Quantum Theoretic Machines (eBook)
600 Seiten
Elsevier Science (Verlag)
978-0-08-054013-9 (ISBN)
'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest challenge is to answer the fundamental question: what precisely does a cognitive state amount to in physical terms?
Albert Einstein insisted that the fundamental ideas of science are essentially simple and can be expressed in a language comprehensible to everyone. When one thinks about the complexities which present themselves in modern physics and even more so in the physics of life, one may wonder whether Einstein really meant what he said. Are we to consider the fundamental problem of the mind, whose understanding seems to lie outside the limits of the mind, to be essentially simple too? Knowledge is neither automatic nor universally deductive. Great new ideas are typically counterintuitive and outrageous, and connecting them by simple logical steps to existing knowledge is often a hard undertaking. The notion of a tensor was needed to provide the general theory of relativity, the notion of entropy had to be developed before we could get full insight into the laws of thermodynamics, the notice of information bit is crucial for communication theory, just as the concept of a Turing machine is instrumental in the deep understanding of a computer. To understand something, consciousness must reach an adequate intellectual level, even more so in order to understand itself. Reality is full of unending mysteries, the true explanation of which requires very technical knowledge, often involving notions not given directly to intuition. Even though the entire content and the results of this study are contained in the eight pages of the mathematical abstract, it would be unrealistic and impractical to suggest that anyone can gain full insight into the theory that presented here after just reading abstract.
In our quest for knowledge we are exploring the remotest areas of the macrocosm and probing the invisible particles of the microcosm, from tiny neutrinos and strange quarks to black holes and the Big Bang. But the greatest mystery is very close to home: the greatest mystery is human consciousness. The question before us is whether the logical brain has evolved to a conceptual level where it is able to understand itself.
Making Sense of Inner Sense 'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest challenge is to answer the fundamental question: what precisely does a cognitive state amount to in physical terms? Albert Einstein insisted that the fundamental ideas of science are essentially simple and can be expressed in a language comprehensible to everyone. When one thinks about the complexities which present themselves in modern physics and even more so in the physics of life, one may wonder whether Einstein really meant what he said. Are we to consider the fundamental problem of the mind, whose understanding seems to lie outside the limits of the mind, to be essentially simple too? Knowledge is neither automatic nor universally deductive. Great new ideas are typically counterintuitive and outrageous, and connecting them by simple logical steps to existing knowledge is often a hard undertaking. The notion of a tensor was needed to provide the general theory of relativity; the notion of entropy had to be developed before we could get full insight into the laws of thermodynamics; the notice of information bit is crucial for communication theory, just as the concept of a Turing machine is instrumental in the deep understanding of a computer. To understand something, consciousness must reach an adequate intellectual level, even more so in order to understand itself. Reality is full of unending mysteries, the true explanation of which requires very technical knowledge, often involving notions not given directly to intuition. Even though the entire content and the results of this study are contained in the eight pages of the mathematical abstract, it would be unrealistic and impractical to suggest that anyone can gain full insight into the theory that presented here after just reading abstract. In our quest for knowledge we are exploring the remotest areas of the macrocosm and probing the invisible particles of the microcosm, from tiny neutrinos and strange quarks to black holes and the Big Bang. But the greatest mystery is very close to home: the greatest mystery is human consciousness. The question before us is whether the logical brain has evolved to a conceptual level where it is able to understand itself.
