Q U I C K   C O N T E N T S

Preface__________________________________________________________ 15

Part I — Introduction to Canonical Thought

Prolog___________________________________________________________ 18

Chapter 1 Canonical Thought and Irresistible Paradigms____________________ 22

Chapter 2 Canonical Thought and Canonical Solutions______________________ 25

Chapter 3 Canonical Thought and the Partitioned Mind_____________________ 30

Chapter 4 The Questions Geniuses Ask_________________________________ 43

Part II — Canonical Patterns and the Foundations of Canonical Thought

Chapter 5 The Origin of Canonical Thought: Canonical Forms in Mathematics___ 47

Chapter 6 The Rosetta Stone of Canonical Thought: Superprogrammer Software 59

Chapter 7 Canonical Thought and the Science of Connectedness_____________ 72

Chapter 8 Canonical Thought, the Scientific Method, and Concepts of God_____ 83

Chapter 9 The Canonical Method: A Canonical Scientific Method____________ 104

Chapter 10 Canonical Thought and First Principles________________________ 112

Chapter 11 Two Fundamental Theorems_______________________________ 113

Part III — Basic Concepts from Science and Engineering

Chapter 12 Database Concepts______________________________________ 115

Chapter 13 Function Concepts_______________________________________ 116

Chapter 14 Linear Algebra Concepts__________________________________ 117

Chapter 15 Computer Science Concepts_______________________________ 118

Chapter 16 Operations Research Concepts_____________________________ 119

Chapter 17 Murphy’s Law and Entropy Concepts_________________________ 120

Chapter 18 Quality Control and Verification Concepts_____________________ 123

Part IV — Canonical Approaches

Chapter 19 Examples of Canonical Solutions____________________________ 126

Chapter 20 The Steps of the Canonical Approach________________________ 131

Chapter 21 Creating the Problem Statement____________________________ 132

Chapter 22 Creating the Solution Goals Statement_______________________ 133

Chapter 23 Listing the Components___________________________________ 134

Chapter 24 Listing the Relationships___________________________________ 135

Chapter 25 Questioning the Problem Statement__________________________ 136

Chapter 26 Varying the Relationships__________________________________ 137

Chapter 27 Looking for Canonical Benefits______________________________ 138

Chapter 28 Verifying the Solution_____________________________________ 139

Chapter 29 Refining the Problem Statement for the Next Iteration____________ 140

Chapter 30 Case Study #4: A Canonical Analysis of Computer Keyboard Layouts 141

Part V — The Promise of Canonical Thought

Chapter 31 Information Age: The Ultimate Era of Human History_____________ 143

Chapter 32 Canonical Discovery: How We Can Find Canonical Solutions______ 150

Chapter 33 Canonical Description: How We Can Describe Our Solutions Canonically_______________________________________________________________ 151

Chapter 34 Canonical Distribution: How We Can Distribute Our Solutions Canonically_______________________________________________________________ 152

Chapter 35 Canonical Education: How We Can Teach Canonical Thinking to Ourselves and Our Students_________________________________________ 153

Chapter 36 Canonical Thinking, the Individual, and the Family_______________ 154

Chapter 37 The Promise of Canonical Thought for Mankind_________________ 155

Reference Material

Appendix A A List of Named Principles in This Book_______________________ 188

Appendix B Questions and Answers___________________________________ 194

Appendix C A History of the Words “Canon” and “Canonical”________________ 195

Appendix D A Primer on Mathematical Logic____________________________ 197

Appendix E Canonical Forms: Examples from Mathematics_________________ 198

Appendix F The Formulas of the Science of Connectedness________________ 207

Appendix G My Route to Canonical Thought_____________________________ 211

Appendix H The New Science of Exosociology and The Big Brass Ring of Galactic Civilization_______________________________________________________ 213

Appendix I Unified Field Theory, Applied Metaphysics, and Canonical Neuroscience_______________________________________________________________ 217

Glossary________________________________________________________ 222

Index___________________________________________________________ 226


C O N T E N T S

Preface________________________________________________________________ 15

A Contract Between You and Me: The Philosopher’s Agreement___________ 15

Read the Glossary____________________________________________________ 15

Other Books on Canonical Thought____________________________________ 16

Part I — Introduction to Canonical Thought

Prolog_________________________________________________________________ 18

The Promise of Canonical Thought for the Individual: Genius Thinking for You____________________________________________________________________ 19

The Canonical Principles___________________________________________ 19

“Why didn’t I think of that?”____________________________________ 19

The Promise of Canonical Thought for Humanity________________________ 20

Chapter 1 Canonical Thought and Irresistible Paradigms___________________ 22

New Paradigms______________________________________________________ 22

The Birthing Effect of Inspiration______________________________________ 23

Chapter 2 Canonical Thought and Canonical Solutions_____________________ 25

“Canonical Solutions” is an Abbreviation_______________________________ 25

Canonical Thought and Optimization__________________________________ 26

Canonical Thought and the Connectedness of All Things_________________ 26

An Example from Daily Life________________________________________ 26

The Second Directive of Canonical Thought__________________________ 26

The Canonical Principles of Connectedness__________________________ 27

The Artificial Simplification of Problems________________________________ 27

Canonical Thought Is About Tendencies________________________________ 28

Example: Different Meanings of “Better”_____________________________ 28

Canonical Benefits: How Much Better?_________________________________ 29

Chapter 3 Canonical Thought and the Partitioned Mind_____________________ 30

The Two Different Logics of the Mind: Mathelogic and Emologic__________ 30

Attributes: Mathelogic versus Emologic______________________________ 31

Attributes of Emologic and Mathelogic______________________________ 31

The Importance of Emotions In Canonical Thought___________________ 32

Thinking: Mathelogic versus Emologic_______________________________ 32

Connections: Mathelogic versus Emologic____________________________ 32

Correctness: Mathelogic versus Emologic____________________________ 33

Logic Errors: Mathelogic versus Emologic____________________________ 34

Denial: The Archenemy of Canonical Thought___________________________ 34

Books with “Denial” in the Title____________________________________ 35

The First Principle of Denial________________________________________ 35

An Example: Mathelogic versus Emologic in a Murder Investigation____ 36

All of Us Are Partitioned______________________________________________ 36

The Second Principle of Denial_____________________________________ 38

Canonical Thought and Feeling________________________________________ 38

Human Optimization of Paradigms from Nature________________________ 38

Dominance and Territoriality_______________________________________ 39

The Conservative Mind_______________________________________________ 40

An Example______________________________________________________ 41

The Canonical Principle of the Conservative Mind_______________________ 41

Canonical Thought and Optimized Natural Paradigms___________________ 41

Canonical Thought and Universal Principles____________________________ 42

Chapter 4 The Questions Geniuses Ask___________________________________ 43

Genius Questions #1 and #2___________________________________________ 44

Part II — Canonical Patterns and the Foundations of Canonical Thought

Chapter 5 The Origin of Canonical Thought: Canonical Forms in Mathematics 47

The History of the Development of Canonical Thought___________________ 47

Attributes of Canonical Forms_________________________________________ 49

Simple Pattern-Matching Examples____________________________________ 50

A Simple-Pattern Matching Task in Recognizing Geometric Forms______ 50

A Simple Pattern Matching Example: Circular Symbols in Non-canonical Picture Forms_____________________________________________________ 50

A Simple Pattern Matching Example: Circular Symbols in Canonical Picture Forms___________________________________________________________ 51

Calculating Canonical Advantage________________________________ 51

Canonical Advantages in Pattern Matching of Pictures: Calculation Time + Writing Time_____________________________________________________ 51

Canonical Advantages in Pattern Matching of Pictures: Calculation Time Only_____________________________________________________________ 52

A Simple Pattern-Matching Task in a Biology Experiment______________ 52

Pattern Matching in DNA Pieces — Non-canonical Form______________ 53

Pattern Matching in DNA Pieces — Canonical Form #1________________ 53

Pattern Matching in DNA Pieces — Canonical Form #2________________ 54

Calculating Canonical Advantage________________________________ 54

Canonical Advantages in Pattern Matching of DNA Pieces: Calculation Time + Writing Time___________________________________________________ 55

Canonical Advantages in Pattern Matching of DNA Pieces: Calculation Time Only_____________________________________________________________ 56

Other Uses of the Canonical DNA Forms_________________________ 56

A Note to the Nontechnical Reader____________________________________ 57

The Canonical Principle of Minimum Work_____________________________ 57

Other Canonical Forms in Science______________________________________ 58

Canonical Forms in Other Sciences and Professions___________________ 58

Chapter 6 The Rosetta Stone of Canonical Thought: Superprogrammer Software 59

The Rosetta Stone____________________________________________________ 59

The Superprogrammer Phenomenon___________________________________ 60

Programmer Time and Program Speed, Size, and Maintainability_______ 61

Example of Superprogrammer Problem Elimination________________ 61

Benefits of Superprogrammer Software_________________________________ 62

Benefits of Canonical Software_____________________________________ 63

Analogous Structure and Cascading Benefits_________________________ 63

Opportunity Costs________________________________________________ 64

The Accelerator Factor of Opportunity Costs_________________________ 64

Company ANC________________________________________________ 65

Company ACC________________________________________________ 66

ANC Versus ACC: Cascading Canonical Benefit___________________ 67

Canonical Software and the Canonical Meta-Pattern_____________________ 68

Examples of Meta-Patterns and Patterns_____________________________ 69

Computer Programs as Canonical Forms in Abstract Reality____________ 70

Computer Programs as Canonical Forms in Physical Reality____________ 70

Scientific Formulas as Canonical Forms______________________________ 70

Occam’s Razor: Canonical Thought as a Meta-Theory_____________________ 71

The Principle of The Canonical Razor________________________________ 71

Chapter 7 Canonical Thought and the Science of Connectedness_____________ 72

Connectedness and the Inverse Square Laws: The Extraordinary Implications 72

Forces Act At Arbitrarily Large Distances____________________________ 73

Forces Act Instantaneously_________________________________________ 74

The Connectedness of Matter and Energy_______________________________ 74

The Connectedness of Space and Time__________________________________ 74

The Connectedness of Space and Matter________________________________ 75

Connectedness in Unified Field Theory_________________________________ 75

Connectedness in Quantum Mechanics_________________________________ 76

Summary of Connectedness in Physics__________________________________ 76

Connectedness in Chaos Theory_______________________________________ 78

Ill-conditioning and Determinism: The Quantum Barrier______________ 78

The Quantum Barrier___________________________________________ 79

Butterflies and the n-Body Problem_________________________________ 79

Connectedness in Biology_____________________________________________ 80

Global Germ Propagation__________________________________________ 80

The Connectedness of Ecosystems___________________________________ 81

Chapter 8 Canonical Thought, the Scientific Method, and Concepts of God___ 83

The Great Historical Conflict: Revelation versus Investigation_____________ 84

Escape from Torture and Superstition__________________________________ 85

Derivation of the Word “Superstition”_______________________________ 85

Four Stages in Mankind’s Evolution of God Concepts_____________________ 86

The God and Logic Square____________________________________________ 87

The God and Logic Square_________________________________________ 87

The Canonical God and Logic Square________________________________ 87

The Concept of a “God Concept”_______________________________________ 88

The Third Choice: God and Logic______________________________________ 88

The Golden Rule and the Enrichment Principle_______________________ 90

A la carte Religion versus Mathelogical Deism_________________________ 91

God Yes, Religion No: A Mathelogical God Concept___________________ 92

Emological versus Mathelogical God Concepts________________________ 92

The Scientist’s Terror of Religion_______________________________________ 93

The Supernatural Becomes Natural_____________________________________ 93

What is the Scientific Method?_________________________________________ 94

Science and World Peace___________________________________________ 94

Hypothesis: The Pivotal Concept of the Scientific Method______________ 95

Testing the Hypothesis____________________________________________ 95

The Working Hypothesis and the Principle of Endless Evolution________ 96

Extraordinary Proof__________________________________________________ 96

Extraordinary Proof and Double Standards of Evidence___________________ 97

Preservation of Dogma Through Demonization and Denial of Funding__ 98

Example: Demonization of the Chiropractic Profession by the Medical Profession_____________________________________________________ 99

