Outer Limits of Reason (73 page)

Bell, John Stewart, 197

Bell's inequality.
See
Theorem, Bell's

Benedict XVI, Pope, 263, 370n34

Berger, Robert, 313

Berra, Yogi, 15, 204, 356n2

Bierce, Ambrose, 31, 158

Birkhoff, Garrett, 210, 337

Birth of Tragedy, The
, 355n2

Bohm, David, 209, 363n8, 364n16

Bohr, Neils, 181, 186, 189, 191, 207, 214, 232

Bolai, Janos, 259

Boltzmann, Ludwig, 368n10

Bond, James, 92

Boone, William W., 318

Born, Max, 365n19

Bourbaki, Nicholas, 360n7

Brandenburger, Adam, xii, 61–63

Branes, 284

Brooklyn Dodgers, 33

“Brown Penny” (Yeats poem), 135

Bruns, Ernst Heinrich, 171

Brynner, Yul, 56

Bub, Jeffrey, 232

Burtt, E. A., 295, 368n14

Butterfly effect, 163, 166, 232, 342

 

Callahan, Harry, ix

Calude, C., 330

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
, 194

Cantor, Georg, 65, 72–77, 88, 94, 334, 359n4, 360n12

Cardano, Gerolamo, 260, 306

Carroll, Lewis, 161

Causality, x, 5, 161, 225, 231, 288, 365n19

Cayley, Arthur, 261

Chapin, Harry, 161

Churchill, Winston, 297

Church-Turing thesis, 372n22

Clarke, Arthur C., 135

Clauser, John, 200

Clay Institute, 127, 134, 362n6

Clinton, Bill, 31

Cohen, Paul J., 89–90, 94, 360n14

Collapse (quantum), 179, 180–185

Complementarity, 185, 186

Complete, weighted graph, 110, 111, 123

Comprehensible Cosmos: Where Do the Laws of Physics Come From?, The
, 290

Conic sections, 255–257, 269

Consciousness, 193, 194, 204, 279, 285, 362n9

Conservation laws, 194, 289–290

Continental Congress, 49, 358n13

Continuum hypothesis, 88–94, 335, 341, 360n14

Conway, John Horton, 366n26

Cook, Stephen, 127, 361n8

Copenhagen interpretation, 207–208, 212

Copernicus, Nicolaus, 240, 241, 245, 247, 256, 278, 347, 367n37

Cosmological constant, 274

Cretica
, 16

Crick, Francis, 169, 368n11

Cubic formula, 306, 374n10

Curie, Marie, 371n43

Cutland, Nigel, 160, 337

 

d'Alembert, Jean-Baptiste, 258

Dalí, Salvador, 275

Dante, 355n3

Dark energy, 347

Dark matter, 347

Darwin, Charles, 278

Dauben, Joseph W., 94

Davies, Paul, 295

Davis, Martin D., 160, 317, 337

D-Branes, 284

Dedekind, Richard, 359n4

Deduction, 53, 236, 332

Deep Blue, 159

Deity, 262, 263, 266, 280, 287, 294, 360n8, 370n37, 371n47, 373n56

Democratic Party, 33

de Sitter, William, 218

d'Espagnat, Bernard, 232, 233, 365n21

Deutsch, David, 209, 212–213

Diaconis, Persi, 363

Dialetheism, 57

Dialogues Concerning Natural Religion
, 367n33

Dijkgraaf, Robbert, xii, 269

Ding an sich
, 40, 357n5

Dirac, Paul A. M., 232, 242, 252, 254

Distributive law, 210, 267–268, 358n7

DNA, 118, 127, 169, 368n11

Double pendulum, 165, 174

Dreams of a Final Theory
, 262

Dyson, Freeman, 294

 

Eddington, Arthur, 229–230, 235, 244, 246, 290–292, 353, 368n13, 371n43

Ehrenpreis, Leon, xiii, 337

Einstein, Albert, ix, 1, 11, 50, 181, 191–195, 201, 214–233, 244, 246–248, 253, 259, 269, 288, 363n8, 365n19, 367n38, 368n10, 371n43

Eldredge, Niles, 368n16

Elegance, 242, 368n10

Elements
(Euclid), 257

Eliot, T. S., 356n6

Emergence, 169

Empty set, 67

End of science, 249–252

Entanglement, 194–201, 231, 264n18, 365n24

Epicycles, 241, 245

Epimenides, 16, 356n3

Epistemology, 2, 40, 137, 251, 290, 369n23

Equation

cubic, 306

Diophantine, 316, 317

Dirac, 254

linear, 305

Maxwell's, 218

quadratic, 306

quartic, 306

quintic, 306–307

Equinumerous, 68, 71–85, 88

Escher, M. C., 311

Ether, 346

Eubulides of Miletus, 54

Euclid, 257–260, 360n12, 374n5

Euler, Leonhard, 105, 108, 114

Euler cycle, 104–109

Everett, Hugh, III, 208, 283, 286

Experiment

delayed-choice quantum erasure, 204–205, 285, 372n55

double-slit, 176–180, 201, 365n20

EPR, 194–197, 200, 364n17

Kochen-Specker (
see
Theorem, Kochen-Specker)

quantum eraser, 201–205

Schrödinger's cat, 192–194, 208, 364n16

Stern-Gerlach, 186–189

Wigner's friend, 193

 

