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4th Rock From the Sun: The Story of Mars by Nicky Jenner
3D printing, Alfred Russel Wallace, Astronomia nova, cuban missile crisis, Elon Musk, game design, hive mind, invention of the telescope, Johannes Kepler, Kickstarter, low earth orbit, On the Revolutions of the Heavenly Spheres, placebo effect, Pluto: dwarf planet, retrograde motion, selection bias, silicon-based life, Skype, Stephen Hawking, technoutopianism
However, as Mars’s orbit is slightly tilted with respect to our planet, we see a different scene play out depending on how the two planets are orientated at that point in their orbits: sometimes it’s a loop, sometimes a zigzag, sometimes a curling ‘S’ shape. The 2003 retrograde motion, for example, zipped by as a loop-the-loop, whereas the 2005 event resembled a more jagged ‘Z’. The concept of retrograde motion is a good example of how the practices of astronomy and astrology are strongly intertwined and have been for centuries. Retrograde motion is a solidly scientific astronomical term. However, the concept is also used in an astrological sense. Astrologers frequently refer to various planets (often Mercury) as being ‘in retrograde’; rather than referring to the aforementioned cosmic trick of perspective, this phrase has a distinct astrological meaning – that of reversing your characteristics, challenging your stereotypes and becoming more introspective, reassessing your life goals and desires, of things becoming muddled or unclear, or seeming to regress or slow down.
In the amount of time it takes Mars to loop the track once, Earth is coming close to completing two circuits – meaning that at some point in orbit, Earth has overtaken its red rival. The moment at which it overtakes is when the apparent retrograde motion takes place. As Earth catches up with Mars, the planet seems to briefly halt. As Earth moves past Mars, briefly overtaking it on its elliptical path around the Sun, Mars seems to fly backwards in the sky – in reality, it is doing no such thing. As Earth carries on around its loop, Mars ‘catches up’ to our perspective and appears to halt briefly before carrying on ‘eastward’ as before. This retrograde loop usually takes Mars a couple of months to complete. Diagram explaining the phenomenon of retrograde motion – the real motion of the Earth (inner ring) and Mars (outer ring) is shown on the left, with Mars’s resulting apparent motion seen in our sky on the right.
The ancient Egyptians also referred to Mars moving backwards in the sky via the moniker sekhed-et-em-khet-ket (‘he who travels/moves backwards’ – rolls off the tongue!), something that may be responsible for the idea of Mars being impulsive, rebellious and non-conformist. This backwards motion, known as ‘retrograde’, has been observed for about as long as humanity has been gazing at the skies and was dutifully noted in various ancient astronomical records. Retrograde motion is simple in theory, but can be difficult to visualise. It all boils down to the motions of Earth and Mars relative to one another. We see the sky – Sun, stars, planets and all – to rise in the east and set in the west. This isn’t a motion inherently applicable to the heavens, but a product of Earth’s direction of rotation (anti-clockwise, if we were to look down on it from the North Pole – only Venus and Uranus rotate the other way, a phenomenon known as ‘retrograde rotation’).
Big Bang by Simon Singh
Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Andrew Wiles, anthropic principle, Arthur Eddington, Astronomia nova, Brownian motion, carbon-based life, Cepheid variable, Chance favours the prepared mind, Commentariolus, Copley Medal, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, Dava Sobel, Defenestration of Prague, discovery of penicillin, Dmitri Mendeleev, Edmond Halley, Edward Charles Pickering, Eratosthenes, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, fudge factor, Hans Lippershey, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, horn antenna, if you see hoof prints, think horses—not zebras, Index librorum prohibitorum, invention of the telescope, Isaac Newton, Johannes Kepler, John von Neumann, Karl Jansky, Kickstarter, Louis Daguerre, Louis Pasteur, luminiferous ether, Magellanic Cloud, Murray Gell-Mann, music of the spheres, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, Paul Erdős, retrograde motion, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, Wilhelm Olbers, William of Occam
Occasionally, some of them even dared to stop momentarily before temporarily reversing their motion in a volte-face known as retrograde motion. These wandering rebels were the five other known planets: Mercury, Venus, Mars, Jupiter and Saturn. Indeed, the word ‘planet’ derives from the Greek planetes, meaning ‘wanderer’. Similarly, the Babylonian word for planet was bibbu, literally ‘wild sheep’ — because the planets seemed to stray all over the place. And the ancient Egyptians called Mars sekded-ef em khetkhet, meaning ‘one who travels backwards’. From our modern Earth-orbits-Sun perspective, it is easy enough to understand the behaviour of these heavenly vagabonds. In reality, the planets orbit the Sun in a steady manner, but we view them from a moving platform, the Earth, which is why their motion appears to be irregular. In particular, the retrograde motions exhibited by Mars, Saturn and Jupiter are easy to explain.