Extraordinary Acceptance and Double Standards of Evidence_____________ 99

The Process of Demonization______________________________________ 100

The Shabby Story of Piltdown Man_________________________________ 100

Scientific Dogma and Double Standards of Evidence_________________ 101

Fraud for One, Fraud for All__________________________________________ 102

Pseudoscience and the “One Fraud, All Fraud” Principle______________ 102

Emological Science versus Mathelogical Science________________________ 103

Chapter 9 The Canonical Method: A Canonical Scientific Method___________ 104

State a Hypothesis__________________________________________________ 104

Canonical Checklist for Hypothesis Content_________________________ 105

Collect Data________________________________________________________ 106

Optimize the Hypothesis to Minimize the Cost of Data Collection_____ 107

Canonical Checklist for Minimum-Cost Hypothesis__________________ 107

Minimize the Cost of Data Collection_______________________________ 107

Canonical Checklist for Minimum-Cost Data Collection______________ 107

Maximize the Quality of Collected Data____________________________ 108

Canonical Checklist for Data Quality_______________________________ 109

Record Data________________________________________________________ 109

Analyze Data_______________________________________________________ 109

Develop an Estimate of the Likelihood that the Hypothesis is Correct_____ 109

Describe Results____________________________________________________ 109

Publish and Distribute Results________________________________________ 109

The Covenant of Scientific Unity______________________________________ 110

Chapter 10 Canonical Thought and First Principles________________________ 112

What Are First and Second Principles?_________________________________ 112

The Catastrophe of Second Principles__________________________________ 112

Chapter 11 Two Fundamental Theorems_________________________________ 113

The Fundamental Theorem of Canonical Patterns_______________________ 113

The Fundamental Theorem of Canonical Self-Correction_________________ 113

Part III — Basic Concepts from Science and Engineering

Chapter 12 Database Concepts__________________________________________ 115

Primary Key________________________________________________________ 115

Database Relations__________________________________________________ 115

1:1______________________________________________________________ 115

1:Many_________________________________________________________ 115

Many:1_________________________________________________________ 115

Many:Many_____________________________________________________ 115

How to Exploit Database Concepts to Solve Problems___________________ 115

Chapter 13 Function Concepts___________________________________________ 116

1:1_________________________________________________________________ 116

1:Many____________________________________________________________ 116

Many:1____________________________________________________________ 116

Many:Many________________________________________________________ 116

How to Exploit Function Concepts to Solve Problems___________________ 116

Chapter 14 Linear Algebra Concepts_____________________________________ 117

Vector_____________________________________________________________ 117

Linear Combination_________________________________________________ 117

Vector-to-Vector Functions as Matrixes________________________________ 117

Rank Order and Basis________________________________________________ 117

Canonical Forms____________________________________________________ 117

How to Exploit Linear Algebra Concepts to Solve Problems______________ 117

Chapter 15 Computer Science Concepts__________________________________ 118

Three Problem Solving Strategies: Detection, Prevention, and Avoidance__ 118

Unity Indexing, Zero Indexing, and Canonical Indexing_________________ 118

Trees, Directed Graphs, Lists, and Pointers_____________________________ 118

Objects and Actions: A Conceptual Model of the World__________________ 118

Scheduling: The Mother of All Problems_______________________________ 118

Simulation of Systems with a Time Dimension_________________________ 118

Queues and Servers_________________________________________________ 118

Software Layering and Emulation_____________________________________ 118

How to Exploit Computer Science Concepts to Solve Problems___________ 118

Chapter 16 Operations Research Concepts________________________________ 119

Decision Trees______________________________________________________ 119

Unconstrained Optimization_________________________________________ 119

Constrained Optimization___________________________________________ 119

Mathematical “Sum” Games_________________________________________ 119

How to Exploit Operations Research Concepts to Solve Problems_________ 119

Chapter 17 Murphy’s Law and Entropy Concepts__________________________ 120

Canonical Thought and Entropy______________________________________ 121

Making Lists: The Canonical Obsession________________________________ 122

Chapter 18 Quality Control and Verification Concepts_____________________ 123

Quality Control_____________________________________________________ 123

Verification of Design and Operation Information______________________ 123

Part IV — Canonical Approaches

Chapter 19 Examples of Canonical Solutions______________________________ 126

Film Credits________________________________________________________ 126

Different Methods of Showing Film Credits_________________________ 126

Episode Names in TV Schedules______________________________________ 127

Identification Problems with Episodic TV___________________________ 128

Motor Vehicle Registration Stickers___________________________________ 129

Win-Win Strategies_________________________________________________ 129

Economic Competition versus Military Competition____________________ 129

Single-blind, Double-blind, and Triple-blind Protocols___________________ 129

Slot-Head Screws, Philips-Head Screws, and Philips-Slot Screws_________ 129

Ball Point Pens______________________________________________________ 129

Space-Saving Designs________________________________________________ 129

Recycling__________________________________________________________ 129

Permaculture_______________________________________________________ 129

NASA: Faster, Better, Cheaper________________________________________ 129

Chapter 20 The Steps of the Canonical Approach__________________________ 131

Creating the Problem Statement______________________________________ 131

Creating the Solution Goals Statement_________________________________ 131

Listing the Components_____________________________________________ 131

Listing the Relationships_____________________________________________ 131

Questioning the Problem Statement___________________________________ 131

Varying the Relationships____________________________________________ 131

Looking for Canonical Benefits_______________________________________ 131

Verifying the Solution_______________________________________________ 131

Refining the Problem Statement for the Next Iteration__________________ 131

Case Study #1: The Hubble Telescope Grinder__________________________ 131

Case Study #2: Mailing Labels for Window Envelopes___________________ 131

Case Study #3: Landowner Water Use Conflict_________________________ 131

Chapter 21 Creating the Problem Statement______________________________ 132

Chapter 22 Creating the Solution Goals Statement________________________ 133

Chapter 23 Listing the Components______________________________________ 134

Chapter 24 Listing the Relationships_____________________________________ 135

Chapter 25 Questioning the Problem Statement___________________________ 136

Chapter 26 Varying the Relationships____________________________________ 137

Chapter 27 Looking for Canonical Benefits_______________________________ 138

Chapter 28 Verifying the Solution_______________________________________ 139

Chapter 29 Refining the Problem Statement for the Next Iteration__________ 140

Chapter 30 Case Study #4: A Canonical Analysis of Computer Keyboard Layouts______________________________________________________________________ 141

Part V — The Promise of Canonical Thought

Chapter 31 Information Age: The Ultimate Era of Human History__________ 143

The Information Age________________________________________________ 143

Information About Information_______________________________________ 144

Three Ultimate Perils in the Ultimate Age: The Canonical Information Problem___________________________________________________________________ 145

Solving New Problems in the Information Age_________________________ 145

Describing Our Solutions in the Information Age_______________________ 146

The Benefits of Canonical Representation___________________________ 146

Distributing Our Solutions in the Information Age______________________ 147

Maxi-Max versus Maxi-Min Societies: The Information Gap______________ 148

Chapter 32 Canonical Discovery: How We Can Find Canonical Solutions____ 150

Chapter 33 Canonical Description: How We Can Describe Our Solutions Canonically___________________________________________________________ 151

Chapter 34 Canonical Distribution: How We Can Distribute Our Solutions Canonically___________________________________________________________ 152

Chapter 35 Canonical Education: How We Can Teach Canonical Thinking to Ourselves and Our Students____________________________________________ 153

Chapter 36 Canonical Thinking, the Individual, and the Family_____________ 154

Chapter 37 The Promise of Canonical Thought for Mankind________________ 155

War and the Malthusian Crisis________________________________________ 156

The Malthusian Crisis_______________________________________________ 156

The Concept of “Carrying Capacity”_______________________________ 156

Arguments Against the Importance of Carrying Capacity_____________ 157

Farmland Can Increase Geometrically___________________________ 157

Geometric Increases in Farmland Can Go On Forever______________ 158

Yield Can Increase Geometrically_______________________________ 158

Geometric Increases in Yield Can Go On Forever__________________ 159

The Carrying Capacity of the Earth for Humans_____________________ 159

Hunger and Death____________________________________________ 160

Time, Precious Time___________________________________________ 160

Canonical Thought and Carrying Capacity__________________________ 161

Carrying Capacity and Contraception______________________________ 162

Solving the Malthusian Crisis______________________________________ 162

The Rule of Emologic: “Us and Them” Thinking________________________ 163

Animal Logic for Humans: The Syllogism of Demonization___________ 163

Mathelogic and the Game of Positive, Rising Sum_______________________ 164

The Principle of Opposites: The Logic of Contradiction__________________ 166

Contradictions of the Form (A and not (A))_________________________ 166

Contradictions of the Form (Property A and not (Property A))_________ 166

Conduct and the Principle of Opposites_____________________________ 167

The Principle of Opposites and Double Standards____________________ 167

The Emologic of Victimless Crimes____________________________________ 167

The First Principle of Victimless Crimes: Nonviolence Is Violence______ 168

A-to-Z Thinking and the Violent Conservation of Traditional Values 169

The Second Principle of Victimless Crimes: Nonviolence is Evil________ 169

Who is a Criminal?_______________________________________________ 171

The Third Principle of Victimless Crimes: The Perpetrator is the Victim_ 172

Validation of Slavery__________________________________________ 172

Double Standards in the Linkage of Ownership and Responsibility__ 172

The Impossibility of the Consistent Application of the Principle “Society Owns Your Mind and Body”___________________________________ 173

Exercises for the Reader___________________________________________ 173

Exercise: The Origin and Justification of Victimless Crimes in Various Countries____________________________________________________ 173

Exercise: Victimless Crime Penalties in Your Country______________ 174

Exercise: United Nations Principles of Universal Human Rights versus Victimless Crime Wars_________________________________________ 174

Review of Victimless Crime Justifications___________________________ 176

Punishment for “Crimes” of Class Membership_________________________ 177

“Us and Them” Thinking and Discrimination___________________________ 177

Building a Universal Civilization with The Canonical Commandment_____ 178

Canonical Thought for a Canonical Society: “Us and Us”_________________ 179

Beyond the Paradigm of Crime and Punishment_____________________ 180

Eliminating the Poverty, Hopelessness, Anger, and Terrorism Created by “Us and Them” Thinking_________________________________________ 181

The Cascading Canonical Benefits of “Us and Us” Societies___________ 182

Canonical Civilization: The Covenant of Unity_________________________ 182

Genius Thinking for Humanity: Endlessly Cascading Benefits____________ 184

Canonical Thought and World Peace__________________________________ 184

Reference Material

Appendix A A List of Named Principles in This Book_____________________ 188

Canonical Principles_________________________________________________ 188

Noncanonical Principles_____________________________________________ 192

Appendix B Questions and Answers_____________________________________ 194

Appendix C A History of the Words “Canon” and “Canonical”_____________ 195

Etymology_________________________________________________________ 195

The Roman Catholic Church__________________________________________ 195

Canonization_______________________________________________________ 195

Mathematicians Import the Word “Canonical”_________________________ 195

Religious, Scientific, and Musical Meanings____________________________ 196

Uses of the Terms “Canon” and “Canonical” in Different Disciplines___ 196

Appendix D A Primer on Mathematical Logic____________________________ 197

Definitions_________________________________________________________ 197

Logical Statements and Truth Tables__________________________________ 197

The Opposite and the Contrapositive__________________________________ 197

The Error of Contradiction___________________________________________ 197

The Error of False Classification_______________________________________ 197

The Error of Ad Hominem Attacks____________________________________ 197

The Concept of a Proof______________________________________________ 197

Proof by Contradiction______________________________________________ 197

Appendix E Canonical Forms: Examples from Mathematics________________ 198

Examples of Canonical Forms in Mathematics__________________________ 198

Types of Objects and Properties of Interest__________________________ 198

Canonical Forms of Straight Lines in x-y Coordinates____________________ 199

Canonical Forms of Lines in x-y Coordinates________________________ 199

Canonical Forms of Circles, Ellipses, Parabolas, and Hyperbolas__________ 200

Canonical Forms and Circles______________________________________ 200

Canonical Forms and Ellipses______________________________________ 200

Ellipse Attributes from a Canonical Form___________________________ 201

Canonical Forms and Parabolas____________________________________ 201

Parabola Attributes from a Canonical Form_________________________ 201

Canonical Forms and Hyperbolas__________________________________ 201

Hyperbola Attributes from a Canonical Form________________________ 202

Canonical Forms of Polynomials______________________________________ 202

Prime Decomposition, a Canonical Form for Integers____________________ 203

Use Canonical Forms to Establish Identity and Properties________________ 203

Determining Identity and Properties with Canonical Forms___________ 204

Discussion_______________________________________________________ 205

Appendix F The Formulas of the Science of Connectedness________________ 207

The “Inverse Square” Laws of Gravitational and Electrical Force__________ 207

The Connectedness of Matter and Energy______________________________ 208

The Connectedness of Space and Time_________________________________ 209

The Connectedness of Space and Matter_______________________________ 210

Appendix G My Route to Canonical Thought_____________________________ 211

My Darwinian Voyage_______________________________________________ 211

Reality is a Canonical Fractal______________________________________ 212

Appendix H The New Science of Exosociology and The Big Brass Ring of Galactic Civilization___________________________________________________________ 213

Exosociology and the Destiny of Mankind______________________________ 214

The Big Brass Ring of Galactic Civilization_____________________________ 215

Appendix I Unified Field Theory, Applied Metaphysics, and Canonical Neuroscience__________________________________________________________ 217

Applied versus Theoretical Metaphysics_______________________________ 218

Canonical Neuroscience_____________________________________________ 220

The Diamond Challenge__________________________________________ 221

Glossary______________________________________________________________ 222

Index_________________________________________________________________ 226


TABLES AND CHECKLISTS

Attributes of Emologic and Mathelogic____________________________________ 31

Books with “Denial” in the Title__________________________________________ 35

A Simple Pattern Matching Example: Circular Symbols in Non-canonical Picture Forms_________________________________________________________________ 50

A Simple Pattern Matching Example: Circular Symbols in Canonical Picture Forms_______________________________________________________________________ 51

Canonical Advantages in Pattern Matching of Pictures: Calculation Time + Writing Time__________________________________________________________________ 51

Canonical Advantages in Pattern Matching of Pictures: Calculation Time Only_ 52

Pattern Matching in DNA Pieces — Non-canonical Form____________________ 53

Pattern Matching in DNA Pieces — Canonical Form #1______________________ 53

Pattern Matching in DNA Pieces — Canonical Form #2______________________ 54

Canonical Advantages in Pattern Matching of DNA Pieces: Calculation Time + Writing Time___________________________________________________________ 55

Canonical Advantages in Pattern Matching of DNA Pieces: Calculation Time Only_______________________________________________________________________ 56

Canonical Forms in Other Sciences and Professions_________________________ 58

Benefits of Canonical Software___________________________________________ 63

Examples of Meta-Patterns and Patterns___________________________________ 69

The God and Logic Square_______________________________________________ 87

The Canonical God and Logic Square______________________________________ 87

Emological versus Mathelogical God Concepts______________________________ 92

Canonical Checklist for Hypothesis Content_______________________________ 105

Canonical Checklist for Minimum-Cost Hypothesis________________________ 107

Canonical Checklist for Minimum-Cost Data Collection____________________ 107

Canonical Checklist for Data Quality_____________________________________ 109

Different Methods of Showing Film Credits_______________________________ 126

Identification Problems with Episodic TV_________________________________ 128

Who is a Criminal?_____________________________________________________ 171

Uses of the Terms “Canon” and “Canonical” in Different Disciplines_________ 196

Types of Objects and Properties of Interest________________________________ 198

Canonical Forms of Lines in x-y Coordinates______________________________ 199

Ellipse Attributes from a Canonical Form_________________________________ 201

Parabola Attributes from a Canonical Form_______________________________ 201

Hyperbola Attributes from a Canonical Form______________________________ 202

Determining Identity and Properties with Canonical Forms_________________ 204


Preface

I prefer to just get on the with story, but if you’d like some background information, see Appendix G, “My Route to Canonical Thought” on page 211.  Before we begin, there’s the matter of The Philosopher’s Contract.

A Contract Between You and Me: The Philosopher’s Agreement

I assume that you are a thinking person because you are reading a book with the word “Thinking” in its title.  If you are a thinking person, you are a philosopher, and I ask you to join me in what I call the “Philosopher’s Agreement” as you read this book.

The Philosopher’s Agreement is a traditional agreement philosophers have observed to place the focus on ideas and not their originators.  The term ad hominem refers to an attack made on a philosopher instead of the ideas of the philosopher, and ad hominem attacks of course violate the Philosopher’s Agreement.

The Philosopher’s Agreement goes much further than merely prohibiting ad hominem attacks — it supports the philosopher’s search for ever greater understanding.  According to this agreement, you have two options when you detect a flaw in my presentation:

1.    If you cannot see how to correct the flaw, it is your privilege to describe the flaw and your obligation to share any thoughts you have about how to correct the flaw.

2.    If you can see how to correct the flaw, it is your obligation to describe both the flaw and your solution for correcting the flaw.

Read the Glossary

If you ever wonder if I am using a word or term in its ordinary meaning, you can look in the Glossary and the Index to see if I define a special meaning for the word or the term.

Other Books on Canonical Thought

In addition to this book, there is also a study guide and a monograph for professional scientists.  This is a list of all three titles:

·       Canonical Thought, Volume 0.  The Canonical Manifesto: A Meta-Theory of Everything.

·       Canonical Thought, Volume 1.  Genius Thinking for Humanity: Building a Universal Civilization with Canonical Thought!

·       Canonical Thought, Volume 1-S.  Genius Thinking for Humanity: A Study Guide.

T. David “dMILL” Millican

[email protected]


Part I — Introduction to Canonical Thought

Consilience is the center which defines the circle that is knowledge.

Anonymous reviewer on Amazon.COM

This series of chapters gives you answers to these basic questions:

·       How does Canonical Thought help us to eliminate problems?

·       How does knowing about the fractal nature of reality help us find canonical solutions — which tend to be at least two to ten times better than solutions which aren’t canonical?

·       What are the two different kinds of logic humans use for solving problems?

·       How is reality connected?

·       Can feeling substitute for thought or vice versa?

·       How can thinkers and feelers find common ground?

·       What makes a person a genius?

·       Why is genius thinking more about asking questions than answering questions?

·       Why does a genius break up one question into many smaller questions?

The science behind the Canonical Principles of Connectedness given in Chapter 2, “Canonical Thought and Canonical Solutions”, is explained in Chapter 7, “Canonical Thought and the Science of Connectedness”.  Relevant material also appears in Appendix F, “The Formulas of the Science of Connectedness” on page 207.

For some basic ideas on mathematical logic which help make precise the concept of “clear thinking” or “mathelogic” (as it is called starting in Chapter Three of this book), see Appendix D, “A Primer on Mathematical Logic” on page 197.


