Johannes Kepler

123 results back to index


pages: 407 words: 116,726

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

,” Scientific American, https://www.scientificamerican.com/article/what-are-josephson-juncti/. 74 longitude problem: Sobel, Longitude. 75 global positioning system: Thompson, “Global Positioning System,” and https://www.gps.gov. 78 Johannes Kepler: For Kepler’s life and work, see Owen Gingerich, “Johannes Kepler,” in Gillispie, Complete Dictionary, vol. 7, online at https://www.encyclopedia.com/people/science-and-technology/astronomy-biographies/johannes-kepler#kjen14, with amendments by J. R. Voelkel in vol. 22. See also Kline, Mathematics in Western Culture, 110–25; Edwards, The Historical Development, 99–103; Asimov, Asimov’s Biographical Encyclopedia, 96–99; Simmons, Calculus Gems, 69–83; and Burton, History of Mathematics, 355–60. 78 “criminally inclined”: Quoted in Gingerich, “Johannes Kepler,” https://www.encyclopedia.com/people/science-and-technology/astronomy-biographies/johannes-kepler#kjen14. 78 “bad-tempered”: Ibid. 78 “such a superior and magnificent mind”: Ibid. 79 “Day and night I was consumed by the computing”: Ibid. 80 “God is being celebrated in astronomy”: Ibid. 81 “this tedious procedure”: Kepler in Astronomia Nova, quoted by Owen Gingerich, The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus (New York: Penguin, 2005), 48. 84 “sacred frenzy”: Quoted in Gingerich, “Johannes Kepler,” https://www.encyclopedia.com/people/science-and-technology/astronomy-biographies/johannes-kepler#kjen14. 85 “My dear Kepler, I wish we could laugh”: Quoted in Martínez, Science Secrets, 34. 86 “Johannes Kepler became enamored”: Koestler, The Sleepwalkers, 33. 4.

See also Kline, Mathematics in Western Culture, 110–25; Edwards, The Historical Development, 99–103; Asimov, Asimov’s Biographical Encyclopedia, 96–99; Simmons, Calculus Gems, 69–83; and Burton, History of Mathematics, 355–60. 78 “criminally inclined”: Quoted in Gingerich, “Johannes Kepler,” https://www.encyclopedia.com/people/science-and-technology/astronomy-biographies/johannes-kepler#kjen14. 78 “bad-tempered”: Ibid. 78 “such a superior and magnificent mind”: Ibid. 79 “Day and night I was consumed by the computing”: Ibid. 80 “God is being celebrated in astronomy”: Ibid. 81 “this tedious procedure”: Kepler in Astronomia Nova, quoted by Owen Gingerich, The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus (New York: Penguin, 2005), 48. 84 “sacred frenzy”: Quoted in Gingerich, “Johannes Kepler,” https://www.encyclopedia.com/people/science-and-technology/astronomy-biographies/johannes-kepler#kjen14. 85 “My dear Kepler, I wish we could laugh”: Quoted in Martínez, Science Secrets, 34. 86 “Johannes Kepler became enamored”: Koestler, The Sleepwalkers, 33. 4. The Dawn of Differential Calculus 90 China, India, and the Islamic world: Katz, “Ideas of Calculus”; Katz, History of Mathematics, chapters 6 and 7; and Burton, History of Mathematics, 238–85. 91 Al-Hasan Ibn al-Haytham: Katz, “Ideas of Calculus,” and J.

This unexpected link between music (the harmony of this world) and numbers (the harmony of an imagined world) led the Pythagoreans to the mystical belief that all is number. They are said to have believed that even the planets in their orbits made music, the music of the spheres. Ever since then, many of history’s greatest mathematicians and scientists have come down with cases of Pythagorean fever. The astronomer Johannes Kepler had it bad. So did the physicist Paul Dirac. As we’ll see, it drove them to seek, and to dream, and to long for the harmonies of the universe. In the end it pushed them to make their own discoveries that changed the world. The Infinity Principle To help you understand where we’re headed, let me say a few words about what calculus is, what it wants (metaphorically speaking), and what distinguishes it from the rest of mathematics.


