The Clockwork Universe

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The Clockwork Universe Page 32

by Edward Dolnick


  Hooke in charge at Royal Society, 59

  new focus on, 61–65

  on poison, 81

  as stunts, 81–82

  vacuum chamber, 4, 59–60, 65, 198n

  Eyam, England, 27–28

  eyeglasses, 107–8

  falling objects, 178n

  acceleration, 93, 96, 209, 254–56

  all objects fall at the same rate, 187–89

  Galileo’s experiments, 172–79, 178, 183–86, 184, 187–89, 200

  Galileo’s law of motion, 174–75, 178, 186n, 244–46, 245, 253–55, 276

  mathematical laws for, 124, 186n

  Newton’s laws of motion and, 180–81, 180, 181, 341n 181

  parabolic paths, 178, 179, 245, 246, 256–57

  televising Olympic divers, 188–89

  vacuum chamber and, 188

  Farriner, Thomas, 30

  Federalist papers, 316

  Fermat, Pierre de, 42, 138n, 226

  Fermat’s Last Theorem (Aczel), 138n

  Feynman, Richard, 94n, 96, 330n 68, 334n 96

  fire

  as common cause of death, 8, 9

  day of judgment and, 19

  as divine punishment, 9

  fighting methods, 31–32

  Great Fire of London, xiv, 29–33

  Flamsteed, John, 75

  Fontenelle, Bernard de, vii, 111, 111n

  force, 91, 95, 156, 174, 180, 180. See also gravity

  Franklin, Benjamin, 239, 316

  Frederick the Great, 45

  Freud, Sigmund, 112

  Gadbury, John, 17

  Galen, 80

  Galileo, xiii, xviii, 5, 93, 96, 97, 145, 159n, 169–79, 304–5

  abstraction and, 198–99, 305, 342n 198

  birth, xiii, 169

  character and personality, 169–70

  clockwork universe and, 182–83

  death, xiii, 98

  experiments with falling objects, 172–79, 178, 183–86, 184, 187–89, 200

  God as mathematician and, 124, 125

  infinity and matching technique, 203–5, 204, 207, 207

  Kepler and, 170

  law of falling objects, 40–41, 172–79, 185–86, 186n, 189, 190, 253–55, 276

  law of pendulums, 183

  Leaning Tower of Pisa and, 184, 187, 188, 244

  mathematics and, 41, 95, 124, 132, 182

  microscope and, 117–18

  movement of the Earth and, 170, 172

  music and, 183

  new star and, 107

  objective reality and, 94

  planetary orbits and, 164

  refutes Aristotle, 93, 94, 172, 188

  telescope and discoveries, 99, 102, 105–13, 110

  telescope and military uses, 108–9, 335n 109

  theory of relativity, 171–72

  trial of, xiii, 98, 205

  worldview, 197–99

  Galle, Joseph, 315

  Gardner, Martin, 143

  Gauss, Carl, 143n

  Geometry (Descartes), 228

  George I, 261, 262–63

  George II, 264

  Gilbert and Sullivan, 228n

  Gillispie, Charles C., 94–95, 183, 297

  Gingerich, Owen, 156

  Glanvill, Joseph, 84, 85n, 111

  God, 327n 35

  chain of being and, 121–23

  clockwork universe and, 182–83

  cosmic harmonies and, 158n

  as creator/controller/designer, 37–38, 37n, 39, 41, 111, 117, 119, 121–25, 126, 127, 128, 154, 235–36, 277, 294, 303, 310–13

  as creator of perfection, xvii, 35, 41, 101, 117, 121, 124–25, 130, 132, 144, 234, 274, 312, 327n 35, 344n 234

  divine messages, 9–10, 29, 30, 33

  divine punishment, xv, 9, 27, 33, 76, 327n 35

  evolutionary theory and, 309

  existence of, 38, 127

  gravity and, 310–13, 315, 316, 317

  laws of nature and, xvii, 37, 124–26, 132

  Leibniz on, 123–24

  as mathematician, 39, 41, 121–25, 127, 132, 157, 294

  miracles and, 311

  Newton on, 273–74, 308, 310–13

  new views of the universe and, 99

  seeking through science, 132, 134, 144, 307–13, 320

  seventeenth century theology and, 10–12

  world as God’s riddle, 143–44, 146, 169, 234, 320

  Graham, Ronald, 229

  graphs, 194

  cannonball’s flight, 213–14, 214

  Cartesian coordinates, 194, 341n 193

  Descartes and, 191–92, 194, 200, 212–13, 213

  Galileo’s rule (d = 16 t2), 245

  slope and, 212–13, 213

  gravity

  baffling nature of, 301–6, 302n

  confirmation by Le Verrier, 315

  God and, 310–13, 315, 316, 317

  inverse-square laws and, 274–75, 279

  moon and, xiv, 273–77, 276, 305

  Newton’s theory, xiv, xvii, 35, 36, 48, 127, 229, 271–77, 276, 283–85, 294, 301–6, 315

  as weak force, 304

  Greece, ancient

  infinite as taboo, 201–2, 253

  manual labor and utility, 40, 327n 40

  mathematics in, 39–40, 42, 129, 135–39, 142, 143

  music in, 129, 129n

  order in the heavens and, 90–91, 91n

  Greece, ancient (cont.)

