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Mathematics: Is God Silent? / Edition 2

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2001 Trade paperback Revised ed. Illustrated. New. Trade paperback (US). Glued binding. 409 p. Contains: Illustrations. Audience: General/trade. New and unmarked copy. This book ... revolutionizes the prevailing understanding and teaching of math. The addition of this book is a must for all upper-level Christian school curricula and for college students and adults interested in math or related fields of science and religion. It will serve as a solid refutation for the claim, often made in court, that mathematics is one subject, which cannot be taught from a distinctively Biblical perspective. Helps support Christian Homeschooling family. Read more Show Less

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Overview

This book revolutionizes the prevailing understanding and teaching of math. This book is a must for all upper-level christian school curricula and for college students and adults interested in math or related fields of science and religion. It will serve as a solid refutation for the claim, often made in court, that mathematics is one subject which cannot be taught from a distinctively biblical perspective.
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Product Details

  • ISBN-13: 9781879998223
  • Publisher: Ross House Books
  • Publication date: 1/28/2001
  • Edition description: REVISED
  • Edition number: 2
  • Pages: 408

Table of Contents

Overview vii
The Details Inside ix
List of Figures xiv
Foreward xviii
Preface to the First Edition xix
Preface to the Second Edition xxi
Introduction xxii
Chapter Summaries xxiv
Part I Mathematics in History 1
1 Does it Really Matter? 3
1.1 Case closed ... or is it? 4
1.2 Penetrating Declarations 4
1.3 Laying Foundations 5
1.4 Worldview and Presuppositions 5
1.5 The Components of a Worldview 7
1.6 The Biblical Worldview 8
1.6.1 Metaphysics 8
1.6.2 Epistemology 9
1.6.3 Ethics 9
Questions for Review, Further Research, and Discussion 10
2 From Adam to Christ 11
2.1 Origins 11
2.2 Early Civilizations 14
2.3 Classical Greece 16
2.4 Reason and Nature Alone 16
2.5 Hebrew Revelation 17
2.6 Revelation Rejected 19
2.7 The Ionian School 19
2.7.1 The Six Propositions of Thales 20
2.8 The Rise and Fall of Pythagoras 21
2.9 Heraclitus, the Obscure 24
2.10 The Eleatic School 25
2.11 Geometry to the Rescue 27
2.12 Pluralistic Metaphysics 27
2.13 The Ideal World of Plato 29
2.14 Aristotelian Metaphysics 32
2.15 The "Elements of Euclid" 34
2.15.1 Euclid's Five Axioms and Five Postulates 35
2.15.2 Applied Geometry 36
2.15.3 Geometry and Latitude 38
2.16 Accomplishments in Alexandria 38
2.16.1 Eratosthenes Measures the Circumference of the Earth 41
2.16.2 The Sieve of Eratosthenes 43
2.16.3 Rudimentary Trigonometric Ratios 46
2.16.4 Finding the Height of a Tree 47
2.16.5 What Happens if a Mountain Gets in the Way? 48
2.16.6 Calculating the Radius of the Earth 49
2.16.7 Determining the Distance Between any Two Points on the Earth 50
2.16.8 Determining the Distance from the Earth to the Moon 51
2.16.9 Determining the Radius of the Moon 51
2.17 Sovereign God at Work 52
2.18 Sandy Foundations 52
Questions for Review, Further Research, and Discussion 54
3 From Christ to Wycliffe 57
3.1 Ptolemaic Theory 57
3.2 Pragmatic Rome 59
3.3 The Advent of Christ 60
3.4 Jerusalem Confronts Athens 62
3.5 The Bishop of Hippo 64
3.6 The Essence of the Conflict 66
3.7 Eventual Compromise 66
3.7.1 The Seven Liberal Arts 67
3.8 Mathematicians of the Early Christian Era 68
3.9 The Dark Ages? 71
3.10 The Medieval Industrial Revolution 73
3.10.1 Three-Field Farming 75
3.11 The Status of Mathematics and Science 79
3.12 Muslim and Byzantine Input 83
3.13 The University 85
3.14 The Scholastics at Oxford 86
3.15 A Champion of Aristotle 88
3.16 Forerunners of Innovative Thoughts 89
3.17 The Role of Scripture 94
3.18 The Morning Star 96
Questions for Review, Further Research, and Discussion 97
4 From Wycliffe to Euler 99
4.1 Medieval Recap 99
4.2 Modern Heritage 101
4.3 Ingredients in the Mix of the Scientific Revolution 102
4.4 The Catalyst: Nature's New Perspective 104
4.5 Two Indispensable Tools of Applied Mathematics 107
4.5.1 Symbolic Algebra 107
4.5.2 Logarithms 108
4.6 Testimonials 112
4.6.1 Nicholaus Copernicus 112
4.6.2 Francis Bacon 113
4.6.3 Johannes Kepler 114
4.6.3.1 Kepler's Three Laws of Planetary Motion 116
4.6.4 Galileo Galilei 118
4.6.4.1 Parallax: Proof of Heliocentrism 121
4.6.5 Isaac Newton 122
4.6.5.1 Newton's Three Laws of Motion 124