Prolog

At each Age of Mankind, the discoveries of the Age bring new questions to the forefront: what can we do with stone, wood, the wheel, water power, the telescope, chemistry, the theory of relativity, and the computer?  At the dawn of the Third Millennium of the Common Era, we ask these ultimate questions:

1.    What is the nature of time, space, matter, and energy?

2.    What is the pattern of patterns?

3.    What information describes information?

4.    What is the structure of (physical, nonphysical, and abstract) reality?

5.    How does an endless and mounting flood of scientific data affect our concept of God and the Universe?

6.    How can we build a universal civilization for all humanity?

Physicists believe they are close to answering Question 1 with the so-called “Theory of Everything”.  Canonical Thought answers the rest of these ultimate questions with what can be called a “Meta-Theory of Everything”, which is a “Theory of Theories” — in principle, a way to answer any sensible question whatsoever.

Canonical Thought has many profound implications for the professional philosopher and the professional scientist, but since it really is a general problem-solving toolkit — literally, a set of Power Tools for the Mind — then the immediate question is for you is, “How can Canonical Thought help me solve my most pressing problems?”  The immediate question for us is, “How can Canonical Thought help us solve Mankind’s most pressing problems as we struggle to form the ultimate tribe: Homo sapiens?”

That help comes at two levels: first, to the individual, and second, to the group — a group which every day becomes less like the country and more like the world!

The Promise of Canonical Thought for the Individual: Genius Thinking for You

Canonical Thought will change your life in the same way that learning to read did.  Those who read live in a much vaster world than non-readers do.  Readers are richer in money and the things that money can’t buy.  Readers understand the world to a far greater extent.  Readers are better problem-solvers and get more enjoyment out of life.  Readers have better relationships with themselves and others, too!

The Canonical Principles

Canonical Thought is expressed in several dozen Canonical Principles.  This book takes you through the Principles one at a time, using a proven technique for effective learning: at each step, you’ll learn some vocabulary and a basic concept from a field such as mathematics, physics, or psychology.  Then you’ll put together this basic concept and the Canonical Principles you have already learned in a new Canonical Principle.

“Why didn’t I think of that?”

A definition for “genius” in this book is that a genius thinks of ideas which cause others to say, “Why didn’t I think of that?”  Many of the Canonical Principles will seem that obvious to you.  As you learn five, ten, then fifteen of these Principles, they will seem more and more inevitable to you.

Part of the promise in the title of this book is that the book teaches genius thinking for individuals.  As you read, you will be able to apply the principles immediately to solve or eliminate problems in your professional and private life, to improve the relationships you have with others, and to improve the relationship you have with yourself.

The Canonical Principles are listed in Appendix A on page 188 for reference purposes.  (You could think of these principles as the alphabet of Canonical Thought.)  If you love to pour over maps or catalogs, you may enjoy reading through Appendix A as an introduction to Canonical Thought.  Please bear in mind, however, that you will probably not understand the full significance of a principle until you read the explanations and examples in the chapter where the principle is presented.

The Promise of Canonical Thought for Humanity

Learning how to read does more than give you just another skill: it makes a fundamental change in who you are and who you are able to become.  Canonical Thought does more than give humanity just another philosophy: it can make a fundamental change in who we are and who we are able to become.

In the Star Trek world of the future, humanity thrives under a stable and benign global government, but how do we build the Global Village so that humanity can create such a government?  In other words, granted that humans must eventually have a global government (which everyone wants to be stable and benign), how can we get from here to there?

When we use Canonical Thought to answer this question, two areas of special concern arise: science and government.  Consequently, you’ll read about a generalization of the Scientific Method called the Canonical Method and you’ll learn about the Canonical Principles which are distilled in the Covenant of Scientific Unity (page 110), a pledge for scientists of a lifetime of ethical service to the potential of each individual and the future of all humanity.

The last chapter of this book shows the Canonical Principles we can use to create a universal civilization with a benign, global government that brings more benefit to each of us than any of us has now!  The blueprint for such a civilization is given by Canonical Thought in general and in particular by The Covenant of Unity, a charter for The United States of Humanity.  A world whose civilization is based on Canonical Thought and The Covenant of Unity looks like paradise in comparison to the world of today, for in this world:

·       Humans reject “us and them” thinking and embrace “us and us” thinking.

·       Humans reject violence as a legitimate way to solve problems — we commit instead to the principle “Humans don’t hurt humans.”

·       Acts without victims are never punished by law or custom.

·       Humans automatically and instinctively look for and find win-win solutions to conflicts.

·       There is no war and no genocide.

·       There is no hatred.

·       There is virtually no crime because no sane person sees any advantage to it.

·       Humans find that God speaks to us through the language of mathematics, physics, astronomy, geology, archeology, chemistry, biology, and psychology.  The mission of ancient religions to hate, dominate, kill, or convert the “infidel” is replaced by the concept that “helping the part helps the whole because all is connected”.  Humans are united by a new God concept or a new World concept based on universal principles such as “God/The Universe/Spirit continuously gives each human the same universal and unconditional support.”

·       The question of the existence of a universal God does not divide people, for people no longer believe in a divisive God!

·       Humans measure their civilization by the status of those with the least status.  Work to improve that measurement brings endlessly cascading benefits to all humans.

The Covenant of Unity (page 182) is designed to be the basis for a stable and global civilization made glorious by the maximum possible contribution from each and every human.  It states in part:

    We, the peoples and governments of Mankind, choose to build our civilization on the principle of celebrating our humanity through the achievement of human potential in every human.  We pledge to work to eliminate all acts which have victims by enforcing nonviolent laws based on universal principles, and by promoting the idea that humans don’t hurt humans.

    We acknowledge the principle that a person’s mind and body belong to that person.  We pledge that we will not make laws or take actions against those whose acts have no victims … .

    We commit to the welfare of the individual human being in the knowledge that the status of the least among us is the measure of our civilization, for the fate of each of us is the fate of all of us.


Chapter 1 Canonical Thought and Irresistible Paradigms

How would you like to make ten times more money than you do now?  Would you like the products you buy to cost ten times less and be ten times more powerful, versatile, and safe than they are now?  Would you like the politicians of the world to be ten time more effective in avoiding war and ten times more effective in promoting commerce and cultural exchange?

A pipe dream?  Not at all — just a description of how things have changed in human history.  Only a few years ago, humans on the average made ten times less money than they do now; ordinary products like salt cost ten times more; tools were ten times less powerful, versatile, and safe; and the politicians of the world were ten times less effective in avoiding war and ten times less effective in promoting commerce and cultural exchange.

We can take control of this “times ten” process.  It’s all in the paradigms we use.

New Paradigms

Canonical Thought gives us a new set of paradigms to deal with the unprecedented challenges of the Third Millennium.  A paradigm[1] is a way of looking at the world and organizing it for survival and value fulfillment.  For example, early humans had a paradigm of hunting and gathering, which was later replaced (for most humans) by the paradigm of growing plants and keeping animals for food.  Part of the paradigm of modern life is to divide time into hours, weeks, and months and to use technology to provide food and shelter.

Canonical Paradigms are irresistible because their opportunity costs relative to non-canonical paradigms are so enormous.  If you can solve a task with Method #1 for $10 and with Method #2 for $1, the opportunity cost of using Method #1 is $9, because you spend $9 = $10 - $1 more than you would with Method #2.

For example, recycling is a Canonical Paradigm.  It costs society much more to ignore recycling than to practice it.

Canonical Thought promises us that we can discover better ways of solving the problems we can’t eliminate by using Canonical Paradigms.  It promises us great rewards from using Canonical Principles to look for better solutions.

The Birthing Effect of Inspiration

Humans as a group or as individuals look for things when those things are thought to exist.  Christopher Columbus sailed west across the Atlantic to find land because he believed it could be done.  Jonas Salk worked to develop a polio vaccine because he believed it could be done.  The countries of the twentieth century worked to create the United Nations because they believed it could be done.

Canonical Thought tells us that there is something out there worth looking for: a better solution to every problem humans have ever faced or ever will face — in many cases, a solution which is at least ten times better or a solution which eliminates the problem.  Canonical Thought inspires us to look for improvements in solutions — to problems we can’t eliminate — which are not 10% better, not 100% better, but 1,000% better.  In conflict situations, it inspires us to look not for win-lose solutions which accommodate some of the interests of some of the people, but rather for win-win solutions which in one way or another accommodate all of the interests of all of the people.

Without the inspiration of Canonical Thought, we may aim for and accept solutions which are dramatically inferior to the solutions which we can discover through canonical thinking.  Imagine you are looking for an improvement in an existing solution.  What would be the difference between setting a goal of a 10% improvement versus a 100% improvement versus a 1,000% improvement versus the infinite improvement of eliminating the problem altogether?  Which goal would stimulate your most intelligent and creative thinking?

The Canonical Principle of Problem Elimination.  The best solution of all is to eliminate the problem.

Later in this book you will see many examples of the improvements which canonical thinking has produced in solving many different kinds of problems.  In many cases, results are at least two or three to ten times better — in scientific jargon, we say about an order of magnitude better.  This gives us the equation:

New Result = Old Result Times Ten

which is the Times Ten Rule of Canonical Thought.[2]

The Times Ten Rule of Canonical Thought.  If canonical thinking does not eliminate a problem, such thinking tends to produce a solution which is at least two to ten times better than an existing solution.


Chapter 2 Canonical Thought and Canonical Solutions

With the exception of abstract problems in pure mathematics, canonical thinking does not produce final answers to nontrivial questions.[3]  Canonical thinking is a process which produces an evolutionary understanding.  This concept is expressed in the Canonical Principle of Endless Evolution, a central feature of canonical thought.

The Canonical Principle of Endless Evolution.  Over time, the continued application of canonical thinking leads to a deeper and broader understanding of any given problem.  Over time, the continued application of canonical thinking leads to better and better solutions to any given problem, where “better” is defined in the statement of the problem.

“Canonical Solutions” is an Abbreviation

If I have developed a solution to a given problem using canonical principles, I may want to claim that my solution is optimal and is the best solution because it is a canonical solution.  Why is it canonical?  Because I have used canonical principles to develop it.

It is convenient for me to tell you that I have “a canonical solution” because it is tedious to say that I have “a solution created through canonical thinking”.  However, it is important to remember that the first quote is only an abbreviation for the second quote.

The Abbreviation Principle of Canonical Solutions.  The term “a canonical solution” is an abbreviation for the phrase “a solution created through canonical thinking.”

Canonical Thought and Optimization

Canonical thinking helps you to solve problems you haven’t yet solved or to solve an already-solved problem in a better way, where “better” is defined in the problem statement.  Canonical Thought is naturally and inevitably oriented to the language and concepts of optimization.  In pure mathematics, it is often possible to state a problem which has a solution which one can prove is the best possible solution, where “best” is defined in the problem statement.

Canonical Thought and the Connectedness of All Things

There is overwhelming, deep, and broad evidence for the principle that all things are connected.[4]  Put another way, all fields of knowledge are connected by interlocking networks of cause and effect — an idea called consilience.

The Canonical Principle of Consilience.  All fields of knowledge are connected by interlocking networks of cause and effect.

An Example from Daily Life

As an example from daily life, say that someone, perhaps one of your children, has told you something that you correctly suspect is a lie.  If you ask enough questions — and all of the other questions are answered truthfully — the lie will be proven, even if it is not admitted.  How will you identify the lie?  As you ask questions, you will get more and more answers which support your suspicion, and no answers will oppose it.  If a body of evidence both supports and refutes a claim, you know that some of the evidence is faulty or false.  You don’t have an acceptable explanation until all of the evidence points in the same direction.

The Second Directive of Canonical Thought

That’s because reality itself is consistent.  One plus one always equals two and an hour after noon is always 1 P.M.  Put another way, all things are connected.

The First Principle of Connectedness (The Second Directive of Canonical Thought).  All things are connected.

This principle is wonderfully evocative, but it is useful to state it more precisely.  Upon examination, we can extract more than one connectedness principle from The Second Directive, as expressed in the following canonical principles of connectedness.

The Canonical Principles of Connectedness

When solving problems outside pure mathematics, it is not usually possible to obtain a solution and prove it is the best possible solution.  Problems in pure mathematics deal with systems of interlocking concepts which form a closed system that is self-referential by design.  In contrast, there are no closed systems in physical reality: each object and each energy field affects each other object and energy field, as explained in Appendix F, “The Formulas of the Science of Connectedness”, starting on page 207.

The Second Canonical Principle of Connectedness.  There are no closed systems in physical reality.

According to The Second Canonical Principle of Connectedness, all physical systems are connected to each other, which implies that all physical problems are connected to each other.  Put another way, your problem and my problem are components of a larger problem — the solution I use to deal with my problem affects the nature of your problem and the solution you use to deal with your problem affects my problem.

The Third Canonical Principle of Connectedness.  Any two physical problems are components of a larger problem.

The Artificial Simplification of Problems

When I state a problem other than one in pure mathematics, I am always limiting the complexity of the problem in order to be able to state the problem.  Even if I can defend the idea that my solution is the best possible solution for the problem as defined, it is still the case that I put an artificial limitation on the problem in the way that I stated it!

The Canonical Principle of Artificial Simplification.  Physical problems are always stated in a way which limits their true complexity.

Therefore, if I tell you that I have a canonical solution to a given problem and the solution is optimal because I derived it through canonical thinking, you know (A) the problem is one in pure mathematics and my claim may be literally true or (B) at best, my solution may be optimal for a problem which is stated in a way which limits its true complexity.  When I say I have a canonical solution to a problem other than one in pure mathematics, I am simply saying that I tried to use canonical thinking as much as I could when devising a solution.  You may use canonical thinking to obtain the same solution as I or a different solution.  In the sense in which the problem is defined, your solution may be better or worse than mine, or my solution and yours may be equivalent.  (It is common for optimization problems in pure mathematics to have more than one optimal solution.)

Canonical Thought Is About Tendencies

Canonical thinking and “canonical solutions” are about tendencies.  Your solution will tend to be better than mine, according to the way that “better” is defined in the statement of the problem, if you use canonical thinking to a greater degree than I do.

The First Principle of Canonical Benefit.  Solutions which use canonical thinking to a high degree will tend to be better than solutions which use canonical thinking to a lesser degree, according to the definition of “better” in the statement of the problem.

Example: Different Meanings of “Better”

For example, say that your problem is to minimize your electricity bill, so that “better” means a lower bill.  If you use candles at night instead of electric lights, your bill will be lower, and that is better in the sense which you defined in your statement of the problem: minimize the electricity bill.  However, if candles are very expensive, or dripping candle wax ruins your clothes and makes it necessary to buy new clothes, you may spend more on candles and clothes than you save on electricity, even though you have done “better” as defined in your problem because you reduced your electricity bill.  If your problem is to minimize the amount of money you spend on candles, clothes, and electricity, you may choose to stay in bed whenever it is dark.  This is “better” because you don’t spend any money buying electricity for lighting, you don’t need any candles, and you don’t have to buy any clothes to replace those ruined by dripping candle wax.  On the other hand, I might not consider you to be in a better situation when you spend all dark hours in bed, but if so, that’s because I have a different definition of “better”!

Canonical Benefits: How Much Better?

The First Principle of Canonical Benefit tells us that canonical is better, but how much better is it?  When dealing with problems which have answers that can be characterized by numbers, the solutions we can get through the aggressive use of canonical thinking tend to be at least an order of magnitude better — ten times better — than solutions derived without the use of canonical thinking.

The Second Principle of Canonical Benefit.  When dealing with problems which have answers that can be characterized by numbers, the solutions we can get through the aggressive use of canonical thinking tend to be at least 200% to 1,000% better than solutions derived without the use of canonical thinking.

