Problem]]
*[[Can We Understand Our Own Minds or Brains?]]
*[[Gödel's Theorem and Personal Nonexistence]]
*[[Science and Dualism]]
*[[Symbol vs. Object in Modern Music and Art]]
*[[Magritte's Semantic Illusions]]
*[[The Code" of Modern Art"]]
*[[Ism Once Again]]
*[[Understanding the Mind]]
*[[Accidental Inexplicability of Intelligence?]]
*[[Undecidability Is Inseparable from a High-Level Viewpoint]]
*[[Consciousness as an Intrinsically High-Level Phenomenon]]
*[[Strange Loops as the Crux of Consciousness]]
*[[The Self-Symbol and Free Will]]
*[[A Gödel Vortex Where All Levels Cross]]
*[[An Escher Vortex Where All Levels Cross]]
*[[A Bach Vortex Where All Levels Cross]]
*[[Six-Part Ricercar]]

Main Page

RobKohr — Mon, 06 Feb 2006 17:58:05 GMT

RobKohr:

Gödel, Escher, Bach - An Eternal Golden Braid

This wiki is for conversations and thoughts on the book. This is the

=[[PART I: GEB]]=
==[[INTRODUCTION: A MUSICO-LOGICAL OFFERING]]==
*[[Author]]
*[[Bach]]
*[[Canons and Fugues]]
*[[An Endlessly Rising Canon]]
*[[Escher]]
*[[Gödel]]
*[[Mathematical Logic: A Synopsis]]
*[[Banishing Strange Loops]]
*[[Consistency, Completeness, Hilbert's Program]]
*[[Babbage, Computers, Artificial Intelligence...]]
*[[...and Bach]]
*[[Gödel Escher Bach]]
*[[Three-Part Invention]]
==[[CHAPTER 1: THE MU-PUZZLE]]==
*[[Formal Systems]]
*[[Theorems, Axioms, Rules]]
*[[Inside and Outside the System]]
*[[Jumping out of the System]]
*[[M-Mode, I-Mode, U-Mode]]
*[[Decision Procedures]]
*[[Two-Part Invention]]
==[[CHAPTER 2: MEANING AND FORM IN MATHEMATICS]]==
*[[The pq-System]]
*[[The Decision Procedure]]
*[[Bottom-up vs. Top-down]]
*[[Isomorphisms Induce Meaning]]
*[[Meaningless and Meaningful Interpretations]]
*[[Active vs. Passive Meanings]]
*[[Double-Entendre!]]
*[[Formal Systems and Reality]]
*[[Mathematics and Symbol Manipulation]]
*[[The Basic Laws of Arithmetic]]
*[[Ideal Numbers]]
*[[Euclid's Proof]]
*[[Getting Around Infinity]]
*[[Sonata for Unaccompanied Achilles]]
==[[CHAPTER 3: FIGURE AND GROUND]]==
*[[Primes vs. Composites]]
*[[The tq-System]]
*[[Capturing Compositeness]]
*[[Illegally Characterizing Primes]]
*[[Figure and Ground]]
*[[Figure and Ground in Music]]
*[[Recursively Enumerable Sets vs. Recursive Sets]]
*[[Primes as Figure Rather than Ground]]
*[[Contracrostipunctus]]
==[[CHAPTER 4: CONSISTENCY, COMPLETENESS, AND GEOMETRY]]==
*[[Implicit and Explicit Meaning]]
*[[Explicit Meaning of the Contracrostipunctus]]
*[[Implicit Meanings of the Contracrostipunctus]]
*[[Mapping Between the Contracrostipunctus and Gödel's Theorem]]
*[[The Art of the Fugue]]
*[[Problems Caused by Gödel's Result]]
*[[The Modified pq-System and Inconsistency]]
*[[Regaining Consistency]]
*[[The History of Euclidean Geometry]]
*[[The Many Faces of Noneuclid]]
*[[Undefined Terms]]
*[[The Possibility of Multiple Interpretations]]
*[[Varieties of Consistency]]
*[[Hypothetical Worlds and Consistency]]
*[[Embedding of One Formal System in Another]]
*[[Layers of Stability in Visual Perception]]
*[[Is Mathematics the Same in Every Conceivable World?]]
*[[Is Number Theory the Same in All Conceivable Worlds?]]
*[[Completeness]]
*[[How an Interpretation May Make or Break Completeness]]
*[[Incompleteness of Formalized Number Theory]]
*[[Little Harmonic Labyrinth]]
==[[CHAPTER 5: RECURSIVE STRUCTURES AND PROCESSES]]==
*[[What Is Recursion?]]
*[[Pushing, Popping, and Stacks]]
*[[Stacks in Music]]
*[[Recursion in Language]]
*[[Recursive Transition Networks]]
*[[Bottoming Out" and Heterarchies"]]
*[[Expanding Nodes]]
*[[Diagram G and Recursive Sequences]]
*[[A Chaotic Sequence]]
*[[Two Striking Recursive Graphs]]
*[[Recursion at the Lowest Level of Matter]]
*[[Copies and Sameness]]
*[[Programming and Recursion: Modularity, Loops, Procedures]]
*[[Recursion in Chess Programs]]
*[[Recursion and Unpredictability]]
*[[Canon by Intervallic Augmentation]]
==[[CHAPTER 6: THE LOCATION OF MEANING]]==
*[[When is One Thing Not Always the Same?]]
*[[Information-Bearers and Information-Revealers]]
*[[Genotype and Phenotype]]
*[[Exotic and Prosaic Isomorphisms]]
*[[Jukeboxes and Triggers]]
*[[DNA and the Necessity of Chemical Context]]
*[[An Unlikely UFO]]
*[[Levels of Understanding of a Message]]
*[[Imaginary Spacescape]]
*[[The Heroic Decipherers]]
*[[Three Layers of Any Message]]
*[[Schrödinger's Aperiodic Crystals]]
*[[Languages for the Three Levels]]
*[[The Jukebox" Theory of Meaning"]]
*[[Against the Jukebox Theory]]
*[[Meaning Is Intrinsic If Intelligence is Natural]]
*[[Earth Chauvinism]]
*[[Two Plaques in Space]]
*[[Bach vs. Cage Again]]
*[[How Universal Is DNA's Message?]]
*[[Chromatic Fantasy, and Feud]]
==[[CHAPTER 7: THE PROPOSITIONAL CALCULUS]]==
*[[Words and Symbols]]
*[[Alphabet and First Rule of the Propositional Calculus]]
*[[Well-Formed Strings]]
*[[More Rules of Inference]]
*[[The Fantasy Rule]]
*[[Recursion and the Fantasy Rule]]
*[[The Converse of the Fantasy Rule]]
*[[The Intended Interpretation of the Symbols]]
*[[Rounding Out the List of Rules]]
*[[Justifying the Rules]]
*[[Playing Around with the System]]
*[[Semi-Interpretations]]
*[[Ganto's Ax]]
*[[Is There a Decision Procedure for Theorems?]]
*[[Do We Know the System Is Consistent?]]
*[[The Carroll Dialogue Again]]
*[[Shortcuts and Derived Rules]]
*[[Formalizing Higher Levels]]
*[[Reflections on the Strengths and Weaknesses of the System]]
*[[Proofs vs. Derivations]]
*[[The Handling of Contradictions]]
*[[Crab Canon]]
==[[CHAPTER 8: TYPOGRAPHICAL NUMBER THEORY]]==
*[[The Crab Canon and Indirect Self-Reference]]
*[[What We Want to Be Able to Express in TNT]]
*[[Numerals]]
*[[Variables and Terms]]
*[[Atoms and Propositional Symbols]]
*[[Free Variables and Quantifiers]]
*[[Translating Our Sample Sentences]]
*[[Tricks of the Trade]]
*[[Translation Puzzles for You]]
*[[How to Distinguish True from False?]]
*[[The Rules of Well-Formedness]]
*[[A Few More Translation Exercises]]
*[[A Nontypographical System]]
*[[The Five Axioms and First Rules of TNT]]
*[[The Five Peano Postulates]]
*[[New Rules of TNT: Specification and Generalization]]
*[[The Existential Quantifier]]
*[[Rules of Equality and Successorship]]
*[[Illegal Shortcuts]]
*[[Why Specification and Generalization Are Restricted]]
*[[Something Is Missing]]
*[[[w]-Incomplete Systems and Undecidable Strings]]
*[[Non-Euclidean TNT]]
