The Clockwork Universe
Page 32
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
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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