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Dewdney A.K. Ч Beyond reason. 8 great problems that reveal the limits of science
Dewdney A.K. Ч Beyond reason. 8 great problems that reveal the limits of science

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Ќазвание: Beyond reason. 8 great problems that reveal the limits of science

јвтор: Dewdney A.K.

јннотаци€:

Inventors and engineers have invested centuries of effort trying to build a perpetual-motion machine. They have never succeeded, but without their valiant attempts, a particularly piquant chapter would be missing from this new book on scientific impossibilities. Science-writer Dewdney teases illuminating logic and formulas from the despair of physicists who wish to predict how electrons will dance, from the frustration of computer programmers who want to resolve certain types of yes-no questions, and from the embarrassment of meteorologists who would like to predict next week's weather. Rigorous enough to challenge intelligent readers but not so daunting as to overwhelm the nonspecialist, the investigation of each impossibility clarifies the barriers that forbid further progress along certain theoretical paths, limning the conceptual boundaries of science and even reflecting the limitations inherent in the structure of human rationality. Still, Dewdney concedes a catalogue of scientific impossibilities may just provoke some maverick to do what the greatest scientists have always done: enlarge the limits of the possible.


язык: en

–убрика: ћатематика/ѕопул€рные издани€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2004

 оличество страниц: 224

ƒобавлена в каталог: 28.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"Big O" notation      184 190 199 204
"Logic and the Understanding of Nature" (Hilbert)      159Ч160
"Naturkennen und Logik" (Hilbert)      159Ч160
"On Certain Difficulties of Proof..." (Goedel)      160
"On Comparable Numbers..." (Turing)      173
"On the Constitution of Atoms and Molecules" (Bohr)      66
"paradigm shift"      7
"Period Three Implies Chaos" (Yorke and Li)      89
"social constructions"      7
"Ueber Formal Unentscheldbare Saetze Principia Mathematica..." (Goedel)      160
$E=mc^{2}$ (mass-energy equation)      31
Absolute space and time      41
Abstract systems      6
Accretion of knowledge      6
Ackermann's function      180Ч181
Ackermann, Willheim      149
Aleph zero      140
Algebra      164
Algorithms      174 177Ч179 203 204
Algorithms as computer programs      185Ч190
Algorithms, big-O bottleneck and      198Ч199
Algorithms, binary search      188Ч189 191
Algorithms, complexities of      189Ч190 199
Algorithms, definitions of      165 185 198Ч199
Algorithms, deterministic      199Ч200
Algorithms, exponential      189 204
algorithms, generic      192Ч193 198 201Ч203
Algorithms, nondeterministic      198Ч202
Algorithms, solution      191Ч192
Algorithms, to find largest number in a list      185Ч188
Algorithms, verification stage of      200 202
Algorithms, worst-case instances of      199
Analog computer      205Ч206
Angstroem, Anders      60 65
Annalen der Physik (journal)      45
Archimedes      19 135
Aristotle      36 117 150
Arithmetic      139 146 149 164 170
Arithmetic, consistency      143Ч148
Arithmetic, Goedel's consistency proof      140 150 153Ч158
Arithmetic, transfinite      140Ч142
Aspect, Alain      79
Astronomy      7Ч8
Atom, excited state      70
Atomic theory of Bohr      65Ч66
Atomic theory of Dalton      6 41
Atomic theory of Rutherford      65
Attractors      97Ч104
Bacon, Francis      36
Balfour, William      17
Balmer, Jacob      60 65
Barriers to knowledge      3Ч8
Bell's theorem      75Ч79
Bell, John      75
Bernays, Paul      160
Bessler, Johann Ernst Elias (Orffyreus)      19Ч21
Beukers Ч Bezevin Ч Robba proof      134Ч135
Beukers, Frits      134
Beweisstheorie (Hilbert's theory of proofs)      147Ч148
Bezevin, Jean-Paul      134
Big-O bottleneck      183Ч204
Binary search      188 191
binary search algorithm      188Ч189
biology      7
Black body problem      63Ч64
Bohm's theory      82
Bohm, David      82
Bohr, Niels      64Ч66
Bohr, Niels, atomic structure and      65Ч66
Bohr, Niels, Copenhagen interpretation of      71
Bohr, Niels, EPR thought experiment and      74
Bohr, Niels, quantum mechanics and      62 64Ч66 72
Born, Max      68
Brahe, Tycho      7
Butterfly effect      87
