Outer Limits of Reason (74 page)

self-referential, x, 7–8, 15, 60, 62, 63, 173, 343–344

small-number, 55

sorites, 53–56, 340

sorites-type, 55, 340

stadium, 47–48

surprise-test, 60–61, 63

time-travel, 31, 49–50, 63, 340, 344

of tolerance, 376n6

twins, 222

Wang's, 55

Yablo's, 24–26

Zeno's, 7, 31, 41–49, 62, 91, 340, 360n10

Parallel postulate, 258

Parikh, Rohit, xi, 63, 326–327, 337, 359n20, 370n38

Paris, Jeff, 331

Parmenides, 41, 48, 242

Pascal, Blaise, 65, 339, 359n1, 371n43, 371n47, 376n1

Pasteur, Louis, 245, 247, 347

Peano, Giuseppe, 320

Peano Arithmetic, 320–328, 330–335, 375n21

Penrose, Roger, 158, 160, 232

Pensées
, 359n1, 376n1

Perelman, Grigori, 361n10

Philosophy of science, 235–252, 294

Phlogiston, 346

Phrenology, 346

Pickering, Andrew, 232, 295

Piggybacking, 8–9, 316, 332, 343.
See also
Reduction

Pinocchio, 93

Planck, Max, 206

Planck's energy, 373n4

Planck's length, 44, 373n4

Planck's time, 373n4

Plato, 91, 263

Platonism, 91–94, 263–265, 284

classical, 38–40

extreme, 38–40, 357n4

Plato's attic, 52, 263, 264, 357n4

Podolsky, Boris, 194

Poincaré, Henri, 161, 163, 171, 235

Poincaré conjecture, 361n10

Point of view invariance, 290

Polarization filters, 182–185, 201–205

Popper, Karl, ix, 238, 241–243, 250

Positron, 254, 272

Post, Emil, 321

Poundstone, William, 13, 29, 133

Pour-El, Marian, 337

Powerset, 67–68, 80–83

Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?
, 163

Pressburger Arithmetic, 328

Priest, Graham, 56, 63, 353

Principle

anthropic, 278–295, 368n8, 372n48

Copernican, 279

Heisenberg's uncertainty, 185–186, 188, 189, 198

mediocrity of, 279

parsimony of (
see
Occam's razor)

participatory anthropic, 285–287, 371n46, 372n55

strong anthropic, 278, 285

weak anthropic, 278–295

Problem

decidable, 139, 152

decision, 113

doubling a cube, 302, 303, 335

Equivalent Program, 149–150

Euler Cycle, 107, 114, 128

Euler Path, 108

exponential, 116–120, 124, 127–128, 132, 157

factorial, 111, 118, 127–128, 132, 156–157

feasible, 109

Halting, 136–160, 315, 316, 343, 344, 351, 362n2

Halting Problem for Halt Oracle Programs, 154

Halting Problem for Halt′ Oracle Programs, 155

Hamilton Cycle, 113–115, 123–124, 128

Hilbert's Tenth, 316–317

of identity, 32–40, 62

induction, 236–240, 250, 287

infeasible, 109

intractable (
see
infeasible)

Königsberg Bridge, 105–108, 133

measurement, 179, 208

Millennium, 127, 134, 361n10, 362n6

Monty Hall, 57–60, 63, 342

n-body, 170, 172

NP
(nondeterministic polynomial), 117–128, 133, 134, 155, 156, 361n6

NP-Complete, 125–131, 133

optimization, 113

P
, 109, 117, 119, 126, 133, 155, 156

P
=?
NP
, 127–128, 134, 156, 157, 361n9

of personal identity, 34–40, 62

polynomial, 109, 117, 119, 126, 133, 155, 156

Printing 42 Problem, 146–147

PSPACE
, 132

Satisfiability, 117, 127

Set Partition, 115–116, 121, 130

squaring the circle, 302, 303, 335

Subset Sum, 116, 121

superexponential, 131

three-body, 169, 170–172, 174, 232

tiling, 309–316

tractable, 109

Traveling Salesman Problem, 109–113, 119, 123–125, 129, 350

trisecting an angle, 302–303, 335

two-body, 170, 174

undecidable, 139, 152, 160, 315–319

unsolvable, 136–140, 172, 343, 345

word problem, 318–319

Zero Program, 147–150

Proof

by contradiction, 6, 42, 77, 80

by stereographic projection, 84

diagonalization, 66, 78–83, 85, 144, 323

necklace, 75, 76

sunshine, 84

zig-zag, 74, 76

Pseudoscience, 244

Psychoanalysis, 244

Ptolemy, 247, 257

Punctuated equilibrium, 368n16

Putnam, Hilary, 317

Pythagoras of Samos, 284, 298

 

