Cambridge University Press 978-1-107-17119-0 — Physical Perspectives on Computation, Computational Perspectives on Physics Edited by Michael E

Cambridge University Press 978-1-107-17119-0 — Physical Perspectives on Computation, Computational Perspectives on Physics Edited by Michael E. Cuffaro , Samuel C. Fletcher Index More Information

Index

k relation, 214 Aristotle, 34 k relation, 214 arithmetical relation, 214 1 relation, 214 arithmetical set, 213 ǫ-closeness condition, 133 asymmetry, temporal, 236 ǫ-commuting diagram, 133–135, 147 asymptotic behavior, 175 λ-calculus, 2, 155, 161, 226 asymptotic methods, 175, 180–183, 194 λ-deﬁnability, 64 Avogadro’s number, 253 μ-recursion, 155, 161 axiomatic method, 60, 62–63 axiomatization of computability, 153–156 Aaronson, Scott, 48 of geometry, see Hilbert’s axiomatization of Abstraction/Representation theory, 15–16, geometry 127–149 of physics, 155, 165 diagram, 128, 133 of quantum theory, 257, 277 essential components, 140 of relativity, 166 Ackermann function, 158–161 afﬁne-linear symmetry, 269, 272 agency, 16, 119–125 Babbage, Charles, see difference engine algebra of concepts, 72 backward error analysis, 181 algorithm, 65, 83–84, 97, 173–174, 176, Banach-Tarski paradox, 147 187, 189 basic linear algebra subprograms, 187 asynchronous, 52 basic polynomial algebra subprograms, 192 feasible, 173 Bell experiment, 263 probabilistic, 52 Berlekamp-Zassenhaus algorithm, 173 quantum, 77, 88, 90–91, 101–102 Bernoulli, Johann, 177 symbolic, 192 black hole, 17, 123, 199–200 analytical engine, 141–142 electrically charged, 208 ancilla bit, 85 Kerr, see rotating anti-hypercomputation thesis, see also rotating, 51, 196, 200–204, 208, 210, 214 physical Church-Turing thesis, 49 Schwarzschild, 200, 203, 208 anti-realism, 43–45 BLAS, see basic linear algebra subprograms Antikythera mechanism, 141 Bloch sphere, 78, 268–269 approximation, 173–177, 179–181, 183–184, blue-shift problem, 210–212 186, 187, 189–191, 193–194, 274 Blum’s speed-up theorem, 160 asymptotic, 180, 191 Bohmian mechanics, see interpretation of error, 181 quantum mechanics, Bohmian feasible, 173 Bohr, Niels, 263 methods in physics, 194 Born rule, 262 solution to a differential equation, 176 boundary layer theory, 175 AR theory, see Abstraction/Representation Bourbaki, Nicolas, 155 theory boxworld, 266–267, 272–273, 276

303

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-17119-0 — Physical Perspectives on Computation, Computational Perspectives on Physics Edited by Michael E. Cuffaro , Samuel C. Fletcher Index More Information