Butterfly metaphor      106Ч107
Calculus      119
Cantor's theorem      142
Cantor, Georg      133 140Ч143
Carnap, Rudolph      149 159
Carnot cycle      30
Carnot, Sadi      28Ч30
Celestial mechanics      7 8 37
Chaos theory      3 6 85Ч112
Chaos theory, attractors and      97Ч104
Chaos theory, butterfly metaphor and      106Ч107
Chaos theory, double pendulum and      98Ч100
Chaos theory, example of      86Ч88
Chaos theory, fractals and      90 97 100
Chaos theory, logistic equation and      90Ч97 101
Chaos theory, researchers in      88Ч90 103Ч108
Chaos theory, sensitivity to initial conditions and      89 95 101
Chaos theory, stretching, folding and      88
Chaos theory, Verhulst equation and      91Ч92
Chaotic systems      See "Dynamical systems"
Charles I, King of England      17
Church's thesis      164 165 177Ч178
Church, Alonzo      69 173
circle      See "Squaring the circle"
Classical physics      24 65 80
Classical physics, conservation of energy and      34
Classical physics, perpetual motion machines and      27Ч28
Classical physics, relativity theory and      59Ч60
Clauser, John      79
Closed-form expressions      2
Color of light      63 64
complex numbers      101 102 131
Complexities algorithms of      189Ч190 199 201Ч202
Complexities reduced to essential size      199
Computers      163Ч180 183Ч206
Computers, algorithms and      185Ч190
Computers, analog      205Ч206
Computers, big-O bottleneck and      183 184 190 198 199 203 204 206
Computers, binary search by      188Ч189 191
Computers, chaos theory simulations by      88
Computers, conceptual birth and development of      165Ч174 178
Computers, fully programmable      164
Computers, future developments in      178Ч179
Computers, intractable problems and      183Ч206
Computers, limitations of      163Ч180
Computers, weather prediction and      103Ч104 108 111Ч112
Conjectures      138 161 164
Conjectures, hypothesis and      140
Consciousness      62 81
Conservation of energy      5 14 27Ч34
Conservation of energy, Helmholtz's law of      30
Constructable      126Ч135 137 138
Continuum Hypothesis      140Ч143
Cook's theorem      193Ч196 199 203
Cook, Stephen      190Ч196 198 199
Cook, Stephen, generic transformation discovery by      192Ч193 198 201Ч203
Copenhagen interpretation      71 72
Copernican theory      7 8 37
Copernicus, Nicolaus      7
Crick, Francis      7
Cromwell, Oliver      117
Dalton, John      6 41
Darwin, Charles      7 91
Data scaling phenomena      89Ч90
Davisson, Clinton      65
de Broglie, Louis      62 64
De Corpore (Hobbes)      118
de Fermat, Pierre      130
Decision problems      165 173Ч177
Decision problems, yes-or-no answers for      191
Deductive science      2 6 7 30
Desaguliers, Jean      19Ч20
Descartes, Rene      36 41Ч42 119
Deterministic algorithms      199Ч200
Dirac transformations      69
Dirac, Paul      69
DNA computers      163 178 179 203Ч204
DNA structure, discovery of      7
Double pendulum      98Ч100
Due Correction for Mr. Hobbes... (Wallis)      118
Dynamical systems      3 6 85Ч90 112 See
Dynamical systems, attractors      97Ч104
Dynamical systems, behavior of      85Ч89
Dynamical systems, boundary between chaotic and nonchaotic behavior in      89
Dynamical systems, double pendulum      99
Dynamical systems, sensitivity to initial conditions of      89 95 101
Dynamical systems, waterwheel example      107Ч108
EDVAC computer      178
Eigenvectors      70
Einstein, Albert, "God does not play dice" quote of      46 60
Einstein, Albert, background of      40Ч41
Einstein, Albert, basic assumptions of      6
Einstein, Albert, energy-mass formulas of      31 55Ч56
Einstein, Albert, gedanken (thought) experiments of      30 40 72Ч74
Einstein, Albert, photoelectric effect paper of      45Ч46 60 64
Einstein, Albert, quantum mechanics and      46 60
Einstein, Albert, relativity theories of      6 45 52 53 57 59
Einstein, Albert, speed of light and      5 6 31 36 42 45Ч46
Electrons      53 59
Electrons, energy level of      63 65 66
Electrons, Lorentz effect and      15
Electrons, measurement/position of      3 60 70 71
Electrons, perpetual motion and      14Ч16
Elements (Euclid)      120
Elenchus Geometriae Hobbianae (Wallis)      118
Empedocles      36
Energy      11Ч34 See
Energy, conservation of      5 14 27Ч34
Energy, Einstein's $E=mc^{2}$ equation      31 52
Energy, exchange of information and      33
Energy, heat as form of      28Ч31