*[[[w]-Inconsistency Is Not the Same as Inconsistency]]
*[[The Last Rule]]
*[[A Long Derivation]]
*[[Tension and Resolution in TNT]]
*[[Formal Reasoning vs. Informal Reasoning]]
*[[Number Theorists Go out of Business]]
*[[Hilbert's Program]]
*[[A Mu Offering]]
==[[CHAPTER 9: MUMON AND GÖDEL]]==
*[[What is Zen?]]
*[[Zen Master Mumon]]
*[[Zen's Struggle Against Dualism]]
*[[Ism, The Un-Mode, and Unmon]]
*[[Zen and Tumbolia]]
*[[Escher and Zen]]
*[[Hemiolia and Escher]]
*[[Indra's Net]]
*[[Mumon on MU]]
*[[From Mumon to the MU-puzzle]]
*[[Mumon Shows Us How to Solve the MU-puzzle]]
*[[Gödel-Numbering the MIU-System]]
*[[Seeing Things Both Typographically and Arithmetically]]
*[[MIU-Producible Numbers]]
*[[Answering Questions about Producible Numbers by Consulting TNT]]
*[[The Dual Nature of MUMON]]
*[[Codes and Implicit Meaning]]
*[[The Boomerang: Gödel-Numbering TNT]]
*[[TNT-Numbers: A Recursively Enumerable Set of Numbers]]
*[[TNT Tries to Swallow Itself]]
*[[G: A String Which Talks about Itself in Code]]
*[[G's Existence Is What Causes TNT's Incompleteness]]
*[[Mumon Has the Last Word]]==
=[[PART II: EGB]]=
*[[Prelude...]]
==[[CHAPTER 10: LEVELS OF DESCRIPTION, AND COMPUTER SYSTEMS]]==
*[[Levels of Description]]
*[[Chunking and Chess Skill]]
*[[Similar Levels]]
*[[Computer Systems]]
*[[Instructions and Data]]
*[[Machine Language vs. Assembly language]]
*[[Programs That Translate Programs]]
*[[Higher-Level Languages, Compilers, and Interpreters]]
*[[Bootstrapping]]
*[[Levels on Which to Describe Running Programs]]
*[[Microprogramming and Operating Systems]]
*[[Cushioning the User and Protecting the System]]
*[[Are Computers Super-Flexible or Super-Rigid?]]
*[[Second-Guessing the Programmer]]
*[[AI Advanced Are Language Advances]]
*[[The Paranoid and the Operating System]]
*[[The Border between Software and Hardware]]
*[[Intermediate Levels and the Weather]]
*[[From Tornados to Quarks]]
*[[Superconductivity: A Paradox" of Renormalization"]]
*[[Sealing-off]]
*[[The Trade-off between Chunking and Determinism]]
*[[Computers Can Only Do What You Tell Them to Do]]
*[[Two Types of System]]
*[[Epiphenomena]]
*[[Mind vs. Brain]]
*[[...Ant Fugue]]
==[[CHAPTER 11: BRAINS AND THOUGHTS]]==
*[[New Perspectives on Thought]]
*[[Intensionality and Extensionality]]
*[[The Brain's Ants]]
*[[Larger Structures in the Brain]]
*[[Mappings between Brains]]
*[[Localization of Brain Processes: An Enigma]]
*[[Specificity in Visual Processing]]
*[[A Grandmother Cell"?"]]
*[[Funneling into Neural Modules]]
*[[Modules Which Mediate Thought Processes]]
*[[Active Symbols]]
*[[Classes and Instances]]
*[[The Prototype Principle]]
*[[The Splitting-off of Instance from Classes]]
*[[The Difficulty of Disentangling Symbols from Each Other]]
*[[Symbols -- Software or Hardware?]]
*[[Liftability of Intelligence]]
*[[Can One Symbol Be Isolated?]]
*[[The Symbols of Insects]]
*[[Class Symbols and Imaginary Worlds]]
*[[Intuitive Laws of Physics]]
*[[Procedural and Declarative Knowledge]]
*[[Visual Imagery]]
*[[English French German Suite]]
==[[CHAPTER 12: MINDS AND THOUGHTS]]==
*[[Can Minds Be Mapped onto Each Other?]]
*[[Comparing Different Semantic Networks]]
*[[Translations of Jabberwocky]]
*[[ASU's]]
*[[A Surprise Reversal]]
*[[Centrality and Universality]]
*[[How Much Do Language and Culture Channel Thought?]]
*[[Trips and Itineraries in ASU's]]
*[[Possible, Potential, and Preposterous Pathways]]
*[[Different Styles of Translating Novels]]
*[[High-Level Comparisons between Programs]]
*[[High-Level Comparisons between Brains]]
*[[Potential Beliefs, Potential Symbols]]
*[[Where is the Sense of Self?]]
*[[Subsystems]]
*[[Subsystems and Shared Code]]
*[[The Self-Symbol and Consciousness]]
*[[Our First Encounter with Lucas]]
*[[Aria with Diverse Variations]]
==[[CHAPTER 13: BlooP AND FlooP AND GlooP]]==
*[[Self-Awareness and Chaos]]
*[[Representability and Refrigerators]]
*[[Ganto's Ax in Metamathmatics]]
*[[Finding Order by Choosing the Right Filter]]
*[[Primordial Steps of the Language BlooP]]
*[[Loops and Upper Bounds]]
*[[Conventions of BlooP]]
*[[IF-Statements and Branching]]
*[[Automatic Chunking]]
*[[BlooP Tests]]
*[[BlooP Programs Contain Chains of Procedures]]
*[[Suggested Exercises]]
*[[Expressibility and Representability]]
*[[Primitive Recursive Predicates Are Represented in TNT]]
*[[Are There Functions Which Are Not Primitive Recursive?]]
*[[Pool B, Index Numbers, and Blue Programs]]
*[[The Diagonal Method]]
*[[Cantor's Original Diagonal Argument]]
*[[What Does a Diagonal Argument Prove?]]
*[[The Insidious Repeatability of the Diagonal Argument]]
*[[From BlooP to FlooP]]
*[[Terminating and Nonterminating FlooP Programs]]
*[[Turing's Trickery]]
*[[A Termination Tester Would Be Magical]]
*[[Pool F, Index Numbers, and Green Programs]]
*[[The Termination Tester Gives Us Red Programs]]
*[[GlooP...]]
*[[...Is a Myth]]
*[[The Church-Turing Thesis]]
*[[Terminology: General and Partial Recursive]]
*[[The Power of TNT]]
*[[Air on G's String]]
==[[CHAPTER 14: ON FORMALLY UNDECIDABLE PROPOSITIONS OF TNT AND RELATED SYSTEMS]]==
*[[The Two Ideas of the Oyster]]
*[[The First Idea: Proof-Pairs]]
*[[Proof-Pair-ness Is Primitive Recursive...]]
*[[...And Is Therefore Represented in TNT]]
*[[The Power of Proof-Pairs]]
*[[Substitution Leads to the Second Idea]]
*[[Arithmoquining]]
*[[The Last Straw]]
*[[TNT Says Uncle!]]
*[[Yields Nontheoremhood When Arithmoquined]]
*[[Gödel's Second Theorem]]
*[[TNT Is [w]-Incomplete]]
*[[Two Different Ways to Plug Up the Hole]]
*[[Supernatural Numbers]]
*[[Supernatural Theorems Have Infinitely Long Derivations]]
*[[Supernatural Addition and Multiplication]]
*[[Supernaturals Are Useful...]]
*[[...But Are They Real?]]
*[[Bifurcations in Geometry, and Physicists]]
*[[Bifurcations in Number Theory, and Bankers]]
*[[Bifurcations in Number Theory, and Metamathematicians]]
*[[Hilbert's Tenth Problem and the Tortoise]]
*[[Birthday Cantatatata...]]
==[[CHAPTER 15: JUMPING OUT OF THE SYSTEM]]==
*[[A More Powerful Formal System]]
*[[The Gödel Method Reapplied]]
*[[Multifurcation]]
*[[Essential Incompleteness]]
*[[The Passion According to Lucas]]
*[[Jumping Up a Dimension]]
*[[The Limits of Intelligent Systems]]
*[[There Is No Recursive Rule for Naming Ordinals]]
*[[Other Refutations of Lucas]]
*[[Self-Transcendence -- A Modern Myth]]
*[[Advertisement and Framing Devices]]
