Index



e (exponential constant)
continued fraction for, 144
digits of, 142
as not from rational integral, 916
and random networks, 963

e-commerce
use of randomness in, 1192

E8 (group) lattice
isotropy of, 980
and sphere packings, 987

Eanna temple, 873

Ear lobes
folding in formation of, 417

Early computers
and cellular automata, 45

Early universe
particles surviving from, 1047
and thermodynamics, 1021

Ears
operation of, 585, 1079
see also Auditory perception

Earth
conditions for life on, 1179
and extrasolar planets, 1179
formation of the, 1179
origin of life on, 1179
viewed from space, 835, 1187

Earth-Moon-Sun system, 313, 972

Earthquakes
1/f noise in, 969
and fracture, 374

Earthworks
as artifacts, 1184

Eastern philosophy, 1195, 1195', 1196

ECAD
multilevel logic in, 1096

Ecology
and complexity research, 863
of extraterrestrial colonization, 1191
iterated maps and models in, 918

Economics
applications to, 429-432
and complexity in science, 861
and computational irreducibility, 1132
and extraterrestrial trade, 1191
and free will, 1135
history of models from, 1015
iterated maps and models in, 918
and notion of purpose, 1185
and pragmatic theory of law, 1136
quantitative laws in, 1014
successes of math in, 859

ed (text editor)
and regular expressions, 958
and substitution systems, 894

Eddies
in fluid flow, 376

Eddington, Arthur S. (England, 1882-1944)
and models of the universe, 1025

Eddy viscosities, 997

Eden, Murray (USA, 1920- )
and aggregation systems, 978

Eden model, 331, 978
see also Aggregation systems

Edge detection in images, 1077
and scale invariance, 1076

Edgerton, Harold E. (USA, 1903-1990)
and splashes, 1000

Edison, Thomas A. (USA, 1847-1931)
and searching for materials, 1193

Education
and defining intelligence, 1178
and exact solutions, 1133
and recognizing intelligence, 825
and the science in this book, 855

EDVAC (computer)
and early CA, 1117

EEG, 1099

Eel
pigmentation pattern of, 426

Effective computability
see Decidability

Effectively computable sets, 1138

Efficiency of computations, 758

Efficient causes, 1185

Efficient Market Hypothesis, 432, 1015

Egg
randomness in fertilization of, 970

Egmont volcano
circular shape around, 1187

Egyptian art, 873

Egyptian fractions, 915

Egyptian mathematics, 1149
and evaluation chains, 1095
and pi, 911

Egyptian pyramids, 874

Ehrlich, Paul (Germany, 1854-1915)
and chemotherapy, 1193

Eigenvalues
and dimension of networks, 1031
of distance matrices, 1031
and entropies of CAs, 958
and fractal dimensions for additive rules, 955
of nested systems, 1081
nesting in pattern of, 1130
of random matrices, 918, 977

Eikonal approximation, 1061

Einstein, Albert (Germany/Switzerland/USA, 1879-1955)
and EPR experiment, 1058
and general relativity, 1047
and math in science, 860
and particles as gravity, 1054
and quantum theory, 1056
and special relativity, 1041
and unified field theory, 1028

Einstein equations, 1052
exact solutions to, 1133
as examples of PDEs, 161, 923
history of, 1047
matter vs. space in, 1028
quantization of, 1054
specifying curvature of space, 531
vacuum solutions to, 1053

Einstein-Hilbert action
and spin networks, 1055

Einstein-Podolsky-Rosen (EPR) experiment, 1064

Elasticity theory
and fracture, 995

Electric breakdown, 302, 995
see also Lightning

Electric fields
particle production in, 1062

Electric light bulb filaments, 1193

Electricity
as defining feature of life, 1178

Electromagnetic fields
and gauge invariance, 1045
quantization of, 1056
and radioactive randomness, 970
and relativistic invariance, 1041
theories of based on space, 1028
as ultimate constituents, 1024
and virtual photons, 1060

Electromagnetic radiation
and information transmission, 1069

Electromagnetic signals
see Radio signals

Electromechanical machines
as computers, 1107
and finite automata, 958

Electron diffraction
and visualizing fracture, 995

Electron levels
in nested potentials, 1081

Electron-photon scattering, 1060

Electronic computers
and Church's Thesis, 1125
history of, 1107
and history of universality, 1110
numbers in history of, 902
and proofs of universality, 1117

Electronic design
and Boolean formulas, 1097

Electronic noise, 302, 968
randomness from, 969

Electronics
making reliable, 981
and studying complexity, 862

Electrons
discovery of, 1024, 1044
as initiators of randomness, 303
lack of intuition about, 537
limits on sizes of, 1044
magnetic moment of in QED, 1060
mass of, 1046
in practical computers, 1108
theories of structure of, 1044
wave-particle duality of, 1056

Elegant theorem
definition of, 1176

Element
in set theory, 1155

Elementary cellular automata, 53, 883
emulation of rules by, 705
legal rules for, 948
my first pictures of, 19, 864
with random initial conditions, 232, 424
rule equivalences, 883
table of Boolean forms for, 884
uniqueness of patterns from, 956
as universal logic functions, 1174
see also Cellular automata
see also Rule 30, Rule 90, etc.