One of the key differences between non-canonical and canonical solutions is that canonical solutions tend to have fewer steps and use fewer resources.  For example, say you needed fifty items at the supermarket.  A canonical approach would be to make one trip to get all fifty items, and a very non-canonical approach would be to make fifty trips, purchasing one item on each trip!

The Third Principle of Canonical Benefit.  Canonical solutions tend to have fewer steps and use fewer resources.


Chapter 3 Canonical Thought and the Partitioned Mind

The intellectual commitment and the emotional commitment,
working together as one, have made the ascent of Man.

J. Bronowski, The Ascent of Man, Vol. 13

Most machines operate according to a fixed, inflexible, and mathematical logic which is created by the designers of the machines and which is embodied in the machines.  If the machines are in proper working order, they will do the same job in the same way every time.

The Two Different Logics of the Mind: Mathelogic and Emologic

If Stupidity got us into this mess, then why can't it get us out?

Will Rogers (1879-1935)

The human mind, unlike the machine, uses not one but two kinds of logic.  For our purposes, logic means a set of rules used to model an aspect of physical or abstract reality.  In Canonical Thought, it is remarkably useful to distinguish between emotional logic emologic for short — which is based on emotion and mathematical logic mathelogic for short —  which is based on mathematics and the consistent performance of the physical universe.  In the language of Canonical Thought, the part of the mind which uses emologic is called the Emological Partition or the Emological Mind.  The part of the mind which uses mathelogic is called the Mathelogical Partition or the Mathelogical Mind.

The First Canonical Principle of the Partitioned Mind.  The human mind uses two different kinds of logic to try to understand and solve problems: the emologic of the Emological Mind and the mathelogic of the Mathelogical Mind. 

Consider two sets of rules which a one-year-old may have learned.  First, a mathelogical rule: “When you let go of an object, it falls.”  The baby may not know it, but this is a universal rule which characterizes everyone’s experience.  Second, an emological rule: “People in white clothes hurt you.”  The child formed this rule because a trip to the doctor’s office means a painful poke from a needle wielded by a doctor or a nurse in a white uniform.  It turns out that this rule is not universal, and although the child will abandon this rule at a later age, in the interim, this rule is used in situations involving people in white clothes.

Attributes: Mathelogic versus Emologic

The following table shows some contrasting attributes of emologic and mathelogic.

Attributes of Emologic and Mathelogic

Attribute

Emologic

Mathelogic

Objectivity

subjective

objective

Obviousness

may miss the obvious

embraces the obvious

Depends on

superstition and assumption

science

Use of evidence

uses only what’s convenient

uses all available evidence

Is like

a chain of islands

a continent

Consistency

may lack self-consistency

strives to be self-consistent

Inferences

tends to be incorrect

tends to be correct

Self-correction

tends not to evolve

evolves endlessly with new information

Involves

feeling without thought

thought with feeling

Is concerned with

the emotional part of a human

all parts of a human

Scope

personal

universal

Considers

only the short term

the short term and the long term

Applies to

one person or group

all persons

 

The Importance of Emotions In Canonical Thought

Are emotions and feelings invalid in Canonical Thought?  To be alive is to have emotions and feelings, which is a very important part of the human experience.  You’ll never find an equation which tells you how to appreciate a multicolored sunset or how to feel when you look at your newborn baby.  Canonical Thought says that emotions can help us understand ourselves and our world, but only when we combine emotions with clear thinking.  Emologic is emotions without thought, but mathelogic is thoughts with emotions, so making decisions with emologic creates problems, and making decisions with mathelogic solves problems.

Thinking: Mathelogic versus Emologic

You will have guessed already that this partition idea is important in Canonical Thought because the Mathelogical Partition of the mind supports canonical thinking and the Emological Partition obstructs it.  This principle is important and useful because each of us tries to understand and solve problems sometimes with the Emological Partition and sometimes with the Mathelogical Partition.  We may apply emologic exclusively to some problems, mathelogic exclusively to other problems, and a combination of emologic and mathelogic to still other problems.

The Second Canonical Principle of the Partitioned Mind.  Mathelogical thinking supports Canonical Thought and emological thinking obstructs it.

Connections: Mathelogic versus Emologic

According to The Second Canonical Principle of Connectedness, all physical systems are connected to each other.  In a useful mathematical system, all components are connected in a way that is completely consistent.[5]  The Mathelogical Mind seeks consistency and completeness in its thoughts.  In contrast, the Emological Mind connects only what it wants to connect.

The Third Canonical Principle of the Partitioned Mind.  The Emological Mind connects the things it wants to connect and views other things as disconnected and irrelevant.

Correctness: Mathelogic versus Emologic

This section divides statements into those which convey thoughts and those which convey emotions.  We consider the correctness of the former and have nothing more to say about the latter, because Canonical Thought is primarily concerned with statements that convey thoughts rather than emotions.

The concept of correctness is central to Canonical Thought, because mathelogical thinking tends to lead to correct statements and solutions that last, whereas emological thinking tends to lead to incorrect statements and solutions that don’t last.

Let’s begin by considering the difference between literal statements and metaphorical statements.  When a novice novelist writes metaphorically “The sea is cruel.”, he or she is presumably referring in a poetic way to the challenges and risks of ocean travel or coastal living.  It is not relevant to ask if “The sea is cruel.” is a correct statement, because the statement is meant to convey an emotion instead of a thought.

In contrast, literal statements are meant to transfer information from one person to another and the information could be completely correct or at least partially incorrect.  Now we need to know what makes a literal statement completely correct.[6]

There are two issues in determining the correctness of a statement: root assumptions and derivations.  You may decide a statement is correct and I may decide it is incorrect if your root assumptions differ from mine.  In this case, the only way we can agree on whether the statement is correct is for one or both of us to alter our root assumptions.

The rules of mathematical logic tell us how we can construct statements which will be correct if the statements from which they were derived are correct.  If your root assumptions are the same as mine, but you decide a given statement is correct and I decide it is incorrect, we can resolve the question by examining our derivations.  One or both of us must have logic errors in our derivations; when these errors are corrected we will both decide that the given statement is correct or we will both decide that the statement is incorrect.

Logic Errors: Mathelogic versus Emologic

Emologic does not follow the principles of mathematical logic.  Only by coincidence does emological thinking lead to the same conclusion as correct mathelogical thinking.

Emologic tends to be incorrect, and mathelogic tends to be correct, but mathelogic is not guaranteed to be correct.  A person using mathelogical thinking will sometimes make an error and derive an incorrect statement by incorrectly combining correct statements.  However, there is a major contrast between the errors of emologic and the errors of mathelogic.

Emologic does not look for errors.  It does not question its root assumptions.  It perpetuates tradition for the sake of tradition.  It tends not to evolve or adjust.

In contrast, mathelogic constantly looks for errors.  It constantly questions its root assumptions.  It perpetuates canonical thinking in pursuit of win-win solutions.  It is always seeking new information and it evolves and adjusts to the new information as it receives the new information.

Denial: The Archenemy of Canonical Thought

Denial is the number one threat to our children’s safety.   
You’d can’t convince someone they’re in denial.

Child Safety Author Gavin de Becker on “The Oprah Winfrey Show”

Chernobyl Survivors Recall a Decade of Death and Denial

A story on CNN, April 26, 1996

The Emological Mind is able to connect only the things it wants to connect because it denies the relevance or perhaps even the existence of connections which the Mathelogical Mind needs to consider and wants to consider.  Denial operates at two levels: denial to self and denial to others.  The Table titled “Books with ‘Denial’ in the Title” gives you a sample of some of the many areas of human life where denial creates and sustains problems.

Books with “Denial” in the Title

Title

Authors or Editors

Discrimination and Denial: Systemic Racism in Ontario’s Legal and Criminal Justice Systems

A book by Clayton James Mosher and John Hagan

Drug War Politics: The Price of Denial

A book edited by Eva Bertram

Facing Our Future from Denial to Environmental Action

A book by Jim Cole

Nelson vs. The United States of America: A System in Denial

A book by Marcus Giavanni and Frank Oberle

The Politics of Denial: Reactionary Rage

A book by Michael A. Milburn

Remembrance and Denial: The Case of the Armenian Genocide

A book by Richard G. Hovannisian

Within the Wall of Denial: Conquering Addictive Behaviors

Robert J. Kearney, Ph.D.

Alcoholism: A Merry-Go-Round Named Denial

Joseph L. Kellerman

The First Principle of Denial

Here is the first of two principles of denial.

The Fourth Canonical Principle of the Partitioned Mind: The First Principle of Denial.  Persons who try to solve a problem with their Emological Minds deny to themselves and to others the relevance or existence of connections which the Mathelogical Mind considers.

An Example: Mathelogic versus Emologic in a Murder Investigation

Let’s look at an example of the effect of denial in a problem-solving situation.  One of the most important problems that humans try to solve is to determine who is responsible when murder happens.  The results obtained from mathelogic may be extremely different from the results obtained with emologic.

A detective who is not emotionally involved with a murder investigation will consider a person to be a suspect only if that person meets three conditions:

1.    The person had a motive to commit the murder.

2.    The person had a method to commit the murder, that is, a way of committing it.

3.    The person had an opportunity to commit the murder.

In order to determine whether a suspect may be involved, the detective who is using his or her mathelogical mind then looks for evidence of involvement.  In dramatic contrast, history shows that a person who is using emologic to investigate a murder may classify a person as a suspect if the person satisfies two of the conditions, or one of the conditions, or none of the conditions!  Even worse, the Emological Mind sometimes judges a person to be guilty — even if there is no evidence that the person is guilty, and the Emological Mind sometimes judges a person to be not guilty — even if the evidence would convince the Mathelogical Mind that the person is guilty.

This example shows that trying to solve a problem with emologic may lead to useless, dangerous, or tragic results.  This principle applies to all problems at all levels of importance.

The Fifth Canonical Principle of the Partitioned Mind.  Trying to solve a problem with emologic may lead to useless, dangerous, or tragic results.

All of Us Are Partitioned

Consider the contrast between a person who is characteristically very emotional and a person who is characteristically very logical (as in mathelogical).  Despite being emotional, the first person will understand clearly that gravity always pulls down, that turning a water faucet one way turns the water on, and turning the faucet the other way turns the water off.  Although the first person tends to solve problems with their Emological Mind, their ability to function in physical reality comes from their Mathelogical Mind.

In contrast, the second person usually solves problems with their Mathelogical Mind.  Yet even with a dedication to mathelogical thinking, the second person will solve some problems with their Emological Mind.  The human mind has many layers at the conscious and subconscious levels, each layer capable of processing thoughts at the same time as the other layers.  We continuously rely on habit and instinct in daily life so that we don’t have to use the full power of the conscious mind to solve basic problems.  We couldn’t examine all of the decisions we make even if we wanted to.

The Sixth Canonical Principle of the Partitioned Mind.  Each of us sometimes tries to solve problems with the Emological Mind.

There are two very different situations under which a person uses his or her Emological Mind to try to solve problems.  In the first situation, a person relies on habit or instinct to solve a problem.  A problem solved by habit or instinct is probably one which happens over and over, such as the problem of gloves for garbage in the next example.

Example: Gloves for Garbage.  One day Bob noticed that he always put on heavy work gloves to take out the garbage, which consisted of moving a garbage bag from a small plastic garbage can in the kitchen to a large plastic garbage can by the garage.  He wondered why his father had taught him to do this and telephoned his father to ask, “Why do you always put on work gloves before taking out the garbage?”  His father explained, “I don’t any more, but when you were growing up, we had an old metal garbage can with a beat-up metal lid that you could easily cut yourself on.  So I always put on heavy gloves to protect my hands.”

Needless to say,  Bob stopped putting on heavy work gloves before taking out the garbage.  He found a better way because one day, all of the sudden, he questioned the way that he had always done it.

The Second Principle of Denial

The second situation under which a person uses his or her Emological Mind to try to solve problems is one in which the person is consciously aware that there may be a connection to consider, but the person chooses not to think about that connection.  This kind of denial reflects human nature and all humans practice it to some degree or another.

The Seventh Canonical Principle of the Partitioned Mind: The Second Principle of Denial.  Each of us is sometimes in denial.

Canonical Thought and Feeling

We can capture the essence of the Canonical Principles of the Partitioned Mind with the aphorism — given precision by the rest of this chapter — that thought and feeling do not substitute for each other.

The First Principle of Canonical Thought (The Nonsubstitution Principle of Thought and Feeling).  Feeling does not substitute for thought and thought does not substitute for feeling.  Canonical solutions use feeling to deal with emotions and thoughts to deal with ideas.

Put in the form of a directive, The First Principle of Canonical Thought would be expressed as The Prime Directive of Canonical Thought.  It is not possible to substitute thought for feeling or vice versa, because the two are not interchangeable.  However, attempting to substitute one for the other leads to decisions which lack both heart and logic.  That’s why The Prime Directive says “Do not try to substitute” instead of “Do not substitute”.

The Prime Directive of Canonical Thought.  Do not try to substitute feeling for thought or vice versa.

Human Optimization of Paradigms from Nature

Humans have taken many paradigms from nature and pushed them to extremes.  For example, animals and plants use camouflage to misrepresent themselves to predators and/or prey.  Humans use camouflage in an obvious way when hunters dress in “wood” colors, but we use camouflage in many other ways, such as when we hide or misrepresent our feelings, when we lie, when lawyers write the notorious “fine print” on legal contracts, when we put facades on buildings, and when we manufacture hollow objects which look solid.  You can probably think of many other human uses of camouflage, such as “trick” photography and “move magic”.  Just as a gas fills every microscopic nook and cranny in a confining container, we humans take a paradigm and try to express it in as many advantageous ways as possible.

Consider the “pack” paradigm in natural predator species such as the wild dog or lion.  A dog pack or lion pride might have at most a few dozen individuals, but humans form associations of numerous types at the levels of dozens, hundreds, thousands, millions, or even billions of individuals!

The Canonical Principle of Natural Paradigm Optimization.  Humans exploit paradigms from nature by generalizing them in both scope and complexity.

Dominance and Territoriality

A successful species must consistently produce individuals capable of creating the next generation, and two fundamental strategies used by many species, including ours, are dominance and territoriality.  In biological terms, dominance is the famous “pecking order”, in which a group of individuals in a species ranks itself on the basis of status, power, and privilege.  Humans have pushed the practice of dominance to extremes not found in nature, such as World War I and World War II.  In military and civilian organizations there is an extensive hierarchy of salary, “grade”, and title rankings.

In nature, some individual animals or groups of animals define and defend a territory.  Of course, in nature, these territories will be no larger than a few square miles, whereas humans have organized themselves in countries or international units containing millions of individuals.

In fact, there are so many millions of humans that there is no separation between competing groups.  In nature, two adult male tigers or two wolf packs might not usually come within miles of each other.  In our cities, different “tribes” live in adjacent neighborhoods, and countries share common — and aggressively defended — borders.

In the survival strategy of territoriality, I count you as one of the “us” if you are a member of my group, be it a wolf pack, fire ant colony, or human tribe.  If you are not one of the “us”, you are one of the “them”.  One of “us” will be attacked if found on the territory of “them”, and one of “them” will be attacked if found on the territory of “us”.

“Us and them” thinking is a good survival strategy for species organized in small and well-separated groups of individuals.  It is a good non-survival strategy for humans, since our groups are neither small nor well-separated.  In natural terms, two populations which lose the separation they formerly had become one population.  Humans are just starting to realize that we literally are all one group — One Tribe.

