Nanobrain

Anirban Bandyopadhyay is Senior Scientist in the Advanced Key Technologies Division at the National Institute for Materials Science (NIMS) in Ibaraki, Japan. He earned his PhD in supramolecular electronics, physics, and materials science in 2005. He was subsequently a research fellow at NIMS’ International Center for Young Scientists as well as a permanent faculty member at NIMS. Dr. Bandyopadhyay was a visiting scientist at the Massachusetts Institute of Techno logy in 2013–2014 and has been recognized with multiple awards, e.g. Hitachi Science & Technology Award 2011, Inamori Foundation Award 2011, etc. In 2016, Dr. Bandyopadhyay established the International Institute of Invincible Rhythms (iioir.org) in Shimla, India.

Contents

Preface ........................................................................................................................................................................................xiii

Author ......................................................................................................................................................................................... xv

Summary of the Chapters ..........................................................................................................................................................xvii

Chapter 1 Philosophical Transformation Essential to Reverse Engineer Consciousness ........................................................ 1

1.1 How Do We Differ from the Existing Worldview? ....................................................................................... 1

1.2 Ten Research Fields That We Cover Here .................................................................................................... 4

1.3 The Universe within and above not Side by Side ......................................................................................... 7

1.3.1 What a Turing-Based Worldview Does Not Consider .................................................................... 9

1.4 Basic Questions to Answer: Ten Popular Human Brain Models .................................................................. 9

1.4.1 What Does the Information Look Like in Nature ......................................................................... 12

1.4.2 Why Two Individuals Understand Each Other or the Universe .................................................... 14

1.5 Different Kinds of Tapes to Recreate Nature in Different Languages ........................................................ 15

1.6 Brain-Inspired Decision-Making—The Outline of Key Discoveries ......................................................... 16

1.7 Energy Transmission in the Brain—It’s Not All about Neuron Skin ......................................................... 16

1.8 Terminologies of Life That Computers Do Not Support ............................................................................ 18

1.9 Linguistics and the Wheel of Space, Time, and Imaginary Worlds ............................................................ 19

1.10 Three Concepts Define Artificial Brain ...................................................................................................... 20

1.10.1 A Language of Time Crystals Written by the Symmetry of Primes ............................................. 22

1.10.2 A Magnetic Light: Creating a Device That Stores Charge and Builds a Time Crystal ................ 23

1.10.3 A Pattern of All Possible Choices to Arrange Primes ................................................................... 23

1.11 Conclusion: The Religion of Science Has a Triangle, Darwin, Turing, and Hodgkin-Huxley .................. 24

Chapter 2 Replacing Turing Tape with a Fractal Tape: Fractal Information Theory (FIT) and Geometric Musical

Language (GML) ................................................................................................................................................... 25

2.1 Incompleteness of Current Information Theory ......................................................................................... 25

2.1.1 Fractal Tape and Surgery of a 2D Image to Place It in a Nested Sphere ...................................... 28

2.1.2 Self-Assembly of Geometric Shapes and the Concept of Singularity .......................................... 30

2.2 The Basics of a Geometric Musical Language ........................................................................................... 32

2.2.1 How a 3D Structure Becomes a Time Crystal or a Tensor: Non-differentiability ........................ 36

2.2.2 Fifteen Geometric Shapes Are Enough to Recreate Any 1D, 2D, or 3D Pattern ......................... 36

2.2.3 How to Convert Waveforms into a Time Crystal: Non-differentiability ....................................... 39

2.3 The Basic Concept of a Time Crystal and the Garden of Gardens (GOG) ................................................ 40

2.4 How to Design a Sensor for Acquiring 11D Data ...................................................................................... 40

2.4.1 Why Fourier Transform Does Not Work ...................................................................................... 41

2.4.2 The Engineering of a Nerve Bundle in Acquiring Hidden Data ................................................... 41

2.4.3 Operational Chart of a Sensor ....................................................................................................... 42

2.5 Comparative Studies between Winfree, Wilczek, and the Universal Time Crystal ................................... 42

2.6 The Definition of a Quaternion, Octonion, and Dodecanion ...................................................................... 43

2.7 The Basic Concept of a Higher-Dimension Data: A Lucid Presentation ................................................... 44

2.8 A Comparison between GML and Software Algorithm ............................................................................. 45

2.8.1 Historical Background on Hypercomputing and Super-Turing Hypothesis ................................. 46

2.9 Creation of a Non-Argument ...................................................................................................................... 47

2.10 FIT Summary in a Single Chart .................................................................................................................. 50