304 Index

BPAS, see basic polynomial algebra criteria for, 117 subprograms feasible BPP (complexity class), 6–7 pattern, 183–187, 190–192, 194 BQP (complexity class), 7 recursive, 187–188 Brillouin, Leon´ , 247 hyper-, 11, 13, 48, 54, 110, 129, 147–148, Brownian motion, 242, 244 168–170, 227 Bub, Jeffrey, 90–92, 258, 262 irreversible, 219 bulk matter, 224, 237 Niagara Falls, 109, 114, 122 objet trouve´, 108 ∗ C -algebra, 258–259 physics of, 219, 227 calculus of variations, 184 relativistic, see also relativistic computer, calculus ratiocinator, 62, 72 17, 195–215 Carnap, Rudolf, 131 reversible, 109, 170 Cauchy, Augustin-Louis, 177 rock, 145–146 CBH theorem, 258–260 slime mold, 16, 139–140, 142–144 cbit, 91, 96 stationary, 109, 114, 118–119, 122 cellular automaton, 13, 16, 25–26, 39–40, quantum, 114 104, 154 super-Turing, 148 number 110, 16, 166–167 symbolic, 174, 190, 192–193 universality proof, 170 unconventional, see computation, exotic Chaitin’s , 165 models of Chalmers, David, 221 universal, 261 characteristic function, 168 vs. scientiﬁc theory, 129 chemotaxis, 139 computational explanation, 84, 86–88, Chinese remainder theorem, 191 100–102 chlorine atoms information storage, 159 computational implementation, 9, 51, 161, CHSH-Bell inequality, 272 220–222, 226–230, 233–235 see also Church, Alonzo, Church-Turing BCC account of, 51 thesis, 14, 64–66 causal account of, 9, 51 Church-Turing thesis, 4, 10–11, 65, 70, 76, 79, counterfactual account of, 9 155, 172, 219 criteria for a logical operation, 116–119 physical, see physical Church-Turing thesis dispositional account of, 9 strong or extended, 6–7 intensional, 18 Clairaut, Alexis, 177, 182 mapping account of, 9, 112–113 classical mechanics, 235 mechanistic account of, 9, 15, 24, 51, Clifton, Robert, 258 83–88, 96, 100, 102 closed computational system, 139–140 Cobham-Edmonds thesis, 5 modally robust, 18 coding function, 156 semantic account of, 9, 24, 51, 130, 136 complexity syntactic account of, 9 see algebraic, 190 computational Pythagoreanism, algorithmic, 159, 173, 185, 190–193 Pythagoreanism, computational see also communication, 260 computational science, scientiﬁc computational, 5, 9, 17, 104, 106–108, computing, 17, 173–174, 187, 192–194 110–111, 153, 161, 168, 170, 173–175, computing system 180, 192–195, 247 quantum, 26–27 computability vs. computer, 24 effective, 2, 4, 10, 14, 64–66, 70, 76, conceptual analysis, 68, 72 172–173 conformal diagram, 207 of nature, 79–80, 274 consciousness, 54 theory, 2, 9, 16–17, 160–161, 165–166, 168, constructive mathematics, 64 169, 173, 192–194, 213 constructive physical theory, see principle computation theory vs. constructive theory analog, 108, 119, 143, 147 constructor theory, 79 exotic models of, 107–109, 114, 126, 148 contextuality, 8, 277

Index 305

continuous computational systems, see electromagnetism, 235 computation, analog empiricism, 132 continuous reversibility postulate, 275–278 encoding of a problem, 136–138, 140–146, control theory, 18 274 controlled operation, 231–233 engineering vs. science and computing, convex hull, 272 136–137 convex-operational framework, 259 entanglement, 8, 26, 90, 92–97, 99, 111, 211, convexity, 268–269 258, 273 cosmology, 224 entropy, 11, 219, 223–226, 232–233, 235–238, counterfactuals, 18, 89, 222, 238 240–241, 243–246, 249 CRT, see recursion theory thermodynamic vs. information theoretic, curve in a differentiable manifold, 205 220 causal, 206 Entscheidungsproblem, 68, 69 lightlike, 206 epistemic humility, 44–45 timelike, 206 Equivalence Principle, 198 cyclic tag system, 167 error analysis, 187 error probability for infinite computation, d’Alembert’s paradox, 175 212–215 d’Alembert, Jean le Rond, 178, 182 error-correction codes, quantum, 116 data, known vs. unknown, 230–231, 237 Euler’s method, 176, 178 Davis, Martin, 157, 168 Euler, Leonhard, 175–178, 181–182, 184 DDMA, see discrete deterministic mechanical evolution, 248 assembly explanation decidable relation, 214 causal, 263 decision problem, 2, 5, 70 structural, 263 Dedekind, Richard, 61 explanatory power, 19, 259, 261–265, density matrix, 266–268, 270, 273–275 278–279 Descartes, Rene,´ 62, 184 determinism, 71, 208–209 feasibly (un)computable problem, 173–174, Deutsch’s principle, 10, 14, 74 181, 184–185, 192 Deutsch, David, 40, 48, 49, 73–74, 76, 79, 258 Feferman, Solomon, 153, 155 Deutsch-Jozsa algorithm, 101 Fermat, Pierre de, 184 diagonal argument, 69, 157 Feynman, Richard, 74, 225, 231, 258 difference engine, 139–142 finite differences method, 177 difference equation, 188–189, 191 finite state automaton or machine, 89, 146, digital particles, 40 161, 169, 195, 221 digital philosophy, see discrete physics floating point number, 189–190, 192 digital physics, see discrete physics Diophantine equation, 168 fluid mechanics, 175, 183 discrete deterministic mechanical assembly, computational, 183 10, 13, 46, 49–51 Fock space, 132 discrete physics, 25, 166 Fourier transform, 190 DTIME, 5 Fredkin, Ed, 32, 166 DTM, see Turing machine, deterministic free energy, 231, 234, 239 Frege, Gottlob, 166 Friedman’s α function, 160–161 Earman, John, 211, 225 see see Friedman’s automaton, ordered partition ECT, Church-Turing Thesis, strong or automaton extended Friedman, Harvey, 160, 163–165, 169 effective procedure, 2–4, 61–62, 226 Fuchs, Christopher, 277 eigenstate, 95 functionalism, computational, 32–33 eigenvalue, 268 Einstein, Albert, 19, 242, 261–262, 264–265, 278 Godel¨ Argument, 54–58 Einstein-tensor, 209 Godel’s¨ incompleteness theorems, 13, 54, 60, Einstein-Tolman method, 234 63, 153