In humans, “us and them” thinking exists in a great variety of forms and its expression varies from mild to lethal.  However, most adults and children are all too familiar with an optimized form of territoriality which is expressed by individuals who would be labeled by themselves and others as political conservatives or fundamentalists.  In the language of Canonical Thought, we would say that such persons use a form of The Emological Mind which is optimized to express territoriality through “us and them” thinking.  It is natural to call this form The Conservative Mind.

The Conservative Mind

The Conservative Mind uses a characteristic kind of emologic based on ignorance, arrogance, and violence, all driven by the underlying mechanism of denial as a means of managing fear, uncertainty, and complexity.  We will explore some manifestations of The Conservative Mind in detail in the last chapter of the book, and when we look at dogma and double standards in science in Part II.

The violence of The Conservative Mind may be expressed in a physical and/or psychological form.  For example, a member of a hated minority might be beaten by police or private citizens just because that person is a minority member.  However, all members of the hated minority know they are hated and constantly experience the incredible stress of knowing that they may be beaten to death at any time.  This constant stress is a psychological form of violence.

An Example

Let’s use the term “Hatems” for members of a minority which is hated by everyone in Pat’s tribe.  Pat may say, “You can’t trust Hatems because they are lazy, or crazy, or criminal, or all three!”  Pat is ignorant of the diversity of the Hatems, who vary in their level of industry, mental health, and law-abiding behavior, just as do the people in Pat’s tribe.

If you say to Pat, “If you’ll get out in the Hatem community and get to know some Hatems, you’ll find out that they vary in their level of industry, mental health, and law-abiding behavior, just as do the people in your tribe.”, Pat will probably say something like, “Why on Earth would I want to get to know any of them?  They’re not really human; they’re dangerous; and they’re a lot more like monkeys than they are like us!  This is of course arrogant, but Pat would deny being either ignorant or arrogant.  Pat’s denial is believing that Pat is well-informed and sensible.

Pat automatically supports the constant psychological violence of maintaining the “hated minority” status of the Hatems.  If some Hatems are beaten by police or civilian members of Pat’s tribe, Pat will say, “They must have deserved it.”

The Canonical Principle of the Conservative Mind

Let’s capture these concepts in a canonical principle.

The Canonical Principle of The Conservative Mind.  The Conservative Mind uses a characteristic kind of emologic based on ignorance, arrogance, and violence, all driven by the underlying mechanism of denial as a means of managing fear, uncertainty, and complexity.  The violence is sometimes expressed in a physical form and is constantly expressed in a psychological form.

Canonical Thought and Optimized Natural Paradigms

Canonical Thought gives us tools and techniques to identify and understand the nature of human behaviors based on optimized natural paradigms.  By using these tools and techniques, we can strip away the camouflage which so often disguises human behaviors, and know things for what they truly are.  To borrow an image from the movie, “The Wizard of Oz”, we can “pay attention to the man behind the curtains”.

Canonical Thought and Universal Principles

According to Canonical Thought, the universe is a canonical fractal, which means that all complex events are produced by the combination of many simple events.  This means that each event can be explained by a few simple and universal ideas.  We know that any explanation which relies on the non-universal principles of The Emological Mind will have circular reasoning and/or internal contradictions.  An explanation which relies on universal principles might be incorrect, but an explanation which relies on non-universal principles is guaranteed to be illogical and/or irrational.


Chapter 4 The Questions Geniuses Ask

I really cannot know whether I am or am not the Genius you are pleased to call me,
but I am very willing to put up with the mistake, if it be one.

Lord Byron (1788-1824)

Who in the same given time can produce more than others has vigor; who can produce more and better, has talents; who can produce what none else can, has genius.

Johann Kaspar Lavater (1741–1801)

What is a genius?  We call people geniuses when their solutions cause others to say, “Why didn’t I think of that?”

Geniuses instinctively use canonical techniques to gain insights that others may have missed when they looked at the same problem.  The genius hunts not so much for answers as for questions.

The First Principle of Genius Questions.  The genius tends to ask questions which other people do not ask.

While it sometimes takes a genius to answer the question of a genius, genius questions are typically easy to answer!  Geniuses find ways to answer one hard question by answering several much easier questions.

The Second Principle of Genius Questions.  Geniuses find ways to answer one hard question by answering several much easier questions.

A genius knows, intuitively if not consciously, that physical reality and abstract reality have a canonical structure, which means that you can explain something complicated as a combination of one or more simple ideas.  The genius looks for these simple ideas.

The Third Principle of Genius Questions.  The genius looks for simple ideas which can be combined to explain a phenomenon or solve a problem.

Genius Questions #1 and #2

When you think canonically, you pursue every idea to its logical conclusion.  In that spirit, it is natural to ask, “What ideas can we use to help us solve any kind of problem that we may have?”  One answer is to constantly ask yourself, “Am I thinking emologically or mathelogically?”  If you are stuck on a problem, ask yourself, “Am I always using mathelogic or am I sometimes using emologic?”

Genius Question #1.  When I work on a problem, am I always using mathelogic or am I sometimes using emologic?

In the example of Bob and the heavy work gloves, Bob asked himself, “Does the traditional way of solving this problem make sense?”  Often the obvious answer to such a question is, “No!”, but as creatures of habit we tend not to question our habits — habits serve us without demanding that we think about them!

Genius Question #2.  Is the traditional way of solving this problem the best way?


Part II — Canonical Patterns and the Foundations of Canonical Thought

The origins of Canonical Thought lie in these areas:

·       the canonical forms of pure mathematics

·       the superprogrammer phenomenon in computer science

·       the support in science and philosophy of the idea that “all things are connected”

The first three chapters in Part II explain each of those origins.  Canonical Thought is a Meta-Theory of Everything, which means that it can be used to generate explanations of anything you like, or to solve any problem which can be precisely defined.  Because of the great historical struggle between the explanations of science and those of religion, Canonical Thought has to be directly concerned with the conflict between science and religion.

In the fourth chapter in Part II, we see how Canonical Thought can give us a concept of God based on logic, universal principles, and scientific knowledge.  In this way, science and religion can be reconciled and religious hatred can become obsolete.

However, another problem emerges.  As we take the concept that God exists from religion while discarding the dogmas of religion, we also have to discard the dogmas of science.  In reaction to the emological explanations of religion, scientists long ago decided that emotion had no place in science and should be ignored.  Unacknowledged emotion is of course an unacknowledged ruler, and its role in science has been to create emological dogmas.

Since science and Canonical Thought are both concerned with explanations, we must examine these dogmas and seek a canonical remedy.  It is a generalization of The Scientific Method called The Canonical Method, the subject of the fifth chapter in Part II.  The Canonical Method is distilled in The Covenant of Scientific Unity, a pledge for scientists like the Hippocratic Oath for doctors.

In the sixth chapter of Part II, we learn the difference between first and second principles.  This fundamental and extremely important scientific concept is easy to grasp from the viewpoint of Canonical Thought.  Furthermore, it is equally obvious why canonical thinkers go towards first principles and away from second principles!

In the final chapter of Part II, we meet two “Fundamental Theorems” whose proofs are beyond the scope of this book, but these theorems express two ideas which are easy to understand:

1.    If you refine Canonical Thought, you just get Canonical Thought again.  There isn’t any theory which is more canonical than Canonical Thought!

2.    A civilization which is based on Canonical Thought will stay that way unless acted on by a strong external force.

The implications are that:

1.    the discovery of Canonical Thought is as inevitable as the discovery of chemistry

2.    once a civilization attains a certain “critical mass” of canonical features, it will become more canonical over time

3.    if there are many long-lived civilizations in the Universe, they are probably all based on canonical principles refined over thousands or perhaps millions of generations

4.    humanity will enter this group of civilizations if our civilization reaches a canonical “critical mass”


Chapter 5 The Origin of Canonical Thought: Canonical Forms in Mathematics

This chapter and the following chapter present the core of Canonical Thought for technical and nontechnical readers.  Understanding these two chapters does require effort, but does not require a mathematical background.  On the other hand, if you are already familiar with canonical forms in pure mathematics, you will see an approach to them which you may not have seen elsewhere.

The object of this chapter is to show you how to use a canonical representation of a mathematical object to quickly identify the type or category of the object, as well as some of its properties.  Accordingly, in this chapter I list several kinds of mathematical objects and associated attributes and canonical forms.  I do not describe the objects and their attributes, because the nature and applications of the objects is irrelevant here.  The activity here is a kind of pattern matching, where we see if we can match the description of an object with one of the canonical forms we know.

The History of the Development of Canonical Thought

Before we start with the details of our examples, I want to briefly describe how the theory of Canonical Thought evolved from the concept of canonical forms in mathematics.  That will establish the context and importance of the material in this chapter.

The theory that I call Canonical Thought started with the canonical forms of pure mathematics, which in turn are related historically to the canons of the Roman Catholic Church.  See Appendix C, ‘A History of the Words “Canon” and “Canonical”’, on page 195, for what we might call the prehistory of the theory of Canonical Thought, whose history is as follows:

1.    I learned about the canonical representation of static mathematical objects in 1965.

2.    I started programming computers in 1970 and quickly discovered that by looking at a problem in the “right” way, I could reduce the size of the program by an order of magnitude and speed it up by an order of magnitude.  These benefits seemed to me to be analogous to the benefits of canonical representations of static mathematical objects, so I generalized the concept of canonical forms to include computer programs.  A canonical form of a computer program is one which tends to do the minimum work required to satisfy the programs’ specification.

3.    In 1980, I met Edward Yourdon’s “superprogrammer” concept and realized that superprogrammer software is canonical software.  I now had a set which contained two canonical patterns — canonical forms in pure mathematics and canonical computer programs.  Were there other canonical patterns?

4.    By 1990, I realized that canonical patterns were everywhere and that there was such a thing as a canonical meta-pattern, which is the pattern of canonical patterns.  How general was the canonical meta-pattern?

5.    By 1995, I had met the concept of a fractal, which in this book means a system in which the defining properties of the system apply at all levels of scale.  I now saw that the abstract reality of pure mathematics is a canonical fractal.  Science has discovered that physical reality seems to be governed by universal, compact, and elegant mathematical principles which apply at all levels of scale, that is, canonical principles, so physical reality is also a canonical fractal.[7]

6.    In 1998, as I began writing down the details of Canonical Thought, I realized that Canonical Thought involved more than just the reductionist idea that the complex as well as the simple phenomena of the physical world could be explained by universal, compact, and elegant mathematical principles.  Canonical Thought depends centrally on the idea that all things are connected, as expressed in the Canonical Principles of Connectedness we saw in Chapter 4.

7.    As the book unfolded, I realized as a result of my background in applied metaphysics that there was a real possibility for investigations based on canonical principles to extend science’s interlocking systems of cause and effect to the allegedly existent realm of the soul.  If successful, this program of research, already being pursued by a number of scientists and scholars, will make the study of phenomena such as telepathy, astral projection, and reincarnation a part of mainstream science.  In that case, abstract reality, physical reality, and spiritual reality will all be shown to be parts of the same unitary and all-encompassing canonical fractal!  See Appendix E, “Unified Field Theory, Applied Metaphysics, and Canonical Neuroscience” for more information.

To summarize: canonical representations of static mathematical objects led me to generalize the concept of canonical forms to include computer programs.  This lead me to the idea of the canonical meta-pattern and stimulated the search for other canonical patterns, which culminated in the discovery that abstract reality and macroscopic physical reality are canonical fractals.

Now let’s look at the original canonical pattern of Canonical Thought: canonical forms in pure mathematics.

Attributes of Canonical Forms

Canonical forms have two wonderful attributes which make them compelling:

1.    Ease of identification.  When a mathematical object is represented canonically, you can tell what the object is just by looking at the canonical representation — no analysis is required.  In scientific language, we would say that we can determine identity by inspection.

2.    Visibility of properties.  An object has essential defining characteristics; for example, a circle has a center and a radius.  Each canonical representation — there may be more than one — exhibits one or more properties that you can determine by inspection and/or some simple computations.  For example, when you look at a canonical representation of a circle, you can tell at a glance the location of the center of the circle and the length of the radius.

Ease of identification and visibility of properties are absolutely central concepts in Canonical Thought.  They are a great deal more important than you might imagine, as we will see over and over again in this book.

Simple Pattern-Matching Examples

Before we turn to the more complex pattern-matching examples of common mathematical objects, let’s look at two simple pattern-matching examples to establish the basic concepts.

A Simple-Pattern Matching Task in Recognizing Geometric Forms

For the purposes of this example, let’s define the term “CCP” to mean “Circle-Containing Picture”.  CCP is the pattern we need to recognize; this is a task of detecting identity.  Also detect the following properties of each picture: the number of circular symbols and their position, as in first, second, and so on.  Put a piece of blank paper (or a PostIt™ pad) over the last three columns.  Use your watch to time how long it takes you to fill in the blanks.

A Simple Pattern Matching Example: Circular Symbols in Non-canonical Picture Forms

Picture

CCP?

Count

Positions

6 n s ª C è u

No

0

N/A

v w y z ó ' ( ) * ,

Yes

1

6

- . / 0 1 2 3 4 5

No

0

N/A

6 7 8 9 : ; < @

No

0

N/A

A B C D E F G H I J K

Yes

1

10

L M N O l m n ò ó

Yes

3

5, 6, 8

 

How long did it take you to do this pattern-matching task?  Did you make any mistakes?  The identity problem was complicated by the fact that you had to search through the symbols in each picture to see if there were any circular symbols.  You also had to count the symbols up to and including each circular symbol to determine each circular symbol’s position in the picture.

What if the pictures were represented in a format which revealed this information to you so that you didn’t have to work to determine identity and properties?  Let’s invent a canonical form for our pictures to save us the trouble of working to determine identity and properties.  If the picture is a CCP, “Yes” will appear in front of the picture and otherwise “No” will appear.  If the picture is a CCP, the word “Yes” will be followed by a list of numbers which show the position of each circular symbol in the picture.  Using this canonical form for our pictures, let’s reconstruct the above table.

A Simple Pattern Matching Example: Circular Symbols in Canonical Picture Forms

Picture

CCP?

Count

Positions

No: 6 n s ª C è u

No

0

N/A

Yes; 1; 6: v w y z ó ' ( ) * ,

Yes

1

6

No: - . / 0 1 2 3 4 5

No

0

N/A

No: 6 7 8 9 : ; < @

No

0

N/A

Yes; 1; 10: A B C D E F G H I J K

Yes

1

10

Yes; 3; 5, 6, 8: L M N O l m n ò ó

Yes

3

5, 6, 8

Calculating Canonical Advantage

Now repeat the exercise of covering the last three columns of the table and timing how long it takes you to fill in the entries.  How long did it take you?  Did you make any errors?  I measured myself taking 55 seconds to determine identity and properties and write them down with the non-canonical picture forms and 34 seconds to do the same with the canonical picture forms.

Canonical Advantages in Pattern Matching of Pictures: Calculation Time + Writing Time

Form

Time in
Seconds

Productivity Ratio to
Non-canonical Form

Likelihood of Error

Non-canonical Form

55

100%

Very likely

Canonical Form

34

162%

Not likely

 

In this case, the productivity increase obtained by using the canonical forms was 162% - 100% = 62%.  However, I timed myself taking 6 seconds just to read the identity and property information at the beginning of the pictures in the second table.  The 34 seconds I took to fill out the identity and property columns in the second table breaks down into 6 seconds to read information and 28 seconds to copy information.  We get a better idea of the canonical benefit when we look only at the calculation time and not the sum of calculation time and writing time, as shown in the following table.