Energy, joules of      32
Energy, kinetic and potential components      5 31 45 55Ч56
Energy, light and      62Ч64
Energy, mechanical      30
Energy, perpetual motion machines and      11Ч34
Energy, quanta of      34 46 63Ч65
Entscheidungsproblem      170 173
EPR (Einstein Ч Podolsky Ч Rosen) thought experiment      72Ч74 76Ч77
Equivalence, problem      191
Ether      41Ч42 44 45 48 49 52
Euclid      117Ч121 127Ч128 149
Euler, Leonhard      149
Everett, Hugh, III      81
Evolution theory      7
Examinatio et Emendatio Mathematicae Hodiernae (Hobbes)      118
Exponential algorithms      189Ч190 204
exponential complexity      190
Exponential growth      183 185 204
Fermat's last theorem      130 139
Finite numbers      155
First International Congress of Mathematics (Zurich)      41
First Men in the Moon, The (Wells)      16
Fisher, Baron      19
Fitzgerald, George      46Ч49 52 57
Fitzgerald, George, Lorentz Ч Fitzgerald transformations and      52Ч56
Fizeau, Armand      39
Fludd, Robert      18Ч19
Foucault, Jean      39
Four-day weather forecasts      108Ч111
Fractals      98
Fractals, coining of term      90
Fractals, definition of      97
Fractals, Mandelbrot set      100Ч102
Frege, Gottlob      145
Fresnel, Augustin-Jean      41 46
Friction      5 13 31 33
Fulton, Robert      22Ч23
Fundamental particles      See also "Electrons" "Photons"
Fundamental particles, Heinsenberg's uncertainty principle and      66Ч68
Fundamental particles, measurement problem      3
Fundamental particles, unpredictability of      6 59 60
Galilean frames      53Ч54
Galileo Galilei      2Ч3 28 30 53
Galileo Galilei, on speed of light      37 39
Galois, Evariste      132
General relativity, theory of      8 57
Generic transformation      192Ч193 198
Geometry      117Ч124 See
Geometry, $\pi$ wars and      117Ч119
Geometry, Euclid and      120Ч121
German Mathematical Union      160
Germer, Lester      65
Goedel number      155Ч158
Goedel's incompleteness theorem      78 153 158Ч161
Goedel's incompleteness theorem, Cantor's theorem and      142
Goedel's incompleteness theorem, language of      139
Goedel, Kurt      139 140 153Ч161 164 165
Goedel, Kurt, background of      148Ч150
Goldbach's conjecture      138Ч139
Goldbach, Christian      138
Golub, Jerry      90
Gravesande, Willem Jakob s'      20
Gravity-blocking material      16
Greece, ancient, light theories      36
Greece, ancient, mathematics      116Ч117
Grundgesetze der Arithmetik (Frege)      145 146
Grundlagen, Die (Neumann)      80
Grundzuege der Theoretischen Logik (Hilbert and Ackermann)      149Ч150
Hahn, Hans      149
Hamiltonian path problem      193
Heat energy      28Ч31
Heisenberg's uncertainty principle      66Ч69
Heisenberg's uncertainty principle, statement of      66
Heisenberg, Werner      62 68
Hilbert space      69
Hilbert, David      69 134 143 146Ч150 159Ч160 164
Hilbert, David, Beweisstheorie (theory of proofs) of      147Ч148
Hilbert, David, twenty-three problem challenge by      140
Hobbes, Thomas      117Ч119
HP (Hamiltonian path problem)      193
Huygens, Christiaan      36 41 46
Hydrogen atom      65Ч66
Hyperspace drive (science fiction)      56
Hypothesis      140
Imaginary number      101 131
Incompleteness theorem      See "Goedel's incompleteness theorem"
Inductive science      6
infinity      140Ч143
Infinity, exponential complexity and      190
Infinity, finite tools and      155
Infinity, fractals and      97
Infinity, mini-Mandelbrots and      102
Integers      129 130 165
Integers, Ackermann's function and      180
Integers, Goedel numbers and      155 157 158
Integers, maximum-integer problem      188
Integers, positive      127 144Ч145
Integers, rational number correspondence      126
Integers, real numbers and      140Ч143 148
Interferometer      43Ч45 48 49
Intractable problems      3 183Ч206
Intractable problems, equivalence among      191
Intractable problems, exponential time and      185 188 204
Intractable problems, finding largest number in a list      186Ч188
Intractable problems, traveling-salesman example      184Ч185
Introduction to Mathematical Philosophy (Russell)      149
Io (Jupiter's moon)      37Ч38
Irrational numbers      116 117 124Ч126
Joules      32
Kant, Immanuel      149
Keats, John      116
Kepler, Johannes      7Ч8
kinetic energy      5 31 45 55Ч56
Kleene, Stephen      60
1 2 3
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