Quantum computers, 120, 134, 336

Quantum gravity, 158, 231–232

Quantum leap, 44

Quantum mechanics, x, 5, 44–49, 120, 161, 174, 175–214, 231–232, 237, 243, 247, 249, 254–255, 260–262, 263, 277, 285, 290, 292–293, 340, 342–343, 347, 363n8, 364n16, 368nn7–8, 373n4

Quantum physics/quantum theory.
See
Quantum mechanics

Quine, Willard Van Orman, 7, 17

 

Rabinowitz, Avi, xii

Raise High the Roof Beams, Carpenters
, 372n48

Ramanujan, Srinivasa, 26

Randi, James, 377n13

Realism, 91

Realism, naïve, 186, 209

Reductio ad absurdum
, 6, 42, 77, 80

Reduction, 9, 147–150, 315, 343, 345.
See also
Piggybacking

polynomial, 121–128 (
see also
Piggybacking)

Regular polygon, 307–308

Relative statement, 51

Rescher, Nicholas, 294, 353, 364n10

Revolutionary science, 246–247

Rice, Henry, 150

Riemann, Bernhard, 259

Riemann hypothesis, 36n6

Rivest, Ron, 119

Robinson, Julia, 317

Rømer, Ole, 217

Rosen, Nathan, 194

Rosser, John B., 375n18

RSA, 119

Rubik's cube, 309

Rucker, Rudy, 50

Ruffini, Paolo, 306, 316

Russell, Bertrand, 15, 19, 22, 85, 368n13

 

Saari, Donald G., 172

Saccheri, Girolamo, 258

Sainsbury, R. M., 29, 63

Salinger, J. D., 372n48

Salk, Jonas, 349

Savalas, Telly, 56

Schopenhauer, Arthur, 377n18

Schrödinger, Erwin, 192

Selective subjectivism, 290

Self-organizing, 169, 232

Self-reference, 12, 13, 18, 28, 140, 141, 150, 158, 160, 298, 320–333, 343, 345, 374n17

Semmelweis, Ignaz, 347

Sensitive dependence on initial conditions.
See
Butterfly effect

Sentence

Gödel, 324–326, 331–333, 351

Gödel-Rosser, 375n18

Löb, 327

Parikh, 326–327

Quine's, 15, 16

Tarski, 323–324

Shainberg, Lawrence, 160

Shakespeare, William, 355n3

Shamir, Adi, 119

Shape

kite and dart, 312–314

Myers, 311, 312

rhombuses, 313

Shaw, George Bernard, 369n20

Ship of Theseus, 32–40, 52, 62, 342, 357n2

Simon, Carly, 18

Simplicity, 240–242

Simplicity of hypothesis, 241, 285

Simplicity of ontology, 241, 285

Simpsons, The
, 276, 277

Simultaneity, 224–225

Sipser, Michael, 160

Six degrees of separation, 107

Smollin, Lee, 284

Solipsism, 369n23

Solipsism of the present moment, 369n23

Solovay, Robert, 157

Sorensen, Roy, 13, 29, 63

Spacetime, 223, 228–230

Space, Time and Gravitation
, 291

Specker, Ernst, 188, 191

Spin (quantum), 187–191, 194–201, 208

Spock, Mister, 352

Spontaneous generation, 346

Spooky action at a distance.
See
Non-locality

Statistical mechanics, 172, 174, 232

Stellar nucleosynthesis, 274, 284

Stenger, Victor J., 290

Stewart, Potter, 359n16

Straightedge and compass, 301–304, 307, 335

Streep, Meryl, 371n43

Structure of Scientific Revolutions, The
, 246

Sudbery, Anthony, 233

Sudkamp, Thomas A., 160

Sundman, Karl, 172

Superposition, 120, 176–214, 285, 347

Supersymmetry, 348

Symbolization, 320–321

Symmetry, 242, 287–293, 307, 308, 318

System

binary star, 218

chaotic, 164, 175, 181, 351

deterministic, 165, 172, 174, 180–185, 206, 210, 231, 286, 363n8

integrable, 164, 174

predictable, 165, 166, 172, 174

random, 166, 174, 180–185, 206, 209, 231, 340, 363n8, 366n25

stable, 164, 174

Szilárd, Leó, 372n49

 