Figure 8 Planets such as Mars, Jupiter and Saturn exhibit so-called retrograde motion when viewed from Earth. Diagram (a) shows a stripped-down Solar System with just the Earth and Mars orbiting (anticlockwise) around the Sun. From position 1, we would see Mars move increasingly ahead of us, which continues as we observe Mars from position 2. But Mars pauses at position 3, and by position 4 is now moving to the right, and even further to the right when Earth arrives at position 5. There it pauses once more, before resuming its original direction of travel, as seen from positions 6 and 7. Of course, Mars is continually moving anticlockwise around the Sun, but it appears to us that Mars is zigzagging because of the relative motions of the Earth and Mars. Retrograde motion makes perfect sense in a Sun-centred model of the universe.
Ptolemy’s world-view started with the widely held assumption that the Earth is at the centre of the universe and stationary, otherwise ‘all the animals and all the separate weights would be left behind floating on the air’. Next, he explained the orbits of the Sun and Moon in terms of simple circles. Then, in order to explain retrograde motions, he developed a theory of circles within circles, as illustrated in Figure 9. To generate a path with periodic retrograde motion, such as the one followed by Mars, Ptolemy proposed starting with a single circle (known as the deferent), with a rod attached to the circle so that it pivoted. The planet then occupied a position at the end of this pivoted rod. If the main deferent circle remained fixed and the rod rotated around its pivot, then the planet would follow a circular path with a short radius (known as the epicycle), as shown in Figure 9(a).
Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz
Albert Einstein, Asperger Syndrome, Astronomia nova, Bernie Sanders, clockwork universe, complexity theory, cosmological principle, Dava Sobel, double helix, Edmond Halley, Eratosthenes, four colour theorem, fudge factor, Henri Poincaré, invention of the telescope, Isaac Newton, Islamic Golden Age, Johannes Kepler, John Harrison: Longitude, Khan Academy, Laplace demon, lone genius, music of the spheres, pattern recognition, Paul Erdős, Pierre-Simon Laplace, precision agriculture, retrograde motion, Richard Feynman, Socratic dialogue, Solar eclipse in 1919, Steve Jobs, the rule of 72, the scientific method
Most of the time they moved eastward relative to the stars, but occasionally they appeared to slow down, stop, and go backward, westward, in what astronomers called retrograde motion. Mars, for example, was seen to move in retrograde for about eleven weeks over the course of its nearly two-year circuit around the sky. Nowadays we can capture this reversal photographically. In 2005 the astrophotographer Tunç Tezel took a series of thirty-five snapshots of Mars, each about a week apart, and aligned the images to the stars in the background. In the resulting composite, the eleven dots in the middle show Mars moving in retrograde. Today we understand that retrograde motion is an illusion. It’s caused by our vantage point on Earth as we pass the slower-moving Mars. It’s like what happens when you pass a car on the highway.
As you approach a slower car from behind, it looks like it’s moving forward when viewed against the backdrop of the mountains. But when you pull alongside and pass it, the slower car momentarily seems to move backward relative to the mountains. Then, once you get far enough ahead of it, the car appears to move forward again. This kind of observation led the ancient Greek astronomer Aristarchus to propose a sun-centered universe almost two millennia before Copernicus did. It neatly solved the riddle of retrograde motion. However, a sun-centered universe raised questions of its own. If the Earth moves, why don’t we fall off? And why do the stars appear fixed? They shouldn’t. As the Earth moves around the sun, the distant stars should appear to shift their positions slightly. Experience shows that if you look at something far away and then move and look again, the position of that faraway object appears to shift when viewed against a more distant backdrop.
Selections translated by Stillman Drake, Discoveries and Opinions of Galileo (New York: Doubleday, 1957), 237–38, https://www.princeton.edu/~hos/h291/assayer.htm. 60 “coeternal with the divine mind”: Johannes Kepler, The Harmony of the World, translated by E. J. Aiton, A. M. Duncan, and J. V. Field, Memoirs of the American Philosophical Society 209 (1997): 304. 60 “supplied God with patterns”: Ibid. 60 Plato had taught: Plato, Republic (Hertfordshire: Wordsworth, 1997), 240. 60 Aristotelian teaching: Asimov, Asimov’s Biographical Encyclopedia, 17–20. 61 retrograde motion: Katz, History of Mathematics, 406. 62 Aristarchus: Asimov, Asimov’s Biographical Encyclopedia, 24–25, and James Evans, “Aristarchus of Samos,” Encyclopedia Britannica, https://www.britannica.com/biography/Aristarchus-of-Samos. 63 Archimedes himself realized: Evans, “Aristarchus of Samos.” 63 Ptolemaic system: Katz, History of Mathematics, 145–57. 64 Giordano Bruno: Martínez, Burned Alive. 64 Galileo Galilei: The Galileo Project, http://galileo.rice.edu/galileo.html, is an excellent online resource for Galileo’s life and work.