*[[Simplicio, Salviati, Sagredo: Why Three?]]
*[[Zen and Stepping Out]]
*[[Edifying Thoughts of a Tobacco Smoker]]
==[[CHAPTER 16: SELF-REF AND SELF-REP]]==
*[[Implicitly and Explicitly Self-Referential Sentences]]
*[[A Self-Reproducing Program]]
*[[What Is a Copy?]]
*[[A Self-Reproducing Song]]
*[[Epimenides Straddles the Channel]]
*[[A Program That Prints Out Its Own Gödel Number]]
*[[Gödelian Self-Reference]]
*[[A Self-Rep by Augmentation]]
*[[A Kimian Self-Rep]]
*[[What Is the Original?]]
*[[Typogenetics]]
*[[Strands, Bases, Enzymes]]
*[[Copy Mode and Double Strands]]
*[[Amino Acids]]
*[[Translation and the Typogenetic Code]]
*[[Tertiary Structure of Enzymes]]
*[[Punctuation, Genes, and Ribosomes]]
*[[Puzzle: A Typogenetical Self-Rep]]
*[[The Central Dogma of Typogenetics]]
*[[Strange Loops, TNT, and Real Genetics]]
*[[DNA and Nucleotides]]
*[[Messenger RNA and Ribosomes]]
*[[Amino Acids]]
*[[Ribosomes and Tape Recorders]]
*[[The Genetic Code]]
*[[Tertiary Structure]]
*[[Reductionistic Explanation of Protein Function]]
*[[Transfer RNA and Ribosomes]]
*[[Punctuation and the Reading Frame]]
*[[Recap]]
*[[Levels of Structure and Meaning in Proteins and Music]]
*[[Polyribosomes and Two-Tiered Canons]]
*[[Which Came First -- The Ribosome or the Protein?]]
*[[Protein Function]]
*[[Need for a Sufficiently Strong Support System]]
*[[How DNA Self-Replicates]]
*[[Comparison of DNA's Self-Rep Method with Quining]]
*[[Levels of Meaning of DNA]]
*[[The Central Dogmap]]
*[[Strange Loops in the Central Dogmap]]
*[[The Central Dogmap and the Contracrostipunctus]]
*[[E. Coli vs. T4]]
*[[A Molecular Trojan Horse]]
*[[Recognition, Disguises, Labeling]]
*[[Henkin Sentences and Viruses]]
*[[Implicit vs. Explicit Henkin Sentences]]
*[[Henkin Sentences and Self-Assembly]]
*[[Two Outstanding Problems: Differentiation and Morphogenesis]]
*[[Feedback and Feedforward]]
*[[Repressors and Inducers]]
*[[Feedback and Strange Loops Compared]]
*[[Two Simple Examples of Differentiation]]
*[[Level Mixing in the Cell]]
*[[The Origin of Life]]
*[[The Magnificrab, Indeed]]
==[[CHAPTER 17: CHURCH, TURING, TARSKI, AND OTHERS]]==
*[[Formal and Informal Systems]]
*[[Intuition and the Magnificent Crab]]
*[[The Church-Turing Thesis]]
*[[The Public-Processes Version]]
*[[Srinivasa Ramanujan]]
*[[Idiots Savants]]
*[[The Isomorphism Version of the Church-Turing Thesis]]
*[[Representation of Knowledge about the Real World]]
*[[Processes That Are Not So Skimmable]]
*[[Articles of Reductionistic Faith]]
*[[Partial Progress in AI and Brain Simulation?]]
*[[Beauty, the Crab, and the Soul]]
*[[Irrational and Rational Can Coexist on Different Levels]]
*[[More Against Lucas]]
*[[An Underpinning of AI]]
*[[Church's Theorem]]
*[[Tarski's Theorem]]
*[[The Impossibility of the Magnificrab]]
*[[Two Types of Form]]
*[[Meaning Derives from Connections to Cognitive Structures]]
*[[Beauty, Truth, and Form]]
*[[The Neural Substrate of the Epimenides Paradox]]
*[[SHRDLU, Toy of Man's Designing]]
==[[CHAPTER 18: ARTIFICIAL INTELLIGENCE: RETROSPECTS]]==
*[[Turing]]
*[[The Turing Test]]
*[[Turing Anticipates Objections]]
*[[Parry Encounters the Doctor]]
*[[A Brief History of AI]]
*[[Mechanical Translation]]
*[[Computer Chess]]
*[[Samuel's Checker Program]]
*[[When Is a Program Original?]]
*[[Who Composes Computer Music?]]
*[[Theorem Proving and Problem Reduction]]
*[[Shandy and the Bone]]
*[[Changing the Problem Space]]
*[[The I-Mode and the M-Mode Again]]
*[[Applying AI to Mathematics]]
*[[The Crux of AI: Representation of Knowledge]]
*[[DNA and Proteins Help Give Some Perspective]]
*[[Modularity of Knowledge]]
*[[Representing Knowledge in a Logical Formalism]]
*[[Deductive vs. Analogical Awareness]]
*[[From Computer Haiku to an RTN-Grammar]]
*[[From RTN's to ATN's]]
*[[A Little Turing Test]]
*[[Images of What Thought Is]]
*[[Higher-Level Grammars...]]
*[[Grammars for Music?]]
*[[Winograd's Program SHRDLU]]
*[[The Structure of SHRDLU]]
*[[PLANNER Facilitates Problem Reduction]]
*[[Syntax and Semantics]]
*[[Contrafactus]]
==[[CHAPTER 19: ARTIFICIAL INTELLIGENCE: PROSPECTS]]==
*[[Almost" Situations and Subjunctives"]]
*[[Layers of Stability]]
*[[Frames and Nested Contexts]]
*[[Bongard Problems]]
*[[Preprocessing Selects a Mini-Vocabulary]]
*[[High-Level Descriptions]]
*[[Templates and Sameness-Detectors]]
*[[A Heterarchical Program]]
*[[The Concept Network]]
*[[Slippage and Tentativity]]
*[[Meta-Descriptions]]
*[[Flexibility is Important]]
*[[Focusing and Filtering]]
*[[Science and the World of Bongard Problems]]
*[[Connections to Other Types of Thought]]
*[[Message-Passing Languages, Frames, and Symbols]]
*[[Enzymes and AI]]
*[[Fission and Fusion]]
*[[Epigenesis of the Crab Canon]]
*[[Conceptual Skeletons and Conceptual Mapping]]
*[[Recombinant Ideas]]
*[[Abstractions, Skeletons, Analogies]]
*[[Multiple Representations]]
*[[Ports of Access]]
*[[Forced Matching]]
*[[Recap]]
*[[Creativity and Randomness]]
*[[Picking up Patterns on All Levels]]
*[[The Flexibility of Language]]
*[[Intelligence and Emotions]]
*[[AI Has Far to Go]]
*[[Ten Questions and Speculations]]
*[[Sloth Canon]]
==[[CHAPTER 20: STRANGE LOOPS, OR TANGLED HIERARCHIES]]==
*[[Can Machines Possess Originality?]]
*[[Below Every Tangled Hierarchy Lies An Inviolate Level]]
*[[A Self-Modifying Game]]
*[[The Authorship Triangle Again]]
*[[Escher's Drawing Hands]]
*[[Brain and Mind: A Neural Tangle Supporting a Symbol Tangle]]
*[[Strange Loops in Government]]
*[[Tangles Involving Science and the Occult]]
*[[The Nature of Evidence]]
*[[Seeing Oneself]]
*[[Gödel's Theorem and Other Disciplines]]
*[[Introspection and Insanity: A Gödelian Problem]]
*[[Can We Understand Our Own Minds or Brains?]]
*[[Gödel's Theorem and Personal Nonexistence]]
*[[Science and Dualism]]
*[[Symbol vs. Object in Modern Music and Art]]
*[[Magritte's Semantic Illusions]]
*[[The Code" of Modern Art"]]
*[[Ism Once Again]]
*[[Understanding the Mind]]
*[[Accidental Inexplicability of Intelligence?]]
*[[Undecidability Is Inseparable from a High-Level Viewpoint]]
*[[Consciousness as an Intrinsically High-Level Phenomenon]]
*[[Strange Loops as the Crux of Consciousness]]
*[[The Self-Symbol and Free Will]]
*[[A Gödel Vortex Where All Levels Cross]]
*[[An Escher Vortex Where All Levels Cross]]
*[[A Bach Vortex Where All Levels Cross]]
*[[Six-Part Ricercar]]