Front Cover 1
Quantum Theoretic Machines: What is Thought from the Point of View of Physics 4
Copyright Page 5
CONTENTS 8
NOTATIONS 14
MATHEMATICAL ABSTRACT 20
PART 1: MATRIX PRINCIPLE 22
CHAPTER 1. MINDWARE 24
Making sense of inner sense 24
The intelligence code 28
The evolution of the machine 31
The brain's unknown statistics 38
Thought as matrix multiplication 40
Heisenberg's matrix mechanics 44
Conversion theorem 45
Matrix statistics 50
Supersymmetry 52
CHAPTER 2. INFORMATION IS PHYSICAL, PHYSICS IS LOGICAL 54
Duality principle 54
Projective logic 57
The dimensions of the mind and the third quantization 64
Closing pandora's quantum box 69
Cognizing is quantizing 71
Quantum computer 73
Reality as a complex number 76
Nonconvex probability 80
Logical quantum numbers 83
Does the mental violate the laws of physics? 87
PART 2: THE BRAIN IS GEOMETRICAL, THE MIND IS TOPOLOGICAL 96
CHAPTER 3. TOPOLOGICAL CHARGES 98
Logical vacuum 104
Multiplicative polarization 107
Additive polarization and the fundamental lattice 109
Thoughts, knots and cross-cups 112
CHAPTER 4. COGNITIVE CIRCUITS 120
Topological current 122
CHAPTER 5. THE LOGICAL DERIVATIVE 124
CUT and ZIP operations 126
The quantum-mechanical derivative 129
The covariant derivative 130
The unbroken topological phase 132
CHAPTER 6. RECASTING LOGIC IN DIRAC NOTATION 134
Translating logic into quantum mechanics 134
CHAPTER 7. PARALLEL AND SERIAL UNIVERSES 138
Factorizing the thought processes 138
Parallel brain, serial mind 140
The suprasymmetric transfer function 142
Operator waves 144
Logical wave operators 145
The exotic statistics 148
CHAPTER 8. MATRIX BRANES 150
Brains and branes 150
Logical volume 151
Irreducible logical branes 152
Consciousness as a unilateral logical membrane 156
CHAPTER 9. THE CAT AND THE LIAR 158
The intellectual catastrophes 158
This is absolutely true±false 164
Quantum mathematics 165
CHAPTER 10. LOGICAL ROTORS 168
Topological phase and atomic orbits 168
Self-measurement and backreaction 171
CHAPTER 11. QUANTUM KNOTS 173
Template supersymmetrization 176
Information solitons 178
CHAPTER 12. LOGICAL MEMBRANE ACTION 180
CHAPTER 13. FROM BLACK HOLES TO GRAY BRAINS 184
Logical Bang Blowing up the Farey Sequence 186
The theory of Everything 187
Information collapse 189
CHAPTER 14. THE INCREDIBLE KNOT OF CONSCIOUSNESS 194
Introducing gauge symmetry into logic 194
Beyond seven crossings 205
PART 3: THOUGHT TELLS THE BRAIN HOW TO SPIN, SPIN TELLS THE BRAIN HOW TO THINK 208
CHAPTER 15. NUMBERS AND OPERATORS 210
Quantum thinking 210
The quantization theorem 216
Speeding thought up 219
Self-"conscious" polynomials 221
CHAPTER 16. LIMITATIONS OF CLASSICAL LOGIC 222
Truth-tables 225
Dealing with absurds 226
Negation 227
An unnoticed operation in Boolean logic 228
Logic interpolates, mind extrapolates 231
Timeless logic 232
CHAPTER 17. SELF AS A FIXED-POINT 233
Solving the problem of being itself 233
The golden ratio 234
Logarithmic fixed point 236
Second-quantized fixed points 237
Logical radar coordinates as fixed point 238
CHAPTER 18. IMPROBABILITIES 239
Probability of impossible and impossible probabilities 239
Probability calculated and probability measured 242
Tensor probability 247
Improbable dispersions 249
Imaginary certainties 251
Negative probability and vacuum 256
Charged sets 257
CHAPTER 19. THINKING SYSTEMS 259
Non-Hermitian reality. From quantum physics to infophysics 259
Effective acausality 261
Fundamental information 262
Cognitive observables 264
Why a tiny 2x2 matrix? 266
The unruly algebra of matrices 267
Truth-value as eigenvalue 272
Truth-value and false-value 275
CHAPTER 20. SQUARE ROOT OF NOTHING 278
The logical vacuum revisited 278
Momentum as tensor product 280
Logical momentum as quantum knot 282
Zero-weight operators 284
PART 4: COGNIZERS 286
CHAPTER 21. STRETCHING NATURE'S LAWS 288
Classical-quantum interface 289
Quantum hypothesis of the brain 291
Singularization theorem 295
The brain-mind interface as a quantum-classical interface 300
CHAPTER 22. COGNITIVE DELTA 302
The delta theorem 309
Lowering the energy barrier: the tunneling of logical operators 310
