Fluid Concepts and Creative Analogies: Computer Models and the Fundamental Mechanisms of Thought

Douglas Hofstadter

List of Illustrations

Prologue: The When, the Where, and the Who of This Book

A Short History of FARG and FARGonauts
The Double-Strandedness of FARG's Intellectual Goals
This Book in a Nutshell
Some Vital Acknowledgments
Post Scriptum

1. To Seek Whence Cometh a Sequence

Pattern-Finding as the Core of Intelligence
Triangles between Squares
Dot dot dot...
Introduction to Mathgod
A Strange Pattern Starts to Appear
Reenactment of a Discovery
A Magical Aperiodic Pattern
Pattern Extrapolation as Research Project and Class Assignment
Trying to Reduce a Sequence to Simpler Sequences
Strategies for Controlling a Search
Heuristics, or the Importance of Sniffing Before You Inhale Deeply
Glimpses of a Very Different Type of Architecture
General Intelligence vs. Expert Knowledge
Mathgod Makes a Booboo
Mathgod Redeemed
Aesthetics-Driven Perception
Elegance and Consistency Unravel a Sample Sequence
Number Savvy vs. Pattern Sensitivity
A Droll Interlude
Segmentation and Unification - Intertwined Facets of Pattern Sensitivity
The Austere Microworld of Seek-Whence
Good-bye, Math... Hello, Music!
The Theme Song of the Seek-Whence Project
The Surprisingly Wide Gulf between Researchers' Goals
Typical Sequences in the Seek-Whence Domain
The Deep Problem of Representing Rules Realistically
A Mountain-Chain Sequence
Building Up Islands of Order
Many Levels of Perception, All Going on in Parallel
The Key Role of Analogies
The Mountain-Chain Sequence - Solved
Polishing the Solution
On Deciphering Shorter vs. Longer Messages
Mathematicians' Deep Ambivalence towards Obvious Patterns
Expanding Conceptual Spheres in Mathematics
Common Sense and Expanding Conceptual Spheres
How Far Can a Conceptual Sphere Stretch Before it Pops?
The "Me-Too" Phenomenon
Outward Generalization in the Seek-Whence Domain
Variations on a Theme by Chopin
The Blurry Edge of Essence
Coming Full Circle to Triangles between Squares
From Seek-Whence to Jumbo, Copycat, and Others

2a. The Unconscious Juggling of Mental Objects

The Joy of Anagrams
Letters Go Up, Words Come Down
The Gulf between Virtual Mental Objects and Their Physical Substrate
Jumbo vs. Brute Force
That Fateful Footnote
The Parallel Terraced Scan Meets the Greek System
To Read, or Toreador
To Learn, or Not to Learn

2b. The Architecture of Jumbo

Prologue: Not Mumbo-Jumbo
Jumbo and Jumbles
The Significance of Jumbo's Task Domain
Two Basic Analogies on which Jumbo Rests
Jumbo and Parallelism
Sparks and Affinities
Codelets and the Coderack
The Concept of a Terraced Scan
Romances among the Letters
Bonds, Chains, Gloms, and Membranes
A Single Reality with Many Parallel Counterfactual Musings
Unhappy Gloms, Squeaky Wheels
Looking for Alternative Solutions to a Given Jumble
Totally Rational Choice vs. Rationally Biased Coin-Flipping
Transformations in Jumbo
Entropy-Preserving Transformation
Fluid Data-Structures: A Principal Aim of Jumbo
Entropy-Increasing Transformations
Temperature and Self-Watching
A Self-Sensitive, Self-Driven System
Epilogue: Jumbo's Epiphenomenal Intelligence

3a. Arithmetical Play and Nondeterminism

"Le Compte Est Bon"
The Human Mind as a Stochastic Processor

3b. Numbo: A Study in Cognition and Recognition

The Game of Numble
The Architecture of Numbo
     The Permanent Network
     The Cytoplasm
A Sample Run of Numbo
     Comparison with Other Computer Models
     Comparison with Human Performance

4a. The Ineradicable Eliza Effect and Its Dangers

Programs with Apparent Real-World Prowess
The Slippery Slope into the Eliza Effect
"Just This Once"
Can Computers Understand Metaphors by Shakespeare and Plato?
The Dubious Claim of Cross-Domain Analogy-Making
Copycat: A Kid Doing a Somersault

4b. High-level Perception, Representation, and Analogy: A Critique of Artificial-intelligence Methodology

The Problem of Perception
     Low-Level and High-Level Perception
Artificial Intelligence and the Problem of Representation
     Objectivism and Traditional AI
     On the Possibility of a Representation Module
     BACON: A Case Study
Models of Analogical Thought
     Current Models of Analogical Thought
     The Necessity of Fusing High-Level Perception with More Abstract Cognitive Processing
The Utility of Small Domains