2.11 GML Summary in a Single Chart ............................................................................................................... 53

2.12 Conclusion: Russel’s Paradox and Higher-Order Logic in a Geometric Language ................................... 54

Chapter 3 Phase Prime Metric (PPM) Links All Symmetries in Our Universe and Governs Nature’s Intelligence ............. 55

3.1 Ten Classes of Phase Prime Metric (PPM)—a Pattern of Primes .............................................................. 55

3.1.1 15 Primes Contribute to 99.99% of All Integers in the Universe .................................................. 58

3.1.2 Ordered Factor Metric and Its 3D Version .................................................................................... 59

3.1.3 How Is a Time Crystal Decomposed and Amplified Using PPM ................................................ 61

3.2 Metric 1: An Integer Is Replaced by a Typical Geometric Shape .............................................................. 62

3.3 Metric 2: Product of Primes Forming Integers Led to a Unique Ordered Factor Metric ........................... 63

3.4 Metric 3: Integers Limited to 360° Phase Build Clockwise and Anticlockwise Paths ............................... 65

3.5 Metric 4: A Domain of Integers Sets a Limit on the Usable 15 Primes ..................................................... 66

3.6 Metric 5: When Ordered Factor Is Much Greater Than the Integer ........................................................... 67

3.7 Metric 6: Empty Space in the Plot of Ordering of Divisors in Phase Plot Presents Holes ......................... 68

3.8 Metric 7: Statistical Dominance of Primes in the Integer Space—Silent and Active Primes .................... 68

3.9 Metric 8: Normalized Ripples on the Metric Plot Shows Periodicity in Events ........................................ 70

3.10 Metric 9: Lattice Group of Primes (Twin Primes, Cousin Primes, Co-primes, and Gaussian Primes) ...... 71

3.11 Metric 10: Multilayer Imaginary Operation on the Real Integers Builds a New Pattern ........................... 72

3.12 Ten Prime Operators to be Applied Step-by-Step ....................................................................................... 73

3.13 Hidden Physical Significance of 15 Primes When PPM Evolves a Time Crystal ..................................... 74

3.14 How to Use PPM ........................................................................................................................................ 75

3.15 Solution of a Big Data Problem on Diabetes—PPM in an Artificial Brain ............................................... 77

3.16 Three Classes of Primes ............................................................................................................................. 81

3.16.1 Ordered Factor Metric (OF), Prime Composition Metric (PC), and Prime Gap Metric (PG) ..... 81

3.16.2 Advantages of PPM ...................................................................................................................... 82

Chapter 4 Fractal Mechanics Is Not Quantum but Original—Geometric Algebra for a Dodecanion Brain ......................... 85

4.1 Revisiting the Basic Concepts of Quantum Mechanics Using Clocks ....................................................... 85

4.1.1 Wave–Particle Duality, Beating, Interference, Entanglement, and Harmonic Oscillator ............ 88

4.1.2 Multiple Imaginary Worlds Operating at a Time Need Fractal Mechanics .................................. 88

4.2 Fractal Mechanics Acts in the Phase Space Connecting Singularity Points .............................................. 89

4.2.1 Multilevel Geometric Architecture of the Hilbert Space .............................................................. 91

4.2.2 Fractal Harmonic Oscillator, Fractal Condensation, and Peculiarities ......................................... 95

4.2.3 Harvesting Noise by Harvesting Singularity—PPM Replaces Statistical Mechanics ................. 96

4.2.4 What Is Energy in the Many Interacting Imaginary Worlds? ....................................................... 98

4.3 A Comparison between Classical, Quantum, and Fractal Mechanics—Scale Symmetry

and Scale Relativity .................................................................................................................................. 100

4.4 Action Is Not Limited to Planks Constant—Every Imaginary World Has One ...................................... 102

4.5 A Table of Fundamental Constants in Nature .......................................................................................... 104

4.6 Quantum Interference- and Fractal Interference-Experiment on a Single Microtubule .......................... 105

4.7 Fractal Absorption–Emission of the Optical Band of a Nanobrain .......................................................... 106

4.8 Basic Mathematics Using Clocks ............................................................................................................. 108

4.8.1 Numbers, Equations, Addition, Subtraction, Multiplication, and Division ................................ 109

4.8.2 Differentiation, Integration, and Partial Differential Equations—Lie Algebra .......................... 110

4.8.3 CFGA Operator That Runs 13 Math Operations in a Time Crystal Structure ............................ 111

4.9 The Fundamentals of Quaternion, Octonion, and Dodecanion ................................................................ 111