Main Page

RobKohr — Mon, 06 Feb 2006 17:57:19 GMT

RobKohr:

Gödel, Escher, Bach - An Eternal Golden Braid

This wiki is for conversations and thoughts on the book. This is the

==[[PART I: GEB]]==
*[[INTRODUCTION: A MUSICO-LOGICAL OFFERING]]==
*[[Author]]
*[[Bach]]
*[[Canons and Fugues]]
*[[An Endlessly Rising Canon]]
*[[Escher]]
*[[Gödel]]
*[[Mathematical Logic: A Synopsis]]
*[[Banishing Strange Loops]]
*[[Consistency, Completeness, Hilbert's Program]]
*[[Babbage, Computers, Artificial Intelligence...]]
*[[...and Bach]]
*[[Gödel Escher Bach]]
*[[Three-Part Invention]]
==[[CHAPTER 1: THE MU-PUZZLE]]==
*[[Formal Systems]]
*[[Theorems, Axioms, Rules]]
*[[Inside and Outside the System]]
*[[Jumping out of the System]]
*[[M-Mode, I-Mode, U-Mode]]
*[[Decision Procedures]]
*[[Two-Part Invention]]
==[[CHAPTER 2: MEANING AND FORM IN MATHEMATICS]]==
*[[The pq-System]]
*[[The Decision Procedure]]
*[[Bottom-up vs. Top-down]]
*[[Isomorphisms Induce Meaning]]
*[[Meaningless and Meaningful Interpretations]]
*[[Active vs. Passive Meanings]]
*[[Double-Entendre!]]
*[[Formal Systems and Reality]]
*[[Mathematics and Symbol Manipulation]]
*[[The Basic Laws of Arithmetic]]
*[[Ideal Numbers]]
*[[Euclid's Proof]]
*[[Getting Around Infinity]]
*[[Sonata for Unaccompanied Achilles]]
==[[CHAPTER 3: FIGURE AND GROUND]]==
*[[Primes vs. Composites]]
*[[The tq-System]]
*[[Capturing Compositeness]]
*[[Illegally Characterizing Primes]]
*[[Figure and Ground]]
*[[Figure and Ground in Music]]
*[[Recursively Enumerable Sets vs. Recursive Sets]]
*[[Primes as Figure Rather than Ground]]
*[[Contracrostipunctus]]
==[[CHAPTER 4: CONSISTENCY, COMPLETENESS, AND GEOMETRY]]==
*[[Implicit and Explicit Meaning]]
*[[Explicit Meaning of the Contracrostipunctus]]
*[[Implicit Meanings of the Contracrostipunctus]]
*[[Mapping Between the Contracrostipunctus and Gödel's Theorem]]
*[[The Art of the Fugue]]
*[[Problems Caused by Gödel's Result]]
*[[The Modified pq-System and Inconsistency]]
*[[Regaining Consistency]]
*[[The History of Euclidean Geometry]]
*[[The Many Faces of Noneuclid]]
*[[Undefined Terms]]
*[[The Possibility of Multiple Interpretations]]
*[[Varieties of Consistency]]
*[[Hypothetical Worlds and Consistency]]
*[[Embedding of One Formal System in Another]]
*[[Layers of Stability in Visual Perception]]
*[[Is Mathematics the Same in Every Conceivable World?]]
*[[Is Number Theory the Same in All Conceivable Worlds?]]
*[[Completeness]]
*[[How an Interpretation May Make or Break Completeness]]
*[[Incompleteness of Formalized Number Theory]]
*[[Little Harmonic Labyrinth]]
==[[CHAPTER 5: RECURSIVE STRUCTURES AND PROCESSES]]==
*[[What Is Recursion?]]
*[[Pushing, Popping, and Stacks]]
*[[Stacks in Music]]
*[[Recursion in Language]]
*[[Recursive Transition Networks]]
*[[Bottoming Out" and Heterarchies"]]
*[[Expanding Nodes]]
*[[Diagram G and Recursive Sequences]]
*[[A Chaotic Sequence]]
*[[Two Striking Recursive Graphs]]
*[[Recursion at the Lowest Level of Matter]]
*[[Copies and Sameness]]
*[[Programming and Recursion: Modularity, Loops, Procedures]]
*[[Recursion in Chess Programs]]
*[[Recursion and Unpredictability]]
*[[Canon by Intervallic Augmentation]]
==[[CHAPTER 6: THE LOCATION OF MEANING]]==
*[[When is One Thing Not Always the Same?]]
*[[Information-Bearers and Information-Revealers]]
*[[Genotype and Phenotype]]
*[[Exotic and Prosaic Isomorphisms]]
*[[Jukeboxes and Triggers]]
*[[DNA and the Necessity of Chemical Context]]
*[[An Unlikely UFO]]
*[[Levels of Understanding of a Message]]
*[[Imaginary Spacescape]]
*[[The Heroic Decipherers]]
*[[Three Layers of Any Message]]
*[[Schrödinger's Aperiodic Crystals]]
*[[Languages for the Three Levels]]
*[[The Jukebox" Theory of Meaning"]]
*[[Against the Jukebox Theory]]
*[[Meaning Is Intrinsic If Intelligence is Natural]]
*[[Earth Chauvinism]]
*[[Two Plaques in Space]]
*[[Bach vs. Cage Again]]
*[[How Universal Is DNA's Message?]]
*[[Chromatic Fantasy, and Feud]]
==[[CHAPTER 7: THE PROPOSITIONAL CALCULUS]]==
*[[Words and Symbols]]
*[[Alphabet and First Rule of the Propositional Calculus]]
*[[Well-Formed Strings]]
*[[More Rules of Inference]]
*[[The Fantasy Rule]]
*[[Recursion and the Fantasy Rule]]
*[[The Converse of the Fantasy Rule]]
*[[The Intended Interpretation of the Symbols]]
*[[Rounding Out the List of Rules]]
*[[Justifying the Rules]]
*[[Playing Around with the System]]
*[[Semi-Interpretations]]
*[[Ganto's Ax]]
*[[Is There a Decision Procedure for Theorems?]]
*[[Do We Know the System Is Consistent?]]
*[[The Carroll Dialogue Again]]
*[[Shortcuts and Derived Rules]]
*[[Formalizing Higher Levels]]
*[[Reflections on the Strengths and Weaknesses of the System]]
*[[Proofs vs. Derivations]]
*[[The Handling of Contradictions]]
*[[Crab Canon]]
==[[CHAPTER 8: TYPOGRAPHICAL NUMBER THEORY]]==
*[[The Crab Canon and Indirect Self-Reference]]
*[[What We Want to Be Able to Express in TNT]]
*[[Numerals]]
*[[Variables and Terms]]
*[[Atoms and Propositional Symbols]]
*[[Free Variables and Quantifiers]]
*[[Translating Our Sample Sentences]]
*[[Tricks of the Trade]]
*[[Translation Puzzles for You]]
*[[How to Distinguish True from False?]]
*[[The Rules of Well-Formedness]]
*[[A Few More Translation Exercises]]
*[[A Nontypographical System]]
*[[The Five Axioms and First Rules of TNT]]
*[[The Five Peano Postulates]]
*[[New Rules of TNT: Specification and Generalization]]
*[[The Existential Quantifier]]
*[[Rules of Equality and Successorship]]
*[[Illegal Shortcuts]]
*[[Why Specification and Generalization Are Restricted]]
*[[Something Is Missing]]
*[[[w]-Incomplete Systems and Undecidable Strings]]
*[[Non-Euclidean TNT]]
*[[[w]-Inconsistency Is Not the Same as Inconsistency]]
*[[The Last Rule]]
*[[A Long Derivation]]
*[[Tension and Resolution in TNT]]
*[[Formal Reasoning vs. Informal Reasoning]]
*[[Number Theorists Go out of Business]]
*[[Hilbert's Program]]
*[[A Mu Offering]]
==[[CHAPTER 9: MUMON AND GÖDEL]]==
*[[What is Zen?]]
*[[Zen Master Mumon]]
*[[Zen's Struggle Against Dualism]]
*[[Ism, The Un-Mode, and Unmon]]
*[[Zen and Tumbolia]]
*[[Escher and Zen]]
*[[Hemiolia and Escher]]
*[[Indra's Net]]
*[[Mumon on MU]]
*[[From Mumon to the MU-puzzle]]
*[[Mumon Shows Us How to Solve the MU-puzzle]]
*[[Gödel-Numbering the MIU-System]]
*[[Seeing Things Both Typographically and Arithmetically]]
*[[MIU-Producible Numbers]]
*[[Answering Questions about Producible Numbers by Consulting TNT]]
*[[The Dual Nature of MUMON]]
*[[Codes and Implicit Meaning]]
*[[The Boomerang: Gödel-Numbering TNT]]
*[[TNT-Numbers: A Recursively Enumerable Set of Numbers]]
*[[TNT Tries to Swallow Itself]]
*[[G: A String Which Talks about Itself in Code]]
*[[G's Existence Is What Causes TNT's Incompleteness]]
*[[Mumon Has the Last Word]]==
=[[PART II: EGB]]=
*[[Prelude...]]
==[[CHAPTER 10: LEVELS OF DESCRIPTION, AND COMPUTER SYSTEMS]]==
*[[Levels of Description]]
*[[Chunking and Chess Skill]]
*[[Similar Levels]]
*[[Computer Systems]]
*[[Instructions and Data]]
*[[Machine Language vs. Assembly language]]
*[[Programs That Translate Programs]]
*[[Higher-Level Languages, Compilers, and Interpreters]]
*[[Bootstrapping]]
*[[Levels on Which to Describe Running Programs]]
*[[Microprogramming and Operating Systems]]
*[[Cushioning the User and Protecting the System]]
*[[Are Computers Super-Flexible or Super-Rigid?]]
*[[Second-Guessing the Programmer]]
*[[AI Advanced Are Language Advances]]
*[[The Paranoid and the Operating System]]
*[[The Border between Software and Hardware]]
*[[Intermediate Levels and the Weather]]
*[[From Tornados to Quarks]]
*[[Superconductivity: A Paradox" of Renormalization"]]
*[[Sealing-off]]
*[[The Trade-off between Chunking and Determinism]]
*[[Computers Can Only Do What You Tell Them to Do]]
*[[Two Types of System]]
*[[Epiphenomena]]
*[[Mind vs. Brain]]
*[[...Ant Fugue]]
==[[CHAPTER 11: BRAINS AND THOUGHTS]]==
*[[New Perspectives on Thought]]
*[[Intensionality and Extensionality]]
*[[The Brain's Ants]]
*[[Larger Structures in the Brain]]
*[[Mappings between Brains]]
*[[Localization of Brain Processes: An Enigma]]
*[[Specificity in Visual Processing]]
*[[A Grandmother Cell"?"]]
*[[Funneling into Neural Modules]]
*[[Modules Which Mediate Thought Processes]]
*[[Active Symbols]]
*[[Classes and Instances]]
*[[The Prototype Principle]]
*[[The Splitting-off of Instance from Classes]]
*[[The Difficulty of Disentangling Symbols from Each Other]]
*[[Symbols -- Software or Hardware?]]
*[[Liftability of Intelligence]]
*[[Can One Symbol Be Isolated?]]
*[[The Symbols of Insects]]
*[[Class Symbols and Imaginary Worlds]]
*[[Intuitive Laws of Physics]]
*[[Procedural and Declarative Knowledge]]
*[[Visual Imagery]]
*[[English French German Suite]]
==[[CHAPTER 12: MINDS AND THOUGHTS]]==
*[[Can Minds Be Mapped onto Each Other?]]
*[[Comparing Different Semantic Networks]]
*[[Translations of Jabberwocky]]
*[[ASU's]]
*[[A Surprise Reversal]]
*[[Centrality and Universality]]
*[[How Much Do Language and Culture Channel Thought?]]
*[[Trips and Itineraries in ASU's]]
*[[Possible, Potential, and Preposterous Pathways]]
*[[Different Styles of Translating Novels]]
*[[High-Level Comparisons between Programs]]
*[[High-Level Comparisons between Brains]]
