Cover image for CALCULUS OF IDEAS : A MATHEMATICAL STUDY OF HUMAN THOUGHT.
CALCULUS OF IDEAS : A MATHEMATICAL STUDY OF HUMAN THOUGHT.
Title:
CALCULUS OF IDEAS : A MATHEMATICAL STUDY OF HUMAN THOUGHT.
Author:
Grenander, Ulf.
ISBN:
9789814383196
Personal Author:
Physical Description:
1 online resource (236 pages)
Contents:
Contents -- Foreword -- Preface -- Abstract -- Part I An Architecture for the Mind -- Chapter 1 Introduction -- 1.1 A Mathematical Theory of Mind? -- 1.2 Substance and Change -- 1.2.1 Substance -- 1.2.2 Change -- 1.2.3 Patterns -- Chapter 2 Creating Thoughts: Algebra of Thinking -- 2.1 What We Shall Do -- 2.2 Judging a Mind Model -- 2.3 Mental Architecture -- 2.4 An Algebra of Human Thought -- 2.4.1 Primitive Ideas -- 2.4.2 Modalities -- 2.4.3 Similarities of Ideas -- 2.4.4 Compositions of Primitive Ideas -- 2.4.5 Regular Thoughts -- 2.4.6 Thought Patterns -- 2.4.7 Completion -- 2.4.8 Generalization -- 2.4.9 Abstraction -- 2.4.10 Caveat -- 2.4.11 Levels, Modalities, and Arities in Mind Space -- 2.4.12 A Concept of Concept -- 2.4.13 Regularity of Mind States: Conformation of Thoughts -- 2.4.14 Creation of New Ideas -- 2.4.15 Patterns of Thought -- 2.5 Some Thoughts in Goethe -- Part II Personality of a Mind -- Chapter 3 A Mind Equation -- 3.1 Personality Profile -- 3.1.1 The Pathological Mind -- 3.1.2 An Intelligent Mind? -- 3.1.3 Randomness and Thinking -- 3.2 Mental Dynamics -- 3.2.1 Topologies of Thinking -- 3.3 Personality Profiles in Literature -- 3.4 Trajectories in Mind Space -- 3.5 Dynamics with Simple Moves -- 3.6 Mental Dynamics with Composite Moves -- 3.6.1 Mental Dynamics with Themes of Attention: Genres -- 3.6.2 Mental Dynamics of Dreaming -- 3.7 A Calculus of Thinking -- 3.7.1 Speci.c Thoughts -- 3.7.1.1 Conscious Thoughts -- 3.7.1.2 Top-thoughts -- 3.7.2 Generalization/Specialization Operation -- 3.7.3 Encapsulation Operation -- 3.7.4 Completion Operation -- 3.7.5 Genre Operation -- 3.7.6 Inference Process -- 3.8 Birth and Death of Thoughts -- 3.8.1 Competition among Unconscious Thoughts -- Part III Two Personalities -- Chapter 4 Building a GOLEM, a Thinking Machine -- 4.1 Data Structures for the Mind.

4.1.1 Data Structures for Elementary Ideas -- 4.1.2 Data Structures for Thoughts -- 4.1.3 Energies of Thoughts and Genres -- 4.1.4 Composite Moves -- 4.2 Program Hierarchy for the Mind -- 4.3 Putting It All Together -- 4.4 A GOLEM Alive? -- 4.4.1 Free Associations -- 4.4.2 Inferential Thinking -- 4.4.3 Associations Driven by Themes -- 4.4.4 Continuous Thought -- 4.4.5 See Created Ideas -- 4.5 Drivers -- 4.5.1 Generalizing Top-Ideas -- 4.6 Judging the Behavior of GOLEM -- 4.6.1 Analysis of a Virtual MIND -- 4.7 Not Yet Implemented -- 4.8 LEGACY -- 4.9 Assembling Mental Pattern Parameters -- 4.10 Running the LEGACY -- Chapter 5 As Thinking Develops -- 5.1 Changes in Personality Parameter -- 5.2 Development of a Young Mind -- 5.3 GOLEM Evolves -- Part IV Realizing a Mind -- Chapter 6 MIND and Brain -- 6.1 Connect to the Brain? -- 6.1.1 Simple Ideas as Building Blocks -- 6.1.2 Connections between Simple Ideas -- 6.1.3 Thoughts are Formed from Simple Ideas -- 6.1.4 Weight and Acceptor Functions -- 6.1.5 Joint Probability Measure for Thoughts -- 6.1.6 Properties of SSF -- 6.1.7 Updating the Personality -- 6.1.8 Processing Thoughts -- 6.2 A Network Example -- 6.2.1 Concept Formation on the Neural Level -- 6.3 Examples -- 6.3.1 The p-Cliques under Free Associations -- 6.3.2 Kantian Thinking -- 6.4 Multi-Level Architecture -- 6.4.1 Manipulating Maximal Cliques -- Chapter 7 Reflections -- 7.1 Generalities on PoT -- 7.1.1 Raymondus Lullus and His Thinking Machine -- 7.1.2 Thinking vs. Language -- 7.1.3 Questioning Introspection -- 7.1.4 Thinking about the Unthinkable -- 7.2 Substance in PoT -- 7.3 Change in PoT -- 7.3.1 Continuity of Thinking -- Chapter 8 Doubts and Certainties -- References -- Appendix A Some Famous Mind Theories -- A.1 A Sample of Mind Theories -- A.2 Syllogisms -- A.3 Formal Logics -- A.4 Psychoanalysis -- A.5 Semantic Networks.

A.6 Formal Grammars -- A.7 Associations -- Appendix B Consistency of Probability Measure -- Appendix C A Modality Lattice -- Appendix D Dynamics of Random Process of Thinking -- Appendix E Software for GOLEM -- E.1 Main Function -- E.2 Simple Moves.
Abstract:
This monograph reports a thought experiment with a mathematical structure intended to illustrate the workings of a mind. It presents a mathematical theory of human thought based on pattern theory with a graph-based approach to thinking. The method illustrated and produced by extensive computer simulations is related to neural networks. Based mainly on introspection, it is speculative rather than empirical such that it differs radically in attitude from the conventional wisdom of current cognitive science.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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