  physics of, 91

  planetary orbits and position of stars, 102

  secrecy about mathematics, 67n

  square root of 2 and, 67n

  “wisdom of the ancients” and, 36

  Gulliver’s Travels (Swift), 87–88

  Hall, A. Rupert, 199, 297, 342n 198

  Halley, Edmond, 278, 279

  calculus and, 257

  diving bell and other accomplishments, 280

  Newton and, xiv, 279–80, 288–90, 291, 293, 296

  Hamlet (Shakespeare), xiii

  Hardy, G. H., 135

  Harmony of the World, The (Kepler), 134

  Harriot, Thomas, 239n, 345n 239fn

  Harvard University, 54

  Harvey, William, 54

  Hawking, Stephen, 115

  Heisenberg, Werner, 129–30, 132, 229

  Henry, John, 303

  Hippasus, 67n

  Hobbes, Thomas, 72, 327n 37

  Hodges, Nathaniel, 24

  Holland, 21

  Hooke, Robert, 4, 59, 86

  on aim of science, 69–70

  appearance, 75, 291

  argument for secrecy, 68

  character and personality, 290–91

  feuds with Newton and others, 75, 290–92, 293

  inverse-square laws and planetary orbits, 279, 280, 289, 290

  microscope and, 114–15, 118, 118–19

  Royal Society experiments, 59, 66

  study of art, 70, 70n

  vacuum chamber, 4, 59–60, 65

  Houtermans, Fritz, 67–68, 330n 68

  Hudson, Henry, 107

  Huxley, Aldous, 319

  Huxley, Thomas, 127

  Huygens, Christiaan, 75, 240, 305

  Hydrostatical Paradoxes (Boyle), 83

  infinity, 200–209, 202, 216n, 219–21

  Galileo and, 203–5, 204

  God and, 234, 344n 234

  Greek’s fear of, 201–2, 253

  Leibniz and, 222–23

  mathematical limits and, 219–21, 224

  mathematics and, 208

  motion and, 202, 208–9, 225

  Newton and, 222

  paradox and, 203

  points on a line and, 207, 207–8

  Zeno’s paradox, 201–2, 215, 215–16, 219–21

  Inquisition, xiii, 205, 314

  inverse-square laws, 228, 274–75, 277, 279, 280, 281–82, 282n, 286, 289, 290, 292, 294

  Italy

  burning of Giordano Bruno, 314

  Galileo’s, 171

  plague (bubonic plague), 21

  scie
ntific decline in, 98, 334n 98

  trial of Galileo, xiii, 205

  Jefferson, Thomas, 316

  Johnson, Samuel, 73

  Jonson, Ben, 75

  Joyce, James, 205–6

  Keats, John, 95

  Kepler, Johannes, xviii, 5, 41, 145–68, 304–5

  birth, xiii

  character and personality, 146, 158–59

  clockwork universe and, 182

  death, xiii

  escape into abstractions, 134

  idea about force propelling the planets and, 156

  as imperial mathematician, 165

  laws of, xiii, 158n, 162–68, 169, 182, 190, 275, 294

  mother’s imprisonment, 134

  Mystery of the Universe, 155–56, 160

  patterns and, 157–58

  planetary orbits and, 146–56, 147, 149, 150, 151, 154, 158, 162–68, 164, 165, 275, 278, 281