4.9.1 The Rule of 11D Manifolds ........................................................................................................ 112

4.10 Twelve Equations That Regulate a Fractal Tape for Prime-Based Computing ........................................ 113

4.10.1 Projection from Infinity—Future Impacting the Present ........................................................... 113

4.11 Different Kinds of Spirals in Nature ......................................................................................................... 114

4.12 A Marriage between Fractal Mechanics and Geometric Algebra............................................................. 116

Chapter 5 Big Data in the Garden of Gardens (GOG)—Universal Time Crystal ................................................................ 117

5.1 Gödel’s Incompleteness Theorem and the Fractal Tape .......................................................................... 117

5.1.1 A Marriage between Frequency Fractal Hardware and the Time Crystal .................................. 120

5.1.2 PPM Allows Two Systems to Sync without Communication ..................................................... 121

5.2 The Origin of Fractal Resolution and Instant Reply ................................................................................ 121

5.2.1 Spontaneous Reply—Search without Searching .......................................................................... 121

5.2.2 Automated Error Correction through Time Crystal Learning ..................................................... 122

5.2.3 Synchronization of Time Crystals and Incomplete Problems ...................................................... 122

5.2.4 Umbrella of Perception—Harvesting Infinity and Projecting from Infinity ................................ 123

5.3 Replacing Fourier Transform by Time Crystal Transform ....................................................................... 125

5.3.1 Image Processing and Sound Analysis Using a Time Crystal...................................................... 125

5.4 Ten Situations When the Turing Machine Fails but Fractal Machines Hold On ..................................... 126

5.5 The Hardware Architecture of an Artificial Brain .................................................................................... 128

5.6 Thermal Breathing by Microtubule and Artificial Brain .......................................................................... 129

5.7 Lotus in the Primes—Revisiting Thermodynamics of Geometry ........................................................... 131

5.8 How Geometric Similarity Builds Creativity in Computing Primes ........................................................ 136

5.9 The Wheel of Intelligence—Difference from Humans ............................................................................ 137

5.10 Could Prime-Based Computing Predict the Future without Prior Knowledge? ...................................... 139

5.11 How Prime-Based Artificial Brain Shrinks Big Data? ............................................................................ 139

5.12 The Limitations and Incredible Features of Prime-Based Computing ..................................................... 142

Chapter 6 Unprecedented Technologies found in Nature Led by Harvesting the Geometry of Singularity ....................... 145

6.1 PPM—The Pattern of Primes Embedded in the Tubulin Protein ............................................................ 145

6.1.1 α-Helices Form Groups of Rings to Complete a Loop ................................................................. 146

6.1.2 Hyperspace Symmetries Follow a Mathematical Identity ............................................................ 148

6.1.3 Ordered Factor of Integers and Coding in Proteins ...................................................................... 149

6.1.4 Biomaterials in and the Remarkable Engineering of Water Channels ......................................... 149

6.2 Experiment on a Single Microtubule or Any Generic System to Find Its Time Crystal .......................... 150

6.2.1 How Do We Experimentally Confirm That an Assembly of the Clocks Is a Time Crystal? ........ 150

6.2.2 Triplet of Triplet Resonance Band in Microtubule ....................................................................... 153

6.2.3 The Biological Relevance of the Time Crystal ............................................................................. 155

6.2.3.1 Exponential Speedup of Time Crystal Transfer via Synchrony—Quantum

Entanglement Is Not the Only Route ............................................................................ 158

6.2.3.2 Tubulin’s Nested Resonance and Synchrony ................................................................ 159

6.3 Single Molecule’s Thermal Diffusion Emerges into a Natural Clock ...................................................... 160

6.4 Brain’s fMRI Images Created on a Molecular Surface ............................................................................ 161

6.5 Massively Parallel Computing by Cellular Automaton ............................................................................ 162

6.6 One-to-Many and Many-to-One Orbital Computing in a Nanowheel ..................................................... 164

6.7 Hidden Communication in the Filaments Well before a Nerve Spike ...................................................... 165

6.7.1 Triplet of Triplet Resonance Band in the Axon of a Neuron ........................................................ 170

6.7.2 Scale-Free Triplet of Triplet Band in Tubulin, Microtubule, and Neuron .................................... 170

6.8 The Measurement of a Complete Time Crystal Map of a Neuron ........................................................... 173

Chapter 7 A Complete, Integrated Time Crystal Model of a Human Brain ........................................................................ 177