4.6.5.2 Newton's Law of Universal Gravitation 126
4.6.6 Gottfried Wilhelm Leibniz 128
4.7 Biblical Theology: The Match that Lit the Fire 129
4.8 The Reformation and Modern Science 130
4.9 Why Europe? 138
4.9.1 China 140
4.9.2 India 140
4.9.3 The Muslim World 142
4.9.4 One Viable Birth 143
4.10 Two Key Recognitions 144
4.11 Sovereign God at Work 146
4.12 The Bernoulli Family 147
4.13 The Incredible Euler 149
Questions for Review, Further Research, and Discussion 151
5 From Euler to Godel 153
5.1 Reason Contra Revelation 153
5.2 Cartesian Geometry 155
5.2.1 The Cartesian Coordinate System 156
5.3 Cartesian Philosophy - Mathematics Absolutized 158
5.4 The "Fruits" of Success 161
5.5 Twentieth Century Ramifications 162
5.6 "I have no need of this hypothesis" 166
5.7 Philosophical Tomfoolery 167
5.8 "I serve the laws of nature" 172
5.9 Mathematical Idolatry? 174
5.10 The Idol Falls 175
5.11 Implications and Insights 179
5.11.1 Plurality of Geometries 180
5.12 Reconstruction 182
5.13 Infinity Strikes Again 182
5.13.1 An ode to infinity 184
5.14 Divergent Schools 186
5.14.1 Logicism 187
5.14.2 Intuitionism 187
5.14.3 Formalism 189
5.15 The Hiroshima of Mathematics 190
5.16 True Foundations 192
Questions for Review, Further Research, and Discussion 194
6 Why Does Mathematics Work? 195
6.1 The Myth of Neutrality 195
6.2 The State of the Art 199
6.2.1 Preestablished Harmony 199
6.2.2 "The Footprint is Our Own" 202
6.3 A Quantum Leap 204
6.4 A Deeper Look into Morris Kline 205
6.5 The Confessions of a Nobel Prize Winner 207
6.5.1 The Structure of the Atom in Quantum Mechanics 208
6.6 More Miracles, Mystery, and Wonder 208
6.7 The Real Issue 211
6.8 The Wonders of Creation 211
6.8.1 The Mathematics of the Honeycomb 212
6.8.2 The Path of Light Through a Water Droplet 215
6.9 Guiltily Blind 217
6.10 Mathematics: Metaphysical and Epistemological Reality 219
6.11 The Unifying Factor 221
Questions for Review, Further Research, and Discussion 226
Part II How Should We Then Teach? 227
7 Objectives 229
7.1 The Biblical Worldview and Mathematics 229
7.1.1 Metaphysics 230
7.1.2 Epistemology 231
7.1.3 Ethics 233
7.2 Three Christian Approaches to Mathematics Education 234
7.3 Four Curriculum Objectives 234
7.4 The Wonders of God's Creation 236
7.4.1 Music, Trigonometry, and Wave Motion 237
7.4.1.1 Middle Octave Frequencies 237
7.4.1.2 The Mathematical Harmony of Music 237
7.4.2 The Fibonacci Sequence 240
7.4.2.1 The Genealogy of the Male Bee 242
7.4.2.2 Some Fascinating Mathematical Properties of [phi] (phi) 246
7.4.3 Spirals 248
7.4.4 Conic Sections 250
7.4.5 Hexagons 250
7.4.6 Crystallography 250
7.4.7 Congruence, Similarity, Symmetry, etc. 251
7.4.8 Trigonometry and the Heavenly Expanse 251
7.5 The "One and the Many" 251
7.5.1 The Problem 251
7.5.2 The Solution in the Ontological Trinity 253
7.5.3 The Solution Applied 255
7.6 The Attributes of the Living God 258
7.6.1 Infinite, Eternal, and Triune 258
7.6.2 Sovereign, Almighty, and Faithful 259
7.6.3 Wise 259
7.6.4 Unchangeable 261
7.6.5 All-Knowing 261
7.6.6 Everywhere Present 262
7.6.7 Good 262
7.6.8 Orderly, Precise, and Just 263
7.7 Subdue the Earth 263
7.7.1 Number 264
7.7.2 Logic 265
7.7.3 Exponents and Logarithms 266
7.7.4 Mathematical Modeling 268
7.7.5 Conic Sections 269
7.7.6 Statistics 270
7.7.7 Probability 271
7.7.8 Trigonometry 273
7.7.8.1 The Motion of a Bob on a Spring 273
7.7.9 Algebraic equations and functions 275
7.7.10 Complex and Imaginary numbers 275
7.7.11 Geometry 276
7.7.12 The Divine Proportion 276
7.7.13 Spirals 276
7.7.14 Crystallography 276
7.7.15 Linear Programming 277
7.7.16 The Calculus 277
7.8 Disciple all Nations 277
Questions for Review, Further Research, and Discussion 279
8 Pedagogy and Resources 281
8.1 Weakness in Modern Mathematics Instruction 282
8.2 Biblical Motivation 283
8.3 Teacher Preparation 285
8.4 Teaching Principles 286
8.4.1 Modeling 286
8.4.2 Integration and History 289
8.4.3 Induction and Deduction 291
8.4.4 Knowledge, Understanding, and Wisdom 292
8.5 Annotated Resources 293
8.5.1 Worldview Analysis 294
8.5.2 Christian Resources 295
8.5.3 History 297
8.5.4 Creational Studies and Dominion Mandate Applications 299
8.5.5 Mental Mathematics 300
8.5.6 General Introduction 301
8.5.7 Textbooks 303
Questions for Review, Further Research, and Discussion 308
Timelines 311
From Adam to Christ 311
From Christ to Wycliffe 312
From Wycliffe to Euler 316
From Euler to Godel 321
After Godel 329
Bibliography 333
Credits 359
Scripture Index 361
General Index 363
About the Author 409
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