pages: 204 words: 58,565

Keeping Up With the Quants: Your Guide to Understanding and Using Analytics by Thomas H. Davenport, Jinho Kim

Black-Scholes formula, business intelligence, business process, call centre, computer age, correlation coefficient, correlation does not imply causation, Credit Default Swap, en.wikipedia.org, feminist movement, Florence Nightingale: pie chart, forensic accounting, global supply chain, Hans Rosling, hypertext link, invention of the telescope, inventory management, Jeff Bezos, Johannes Kepler, longitudinal study, margin call, Moneyball by Michael Lewis explains big data, Myron Scholes, Netflix Prize, p-value, performance metric, publish or perish, quantitative hedge fund, random walk, Renaissance Technologies, Robert Shiller, Robert Shiller, self-driving car, sentiment analysis, six sigma, Skype, statistical model, supply-chain management, text mining, the scientific method, Thomas Davenport

“Tycho Brahe,” Wikipedia, http://en.wikipedia.org/wiki/Tycho_Brahe; Michael Fowler, “Tycho Brahe,” http://galileoandeinstein.physics.virginia.edu/1995/ lectures/tychob.html; Arthur Koestler, The Watershed: A Biography of Johannes Kepler (Doubleday, 1960); “Johannes Kepler,” Wikipedia, http://en.wikipedia.org/wiki/ Johannes_Kepler; “Johannes Kepler: The Laws of Planetary Motion,” http://csep10 .phys.utk.edu/astr161/lect/history/kepler.html; Michael Fowler, “Tycho Brahe and Johannes Kepler,” http://galileoandeinstein.physics.virginia.edu/lectures/tycho.htm; Michael Fowler, “Johannes Kepler,” http://galileoandeinstein.physics.virginia.edu/ 1995/lectures/kepler.html; “Johannes Kepler,” Encyclopædia Britannica Online Academic Edition, http://www.britannica.com/EBchecked/topic/315225/Johannes-Kepler; Ann Lamont, “Johannes Kepler: Outstanding Scientist and Committed Christian,” 1:1, http://www.answersingenesis.org/creation/v15/i1/kepler.asp, December 1, 1992. 12.

The use of secondary data saves time that would otherwise be spent redundantly collecting the same data. Common sources of secondary data include censuses, surveys, organizational records, and so on. The world is full of it these days, and it’s just waiting to be analyzed. In some cases, secondary data has been used to create very important results. Take, for example, the work of astronomer Johannes Kepler. Although born to a poor family under adverse circumstances, Kepler was lucky enough to acquire very precise secondary data, carefully amassed for several decades, on the motions of objects in the celestial sphere. With his luck and superior mathematical talent, Kepler solved the mystery of the planets. Kepler’s data was primarly gathered by Tycho Brahe (1546–1601), a Danish nobleman and brilliant astronomer who made the most accurate astronomical observations of his time by devising the most precise instruments available prior to the invention of the telescope.


pages: 271 words: 68,440

More Perfect Heaven: How Copernicus Revolutionised the Cosmos by Dava Sobel

Astronomia nova, Commentariolus, dark matter, Dava Sobel, Edmond Halley, invention of movable type, invention of the telescope, Isaac Newton, Johannes Kepler, On the Revolutions of the Heavenly Spheres

Chapter 10 Epitome of Copernican Astronomy I deem it my duty and task to advocate outwardly also, with all the powers of my intellect, the Copernican theory, which I in my innermost have recognized as true, and whose loveliness fills me with unbelievable rapture when I contemplate it. —JOHANNES KEPLER, Epitome of Copernican Astronomy, 1617–21 Content with thePrutenic Tables, European astronomers took Copernicus at Osiander’s cautious word for the remainder of the sixteenth century—with two monumental exceptions. Between them, the flamboyant Tycho Brahe and the studious, passionately reverent Johannes Kepler carried Copernicus’s work to completion. The Danish Tycho was literally star-struck in 1559, during his thirteenth summer, when a lunar eclipse illuminated the mathematics he was learning at a Lutheran university in Copenhagen. His noble birth gave him the means to purchase his own astronomy books, which he bought secretly, he said, and also read in secret, since his elders considered such pastimes beneath him.