306 Index

Godel,¨ Kurt, 14, 54–56, 60–61, 63–67, 69–70, Halvorson, Hans, 258 79, 161, 172 Hamiltonian, 108, 236, 249, 251 Galois theory, 184 Hamiltonian dynamics, 250–255 Game of Life, 39–44, 47 Hardy, Lucien, 260 Gandy machine, see also discrete deterministic Hartle, James, 53 mechanical assembly, 46–48, 50, 69 Heisenberg’s microscope, 247 Gandy’s principles for mechanisms, 46–52, 69 Heisenberg’s uncertainty principle, 71 Gandy’s thesis, 10–11, 13, 39, 45–49 Heisenberg, Werner, 263 Gandy, Robin, see also Gandy’s thesis, 39, Hensel construction, 191 69–70, 73 Herbrand, Jacques, 14, 63, 64 gate, logical, 77, 86, 221, 269 Herbrand-Godel¨ recursiveness, 64, 155, 161 π/2-phase, 94 physical realization, 161 ADD, 87 Hermitian matrix, 270 AND, 112–113, 122–123, 222, 227 heuristic algorithm, 194 bit-flip (X), 86, 92, 94 hidden variables, 259 Boolean, 126 Higman’s theorem, 160 Clifford group of, 94–95 Hilbert space, 19, 54, 71, 78, 114, 115, 153, controlled-not (CNOT), 86–87, 93–94, 232, 250–251, 253–257, 259, 262, 270 276 Hilbert’s axiomatization of geometry, 169–170 COPY, 227 Hilbert’s finitism, see Hilbert’s program CPHASE, 93 Hilbert’s program, 14, 60, 64, 70 Hadamard (H), 94 Hilbert, David, see also Hilbert’s program, 55, NAND, 167, 227 60–64, 66, 70, 71, 79, 155, 165 OR, 113, 122–123, 222 Hodges, Andrew, 58 quantum, 93 Hogarth, Mark, 209–211, 214 universal set of, 94, 97, 116, 274 hydrogen atom problem, 184 Toffoli (T), 86–87 UNCOPY, 230 ideal objects, 61 unitary, 88 idealism, 131 universal, 227 mathematical, 73 Y, Z, 94 idealization, 234, 239 gbit, 261, 267–271, 273, 276 ignorance probability, 252 general no-signaling theory, 266 index theorem, 156 General Positioning System (GPS), 198 infinite speed-up, 200–202, 204, 210 generalized probabilistic theories (GPTs), 110, information, 148, 206, 211, 240–241, 259–261, 263, 266–276, 278 245–249, 258, 262, 264, 275 geodesic message, 211 causality, 260 geometry, 60–62, 79, 165–167 content, operational definition of, 104 algebraic, 184 erasure of, 224–226, 228, 230–231, 236, analytic, 184 241 differential, 153, 166 meaning and properties of, 120 non-Euclidean, 61 ontological status of, 220 Geroch, Robert, 53 physics of, 15, 103–104, 111, 120, 125 Gibbs entropy, 105 randomness of, 224 see GL, Game of Life semantic and intentional definition of, 138 global time, 208–211 information theory, 19, 103, 104, 107, 115, function, 210 223, 236, 240, 261–263, 277 Goldbach conjecture, 165 quantum, 258, 263, 272–273 see GPT, generalized probabilistic theories information unit existence postulate, gravitational well, 198 274, 275 see GTD, time dilation information-bearing degrees of freedom, 239 halting function, 4, 50, 51, 53, 57, 110, 157, initial value problem, 176 168–169, 197 instrumentalism, 42–45 halting problem, see halting function intentionality, 130

