The Future of Post-Human Geometry: A Preface to a New Theory of Infinity, Symmetry, and Dimensionality

Overview

Why should some essential properties of geometry (i.e., infinity, symmetry, and dimensionality) be both necessary and desirable in the way that they have been constructed-albeit with different modifications over time-since time immemorial?

Contrary to the conventional wisdom in all history hitherto existing, the essential properties of geometry do not have to be both necessary and desirable.

This is not to suggest, of course, that one has ...

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Overview

Why should some essential properties of geometry (i.e., infinity, symmetry, and dimensionality) be both necessary and desirable in the way that they have been constructed-albeit with different modifications over time-since time immemorial?

Contrary to the conventional wisdom in all history hitherto existing, the essential properties of geometry do not have to be both necessary and desirable.

This is not to suggest, of course, that one has nothing to learn from geometry. On the contrary, geometry has contributed to the advancement of knowledge in many ways since its inception as a field of knowledge some millennia ago.

The point in this book, however, is to show an alternative (better) way to understand the nature of geometry, which goes beyond human conception, intuition, and imagination, together with worldly experience of course, as its foundation, while learning from them all-with theoretical implications for time travel, hyperspace, and other important issues.

If true, this seminal view will fundamentally change the way that the nature of abstraction in the thinking process is to be understood, with its enormous implications for the future advancement of knowledge, in a small sense, and what I originally called its "Post-human" fate, in a large one.

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Product Details

  • ISBN-13: 9781443805247
  • Publisher: Cambridge Scholars Publishing
  • Publication date: 5/1/2009
  • Pages: 405
  • Product dimensions: 6.10 (w) x 8.40 (h) x 1.20 (d)

Table of Contents

List of Tables xi

Foreword xvii

Acknowledgments xix

List of Abbreviations xxi

Part 1 Introduction

Chapter 1 Introduction-The Importance of Geometry 3

The Millennial Concern with Geometry 3

Mathematics and Geometry 4

The Varieties of Geometry 9

The Foundational Dogma of Geometry 12

The Theoretical Debate 14

The Selective Theory of Geometry 18

Geometry and Meta-Geometry 18

The Logic of Existential Dialectics 19

Sophisticated Methodological Holism 41

Chapter Outline 47

Three Clarifications 48

Part 2 Infinity

Chapter 2 Infinity and Its Finitude 99

The Awe of Infinity 99

Infinity and the Mind 101

Infinity and Nature 113

Infinity and Society 123

Infinity and Culture 128

The Counterweight of Finitude 135

Part 3 Symmetry

Chapter 3 Symmetry and Its Asymmetry 145

The Beauty of Symmetry 145

Symmetry and the Mind 146

Symmetry and Nature 151

Symmetry and Society 162

Symmetry and Culture 168

The Challenge of Asymmetry 176

Part 4 Dimensionality

Chapter 4 Dimensionality and Its Multiplicity 181

The Familarity of Three-Dimensionality 181

Dimensionality and the Mind 182

Dimensionality and Nature 190

Dimensionality and Society 199

Dimensionality and Culture 216

The Difference of Higher-Dimensionality 224

Part 5 Conclusion

Chapter 5 Conclusion-The Future of Geometry 237

The Unfinished Work of Geometry 237

1st Thesis: The Finiteness-Transfiniteness Principle 244

2nd Thesis: The Absoluteness-Relativeness Principle 245

3rd Thesis: The Explicability-Inexplicability Principle 246

4th Thesis: The Simpleness-Complicatedness Principle 248

5th Thesis: The Openness-Hiddenness Principle 249

6thThesis: The Symmetry-Asymmetry Principle 250

7th Thesis: The Convention-Novelty Principle 252

8th Thesis: The Post-Human Alteration 254

Beyond Conception, Intuition, and Imagination 256

Bibliography 345

Index 355

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