A topology of mind: spiral thought patterns, the hyperlinking of text, ideas and more
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2022]
|
| Schriftenreihe: | Mathematics in mind
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 245 Seiten Illustrationen |
| ISBN: | 9783030964351 |
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Datensatz im Suchindex
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| adam_text | Contents Prologue to Part I 1 2 3 Mathematics in Mind The Origin of Mathematics in the Mind............................................... Introduction............................................................................................ What Is Mathematics?............................................................................ Table of Words Related to Quantitative Analyses or Comparisons .... Table of Mathematical Terms and Their Etymology That Also Have Significance Outside of Mathematical Studies...................................... Organization and Classification as a Form of Mathematical Thinking.. Mathematics: A Practical Tool and a Theoretical Discipline................ The Different Divisions and Sub-disciplines of Mathematics.............. 3 3 3 5 6 7 7 7 Mathematics, the Human Mind, Verbal Language: Mathematics in Mind............................................................................................ 9 Introduction............................................................................................ The Origin of Mind and the Role of Mathematical Thinking................ Language Facilitates Thinking and Is the Medium in Which Thought Is Conceived.......................................................................................... Language Extends the Brain into a Mind.............................................. The Origin of Verbal Language: The Bifurcation from Percepts to Concepts The Mechanism for the Transition from Percept-Base Thinking to Concept-Based
Thinking.................................................................. Percepts, Concepts, Their Relationship and Mathematics in Mind .... The Emergence of Grammar or Syntax................................................ The Emergence of Enumeration . ...................................................... The Emergence of Grammar: The Lexical Hypothesis.......................... Conclusion: The Mind as a Supervenient System ................................ 15 16 17 18 19 20 Mathematics, Writing and Notation..................................................... Introduction............................................................................................ What Is a Language? A New Concept.................................................. 23 23 24 9 9 11 12 14 xiii
Contents xiv Alphabet, Mother of Invention and the Alphabet Effect........................ The Six Languages of Speech, Writing, Math, Science, Computing and the Internet...................................................................................... The Origin of Spoken Language and Its Evolution into the Languages of Writing and Mathematics.................................................................. The Origin of Writing and Mathematical Notation.............................. The Origin of Schools of Instruction for Reading, Writing and Arithmetic............................................................................................... The Fourth Language of Science.......................................................... Phonetic Writing and the Alphabet Effect............................................ Alphabet and Monotheism.................................................................... The Role of the Alphabet in the Invention of Zero and the Place Number System............................................................................ 4 5 Mathematics, Deductive Logic and Abstract Science........................ Alphabet Mother of Invention................................................................ The Role of the Alphabet in the Emergence of Deductive Logic by the Ancient Greeks............................................................................ The Intimate Connection of Geometry and Logic................................ The Role of Logic in the Formulation of Abstract Science.................. The Paradoxes of Parmenides and
Zeno and the Disservice of Logic: Too Much of a Good Thing.................................................................... Resolving the Paradox.......................................................................... Science as a Language and the Non-Probativity Theorem.................... Conclusion............................................................................................ Computing and the Internet: The Six Languages of Speech, Writing, Math, Science, Computing and the Internet.............................. 53 The Advent of Computing.................................................................... The Advent of the Internet.................................................................... The Mind in Mathematics...................................................................... Curiosity................................................................................................ Values and Morality............................................................................... Decision Making, Experience, Judgement and Wisdom........................ A Partnership of Mathematics in Mind and Mind in Mathematics .... Conclusion............................................................................................ 25 26 27 28 31 31 32 34 35 39 39 40 42 44 46 46 49 52 56 57 58 60 60 60 61 62 Prologue to Part II Spiral Patterns in Nature and Human Thought 6 The Mathematical Structure of Cyclic Phenomena: Spirals, Helixes, Revolutions, Waves and Oscillations....................................................