No; rather, he wanted to warn people of their own mutability, while the Earth, home of the human race, remains always the same, the motion of the Sun perpetually returns to the same place, the wind blows in a circle and returns to its starting point, rivers flow from their sources into the sea, and from the sea return to the sources, and finally, as these people perish, others are born. Life’s tale is ever the same; there is nothing new under the Sun. You do not hear any physical dogma here. The message is a moral one, concerning something self-evident and seen by all eyes but seldom pondered. Solomon therefore urges us to ponder. —JOHANNES KEPLER, Astronomia nova, 1609 (TRANSLATED FROM THE LATIN BY WILLIAM H. DONAHUE) Chapter 7 The First Account It is also clearer than sunlight that the sphere which carries the Earth is rightly called the Great Sphere. If generals have received the surname “Great” on account of successful exploits in war or conquests of peoples, surely this circle deserved to have that august name applied to it.

The search for a new patron led him to Prague in 1599, to the court of the Holy Roman Emperor, Rudolf II. Although Catholic, Rudolf acted liberally toward Lutherans in general, and smiled with special warmth on one so skilled in the art of astrology as Tycho Brahe. The emperor gave him his choice of castles and put him to work prognosticating affairs of state. The move to Prague also put Tycho in proximity to Johannes Kepler, thereby facilitating their fateful collaboration. Kepler, not yet well known to most astronomers and living in modest circumstances, could never have afforded a visit to Tycho’s island. He welcomed Tycho’s presence in Bohemia as an act of God. By further provision of Providence, Kepler found Tycho’s chief assistant engaged in Mars studies when he joined the team at Benatky Castle in the spring of 1600.


The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio

Albert Einstein, Albert Michelson, Alfred Russel Wallace, Benoit Mandelbrot, Brownian motion, Buckminster Fuller, cosmological constant, Elliott wave, Eratosthenes, Gödel, Escher, Bach, Isaac Newton, Johann Wolfgang von Goethe, Johannes Kepler, mandelbrot fractal, music of the spheres, Nash equilibrium, Ralph Nelson Elliott, Ralph Waldo Emerson, random walk, Richard Feynman, Ronald Reagan, Thales of Miletus, the scientific method

Suddenly the Renaissance intellectuals saw a real opportunity to relate mathematics and rational logic to the universe around them, in the spirit of the Platonic worldview. Concepts like the “Divine Proportion” built, on one hand, a bridge between mathematics and the workings of the cosmos and, on the other, a relation among physics, theology, and metaphysics. The person who, in his ideas and works, exemplifies more than any other this fascinating blending of mathematics and mysticism is Johannes Kepler. MYSTERIUM COSMOGRAPHICUM Johannes Kepler is best remembered as an outstanding astronomer responsible (among other things) for the three laws of planetary motion that bear his name. But Kepler was also a talented mathematician, a speculative metaphysician, and a prolific author. Born at a time of great political upheaval and religious chaos, Kepler's education, life, and thinking were critically shaped by the events around him.

I will use the names Golden Ratio, Golden Section, Golden Number, phi, and also the symbol φ interchangeably throughout, because these are the names most frequently encountered in the recreational mathematics literature. Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

After enumerating more of Pythagoras' exquisite qualities, Porphyry continues: “Pythagoras affirmed that the Nine Muses were constituted by the sounds made by the seven planets, the sphere of the fixed stars, and that which is opposed to our earth, called the ‘counter-earth’ (the latter, according to the Pythagorean theory of the universe, revolved in opposition to Earth, around a central fire). The concept of the “harmony of the spheres” was elaborated upon again, more than twenty centuries later, by the famous astronomer Johannes Kepler (1571–1630). Having witnessed in his own life much agony and the horrors of war, Kepler concluded that Earth really created two notes, mi for misery (“miseria” in Latin) and fa for famine (lames in Latin). In Kepler s words: “the Earth sings MI FA MI, so that even from the syllable you may guess that in this home of ours Misery and Famine hold sway.” Figure 8 The Pythagorean obsession with mathematics was mildly ridiculed by the great Greek philosopher Aristotle.