CHAPTER 23. ENERGY FUNCTION 314
The momentum theorem 320
Logical momentum and the klein-gordon equation 323
Logical isospin 324
Truth-dependent Lagrangian 326
The missing energy level 327
CHAPTER 24. BRAIN STATES ARE NONCLASSICAL 330
Denktors 333
Understanding the information phase 337
Quantization of the classical systems 344
The s-matrix and the synaptic matrix 350
The brain's sparse matrix 352
CHAPTER 25. BETHE'S DOUBLE GROUP AND CONSCIOUSNESS 354
CHAPTER 26. LOGICAL OSCILLATOR 361
CHAPTER 27. TIME AS CONSCIOUSNESS' DYNAMICAL VARIABLE 366
Still time 370
The time wraps 370
Is there time to see? stroboscopic consciousness 373
CHAPTER 28. CONVERTING THOUGHT INTO ACTION 374
Conservation of time charges 378
Making use of forbidden interactions 379
CHAPTER 29. ENERGY-TIME PHASE SPACE 380
CHAPTER 30. 5-VALUED CONSCIOUSNESS 382
The included middles 382
A forbidden fivefold symmetry 384
Pseudo-Galilean space and the 5-space correction to energy 386
Constructing causal systems from acausal components 388
Thought and Lorentz transformation 390
CHAPTER 31. RELATIVISTIC BRAIN 391
The self's attempt about self 391
Violating pauli exclusion 394
Fundamental supercommutator 395
True and false times. crossing the NOT barrier 399
CHAPTER 32. THE ASYMMETRIC MIND 400
Thought is processed forwards but understood backwards 400
Reversing the irreversible 403
Recovering lost data 404
Left!=right 406
PART 5: HOW MANY LOGICAL THEORIES? 408
CHAPTER 33. SEARCH FOR UNIVERSAL LOGIC 410
Intuition versus intuition 410
Truth series 413
Five fundamental logics 414
Boolean logic 416
Multivalued logic 418
Tense logic 419
Quantum logic 420
Fuzzy logic 422
CHAPTER 34. M(ATRIX) LOGIC 425
Tensorization of truth-values 425
From truth-tables to operators 426
Logical connectives interact 430
Logic without connectives 433
Quantum strings 436
Quantum basis sets 440
Logical superposition principle 442
Unitary inferences 446
Induction. Vacuum terms 451
If-then-else 451
Logic with division. solving logical ratios 452
Differential formal systems 455
CHAPTER 35. VIRTUAL LOGIC 460
Understanding septons 463
CHAPTER 36. MIND'S DYNAMICAL EQUATIONS 467
Canonical equations of motion 472
Supercommutation theorem 475
Satellite equations 477
Suprasymmetry 479
The integral equation of motion 481
The commutation equation of motion 482
Relation to the Heisenberg equation 486
Cognitive constants of motion 488
Spectral theorem 491
CHAPTER 37. LOGICAL POLYMERS 494
Phase transition 495
CHAPTER 38. COGNITIVE DIAGRAMS 500
Connecting logic to the vacuum 500
Matrix nets and the self-solving brain 502
Renormalization 503
Open ended diagrams and vacuum traps 505
CHAPTER 39. QUANTUM-LOGICAL COMPUTER 508
Superbits 509
The computer as a quantum particle 512
Quantum Turing Machine 519
Atomic registers 521
Differential quantum algorithms 526
Quantum engineering: Spintronics 528
Dialing quantum numbers 533
Quantum codes 536
Self-correcting codes 540
Codewords and inwords 541
Quantum codes and the intelligence code 550
CHAPTER 40. EVERYTHING IS LOGIC 558
Quark logic 558
Double parity check 562
Unitarization of implication and supercommutators 566
Matrix base 568
Transmultiplication 575
Basis sets 577
Logical mesons 578
Monologic 581
Consciousness as the macroanalogue of quarks 582
CHAPTER 41. POSTSCRIPT 587
APPENDIX 588
24+2 roots of IS 588
40 factorizations of NOT 589
136 commutators of NOT 590
40 anticommutators of NOT 591
180 commutators of NOT diag 592
REFERENCES 594
GLOSSARY 600
| Erscheint lt. Verlag | 8.12.2000 |
|---|---|
| Sprache | englisch |
| Themenwelt | Geisteswissenschaften ► Psychologie ► Allgemeine Psychologie |
| Geisteswissenschaften ► Psychologie ► Verhaltenstherapie | |
| Mathematik / Informatik ► Informatik ► Theorie / Studium | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Naturwissenschaften ► Biologie ► Humanbiologie | |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| ISBN-10 | 0-08-054013-9 / 0080540139 |
| ISBN-13 | 978-0-08-054013-9 / 9780080540139 |
| Haben Sie eine Frage zum Produkt? |
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