Introduction............................................................................................ Mathematical Spiral Structures.............................................................. The Spiral of Archimedes.................................................................. The Euler Spiral................................................................................ Fermat’s Spiral.................................................................................. 65 65 67 67 68 68
Contenís 7 xv The Hyperbolic Spiral........................................................................ The Lituus.......................................................................................... The Logarithmic Spiral...................................................................... The Spiral of Theodorus.................................................................... Fibonacci Sequence.......................................................................... The Golden Spiral.............................................................................. Fractals and Spirals............................................................................ Helixical Structures: A Three-Dimensional Spiral............................ 68 70 70 72 73 73 74 74 Spiral and Cyclic Structures in the Abiotic Inorganic Material World............................................................................................... 77 The Scale of Spiralicity and Cyclic Motion in the Universe................ Spiral Galaxies...................................................................................... Double Helix Nebulae............................................................................ Cyclic Time and Ancient Astronomy.................................................... The Weekly Cycle.................................................................................. A Cyclical Model of the Evolution of the Universe.............................. Electromagnetic Waves and Cycles...................................................... Whirlpools, Maelstroms and
Vortices.................................................... Cyclones, Hurricanes, Tornados............................................................ The Cycle of Ice Ages............................................................................ Sunspot, Solar Flare Cycles and the Van Allen Radiation Belt.............. Miscellaneous Spiral Structures............................................................ Conclusion............................................................................................ 77 78 79 79 82 83 83 84 88 89 89 90 92 8 Life Is a Spiral and It Is Cyclic: The Spiral Structures of the Biosphere........................................................................................ 93 Introduction: Life Began on Planet Earth with the Spirals of RNA and DNA...................................................................................................... 93 Extra-Cellular Spiral Structures in Animals andPlants......................... 94 Collagen............................................................................................ 94 Human Stomach Muscles.................................................................. 95 Spiral Structure in Plants and Animals.............................................. 95 Aloe Polyphylla................................................................................ 97 Human Cochlea of the Inner Ear.......................................................... 100 Pineapples.............................................................................................. 102 9 Spiral Thought Structures in
History and Philosophy...................... Introduction............................................................................................ Ancient Indian Notions of Cyclic Time (3300 BC).............................. The Ancient Chinese Notion of the Dynastic Cycle (2070 BC)............ Ancient Hebrew Biblical Idea of Recurrence (453 BC)........................ Ancient Greek Myths, the Political Cycle of Kyklos and Pythagorean Recurrence (500 BC)........................................................ Arab Historian Ibn Khaldun (1377)...................................................... Vico’s Notion of Corso and Ricorso (1725).......................................... Ill Ill 112 112 112 113 114 114
xvi 10 11 Contents The Spiral Structure of Dialectical Thinking of Fichte and Hegel........ Nietzsche s Notion of Eternal Return (1882)........................................ Eliade’s Notion of Eternal Return (1971).............................................. 115 116 117 The Spiral Structure of Marshall McLuhan’s Thinking.................... Introduction............................................................................................ Sources of McLuhan’s Spiral Thinking................................................ Marshall McLuhan’s Intellectual Roots................................................ The Spiral Structure of the Tetrad or Laws of Media............................ Artistic and Literary Roots of McLuhan’s Spiral Thinking and His Laws of Media................................................... 126 Vorticism................................................................................................ Understanding McLuhan in Terms of Spiral Structures........................ McLuhan Use of the Spiral Image in His Writings.............................. The Implicit Use of Spiral Structures in the Thought Processes and Scholarship of Marshall McLuhan................................... 132 McLuhan on Artists................................................................................ Media as Extension of Man, Yet Man as Their Servomechanisms........ The Figure and Ground Spiral.............................................................. The Environment and Anti-environment Spiral.................................... Cause and Effect
Spiral.......................................................................... Service/Disservice.................................................................................. Two More McLuhan Figure/Ground Reversals.................................... Conclusion............................................................................................. 121 121 122 123 125 Spirals and the Arts.............................................................................. Introduction.................................................................................... Poetry and Literature.............................................................................. Gertrude Stein: Repetition as a Spiral of Sensuous Revolutions.......... Cinema: “The Medium is the Message”................................................ Analog Cinema...................................................................................... Film.................................................................................................... Music and Sound Art........................................................................ An Example of Spiral Structures in Dance: Loie Fuller and Martha Graham.......................................................................... Spiral Structures in Twentieth and Twenty-First Century Architecture Twist Scrapers.................................................................................... Sculpture............................................................................................. Visual