pages: 404 words: 131,034

Cosmos by Carl Sagan

Albert Einstein, Alfred Russel Wallace, Arthur Eddington, clockwork universe, dematerialisation, double helix, Drosophila, Edmond Halley, Eratosthenes, Ernest Rutherford, germ theory of disease, global pandemic, invention of movable type, invention of the telescope, Isaac Newton, Johannes Kepler, Lao Tzu, Louis Pasteur, Magellanic Cloud, Mars Rover, Menlo Park, music of the spheres, pattern recognition, planetary scale, Search for Extraterrestrial Intelligence, spice trade, Thales and the olive presses, Thales of Miletus, Tunguska event

But the Thirty Years’ War obliterated his grave. If a marker were to be erected today, it might read, in homage to his scientific courage: “He preferred the hard truth to his dearest illusions.” Johannes Kepler believed that there would one day be “celestial ships with sails adapted to the winds of heaven” navigating the sky, filled with explorers “who would not fear the vastness” of space. And today those explorers, human and robot, employ as unerring guides on their voyages through the vastness of space the three laws of planetary motion that Kepler uncovered during a lifetime of personal travail and ecstatic discovery. The lifelong quest of Johannes Kepler, to understand the motions of the planets, to seek a harmony in the heavens, culminated thirty-six years after his death, in the work of Isaac Newton. Newton was born on Christmas Day, 1642, so tiny that, as his mother told him years later, he would have fit into a quart mug.

For clarity, I have in a number of cases introduced an idea more than once—the first time lightly, and with deeper passes on subsequent appearances. This occurs, for example, in the introduction to cosmic objects in Chapter 1, which are examined in greater detail later on; or in the discussion of mutations, enzymes and nucleic acids in Chapter 2. In a few cases, concepts are presented out of historical order. For example, the ideas of the ancient Greek scientists are presented in Chapter 7, well after the discussion of Johannes Kepler in Chapter 3. But I believe an appreciation of the Greeks can best be provided after we see what they barely missed achieving. Because science is inseparable from the rest of the human endeavor, it cannot be discussed without making contact, sometimes glancing, sometimes head-on, with a number of social, political, religious and philosophical issues. Even in the filming of a television series on science, the worldwide devotion to military activities becomes intrusive.

*We use the American scientific convention for large numbers: one billion = 1,000,000,000 = 109; one trillion = 1,000,000,000,000 = 1012, etc. The exponent counts the number of zeroes after the one. *Or is you like to measure things in miles, the distance between Alexandria and Syene is about 500 miles, and 500 miles × 50 = 25,000 miles. *So called because they can be produced by slicing through a cone at various angles. Eighteen centuries later, the writings of Apellecios on comic sections would be employed by Johannes Kepler in understanding for the first time the movement of the planets. CHAPTER II ONE VOICE IN THE COSMIC FUGUE Probably all the organic beings which have ever lived on this earth have descended from some one primordial form, into which life was first breathed.… There is grandeur in this view of life … that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.


pages: 439 words: 104,154

The Clockwork Universe: Saac Newto, Royal Society, and the Birth of the Modern WorldI by Edward Dolnick

Albert Einstein, Apple's 1984 Super Bowl advert, Arthur Eddington, clockwork universe, complexity theory, double helix, Edmond Halley, Isaac Newton, Johannes Kepler, lone genius, music of the spheres, Pierre-Simon Laplace, Richard Feynman, Saturday Night Live, scientific worldview, Simon Singh, Stephen Hawking, Thomas Kuhn: the structure of scientific revolutions

