Quantum Theoretic Machines. What Is Thought from the Point of View of Physics

Quantum Theoretic Machines: What is Thought from the Point of View of Physics......Page 4
Copyright Page......Page 5
CONTENTS......Page 8
NOTATIONS......Page 14
MATHEMATICAL ABSTRACT......Page 20
PART 1: MATRIX PRINCIPLE......Page 22
Making sense of inner sense......Page 24
The intelligence code......Page 28
The evolution of the machine......Page 31
The brain's unknown statistics......Page 38
Thought as matrix multiplication......Page 40
Heisenberg's matrix mechanics......Page 44
Conversion theorem......Page 45
Matrix statistics......Page 50
Supersymmetry......Page 52
Duality principle......Page 54
Projective logic......Page 57
The dimensions of the mind and the third quantization......Page 64
Closing pandora's quantum box......Page 69
Cognizing is quantizing......Page 71
Quantum computer......Page 73
Reality as a complex number......Page 76
Nonconvex probability......Page 80
Logical quantum numbers......Page 83
Does the mental violate the laws of physics?......Page 87
PART 2: THE BRAIN IS GEOMETRICAL, THE MIND IS TOPOLOGICAL......Page 96
CHAPTER 3. TOPOLOGICAL CHARGES......Page 98
Logical vacuum......Page 104
Multiplicative polarization......Page 107
Additive polarization and the fundamental lattice......Page 109
Thoughts, knots and cross-cups......Page 112
CHAPTER 4. COGNITIVE CIRCUITS......Page 120
Topological current......Page 122
CHAPTER 5. THE LOGICAL DERIVATIVE......Page 124
CUT and ZIP operations......Page 126
The quantum-mechanical derivative......Page 129
The covariant derivative......Page 130
The unbroken topological phase......Page 132
Translating logic into quantum mechanics......Page 134
Factorizing the thought processes......Page 138
Parallel brain, serial mind......Page 140
The suprasymmetric transfer function......Page 142
Operator waves......Page 144
Logical wave operators......Page 145
The exotic statistics......Page 148
Brains and branes......Page 150
Logical volume......Page 151
Irreducible logical branes......Page 152
Consciousness as a unilateral logical membrane......Page 156
The intellectual catastrophes......Page 158
This is absolutely true±false......Page 164
Quantum mathematics......Page 165
Topological phase and atomic orbits......Page 168
Self-measurement and backreaction......Page 171
CHAPTER 11. QUANTUM KNOTS......Page 173
Template supersymmetrization......Page 176
Information solitons......Page 178
CHAPTER 12. LOGICAL MEMBRANE ACTION......Page 180
CHAPTER 13. FROM BLACK HOLES TO GRAY BRAINS......Page 184
Logical Bang Blowing up the Farey Sequence......Page 186
The theory of Everything......Page 187
Information collapse......Page 189
Introducing gauge symmetry into logic......Page 194
Beyond seven crossings......Page 205
PART 3: THOUGHT TELLS THE BRAIN HOW TO SPIN, SPIN TELLS THE BRAIN HOW TO THINK......Page 208
Quantum thinking......Page 210
The quantization theorem......Page 216
Speeding thought up......Page 219
Self-"conscious" polynomials......Page 221
CHAPTER 16. LIMITATIONS OF CLASSICAL LOGIC......Page 222
Truth-tables......Page 225
Dealing with absurds......Page 226
Negation......Page 227
An unnoticed operation in Boolean logic......Page 228
Logic interpolates, mind extrapolates......Page 231
Timeless logic......Page 232
Solving the problem of being itself......Page 233
The golden ratio......Page 234
Logarithmic fixed point......Page 236
Second-quantized fixed points......Page 237
Logical radar coordinates as fixed point......Page 238
Probability of impossible and impossible probabilities......Page 239
Probability calculated and probability measured......Page 242
Tensor probability......Page 247
Improbable dispersions......Page 249
Imaginary certainties......Page 251
Negative probability and vacuum......Page 256
Charged sets......Page 257
Non-Hermitian reality. From quantum physics to infophysics......Page 259
Effective acausality......Page 261
Fundamental information......Page 262
Cognitive observables......Page 264
Why a tiny 2x2 matrix?......Page 266
The unruly algebra of matrices......Page 267
Truth-value as eigenvalue......Page 272
Truth-value and false-value......Page 275
The logical vacuum revisited......Page 278
Momentum as tensor product......Page 280
Logical momentum as quantum knot......Page 282
Zero-weight operators......Page 284
PART 4: COGNIZERS......Page 286
CHAPTER 21. STRETCHING NATURE'S LAWS......Page 288
Classical-quantum interface......Page 289