To Explain the World: The Discovery of Modern Science by Steven Weinberg
Albert Einstein, Alfred Russel Wallace, Astronomia nova, Brownian motion, Commentariolus, cosmological constant, dark matter, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Ernest Rutherford, fudge factor, invention of movable type, Isaac Newton, James Watt: steam engine, Johannes Kepler, music of the spheres, On the Revolutions of the Heavenly Spheres, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Thomas Kuhn: the structure of scientific revolutions
(Presumably Copernicus made this assumption to explain why we do not see annual parallax, the apparent annual motion of the stars caused by the Earth’s motion around the Sun. But the problem of parallax is nowhere mentioned in the Commentariolus.) 5. The apparent daily motion of the stars around the Earth arises entirely from the Earth’s rotation on its axis. 6. The apparent motion of the Sun arises jointly from the rotation of the Earth on its axis and the Earth’s revolution (like that of the other planets) around the Sun. 7. The apparent retrograde motion of the planets arises from the Earth’s motion, occurring when the Earth passes Mars, Jupiter, or Saturn, or is passed in its orbit by Mercury or Venus. Copernicus could not claim in the Commentariolus that his scheme fitted observation better than that of Ptolemy. For one thing, it didn’t. Indeed, it couldn’t, since for the most part Copernicus based his theory on data he inferred from Ptolemy’s Almagest, rather than on his own observations.3 Instead of appealing to new observations, Copernicus pointed out a number of his theory’s aesthetic advantages.
., 379 logarithm, 223n Lorentz, Hendrik, 34 Louis XI, king of France, 253 Lucas, Henry, 217 Lucretius, 46 luminosity, 87 magnitude and, 88n Luther, Martin, 155–56, 183 Lyceum, 22, 32–33, 66, 75 M31 (galaxy), 108 Machiavelli, Niccolò, 46 magnetic field, 109, 220, 250, 257–58, 263 magnetism, xiv, 170, 237, 257–59, 268. See also electromagnetism magnification, 174–75, 219, 334–36 magnitude of stars, 88n Maimon, Moses ben (Maimonides), 98, 114–15 Malebranche, Nicolas de, 122, 246 Marcellus, Claudius Marcus, 39, 71 Maria Celeste, Sister, 187 mariners, 65, 175 Marriage of Mercury and Philology, The (Martianus Capella), 124 Mars, 77, 245n apparent retrograde motion of, 90, 148 brightness of, 87 Copernicus and, 148–51 distance to, 239–40 eccentricity of orbit, 167 epicycles and, 303–6 Greeks and, 81–82, 84, 87–90, 94 as ideal test case, 165n Kepler and, 162, 165, 169 Ptolemy and, 89, 90, 94, 255 sidereal period of, 171 Martianus Capella, 124–25 Martinez, A. M., 269, 368 mass, 232–33, 237–38 mathematics, 1. See also algebra; calculus; geometry; and specific individuals and theories Arabs and, 105–7, 111, 117, 123 Babylonian, 15 Copernicus and, 158–59 Descartes and, 203, 213–14 Einstein and, 253 field approach and, 250 Galileo and, 172, 179 Glaber, Raoul (Radulfus), 125 Greeks and, 15–21, 35, 39–40, 47, 63, 65–70, 79, 105 Kepler and, 161–62, 255 medieval Europe and, 126, 137–40 Neoplatonists and, 47 Newton and, 218, 223–25, 246, 253 Ptolemaic models and, 79–80, 88–99 Pythagoreans and, 16–18 role of, in science, xv, 19–21, 79, 101, 140, 146, 197 matter alchemists and, 11 Aristotle and, 64–65 atomic theory of, 259–60 dark matter and, 9 early Greeks and, 4–14, 44–45 Newton and, 256–57 Plato and, 10, 13 Matthews, Michael, 30, 369 Maxwell, James Clerk, 220, 258–60, 267 Maxwell’s equations, 258n Mayr, Simon, 177n mean speed theorem, 138–41, 191–92, 313–15 Mechanice syntaxism (Philo), 35 medicine, 41–43, 106, 111–12, 114–16, 118, 141 medieval Europe, xiv, 26–28, 101, 124–43 Melanchthon, Philipp, 155, 157, 158, 161 mercury, 11, 198–200 Mercury, 77, 165n, 245n, 250 apparent retrograde motion of, 148 Aristotle and, 84–85 Copernicus and, 86, 148–51, 155 eccentricity of orbit, 167, 324 elongations and orbit of, 320–21 epicycles and, 303–5 Greek models and, 81–82, 84–86, 88–91, 94, 124 Kepler and, 162–63, 171–72 Ptolemy and, 88–91, 94, 149, 155, 255 Mersenne, Marin, 16 Merton, Robert, 253, 382 Merton, Walter de, 138 Merton College, Oxford, 138–41, 191 Merton thesis, 253 Mesopotamia, 104, 107, 110 Metaphysics (Aristotle), 4, 16, 83–84 Meteorology (Aristotle), 127 Meteorology (Descartes), 208 Metonic cycle, 60–61 Meton of Athens, 60 metric system, 240–41 microwave radar, 180 Midsummer Night’s Dream, A (Shakespeare), 34 Miletus, 3–4, 7–8, 11, 33, 254 Milky Way, 128, 176 Millikan, Robert, 260 mirrors, 35–38, 289–91, 348 curved, 37–38, 79 telescope and, 79, 219 modern science, xiii–xiv, 254–55 beginning of, in 17th century, 189–200 Descartes and, 212 early Greeks and, 11–12 Galileo and, 172, 190 Huygens and, 197 impersonal nature of, 254 Newton and, 216 molecules, 249, 259, 262, 266 momentum, 133–34, 232, 234–35.