Index 307

interference, 74–77 Leibniz, Gottfried Wilhelm, 62–63, 72–73, complex, 79 78–79 destructive or constructive, 75–76, 79 lightlike geodesic, see also curve in a higher-order, 260 differentiable manifold, lightlike, quantum, 74, 77 202, 210 interpolation, 177, 186, 190 linear algebra, 187 interpretation of quantum mechanics Liouville Equation ψ-epistemic, 19, 257–258, 264–265 classical, 251–254 ψ-ontic, 19, 257, 261–262, 265–266, 279 quantum, 251–254 Bohmian, 89, 257, 265–266 Liouville’s theorem, 19, 224, 240–241, Copenhagen, 257, 263 249–250 dynamical collapse, 257, 265 quantum analog, 241 many worlds, 89, 257, 265 Lloyd, Seth, 28, 40 computational, 8 logic, 239 partial, 19, 261–266, 278 Boolean, 141 participatory realist, 263 non-constructive, 68 quantum Bayesian (QBist), 89, 258, of information processing, 126 264, 266 quantum, 8, 14 intuition, mathematical, 60–63, 67–68 logical positivism, 131 isomorphism, 36, 37, 223 Lorentz transformation, 259 between simulations and physical systems, Lotka-Volterra model, 147 29–32, 36 LP, see Landauer’s principle partial vs. complete, 30 Lucas, John, 54, 58 isothermal compression, 232, 234 isothermal expansion, 232, 234 Mach, Ernst, 42 Mach-Zehnder interferometer, 75 Konig’s¨ lemma, 160 Maclaurin, Colin, 178 Kalmar elementary recursive function, 156 MAPLE, 187, 192 Kant, Immanuel, 60, 62–63, 79 Markov algorithms, 2, 226 Kaufmann, Walter, 244 MATHEMATICA, 187 MATLAB, 187–189 kinetic theory, 264, 265 ode45 Kleene’s Formal system, 226 routine , 188 Kleene’s recursion theorem, 157, 165 matrix mechanics, 257 Kleene, Stephen Cole, 155–156, 168 Maxwell’s demon, 11, 18, 224–226, 231, 234, 240–246, 248–250, 255–256 Kolmogorov’s additivity axiom, 74 see also Kolmogorov, Andrey, 166 Maxwell, James Clerk, Maxwell’s Komar model, 54 demon, 11, 236, 238, 241 MBQC, see quantum computer, Kreisel, Georg, 52 measurement-based Kronecker, Leopold, 61–62 measurement, 70–74, 76, 79, 89–100, 116, 257, 259, 266–268, 270–272, 275–276 L-machine, 220, 223, 229, 231 local, postulate of, 270 probabilistic version, 229 mechanical device vs. physical device, 48 Ladyman, James, 120 mechanism, 85 Lagrange, Joseph-Louis, 182, 184 Mercator, Nicholas, 178 Laguerre polynomials, 185 metamathematics, 61–62 Landauer’s principle, 12, 18, 105–106, 111, metaphysics, 132 116, 219–220, 223–233, 235, 237–240, method of differences, 141 246–247, 249 metric tensor, 205 qualitative version, 223, 233 MH event, see spacetime, Malament-Hogarth quantitative version, 223 mind-body problem, 131 Landauer, Rolf, see also Landauer’s principle, modality, 220–223 12, 19, 103, 148, 154, 230 modular method, 191 language, computational notion of, 5 Monadology, 72–73, 78 Laplace, Pierre-Simon, 182 multiverse, 79

