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



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

Àâòîð: Dewdney A.K.

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/Ïîïóëÿðíûå èçäàíèÿ/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 2004

Êîëè÷åñòâî ñòðàíèö: 224

Äîáàâëåíà â êàòàëîã: 28.04.2005

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
"Big O" notation      184 190 199 204
"Logic and the Understanding of Nature" (Hilbert)      159—160
"Naturkennen und Logik" (Hilbert)      159—160
"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      180—181
Ackermann, Willheim      149
Aleph zero      140
Algebra      164
Algorithms      174 177—179 203 204
Algorithms as computer programs      185—190
Algorithms, big-O bottleneck and      198—199
Algorithms, binary search      188—189 191
Algorithms, complexities of      189—190 199
Algorithms, definitions of      165 185 198—199
Algorithms, deterministic      199—200
Algorithms, exponential      189 204
algorithms, generic      192—193 198 201—203
Algorithms, nondeterministic      198—202
Algorithms, solution      191—192
Algorithms, to find largest number in a list      185—188
Algorithms, verification stage of      200 202
Algorithms, worst-case instances of      199
Analog computer      205—206
Angstroem, Anders      60 65
Annalen der Physik (journal)      45
Archimedes      19 135
Aristotle      36 117 150
Arithmetic      139 146 149 164 170
Arithmetic, consistency      143—148
Arithmetic, Goedel's consistency proof      140 150 153—158
Arithmetic, transfinite      140—142
Aspect, Alain      79
Astronomy      7—8
Atom, excited state      70
Atomic theory of Bohr      65—66
Atomic theory of Dalton      6 41
Atomic theory of Rutherford      65
Attractors      97—104
Bacon, Francis      36
Balfour, William      17
Balmer, Jacob      60 65
Barriers to knowledge      3—8
Bell's theorem      75—79
Bell, John      75
Bernays, Paul      160
Bessler, Johann Ernst Elias (Orffyreus)      19—21
Beukers — Bezevin — Robba proof      134—135
Beukers, Frits      134
Beweisstheorie (Hilbert's theory of proofs)      147—148
Bezevin, Jean-Paul      134
Big-O bottleneck      183—204
Binary search      188 191
binary search algorithm      188—189
biology      7
Black body problem      63—64
Bohm's theory      82
Bohm, David      82
Bohr, Niels      64—66
Bohr, Niels, atomic structure and      65—66
Bohr, Niels, Copenhagen interpretation of      71
Bohr, Niels, EPR thought experiment and      74
Bohr, Niels, quantum mechanics and      62 64—66 72
Born, Max      68
Brahe, Tycho      7
Butterfly effect      87
Butterfly metaphor      106—107
Calculus      119
Cantor's theorem      142
Cantor, Georg      133 140—143
Carnap, Rudolph      149 159
Carnot cycle      30
Carnot, Sadi      28—30
Celestial mechanics      7 8 37
Chaos theory      3 6 85—112
Chaos theory, attractors and      97—104
Chaos theory, butterfly metaphor and      106—107
Chaos theory, double pendulum and      98—100
Chaos theory, example of      86—88
Chaos theory, fractals and      90 97 100
Chaos theory, logistic equation and      90—97 101
Chaos theory, researchers in      88—90 103—108
Chaos theory, sensitivity to initial conditions and      89 95 101
Chaos theory, stretching, folding and      88
Chaos theory, Verhulst equation and      91—92
Chaotic systems      See "Dynamical systems"
Charles I, King of England      17
Church's thesis      164 165 177—178
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      27—28
Classical physics, relativity theory and      59—60
Clauser, John      79
Closed-form expressions      2
Color of light      63 64
complex numbers      101 102 131
Complexities algorithms of      189—190 199 201—202
Complexities reduced to essential size      199
Computers      163—180 183—206
Computers, algorithms and      185—190
Computers, analog      205—206
Computers, big-O bottleneck and      183 184 190 198 199 203 204 206
Computers, binary search by      188—189 191
Computers, chaos theory simulations by      88
Computers, conceptual birth and development of      165—174 178
Computers, fully programmable      164
Computers, future developments in      178—179
Computers, intractable problems and      183—206
Computers, limitations of      163—180
Computers, weather prediction and      103—104 108 111—112
Conjectures      138 161 164
Conjectures, hypothesis and      140
Consciousness      62 81
Conservation of energy      5 14 27—34
Conservation of energy, Helmholtz's law of      30
Constructable      126—135 137 138
Continuum Hypothesis      140—143
Cook's theorem      193—196 199 203
Cook, Stephen      190—196 198 199
Cook, Stephen, generic transformation discovery by      192—193 198 201—203
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      89—90
Davisson, Clinton      65
de Broglie, Louis      62 64
De Corpore (Hobbes)      118
de Fermat, Pierre      130
Decision problems      165 173—177
Decision problems, yes-or-no answers for      191
Deductive science      2 6 7 30
Desaguliers, Jean      19—20
Descartes, Rene      36 41—42 119
Deterministic algorithms      199—200