See also algebra; calculus; geometry; and specific individuals and theories Arabs and, 105–7, 111, 117, 123 Babylonian, 15 Copernicus and, 158–59 Descartes and, 203, 213–14 Einstein and, 253 field approach and, 250 Galileo and, 172, 179 Glaber, Raoul (Radulfus), 125 Greeks and, 15–21, 35, 39–40, 47, 63, 65–70, 79, 105 Kepler and, 161–62, 255 medieval Europe and, 126, 137–40 Neoplatonists and, 47 Newton and, 218, 223–25, 246, 253 Ptolemaic models and, 79–80, 88–99 Pythagoreans and, 16–18 role of, in science, xv, 19–21, 79, 101, 140, 146, 197 matter alchemists and, 11 Aristotle and, 64–65 atomic theory of, 259–60 dark matter and, 9 early Greeks and, 4–14, 44–45 Newton and, 256–57 Plato and, 10, 13 Matthews, Michael, 30, 369 Maxwell, James Clerk, 220, 258–60, 267 Maxwell’s equations, 258n Mayr, Simon, 177n mean speed theorem, 138–41, 191–92, 313–15 Mechanice syntaxism (Philo), 35 medicine, 41–43, 106, 111–12, 114–16, 118, 141 medieval Europe, xiv, 26–28, 101, 124–43 Melanchthon, Philipp, 155, 157, 158, 161 mercury, 11, 198–200 Mercury, 77, 165n, 245n, 250 apparent retrograde motion of, 148 Aristotle and, 84–85 Copernicus and, 86, 148–51, 155 eccentricity of orbit, 167, 324 elongations and orbit of, 320–21 epicycles and, 303–5 Greek models and, 81–82, 84–86, 88–91, 94, 124 Kepler and, 162–63, 171–72 Ptolemy and, 88–91, 94, 149, 155, 255 Mersenne, Marin, 16 Merton, Robert, 253, 382 Merton, Walter de, 138 Merton College, Oxford, 138–41, 191 Merton thesis, 253 Mesopotamia, 104, 107, 110 Metaphysics (Aristotle), 4, 16, 83–84 Meteorology (Aristotle), 127 Meteorology (Descartes), 208 Metonic cycle, 60–61 Meton of Athens, 60 metric system, 240–41 microwave radar, 180 Midsummer Night’s Dream, A (Shakespeare), 34 Miletus, 3–4, 7–8, 11, 33, 254 Milky Way, 128, 176 Millikan, Robert, 260 mirrors, 35–38, 289–91, 348 curved, 37–38, 79 telescope and, 79, 219 modern science, xiii–xiv, 254–55 beginning of, in 17th century, 189–200 Descartes and, 212 early Greeks and, 11–12 Galileo and, 172, 190 Huygens and, 197 impersonal nature of, 254 Newton and, 216 molecules, 249, 259, 262, 266 momentum, 133–34, 232, 234–35.
The Laws of Medicine: Field Notes From an Uncertain Science by Siddhartha Mukherjee
His strength as a cosmologist was the exquisite accuracy of his measurements, and his model worked perfectly for nearly every measured orbit. The rules were beautiful, except for a pesky planet called Mars. Mars just would not fit. It was the outlier, the aberration, the grain of sand in the eye of Tychonian cosmology. If you carefully follow Mars on the horizon, it tracks a peculiar path—pitching forward at first and then tacking backward in space before resuming a forward motion again. This phenomena—called the retrograde motion of Mars—did not make sense in either Ptolemy’s or Brahe’s model. Fed up with Mars’s path across the evening sky, Brahe assigned the problem to an indigent, if exceptionally ambitious, young assistant named Johannes Kepler, a young mathematician from Germany with whom he had a stormy, on-again, off-again relationship. Brahe quite possibly threw Kepler the “Mars problem” to keep him distracted with an insoluble conundrum of little value.
Kepler, however, did not consider Mars peripheral: if a planetary model was real, it had to explain the movements of all the planets, not just the convenient ones. He studied the motion of Mars obsessively. He managed to retain some of Brahe’s astronomical charts even after Brahe’s death, fending off rapacious heirs for nearly a decade while he pored carefully through the borrowed data. He tried no less than forty different models to explain the retrograde motion of Mars. The drunken “doubling back” of the planet would not fit. Then the answer came to him in an inspired flash: the orbits of all the planets were not circles, but ellipses around the sun. All the planets, including Mars, orbit the sun in concentric ellipses. Seen from the earth, Mars moves “backward” in the same sense that one train appears to pitch backward when another train overtakes it on a parallel track.