Quantum hypothesis of the brain......Page 291
Singularization theorem......Page 295
The brain-mind interface as a quantum-classical interface......Page 300
CHAPTER 22. COGNITIVE DELTA......Page 302
The delta theorem......Page 309
Lowering the energy barrier: the tunneling of logical operators......Page 310
CHAPTER 23. ENERGY FUNCTION......Page 314
The momentum theorem......Page 320
Logical momentum and the klein-gordon equation......Page 323
Logical isospin......Page 324
Truth-dependent Lagrangian......Page 326
The missing energy level......Page 327
CHAPTER 24. BRAIN STATES ARE NONCLASSICAL......Page 330
Denktors......Page 333
Understanding the information phase......Page 337
Quantization of the classical systems......Page 344
The s-matrix and the synaptic matrix......Page 350
The brain's sparse matrix......Page 352
CHAPTER 25. BETHE'S DOUBLE GROUP AND CONSCIOUSNESS......Page 354
CHAPTER 26. LOGICAL OSCILLATOR......Page 361
CHAPTER 27. TIME AS CONSCIOUSNESS' DYNAMICAL VARIABLE......Page 366
The time wraps......Page 370
Is there time to see? stroboscopic consciousness......Page 373
CHAPTER 28. CONVERTING THOUGHT INTO ACTION......Page 374
Conservation of time charges......Page 378
Making use of forbidden interactions......Page 379
CHAPTER 29. ENERGY-TIME PHASE SPACE......Page 380
The included middles......Page 382
A forbidden fivefold symmetry......Page 384
Pseudo-Galilean space and the 5-space correction to energy......Page 386
Constructing causal systems from acausal components......Page 388
Thought and Lorentz transformation......Page 390
The self's attempt about self......Page 391
Violating pauli exclusion......Page 394
Fundamental supercommutator......Page 395
True and false times. crossing the NOT barrier......Page 399
Thought is processed forwards but understood backwards......Page 400
Reversing the irreversible......Page 403
Recovering lost data......Page 404
Left ≠ right......Page 406
PART 5: HOW MANY LOGICAL THEORIES?......Page 408
Intuition versus intuition......Page 410
Truth series......Page 413
Five fundamental logics......Page 414
Boolean logic......Page 416
Multivalued logic......Page 418
Tense logic......Page 419
Quantum logic......Page 420
Fuzzy logic......Page 422
Tensorization of truth-values......Page 425
From truth-tables to operators......Page 426
Logical connectives interact......Page 430
Logic without connectives......Page 433
Quantum strings......Page 436
Quantum basis sets......Page 440
Logical superposition principle......Page 442
Unitary inferences......Page 446
If-then-else......Page 451
Logic with division. solving logical ratios......Page 452
Differential formal systems......Page 455
CHAPTER 35. VIRTUAL LOGIC......Page 460
Understanding septons......Page 463
CHAPTER 36. MIND'S DYNAMICAL EQUATIONS......Page 467
Canonical equations of motion......Page 472
Supercommutation theorem......Page 475
Satellite equations......Page 477
Suprasymmetry......Page 479
The integral equation of motion......Page 481
The commutation equation of motion......Page 482
Relation to the Heisenberg equation......Page 486
Cognitive constants of motion......Page 488
Spectral theorem......Page 491
CHAPTER 37. LOGICAL POLYMERS......Page 494
Phase transition......Page 495
Connecting logic to the vacuum......Page 500
Matrix nets and the self-solving brain......Page 502
Renormalization......Page 503
Open ended diagrams and vacuum traps......Page 505
CHAPTER 39. QUANTUM-LOGICAL COMPUTER......Page 508
Superbits......Page 509
The computer as a quantum particle......Page 512
Quantum Turing Machine......Page 519
Atomic registers......Page 521
Differential quantum algorithms......Page 526
Quantum engineering: Spintronics......Page 528
Dialing quantum numbers......Page 533
Quantum codes......Page 536
Self-correcting codes......Page 540
Codewords and inwords......Page 541
Quantum codes and the intelligence code......Page 550
Quark logic......Page 558
Double parity check......Page 562
Unitarization of implication and supercommutators......Page 566
Matrix base......Page 568
Transmultiplication......Page 575
Basis sets......Page 577
Logical mesons......Page 578
Monologic......Page 581
Consciousness as the macroanalogue of quarks......Page 582
CHAPTER 41. POSTSCRIPT......Page 587
24+2 roots of IS......Page 588
40 factorizations of NOT......Page 589
136 commutators of NOT......Page 590
40 anticommutators of NOT......Page 591
180 commutators of NOT diag......Page 592
REFERENCES......Page 594
GLOSSARY......Page 600