  theory of, 155

  Tycho Brahe and, 158–61

  Keynes, John Maynard, 48, 56

  King Lear (Shakespeare), 231

  Kircher, Athanasius, 79, 79–80

  Kline, Morris, 10, 131

  Koestler, Arthur, 101, 339n 145

  Kuhn, Thomas, 99

  Laplace, Pierre-Simon, 73n, 316–17, 331n 73

  Laws (Plato), 327n 40

  laws of nature, xvii–xviii

  cosmos ordered by, 34–35

  as few and simple, 124–25, 126, 132

  Galileo’s law of pendulums, 183

  Galileo’s on motion, 40–41, 173, 185–86, 189, 294

  as God’s mind, xviii, 35, 132, 143–44, 146

  Greeks and geometry, 130, 130

  Kepler’s laws, xiii, 158n, 162–68, 169, 182, 190, 294

  in mathematical form, 123–24

  Newton’s laws of motion, 42–44, 173–74, 179–81, 180, 181, 294

  Pythagorean theorem and, 142

  randomness discounted, 127–28

  Leeuwenhoek, Antonie van, 114, 115, 115n, 223

  microscopic world and, xiv, 114, 115–16, 336n 114

  sperm cells seen by, 115–16, 116n, 336n 115

  Vermeer and, 115n

  Leibniz, Gottfried, 34–35, 47, 233–44, 303, 328n 47

  alchemy and, 55

  appearance, 46, 239

  “best of all possible worlds,” 234, 235, 327n 35

  binary language and computer, 239, 239n

  birth, xiv, 239

  calculus discovery published, xiv, 242, 243, 268

  calculus invented, xiv, 43–44, 47, 241–52, 268

  calculus notations, 268–69, 268n

  Candide and, 235

  Caroline, Princess of Wales and, 263–65, 317–18

  character and personality, 46, 225, 239–40, 268

  Clarke correspondence, 265

  Collected Works, 238

  Leibniz, Gottfried (cont.)

  death, xiv, 317, 318

  as genius, 46–47, 233, 237, 238–39, 241

  God, view of, 123–24, 234, 235–36, 312

  gravitational theory and, 303, 305, 306

  Hanoverian court and, 261–64, 346n 262

  infinitesimals, 222–23, 241

  mathematics and, 240–42

  “miracle year,” xiv, 241

  on music, 183n

  on nature, 125

  Newton and, xiv, 75, 242–43, 259–70, 306, 308, 310–13, 317

  reputation, 317

  style as frenetic, 47, 238

  talents and accomplishments, 45–46, 237–39

  vacuums and, 198n

  Websites, 344n 237, 346n 262

  Lely, Peter, 70n

  lenses, 107–8, 114

  Le Verrier, Urbain, 315

  L’Hôpital, Marquis de, 320

  light

  angles of, 130, 130, 131, 131

  brightness of, 274

  Newton’s properties of, 48, 51, 74, 136, 291

  speed and medium for, 131, 131

  Lincoln, Abraham, 219

  Locke, John, 52, 176, 288

  London

  bear- and bull-baiting, 80

  buildings and structures, 31

  coffeehouses, 278–79, 278n

  as disease-ridden, 7

  executions, 77–78, 78, 331n 78

  Globe Theatre, xvi

  Great Fire of, xiv, 29–33

  Hanging Days, 53

  living conditions, xv, 3

  Newton in, xiv, 262

  plague and, xiv, 21, 23–24, 25–28

  St. Paul’s Cathedral, 5, 33

  theaters, 3

  Thomas Gresham’s mansion, 3

  London Bridge, 29, 30, 32, 78, 78

  Louis XIV, xvi, 44, 58, 239, 240

  Luther, Martin, 16

  Macauley, Thomas, 262

  Manuel, Frank, 328n 44

  mathematics, 39–40, 42

  abstraction and, 73, 195–99, 222

  beauty of, 93–94, 94n, 95

  binomial theorem, 228

  calculus, xiv, 43, 221–22, 241–52, 254–56, 258

  of change, 214–15 (see also calculus)

  Descartes’ coordinate geometry, xiii, 190–93, 226, 227, 228, 240

  as escape from ordinary world, 133

  Fermat’s last theorem, 138n

  Galileo’s rule (d = 16 t2), 245, 245–46, 253–55

  God as mathematician, 39, 41, 121–25, 127, 132, 157, 294

  graphs, 191–92, 192n, 194

  great discoveries and youth, 229–31

  great-man theories, 267

  Greeks and, 39–40, 42, 135–39

  imaginary numbers, 196

  infinity and, 208, 219–21

  as language of nature, xvii, xviii, 6, 41, 93–95, 94n

  as language of science, 199

  moving objects and, 42–43 (see also falling objects; motion)