Falsifiability, 243–246, 250, 369n21

Feedback, 169

Ferrari, Lodovico, 306

Feyerabend, Paul K., 377n11

Feynman, Richard, 176, 370n37

Fictionalism.
See
Nominalism

Fine-tuned universe, 272–295, 372n48

Finnegans Wake
, 356n6

Fixed point machine, 322–329, 341

Flammarion, Camille, 377n14

Flash, The
, 45

Fogelin, Robert, xii, 353

Fractals, 168

Fraenkel, Abraham, 86

Free will, 158, 204–205, 366nn25–28

Frege, Gottlob, 85

Freud, Sigmund, 279, 371n45

Friedman, Harvey, 333, 334

 

Galilei, Galileo, 71, 215–216, 227, 252, 288, 347, 370n24

Galle, Johann, 254

Galois, Évariste, 304–309, 317, 337

Gamow, George, 94, 232

Gardner, Martin, 233, 264

Gauss, Karl Friedrich, 259, 304

Gelfand, Israel M., 265

Gell-Mann, Murray, 207

Gentzen, Gerhard, 332, 335

Geocentrism, 241, 247, 248, 256, 367n37

Geometry, 319

Greek, 297–304

noncommutative (
see
Theory, noncommutative geometry)

non-Euclidean, 259, 264, 269, 360n12

Gibbon, Edward, 297

Gilder, Louisa, 232

Gill, J., 157

Gleick, James, 232

Gödel, Kurt, x, 41, 50, 63, 88, 89, 94, 95, 158, 320, 339

Goethe, Johann, 364n11

Goldbach conjecture, 153, 154, 362n6

Goldilocks enigma.
See
Fine-tuned universe

Goodman-Strauss, Chaim, xii, 337, 374nn12–13

Goodstein, Reuben, 331

Gould, Stephen Jay, 368n16

Grassmann, Hermann, 261

Greene, Brian, 232, 233, 283, 295

Grossmann, Marcel, 259

Group, 307–309

Guide for the Perplexed
,
The
, 368n7

Gurwitz, Chaya, xii

 

Hall, Monty, 57–60

Halt Program, 142–144

Hamilton, William R., 261

Hamiltonian cycle, 113

Hardy, Godfrey H., 26

Harel, David, 133, 134

Hartmanis, Juris, 157

Hatfield, Doug, 192

Hawking, Stephen, x

Hayes, Brian, 337

Heisenberg, Werner, 192, 232, 261

Held, Carsten, 233

Heliocentrism, 240, 241, 247, 248, 256, 367n37

Heller, Alex, xiii, 166, 370n37

Heraclitus, 33

Herschel, William, 253

Hershfeld, Shayna Leah, xiv

Hertz, Heinrich, 264

Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, The
, 283

Hidden variables, 181, 196, 197, 200, 201, 209, 212, 363n8

non-local, 200

Higgs boson, 347

Hilbert, David, 69, 88, 316, 374n14

Hilbert's hotel, 69, 73, 94

Hippasus of Metapontum, 298–299

Hitchhiker's Guide to the Galaxy, The
, 65, 362n4

Hofstadter, Douglas R., 135, 158, 337

Hopcroft, John E., 157

Horgan, John, 295, 355n2, 369n21

Hume, David, 62, 213, 236, 238, 243, 280, 287, 367n33, 371n43, 377n18

Humorism, 346

Hypergeometric functions, xiv

 

I Am a Strange Loop
, 135

Ichthyology, 291

Incommensurability, 247–249

Induction.
See
Problem, induction

Infinite loop, 139–146, 157, 362n2

Infinity, 65–95, 271, 272, 331, 332, 342, 344, 375n21

countable, 72–78, 80, 151, 152, 175, 329, 345, 375n19

uncountable, 77–85, 151, 152, 175, 329, 345, 375n19

Instrumentalism, 212–213

Interference effect, 177–178, 180, 201–205

Io (moon of Jupiter), 217

 

Jacobi, Carl, 304

Jefferson, Thomas, 334

Jeopardy
, 159

Joyce, James, 356n6

Jupiter, 217

 

Kac, Mark, 370n37

Kant, Immanuel, 1, 250, 287, 357n5, 361n3

Kasparov, Garry, 159

Keisler, H. Jerome, 61–63

Kepler, Johannes, 241, 255–257, 262, 266, 269, 368n11

Kirby, Laurie, 331

Kirk, Captain James Tiberius, 219

Kneiphof Island, 104, 361n3

Kochen, Simon, 188, 191, 366n26

Königsberg, 104, 361n3

Kuhn, Thomas S., 246–249, 250, 369n18

 