Dirac transformations      69
Dirac, Paul      69
DNA computers      163 178 179 203—204
DNA structure, discovery of      7
Double pendulum      98—100
Due Correction for Mr. Hobbes... (Wallis)      118
Dynamical systems      3 6 85—90 112 See
Dynamical systems, attractors      97—104
Dynamical systems, behavior of      85—89
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      107—108
EDVAC computer      178
Eigenvectors      70
Einstein, Albert, "God does not play dice" quote of      46 60
Einstein, Albert, background of      40—41
Einstein, Albert, basic assumptions of      6
Einstein, Albert, energy-mass formulas of      31 55—56
Einstein, Albert, gedanken (thought) experiments of      30 40 72—74
Einstein, Albert, photoelectric effect paper of      45—46 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 45—46
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      14—16
Elements (Euclid)      120
Elenchus Geometriae Hobbianae (Wallis)      118
Empedocles      36
Energy      11—34 See
Energy, conservation of      5 14 27—34
Energy, Einstein's $E=mc^{2}$ equation      31 52
Energy, exchange of information and      33
Energy, heat as form of      28—31
Energy, joules of      32
Energy, kinetic and potential components      5 31 45 55—56
Energy, light and      62—64
Energy, mechanical      30
Energy, perpetual motion machines and      11—34
Energy, quanta of      34 46 63—65
Entscheidungsproblem      170 173
EPR (Einstein — Podolsky — Rosen) thought experiment      72—74 76—77
Equivalence, problem      191
Ether      41—42 44 45 48 49 52
Euclid      117—121 127—128 149
Euler, Leonhard      149
Everett, Hugh, III      81
Evolution theory      7
Examinatio et Emendatio Mathematicae Hodiernae (Hobbes)      118
Exponential algorithms      189—190 204
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      46—49 52 57
Fitzgerald, George, Lorentz — Fitzgerald transformations and      52—56
Fizeau, Armand      39
Fludd, Robert      18—19
Foucault, Jean      39
Four-day weather forecasts      108—111
Fractals      98
Fractals, coining of term      90
Fractals, definition of      97
Fractals, Mandelbrot set      100—102
Frege, Gottlob      145
Fresnel, Augustin-Jean      41 46
Friction      5 13 31 33
Fulton, Robert      22—23
Fundamental particles      See also "Electrons" "Photons"
Fundamental particles, Heinsenberg's uncertainty principle and      66—68
Fundamental particles, measurement problem      3
Fundamental particles, unpredictability of      6 59 60
Galilean frames      53—54
Galileo Galilei      2—3 28 30 53
Galileo Galilei, on speed of light      37 39
Galois, Evariste      132
General relativity, theory of      8 57
Generic transformation      192—193 198
Geometry      117—124 See
Geometry, $\pi$ wars and      117—119
Geometry, Euclid and      120—121
German Mathematical Union      160
Germer, Lester      65
Goedel number      155—158
Goedel's incompleteness theorem      78 153 158—161
Goedel's incompleteness theorem, Cantor's theorem and      142
Goedel's incompleteness theorem, language of      139
Goedel, Kurt      139 140 153—161 164 165
Goedel, Kurt, background of      148—150
Goldbach's conjecture      138—139
Goldbach, Christian      138
Golub, Jerry      90
Gravesande, Willem Jakob s'      20
Gravity-blocking material      16
Greece, ancient, light theories      36
Greece, ancient, mathematics      116—117
Grundgesetze der Arithmetik (Frege)      145 146
Grundlagen, Die (Neumann)      80
Grundzuege der Theoretischen Logik (Hilbert and Ackermann)      149—150
Hahn, Hans      149
Hamiltonian path problem      193
Heat energy      28—31
Heisenberg's uncertainty principle      66—69
Heisenberg's uncertainty principle, statement of      66
Heisenberg, Werner      62 68
Hilbert space      69
Hilbert, David      69 134 143 146—150 159—160 164
Hilbert, David, Beweisstheorie (theory of proofs) of      147—148
Hilbert, David, twenty-three problem challenge by      140
Hobbes, Thomas      117—119
HP (Hamiltonian path problem)      193
Huygens, Christiaan      36 41 46
Hydrogen atom      65—66
Hyperspace drive (science fiction)      56
Hypothesis      140
Imaginary number      101 131
Incompleteness theorem      See "Goedel's incompleteness theorem"
Inductive science      6
infinity      140—143
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      127 144—145
Integers, rational number correspondence      126
Integers, real numbers and      140—143 148
Interferometer      43—45 48 49
Intractable problems      3 183—206
Intractable problems, equivalence among      191
Intractable problems, exponential time and      185 188 204
Intractable problems, finding largest number in a list      186—188
Intractable problems, traveling-salesman example      184—185
Introduction to Mathematical Philosophy (Russell)      149
Io (Jupiter's moon)      37—38
Irrational numbers      116 117 124—126
Joules      32
Kant, Immanuel      149
Keats, John      116
Kepler, Johannes      7—8
kinetic energy      5 31 45 55—56
Kleene, Stephen      60
1 2 3
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