Index



T1 and T2 processes in networks, 1038
Table
     basic examples of, 853
Tables
     for Boolean formulas, 1095
     leading digits in, 914
     of primes, 910
     of random numbers, 968
     see also Multiplication tables
Tabulating machines, 1107
Tachyons, 1041
     spin of, 1046
Taffy
     as chaos theory example, 306
     fracture in, 994
Tag systems, 93-94
     cyclic, 95
         see also Cyclic tag systems
     density in, 894
     emulated by correspondence systems, 1140
     emulated by recursive functions, 1121
     emulated by universal TM, 706, 1119
     emulating CAs, 667, 1113
     emulating TMs, 670, 1114
     implementation of, 894
     multiway, 1141
     one-element-dependence, 1114
     as precursors to my work, 879
     random initial conditions in, 949
     and TM 596440, 1120
     undecidability in, 1136
     uniform, 82
         see also Substitution systems
     universality in simple, 1120
     universality of one-element dependence, 1120
Tail recursion
     and recursive functions, 907
Tails (of data), 1083
Taj Mahal
     nesting in gardens of, 874
Take (take elements)
     basic example of, 853
Tally sticks
     and application of randomness, 968
Tan
     curve of, 145
Tang, Chao (USA, 1958- )
     and self-organized criticality, 989
Tangencies
     in circle packings, 986
     in ornamental art, 873
Tanh
     in neural network models, 1102
     and solving Ising model, 982
Taoism, 1196
Tape
     of Turing machine, 78
Tapir
     pigmentation pattern of, 426
Taps in shift registers, 975
Tarski, Alfred (Poland/USA, 1902-1983)
     and axioms for geometry, 1154
     and axioms for groups, 1153
     and axioms for predicate logic, 1152
     and real algebra, 1154
     and undecidability of group theory, 1159
Taste
     sense of, 1105
Tate-Shafarevich group, 1164
Tau lepton
     mass of, 1046
     as type of particle, 1043
Tautologies
     based on Nand, 781, 1157
Tautology
     laws of, 817
Tea leaves, 968
Tearing of materials, 995
Technical analysis
     of financial markets, 1015
Technology
     components used in, 1195
     dating of jargon about, 849
     discussions of in this book, 1192
     future of, 832
     history of vs. fossil record, 398
     and human condition, 846
     implications for, 840-843
     new purposes for, 843
     and Occam's razor, 1025
     optimization in advanced, 829
     search-based development of, 1193
     as stimulus for basic science, 42
     summary of relations to, 11, 863
TECO (text editor), 894
Tectonic activity, 1001
Teeth
     folding in formation of, 417
     patterns in ray and shark, 1007
Teichmüller spaces (parameter spaces), 1006
Telegraphy
     and data compression, 1069
     and SETI, 1189
Teleology, 1185
     and argument by design, 861
     and biological evolution, 387
Telepathy
     as feature of extraterrestrials, 1190
Telephone
     bandwidth of, 1079
     development of, 1080
     and sound compression, 1072
Telephone information services, 1100
Telephone networks
     Monte Carlo studies of, 1192
Teleportation, 1058
Telescopes
     as analogy, 42
     and SETI, 835
Television
     bandwidth of, 1079
     data compression for, 1072
     as source of radio signals, 1188
Telos (final cause), 1185
Temperament (in music), 917, 1079
Temperature
     of black holes, 1062
     as characterizing equilibrium, 450
     in crystal growth, 993
     differences in convection, 1000
     in Ising model, 982
     repeatable randomness in, 976
     and weather, 1177
Templates
     for 2D constraints, 941
     in aggregation systems, 978
     and hash codes in neural networks, 624
     in tilings, 213
     in visual perception, 579
Temporal logics
     and causal invariance, 1035
Temporal sequences
     in cellular automata, 960
TensorRank
     and tensors in differential geometry, 1049
Tensors
     characterizing symmetry of pattern, 980
     in differential geometry, 1049
     duals of, 1050
     Einstein equations and, 1052
     manipulation of, 1048
     norms of, 1050
Tent map, 150
     exact iterates of, 919
     and history of chaos theory, 971
Tent olive shell
     pattern on, 423
Tent patterns on shells, 423
Tentacles
     of octopus, 385
     and spines on shells, 1008
Term rewrite systems
     see Multiway systems
Termination
     of function computations, 1163
     in multiway systems, 1036