308 Index

nakedly singular event, 208 ordinal number, 155 strongly, 208–209 ordinary differential equation, 184 weakly, 208–209 OSR, see realism, ontic structural nanoscience, 248 Napier, John, 185 P (complexity class), 5 natural philosophy, 73 P vs. NP problem, 153 natural selection, 223 pancomputationalism, 9, 13, 23, 127–129, Navier, Claude-Louis, 175 138, 145–146 Newton’s forward difference interpolation metaphorical form of, 24, 38 formula, 176 ontic, see ontic pancomputationalism Newton’s method, 191 strong form of, 146 Newton, Isaac, 177–178, 181 weak form of, 145 Newtonian mechanics, 154, 170, 201 partial differential equation, 184 No Simultaneous Encoding postulate, 276 nonlinear, 190 no-signaling partial recursive function, 155–157, 168 polytope, 267, 270, 272–273 PC, see pancomputationalism postulate, 270–271, 275 Peano arithmetic, 158, 170 nominalism, 131 Penrose diagram, see conformal diagram non-locality, 96, 259–261 Penrose’s strong Cosmic Censorship normal form, 68 Hypothesis, 209 normal system, 68 Penrose’s thesis, 13, 39, 54–59 Norton’s no-go theorem, 220, 233, 235 Penrose, Roger, see Penrose’s thesis Norton, John, 106, 220, 224–226, 230–238 perturbation theory, 175–177, 181–183 NP (complexity class), 5 phase shift, 77 NTIME, 5 phase space, 19, 249–256 see NTM, Turing machine, nondeterministic accessible, 239 numerical methods, 175–177, 182–184, compression argument, 224–226 188–192, 194 PhCT, see physical Church-Turing thesis geometric, 183 physical Church-Turing thesis, 10–11, 17, 48–49, 58, 74, 195–197, 214 o-machine, see oracle machine bold, 10, 48–49, 52 ontic pancomputationalism, 13, 23–38 modest, 10, 49, 51–52, 195 computational formulation of, 23 super bold, 52–54 digital, 25–26 physical interpretation of computability, see empirical component of, 23–27, 37 computational implementation informational formulation of, 23 physical realizability of a function, 195 metaphysical component of, 24, 27, 37 physical thought experiment, 195 quantum, 26–27, 31 Piccinini, Gualtiero, 49, 84, 87, 209, 212–215 ontology, 89, 131–132, 257, 266, 278 Pitowsky, Itamar, 198 OPA, see ordered partition automaton Planck scale, 25 open-oracle, see oracle machine Plato machine, see also Turing machine, operator accelerating, 197 -valued measure, positive, 270, 275 Platonism, mathematical, 64 density, 251, 253–254 platonism, mathematical (“small ‘p’”), 35 linear, 251 Poincare,´ Henri, 44, 182 projection, 253–255 POLYMAKE, 273 semideﬁnite, 270 Popescu-Rohrlich box, 110, 271–273 oracle gate, see oracle machine Post machine, see Post’s canonical system oracle machine, 56–57, 97–98, 102, 153, Post’s canonical system, 155, 161, 226 157, 168 Post’s Formulation I, 68 cautious, 57 Post’s Problem, 168 ordered partition automaton, 16, 163–165, Post, Emil, 14, 54, 66–69, 79, 168 169–171 POVM, see operator-valued measure, positive hybrid, 164 PR-box, see Popescu-Rohrlich box physical realization of, 165 Prandtl, Ludwig, see boundary layer theory