5a. Conceptual Halos and Slippability

Analogy Puzzles in the Seek-Whence Domain
The Nancy Reagan of England
Words, Concepts, and Halos
From Conceptual-Halo Slips to Conceptual Slippages
Copycat Is Conceived

5b. The Copycat Project: A Model of Mental Fluidity and Analogy-Making

Copycat and Mental Fluidity
     Analogy Problems in the Copycat Domain
     Mental Fluidity: Slippages Induced by Pressures
     The Intended Universality of Copycat's Microdomain
     A Perception-Based, Emergent Architecture for Mental Fluidity
The 3 Major Components of the Copycat Architecture
     The Slipnet - Copycat's Network of Platonic Concepts
          Conceptual Depth
          Activation Flow and Variable Link-Lengths
          Concepts as Diffuse, Overlapping Clouds
     The Workspace - Copycat's Locus of Perceptual Activity
          The Constant Fight for Probabilistic Attention
          The Parallel Emergence of Multi-Level Perceptual Structures
          The Drive Towards Global Coherence and Towards Deep Concepts
     The Coderack - Source of Emergent Pressures in Copycat
          Pressures Determine the Speeds of Rival Processes
          The Shifting Population of the Coderack
The Emergence of Fluidity in the Copycat Architecture
     Commingling Pressures - The Crux of Fluidity
     The Parallel Terraced Scan
     Time-Evolving Biases
     Temperature as a Regulator of Open-Mindedness
     Overall Trends during a Run
The Intimate Relation between Randomness and Fluidity
     Biased Randomness Gives Each Pressure Its Fair Share
     Randomness and Asynchronous Parallelism
     A Seeming Paradox: Randomness in the Service of Intelligence
Copycat's Performance: A Forest-Level Overview
     The Statistically Emergent Robustness of Copycat
     Copycat's "Personality" is Revealed through Bar Graphs
     Systematically Studying the Effects of Variant Problems
     How Hidden Concepts Emerge from Dormancy
     Paradigm shifts in a Microworld
     Families of Problems as a "Miniature Turing Test"
Copycat's Performance: A Tree-Level Close-Up
     A Problem where Perception Plays a Crucial Role Is Chosen as a Focus
     The Story in Quick Strokes
     Screen Dumps Tell the Story in Detail
     Micro-Anatomy of a Paradigm Shift
     Emergency Measures Concert a Serious Snag into a Set of Exploratory Pressures
     How Resistance to a Deep Slippage is Overcome - A Tricky Matter
     Locking-In of a New View
     How Hard Is It to Make this Paradigm Shift?
Conclusion: The Generality of Copycat's Mechanisms
     The Crucial Question of Scaling-Up
     Shades of Gray and the Mind's Eye
     Copycat's Shaded Exploration Strategy
          Shades of Gray in the Slipnet
          Shades of Gray in the Workspace
          Shades of Gray Associated with the Coderack
          Dynamic Emergence of Unpredictable Objects and Pathways

6a. Two Early AI Approaches to Analogy

Thomas Evans' Program ANALOGY
Walter Reitman's Argus Program

6b. Perspectives on Copycat: Comparisons with Recent Work

How to Judge Copycat?
SME, the Structure Mapping Engine
     Points of Agreement between Copycat and SME
     Points of Disagreement between Copycat and SME
ACME, the Analogical Constraint Mapping Engine
     Agreements and Disagreements between Copycat and ACME
How Real are These "Real-World" Analogies?
Copycat's Position along the Symbolic/Subsymbolic Spectrum
Indurkya's View of Creativity, and the PAN Model
Kokinov's AMBR System -- Associative Memory-Based Reasoning

7a. Retrieval of Old and Invention of New Analogies

The Lifelike Appearance of Copycat
An Axed Pet Analogy
Meta-Analogies, Caricature Analogies, and Memory Retrieval
Analogy-Puzzle Invention as a Cognitive Challenge

7b. Prolegomena to Any Future Metacat

An Incipient Model of Fluidity, Perception, Creativity
Copycat: Self-Aware, But Very Little
Shades of Gray along the Consciousness Continuum
The Key Role of Self-Monitoring in Creativity
A Stab at Defining Creativity
Five Challenges Defining What Any Future Metacat Must Do