     problems
         see Halting problems
     in symbolic systems, 897
Termite structures
     and aggregation systems, 1011
     as animal artifacts, 1184
Ternary
     binary-coded, 1070
Ternary cellular automata, 60
Ternary logic, 814
Ternary operators, 1171
Terraces in crystals (hoppering), 993
Territories
     defending and bird songs, 1180
     and Voronoi diagrams, 987
Tertiary structure (of proteins), 1003, 1184
Terza rima
     and rules for poetry, 875
Tesla, Nikola (USA, 1856-1943)
     and SETI, 1188, 1189
Tessellation automata
     see Cellular automata
Tessellations
     defined by constraints, 213
     of fixed blocks, 582
Tests of models, 364
Tests of randomness, 1084
     for digit sequences, 912
     for rule 30, 871
Tetrad formulation of general relativity, 1048
Tetradecahedron, 930, 987, 988
Tetrahedral group (A_4)
     with trivalent Cayley graph, 1032
Tetrahedron
     as cluster shape in sphere packings, 986
     network as net of, 476
     network transformed to cube, 1038
     as rigid 3D structure, 1031
     in spin networks, 1055
     as tip of plant stem, 1004
Tetrakaidecahedron
     see Tetradecahedron
Tetration
     and Ackermann function, 906
     and halting in symbolic systems, 897
     and symbolic systems, 897
Text
     compression of, 1084
     in databases, 621
     in practical computers, 1108
     redundancy of, 1086
Text-based interfaces, 1102
Text editors, 88, 894
Textbooks
     and computational irreducibility, 1133
     of computer science and Church's Thesis, 1126
     math in, 773
Textile cone shell
     pattern on, 423
Textile making
     rules in, 874
Textons
     and texture perception, 1076
Texture perception, 577
     history of, 1076
Textures
     in biology, 387
     generating, 841, 1078
     of physical surfaces, 1077
Texturing
     use of randomness in, 1192
Thallus
     shape of, 385
Theism, 1195
Theology
     and complexity, 3, 861
     and form of extraterrestrials, 1191
     and free will, 1135
     and issues of modelling, 991
     and teleology, 1185
     and ultimate theory of physics, 1025
     and uniqueness of life on Earth, 1180
     and universe as intelligent, 1195
     see also God
     see also Religion
Theophrastus (Greece, ~371 - ~287 BC)
     and shapes of leaves, 1005
Theorems, 779
     automated proving of, 1157
         see also Automated theorem proving
     character of different types, 820
     vs. computer experiments, 899
     and definition of math, 860
     distributions of in fields of math, 1175
     general characterizations of, 1176
     interesting ones in logic, 816
     involving Nand, 818, 1175
     in operator systems, 801
     pattern of in logic, 812
     pattern of in simple axiom systems, 812
     of shortest axioms for logic, 811
Theoretical biology
     and complexity, 861
     history of, 1003
     undecidability in, 1138
Theoretical science
     and computational reducibility, 749
     traditional methods of, 737
Theory of being (ontology)
     implications for, 1197
Theory of biology
     possibilities for a, 397
Theory of computation, 753
Theory of everything, 1025
Theory of knowledge (epistemology)
     implications for, 1196
Theory of structures
     in mathematics, 1150
Theory of universe
     see Ultimate theory of physics
Thermal diffusion
     and randomization times, 970
Thermal equilibrium
     in early universe, 1055
     and Ising model, 982
     see also Equilibrium
Thermal noise, 968
     in microprocessors, 970
Thermal perception, 1105
Thermodynamic formalism (for dynamical systems), 959
Thermodynamic limit
     for diffusion equation, 1024
     and phase transitions, 983
Thermodynamics
     analogies to computation, 726
     vs. biological evolution, 1003
     of computation, 1020
     and crystal growth, 993
     and defining life, 824, 1178
     history of, 1019
     and history of complexity, 862
     Second Law of, 441-457
         see also Second Law of Thermodynamics
     vs. strange attractors, 1020
     summary of relations to, 16
Theta functions
     see EllipticTheta
Thinking
     attributed to universe, 1195
     communication and, 1181
     emulation by computers of, 733
     and foundations of math, 1176
     and Gödel's Theorem, 1159
     in higher math, 1177
     history of studying, 1099
     human, 620-631