Index 309

predictability, 208 quantum speedup, 14, 77, 83–84, 90–92, prediction 100–106 abstract, 136 quantum system in science, 132 local preparations postulate, 270 primitive recursive function, 64, 156 preparation procedure, 259, 266, 268 Principia Mathematica, 61, 63 qubit, 7–8, 26, 73, 76–78, 85–86, 88–100, 132, principle of continuity, 73 267–269, 273–275, 278 principle of continuous reversible time qudit, 26 evolution, 19 Quine, Willard Van Orman, 35, 131–132 principle of local causation, see Gandy’s principles for mechanisms ratchet and pawl demon, 242, 247 principle theory, 19 realism quantum mechanics as, 19, 261–266, about computation, 221–223, 239 278–279 about modality, 222–223 thermodynamics as, 236 about representation, 222–223, 228 vs. constructive theory, 261–265 ontic structural, 263 probabilistic modular method, 191 scientific, 131–132, 139 probabilistic physics, 237 recursion theory, 2, 16, 65–66, 153, 155–158, probabilistic theories, 260 172 probability recursively enumerable amplitude, 71, 75–76, 78 degrees, 17, 153 density, 251–254 relation, 214 problem of representation, 87, 104, 112–115, set, 153, 196, 197, 203, 214 118, 122–124 register machine, 2, 154–155, 164 in Church-Turing computability, 115 physical realization, 162–163 in computational theories of mind, 114 universal, 162 in information theory, 115 relativistic computer, see also computation, projection function, 156 relativistic, 214 projection postulate, 71 abstract definition, 205–206 proof theory, 61–62, 153 implementation, 203–204, 210–213 proper time, 197, 206 relativistic machine, see also relativistic see PTM, Turing machine, probabilistic computer, 49–52 Putnam, Hilary, 221–222 relativity, 48, 69, 110, 170, 197–200, 259–261 Pythagoreanism, 34 general, 17, 50, 166, 186, 198, 209, 214 computational, 34–37 special, 198, 208, 262 representability in a formal system, 2 QBism, see interpretation of quantum representation mechanics, quantum Bayesian ambiguity problem, see problem of QPT, see quantum parallelism, thesis representation ′ QPT , see quantum parallelism, thesis asymmetry, 135 quantum annealing, 116 fundamental problem, 132 quantum computer, 258, 274 mapping between physical and circuit, 84–87, 93–98, 101 mathematical objects, 127–128 measurement-based, 84, 92–102, 114, 116 naturalized, 131–132 universal, 11, 72, 74, 78, 107, 116 relation, 127–130, 133, 139–140, 145–146 quantum computing, DiVincenzo’s criteria, scientific, 129–132, 222 115–116 space, 62 quantum correlation table, 260 complex, 77–78 quantum field theory, 132, 183, 259 teleosemantic account of, 223 quantum gravity, 277 representational entity, 128, 139–140, quantum information channel capacity, 107 145–146 quantum parallelism, 8 human, 139–140 process, 89 representational system thesis, 14, 83 closed, 139–140, 145–146 quantum register, 77 open, 139

310 Index

RESET, see information, erasure of anti-de-Sitter, 204, 208–209 reversibility postulate, 273 general relativistic, 196, 198, 205–208 reversible transformations, 266, 269, 272–275, globally hyperbolic, 209 278 Kerr, 203, 212, 215 ribosome, 248 Malament-Hogarth, 50, 110, 198, 200, Riemann hypothesis, 165 206–212 RM, see relativistic machine MH, see Malament-Hogarth Rorty, Richard, 130 Minkowski, 208 Russell, Bertrand, 44 Reissner-Nordstrom,¨ 208 Schwarzschild, 199 Schrodinger¨ equation, 251–252, 255, 269 special relativistic, 198, 206 Schumacher information measure, 126 stably causal, 210 scientific computing, 17, 174, 183, 187, structure, 205, 259 190, 192 spectral gap problem, 53–54, 58 scientific inference, 17, 172, 174, 183, speed bump, 110 187, 194 standard model of particle physics, 166 feasible, 192 state see scientific modeling, 127 entangled, entanglement scientific representation, see representation, fiducial, 85–86, 93, 115 scientific modal properties, 220–221 Searle, John, 29, 221–222 physical self-avoiding word, 160 modal structure, 239 semi-decidable set, see also recursively quantum, mixed, 268 enumerable, set, 168 representational, 128 sense-data language, 131 space, composite, 271 Separation Thesis, and challenges to it, statistical mechanical, 239 105–112, 125 thermodynamic, 221, 229, 236, 237, 239 set theory, Zermelo-Frankel, 63, 165, 197, equilibrium, 249, 250, 253–256 198, 203–204, 211–213 intermediate, 249–250, 255–256 Shannon coding theorems, 115 mixed, 251 Shannon information measure, 105–107, 126 tomography, 275 Shannon theorem, see Shannon information vector, 7–8, 251–252 measure statistical mechanics, 220, 224–225, 231, Shannon, Claude, see also Shannon 233–237, 239–241, 249–251, 253, 278 information measure, 104, 240 quantum, 224, 259 shared epistemic communities, 124 quantum vs. classical Hamiltonian shock wave, 175 dynamics, 251–255 Shor’s algorithm, 7 Steane, Andrew Martin, 84, 90–92, 97 side-channel, 129, 147–149 Sterling number, 163 Sieg, Wilfried, 47, 62 Stern-Gerlach device, 267 simulation, 28–33, 36–37, 49, 52, 74, 79, 97, Stonehenge computer, 141 see also 98, 154, 189, 261, 274 super-computer, Turing machine, quantum, 26 accelerating, 197 simulationism superposition, 26, 71, 73, 76–77, 79, 88–90 see also strong, 31–34, 36 supertask machine, Turing machine, weak, 27–32, 36 accelerating, 49 simulator, universal, 74 Svedberg’s colloid demon, 242 singularity, 201, 208–209 symbol space, 68 slide rule, 185 synchronous transduction, 161 Smoluchowski trapdoor, see Smoluchowski, Szilard’s principle, 240, 245–247, 249 Marian Szilard, Leo, 12, 19, 245 Smoluchowski, Marian, 234, 240–245, 247–249 Taylor series, 175–179 Soare, Robert Irving, 153 Tegmark, Max, 35–36, 42, 170 spacetime, 199 teleological function, 84–87