*[[Potential Beliefs, Potential Symbols]]
*[[Where is the Sense of Self?]]
*[[Subsystems]]
*[[Subsystems and Shared Code]]
*[[The Self-Symbol and Consciousness]]
*[[Our First Encounter with Lucas]]
*[[Aria with Diverse Variations]]
==[[CHAPTER 13: BlooP AND FlooP AND GlooP]]==
*[[Self-Awareness and Chaos]]
*[[Representability and Refrigerators]]
*[[Ganto's Ax in Metamathmatics]]
*[[Finding Order by Choosing the Right Filter]]
*[[Primordial Steps of the Language BlooP]]
*[[Loops and Upper Bounds]]
*[[Conventions of BlooP]]
*[[IF-Statements and Branching]]
*[[Automatic Chunking]]
*[[BlooP Tests]]
*[[BlooP Programs Contain Chains of Procedures]]
*[[Suggested Exercises]]
*[[Expressibility and Representability]]
*[[Primitive Recursive Predicates Are Represented in TNT]]
*[[Are There Functions Which Are Not Primitive Recursive?]]
*[[Pool B, Index Numbers, and Blue Programs]]
*[[The Diagonal Method]]
*[[Cantor's Original Diagonal Argument]]
*[[What Does a Diagonal Argument Prove?]]
*[[The Insidious Repeatability of the Diagonal Argument]]
*[[From BlooP to FlooP]]
*[[Terminating and Nonterminating FlooP Programs]]
*[[Turing's Trickery]]
*[[A Termination Tester Would Be Magical]]
*[[Pool F, Index Numbers, and Green Programs]]
*[[The Termination Tester Gives Us Red Programs]]
*[[GlooP...]]
*[[...Is a Myth]]
*[[The Church-Turing Thesis]]
*[[Terminology: General and Partial Recursive]]
*[[The Power of TNT]]
*[[Air on G's String]]
==[[CHAPTER 14: ON FORMALLY UNDECIDABLE PROPOSITIONS OF TNT AND RELATED SYSTEMS]]==
*[[The Two Ideas of the Oyster]]
*[[The First Idea: Proof-Pairs]]
*[[Proof-Pair-ness Is Primitive Recursive...]]
*[[...And Is Therefore Represented in TNT]]
*[[The Power of Proof-Pairs]]
*[[Substitution Leads to the Second Idea]]
*[[Arithmoquining]]
*[[The Last Straw]]
*[[TNT Says Uncle!]]
*[[Yields Nontheoremhood When Arithmoquined]]
*[[Gödel's Second Theorem]]
*[[TNT Is [w]-Incomplete]]
*[[Two Different Ways to Plug Up the Hole]]
*[[Supernatural Numbers]]
*[[Supernatural Theorems Have Infinitely Long Derivations]]
*[[Supernatural Addition and Multiplication]]
*[[Supernaturals Are Useful...]]
*[[...But Are They Real?]]
*[[Bifurcations in Geometry, and Physicists]]
*[[Bifurcations in Number Theory, and Bankers]]
*[[Bifurcations in Number Theory, and Metamathematicians]]
*[[Hilbert's Tenth Problem and the Tortoise]]
*[[Birthday Cantatatata...]]
==[[CHAPTER 15: JUMPING OUT OF THE SYSTEM]]==
*[[A More Powerful Formal System]]
*[[The Gödel Method Reapplied]]
*[[Multifurcation]]
*[[Essential Incompleteness]]
*[[The Passion According to Lucas]]
*[[Jumping Up a Dimension]]
*[[The Limits of Intelligent Systems]]
*[[There Is No Recursive Rule for Naming Ordinals]]
*[[Other Refutations of Lucas]]
*[[Self-Transcendence -- A Modern Myth]]
*[[Advertisement and Framing Devices]]
*[[Simplicio, Salviati, Sagredo: Why Three?]]
*[[Zen and Stepping Out]]
*[[Edifying Thoughts of a Tobacco Smoker]]
==[[CHAPTER 16: SELF-REF AND SELF-REP]]==
*[[Implicitly and Explicitly Self-Referential Sentences]]
*[[A Self-Reproducing Program]]
*[[What Is a Copy?]]
*[[A Self-Reproducing Song]]
*[[Epimenides Straddles the Channel]]
*[[A Program That Prints Out Its Own Gödel Number]]
*[[Gödelian Self-Reference]]
*[[A Self-Rep by Augmentation]]
*[[A Kimian Self-Rep]]
*[[What Is the Original?]]
*[[Typogenetics]]
*[[Strands, Bases, Enzymes]]
*[[Copy Mode and Double Strands]]
*[[Amino Acids]]
*[[Translation and the Typogenetic Code]]
*[[Tertiary Structure of Enzymes]]
*[[Punctuation, Genes, and Ribosomes]]
*[[Puzzle: A Typogenetical Self-Rep]]
*[[The Central Dogma of Typogenetics]]
*[[Strange Loops, TNT, and Real Genetics]]
*[[DNA and Nucleotides]]
*[[Messenger RNA and Ribosomes]]
*[[Amino Acids]]
*[[Ribosomes and Tape Recorders]]
*[[The Genetic Code]]
*[[Tertiary Structure]]
*[[Reductionistic Explanation of Protein Function]]
*[[Transfer RNA and Ribosomes]]
*[[Punctuation and the Reading Frame]]
*[[Recap]]
*[[Levels of Structure and Meaning in Proteins and Music]]
*[[Polyribosomes and Two-Tiered Canons]]
*[[Which Came First -- The Ribosome or the Protein?]]
*[[Protein Function]]
*[[Need for a Sufficiently Strong Support System]]
*[[How DNA Self-Replicates]]
*[[Comparison of DNA's Self-Rep Method with Quining]]
*[[Levels of Meaning of DNA]]
*[[The Central Dogmap]]
*[[Strange Loops in the Central Dogmap]]
*[[The Central Dogmap and the Contracrostipunctus]]
*[[E. Coli vs. T4]]
*[[A Molecular Trojan Horse]]
*[[Recognition, Disguises, Labeling]]
*[[Henkin Sentences and Viruses]]
*[[Implicit vs. Explicit Henkin Sentences]]
*[[Henkin Sentences and Self-Assembly]]
*[[Two Outstanding Problems: Differentiation and Morphogenesis]]
*[[Feedback and Feedforward]]
*[[Repressors and Inducers]]
*[[Feedback and Strange Loops Compared]]
*[[Two Simple Examples of Differentiation]]
*[[Level Mixing in the Cell]]
*[[The Origin of Life]]
*[[The Magnificrab, Indeed]]
==[[CHAPTER 17: CHURCH, TURING, TARSKI, AND OTHERS]]==
*[[Formal and Informal Systems]]
*[[Intuition and the Magnificent Crab]]
*[[The Church-Turing Thesis]]
*[[The Public-Processes Version]]
*[[Srinivasa Ramanujan]]
*[[Idiots Savants]]
*[[The Isomorphism Version of the Church-Turing Thesis]]
*[[Representation of Knowledge about the Real World]]
*[[Processes That Are Not So Skimmable]]
*[[Articles of Reductionistic Faith]]
*[[Partial Progress in AI and Brain Simulation?]]
*[[Beauty, the Crab, and the Soul]]
*[[Irrational and Rational Can Coexist on Different Levels]]
*[[More Against Lucas]]
*[[An Underpinning of AI]]
*[[Church's Theorem]]
*[[Tarski's Theorem]]
*[[The Impossibility of the Magnificrab]]
*[[Two Types of Form]]
*[[Meaning Derives from Connections to Cognitive Structures]]
*[[Beauty, Truth, and Form]]
*[[The Neural Substrate of the Epimenides Paradox]]
*[[SHRDLU, Toy of Man's Designing]]
==[[CHAPTER 18: ARTIFICIAL INTELLIGENCE: RETROSPECTS]]==
*[[Turing]]
*[[The Turing Test]]
*[[Turing Anticipates Objections]]
*[[Parry Encounters the Doctor]]
*[[A Brief History of AI]]
*[[Mechanical Translation]]
*[[Computer Chess]]
*[[Samuel's Checker Program]]
*[[When Is a Program Original?]]
*[[Who Composes Computer Music?]]
*[[Theorem Proving and Problem Reduction]]
*[[Shandy and the Bone]]
*[[Changing the Problem Space]]
*[[The I-Mode and the M-Mode Again]]
*[[Applying AI to Mathematics]]
*[[The Crux of AI: Representation of Knowledge]]
*[[DNA and Proteins Help Give Some Perspective]]
*[[Modularity of Knowledge]]
*[[Representing Knowledge in a Logical Formalism]]
*[[Deductive vs. Analogical Awareness]]
*[[From Computer Haiku to an RTN-Grammar]]
*[[From RTN's to ATN's]]
*[[A Little Turing Test]]
*[[Images of What Thought Is]]
*[[Higher-Level Grammars...]]
*[[Grammars for Music?]]
*[[Winograd's Program SHRDLU]]
*[[The Structure of SHRDLU]]
*[[PLANNER Facilitates Problem Reduction]]
*[[Syntax and Semantics]]
*[[Contrafactus]]
==[[CHAPTER 19: ARTIFICIAL INTELLIGENCE: PROSPECTS]]==
*[[Almost" Situations and Subjunctives"]]
*[[Layers of Stability]]
*[[Frames and Nested Contexts]]
*[[Bongard Problems]]
*[[Preprocessing Selects a Mini-Vocabulary]]
*[[High-Level Descriptions]]
*[[Templates and Sameness-Detectors]]
*[[A Heterarchical Program]]
*[[The Concept Network]]
*[[Slippage and Tentativity]]
*[[Meta-Descriptions]]
*[[Flexibility is Important]]
*[[Focusing and Filtering]]
*[[Science and the World of Bongard Problems]]
*[[Connections to Other Types of Thought]]
*[[Message-Passing Languages, Frames, and Symbols]]
*[[Enzymes and AI]]
*[[Fission and Fusion]]
*[[Epigenesis of the Crab Canon]]
*[[Conceptual Skeletons and Conceptual Mapping]]
*[[Recombinant Ideas]]
*[[Abstractions, Skeletons, Analogies]]
*[[Multiple Representations]]
*[[Ports of Access]]
*[[Forced Matching]]
*[[Recap]]
*[[Creativity and Randomness]]
*[[Picking up Patterns on All Levels]]
*[[The Flexibility of Language]]
*[[Intelligence and Emotions]]
*[[AI Has Far to Go]]
*[[Ten Questions and Speculations]]
*[[Sloth Canon]]
==[[CHAPTER 20: STRANGE LOOPS, OR TANGLED HIERARCHIES]]==
*[[Can Machines Possess Originality?]]
*[[Below Every Tangled Hierarchy Lies An Inviolate Level]]
*[[A Self-Modifying Game]]
*[[The Authorship Triangle Again]]
*[[Escher's Drawing Hands]]
*[[Brain and Mind: A Neural Tangle Supporting a Symbol Tangle]]
*[[Strange Loops in Government]]
*[[Tangles Involving Science and the Occult]]
*[[The Nature of Evidence]]
*[[Seeing Oneself]]
*[[Gödel's Theorem and Other Disciplines]]
*[[Introspection and Insanity: A Gödelian Problem]]
*[[Can We Understand Our Own Minds or Brains?]]
*[[Gödel's Theorem and Personal Nonexistence]]
*[[Science and Dualism]]
*[[Symbol vs. Object in Modern Music and Art]]
*[[Magritte's Semantic Illusions]]
*[[The Code" of Modern Art"]]
*[[Ism Once Again]]
*[[Understanding the Mind]]
*[[Accidental Inexplicability of Intelligence?]]
*[[Undecidability Is Inseparable from a High-Level Viewpoint]]
*[[Consciousness as an Intrinsically High-Level Phenomenon]]
*[[Strange Loops as the Crux of Consciousness]]
*[[The Self-Symbol and Free Will]]
*[[A Gödel Vortex Where All Levels Cross]]
*[[An Escher Vortex Where All Levels Cross]]
*[[A Bach Vortex Where All Levels Cross]]
*[[Six-Part Ricercar]]