Canonical Advantages in Pattern Matching of Pictures: Calculation Time Only

Form

Time in
Seconds

Productivity Ratio to
Non-canonical Form

Likelihood of Error

Non-canonical Form

27

100%

Very likely

Canonical Form

6

450%

Not likely

 

If we consider only “brain” time and not also the writing time, we see that we can determine identity and properties of the canonical form 450% - 100% = 350% faster!  Furthermore, we are very unlikely to make an error in determining identity and properties from the canonical form, whereas errors are very likely with the non-canonical form.

A Simple Pattern-Matching Task in a Biology Experiment

The famous DNA molecule which is the basis and blueprint for all life on Earth can be described by a (very long) character string consisting of combinations of the letters A, C, G, and T.  Let’s say that in a particular experiment we snip out tiny pieces of DNA which can be described as strings of 20 characters, each of which is A, C, G, or T; for example,

GTTTCAACCTGGGACTGCTG.

In this experiment, we are interested in pieces which have 5 occurrences of “A”.  Let’s call any piece which has 5 occurrences of “A” an “A-5” pattern.  Here are two pieces which match the A-5 pattern:

TGGGACCAAGTTTCAGTAGT and

ACCCTGGTTCAAAGTCACTT.

Other pieces would match an “A-0” pattern if the piece had no occurrences of “A”, “A-1” for one “A”, and so on, up to “A-20” for 20 occurrences of “A”.  The first column in the following table lists six pieces of DNA; the second column shows the number of occurrences of “A” in each piece; and the third column lists the pattern which each piece matches.  For example, the first piece and the last piece match pattern A-5 because each has 5 occurrences of “A”.

Pattern Matching in DNA Pieces — Non-canonical Form

DNA Piece Description

Occurrences of “A”

Matches Pattern

ACCCTGGTTCAAAGTCACTT

5

A-5

ACCCTGGTTCAAAGTCACTA

6

A-6

GTTTCAACCTGGGACTGCTG

3

A-3

AAAAAAAAAAAAAAAAAAAA

20

A-20

GTCACATTAACCCCGATCAA

7

A-7

TGGGACCAAGTTTCAGTAGT

5

A-5

 

You can see that we get the entries in the second column by counting the number of times “A” occurs in the first column.  This is not particularly difficult, but it is tedious and we are likely to make mistakes if we are in a hurry, if we are distracted, or if we have to count the occurrences of “A” in a large number of DNA pieces.

If we don’t care about the order of the letters — only the number of occurrences of “A” — then there is a much more convenient way to represent the pieces, which is to sort them by letter.  Let’s call this form of writing down the contents of the pieces “Canonical Form #1”.  This form makes it much easier to count the occurrences of “A”, as shown in the next table.

Pattern Matching in DNA Pieces — Canonical Form #1

DNA Piece Description

Occurrences of “A”

Matches Pattern

AAAAACCCCCCGGGTTTTTT

5

A-5

AAAAAACCCCCCGGGTTTTT

6

A-6

AAACCCCGGGGGGGTTTTTT

3

A-3

AAAAAAAAAAAAAAAAAAAA

20

A-20

AAAAAAACCCCCCCGGTTTT

7

A-7

AAAAACCCGGGGGGTTTTTT

5

A-5

 

It is not too hard to see that we can improve on Canonical Form #1 by using a description of the DNA pieces which shows the counts of each letter, as in the next table.

Pattern Matching in DNA Pieces — Canonical Form #2

DNA Piece Description

Occurrences of “A”

Matches Pattern

A5C6G3T6

5

A-5

A6C6G3T5

6

A-6

A3C4G7T6

3

A-3

A20C0G0T0

20

A-20

A7C7G2T4

7

A-7

A5C3G6T6

5

A-5

 

When we use Canonical Form #2 to describe the DNA pieces, it is trivially easy to say which pieces match pattern A-5.  All we do is look at the little number (the superscript) after the “A” and that number tells us at a glance how many times “A” occurs in each piece.  If that number is 0, the piece matches pattern A-0; if that number is 1, the piece matches pattern A-1; and so on.

Calculating Canonical Advantage

To see how much advantage Canonical Form #1 and Canonical Form #2 offers, do the following.  Put a piece of blank paper (or PostIt™ pad) over the last two columns in the first table and use your watch to measure how long it takes you to count the occurrences of “A” in each piece of DNA and fill in the entries in columns 2 and 3.  Then compare your entries with the ones in the table to see if your numbers are correct.  Counting the occurrences of “A” in each piece is very tedious and it is easy to make a mistake.

Now put a piece of blank paper over the last two columns of the second table and measure how long it takes you to fill in the entries for columns 2 and 3.  Then compare your entries with the ones in the table to see if your numbers are correct.  Counting the occurrences of “A” in each piece is still tedious, but much easier now, and it is much less likely that you made a mistake.

Now put a piece of blank paper over the last two columns of the third table and measure how long it takes you to fill in the entries for columns 2 and 3.  The entries in the second and third columns are surely correct because you didn’t have to count at all: you could simply write down the entries in the last two columns by glancing at the entries in the first column.

You get the idea by now: a moderately canonical form is much better than any non-canonical form and a highly canonical form makes pattern matching as easy as it can possibly be!  Let’s compare the time it takes to do our pattern matching task with the three kinds of descriptions we have of our DNA pieces, as shown in the next table, which contains the numbers I measured when I did this experiment.

Canonical Advantages in Pattern Matching of DNA Pieces: Calculation Time + Writing Time

Form

Time in
Seconds

Productivity Ratio to
Non-canonical Form

Likelihood of Error

Non-canonical Form

60

100%

Very likely

Canonical Form #1

50

120%

Somewhat likely

Canonical Form #2

17

353%

Not likely

 

Canonical Form #1 is only mildly canonical, and I only got a productivity ratio of 120%, or an improvement in productivity of 120% - 100% = 20% on this task by using it instead of the non-canonical form.  However, Canonical Form #2 is quite canonical, and it gave me a productivity ratio of 353%, or an improvement in productivity of 353% - 100% = 253%.

Of course, a lot of the time it took to do this task was involved in writing down what my brain calculated.  It looks like I took about 15 seconds just to write down what my brain figured out.  Let’s subtract out the 15 seconds of writing to look just at the calculation time, which will give us a better idea of the advantage of using the canonical forms instead of the non-canonical forms.

Canonical Advantages in Pattern Matching of DNA Pieces: Calculation Time Only

Form

Time in
Seconds

Productivity Ratio to
Non-canonical Form

Likelihood of Error

Non-canonical Form

45

100%

Very likely

Canonical Form #1

35

129%

Somewhat likely

Canonical Form #2

2

2,250%

Not likely

 

Remember the “Times Ten Rule of Canonical Thought”?  Ten times faster means 1,000% faster.  In terms of calculation time — brain time — Canonical Form #2 is 2,250% - 100% = 2,150% faster than the non-canonical form and 2,250% - 129% = 2,121% faster than the mildly canonical form, Canonical Form #1.  Furthermore, when we use Canonical Form #2, we are very unlikely to make a mistake in our pattern-matching task.

The payoff from using canonical forms is very, very big.  Put another way, would you like to spend 45 seconds doing a task or 2 seconds?  If you had a large number of DNA pieces to match — say you work as a lab assistant and it is your job to match these patterns — would you like to spend 45 days or 2 days?  If you are running the lab, would you like your assistant to spend 45 days or 2 days?  Would you like to pay your assistant for 45 days or 2 days to do this task?

And finally, would you like your assistant to have an error rate of 1% or 2%, or 0%?  In science, errors can mean that a research team misses a discovery of major importance, or that it reports erroneous results, with the consequent loss of prestige and perhaps funding….

Other Uses of the Canonical DNA Forms

Note that there are many other possible uses of the canonical DNA forms.  For example, if it turns out that the A-6 patterns are the important ones instead of the A-5 patterns, we can pick out the DNA pieces which match the A-6 pattern just as easily as we can pick out the DNA pieces which match the A-5 pattern.

It would also be easy to pick out the DNA pieces which have 7 occurrences of “G” — the “G-7” pattern.  We could easily identify all pieces which had at least 10 occurrences of “T”, or pieces which had 3 occurrences of “C” and 11 occurrences of “G”, and so on.

The Unexpected Benefit Principle of Canonical Forms.  The benefits of a canonical representation are likely to increase over time.

A Note to the Nontechnical Reader

If you are not technically oriented, you may wish to skip to the heading “The Canonical Principle of Minimum Work” on page 57, near the end of this chapter.  The final sections of this chapter give some examples of canonical forms in sciences and professions other than mathematics and cement the key concepts in the chapter.  (The key concepts to take away from this chapter are that objects have identities and properties which are usually very, very easy to determine if the objects are represented canonically and usually rather difficult or even extremely difficult to determine if the objects are not represented canonically.)

On the other hand, if you are technically oriented, the remaining material in this chapter will help you to understand the historical origin and motivation for canonical forms in mathematics.  Understanding the role of canonical forms in mathematics will enable you to better understand the history of the development of Canonical Thought.

The Canonical Principle of Minimum Work

Note that you did not have to know what use is made of any of the objects or properties you examined in this chapter!  You did not even need to know the definitions of the objects or their properties in order to identify the objects and their properties.  You identified objects and determined various properties of interest by simple pattern matching.

Canonical forms permit you to get the information you need with the minimum possible effort.  That idea is one of the most basic principles in Canonical Thought.

The Canonical Principle of Minimum Work.  Canonical forms tend to require minimum effort to obtain needed information.

Other Canonical Forms in Science

You are probably aware that physical scientists have organized basic information about the different kinds of atoms into a representation called the Periodic Table of the Elements,  or Periodic Table, for short.  This table is a kind of canonical form, and like many other canonical forms, it is not unique and exists in several variations.  Here are some canonical forms in branches of science other than mathematics:

Canonical Forms in Other Sciences and Professions

Science

Canonical Form

Represents

Chemistry

Periodic Table of the Elements

elements (hydrogen, helium, etc.)

Computer Science

BNF grammars

computing languages

Computer Science

hardware description languages

computer hardware architectures

Computer Science

property lists in user interfaces

essential properties of objects

Engineering

decision trees

decision processes

Engineering

flowcharts

processes

Library Science

card catalog author index

standard contents of a collection ordered by author

Library Science

card catalog title index

standard contents of a collection ordered by title

Linguistics

dictionaries

derivations and meanings of the words of a language

Linguistics

sentence diagrams

sentences

Publishing

bibliography

works referenced in a document

Publishing

index

essential topics in a document

Publishing

glossary

essential terms in a document

Publishing

tables of contents

outline structure of a document


Chapter 6 The Rosetta Stone of Canonical Thought: Superprogrammer Software

This chapter explains how the twentieth century invention of programmable digital computers and the subsequent emergence of the superprogrammer phenomenon provided the second great clue to the existence and nature of Canonical Thought.  The following chapter explains the third great clue, “All things are connected”, and presents several important examples of connectedness from different branches of science.

The Rosetta Stone

Everyone knows that ancient Egyptian tombs and stone architecture are covered with hieroglyphics, a form of writing.  The Egyptians also used a form of writing called demotic, but unlike the Greek language, which has been in use continuously since ancient times, the ancient Egyptian language did not survive and humans lost the ability to read either hieroglyphics or demotic text long ago.

In 1799, near the town of Rosetta, Egypt, a French soldier found a stone slab with three sections: one in hieroglyphics, one in demotic text, and one in Greek!  You may have guessed that the three sections each contained the same message, so based on their knowledge of Greek, scholars were able to translate the other text and unlock the secrets of ancient Egypt, written on the walls of tombs and monuments for anyone who could read them.

The Rosetta Stone was a key that opened the door from one world to another.  The handle of the key was Greekhieroglyphics and demotic were the teeth of the key, hidden when the key was inserted in the lock.  When the key was turned, ancient Egypt was revealed, and we could know ancient Egypt because we knew ancient Greece.

In this chapter, superprogrammer software plays the role of Greek, canonical patterns play the role of hieroglyphics, and when we turn the key, the world of Canonical Thought is revealed.

The Superprogrammer Phenomenon

Scientific investigation frequently involves years of difficult and tedious work before results are obtained, but one of the motivations of such work is the possibility of the unexpected discovery.  The now famous 1968 Harold Sackman study[8] is a case in point.

Card punches are museum pieces now, but they were used until well into the 1980s as a kind of typewriter which punches coded patterns of holes into the so-called “IBM card”.  Programmers would write their programs on these cards and feed the resultant card deck into a card reader which was the input device for the computer.  Users of programs stored on the computer punched their data onto cards and ran the programs on their data by feeding card decks into card readers.

In the 1960s, the now-standard keyboard-and-monitor access equipment was being developed and the question naturally arose of how much of a productivity gain programmers would receive from terminal access versus card reader access.  The Sackman study was done to investigate this question.

Several programmers, some using card equipment and others using terminal equipment, worked independently on the same program.  The study is not known for the difference between the programmers who used cards and the programmers who used terminals, as one might expect.

Instead, Sackman was astonished, one presumes, to find order-of-magnitude differences between programmers with equivalent amounts of education and experience.  His study has become famous for this remarkable result.

Of course, in science, one regards the Great Experiment which cannot be duplicated as “the fish that got away”.  Sackman’s results have been duplicated thousands of times in computer courses!  In this case, a group of programmers with (usually) equivalent amounts of education and experience work independently on the same program.

Some of the programmers will produce programs which are an order of magnitude smaller and faster than the programs of the average programmer.  Software engineering guru Edward Yourdon has coined the term superprogrammer to label programmers who exhibit this order of magnitude advantage.[9]

Programmer Time and Program Speed, Size, and Maintainability

The superprogrammer’s product exhibits what I have called “canonical benefit” in Part I of this book, that is, the superprogrammer product is about an order of magnitude, or at least 500% to 1,000%, better than the typical product.  This canonical benefit is paradoxical, because the usual tradeoffs are violated:

·       more program speed should mean more program size

·       more program speed should mean more programmer time

·       more program speed should mean less maintainability

Instead, the superprogrammer’s product shows several win-win strategies.  In contrast to the typical programmer, the superprogrammer has solved many problems by eliminating them.  That is why the superprogrammer’s program is shorter.  Of course, the superprogrammer’s program is not somewhat shorter, it is dramatically shorter.  That is because the superprogrammer is applying the principle of eliminating problems in a fractal fashion at all levels of the problem!

Example of Superprogrammer Problem Elimination

Here is a common example of the way in which the approach of a superprogrammer might differ from that of a typical programmer.  In the typical programmer’s approach, the information is processed with not one, but two separate programs.

Program 1 reads the user data and writes an intermediate file to disk.  Program 2 reads the intermediate file and produces a report.  The programs have to be run separately.  The name and location of the temporary file is not documented or taught to the user, who may consequently erase the file between the time Program 1 is run and the time Program 2 is run.  After all, says the remorseful user, “The file’s name begins with ‘TEMP’, so isn’t it all right to erase it?”

The superprogrammer will use only one program — let’s call it Program 3 — to produce the report, thus eliminating the problem of the user erasing the temporary file.  In fact, the superprogrammer will look first for a way to produce the report without writing an intermediate file.  If this is not possible, the superprogrammer will use an intermediate file to produce the report, but the file will be created and erased during program execution without user intervention.

It is likely that:

·       Program 3 is much shorter than the combined length of Programs 1 and 2.

·       Program 3 is much easier to understand than Programs 1 and 2.

·       Program 3 is much easier to verify than Programs 1 and 2.

·       Program 3 is much easier to modify without introducing errors than Programs 1 and 2.

·       Program 3 uses fewer computer resources than Programs 1 and 2 combined.