(Each angle of a hexagon is 120 degrees, for instance, so three or more hexagons cannot meet at one vertex.) 153 If you needed dice: Marcus du Sautoy, Symmetry (New York: Harper, 2008), p. 5. 154 He burst into tears: Caspar, Kepler, p. 63. 154 “Now I no longer regretted”: Koestler, The Sleepwalkers, p. 251. 155 “For a long time I wanted”: Owen Gingerich, “Johannes Kepler and the New Astronomy,” available at http://adsabs.harvard.edu/full/1972QJRAS..13..346G. 155 He happily devoted: Koestler, The Sleepwalkers, p. 269. 155 “No one,” he boasted: Caspar, Kepler, p. 71. 155 “too pretty not to be true”: James Watson, The Double Helix (New York: Touchstone, 2001), p. 204. 156 “Never in history”: Gingerich, “Johannes Kepler and the New Astronomy,” p. 350. CHAPTER 26. WALRUS WITH A GOLDEN NOSE 157 “Would that God deliver me”: Rossi, The Birth of Modern Science, p. 70. 158 “the heavenly motions are nothing but”: Koestler, The Sleepwalkers, p. 392. 158fn Not by the human ear: Rattansi, “Newton and the Wisdom of the Ancients,” p. 189. 158fn The first person to refer: Curtis Wilson, “Kepler’s Laws, So-Called,” HAD News (newsletter of the Historical Astronomy Division of the American Astronomical Society), no. 31, May 1994. 158 “My brain gets tired”: Giorgio de Santillana, The Crime of Galileo, p. 106fn. 159 In his student days: Ferguson, Tycho and Kepler, pp. 31–32. 160 had cost a ton of gold: Gingerich, “Johannes Kepler and the New Astronomy,” p. 350. 160 “any single instrument cost more”: Koestler, The Sleepwalkers, p. 278. 160 “I was in possession”: Ibid., p. 345.

Not just new facts, moreover, but facts that will stand forever, unchallengeable. “The certainty that [a mathematician’s] creations will endure,” wrote Rota, “renews his confidence as no other pursuit.” It is heady, seductive business. Perhaps this accounts for the eagerness of so many seventeenth-century intellectuals to look past the wars and epidemics all around them and instead to focus on the quest for perfect, abstract order. Johannes Kepler, the great astronomer, barely escaped the religious battles later dubbed the Thirty Years’ War. One close colleague was drawn and quartered and then had his tongue cut out. For a decade his head, impaled on a pike, stood on public display next to the rotting skulls of other “traitors.” Kepler came from a village in Germany where dozens of women had been burned as witches during his lifetime.

The mission of science was to honor God, and the best way to pay Him homage was to discover and proclaim the perfection of His plans. Chapter Twenty-Four The Secret Plan When Newton declared that he stood on the shoulders of giants, he was at least partly sincere. He did genuinely admire some of his fellow scientists, particularly those who’d had the good judgment to die before he came along. One of the great predecessors he had in mind was the astronomer Johannes Kepler. A contemporary of Galileo, Kepler was a genius and a mystic whose faith in God and faith in mathematics had fused into an inseparable unit. Kepler was both astronomer and astrologer, though he never sorted out just how much the heavens influenced human affairs. “In what manner does the countenance of the sky at the moment of a man’s birth determine his character?” he wrote once, and then he answered his own question.


pages: 1,197 words: 304,245

The Invention of Science: A New History of the Scientific Revolution by David Wootton

agricultural Revolution, Albert Einstein, British Empire, clockwork universe, Commentariolus, commoditize, conceptual framework, Dava Sobel, double entry bookkeeping, double helix, en.wikipedia.org, Ernest Rutherford, Fellow of the Royal Society, fudge factor, germ theory of disease, Google X / Alphabet X, Hans Lippershey, interchangeable parts, invention of gunpowder, invention of the steam engine, invention of the telescope, Isaac Newton, Jacques de Vaucanson, James Watt: steam engine, Johannes Kepler, John Harrison: Longitude, knowledge economy, lateral thinking, lone genius, Mercator projection, On the Revolutions of the Heavenly Spheres, Philip Mirowski, placebo effect, QWERTY keyboard, Republic of Letters, social intelligence, spice trade, spinning jenny, the scientific method, Thomas Kuhn: the structure of scientific revolutions