Arts.......................................................................................... Photography...................................................................................... 139 139 140 141 144 144 144 147 Prologue to Part III 128 129 130 133 133 134 134 135 136 137 137 149 150 156 167 173 183 Hyperlinking as Patterns of Connection 12 Pre-digital Forms of Hypertext............................................................ Introduction: The Early History of Hypertexting.................................. Oral Hyperlinking.................................................................................. 191 191 194
Contenis Wisdom Lore and Literature and the Metaphor of the Tree: The Tree of Knowledge, the Tree of Life, the World Tree and the Tree of the Knowledge of Good and Evil.............................................. 195 The Tree of the Knowledge of Good and Evil............................. The Metaphor of the Tree, the Tree of Life, the World Tree and the Tree of the Knowledge: An Ancient Symbol of Wisdom and the Interconnectivity of Knowledge...................................... The Metaphor of the Tree as a Symbol of Interconnectivity in Modern Times................................................................. 199 The Talmud.................................................................................................. xvii 195 197 200 Hypertext in the Digital Domain of Cyberspace.................................. Introduction.................................................................................................. Vannevar Bush and the Memex.................................................................. Theodor Nelson and Project Xanadu........................................................ Tim Berners-Lee, Hypertext Transfer Protocol and the World Wide Web....................................................................................... 208 Hypertext Is a Labyrinth That Tames and Contains Information Overload................................................................................ 208 Hypertext and Hyperlinking Have the Structure of a Multicursal Labyrinth.............................................................................. 210
Hypertexted Cyberspace and the Structure of McLuhan’s Acoustic Space.................................................................................... 215 Ergodic Literature........................................................................................ 205 205 206 207 14 Hypermedia: Hyperlinking Cinema and Television............................ The Origin of Hypertext and Hypermedia............................................... 221 221 15 Hyperlinking in the Spheres: The Physiosphere, Biosphere, Technosphere, Sociosphere and Econosphere.............................. 225 Introduction.................................................................................................. The Physiosphere and the Absence of Hyperlinking.............................. Hyperlinking in the Biosphere.................................................................. Hyperlinking in Animals............................................................................. Hyperlinking in Plants, Fungi, and Microorganisms.............................. Intercellular and Intracellular Signaling Within a Single Organism.... Hyperlinking in the Technosphere............................................................ Hyperlinking in the Econosphere.............................................................. Hyperlinking in the Sociosphere................................................................ 225 226 227 229 230 231 232 233 236 13 218 Epilogue: Closing the Spiral Loop: The Eternal Return of This Study. . . 237
References............................................................................................................. 239
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| adam_txt |
Contents Prologue to Part I 1 2 3 Mathematics in Mind The Origin of Mathematics in the Mind. Introduction. What Is Mathematics?. Table of Words Related to Quantitative Analyses or Comparisons . Table of Mathematical Terms and Their Etymology That Also Have Significance Outside of Mathematical Studies. Organization and Classification as a Form of Mathematical Thinking. Mathematics: A Practical Tool and a Theoretical Discipline. The Different Divisions and Sub-disciplines of Mathematics. 3 3 3 5 6 7 7 7 Mathematics, the Human Mind, Verbal Language: Mathematics in Mind. 9 Introduction. The Origin of Mind and the Role of Mathematical Thinking. Language Facilitates Thinking and Is the Medium in Which Thought Is Conceived. Language Extends the Brain into a Mind. The Origin of Verbal Language: The Bifurcation from Percepts to Concepts The Mechanism for the Transition from Percept-Base Thinking to Concept-Based
Thinking. Percepts, Concepts, Their Relationship and Mathematics in Mind . The Emergence of Grammar or Syntax. The Emergence of Enumeration . . The Emergence of Grammar: The Lexical Hypothesis. Conclusion: The Mind as a Supervenient System . 15 16 17 18 19 20 Mathematics, Writing and Notation. Introduction. What Is a Language? A New Concept. 23 23 24 9 9 11 12 14 xiii
Contents xiv Alphabet, Mother of Invention and the Alphabet Effect. The Six Languages of Speech, Writing, Math, Science, Computing and the Internet. The Origin of Spoken Language and Its Evolution into the Languages of Writing and Mathematics. The Origin of Writing and Mathematical Notation. The Origin of Schools of Instruction for Reading, Writing and Arithmetic. The Fourth Language of Science. Phonetic Writing and the Alphabet Effect. Alphabet and Monotheism. The Role of the Alphabet in the Invention of Zero and the Place Number System. 4 5 Mathematics, Deductive Logic and Abstract Science. Alphabet Mother of Invention. The Role of the Alphabet in the Emergence of Deductive Logic by the Ancient Greeks. The Intimate Connection of Geometry and Logic. The Role of Logic in the Formulation of Abstract Science. The Paradoxes of Parmenides and
Zeno and the Disservice of Logic: Too Much of a Good Thing. Resolving the Paradox. Science as a Language and the Non-Probativity Theorem. Conclusion. Computing and the Internet: The Six Languages of Speech, Writing, Math, Science, Computing and the Internet. 53 The Advent of Computing. The Advent of the Internet. The Mind in Mathematics. Curiosity. Values and Morality. Decision Making, Experience, Judgement and Wisdom. A Partnership of Mathematics in Mind and Mind in Mathematics . Conclusion. 25 26 27 28 31 31 32 34 35 39 39 40 42 44 46 46 49 52 56 57 58 60 60 60 61 62 Prologue to Part II Spiral Patterns in Nature and Human Thought 6 The Mathematical Structure of Cyclic Phenomena: Spirals, Helixes, Revolutions, Waves and Oscillations.