·       Program 3 is much faster than the execution time of Program 1, plus the execution time of Program 2, plus the time for the user to run Program 2.

·       Program 3 took much less human time to write, debug, and test than Programs 1 and 2.

Benefits of Superprogrammer Software

When the superprogrammer applies canonical thinking fractally, that is, at all levels of scale, the end result is about an order of magnitude improvement in the cost, speed, and quality of design, development, implementation, operations, and maintenance.

In other words, superprogrammer software is canonical software.

Superprogrammer software displays that characteristic “times ten” benefit of canonical thinking.  You can see that the benefit is not limited to a single characteristic of the software: the benefits are multidimensional, interdisciplinary, and fractal.

At first, it may seem that superprogrammer software has no implications outside computer science.  However, superprogrammer software is the Greek text on the Rosetta Stone of Canonical Thought.

If we can understand something fundamental about the attributes of superprogrammer software, we can understand something fundamental about canonical patterns, so let’s consider these attributes.  The following table shows the benefits of canonical software as contrasted to non-canonical software.

The table refers to “opportunity costs”, a concept which we will explore in depth later in this chapter.  For now, let’s define “opportunity costs” as the difference between the cost of an action you did take minus the cost of a cheaper, equivalent action which you did not take.

Benefits of Canonical Software

Attribute

Canonical Benefit:
tends to be

Areas of Cost Reduction

Programmer time to design

Much less

Programmer salaries, opportunity costs

Programmer time to develop

Much less

Programmer salaries, opportunity costs

Program length

Much shorter

Programmer salaries, disk space, printout storage space

Source code ease of understanding

Much higher

Programmer salaries

Source code ease of verification

Much higher

Programmer salaries

Source code ease of modification

Much higher

Maintenance programmer salaries, user salaries, opportunity costs

Running program’s use of storage

Much less

Operations, equipment

Execution time

Much less

User salaries, operations, equipment

Staff time to deploy (implementation)

Much less

Programmer salaries, user salaries, opportunity costs

Staff time to operate (operations)

Much less

User salaries

Down time (operations)

Much less

Programmer salaries, user salaries, possibly mission-critical opportunity costs

Staff time to modify and deploy again (operations)

Much less

Programmer salaries, user salaries, opportunity costs

 

Analogous Structure and Cascading Benefits

We expect to see similar attributes and benefits in other canonical solutions.  Furthermore, we expect to also see in other canonical solutions the overall pattern of cascading benefits.  Fundamental attributes of canonical software lead to cost reductions, not in just one area, but in most or all areas.  For example, smaller size means lower costs in virtually all parts of the software lifecycle: design, development, testing, etc.  If design is about five times faster, development may be about five times faster, testing may be about five times faster, and so on.

The Canonical Principle of Cascading Benefits.  Canonical improvements in one part of a solution tend to benefit all of the other parts of the solution.

Opportunity Costs

All of the cost categories in the above table are self-defining except for “opportunity costs”, which refer to the difference between the path you took and a more profitable path you did not take!  Let’s say that you have a grocery list, and you can buy the items on the list in a store near your house for $15, or for $10 in a store slightly further away.  Now if you bought those groceries for $15 in the nearby store and ignored the existence of alternative stores, the cost of the groceries would be $15 and that is that.  However, if you calculate the cost of your groceries with the additional information that the groceries cost only $10 at the other store, you’ll break down the $15 into $10 for the groceries (that’s what you would pay at the second store) plus $5 opportunity costs.  You paid $5 for the opportunity to buy your groceries at the nearby store.

If you are not willing to consider any alternatives to existing solutions or the possibility of solving as-yet unsolved problems, then you would always calculate your opportunity costs as zero — there’s no opportunity cost because there’s no opportunity to do anything different!  However, if you are reading this book, you are sure to be looking for alternatives to what you are doing now!

The Accelerator Factor of Opportunity Costs

One of the claims for Canonical Thought is that it can help us seize control of the “times ten” processes of human history.  Let’s look at a case study comparing Company A following a non-canonical strategy in its first year of operations (call it ANC, A Non-canonical Company) versus Company A following a canonical strategy in its first year (call it ACC, A Canonical Company).

We will see that ACC does things that let it get one step ahead of the competition, and it turns one step into two steps, and two steps into four.  ACC uses canonical thinking to turn one level of success into an even higher level of success.

At ACC, the president gets people in the habit of thinking about and talking about how to do their jobs better.  The president gives employees a monthly presentation of where income has come from and where expenses have gone, so they understand the relationship between what they do and ACC’s profitability.

In contrast, the ANC president concentrates on getting people to do what they are told and never gives any financial information to employees.  The ANC president believes that a successful company can be built on obedience, deference, constant cost-cutting, and the president’s assumptions about what the customer wants.  At ANC, the focus is on cost, not on benefit, the customer, the competition, or — ultimately — on profitability.

Company ANC

An investor has a business idea, forms a company, and hires a president to build the investor’s idea into a staff, offices, revenue flow, and so on.  The ANC president is intelligent but does not make much use of canonical thinking.

Month 1.  The president hires a programmer to write the mission-critical software upon which the company will depend.  The programmer selected seems to have about the right amount of education and experience, but the president does not know about canonical thinking and does not hire a programmer who knows about canonical thinking.

Month 2.  The sales representatives are hired and trained to be ready to take orders in month 3.

Month 3.  The ANC software is not ready, although it was required for month 3.  Sales representatives are now a month behind schedule, which means that all revenue projections must be moved forward by one month.  It also means that the sales representatives have been drawing salary for a month in which they have not been able to produce income.

Month 4.  In month 4, a competitor obtains a big contract that could have gone to ANC.  The software becomes operational but there are many problems with the functionality of the software.  Even though internal testers had blessed the design, it is found to be inadequate in many ways once the software goes into use.  The software also crashes or produces obviously incorrect results on a daily basis.

Month 5.  The software upgrade is needed immediately, since the first version was inadequately designed.  However, the ANC programmer must spend time every day to take bug reports, try to fix the bugs, keep the software from crashing, and help users get going again after problems happen.  Software problems lead to problems in taking orders and in fulfilling orders, causing revenues to be less than expected in the business plan.

Month 6.  The first programmer is fired and the second programmer needs all month to understand the mostly undocumented intricate inefficiencies in the work of the first programmer.  The second ANC programmer — who has a lot more experience than the first ANC programmer — tells the ANC president that the work of the first programmer is a replace rather than a repair option.

Month 8.  Software developed by the second programmer goes online and is a lot more functional and stable, but there still are problems.  In the meantime, there has been a lot of turnover of sales representatives and morale is low.  Revenues continue to run well below expectations.

Month 9.  ANC is finally in the position the business plan specified for month 3: the mission-critical software is working and the sales representatives are taking orders which are being filled.  However, the competition continues to take business from ANC and to add features to their mission-critical software — features which impart competitive advantage!  The ANC programmer and ANC as a company must try to catch up.

Month 12.  ANC has not met revenue expectations and the investor is not sure that ANC can become competitive.  Its future is uncertain.

Company ACC

An investor has a business idea, forms a company, and hires a president to build the investor’s idea into a staff, offices, revenue flow, and so on.  The ACC president is intelligent and makes aggressive use of canonical thinking.

Month 1.  The ACC president advertises for a canonical thinker and hires a superprogrammer with design, analysis, and communications skills to write the mission-critical software upon which the company will depend.  The ACC programmer costs almost three times more than the ANC programmer, but brings far more than three times the benefit.

The ACC programmer gets information from internal users about the mission-critical software, develops a design document, and circulates drafts of it endlessly, reminding the recipients that they will have to sign off on each and every page.  The ACC programmer does endless thought experiments about how the software will be used, thinks of how the software can be designed and used canonically, and asks many probing questions about its intended use to its intended users.  As a consequence, the software is created from the beginning to have many integrated features that provide competitive advantage.

Month 2.  The sales representatives are hired and trained to be ready to take orders in month 3.  The first ANC programmer started programming in the first week, never really finished, and got fired in month 6.  In contrast, the ACC programmer does not begin programming until the design process is done in week 1 of month 2.  By week 3 of month 2, early versions are ready for the sales representatives to test.

Month 3.  The ACC software is online, as required for month 3 by the business plan.  Sales representatives are taking orders as expected, but competitive features of the ACC software mean that ACC sales representatives are able to win existing customers from the competition, even in the first month of taking orders!

Month 4.  In month 4, a competitor obtains a big contract that could have gone to ACC.  The software becomes operational but there are many problems with the functionality of the software.  Even though internal testers had blessed the design, it is found to be inadequate in many ways once the software goes into use.  The software also crashes or produces obviously incorrect results on a daily basis.

Month 5.  The ACC programmer and the ACC president have frequent, intense conversations in which they search for canonical benefits for ACC.  The programmer releases ACC software version 2, which has features the competition has scarcely dreamed of — even though the customers have!

Month 6.  The business plan is revised on the basis of the canonical thinking of the president and the superprogrammer.  Not only are projected revenues set at markedly higher levels than in the original plan, the revenue model is now built on ongoing canonical improvements in infrastructure and mission-critical software, combined with a merge or buy strategy.

Month 12.  ACC buys a competitor and doubles its staff size.  It is in talks with three other competitors about mergers or the licensing of ACC technology.

ANC Versus ACC: Cascading Canonical Benefit

Very few business reach profitability and there are a lot of reasons for that.  However, in this case study comparing the results the investor got with the two different presidents, we see in ANC a situation which is more than just realistic — it is routine.  ACC is a hypothetical company, but look at the companies that are doing better than the competition and see if they aren’t doing a lot more canonical thinking than the others are.

Every time that ANC made a decision or took an action that was not canonical, ANC bore an opportunity cost which is shown by the difference between ANC and ACC.  Since the management and employees of ACC continuously and systematically looked for canonical thinking, they kept converting one level of canonical benefit into an even higher level of canonical benefit.

Thus, the gap between ANC and ACC kept getting wider and wider.  ACC created cascading canonical benefit and a bright future for itself.  ANC used up its initial investment before reaching profitability or even really the prospect of profitability.

Canonical Thought shows you how to achieve the most you can with a given set of resources.  In the case of creating and running a company, Canonical Thought can show you how to be efficient for a profitable present and innovative for a profitable future.

Canonical Software and the Canonical Meta-Pattern

Canonical Thought is a comprehensive theory of knowledge, discovery, and problem solving, but more specifically, it is a meta-theory, which is a very special kind of theory.  A meta-theory is a theory behind the theory — it is a theory of theories, just as a meta-pattern is a pattern of patterns.

The following table gives some examples of patterns and meta-patterns.  You can see that the patterns are special cases of the meta-patterns.  When you create an example of a meta-pattern, you create a pattern.

Creating or discovering a meta-pattern is trickier!  The trick is to define just the right set of patterns, a set whose members are all special cases of a more general pattern.  This more general pattern is the meta-pattern of the set of patterns.

When you read a description of meta-patterns and patterns, the whole subject seems a lot more complicated than it is.  But take a look at the following table and you’ll see that you already know what a meta-pattern is!

Examples of Meta-Patterns and Patterns

Meta-Pattern

Pattern

knots

a square knot

knots

a bowline

 

 

curves

a circle

curves

a hyperbola

 

 

dresses

a strapless, powder blue, pinch waist taffeta mini-dress with a built-in brassiere and petticoat

dresses

a below-the-knee, waistless yellow frock with a white square-neck flap

 

 

dress patterns

ACME Dress Pattern #6473

dress patterns

ACME Dress Pattern #6474

 

 

systems of measurement

the English system of measurement

systems of measurement

the metric system of measurement

 

 

quality control standards

General Motors quality control standards

quality control standards

Intel quality control standards

 

 

standards

quality control standards

standards

building codes

 

 

canonical patterns

the canonical representation of a circle in rectangular coordinates

canonical patterns

a superprogrammer’s program

 

 

meta-theories

Darwin’s theory of evolution

meta-theories

Einstein’s theory of Special Relativity

 

 

canonical meta-patterns

canonical representations of mathematical objects

canonical meta-patterns

superprogrammer programs

canonical meta-patterns

the canonical, fractal structure of abstract reality (pure mathematics)

canonical meta-patterns

the canonical, fractal structure of physical reality

 

 

 

In the language of Canonical Thought, superprogrammer programs may be called generically canonical software.  The existence of canonical software, depending as it does on the fractal application of canonical thinking, implies that the Universe — that is, both physical and abstract reality — has a canonical and fractal structure.

When executed, a computer program is a sequence of instructions to the CPU; the instructions are processed one by one, until the program terminates.  A computer program is an analog of the world.

Computer Programs as Canonical Forms in Abstract Reality

On the one hand, the computer program is a mathematical entity which exists apart from the hardware on which the program is executed.  The existence of canonical software implies that abstract mathematical processes have the same properties as representations of mathematical objects.  These representations reveal at a glance the identity and essential properties of the object when the representations are canonical, and otherwise, the identity and essential properties of the object may require considerable (and possibly error-prone) analysis to identify.

We can find canonical representations for static mathematical objects which have no time dimension as well as for sequences in time of mathematical objects.  This fact is the basis for the claim that Canonical Thought is a comprehensive theory of abstract reality.

Computer Programs as Canonical Forms in Physical Reality

On the other hand, a computer program, when executed, is a physical process.  The complete set of resources available to the program when it is running can be thought of as a server.  As the program’s instructions are executed one after another, the server provides various services.

Note that there is nothing about this server model which is specific to computers.  This is a general model of physical processes.  This fact — plus all of the canonical discoveries of science to date — is the basis for the claim that Canonical Thought is a comprehensive theory of physical reality.

Scientific Formulas as Canonical Forms

Consider, for example, the remarkable brevity of E = mc2.  This incredibly simple equation expresses two fundamental and fundamentally important properties of the physical universe:

1.    energy and mass are different forms of the same thing

2.    a small amount of mass holds the equivalent of a large amount of energy

This pattern of simple equations holding profound information about the Universe holds throughout science, because physical reality seems to operate not just according to mathematical principles, but to simple mathematical principles.  In the language of Canonical Thought, we would say that the Universe has a canonical organization.

Occam’s Razor: Canonical Thought as a Meta-Theory

Canonical Thought is perhaps best described as a meta-theory, because it tells us that we can exploit canonical principles to develop theories of specific aspects of the Universe and to find canonical solutions for problems.  Canonical software is the Rosetta Stone of Canonical Thought because its existence — plus the canonical formulas of science — imply that both physical and abstract reality have a canonical structure at all levels of scale.  Put another way, reality is a canonical fractal.

Occam’s Razor is a principle of scientific decision-making, dating back to William of Ockham of the fourteenth century.  This principle states that the simplest explanation is the best explanation.

The Principle of The Canonical Razor

Canonical Thought can make a stronger statement — let’s call it the Canonical Razor.

The Canonical Razor.  The most canonical explanation is the best one.

This principle immediately leads to two related principles, called corollaries.  The first corollary tells us that if our explanation isn’t canonical, we probably aren’t very close to the understanding that further investigation will bring.

Corollary #1 to the Canonical Razor.  An explanation which is not canonical can be replaced by one that is.

The Canonical Principle of Endless Evolution applied to the principle of the Canonical Razor gives us the second corollary:

Corollary #2 to the Canonical Razor.   The degree to which an explanation is canonical can be increased by canonical thinking.


Chapter 7 Canonical Thought and the Science of Connectedness

A human being is part of the whole.

Albert Einstein

All things are connected.  Whatever befalls the Earth, befalls the sons of the Earth.
Man did not weave the web of life; he is merely a strand in it.
Whatever he does to the web, he does to himself.