7.1 Brain Is the Engineering of Prime Numbers Embedded in a Triplet of Triplet Cage .............................. 177

7.1.1 Four, Eight, and Twelve Imaginary Worlds Work Together ......................................................... 181

7.1.2 Singularity on a Sphere—The Key to a Clock of a Time Crystal ................................................ 183

7.2 Primes in the Five Sensory Systems ......................................................................................................... 183

7.3 Primes in the Cerebellum, Hippocampus, and Hypothalamus ................................................................. 186

7.4 Primes in the Connectome, Spinal Cord, Amygdala, Nucleus, and Cortical Column ............................. 191

7.5 Primes in the Neuron, Glia, Dendro-Dendritic, Astrocytes, Microtubule, and Proteins DNA ................ 192

7.6 Twelve Ways of Memorizing and Twelve Carriers Operating Rhythms/Clocks ..................................... 195

7.7 The Brain’s Wheel of Primes ................................................................................................................... 197

7.7.1 Eight Sensors Hold Crossover Magic of Octonion ...................................................................... 199

7.7.2 Eight Mathematical Operators Run Two Orthogonal Math Engines ............................................ 200

7.8 The Basic Device for Decision-Making in the Brain ............................................................................... 201

7.8.1 H3 Device That the Brain Uses Everywhere ................................................................................ 203

7.9 Fusion of Cavity and Dielectric Resonator Model of a Human Brain ..................................................... 203

7.10 Time Crystal Model of the Human Brain ................................................................................................. 207

7.11 Four Metrics of Primes Run in Parallel—The Saga of Hexagonal Lattice .............................................. 208

7.11.1 Composition of Four, Eight, and Twelve Dimension Tensors .................................................... 209

7.11.2 Quaternion, Octonion, and Dodecanion ..................................................................................... 210

7.12 Time Crystal Made Meander Flower to a Garden of Gardens ................................................................. 210

7.12.1 Twelve Dodecanion and Eight Octonions Build 20 Conscious Human Expressions ................. 210

Chapter 8 Hinductor Not Memristor—Synthesis of Atoms and Crystals Made of Magnetic Light .................................... 219

8.1 It Is Resistance for Vortex Atoms but Not for Electrons .......................................................................... 219

8.1.1 Quantum Non-Demolition: e − π − □□ Quadratic Sensors .......................................................... 223

8.1.2 Rapidly Oscillating Cell Membrane Holding a Long Wave ....................................................... 224

8.1.3 Paraxial Systems ......................................................................................................................... 224

8.1.4 Anisotropy and Avoided Crossing .............................................................................................. 225

8.2 Fundamental Structural Parameters of a Fourth-Circuit Element—Hinductor ........................................ 226

8.2.1 Periodically Oscillating Edge and Screw Dislocations ............................................................... 227

8.2.2 Topology Regulating the Polarization ........................................................................................ 228

8.3 The Hamiltonian or Energy of Four Clocks Creating Magnetic Light .................................................... 229

8.3.1 Birefringence, Quantum Beating and Classical Beating ............................................................ 230

8.3.2 Pancharatnam Berry Phase ......................................................................................................... 231

8.3.3 Pyroelectric, Ferroelectric, and Piezoelectric Properties ............................................................ 232

8.4 Linear Variation of Magnetic Flux and Stored Charge in H ..................................................................... 232

8.4.1 Flow of Thermal Wave—Friend or Foe? .................................................................................... 233

8.4.2 Wireless Communication between Two H Devices .................................................................... 234

8.4.3 Tomasch Oscillations and Harvesting Noise .............................................................................. 236

8.5 Periodic Oscillation of Capacitance, Inductance, and Hinductance with Its Geometry .......................... 236

8.5.1 The Concept of Phase Space with 12 Holes That Blink ............................................................. 237

8.5.2 Periodic Oscillations with Length, Pitch, Lattice Area/Diameter—Theory and Experiment .... 238

8.5.3 Knots of Darkness on the H Interface ......................................................................................... 241

8.6 Three Interactive Cylinders Perturbing the Knots ................................................................................... 242

8.6.1 Knots of Dark Lines Act Like a Spin of a Particle ..................................................................... 243

8.6.2 Synthesis of Super-Super Coil Made of Dark Lines ................................................................... 244

8.6.3 Morphogenesis of Knots in Vortex-Like Magnetic Atoms ........................................................ 245

8.7 Magnetic Knots’ Driven Self-Assembly ................................................................................................... 246

8.8 Design Application and Operation of H—The Novelty of H ................................................................... 247