Lambert, Johann Heinrich, 258

Laplace, Pierre-Simon, 162–163, 166, 363n3

Law of excluded middle, 53

Lawvere, F. William, 29

Lawyers, 52, 276, 281

Lederman, Leon M., 295

Legendre, Adrien-Marie, 258

Length contraction, 219–223, 227

Leslie, John, 279

Let's Make a Deal
, 57

Leverrier, Urbain, 245, 253–254, 263

Levin, Leonid, 127, 361n8

Libet, Benjamin, 366n28

Life of the Cosmos, The
, 284

Lightyear, Buzz, 65

Limitations

absolute, 335–336, 376n22

of intuition, 342–343

mental-construct, 340–343

physical, 340, 343

practical, 342

relative, 335–336, 376n22

Lindermann, Ferdinand von, 303

Little Red Riding Hood, 93

Lobachevsky, Nicolai Ivanovitch, 259

Locality, 194–201, 208, 209, 213

Logarithm, 101

Logic, 320–331

fuzzy, 56

paraconsistent, 57, 63

quantum, 210–211

three-valued, 56

Lorenz, Edward, 163

Love Song of J. Alfred Prufrock, The
, 356n6

Löwenheim, Leopold, 375n20

Lucian of Samosata, 363n7

Luthor, Lex, 119

 

Mac Lane, Saunders, 337

Magnum Force
, ix

Maimonides, Moses, 368n7

Mandelbrot set, 166–168, 367n35

Manin, Yuri I., 233, 237

Manson, Neil, 287

Many-worlds hypothesis.
See
Multiverse

Marx, Groucho, 12

Marxism, 244

Mass-energy equivalence, 225–226

Materialism, 193

Mathen, Jolly, 372n51

Matiyasevic, Yuri, 317

Matryoshka doll, 274

Maxwell, James Clerk, 218

Measurement, 184, 186, 189, 191, 196, 198–200, 208

Mendelson, Elliott, 337

Mickens, Ronald E., 295

Mickey Mouse, 40, 92

Milky Way galaxy, 235, 282

Modus ponens, 53–55, 117, 327, 341

Morgenbesser, Sidney, 371n41

Morissette, Alanis, 363n2

Morphogenesis, 169, 232

Multiverse, 208–209, 212, 282–287, 294, 347, 372n53

Mutilated chessboard puzzle, 2–4, 340, 356n4

 

Nash, John, 339

Natural selection, 284

Nearest neighbor heuristic, 129–130

Neptune, 253–254, 263

Newton, Isaac, 1, 162, 166, 170, 171, 226, 237, 241, 244–249, 253, 263, 345

Nietzsche, Friedrich, 355n2

Noether, Emmy, 289, 290, 371n43

Nominalism, 92–94, 360n11

classical, 39–40

extreme, 39–40

Non-locality, 194–201, 209, 213, 364n18, 365n23

Normal science, 246–248

Nørretranders, Tor, 366n28

Novikov, Pyotr, 318

Number

algebraic, 303–304, 345

complex, 167–168, 181, 205, 260, 261, 264, 292, 293, 363n5, 373n4, 374n9

constructible/Euclidean, 302–303

Gödel, 323–327

Hamiltonian/quaternion, 261

imaginary, 205, 260, 347

irrational, 70, 298–301, 337

negative, 72–73, 91, 271–272, 347, 357n7, 360n10

transcendental, 303–304, 345

 

Occam's razor, 208, 212, 240–242, 250, 264, 285, 357n4, 368n7

On the Einstein-Podolsky-Rosen Paradox
, 197

Oracle, 152–157, 212–213, 252

Ornithology, 236–237, 238–240, 367n2

Outer Limits of Reason, The
, 12, 377n15

Oxford English Dictionary
, 5, 13

Oxymoron, 15–16

 

P
=?
NP
question.
See
Problem,
P
=?
NP

Parade Magazine
, 57, 63

Paradigm shift, 246–249, 250

Paradox, 5–8, 11, 13, 360n12

Achilles and the Tortoise, 45–46

arrow, 46–47

bald-man, 53

Banach-Tarski, 90–94

barber, 19, 20, 23, 340, 344, 357n4

Berry, 26–27, 340

Brandenburger-Keisler, 61–63

coastline, 214–215

crocodile's dilemma, 173

dichotomy, 41–45

Epimenides, 16

Fermi, 372n49

grandfather, 49

Grelling's, 20–23, 340, 341

Hempel's, 238–240

heterological, 20–23, 340, 341

interesting number, 26, 340

liar, 7, 10, 15–20, 28, 60, 141, 144, 173, 340

linguistic, 15–22, 344

Löb, 327–328, 341

of nirvana, 376n6

ravens, 238–240

reference-book, 22, 23, 340

Richard's, 27–28, 340, 357n9

Russell's, 22, 23, 85–86, 88, 341, 344