Elementary functions
difficulty of evaluating, 1134
and math impossibilities, 1137
numbers generated from, 916
vs. special functions, 1092

Elementary particles, 525-530
decays and time quantization, 1032
detection of, 969
discovery dates of, 1043
as dual to black holes, 1045
enumerating in networks, 1045
interactions between, 539
known types of, 1043
and limit of networks, 1030
masses of, 528, 1046
motion of, 528
motion of along geodesics, 531
motion of through network, 536
quantum threads between, 544
searching for additional, 1047
spin of, 1046
in unified field theory, 1028
upper limits on mass of, 1047

Elements
of Euclid, 909

Elephants
communication by, 1181

Elkies, Noam D. (USA, 1966- )
and nearby powers, 1166
in Preface, xiii

Elliott 903 computer
my use of, 854, 864

Elliptic curves
and Diophantine equations, 1164, 1165
and Fermat's Last Theorem, 1166

Elliptic equations (PDEs), 923, 940

Elliptic functions
and background for PDE, 924
difficulty of evaluating, 1134
and logistic map formulas, 1098

EllipticK (elliptic integral)
in 2D Ising model, 982, 1133

EllipticTheta (elliptic theta functions)
and algebraic equations, 1092
as generating function, 1092
nested patterns from, 1093
and quintic equations, 945, 1133
and runs of digits, 914

Embeddings of networks, 193, 476, 1031

Embryos
development of, 417, 419, 1009
history of study of, 1004, 1010
pigmentation precursors in, 425
randomness in, 970

Emergence
of order from randomness, 223

Emergent behavior
general theory of, 3

Emotions
and learning, 1102

Empirical mathematics
see Experimental mathematics

Empiricism
and theories of communication, 1181
and visual perception, 1076

Emulation
between cellular automata, 1118
by universal CA, 652
and computational irreducibility, 742
rates of, 765
and universality, 642
see also entries for specific systems

Encoding
arithmetic, 1071
of arithmetic by set theory, 1160
block, 563
dictionary-based, 565
Huffman, 564
in mathematics, 815
pointer-based, 565
run-length, 560
theory of cellular automaton, 1118
of three colors by two, 655, 1111
in universal CA, 652
and universality proofs, 1126

Encryption
see Cryptography

Encyclopedia Britannica
leaf shapes in first edition of, 1005

Endogenous randomness
see Intrinsic randomness generation

Endomorphisms
cellular automata as, 959
and generalized additivity, 952

Endpapers in this book, 851

Energy
and advanced technology, 1191
in gravity theory, 537
heat as form of, 1019

Energy conditions
and general relativity, 1053

Energy conservation
in cellular automata, 458
in Einstein equations, 1052
in Ising model CAs, 982
in network evolution, 529
in PDE, 923
in physics, 1022
and thermodynamics, 445
in three-body problem, 972

Energy levels
in nested potentials, 1081

Energy minimization
and adaptation, 823
in chemistry, 1194
and NP completeness, 1146
in proteins, 988, 1003
and purpose, 831
and quasicrystals, 994

Energy-momentum tensor
in Einstein equations, 1052

Engineering
avoiding complexity in, 723
vs. biological evolution, 393
vs. biological forms, 1004, 1180
and computational reducibility, 829
correctness proofs in, 1157
fracture as issue in, 995
future of, 840
historical forms in, 828, 1183
and history of complexity, 862
intuition from, 40
optimization of designs in, 1193
of universal systems, 678
and universality proofs, 698
used in building computers, 822

English
and cryptanalysis, 599
frequency of letters in, 1069
hashing of words in, 1100
logic operations in, 1173
redundancy of, 1086

ENIAC (computer)
and digits of pi, 911
and history of computing, 1107

Enigma rotor machine, 1085

Ensembles
evolution of in CAs, 278
in Ising model, 982
in rule 37R, 457
in statistical mechanics, 1020
in statistics, 593

Entanglement (in quantum theory), 544
as basic quantum effect, 1059
and Bell's inequalities, 1064

Entrails of goats
and fortune-telling, 968

Entropy
as algebraic number in CA, 958
analogy of to amount of computation, 1133
vs. biological complexity, 1003
in block encoding, 1071
in cellular automata, 958
as defining CA classes, 960
and definition of life, 1178
estimation of, 959, 1084
history of, 1019
and Lyapunov exponents, 960
measure, 959
origins of increasing, 441-457
of particles in box, 1022
and redundancy of text, 1086
and repetitive CA behavior, 954
of rule 30 mapping, 1087
and self-organization, 948
spacetime, 960
temporal, 960
in thermodynamic systems, 448
undecidability of in CAs, 958, 1138
see also Second Law of Thermodynamics

Entscheidungsproblem (decision problem), 1110

Enumeration of
alkanes, 1194
balanced parenthesis strings, 989
CA periodic points, 954
CAs to find doubling rules, 832
cases in proofs, 1177
commutative monoids, 952
cycles in shift rules, 963
finite automata, 957
programs, 758
reachable states in CAs, 958
string constraints, 1140
surjective cellular automata, 959
tiling configurations, 959
Turing machines, 888, 1120

Envelopes
masking patterns on, 1077

Environmental sciences
math morphology in, 1077
and systems theory, 862