Amerigo Vespucci) 121 Muslims 66, 113 see also Islam Mysterium cosmographicum (Johannes Kepler) 213 Mystery of Jesuitisme (Blaise Pascal) 293 Napier, John 90, 94, 416 Napoleon Bonaparte 149n, 480, 549 Natural and Political Observations (John Graunt) 261 Natural History (Pliny) Earth as a dot 230n flood stories 113 Pliny’s reputation falls 26 Polydore Vergil and 67 Ziegler’s commentary 128 Natural History (Gilbert White) 12 natural knowledge 26 see also knowledge Natural Theology (William Paley) 419 Nature and Nature’s Laws (Marie Boas Hall) 367 navigation 207 see also discovery Needham, Joseph 105, 502 Neolithic Revolution 3, 4, 14, 476 neo-Platonism 235, 321, 516 Neptune 89, 99 Netherlands 214, 362–3 see also Dutch networks 340–1, 348 New . . . (as title for various publications) 36 New Almagest (Giovanni Alberti Riccioli) 224, 227, 305 New Astronomy (Johannes Kepler) 24, 265, 305 New Atlantis (Francis Bacon) 103, 341 New Digester, The (Denis Papin) 504 New Discoveries (Johannes Stradanus) 56 New Experiments (Robert Boyle) 294, 337, 344, 392, 516 New Science (Tartaglia) 203, 204 New Star (Tycho Brahe) 14 New Star (Johannes Kepler) 263, 264, 265 New Theory of the Earth, The (William Whiston) 396, 467, 474 New Treatise of Natural Philosophy (Robert Midgeley) 279 New Treatise Proving a Multiplicity of Worlds, A (Pierre Borel) 231 New World see America New World, The (Amerigo Vespucci) 255 New Zealand 120n Newcomen, Thomas 20, 490, 499–508, 538 Newe Attractive, The (Robert Norman) 80 Newton, Isaac 380–5 see also Opticks; Principia alchemist, an 206, 353, 355, 358, 359 alternative argument to faith, an 471 Arianism 379 Aristotle and 51 as part of contemporary libraries 11 at Cambridge 15 Bentley and 467 Blake and 448 calculus 564n clergymen interested in 473 corpuscular philosophy and 447 Diderot and 53 Earth’s shape 367 Einstein and 568–9 eventual triumph of 228 experimentum crucis 352n, 381, 383 ‘fact’ – use of term avoided 417 fact and theory 418 French expeditions validate 524 gravity theory 393, 466, 516, 517 see also gravity hunger for experimental knowledge 357 hypothesis, on 389, 390, 551 ideas triumph 5 inertia 372 Kepler and 24n Leibniz, dispute with 93, 488–9, 498 literary style and 265 making machines 319 physics as modern science 16 Pope’s epitaph 361 prism experiments 311 professorship at Cambridge 32 ‘revolution’, the word 33 Richard Davies on 34n Royal Society 396 Scientific Revolution ends 54 shape of globe and 481 space and time 105 standing on shoulders of giants quote 341 substance and property 397 temperature scales 235 theory and observation 394 theory of light 522 three laws 376 two types of knowledge 321 was a scientist 159 writing the Principia 108–9 Niceron, Father 173, 174 Nicholas of Cusa 147–8, 151, 217, 525 Nicot, Jean 286 Noah 113 Nobel Prize 103 ‘Nobody Invented the Scientific Method’ (Thony Christie) 529n nominalism 322, 369–70 Norman, Robert 80, 81, 329–30, 331, 387 North, Roger 494–5 North Pole 235 North West passage 525, 527 Northumberland, Earl of 302 nostalgia 63 Notizie istoriche (Vincenzo Antinori) 310 Nouvelle théorie du centre d’oscillation (Johann Bernoulli) 396 Nouvelles de la République des Lettres (Pierre Bayle) 433 Nova de universis philosophia (Francesco Patrizi) 25 Novum organum (Francis Bacon) ii, 312n, 371n Objective Knowledge (Karl Popper) 249, 556 obligation 368 observation 294, 313, 394 occasionalism 378 oceans 113 Odyssey, The (Homer) 6, 10 Of Libertie and Necessitie (Thomas Hobbes) 288 ‘Of Miracles’ (David Hume) 427, 465 Of Natural Magic (Giambattista della Porta) 268, 270–2 Of the Popular Errors of Italy (Girolamo Mercurii) 304 Of the Populousness of Ancient Nations (David Hume) 259 Of the Principles and Duties of Natural Religion (John Wilkins) 418, 443 Of the Proficiency and Advancement of Learning (Francis Bacon) 83 Old Regime and the Revolution, The (Alexis de Tocqueville) 20n Oldenburg, Henry edits Newton 383, 384, 396 intellectual property, concept of 337 interest in alchemy 357 introduction to Wallis on tides 396 network of corresponders 341 Royal Society office holder 296 O’Meara, Edmund 74n ‘On Aerial Navigation’ (Sir George Cayley) 552 On All Sorts of Triangles (Regiomontanus) 187 On Certainty (Ludwig Wittgenstein) 43n, 46–8, 577, 580 On Discovery (Polydore Vergil) 65, 93, 176 On Divine Proportion (Luca Pacioli) 173, 176 On Learned Ignorance (Nicholas of Cusa) 147 On Motion (Galileo Galilei) 199 On Painting (Leon Battista Alberti) 167, 171 On Perspective for Painting (Piero della Francesca) 176 On Poetry (Jonathan Swift) 239n On the Demon-Mania of Witches (Jean Bodin) 533 On the Heavens (Aristotle) 252 On the History of Plants (Leonhart Fuchs) 186 On the Magnet (William Gilbert) beginning of experimental science 273 ‘experiment’, use of word 347 Galileo reads 92n, 318 huge impact of 331 influence on Kepler 485, 517 philosophy of 328 prefatory letter 330 vocabulary used 315 On the Nature of Things (Lucretius) 8n, 365, 372, 558 On the Nothingness of a Fart (Girolamo Cardano) 9 On the Revolutions of the Heavenly Spheres (Nicolaus Copernicus) 136–40 annotations 306 anonymous introduction 388 Bruno on the preface to 149 Copernicus’s diagram 153 delayed publication 108 Digges’ version of Book I 154 first hundred years of publication 19 marginal comments by readers 145 mathematics, on 205 not the beginning of modern science 159 quotation from 55 terraqueous globe 142 Tycho Brahe’s work and 194 On the Six-cornered Snowflake (Johannes Kepler) 212 On the Theory of Coinage (Nicolaus Copernicus) 206 On the Universe (William Gilbert) 158 ‘On Understanding Science’ (James B.