Main Page

RobKohr — Mon, 06 Feb 2006 17:52:37 GMT

RobKohr:

Gödel, Escher, Bach - An Eternal Golden Braid

This wiki is for conversations and thoughts on the book. This is the

*[[PART I: GEB]]
*[[]]
*[[INTRODUCTION: A MUSICO-LOGICAL OFFERING]]
*[[]]
*[[Author]]
*[[Bach]]
*[[Canons and Fugues]]
*[[An Endlessly Rising Canon]]
*[[Escher]]
*[[Gödel]]
*[[Mathematical Logic: A Synopsis]]
*[[Banishing Strange Loops]]
*[[Consistency, Completeness, Hilbert's Program]]
*[[Babbage, Computers, Artificial Intelligence...]]
*[[...and Bach]]
*[[Gödel Escher Bach]]
*[[ Three-Part Invention]]
*[[]]
*[[]]
*[[CHAPTER 1: THE MU-PUZZLE]]
*[[]]
*[[Formal Systems]]
*[[Theorems, Axioms, Rules]]
*[[Inside and Outside the System]]
*[[Jumping out of the System]]
*[[M-Mode, I-Mode, U-Mode]]
*[[Decision Procedures]]
*[[ Two-Part Invention]]
*[[]]
*[[]]
*[[CHAPTER 2: MEANING AND FORM IN MATHEMATICS]]
*[[]]
*[[The pq-System]]
*[[The Decision Procedure]]
*[[Bottom-up vs. Top-down]]
*[[Isomorphisms Induce Meaning]]
*[[Meaningless and Meaningful Interpretations]]
*[[Active vs. Passive Meanings]]
*[[Double-Entendre!]]
*[[Formal Systems and Reality]]
*[[Mathematics and Symbol Manipulation]]
*[[The Basic Laws of Arithmetic]]
*[[Ideal Numbers]]
*[[Euclid's Proof]]
*[[Getting Around Infinity]]
*[[ Sonata for Unaccompanied Achilles]]
*[[]]
*[[]]
*[[CHAPTER 3: FIGURE AND GROUND]]
*[[]]
*[[Primes vs. Composites]]
*[[The tq-System]]
*[[Capturing Compositeness]]
*[[Illegally Characterizing Primes]]
*[[Figure and Ground]]
*[[Figure and Ground in Music]]
*[[Recursively Enumerable Sets vs. Recursive Sets]]
*[[Primes as Figure Rather than Ground]]
*[[ Contracrostipunctus]]
*[[]]
*[[]]
*[[CHAPTER 4: CONSISTENCY, COMPLETENESS, AND GEOMETRY]]
*[[]]
*[[Implicit and Explicit Meaning]]
*[[Explicit Meaning of the Contracrostipunctus]]
*[[Implicit Meanings of the Contracrostipunctus]]
*[[Mapping Between the Contracrostipunctus and Gödel's Theorem]]
*[[The Art of the Fugue]]
*[[Problems Caused by Gödel's Result]]
*[[The Modified pq-System and Inconsistency]]
*[[Regaining Consistency]]
*[[The History of Euclidean Geometry]]
*[[The Many Faces of Noneuclid]]
*[[Undefined Terms]]
*[[The Possibility of Multiple Interpretations]]
*[[Varieties of Consistency]]
*[[Hypothetical Worlds and Consistency]]
*[[Embedding of One Formal System in Another]]
*[[Layers of Stability in Visual Perception]]
*[[Is Mathematics the Same in Every Conceivable World?]]
*[[Is Number Theory the Same in All Conceivable Worlds?]]
*[[Completeness]]
*[[How an Interpretation May Make or Break Completeness]]
*[[Incompleteness of Formalized Number Theory]]
*[[ Little Harmonic Labyrinth]]
*[[]]
*[[]]
*[[CHAPTER 5: RECURSIVE STRUCTURES AND PROCESSES]]
*[[]]
*[[What Is Recursion?]]
*[[Pushing, Popping, and Stacks]]
*[[Stacks in Music]]
*[[Recursion in Language]]
*[[Recursive Transition Networks]]
*[[Bottoming Out" and Heterarchies"]]
*[[Expanding Nodes]]
*[[Diagram G and Recursive Sequences]]
*[[A Chaotic Sequence]]
*[[Two Striking Recursive Graphs]]
*[[Recursion at the Lowest Level of Matter]]
*[[Copies and Sameness]]
*[[Programming and Recursion: Modularity, Loops, Procedures]]
*[[Recursion in Chess Programs]]
*[[Recursion and Unpredictability]]
*[[ Canon by Intervallic Augmentation]]
*[[]]
*[[]]
*[[CHAPTER 6: THE LOCATION OF MEANING]]
*[[]]
*[[When is One Thing Not Always the Same?]]
*[[Information-Bearers and Information-Revealers]]
*[[Genotype and Phenotype]]
*[[Exotic and Prosaic Isomorphisms]]
*[[Jukeboxes and Triggers]]
*[[DNA and the Necessity of Chemical Context]]
*[[An Unlikely UFO]]
*[[Levels of Understanding of a Message]]
*[[Imaginary Spacescape""]]
*[[The Heroic Decipherers]]
*[[Three Layers of Any Message]]
*[[Schrödinger's Aperiodic Crystals]]
*[[Languages for the Three Levels]]
*[[The Jukebox" Theory of Meaning"]]
*[[Against the Jukebox Theory]]
*[[Meaning Is Intrinsic If Intelligence is Natural]]
*[[Earth Chauvinism]]
*[[Two Plaques in Space]]
*[[Bach vs. Cage Again]]
*[[How Universal Is DNA's Message?]]
*[[ Chromatic Fantasy, and Feud]]
*[[]]
*[[]]
*[[CHAPTER 7: THE PROPOSITIONAL CALCULUS]]
*[[]]
*[[Words and Symbols]]
*[[Alphabet and First Rule of the Propositional Calculus]]
*[[Well-Formed Strings]]
*[[More Rules of Inference]]
*[[The Fantasy Rule]]
*[[Recursion and the Fantasy Rule]]
*[[The Converse of the Fantasy Rule]]
*[[The Intended Interpretation of the Symbols]]
*[[Rounding Out the List of Rules]]
*[[Justifying the Rules]]
*[[Playing Around with the System]]
*[[Semi-Interpretations]]
*[[Ganto's Ax]]
*[[Is There a Decision Procedure for Theorems?]]
*[[Do We Know the System Is Consistent?]]
*[[The Carroll Dialogue Again]]
*[[Shortcuts and Derived Rules]]
*[[Formalizing Higher Levels]]
*[[Reflections on the Strengths and Weaknesses of the System]]
*[[Proofs vs. Derivations]]
*[[The Handling of Contradictions]]
*[[ Crab Canon]]
*[[]]
*[[]]
*[[CHAPTER 8: TYPOGRAPHICAL NUMBER THEORY]]
*[[]]
*[[The Crab Canon and Indirect Self-Reference]]
*[[What We Want to Be Able to Express in TNT]]
*[[Numerals]]
*[[Variables and Terms]]
*[[Atoms and Propositional Symbols]]
*[[Free Variables and Quantifiers]]
*[[Translating Our Sample Sentences]]
*[[Tricks of the Trade]]
*[[Translation Puzzles for You]]
*[[How to Distinguish True from False?]]
*[[The Rules of Well-Formedness]]
*[[A Few More Translation Exercises]]
*[[A Nontypographical System]]
*[[The Five Axioms and First Rules of TNT]]
*[[The Five Peano Postulates]]
*[[New Rules of TNT: Specification and Generalization]]
*[[The Existential Quantifier]]
*[[Rules of Equality and Successorship]]
*[[Illegal Shortcuts]]
*[[Why Specification and Generalization Are Restricted]]
*[[Something Is Missing]]
*[[[w]-Incomplete Systems and Undecidable Strings]]
*[[Non-Euclidean TNT]]
*[[[w]-Inconsistency Is Not the Same as Inconsistency]]
*[[The Last Rule]]
*[[A Long Derivation]]
*[[Tension and Resolution in TNT]]
*[[Formal Reasoning vs. Informal Reasoning]]
*[[Number Theorists Go out of Business]]
*[[Hilbert's Program]]
*[[ A Mu Offering]]
*[[]]
*[[]]
*[[CHAPTER 9: MUMON AND GÖDEL]]
*[[]]
*[[What is Zen?]]
*[[Zen Master Mumon]]
*[[Zen's Struggle Against Dualism]]
*[[Ism, The Un-Mode, and Unmon]]
*[[Zen and Tumbolia]]
*[[Escher and Zen]]
*[[Hemiolia and Escher]]