Coming of Age in the Milky Way by Timothy Ferris
Albert Einstein, Albert Michelson, Alfred Russel Wallace, anthropic principle, Arthur Eddington, Atahualpa, Cepheid variable, Commentariolus, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, delayed gratification, Edmond Halley, Eratosthenes, Ernest Rutherford, Gary Taubes, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, invention of writing, Isaac Newton, Johannes Kepler, John Harrison: Longitude, Karl Jansky, Lao Tzu, Louis Pasteur, Magellanic Cloud, mandelbrot fractal, Menlo Park, Murray Gell-Mann, music of the spheres, planetary scale, retrograde motion, Richard Feynman, Search for Extraterrestrial Intelligence, Searching for Interstellar Communications, Solar eclipse in 1919, source of truth, Stephen Hawking, Thales of Miletus, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Wilhelm Olbers
.* The problem in deciphering these complexities, unrecognized at the time, was that the earth from which we view the planets is itself a planet in motion. It is because the earth orbits the sun while rotating on its tilted axis that there is a night-by-night shift in the time when any given star rises and sets at a given latitude. The earth’s precessional wobble slowly alters the position of the north celestial pole. Retrograde motion results from the combined wanderings of the earth and the other planets; we overtake the outer planets like a runner on an inside track, and this makes each appear first to advance, then to balk and retreat across the sky as the earth passes them. Furthermore, since their orbits are tilted relative to one another, the planets meander north and south as well as east and west. These complications, though they must have seemed a curse, were in the long run a blessing to the development of cosmology, the study of the universe at large.
Instead, they proved to be so intricate and subtle that they could not be predicted accurately without eventually coming to terms with the physical reality of how and where the sun, moon, and planets actually move, in real, three-dimensional space. The truth is beautiful, but the beautiful is not necessarily true: However aesthetically pleasing it may have been for the Sumerians to imagine that the stars and planets swim back from west to east each day via a subterranean river beneath a flat earth, such a conception was quite useless when it came to determining when Mars would go into retrograde or the moon occult Jupiter. Retrograde motion of Mars occurs when Earth overtakes the more slowly moving outer planet, making Mars appear to move backward in the sky. Consequently the idea slowly took hold that an adequate model of the universe not only should be internally consistent, like a song or a poem, but should also make accurate predictions that could be tested against the data of observation. The ascendency of this thesis marked the beginning of the end of our cosmological childhood.
But the Eudoxian universe was also intended to better fit the observed phenomena, and this aspiration mandated complexity. To the simple, spherical cosmos that had been proposed by Parmenides a century earlier, Eudoxus added more spheres. The new spheres dragged and tugged at those of the sun, moon and planets, altering their paths and velocities, and by adjusting their rates of rotation and the inclination of their axes Eudoxus found that he could, more or less, account for retrograde motion and other intricacies of celestial motion. It took a total of twenty-seven spheres to do the job. This was more than Plato would have preferred, but it answered somewhat more closely to the data than had the preceding models. The hegemony of pure, abstract beauty had begun its slow retreat before the sullen but insistent onslaught of the material world. But, ultimately, even so complex a cosmos as that of Eudoxus proved inadequate.
Zero: The Biography of a Dangerous Idea by Charles Seife
Albert Einstein, Albert Michelson, Arthur Eddington, Cepheid variable, cosmological constant, dark matter, Edmond Halley, Georg Cantor, Isaac Newton, Johannes Kepler, John Conway, Pierre-Simon Laplace, place-making, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Richard Feynman, Solar eclipse in 1919, Stephen Hawking
Ptolemy’s clockwork heavens—with Earth at the center—were extremely accurate. However, they were terribly complex. Planets course around the sky throughout the year, but every so often they stop, move backward, and then shoot ahead once more. To account for the planets’ bizarre behavior, Ptolemy added epicycles to his planetary clockwork: little circles within circles could explain the backward, or retrograde, motion of the planets (Figure 19). The power of Copernicus’s idea was in its simplicity. Instead of placing Earth at the center of the universe filled with epicycle-filled clockworks, Copernicus imagined that the sun was at the center instead, and the planets moved in simple circles. Planets would seem to zoom backward as Earth overtook them; no epicycles were needed. Though Copernicus’s system didn’t agree with the data completely—the circular orbits were wrong, though the heliocentric idea was correct—it was much simpler than the Ptolemaic system.
“Luther’s release from the constricting bondage of fear corresponded to the release of his bowels,” notes one text, commenting on this theory.) This was the beginning of the Reformation; intellectuals everywhere began to reject the authority of the pope. By the 1530s, in a quest to ensure an orderly succession to the throne, Henry VIII had spurned the authority of the pope, declaring himself the head of the English clergy. Figure 19: Epicycles, retrograde motion, and heliocentrism The Catholic Church had to strike back. Though it had been experimenting with other philosophies for several centuries, when threatened with schism it turned orthodox once again. It fell back upon its orthodox teachings—the Aristotelian-based philosophies of scholars like Saint Augustine and Boethius, as well as Aristotle’s proof of God. No longer could cardinals and clerics question the ancient doctrines.