  mystical properties of numbers, 130

  negative numbers, 195–96, 219

  Newton’s Principia as world’s most difficult geometry book, 73

  passion for, 132–33

  patterns and, 135–39

  plain speaking and, 70

  Platonic solids, 152–53, 153, 154, 339n 153

  prime numbers, 136, 136n

  problem of square root of 2, 67n

  proof, 136–37, 139–41, 140

  Pythagorean theorem, 137, 137–39, 139, 139–41, 140, 143n

  ridicule of mathematicians, 87–88

  secrecy in, 66–67, 67n

  sequences, 220, 220n

  triangle, 149

  as universal tool, 214

  zero, 195, 219

  medicine, 7–8, 53–54, 80–81

  Mermin, David, 334n 96

  Michelangelo, 231, 307

  Michelet, Jules, xvin, 323n xviiifn

  Micrographia (Hooke), 118, 118–19

  microscope, 52, 83n, 114–19

  discoveries with, 114–16

  fly’s eyes, 118, 119

  geometric shapes seen, 120, 336n 120

  glory of God and, 117, 119, 120

  Hooke and, 114–15, 118, 118–19

  Leeuwenhoek and, xiv, 52, 114, 115–16, 116n, 336n 114, 336n 115

  Pepys and, 83

  sperm cells seen, 115–16, 116n, 336n 115

  “Mistress of Vision, The” (Thompson), 348n 295

  Molière, 301

  Montaigne, Michel de, 112–13

  Montesquieu, 125

  moon, 138n

  Newton’s theory of gravity and, 273–77, 276, 305

  as a problem for the Greeks, 91n

  telescope and revelations, 86, 106, 109–10

  More, Henry, 99, 128

  More, Thomas, 78n

  Moses, 36

  motion, 143, 208, 252. See also falling objects

  acceleration and, 93, 96, 209, 254–56

  Aristotle’s theory, 94

  average speed, 209

  calculus and, 143, 244–52, 257

  cannonball’s flight, 178, 180–81, 213–14, 214, 257, 341n 181
>
  Galileo’s concept of time as variable, 183–86

  Galileo’s experiments and, 124, 172–79, 178, 183–86, 184

  Galileo’s law of, 178, 189, 244–46, 245, 253–55

  graphs and, 212, 213

  infinity and, 202, 208–9, 221, 225, 241

  instantaneous speed, 210–11, 215–16, 221, 247–52, 248, 249, 251

  Newton’s laws of motion, 42, 173–74, 179–81, 180, 181, 341n 181

  speed, 254

  steady change, 209, 212–13, 213

  Zeno’s paradox and, 201–2, 215, 215–16

  Munch, Edvard, 333n 92fn

  music, 95

  Galileo and, 183

  Kepler and, 157–58

  Leibniz on, 183n

  Pythagoras and, 129, 129n, 157–58

  staff as Europe’s first graph, 192n

  Mystery of the Universe, The (Kepler), 155–56, 160

  Nabokov, Vladimir, 132

  Napoleon Bonaparte, 317

  natural philosophers, 4, 7n

  Nayler, James, 77

  Never at Rest (Westfall), 319, 351n 319

  New Astronomy (Galileo), 170

  Newton, Hannah, 44, 328n 44

  Newton, Isaac, 35, 41, 44–45, 125, 225–32

  admiration of and fame, 45, 261, 264, 271, 315, 316, 317, 318

  alchemy and, 48, 55–56, 72

  animals, concern for, 79

  appearance, 46

  apple story, 272, 272n

  belief he was chosen, 231–32, 233

  Bible study by, 18, 35, 48, 231–32, 274, 311, 325n 18

  birth, xiv, 44, 98, 231

  calculus invented, xiv, 43, 44, 225–32, 241–52, 268, 269

  in Cambridge, xiv, 5, 28, 48, 241, 271, 272, 278–80, 290, 320

  character and personality, 5, 35, 36–37, 46, 73, 135, 225, 226, 267–70, 288–89, 319–20

  death, xiv, 5, 45

  deliberate arcaneness of publications, 72–73

  Descartes’ coordinate geometry and, 227–28, 240

  elliptical orbits and, 279–82

  experiments on his eye, 49, 49

  feud with Flamsteed, 75

  feud with Hooke, 75, 289–90, 291–92, 293

  genius of, 46–47, 232, 256, 262, 318–20

  God, view of, 41, 273, 277, 312, 320

  God and gravity, 307–13, 315

  God as mathematician, 124, 125

  gravity and, xiv, xvii, 35, 48, 73, 127, 190, 229, 271–77, 276, 283–85, 295, 315

  Halley and, xiv, 279–80, 288–90, 293

  infinity and, 222

  intelligent design and, 128

  inverse-square laws, 228, 274–75, 277, 279, 280, 281–82, 282n, 286, 289, 290, 292, 294

  knighting of, xiv, 261–62, 314

  lack of travel, 48

  laws of motion, 42–44, 173–74, 179–81, 180, 181, 341n 181

  Leibniz and, xiv, 75, 242–43, 259–70, 306, 310–13, 317

  light, properties of, 48, 51, 74, 136, 229, 291

  list of sins compiled, 11–12

  in London, xiv

  mathematics and, 132, 135, 226–29, 231, 232, 282–85, 343n 226

 

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