*[[Indra's Net]]
*[[Mumon on MU]]
*[[From Mumon to the MU-puzzle]]
*[[Mumon Shows Us How to Solve the MU-puzzle]]
*[[Gödel-Numbering the MIU-System]]
*[[Seeing Things Both Typographically and Arithmetically]]
*[[MIU-Producible Numbers]]
*[[Answering Questions about Producible Numbers by Consulting TNT]]
*[[The Dual Nature of MUMON]]
*[[Codes and Implicit Meaning]]
*[[The Boomerang: Gödel-Numbering TNT]]
*[[TNT-Numbers: A Recursively Enumerable Set of Numbers]]
*[[TNT Tries to Swallow Itself]]
*[[G: A String Which Talks about Itself in Code]]
*[[G's Existence Is What Causes TNT's Incompleteness]]
*[[Mumon Has the Last Word]]
*[[]]
*[[PART II: EGB]]
*[[]]
*[[ Prelude...]]
*[[]]
*[[CHAPTER 10: LEVELS OF DESCRIPTION, AND COMPUTER SYSTEMS]]
*[[]]
*[[Levels of Description]]
*[[Chunking and Chess Skill]]
*[[Similar Levels]]
*[[Computer Systems]]
*[[Instructions and Data]]
*[[Machine Language vs. Assembly language]]
*[[Programs That Translate Programs]]
*[[Higher-Level Languages, Compilers, and Interpreters]]
*[[Bootstrapping]]
*[[Levels on Which to Describe Running Programs]]
*[[Microprogramming and Operating Systems]]
*[[Cushioning the User and Protecting the System]]
*[[Are Computers Super-Flexible or Super-Rigid?]]
*[[Second-Guessing the Programmer]]
*[[AI Advanced Are Language Advances]]
*[[The Paranoid and the Operating System]]
*[[The Border between Software and Hardware]]
*[[Intermediate Levels and the Weather]]
*[[From Tornados to Quarks]]
*[[Superconductivity: A Paradox" of Renormalization"]]
*[[Sealing-off""]]
*[[The Trade-off between Chunking and Determinism]]
*[[Computers Can Only Do What You Tell Them to Do""]]
*[[Two Types of System]]
*[[Epiphenomena]]
*[[Mind vs. Brain]]
*[[ ...Ant Fugue]]
*[[]]
*[[]]
*[[CHAPTER 11: BRAINS AND THOUGHTS]]
*[[]]
*[[New Perspectives on Thought]]
*[[Intensionality and Extensionality]]
*[[The Brain's Ants""]]
*[[Larger Structures in the Brain]]
*[[Mappings between Brains]]
*[[Localization of Brain Processes: An Enigma]]
*[[Specificity in Visual Processing]]
*[[A Grandmother Cell"?"]]
*[[Funneling into Neural Modules]]
*[[Modules Which Mediate Thought Processes]]
*[[Active Symbols]]
*[[Classes and Instances]]
*[[The Prototype Principle]]
*[[The Splitting-off of Instance from Classes]]
*[[The Difficulty of Disentangling Symbols from Each Other]]
*[[Symbols -- Software or Hardware?]]
*[[Liftability of Intelligence]]
*[[Can One Symbol Be Isolated?]]
*[[The Symbols of Insects]]
*[[Class Symbols and Imaginary Worlds]]
*[[Intuitive Laws of Physics]]
*[[Procedural and Declarative Knowledge]]
*[[Visual Imagery]]
*[[ English French German Suite]]
*[[]]
*[[]]
*[[CHAPTER 12: MINDS AND THOUGHTS]]
*[[]]
*[[Can Minds Be Mapped onto Each Other?]]
*[[Comparing Different Semantic Networks]]
*[[Translations of Jabberwocky""]]
*[[ASU's]]
*[[A Surprise Reversal]]
*[[Centrality and Universality]]
*[[How Much Do Language and Culture Channel Thought?]]
*[[Trips and Itineraries in ASU's]]
*[[Possible, Potential, and Preposterous Pathways]]
*[[Different Styles of Translating Novels]]
*[[High-Level Comparisons between Programs]]
*[[High-Level Comparisons between Brains]]
*[[Potential Beliefs, Potential Symbols]]
*[[Where is the Sense of Self?]]
*[[Subsystems]]
*[[Subsystems and Shared Code]]
*[[The Self-Symbol and Consciousness]]
*[[Our First Encounter with Lucas]]
*[[ Aria with Diverse Variations]]
*[[]]
*[[]]
*[[CHAPTER 13: BlooP AND FlooP AND GlooP]]
*[[]]
*[[Self-Awareness and Chaos]]
*[[Representability and Refrigerators]]
*[[Ganto's Ax in Metamathmatics]]
*[[Finding Order by Choosing the Right Filter]]
*[[Primordial Steps of the Language BlooP]]
*[[Loops and Upper Bounds]]
*[[Conventions of BlooP]]
*[[IF-Statements and Branching]]
*[[Automatic Chunking]]
*[[BlooP Tests]]
*[[BlooP Programs Contain Chains of Procedures]]
*[[Suggested Exercises]]
*[[Expressibility and Representability]]
*[[Primitive Recursive Predicates Are Represented in TNT]]
*[[Are There Functions Which Are Not Primitive Recursive?]]
*[[Pool B, Index Numbers, and Blue Programs]]
*[[The Diagonal Method]]
*[[Cantor's Original Diagonal Argument]]
*[[What Does a Diagonal Argument Prove?]]
*[[The Insidious Repeatability of the Diagonal Argument]]
*[[From BlooP to FlooP]]
*[[Terminating and Nonterminating FlooP Programs]]
*[[Turing's Trickery]]
*[[A Termination Tester Would Be Magical]]
*[[Pool F, Index Numbers, and Green Programs]]
*[[The Termination Tester Gives Us Red Programs]]
*[[GlooP...]]
*[[...Is a Myth]]
*[[The Church-Turing Thesis]]
*[[Terminology: General and Partial Recursive]]
*[[The Power of TNT]]
*[[ Air on G's String]]
*[[]]
*[[]]
*[[CHAPTER 14: ON FORMALLY UNDECIDABLE PROPOSITIONS OF TNT AND RELATED SYSTEMS]]
*[[]]
*[[The Two Ideas of the Oyster""]]
*[[The First Idea: Proof-Pairs]]
*[[Proof-Pair-ness Is Primitive Recursive...]]
*[[...And Is Therefore Represented in TNT]]
*[[The Power of Proof-Pairs]]
*[[Substitution Leads to the Second Idea]]
*[[Arithmoquining]]
*[[The Last Straw]]
*[[TNT Says Uncle!""]]
*[[Yields Nontheoremhood When Arithmoquined""]]
*[[Gödel's Second Theorem]]
*[[TNT Is [w]-Incomplete]]
*[[Two Different Ways to Plug Up the Hole]]
*[[Supernatural Numbers]]
*[[Supernatural Theorems Have Infinitely Long Derivations]]
*[[Supernatural Addition and Multiplication]]
*[[Supernaturals Are Useful...]]
*[[...But Are They Real?]]
*[[Bifurcations in Geometry, and Physicists]]
*[[Bifurcations in Number Theory, and Bankers]]
*[[Bifurcations in Number Theory, and Metamathematicians]]
*[[Hilbert's Tenth Problem and the Tortoise]]
*[[ Birthday Cantatatata...]]
*[[]]
*[[]]
*[[CHAPTER 15: JUMPING OUT OF THE SYSTEM]]
*[[]]
*[[A More Powerful Formal System]]
*[[The Gödel Method Reapplied]]
*[[Multifurcation]]
*[[Essential Incompleteness]]
*[[The Passion According to Lucas]]
*[[Jumping Up a Dimension]]
*[[The Limits of Intelligent Systems]]
*[[There Is No Recursive Rule for Naming Ordinals]]
*[[Other Refutations of Lucas]]
*[[Self-Transcendence -- A Modern Myth]]
*[[Advertisement and Framing Devices]]
*[[Simplicio, Salviati, Sagredo: Why Three?]]
*[[Zen and Stepping Out""]]
*[[ Edifying Thoughts of a Tobacco Smoker]]
*[[]]
*[[]]
*[[CHAPTER 16: SELF-REF AND SELF-REP]]
*[[]]
*[[Implicitly and Explicitly Self-Referential Sentences]]