ellipses elliptic curve energy, in vacuum Engels, Friedrich Epic of Gilgamesh epicycles equations beauty of differential linear quadratic escape velocity Euler, Leonhard event horizon evil exclusion principle Feynman, Richard Fibonacci five-based (quinary) system fluxions fractions free energy machines French Revolution galaxies see also universe Galileo Galilei gases plasma Gauss, Carl Friedrich gematria geometry Cartesian coordinates in Egyptian invention of projective God Aristotelian doctrine as proof of complex numbers and Pascal’s wager and universe created by golden ratio Grandi, Guido Graves, Robert gravitational lenses gravity light bent by Greeks number-philosophy of numerals of guitar strings Guy, Richard Halley, Edmund Hamlet (Shakespeare) Hardy, Thomas harmonic series Hawking, Stephen heat death Hebrew creation myths Hebrew numerals Heisenberg, Werner Hertz, Heinrich Hilbert, David Hinduism Hippasus “Hollow Men, The” (Eliot) Hooke, Robert Hubble, Edwin imaginary numbers India infinitesimals infinite vacuum infinite zeros infinity Euler and in Indian mathematics limit and and measuring area and volume Pascal’s wager and Renaissance and of universe vanishing point and integers integration interference irrationality irrational numbers irregular shapes, measuring of Islam Jansenists Jesuits Jesus Jews John I, Pope Julian Date kabbalism Kelvin, William Thomson, Lord Kepler, Johannes Koran Kronecker, Leopold Lamoreaux, Steven Laplace, Pierre-Simon Leibniz, Gottfried Wilhelm length Leonardo da Vinci L’Hôpital, Guillaume-François-Antoine de Liber Abaci (Fibonacci) light bending of interference in speed of ultraviolet limit line, slope of linear equations lottery Lucretius Luther, Martin Maclaurin, Colin Maimonides, Moses Manichaean heresy mass inflation of mathematics beauty in birth of Indian Mayans calendar of numerals of Michelson, Albert millennium, controversy over start of Millis, Marc Mohammed Monge, Gaspard monochord Morley, Edward motion of planets multiplication by zero musical scale Muslims myriads mysticism, Jewish NASA nature Nature nautilus negative numbers square roots of neutron star Newton, Isaac calculus of Nicholas of Cusa Number: The Language of Science (Danzig) numbers and counting Indian starting with zero numerals Arabic Babylonian Mayan omicron “On Poetry: A Rhapsody” (Swift) orders ordinal numbers Oresme, Nicholas origin of zero painting and drawing, dimension in parabola Parmenides Parthenon particle accelerators particles string theory and virtual Pascal, Blaise experiments of wager of Pascal, Étienne Pauli, Wolfgang Pensées (Pascal) pentagram perpetual-motion machines perspective, in painting and drawing photoelectric effect photons physics Planck, Max plane, complex planets: motion of Pythagorean model of see also universe plasma point vanishing Polder, Dik pole polynomials Poncelet, Jean-Victor probability projective geometry Ptolemy Puthoff, Harold Pythagoras, Pythagoreans planetary model of quadratic polynomials and equations quanta quantum leap quantum mechanics string theory and quantum sail quarks quartic polynomials quinary system quintic polynomials rate times time equals distance rationality, rational numbers ratios golden Rayleigh-Jeans law real numbers Rees, Martin Reformation relativity string theory and Renaissance renormalization retrograde motion Riemann, Georg Friedrich Bernhard Rig Veda Romans numerals of Scaliger, Joseph Schrödinger equation scientific revolution sets Seven Years’ War sexagesimal system Shakespeare, William Shiva Sierpinski, Waclaw singularities essential naked slope of tangent space-time space travel speed of light sphere square diagonal of square numbers square roots of negative numbers stain, measuring of standard candles stars Cepheid collapsing of light bent around movement of statistical mechanics steady-state theory Stefan-Boltzmann equation Stone Age string theory Suiseth, Richard supernovas Swift, Jonathan Sylvester II, Pope tachyons tally sticks tangent Taylor, Brook Tempier, Étienne Thales theories, beauty in Theory of Everything thermodynamics Thomas Aquinas, Saint time: relativity of space-time travel in timekeeping see also calendars time machine, making Times (London) Torricelli, Evangelista transfinite numbers triangle, estimating size of triangular numbers trigonometry two-based (binary) system ultraviolet catastrophe ultraviolet light uncertainty principle universe: Aristotelian model of, see Aristotle, Aristotelian doctrine big bang theory of origin of Earth’s position in as eternal expansion of fate of God as creator of Hindu model of as infinite lumpiness of size of steady-state theory of vacuum and vacuum energy in infinite and lumpiness of universe see also void vanishing point velocity escape vigesimal (base-20) system void atomism and Descartes and in Hinduism Leibniz and see also vacuum Washington Post wave functions wavelength waves interference in Wheeler, John Whitehead, Alfred North wormholes wormhole time machine, making Yorktown, USS Zeno Achilles paradox of zero: birth of as dangerous division by infinite, see also infinity life without multiplication by origins of as placeholder roots of word for starting counting with transformation of, from placeholder to number Western rejection of zero-dimensional objects zero-point energy * The Greek word for ratio was (logos), which is also the term for word.