8.9 Transition from the Old Era of Electronics to Modern Magnonics .......................................................... 250

Chapter 9 Brain Jelly to Humanoid Avatar—Fractal Reaction Kinetics, Fractal Condensation, and Programmable

Matter for Primes................................................................................................................................................. 253

9.1 Neuromorphic Devices Are Not Alone—17 Biomorphic Devices Sing Together.................................... 253

9.1.1 A Description of Peculiar Designs of Critical Brain Components Using an Organic Gel ......... 257

9.2 A Hexagonal 2D Sheet of Cortical Columns—A Carpenter’s Job........................................................... 259

9.2.1 The Collective Response of Quad Patterns of Primes ................................................................ 260

9.2.2 Electric, Magnetic, and Mechanical Rhythms Bind Them ........................................................ 261

9.3 Anomalous Quantum Cloaking—Vanishing and Seeing the One We Want to ........................................ 262

9.3.1 Randomness Is Not Random Anymore ....................................................................................... 264

9.4 A Living Gel That Listens and Then Grows from Atomic Size to Centimeters Long ............................. 264

9.5 Fractal Condensation—Condensing Everywhere at Once ....................................................................... 267

9.5.1 Pattern of Primes Need Not to Be Instructed ............................................................................. 271

9.6 Fractal Reaction Kinetics—Parallel Syntheses in One Beaker at a Time ............................................... 271

9.7 Nanobrain, the Smallest Life Form .......................................................................................................... 272

9.7.1 Jelly of Megamers Following a Resonance Chain ...................................................................... 273

9.7.2 EEG of a Nanobrain .................................................................................................................... 276

9.8 Tuning Undefined Holes to Sense Magnetic Light ................................................................................... 277

9.8.1 Spiral Nanowire Writes Time Crystal—Sense It as a Crystal of Light ...................................... 278

9.8.2 Writing Prime Numbers in a Jelly .............................................................................................. 279

9.9 Entropy Drives the Synthesis of a Pattern of Primes .............................................................................. 280

9.9.1 Hesse Diagram for Entropy Builds Material Analog of Integers ............................................. 280

9.10 The Cortical Pen That Freezes Unknown Dynamics into a Time Crystal .............................................. 282

9.10.1 Capsules of Brain Jelly—One Each for One Big Problem ....................................................... 282

9.11 A Sensor That Searches for Given Keys, Do Not Sense Any Input ....................................................... 284

9.11.1 Eleven Dimensional Signals in the Human Brain and in Brain Jelly ....................................... 286

9.11.2 Humanoid Avatar—An Ultimate Sensor .................................................................................. 286

9.12 Sensor Triad, Sensor Jelly, Muscle Jelly, and Brain Jelly ...................................................................... 287

9.12.1 A Total Transformation from the Biological Neural Net to a Jelly of Time Crystals .............. 288

Chapter 10 Uploading Consciousness—The Evolution of Conscious Machines of the Future ............................................ 291

10.1 A Journey from Cortical Pen to a Conscious Egg as a Companion of Life ........................................... 291

10.1.1 How We Construct a Sentence Is How We Think .................................................................... 293

10.2 Ten Key Guidelines to Reverse Engineer a Human Brain ...................................................................... 294

10.3 Twelve Paradoxes That Would Change Our Thoughts Forever .............................................................. 296

10.4 Consciousness Is Not on the Neuron Skin—Time Crystal Model Is Nowhere but Everywhere ........... 301

10.4.1 The Difference between a Neurogenic Brain Model and a Time Crystal Model ..................... 301

10.5 When We Carry It and Why We Make It ............................................................................................... 302

10.6 How to Cut 11D Manifolds of Time in a Piece of Paper ........................................................................ 304

10.7 The Marriage of Primes with Geometry Would Reshape Humanity ...................................................... 304

10.8 Machines of the Future ........................................................................................................................... 305

10.8.1 The Difference between Circuits of Wand Circuits of Time .................................................... 305

10.8.2 Future Applications .................................................................................................................. 306

10.9 Playing with Cheap, Handy Tools to Break the Paradigm of Thought ...................................................... 309

10.10 Numerology of Human Consciousness .................................................................................................. 309

10.11 Frequency Wheels of an Evolving Brain ................................................................................................ 311

10.12 Synthesis of Critical Brain Features Even before We Meet the Aliens .................................................. 312

10.13 A Cycle of a Garden from Flower to a Petal .......................................................................................... 314

Bibliography ............................................................................................................................................................................ 315

Index ......................................................................................................................................................................................... 347