Main Page

From Geb

(Difference between revisions)
(csitdomcola)
(pasaltrca)
Line 1: Line 1:
 +
cocelv
sitdarvardro
sitdarvardro
basdardelbo
basdardelbo
Line 12: Line 13:
dronrolalao
dronrolalao
aceralm
aceralm
-
Gödel, Escher, Bach - An Eternal Golden Braid
+
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.
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.
Line 28: Line 29:
*[[An Endlessly Rising Canon]]
*[[An Endlessly Rising Canon]]
*[[Escher]]
*[[Escher]]
-
*[[Gödel]]
+
*[[Gödel]]
*[[Mathematical Logic: A Synopsis]]
*[[Mathematical Logic: A Synopsis]]
*[[Banishing Strange Loops]]
*[[Banishing Strange Loops]]
Line 34: Line 35:
*[[Babbage, Computers, Artificial Intelligence...]]
*[[Babbage, Computers, Artificial Intelligence...]]
*[[...and Bach]]
*[[...and Bach]]
-
*[[Gödel  Escher  Bach]]
+
*[[Gödel  Escher  Bach]]
*[[Three-Part Invention]]
*[[Three-Part Invention]]
==[[CHAPTER 1: THE MU-PUZZLE]]==
==[[CHAPTER 1: THE MU-PUZZLE]]==
Line 73: Line 74:
*[[Explicit Meaning of the Contracrostipunctus]]
*[[Explicit Meaning of the Contracrostipunctus]]
*[[Implicit Meanings of the Contracrostipunctus]]
*[[Implicit Meanings of the Contracrostipunctus]]
-
*[[Mapping Between the Contracrostipunctus and Gödel's Theorem]]
+
*[[Mapping Between the Contracrostipunctus and Gödel's Theorem]]
*[[The Art of the Fugue]]
*[[The Art of the Fugue]]
-
*[[Problems Caused by Gödel's Result]]
+
*[[Problems Caused by Gödel's Result]]
*[[The Modified pq-System and Inconsistency]]
*[[The Modified pq-System and Inconsistency]]
*[[Regaining Consistency]]
*[[Regaining Consistency]]
Line 121: Line 122:
*[[The Heroic Decipherers]]
*[[The Heroic Decipherers]]
*[[Three Layers of Any Message]]
*[[Three Layers of Any Message]]
-
*[[Schrödinger's Aperiodic Crystals]]
+
*[[Schrödinger's Aperiodic Crystals]]
*[[Languages for the Three Levels]]
*[[Languages for the Three Levels]]
*[[The Jukebox" Theory of Meaning"]]
*[[The Jukebox" Theory of Meaning"]]
Line 278: Line 279:
*[[TNT Says Uncle!]]
*[[TNT Says Uncle!]]
*[[Yields Nontheoremhood When Arithmoquined]]
*[[Yields Nontheoremhood When Arithmoquined]]
-
*[[Gödel's Second Theorem]]
+
*[[Gödel's Second Theorem]]
*[[TNT Is ω-Incomplete]]
*[[TNT Is ω-Incomplete]]
*[[Two Different Ways to Plug Up the Hole]]
*[[Two Different Ways to Plug Up the Hole]]
Line 294: Line 295:
==[[CHAPTER 15: JUMPING OUT OF THE SYSTEM]]==
==[[CHAPTER 15: JUMPING OUT OF THE SYSTEM]]==
*[[A More Powerful Formal System]]
*[[A More Powerful Formal System]]
-
*[[The Gödel Method Reapplied]]
+
*[[The Gödel Method Reapplied]]
*[[Multifurcation]]
*[[Multifurcation]]
*[[Essential Incompleteness]]
*[[Essential Incompleteness]]
Line 409: Line 410:
*[[The Nature of Evidence]]
*[[The Nature of Evidence]]
*[[Seeing Oneself]]
*[[Seeing Oneself]]
-
*[[Gödel's Theorem and Other Disciplines]]
+
*[[Gödel's Theorem and Other Disciplines]]
-
*[[Introspection and Insanity: A Gödelian Problem]]
+
*[[Introspection and Insanity: A Gödelian Problem]]
*[[Can We Understand Our Own Minds or Brains?]]
*[[Can We Understand Our Own Minds or Brains?]]
-
*[[Gödel's Theorem and Personal Nonexistence]]
+
*[[Gödel's Theorem and Personal Nonexistence]]
*[[Science and Dualism]]
*[[Science and Dualism]]
*[[Symbol vs. Object in Modern Music and Art]]
*[[Symbol vs. Object in Modern Music and Art]]
Line 424: Line 425:
*[[Strange Loops as the Crux of Consciousness]]
*[[Strange Loops as the Crux of Consciousness]]
*[[The Self-Symbol and Free Will]]
*[[The Self-Symbol and Free Will]]
-
*[[A Gödel Vortex Where All Levels Cross]]
+
*[[A Gödel Vortex Where All Levels Cross]]
*[[An Escher Vortex Where All Levels Cross]]
*[[An Escher Vortex Where All Levels Cross]]
*[[A Bach Vortex Where All Levels Cross]]
*[[A Bach Vortex Where All Levels Cross]]
*[[Six-Part Ricercar]]
*[[Six-Part Ricercar]]

Revision as of 13:07, 31 December 2007

cocelv sitdarvardro basdardelbo pasgetboelsi laolooudomch cnac4tcotrc domricpasel darcadron bocoloord ougettre errolcrelcar bascaoulil dronrolalao aceralm 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.

-->All pages with content

Red links are pages that have no comment, but you can add your own comments. Blue links contain comments.


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

CHAPTER 2: MEANING AND FORM IN MATHEMATICS

CHAPTER 3: FIGURE AND GROUND

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

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

CHAPTER 8: TYPOGRAPHICAL NUMBER THEORY

PART II: EGB

CHAPTER 11: BRAINS AND THOUGHTS

CHAPTER 12: MINDS AND THOUGHTS

CHAPTER 13: BlooP AND FlooP AND GlooP

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 ω-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 17: CHURCH, TURING, TARSKI, AND OTHERS

CHAPTER 18: ARTIFICIAL INTELLIGENCE: RETROSPECTS

CHAPTER 19: ARTIFICIAL INTELLIGENCE: PROSPECTS

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
Retrieved from "http://editthis.info/GEB/Main_Page"
Personal tools