H theorem of Boltzmann, 1020
Haar wavelets, 1074
Hackers
and precursors to my work, 879
and universe as computer, 860
Hadamard, Jacques S. (France, 1865-1963)
and chaos theory, 971
and Hadamard matrices, 1073
Hadamard matrices, 1073
Hadamard order
for Walsh functions, 1073
Hadrons
as particles, 1043
in QCD, 1061
Hailstone numbers (3n+1 problem), 904
Hair cells
in inner ear, 585, 1079
Hair follicles
and animal coloration, 1012
Haken, Hermann P. J. (Germany, 1927- )
and reaction-diffusion, 1013
Hales, Stephen (England, 1677-1761)
and leaf growth, 1005
Hales, Thomas C. (USA, 1958- )
and sphere packings, 986
Halftoning, 1077
Halite (rock salt) hopper crystals, 993
Halting
in aggregation systems, 979
in function definitions, 1163
longest times for, 1144
in one-way TMs, 759, 1143
in register machines, 896
in small Turing machines, 1119
in symbolic systems, 897, 897'
in Turing machines, 889
Halting probabilities
and algorithmic randomness, 1067
for code 20, 964
for Turing machines, 1143
and universal objects, 1127
Halting problems, 1137
analog of, 754
axioms for proofs about, 1167
for cellular automata, 1137
and correspondence systems, 1140
and integer equations, 788
in Mathematica, 1138
for multiway systems, 1137
and negation, 1158
and oracles, 1126
proofs of undecidability of, 1137
and proving undecidability, 1130
and sets, 1139
in specific axiom systems, 1163
trivial for primitive recursion, 907
for Turing machines, 1137
undecidability of, 1128, 1136
Halton (digit reversal) sequences, 905
Hamiltonian paths
and NP completeness, 1146
trivalent networks with, 1029
Hamiltonians
in discrete quantum systems, 1060
for PDEs, 923
Hamming, Richard W. (USA, 1915-1998)
and error-correcting codes, 1101
Hamming codes, 1101
Hamming distance
and error correction, 1101
and layout of networks, 1031
Hamming weight (DigitCount), 902
Handles on networks, 527, 1045
Handprints
purpose of in cave paintings, 1184
Handwriting
randomness in, 1192
Hankel, Hermann (Germany, 1839-1873)
and generalization in math, 1168
Haploid cells
and randomness in biology, 970
Hard hexagon model
and 2D entropies, 959
as exactly soluble, 1133
Hard sphere gas, 1022
and CA fluids history, 999
CA idealization of, 446
and chaos theory, 971
on inspirational book cover, 864
with stationary scattering, 312
and thermodynamics, 1020
Hard square models (lattice gases), 999
Hardware
for 1D cellular automata, 868
for 2D cellular automata, 928
structure of computer, 1108
Hardy, G. Harold (England, 1877-1947)
and Goldbach's Conjecture, 911
and iterated maps, 919
Harmonic analysis
of substitution systems, 1081
and Walsh functions, 1073
Harmonic analyzer, 1107
Harmonic functions
and flatness in tissue growth, 1007, 1010
Harmonic oscillator
as exactly soluble, 1133
Harmony (musical)
and math thinking, 1177
perception of, 1079
Harmony in nature, 967
Harrington, Leo A. (USA, 1946- )
and unprovable statements, 1163
Hartley, Ralph V. L. (USA, 1888-1970)
and information theory, 1181
Hartman, Hyman (USA, 1936- )
and CA classes, 948
in Preface, xiii
Harvard Mark I computer, 1107
Hashing, 622, 1100
as application of randomness, 1192
to speed up evolution, 1134
Hasse diagrams of posets
and causal networks, 1040
Hasse's algorithm (3n+1 problem), 904
Hasse's Principle
for Diophantine equations, 1165
Hastings, Stuart P. (USA, 1937- )
and reaction-diffusion, 1013
Hauptvermutung (of combinatorial topology), 1051
Hausdorff dimension, 933, 958, 1030
Hawking, Stephen W. (England, 1942- )
and black hole radiation, 1062
Hawking radiation, 1062
and uniform spectra, 988
Hayek, Friedrich A. (Austria/England/USA/Germany, 1899-1992)
and free will, 1135
hcp (hexagonal close packing), 986
Head size
in animal growth, 421
Heads (of expressions), 896
depth of in trees, 897
as type specifications, 898
Hearing, 585-588
of elephants, 1181
human, 1079
Heart (human)
1/f noise in beating of, 969
as excitable medium, 1013
modelling and history of CAs, 878
Hearts of palm, 1004
Heat
analogies with computation, 726
character of, 445
history of theories of, 1019
Heat bath
and 2D Ising model, 982
Heat capacities
and quantum history, 1056
Heat exchangers