Introduction. Mathematical Spiral Structures. The Spiral of Archimedes. The Euler Spiral. Fermat’s Spiral. 65 65 67 67 68 68
Contenís 7 xv The Hyperbolic Spiral. The Lituus. The Logarithmic Spiral. The Spiral of Theodorus. Fibonacci Sequence. The Golden Spiral. Fractals and Spirals. Helixical Structures: A Three-Dimensional Spiral. 68 70 70 72 73 73 74 74 Spiral and Cyclic Structures in the Abiotic Inorganic Material World. 77 The Scale of Spiralicity and Cyclic Motion in the Universe. Spiral Galaxies. Double Helix Nebulae. Cyclic Time and Ancient Astronomy. The Weekly Cycle. A Cyclical Model of the Evolution of the Universe. Electromagnetic Waves and Cycles. Whirlpools, Maelstroms and
Vortices. Cyclones, Hurricanes, Tornados. The Cycle of Ice Ages. Sunspot, Solar Flare Cycles and the Van Allen Radiation Belt. Miscellaneous Spiral Structures. Conclusion. 77 78 79 79 82 83 83 84 88 89 89 90 92 8 Life Is a Spiral and It Is Cyclic: The Spiral Structures of the Biosphere. 93 Introduction: Life Began on Planet Earth with the Spirals of RNA and DNA. 93 Extra-Cellular Spiral Structures in Animals andPlants. 94 Collagen. 94 Human Stomach Muscles. 95 Spiral Structure in Plants and Animals. 95 Aloe Polyphylla. 97 Human Cochlea of the Inner Ear. 100 Pineapples. 102 9 Spiral Thought Structures in
History and Philosophy. Introduction. Ancient Indian Notions of Cyclic Time (3300 BC). The Ancient Chinese Notion of the Dynastic Cycle (2070 BC). Ancient Hebrew Biblical Idea of Recurrence (453 BC). Ancient Greek Myths, the Political Cycle of Kyklos and Pythagorean Recurrence (500 BC). Arab Historian Ibn Khaldun (1377). Vico’s Notion of Corso and Ricorso (1725). Ill Ill 112 112 112 113 114 114
xvi 10 11 Contents The Spiral Structure of Dialectical Thinking of Fichte and Hegel. Nietzsche's Notion of Eternal Return (1882). Eliade’s Notion of Eternal Return (1971). 115 116 117 The Spiral Structure of Marshall McLuhan’s Thinking. Introduction. Sources of McLuhan’s Spiral Thinking. Marshall McLuhan’s Intellectual Roots. The Spiral Structure of the Tetrad or Laws of Media. Artistic and Literary Roots of McLuhan’s Spiral Thinking and His Laws of Media. 126 Vorticism. Understanding McLuhan in Terms of Spiral Structures. McLuhan Use of the Spiral Image in His Writings. The Implicit Use of Spiral Structures in the Thought Processes and Scholarship of Marshall McLuhan. 132 McLuhan on Artists. Media as Extension of Man, Yet Man as Their Servomechanisms. The Figure and Ground Spiral. The Environment and Anti-environment Spiral. Cause and Effect
Spiral. Service/Disservice. Two More McLuhan Figure/Ground Reversals. Conclusion. 121 121 122 123 125 Spirals and the Arts. Introduction. Poetry and Literature. Gertrude Stein: Repetition as a Spiral of Sensuous Revolutions. Cinema: “The Medium is the Message”. Analog Cinema. Film. Music and Sound Art. An Example of Spiral Structures in Dance: Loie Fuller and Martha Graham. Spiral Structures in Twentieth and Twenty-First Century Architecture Twist Scrapers. Sculpture. Visual
Arts. Photography. 139 139 140 141 144 144 144 147 Prologue to Part III 128 129 130 133 133 134 134 135 136 137 137 149 150 156 167 173 183 Hyperlinking as Patterns of Connection 12 Pre-digital Forms of Hypertext. Introduction: The Early History of Hypertexting. Oral Hyperlinking. 191 191 194
Contenis Wisdom Lore and Literature and the Metaphor of the Tree: The Tree of Knowledge, the Tree of Life, the World Tree and the Tree of the Knowledge of Good and Evil. 195 The Tree of the Knowledge of Good and Evil. The Metaphor of the Tree, the Tree of Life, the World Tree and the Tree of the Knowledge: An Ancient Symbol of Wisdom and the Interconnectivity of Knowledge. The Metaphor of the Tree as a Symbol of Interconnectivity in Modern Times. 199 The Talmud. xvii 195 197 200 Hypertext in the Digital Domain of Cyberspace. Introduction. Vannevar Bush and the Memex. Theodor Nelson and Project Xanadu. Tim Berners-Lee, Hypertext Transfer Protocol and the World Wide Web. 208 Hypertext Is a Labyrinth That Tames and Contains Information Overload. 208 Hypertext and Hyperlinking Have the Structure of a Multicursal Labyrinth. 210