Tartaglia, Niccolò Fontana, 306

Tegmark, Max, 209, 284, 285, 295

Teleological argument, 280

Tenenbaum, Stanley, 337

Tequila, 158, 277

Theorem

Bell's, 197–201, 209, 233, 365n21

Cook-Levin, 127

downward Löwenheim-Skolem, 375n20

Edge-of-the-wedge, xiv

Free-Will, 366n26

Gödel's first incompleteness, x, 298, 324–326, 327, 329, 330, 332, 334–335, 337, 344

Gödel's second incompleteness, x, 88, 331–334, 335, 337

Goodstein's, 330–331, 333, 337

Kochen-Specker, xiv, 186–192, 233, 365n20

Parikh's, 326–327

Pythagoras', 298

Rice's, 150, 160

Tarski's, 323, 337

Theory

chaos, 161–175, 232, 342, 351

electromagnetic, 218, 264, 363n8

Galilean relativity, 215–216

Galois, 304–309, 335

general relativity, 226–231, 237, 243, 246, 288

Grand Unified Theory (
see
Theory of Everything)

graph, 106–107, 118, 252

group, 232, 252, 262–263, 290, 317–319

loop quantum gravity, 232

noncommutative geometry, 232

quantum theory (
see
Quantum mechanics)

relativity, x, 5, 48, 49, 161, 214–233, 249, 254–255, 260, 288, 342–343, 347

set, 66–95, 328, 331, 348, 359n4, 360n12

special relativity, 217–226, 254, 271, 288

string, 232, 242–243, 250, 254–255, 269, 284, 286, 295, 347

Theory of Everything (TOE), 231, 233, 243, 250, 254–255

Zerrmelo-Fraenkel set theory, 86–94, 359n6, 362n7

Zerrmelo-Fraenkel set theory with choice, 90–91, 332–336, 375n21

Theseus, 32–40, 342

Thought and Language
, 356n6

Through the Looking Glass
, 10

Tierney, John, 63

Tiles, 309–316

aperiotic, 312–316

Tilings, 309–316

nonperiodic, 312–314

periodic, 312

Time dilation, 219–223, 227

Tiramisu, 371n43

Toy Story
, 65

Tractatus Logico-Philosophicus
, 15, 376n8

Transitivity of identity, 35, 359n17

Turing, Alan M., 139–140, 152, 155, 160, 169, 232

 

Unicorn, 40, 93, 377n16

Unreasonable Effectiveness of Mathematics in the Natural Sciences, The
, 253

Uranus, 245, 253

Urban VIII, Pope, 347

USS Constitution
, 357n1

USS Intrepid
, 357n1

 

Vagueness, 11, 31, 40, 50–57, 63, 340, 341, 360n14

epistemic, 52, 55, 364n13

ontological, 52, 364n13

van Gogh, Vincent, 38

Verne, Jules, 262

von Neumann, John, 210, 280

vos Savant, Marilyn, 57

Vygotsky, Lev, 356n6

 

Wang, Hao, 376

Wang, Quidong (Don), 172

Wapner, Leonard M., 94

Washington's Ax, 33

Watson, 159

Watson, James, 169, 368n11

Webb, Stephen, 372n48

Webber, Andrew Lloyd, 371n43

Weinberg, Steven, 235, 294, 368n11, 369n19

Weyl, Hermann K. H., 242, 305, 321, 360n8

Wheeler, John Archibald, 237, 285, 355n2

Whitehead, Alfred North, 97

Wholeness Postulate, 176, 180, 200, 202, 204, 206

Wigner, Eugene Paul, 193, 253, 264, 266, 290

Wigner's unreasonable effectiveness, 253–272, 295

William of Ockham, 240, 250, 367n7

Wittgenstein, Ludwig, 175, 356n6, 376n8

Wojtowicz, Ralph, xii

Wright, Steven, 12

Wright brothers, 245

 

X-Files
, 372n49

Xia, Zhihong (Jeff), 172

 

Yablo, Stephen, 24

Yanofsky, Hadassah, xiv, 227, 228, 286, 370n29, 372n54

Yanofsky, Rivka, xiv, 372n54

Yeats, William Butler, 135

Young, Thomas, 176

 

Zeno of Elea, 5, 41–49, 90, 359n19

Zerrmelo, Ernst, 86

Zorba the Greek
, 1