2312 by Kim Stanley Robinson
agricultural Revolution, double helix, full employment, hive mind, if you see hoof prints, think horses—not zebras, Kuiper Belt, late capitalism, mutually assured destruction, Nelson Mandela, offshore financial centre, orbital mechanics / astrodynamics, pattern recognition, phenotype, post scarcity, precariat, retrograde motion, stem cell, strong AI, the built environment, the High Line, Turing machine, Turing test, Winter of Discontent
Eventually the smaller moon splatted onto the larger one, leaving behind the jagged mountains on the anti-terran side of the resulting moon, Luna. Around the same time, a small planet about three thousand kilometers in diameter struck Mars and created the Borealis Basin, which is basically Mars’s northern hemisphere, still six kilometers lower than the southern hemisphere. Venus was struck by a Mars-sized planet, creating a moon like Earth’s, called Neith; ten million years later, another impactor gave Venus its slow retrograde motion. This change in rotation slowed Neith and caused it to plunge back into Venus and merge with it. Mercury was struck by a protoplanet half its size, at such a speed and angle that Mercury’s mantle was stripped off and cast throughout Mercury’s orbit. Ordinarily Mercury would have swept these pieces back up, but in the four million years this process would have taken, most of the material was pushed outward by solar radiation and thus never made it back to Mercury.
If it is done carefully, however, Venus could ultimately end up with about twice the land surface that Earth has. At this point (140 years freezing and preparation, 50 years scraping and poaching, so be patient!) you might think that the planet is ready for biological occupation. But remember, combining the Venusian year of 224 days with its daily rotation period of 243 days, you get a screwball curve (retrograde motion, sun rising in the west) in which the solar day for any particular point on the planet is 116.75 days. Tests have long since determined that that’s too long for most Terran life-forms to survive, tweaked or not. So at this point, two main options have been identified. First is to program the sunshield so that it lets through sunlight to the surface and then blocks it off again, flexing like a circular venetian blind to make a more Terran rhythm of night and day.
Galileo's Daughter: A Historical Memoir of Science, Faith and Love by Dava Sobel
Albert Einstein, back-to-the-land, cognitive dissonance, Dava Sobel, Defenestration of Prague, Edmond Halley, germ theory of disease, Hans Lippershey, Isaac Newton, Johannes Kepler, Louis Pasteur, Murano, Venice glass, On the Revolutions of the Heavenly Spheres, Peace of Westphalia, retrograde motion
The denouement at that day’s end, when it came time for the three characters to close discussion and draw conclusions, demanded delicate diplomacy, for the text of the third and fourth days advanced compelling physical arguments in support of Copernicus, while the overall tenor of the book needed to preserve the spirit of hypothesis, as Galileo had promised Urban it would. “In the conversations of these four days we have, then, strong evidences in favor of the Copernican system,” sums up the hospitable Sagredo, “among which three have been shown to be very convincing—those taken from the stoppings and retrograde motions of the planets, and their approaches toward and recessions from the Earth; second, from the revolution of the Sun upon itself, and from what is to be observed in the sunspots; and third, from the ebbing and flowing of the ocean tides.” But Salviati-cum-Galileo, although he has led the discussion in this direction, refuses to endorse Copernicus in the end. He concedes that “this invention“—meaning the heliocentric design— “may very easily turn out to be a most foolish hallucination and a majestic paradox.”
Range: Why Generalists Triumph in a Specialized World by David Epstein
Airbnb, Albert Einstein, Apple's 1984 Super Bowl advert, Atul Gawande, Checklist Manifesto, Claude Shannon: information theory, Clayton Christensen, clockwork universe, cognitive bias, correlation does not imply causation, Daniel Kahneman / Amos Tversky, deliberate practice, Exxon Valdez, Flynn Effect, Freestyle chess, functional fixedness, game design, Isaac Newton, Johannes Kepler, knowledge economy, lateral thinking, longitudinal study, Louis Pasteur, Mark Zuckerberg, medical residency, meta analysis, meta-analysis, Mikhail Gorbachev, Nelson Mandela, Netflix Prize, pattern recognition, Paul Graham, precision agriculture, prediction markets, premature optimization, pre–internet, random walk, randomized controlled trial, retrograde motion, Richard Feynman, Richard Feynman: Challenger O-ring, Silicon Valley, Stanford marshmallow experiment, Steve Jobs, Steve Wozniak, Steven Pinker, Walter Mischel, Watson beat the top human players on Jeopardy!, Y Combinator, young professional
Kepler was a young man when he showed up to work at Tycho Brahe’s observatory—so cutting edge at the time that it cost 1 percent of the national budget of Denmark. He was given the assignment nobody wanted: Mars and its perplexing orbit. The orbit had to be a circle, Kepler was told, so he had to figure out why Brahe’s observations didn’t match that. Every once in a while, Mars appears to reverse course in the sky, do a little loop, and then carry on in the original direction, a feat known as retrograde motion. Astronomers proposed elaborate contortions to explain how Mars could accomplish this while riding the interlocking spheres of the sky. As usual, Kepler could not accept contortions. He asked peers for help, but his pleas fell on deaf ears. His predecessors had always managed to explain away the Mars deviations without scrapping the overall scheme. Kepler’s short Mars assignment (he guessed it would take eight days) turned into five years of calculations trying to describe where Mars appeared in the sky at any given moment.