Index 311

teleosemantics, 223, 228 unitary matrix, 76 thermal physics, see thermodynamics universal bit, 19, 260, 274–276 thermodynamics, 11–12, 18, 219–221, 223, universal characteristic, see also Leibniz, 234–240, 262, 264, 265, 278 G. W., 72, 78 as control theory, 235–238 universal function, 156 as principle theory, 236 universal information quantity, see universal interpretation, 235 bit of computation, 220, 231, 233, 238, universality, 24, 156–157, 162, 164–170 246–249 universe second law, 11–12, 220, 224–225, 231–234, as cellular automaton, 25, 27, 39 236–238, 240–242, 244–246, 249 as mathematical entity, 35–36, 42 probabilistic, 238 as Matrix, 32 statistical, 231, 238 rotating, 209 Thesis M, see Gandy’s thesis ’t Hooft, Gerard, 40 van der Pol equation, 187 time dilation, 17, 197–199 van Fraassen, Bas, 124, 130–132, 222 timelike length, see proper time vector space, 71, 269 TM, see Turing machine veriﬁcationalism, 131 tomographic locality postulate, 270–276 vitalism, 244 topology, algebraic, 184 von Neumann architecture, 16, 141 traveling salesman problem, 194 von Neumann, John, 61, 71, 119, 257 Turing machine, 2–4, 10, 11, 17–18, 45, 47, 49–50, 52, 57, 65–70, 77–78, 89, 104, Wuthrich,¨ Christian, 211 148, 154–158, 160, 164–166, 195–197, Wallace, David, 220, 235–238 205, 213–214, 226 wave equation, non-computability of, 52 accelerating, 197, 210 wave function, 71, 89, 257 deterministic, 5 wave mechanics, 257 nondeterministic, 5–6 Weil conjectures, 184 physical realization, 161–162 Weyl, Hermann, 70 probabilistic, 6, 74 Wheeler, John, 35, 43, 258 quantum, 78, 261, 274 Wittgenstein, Ludwig, 130–132 universal, 4, 28, 40–42, 48, 52, 56, 70, 104, Wolfram’s thesis, 49 106–108, 110 Wolfram, Stephen, 48, 166 Turing’s thesis, see Church-Turing thesis wormhole, 204 Turing, Alan, 14, 24, 39, 46, 54–56, 58, 65–70, 72–73, 156, 168, 226 Zeno machine, see also Turing machine, Twin Paradox, 197 accelerating, 197 two-body problem, 181 Zeus machine, see also Turing machine, accelerating, 197 uncertainty principle, 71, 247 Zuse’s thesis, 13, 39–41, 43–45, 166 undecidability, 157, 164, 166 evidence problem, 41 underdetermination, computational, see implementation problem, 41–45 problem of representation reduction problem, 41 union-ﬁnd algorithm, 159 Zuse, Konrad, see Zuse’s thesis