8a. Analogy-making in a Coffeehouse

Singin' the Copycat Blues
Mimicking "Real" Analogies in Tabletop's Mini-Universe

8b. Tabletop, BattleOp, Ob-Platte, Potelbat, Belpatto, Platobet

Analogy Problems in Microdomains
     "Do This!" Puzzles on a Tabletop
     Realistically Modeling Analogy-Makinng on a Highly Idealized Tabletop
     A Brute-Force Approach to Tabletop Analogy Problems
     Why Developing a Brute-Force Program would Miss the Point
     Generality: The Fundamental Goal of the Tabletop Project
Analogy Problems in Scaled-Up Domains
     Tabletop Gets Mentally Scaled Up to Global Proportions
     BattleOp, in Turn, Gets Cut Down to Reasonable Proportions
     Are Ob-Platte Puzzles about Analogical Mapping or Analogical Retrieval?
Fundamental Obstacles Facing a Formula-Based Architecture
     A Brute-Force Approach to Ob-Platte Puzzles
     Exhaustive Search Is Deeply Wrong
     Could Pruning Help Matters?
     Shades of Gray Are Needed - But they Quickly Lead Far Outside the Domain
     Trying to Capture the "Essence" of a Town
     Analogy Problems at all Levels - The Nightmare of a Potentially Infinite Regress
     Town Names Alone Constitute a Bottomless Barrel of Worms
     What Constitutes a Town?
     Violations of Geographical and Conceptual Boundaries
     Local vs. Locational Aspects of a Town
Bringing These Ideas Back to Tabletop
     Downward Transfer of Lessons from the Big Domain to the Tiny Domain
     Crude Mirrorings, in Tabletop, of Some Tricky Ob-Platte Puzzles
     Other Tricky Tabletop Problems and Mechanisms Tailor-Made to Handle Them
Concluding Words

9a. The Knotty Problem of Evaluating Research in AI and Cognitive Science

Striving to Simulate the Style of an Individual Human Mind
A Throng of Interacting Subcognitive Mechanisms
How Are Natural-Language Programs Validated?
Concrete Criteria for the Validation of Our Computational Models
The Substrate of Cognition is Culture-Independent
A Crazy Bazaar
CBR - Case-Based Reasoning
Private Hunches vs. Public Stances

9b. The Emergent Personality of Tabletop, a Perception-based Model of Analogy-Making

Striving for Cognitive Generality in a Mundane Microdomain
Perceptual Processes in Tabletop
Structures, Strengths, and Fights for Survival
Codelets and the Interleaving of Perceptual Processes
The Pervasiveness of Dynamic Perceptual Biases
The Gradual Emergence of Coherence
Tabletop Gauges Its Own Progress
Some Differences between Tabletop's and Copycat's Domains
Some Differences between Tabletop's and Copycat's Architectures
Tabletop's Personality as a Statistically Emergent Phenomenon

10a. The Intoxicating World of Alphabets and Their Styles

Infected with Letter Mania from the Word "Go"
From Real Letters to Stick Letters
The Letter Spirit Computer Program Is Born

10b. Letter Spirit: Esthetic Perception and Creative Play in the Rich Microcosm of the Roman Alphabet

The Goal of Imparting a Sense of Deep Style to a Machine
But Hasn't That Already Been Done?
A Non-Creative Computer Model of Letter Design
True Creativity Implies Autonomy
Letters as Rich, Full-Fledged Concepts
Wholes and Roles
Letter and Spirit as Orthogonal Categories
Retreating from Real-World to Microworld Typeface Design
Gridletters and Gridfonts
The Grid Engenders Exotic Letterforms and Wild Styles
The Principal Varieties of Stylistic Determiners
The Spirits behind Four Sample Gridfonts
Creating a Gridfont - A Broad View
The Implementation of Emergent Processing
Four Global Memory Structures
     Conceptual Memory
     Visual Focus
     Thematic Focus
The Predictable Unpredictability of the Creative Process
Four Interacting Emergent Agents
The Central Feedback Loop of Creativity
The Strangely Circular Origin of a Style
Towards the Implementation of the Central Feedback Loop
Brief Comments on Related Work in Letter Recognition
A Connectionist Approach to the Letter Spirit Challenge
The Inescapable Temporality of the Act of Creation
Genuine Cognition Is Not a Free Lunch

Epilogue: On Computers, Creativity, Credit, Brain Mechanisms, and the Turing Test

A Somewhat Skeptical Perspective on Computers and Creativity
A Computer Artist
A Computer Author
A Computer Mathematician
Another Computer Mathematician
Plagiarism vs. Creativity
Mechanisms, Probes, and the Turing Test
Brain Structures vs. Cognitive Mechanisms
Some Levels of Description Are Certainly Too Low
The Need for Criteria by Which to Recognize Thinking
Scattering Experiments vs. "Direct" Observation of Phenomena
The Turing Test and the Visibility of Deep Mechanisms
The Turing Test and Basic Research


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