geometrical forms of, 1183
Heated fluids
and convection, 1000
Heaven
and form of extraterrestrials, 1191
Heavenly bodies
perfection of, 875
Hebb, Donald O. (Canada, 1904-1985)
and neural networks, 1099
Hebrew religion
and free will, 1135
Hedlund, Gustav A. (USA, 1904-1993)
in Preface, xiii
and shift-commuting block maps, 878
and surjective CAs, 960
Heights of humans
distribution of, 977, 1003
Heighway, John E. (USA, 1930- )
and dragon curves, 893
Heisenberg, Werner K. (Germany, 1901-1976)
and matrix mechanics, 1056
Heliozoan
pattern formed in, 385
Helium
lack of quantum solution to, 1133
randomness in convection of, 976
Helix
in shell models, 1008
Hellman, Martin E. (USA, 1945- )
and math cryptography, 1089
Helmholtz, Hermann L. F. v. (Germany, 1821-1894)
and sound perception, 1080
Henkin semantics (for higher-order logics), 1167
Heptagons
hyperbolic tiling with, 1050
and negative curvature, 532
Herbs
leaf shapes for identifying, 1005
Herds
and randomness in markets, 1015
Heredity
use of simple rules in, 860
HermiteH (Hermite polynomials)
in solution of harmonic oscillator, 1133
Hero (Heron) (Egypt, ~62 AD)
and computing devices, 1107
Heterostructures, 1082
Hewlett-Packard calculators
reverse Polish in, 896
Hexagonal cellular automata
and fluid flow, 378
implementation of, 992
as models of crystal growth, 369
and momentum conservation, 1024
number of rules in, 928
Hexagonal close packing, 986
Hexagonal lattice
of animal pigment cells, 1012
circle packings in, 349, 985
of circles in ornament, 873
of deformable objects, 988
enumeration on, 959
implementation of CAs on, 992
isotropy on, 980
and r=1/2 1D CA, 885
random walks on, 329
and shapes of cells, 1007
Turing machines on, 930
Hexagonal prism, 929
Hexagrams
of I Ching, 893
Hidden Markov models, 590, 1084
Hidden units
in neural networks, 1102
Hidden-variables theories, 543, 1058, 1064
Hierarchies
as avoiding thermodynamics, 453
in computational complexity theory, 1142
and defining complexity, 1069
in embryo development, 419
of function growth rates, 1163
and history of complexity, 862
in probabilistic models, 1084
and randomness in markets, 1015
|  | Higgs field
and expansion of universe, 1055
and notion of ether, 1042
particle associated with, 1047
and particle masses, 1047
High-energy collisions
Monte Carlo simulation of, 968
High-level programming
and programs in notes, 854
High-school algebra
axioms of, 1153, 1153'
Higher-order logics, 1167
Higher organisms
phenomenon of existence of, 398
Highest common factor
see GCD (greatest common divisor)
HighLife (2D class 4 CA), 949
Higman, Graham (England, 1917- )
and axioms for groups, 1153
Hilbert, David (Germany, 1862-1943)
and axioms for geometry, 1154
and character of math, 1176
and Diophantine equations, 1161
and foundations of math, 1149
and general relativity, 1052
and math in science, 859
and metamathematics, 1150
and space-filling curves, 893
and undecidability, 1136
and zeros of zeta function, 918
Hilbert space
in quantum theory, 1059
Hilbert's Tenth Problem, 1161
Hilbert's Thirteenth Problem, 1128
Hill climbing, 346
Hillenbrand, Thomas (Germany, 1970- )
and automated proofs, 1158
Hillman, David (USA, 1955- )
and axioms for logic, 1151
in Preface, xii
Hindu-Arabic number system, 902, 1182
Hindu temples
nesting in, 874
Hinton, Geoffrey E. (England/USA/Canada, 1947- )
and neural networks, 1100
Hippocampus (in brain), 1102
Hippocrates of Chios (Greece, ~460 BC)
and embryology, 1010
Hiss
sound of random sequence, 585
Historians
and free will, 1135
Historical perspectives, 844-846
see also history items in specific entries
History
accidents of in universe, 505
as central to human condition, 846, 1196
of complexity research, 862
computations done in human, 837
of definition of sciences, 863
effect on math of, 792
as explaining axiom systems, 816
general comments about, 850
of life on Earth, 387, 825
of math and ease of concepts, 1177
recorded by physical objects, 1195
role of in biological evolution, 388
theory of and chaos, 971
uniqueness of for universe, 504
History register
see Shift registers
Hobbes, Thomas (England, 1588-1679)
and free will, 1135
and nature of space, 1028