Hypertexted Cyberspace and the Structure of McLuhan’s Acoustic Space. 215 Ergodic Literature. 205 205 206 207 14 Hypermedia: Hyperlinking Cinema and Television. The Origin of Hypertext and Hypermedia. 221 221 15 Hyperlinking in the Spheres: The Physiosphere, Biosphere, Technosphere, Sociosphere and Econosphere. 225 Introduction. The Physiosphere and the Absence of Hyperlinking. Hyperlinking in the Biosphere. Hyperlinking in Animals. Hyperlinking in Plants, Fungi, and Microorganisms. Intercellular and Intracellular Signaling Within a Single Organism. Hyperlinking in the Technosphere. Hyperlinking in the Econosphere. Hyperlinking in the Sociosphere. 225 226 227 229 230 231 232 233 236 13 218 Epilogue: Closing the Spiral Loop: The Eternal Return of This Study. . . 237
References. 239 |
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| record_format | marc |
| series2 | Mathematics in mind |
| spelling | Logan, Robert K. 1939- Verfasser (DE-588)135680689 aut A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more Robert K. Logan, Izabella Pruska-Oldenhof Cham, Switzerland Springer [2022] © 2022 xvii, 245 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematics in mind Psycholinguistik (DE-588)4127537-8 gnd rswk-swf Kommunikation (DE-588)4031883-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematics. Social sciences. Philosophy of mind. Topology. Communication. Computer science—Mathematics. Psycholinguistics. Mathematik (DE-588)4037944-9 s Psycholinguistik (DE-588)4127537-8 s Kommunikation (DE-588)4031883-7 s DE-604 Pruska-Oldenhof, Izabella ca. 20. Jh. Verfasser (DE-588)1077053053 aut Erscheint auch als Online-Ausgabe 978-3-030-96436-8 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033833394&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Logan, Robert K. 1939- Pruska-Oldenhof, Izabella ca. 20. Jh A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more Psycholinguistik (DE-588)4127537-8 gnd Kommunikation (DE-588)4031883-7 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4127537-8 (DE-588)4031883-7 (DE-588)4037944-9 |
| title | A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more |
| title_auth | A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more |
| title_exact_search | A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more |
| title_exact_search_txtP | A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more |
| title_full | A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more Robert K. Logan, Izabella Pruska-Oldenhof |
| title_fullStr | A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more Robert K. Logan, Izabella Pruska-Oldenhof |
| title_full_unstemmed | A topology of mind spiral thought patterns, the hyperlinking of text, ideas and more Robert K. Logan, Izabella Pruska-Oldenhof |
| title_short | A topology of mind |
| title_sort | a topology of mind spiral thought patterns the hyperlinking of text ideas and more |
| title_sub | spiral thought patterns, the hyperlinking of text, ideas and more |
| topic | Psycholinguistik (DE-588)4127537-8 gnd Kommunikation (DE-588)4031883-7 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Psycholinguistik Kommunikation Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033833394&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT loganrobertk atopologyofmindspiralthoughtpatternsthehyperlinkingoftextideasandmore AT pruskaoldenhofizabella atopologyofmindspiralthoughtpatternsthehyperlinkingoftextideasandmore |