Pathfinders: The Golden Age of Arabic Science by Jim Al-Khalili
agricultural Revolution, Albert Einstein, Andrew Wiles, Book of Ingenious Devices, colonial rule, Commentariolus, Dmitri Mendeleev, Eratosthenes, Henri Poincaré, invention of the printing press, invention of the telescope, invention of the wheel, Isaac Newton, Islamic Golden Age, Johannes Kepler, Joseph Schumpeter, Kickstarter, liberation theology, retrograde motion, scientific worldview, Silicon Valley, Simon Singh, stem cell, Stephen Hawking, the scientific method, Thomas Malthus, trade route, William of Occam
One can even go so far as to say that this was almost a proper scientific theory.7 It seems to have been accepted universally soon after its inception, even though new observational data from Hipparchus and others necessitated certain modifications to it. One of the most serious anomalies was to do with the motion of the planets, particularly Mars. It was known that planets moved across the sky from east to west at a faster rate than the fixed stars. But this rate was not constant. In fact, relative to the stars, they would slow down, speed up, and sometimes even double back on themselves. This ‘retrograde’ motion could not be accommodated in Aristotle’s model and a fix was devised by Hipparchus and later perfected by Ptolemy. By the time Ptolemy published his Mathematical Treatise, around 150 CE, later to be known of course by its Arabic title of Almagest, Aristotle’s model had been extended, tweaked and modified in order to match the observed motion of the heavens. But it had strayed from the ideal of perfect concentric spheres that Aristotle had proposed.
Quicksilver by Neal Stephenson
Danny Hillis, dark matter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Isaac Newton, joint-stock company, out of africa, Peace of Westphalia, retrograde motion, short selling, the scientific method, trade route, urban planning
Or, like a billiard ball, is he following some rational trajectory I have not the wit to understand?” “I understand your question now,” Daniel said. “Astronomers used to explain the seeming retrograde movements of the planets by imagining a phantastic heavenly axle-tree fitted out with crystalline spheres. Now we know that in fact the planets move in smooth ellipses and that retrograde motion is an illusion created by the fact that we are making our observations from a moving platform.” “Viz. the Earth.” “If we could see the planets from some fixed frame of reference, the retrograde motion would disappear. And you, Roger, observing Newton’s wandering trajectory—one year devising new receipts for the Philosophic Mercury, the next hard at work on Conic Sections—are trying to figure out whether there might be some Reference Frame within which all of Isaac’s moves make some kind of damned sense.”
Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals by David Aronson
Albert Einstein, Andrew Wiles, asset allocation, availability heuristic, backtesting, Black Swan, butter production in bangladesh, buy and hold, capital asset pricing model, cognitive dissonance, compound rate of return, computerized trading, Daniel Kahneman / Amos Tversky, distributed generation, Elliott wave, en.wikipedia.org, feminist movement, hindsight bias, index fund, invention of the telescope, invisible hand, Long Term Capital Management, mental accounting, meta analysis, meta-analysis, p-value, pattern recognition, Paul Samuelson, Ponzi scheme, price anchoring, price stability, quantitative trading / quantitative ﬁnance, Ralph Nelson Elliott, random walk, retrograde motion, revision control, risk tolerance, risk-adjusted returns, riskless arbitrage, Robert Shiller, Robert Shiller, Sharpe ratio, short selling, source of truth, statistical model, stocks for the long run, systematic trading, the scientific method, transfer pricing, unbiased observer, yield curve, Yogi Berra
For a time, bewildered astronomers were able to patch up the Church’s theory to make it agree with observed planetary paths. As discordant observations occurred, new assumptions were added to the theory, in the form of smaller orbits revolving about a planet’s principal orbit. These ad hoc ﬁxes, called epicycles, permitted the theory to account for the troublesome observations. For example, epicycles were able to explain why planets were sometimes seen to move backwards (retrograde motion) rather than follow a continuous path across the sky. Over time, a succession of epicycle ﬁxes transformed the fundamentally incorrect theory of an Earth-centered universe into an unwieldy monstrosity of complexity with epicycles upon smaller epicycles upon even smaller epicycles. A landmark in scientiﬁc history took place when the telescope of Galileo Galilei (1564–1642) showed that four moons circled the planet Jupiter.
The Man Who Saved the Union: Ulysses Grant in War and Peace by H. W. Brands
Gordon had never experienced, or read of, such a position, and he didn’t know how to get out of it. “Further movement to Grant’s rear was not to be considered, for his unbroken lines on each side of me would promptly close up the gap which my men had cut through his center, thus rendering the capture of my whole command inevitable.” Retreat was almost as fatal. “Those same unbroken and now unopposed ranks on each side of me, as soon as such retrograde motion began, would instantly rush from both directions upon my retreating column and crush it.” So Gordon improvised. He ordered half his line to file right and the other to file left, thereby arraying each half perpendicular to the flank of the corresponding segment of the Union line. He then ordered a double charge, with his twin lines surging away from each other but wreaking havoc on the Federal flanks.