*[[A Self-Reproducing Program]]
*[[What Is a Copy?]]
*[[A Self-Reproducing Song]]
*[[Epimenides Straddles the Channel]]
*[[A Program That Prints Out Its Own Gödel Number]]
*[[Gödelian Self-Reference]]
*[[A Self-Rep by Augmentation]]
*[[A Kimian Self-Rep]]
*[[What Is the Original?]]
*[[Typogenetics]]
*[[Strands, Bases, Enzymes]]
*[[Copy Mode and Double Strands]]
*[[Amino Acids]]
*[[Translation and the Typogenetic Code]]
*[[Tertiary Structure of Enzymes]]
*[[Punctuation, Genes, and Ribosomes]]
*[[Puzzle: A Typogenetical Self-Rep]]
*[[The Central Dogma of Typogenetics]]
*[[Strange Loops, TNT, and Real Genetics]]
*[[DNA and Nucleotides]]
*[[Messenger RNA and Ribosomes]]
*[[Amino Acids]]
*[[Ribosomes and Tape Recorders]]
*[[The Genetic Code]]
*[[Tertiary Structure]]
*[[Reductionistic Explanation of Protein Function]]
*[[Transfer RNA and Ribosomes]]
*[[Punctuation and the Reading Frame]]
*[[Recap]]
*[[Levels of Structure and Meaning in Proteins and Music]]
*[[Polyribosomes and Two-Tiered Canons]]
*[[Which Came First -- The Ribosome or the Protein?]]
*[[Protein Function]]
*[[Need for a Sufficiently Strong Support System]]
*[[How DNA Self-Replicates]]
*[[Comparison of DNA's Self-Rep Method with Quining]]
*[[Levels of Meaning of DNA]]
*[[The Central Dogmap]]
*[[Strange Loops in the Central Dogmap]]
*[[The Central Dogmap and the Contracrostipunctus]]
*[[E. Coli vs. T4]]
*[[A Molecular Trojan Horse]]
*[[Recognition, Disguises, Labeling]]
*[[Henkin Sentences and Viruses]]
*[[Implicit vs. Explicit Henkin Sentences]]
*[[Henkin Sentences and Self-Assembly]]
*[[Two Outstanding Problems: Differentiation and Morphogenesis]]
*[[Feedback and Feedforward]]
*[[Repressors and Inducers]]
*[[Feedback and Strange Loops Compared]]
*[[Two Simple Examples of Differentiation]]
*[[Level Mixing in the Cell]]
*[[The Origin of Life]]
*[[ The Magnificrab, Indeed]]
*[[]]
*[[]]
*[[CHAPTER 17: CHURCH, TURING, TARSKI, AND OTHERS]]
*[[]]
*[[Formal and Informal Systems]]
*[[Intuition and the Magnificent Crab]]
*[[The Church-Turing Thesis]]
*[[The Public-Processes Version]]
*[[Srinivasa Ramanujan]]
*[[Idiots Savants""]]
*[[The Isomorphism Version of the Church-Turing Thesis]]
*[[Representation of Knowledge about the Real World]]
*[[Processes That Are Not So Skimmable]]
*[[Articles of Reductionistic Faith]]
*[[Partial Progress in AI and Brain Simulation?]]
*[[Beauty, the Crab, and the Soul]]
*[[Irrational and Rational Can Coexist on Different Levels]]
*[[More Against Lucas]]
*[[An Underpinning of AI]]
*[[Church's Theorem]]
*[[Tarski's Theorem]]
*[[The Impossibility of the Magnificrab]]
*[[Two Types of Form]]
*[[Meaning Derives from Connections to Cognitive Structures]]
*[[Beauty, Truth, and Form]]
*[[The Neural Substrate of the Epimenides Paradox]]
*[[ SHRDLU, Toy of Man's Designing]]
*[[]]
*[[]]
*[[CHAPTER 18: ARTIFICIAL INTELLIGENCE: RETROSPECTS]]
*[[]]
*[[Turing]]
*[[The Turing Test]]
*[[Turing Anticipates Objections]]
*[[Parry Encounters the Doctor""]]
*[[A Brief History of AI]]
*[[Mechanical Translation]]
*[[Computer Chess]]
*[[Samuel's Checker Program]]
*[[When Is a Program Original?]]
*[[Who Composes Computer Music?]]
*[[Theorem Proving and Problem Reduction]]
*[[Shandy and the Bone]]
*[[Changing the Problem Space]]
*[[The I-Mode and the M-Mode Again]]
*[[Applying AI to Mathematics]]
*[[The Crux of AI: Representation of Knowledge]]
*[[DNA and Proteins Help Give Some Perspective]]
*[[Modularity of Knowledge]]
*[[Representing Knowledge in a Logical Formalism]]
*[[Deductive vs. Analogical Awareness]]
*[[From Computer Haiku to an RTN-Grammar]]
*[[From RTN's to ATN's]]
*[[A Little Turing Test]]
*[[Images of What Thought Is]]
*[[Higher-Level Grammars...]]
*[[Grammars for Music?]]
*[[Winograd's Program SHRDLU]]
*[[The Structure of SHRDLU]]
*[[PLANNER Facilitates Problem Reduction]]
*[[Syntax and Semantics]]
*[[ Contrafactus]]
*[[]]
*[[]]
*[[CHAPTER 19: ARTIFICIAL INTELLIGENCE: PROSPECTS]]
*[[]]
*[[Almost" Situations and Subjunctives"]]
*[[Layers of Stability]]
*[[Frames and Nested Contexts]]
*[[Bongard Problems]]
*[[Preprocessing Selects a Mini-Vocabulary]]
*[[High-Level Descriptions]]
*[[Templates and Sameness-Detectors]]
*[[A Heterarchical Program]]
*[[The Concept Network]]
*[[Slippage and Tentativity]]
*[[Meta-Descriptions]]
*[[Flexibility is Important]]
*[[Focusing and Filtering]]
*[[Science and the World of Bongard Problems]]
*[[Connections to Other Types of Thought]]
*[[Message-Passing Languages, Frames, and Symbols]]
*[[Enzymes and AI]]
*[[Fission and Fusion]]
*[[Epigenesis of the Crab Canon]]
*[[Conceptual Skeletons and Conceptual Mapping]]
*[[Recombinant Ideas]]
*[[Abstractions, Skeletons, Analogies]]
*[[Multiple Representations]]
*[[Ports of Access]]
*[[Forced Matching]]
*[[Recap]]
*[[Creativity and Randomness]]
*[[Picking up Patterns on All Levels]]
*[[The Flexibility of Language]]
*[[Intelligence and Emotions]]
*[[AI Has Far to Go]]
*[[Ten Questions and Speculations]]
*[[ Sloth Canon]]
*[[]]
*[[]]
*[[CHAPTER 20: STRANGE LOOPS, OR TANGLED HIERARCHIES]]
*[[]]
*[[Can Machines Possess Originality?]]
*[[Below Every Tangled Hierarchy Lies An Inviolate Level]]
*[[A Self-Modifying Game]]
*[[The Authorship Triangle Again]]
*[[Escher's Drawing Hands]]
*[[Brain and Mind: A Neural Tangle Supporting a Symbol Tangle]]
*[[Strange Loops in Government]]
*[[Tangles Involving Science and the Occult]]
*[[The Nature of Evidence]]
*[[Seeing Oneself]]
*[[Gödel's Theorem and Other Disciplines]]
*[[Introspection and Insanity: A Gödelian Problem]]
*[[Can We Understand Our Own Minds or Brains?]]
*[[Gödel's Theorem and Personal Nonexistence]]
*[[Science and Dualism]]
*[[Symbol vs. Object in Modern Music and Art]]
*[[Magritte's Semantic Illusions]]
*[[The Code" of Modern Art"]]
*[[Ism Once Again]]
*[[Understanding the Mind]]
*[[Accidental Inexplicability of Intelligence?]]
*[[Undecidability Is Inseparable from a High-Level Viewpoint]]
*[[Consciousness as an Intrinsically High-Level Phenomenon]]
*[[Strange Loops as the Crux of Consciousness]]
*[[The Self-Symbol and Free Will]]
*[[A Gödel Vortex Where All Levels Cross]]
*[[An Escher Vortex Where All Levels Cross]]
*[[A Bach Vortex Where All Levels Cross]]
*[[Six-Part Ricercar]]

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