Hodgkin-Huxley equation
as example of PDE, 161
Hofmeister, Wilhelm F. B. (Germany, 1824-1877)
and phyllotaxis, 1007
Hofstadter, Douglas R. (USA, 1945- )
and recursive sequences, 880, 907
Hokusai, Katsushika (Japan, 1760-1849)
and fluid turbulence, 997
Hölder exponents, 959
Holland, John H. (USA, 1929- )
and genetic algorithms, 985
in Preface, xiii
Homeobox genes, 419, 1010
Homoclinic tangles, 972
Homogeneity
origins of, 353
Homogeneous structures
see Cellular automata
Homomorphisms
and generalized additivity, 952
Homoplectic processes (extrinsic randomness generation), 973
Homotopy
and structures in networks, 1046
and topological defects, 1045
Homunculus hypothesis, 1010
Honda, Hisao (Japan, 1943- )
and branching in plants, 1005
Honeycomb
form of, 1011
length minimization in, 988
Hooke, Robert (England, 1635-1703)
and snowflakes, 992
Hopfield, John J. (USA, 1933- )
and neural networks, 1100, 1102
in Preface, xiii
Hopi language
and Sapir-Whorf hypothesis, 1181
Hopper crystals, 993
Horizon problem (in cosmology), 1055
Hormones
in brains, 1099
in plants, 404
Horn shell
growth of, 415
Horner form
and evaluation of powers, 1093
Horns (animal)
as artificial-looking, 828
compared to antlers, 1008
growth of, 413
Horse races
as source of randomness, 968
Horton stream order (in tributaries), 1001
Hours-minutes-seconds
origin of, 902
Hoyle, Fred (England, 1915-2001)
and extraterrestrials, 1190
HP 700
and creation of this book, 854
HP calculators
reverse Polish notation in, 896
Huffman, David A. (USA, 1925-1999)
and data compression, 1069
Huffman coding, 564
adaptive, 1069
implementation of, 1071
and JPEG compression, 1074
Human behavior
and computational irreducibility, 1132
free will in, 750-753, 1135
and game theory, 1104
laws of, 1014
Occam's razor for, 1025
Human condition
defining features of, 1196
scientific approaches to, 845
Human form
parametrizations of, 1010
Human history
vs. biological evolution, 399
Human languages
see Languages (human)
Human relics in archeology, 1183
Human thinking, 620-631
and constructs in math, 1177
emulation by computers of, 733
and Gödel's Theorem, 1159
and Principle of Computational Equivalence, 733, 1130
Human will
see Free will
Humanities
relativism in, 1131
summary of relations to, 9, 863
Humans
artifacts of early, 1184
defining properties of intelligence of, 822
and future technology, 1195, 1196
genetic programs of, 383, 1002
height distributions of, 977, 1003
making randomness, 306, 970
mathematical power of, 1126
as only intelligence, 822
uniqueness of, 844, 1195
visual system of, 577
weight distributions of, 977
Humboldt, F. W. H. Alexander v. (Germany, 1769-1859)
and branching in plants, 1004
Hume, David (Scotland, 1711-1776)
and purposes in nature, 1185
Humidity
and weather, 1177
Huntington, Edward V. (USA, 1874-1952)
and axioms for logic, 1151
Huntington axioms for logic, 773, 1151
Hurwitz numbers, 914
Hydraulic jump, 377
Hydrocarbons
considered interesting, 1194
Hydrodynamics
see Fluid flow
Hydrogen atom
as exactly soluble, 1133
and history of quantum theory, 1056
Hydrology
and forms of landscapes, 1001
Hyena
pigmentation pattern of, 426
Hyperbolic equations, 923, 940
Hyperbolic space, 1049
Hypercube
Boolean, 1095
and trivalent networks, 1029
Hypercycles
and origin of life, 1179
Hyperelliptic Diophantine equations, 1164
Hyperelliptic functions
in solution of spinning top, 1133
Hypergeometric functions
asymptotic behavior of, 917
and continued fractions, 914
and curves from curvature, 1009
and nested patterns, 612
Hypergeometric1F1
in Calogero-Moser model, 1133
Hypergeometric2F1
and caps on hyperspheres, 1050
and quintic equations, 945
in Seiberg-Witten model, 1133
and special functions, 1092
and Thue-Morse sequence, 1092
and trinomial coefficients, 1091
HypergeometricPFQ
and 6j symbols, 1055
difficulty of evaluating, 1134
from rational integral, 916
Hypergraphs, 1029
Hyperreals
as generalizing numbers, 1168
Hypersonic flow
see Supersonic flow
Hypersphere
volume of, 479, 1050
Hyphenation
lack of in this book, 852
I-1 base, 932
I Ching
and substitution systems, 893
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