     influence of language on, 1181
     logic as representation of, 860
     machines, 628
     and Principle of Computational Equivalence, 733
     and ultimate theory of universe, 465
Thinking Machines Corporation, xiii, 881
Thirteenth problem (of Hilbert), 1128
Thom, René F. (France, 1923-[2002])
     in Preface, xiii
     and structure in animals, 1009
     and theoretical biology, 1004
Thompson, D'Arcy W. (Scotland, 1860-1948)
     and forms in nature, 967
     and growth processes, 1010
     and leaf shapes, 1006
     and theoretical biology, 1004
Thomson, William
     see Kelvin
Threads between particles, 544
Three-body problem, 972
     and computational irreducibility, 1132
     and history of chaos, 971
     and history of complexity, 862, 1068
     as precursor to my work, 879
     randomness in, 314
     and undecidability, 1138
Three-dimensional
     cellular automata, 182-183
     networks, 195, 1030
     wave equation, 923
Three squares problem, 910
Through
     and recursive functions, 907
Throw
     and context-free parsing, 1103
     and pointer-based encoding, 1071
     and testing invariances, 1022
     and testing reversibility, 1017
Thue, Axel (Norway, 1863-1922)
     and circle packings, 985
     and Diophantine equations, 1164
     and multiway systems, 938
     and repetition-free sequences, 944
     and substitution systems, 879, 893
     and word problem for semigroups, 1141
Thue equations, 1164
Thue-Morse sequence, 890
     atomic layers in, 1082
     as cube-free sequence, 944
     and cyclic tag systems, 895
     generating function for, 1092
     and period-doubling sequence, 892
     represented by special functions, 1092
     rule 60 applied to, 1091
     simplest CA generating, 1186
     spectrum of, 586, 1081
     statistics of blocks in, 594
     from substitution system, 83
     and Walsh functions, 1073
Thunderstorms
     1/f noise in, 969
Thwaites conjecture (3n+1 problem), 904
Tic-tac-toe
     network for, 939
Tidal forces
     and Einstein equations, 1052
Tides
     machine for predicting, 1107
TIFF format
     compression in, 1070
Tiger
     pigmentation pattern of, 426
Tilings, 211-221
     from 2 x 2 squares, 1078
     and aggregation systems, 979
     approximate solutions of, 345
     and cellular automata, 943, 1139
     as cellular automaton lattices, 930
     density of difficult cases of, 1147
     diffraction patterns of, 1082
     enumeration of, 959
     of fixed blocks, 582
     history of, 943
     in hyperbolic space, 1050
     as invariant states of 2D CAs, 349
     and Ising models, 1138
     and melting points, 1194
     NP completeness in, 984, 1145
     Penrose, 932
         see also Penrose tilings
     and reversibility of 2D CAs, 1017
     Truchet, 875
     undecidability in, 1138, 1139
     see also Domino problems
Time
     alignment of in universe, 1021
     branching in, 504
     compression in PDEs, 732
     computation between moments of, 1033
     and definition of motion, 521
     discreteness in, 1032
     graphical representation of, 1031
     in gravity and computation, 1130
     in Hopi language, 1181
     network for in multiway systems, 209
     and randomness in causal networks, 494
     in relation to space, 481-486
     and single active cell, 487
     in ultimate theory of physics, 486-508, 516-524
Time-and-motion studies
     and causal networks, 1033
Time complexity (in computational complexity theory), 1142
Time dilation (relativistic), 524
Time Machine (science fiction book), 1031
Time reversal
     in particle physics, 1019
     and thermodynamics, 443, 1020
Time series analysis, 587, 1081, 1083
Time standards
     as source of radio signals, 1188
Time travel, 1043
     and character of time, 1031
     and energy conditions, 1053
TimeConstraint
     and avoiding undecidability, 1138
Timeline
     of close approaches, 878
     of my scientific activities, 864
     of publications of mine, 881
     of writing this book, 850
Times
     combinator for, 1122
     and NC computations, 1149
     in ordering of math constructs, 1177
     primitive recursive definition of, 907
Tippett, Leonard H. C. (England, 1902-1985)
     and random number tables, 968
Tire treads
     characteristic shapes of, 1183
Tit-for-tat strategy
     in game theory, 1104
Titan
     and extraterrestrial life, 1179