Chief Seattle, 1854

We must … universally allow, that all bodies whatsoever
are endowed with a principle of mutual gravitation.

Isaac Newton, 1729

Arguably the central tenet in Canonical Thought is “all things are connected”.  This principle is a maxim not only of modern metaphysics and some traditional worldviews, but also of scientific disciplines as diverse as classical physics, quantum mechanics, chaos theory, and biology.  Let’s look first at the astonishing philosophical implications of the laws of gravitational and electrical attraction in classical physics.

Connectedness and the Inverse Square Laws: The Extraordinary Implications

There are two laws of classical physics governing the gravitational attraction between two objects with mass and the electrical attraction or repulsion between two objects with electrical charge.  As one manifestation of the connectedness of all things, both of these laws have the same mathematical form!  Accordingly, both laws are called “inverse square laws”.  (The formulas are given in Appendix F, “The Formulas of the Science of Connectedness”.)

It is really quite extraordinary that phenomena as seemingly different as gravity and electricity should obey laws which have the same mathematical form.  There are two commonalities:

·       The first commonality is that the gravitational force between two objects with mass or the electrical force between two objects with charge is directly proportional to the amount of mass or charge: double the mass or charge of one of the objects and you double the force; halve the mass or charge of one of the objects and you halve the force.

·       The second commonality is in the way that the force varies with the distance between the objects: double the distance and the force decreases by four times; halve the distance and the force increases by four times.

One of the essential claims of Canonical Thought is that the historical distinction between the natural and the supernatural will disappear as more and more scientists overcome their fear of supposedly supernatural phenomena, so that the study of such phenomena can become mainstream science.  Many scientists — particularly physicists — are dedicated materialists.  In the philosophy of materialism, phenomena which can be measured by today’s laboratory devices are considered to be real and all other phenomena are considered to be at best figments of the imagination, and at worst the delusions of the deranged!

However, there are remarkable metaphysical implications in the inverse square laws, even though these laws are as mainstream as algebra and geometry!  These implications support the Canonical Principles of Connectedness given in Chapter 2, “Canonical Thought and Canonical Solutions”.

Forces Act At Arbitrarily Large Distances

One extraordinary feature of the inverse square laws is that masses have a gravitational attraction no matter how far apart they are and charged masses have an electrical attraction (or repulsion) no matter how far apart they are.

Of course, the evidence for these laws is limited to laboratory measurements and to certain astronomical observations.  There is no way that we could verify the action of these laws at all the distances in the universe, yet scientists believe that these laws are valid for all distances, no matter how large.

Forces Act Instantaneously

Note that the inverse square laws have no component that depends on time, which is truly amazing.  According to Albert Einstein’s Theory of Special Relativity, no object can travel as fast as the speed of light, so presumably the fastest way to send a signal — that is, to send information — is with a light beam.

In a sense, objects exchange information when they attract or repulse each other based on mass and any electrical charge.  The inverse square laws claim that this information travels instantaneously — at infinite speed!

Your muscles, bones, and organs operate beneath your skin to give the outside world the (correct) impression that you are a living human being — unless, of course, you are a zombie or an android!  In the same way, some connecting mechanism — a connection layer — seems to operate “beneath the skin” of the universe to support the instantaneous transmission of information reflected in the inverse square laws.

The inverse square laws predate the twentieth century, when a new branch of physics produced a new set of claims about the connectedness of all things.  Quantum mechanics gave new dimensions to the concept of a connection layer, as we will see later in this chapter.

The Connectedness of Matter and Energy

In the world of Isaac Newton, matter and energy cannot be converted into each other, but according to Einstein’s famous equation

E = mc2

where E is Energy, m is mass,[10] and c is the speed of light, matter and energy are two forms of the same thing — mass-energy — something more fundamental than either matter or energy.  (See page 208 for details.)

The Connectedness of Space and Time

In Isaac Newton’s worldview and in his equations, all things really are relative, but in Einstein’s world, all things except the speed of light are relative.  For example, according to Newton, if you can throw a stone at 50 miles an hour while standing on the ground, when you stand on the front of a train going 25 miles per hour you can throw a stone at 75 miles an hour — as measured by someone standing next to the train  track: 75 = 50 + 25.  However, if you shine a light beam travelling at speed c relative to the train, the observer on the ground does not measure the speed of the light beam as c + 25 — the observer on the ground measures speed c!

If the speed of light is the same for all observers travelling with constant velocity relative to each other, that means light is a fixed quantity, but space and time are relative quantities.  Newton’s universe consists of three space dimensions and one time dimension — space can never be exchanged for time or vice versa.  Einstein’s universe consists of four dimensions of a combined dimension called space-time — the relation of space to time in an event depends on the observer’s velocity relative to the event.

In the model of the universe given to us by Einstein’s Theory of Special Relativity, space and time are connected.  In this model, the universe consists of four dimensions of space-time.  It is no longer meaningful to speak or think of space and time as fundamentally different, independent, and  unconvertible.  (See page 209 for details.)

The Connectedness of Space and Matter

Einstein noticed that there seemed to be a connection between acceleration and gravitation.  His Theory of General Relativity explains gravity by showing how matter warps space itself.

In Special Relativity, space and time are connected.  In General Relativity, space and matter are connected.  (See page 210 for details.)

Connectedness in Unified Field Theory

Physicists are aware of four fundamental forces which act on matter: electromagnetism, the weak nuclear force, the strong nuclear force, and gravity.  At the time of writing, there are theories which combine the first three into a single force, while work continues to generate a model in which all four forces can be described by a single theory which shows that each force is a different manifestation of a single underlying principle.

Connectedness in Quantum Mechanics

Quantum mechanics is a theory or set of theories about the behavior of the universe at the scale of subatomic particles, where objects behave in ways which are quite different from ways in which macroscopic objects behave.  For example, if you know the starting point and ending point of a billiard ball after a strike, you know that there is some path on the billiard table which connects the two points and over which the ball has passed.  According to quantum mechanics, particles get from “here” to “there” without following a path.

In the macroscopic world, the action of simple systems like a game of billiards is predictable, that is, deterministic.  In contrast, the subatomic world is probabilistic.  We can never say with certainty where a given electron is located at a given time.  We can only state a probability that the electron is near a given location.

According to the theory, there is a nonzero probability — however small — that a given electron may be anywhere in the universe at a given time.  Have you seen dolphins swimming beside a  boat, going in and out of the water?  Subatomic particles appear to surf in and out of physicality, alternating between the observable world and a connecting layer.

To complete the picture, remember that subatomic particles form atoms, atoms form macroscopic objects, and you and everything else you can see is a macroscopic object, surfing in and out of physicality, alternating between the observable world and a connecting layer in which all points are linked.

Is this connecting layer God, or a manifestation of God?  Whatever you call it, both classical physics and quantum mechanics give us models of the universe in which all points are connected by an underlying nonphysical connecting layer.

Summary of Connectedness in Physics

To see a world in a grain of sand
and a heaven in a wild flower:
hold infinity in your hand,
and eternity in an hour.

William Blake, The Auguries of Innocence, circa 1808

Here is a summary of the kinds of connectedness ideas given above for classical, relativistic, and quantum physics:

1.    Electromagnetic forces connect all places.  Electromagnetic forces act at all distances, according to the inverse square law for electricity.

2.    Gravitational forces connect all places.  Gravitational forces act at all distances, according to the inverse square law for gravitation.

3.    Electromagnetic forces transcend time.  Electromagnetic forces act instantaneously at all distances.

4.    Gravitational forces transcend time.  Gravitational forces act instantaneously at all distances.

5.    Electromagnetism and gravitation attract in the same way.  The inverse square laws for electromagnetic and gravitational forces are identical in form.

6.    Matter and energy are aspects of mass-energy.  Matter and energy are different forms of mass-energy, which is more fundamental than either matter or energy.

7.    Space and time are aspects of space-time.  We live in a universe of four space-time dimensions.  Space and time are two different forms of space-time, which is more fundamental than either space or time.

8.    Space, time, mass, and energy are aspects of physical reality.  Space-time is not flat: it is warped by the presence of mass.  Space, time, mass, and energy are four different forms of something even more fundamental.

9.    Physical reality and nonphysical reality are aspects of reality.  Matter is made of subatomic particles which alternate between physical and non-physical existence.  There is a fundamental connection between the physical layer of manifestation and the nonphysical underlying connecting layer.  These layers are two forms of something even more fundamental.

According to physics, every part of our universe is connected to every other part, through electromagnetism, gravity, the quantum layer, and the very fabric of space-time.  Each part of our universe is also connected to a quantum universe which we cannot directly detect.  Mass, energy, space, time, and gravity seem to be different forms of something more fundamental still.  We can no longer define “nonphysical reality” to be “unreal”.

Connectedness in Chaos Theory

In the last section, I said:

In the macroscopic world, the action of simple systems like a game of billiards is predictable, that is, deterministic.

Before quantum mechanics and chaos theory, scientists believed that all action in the macroscopic world was deterministic: if you knew enough about the universe at any given time — the so-called initial conditions — you could predict what would happen from then on.  Now it appears that for a nontrivial system such as the Earth’s atmosphere, there can be a large change in the behavior of the system when there is a small change in the initial conditions.

Ill-conditioning and Determinism: The Quantum Barrier

In the jargon, a mathematical model is said to be ill-conditioned if small changes in the starting conditions lead to large changes in the final result.  For example, pretend you have the strength to draw a Welsh longbow — capable of sending an arrow 400 yards or nearly half a kilometer — and you are shooting an arrow at a target which is six feet away.  Even if your aim is rather wobbly, you can probably hit the bull’s eye every time.  If the target is 400 yards distant, the smallest wobble in your aim will cause you to miss the target altogether, and you will be lucky to hit the target even after shooting hundreds of arrows.

Chaos theory arose when scientists realized that nontrivial systems such as an ecosystem, the Earth’s atmosphere, or the solar system cannot be accurately modeled for any significant length of time, even with the knowledge of the initial conditions to many decimal places.  For example, knowing the initial conditions to five decimal places might enable us to know the state of the system in one hour to one decimal place.  Knowing the initial conditions to ten decimal places might enable us to know the state of the system in three hours to one decimal place.  Knowing the initial conditions to fifteen decimal places might enable us to know the state of the system in five hours to one decimal place.

Quantum mechanics tells us that we cannot — even in theory — measure the position and velocity of system components to a number of decimal places which takes us inside the atom.  In trying to make measurements to that level of accuracy, we encounter what we might call the quantum barrier.  Inside the atom, some of the common-sense properties of matter that we take for granted disappear.  In particular, the theory of quantum mechanics tells us that we cannot simultaneously measure the position and velocity of subatomic particles.  If that principle applied to macroscopic reality such as a car accident, we could say either (1) “the car hit the brick wall at 50 miles per hour, but we can’t say what direction it came from” or (2) “the car hit the wall travelling from south to north, but we can’t say how fast it was going!”.

The Quantum Barrier

For example, we might be able to determine through analysis that a given mathematical model can generate results accurate to one decimal place after H hours if we know the initial conditions to H decimal places.  But we might encounter the quantum barrier in trying to measure the initial conditions to, say, twenty decimal places.  In that case, our model could never work for more than twenty hours!

The ill-conditioning of nontrivial systems means that we encounter the quantum barrier when we try to use the model to predict system behavior for more than rather short amounts of time.  Let’s look at some favorite examples of chaos theorists.

Butterflies and the n-Body Problem

A favorite example in chaos theory is the claim that the way a butterfly beats its wings may determine whether a hurricane forms days later and hundreds of miles away.  If that’s more than you can believe, consider this question: to how many decimal places would we need to measure the initial conditions of the objects in the solar system to know if any objects bigger than a mile across were going to hit the Earth?

If two objects — isolated from other objects — are interacting according to the inverse square law of gravitational attraction given on page 207, the mathematics of their motion is not too complex.  This is called the two-body problem.  Systems with three masses isolated from other masses are three-body problems, and systems with n masses isolated from other masses are n-body problems.

The mathematics of the three-body problem are far more complicated than the mathematics of the two-body problem, and for n greater than 2, positions of objects in the n-body problem can only be computed approximately by computers.

There are two limitations on the accuracy of any simulation of the solar system.  First, the computations are done to only a certain number of decimal places, so eventually round-off error destroys the accuracy.  The longer the simulation runs, the less accurate it will be.

Second, the initial conditions are known only to a (small) number of decimal places.  This means that the simulation has limited fidelity from the very beginning, and this fidelity eventually disappears.

Current science can give us a few weeks warning of objects wider than a mile across which are heading towards the Earth.  Ideally, we would like hundreds or even thousands of years of advance warning, but this much advance warning is not available even in theory.

Consider a large comet which orbits the sun (in the plane of the Earth’s orbit) from beyond the orbit of Pluto to within the orbit of Earth.  It crosses Earth’s orbit millions and millions of times and let’s say it eventually hits the Earth.  Consider what a small variation in its previous orbit would have made it miss the Earth.  Consider that an even smaller variation ten orbits ago would have saved the Earth, an even smaller one than that a hundred orbits ago would have saved the Earth, and so on.

In our solar system, thousands of objects wider than a mile across interact with each other via gravity and change each other’s orbits.  Tiny variations in an object’s orbit today means the difference between impact and no impact in the future.

Chaos theory suggests not merely that the components of the universe are connected to each other, but that the influence of each component on the others may be far greater than one would imagine!

Connectedness in Biology

Let’s look at two examples of connectedness from biology: germ propagation and ecosystems.

Global Germ Propagation

In the modern world, there is a constant flow of people and materials between different parts of the planet.  Trans-oceanic shipping takes at most a few weeks and air travel takes at most a few hours.

The consequence of this rapid and constant flow is that a communicable disease which develops in one part of the world can quickly spread across the world, jumping from continent to continent, from city to town to farm.  Many diseases are host-specific, which means that a disease which requires a non-human host cannot infect humans.  Many other known diseases can infect humans as well as other species.

As humans cut down the remaining rain forests — which contain literally millions of unknown species — men, women, and children will come in contact with a vast number of possibly dangerous microorganisms.  Any of those microorganisms which can infect humans will infect humans.

If the diseases caused by those microorganisms are contagious, they will spread outward from the sites of their origins.  If the diseases are highly contagious, they will spread rapidly to parts of the world where living humans and their ancestors have never been exposed to the diseases, as happened with bubonic plague in the 1300s.

If the diseases are not only highly contagious but also deadly to humans, many people will die before they have any chance to develop natural immunity.  If the diseases strike rapidly, there will not be enough time for scientists to develop vaccines and inoculate whole populations.  It is thought that at least one in three Europeans died from bubonic plague in the fourteenth century.

It the interconnected world of today, one or more diseases exploding out of the tropics could kill at least one in three humans worldwide.  It is easy to imagine that you as a healthy person living in a wealthy country have virtually nothing in common with a poor woodcutter laboring in the forests of Malaysia or Madagascar, but a deadly new virus that kills him today could kill you tomorrow.

The Connectedness of Ecosystems

Not so long ago, ecology was a word known only to biologists, but today everyone knows the ecology is the study of ecosystems, which are systems where plants and animals use the resources of an area of land or water to propagate themselves.  The concept of connectedness is inherent in the concept of a system, which is a set of components in which each component is considered to have an influence on each other component.  In the twentieth century, humans learned over and over that altering one part of an ecosystem is liable to affect all other parts of the ecosystem in ways that are complex, pervasive, and persistent.

Alterations of components affect the entire ecosystem because the components of the ecosystem are connected to each other.  The worlds of classical physics, quantum mecha