Are there hermaphrodite atoms?ix Donne would have learnt from Hill about the possibility of life on other planets, and of planets circling other stars; he would also have learnt that these strange ideas derived from Giordano Bruno.17 If he read Galileo’s Starry Messenger, with its account of the moon as having mountains and valleys, Donne would surely have responded exactly as the great German astronomer Johannes Kepler did that spring when he read one of the first copies to arrive in Germany – he saw a remarkable vindication of Bruno’s perverse theory that there might be life elsewhere in the universe. If Donne read Kepler’s Conversation he would have found the link with Bruno spelled out.18 Jokes about farts were now beside the point. The gathering recognition was too late for Bruno, who had been burnt alive by the Roman Inquisition in 1600; it was probably too late for Hill too, who, according to a later report, committed suicide in 1610, eating rat poison and dying blaspheming and cursing.

A decade before Galileo’s telescopic discoveries, William Gilbert, the first great experimental scientist of the new age, had acknowledged: ‘Sometimes therefore we use new and unusual words, not that by means of foolish veils of vocabularies we should cover over the facts [rebus] with shades and mists (as Alchemists are wont to do) but that hidden things which have no name, never having been hitherto perceived, may be plainly and correctly enunciated.’lvii 84 His book begins with a glossary to help the reader make sense of these new words. Then a few months after Galileo discovered what we call the moons of Jupiter (Galileo does not call them moons, but first stars and then planets), Johannes Kepler invented a new word for these new objects: they were ‘satellites’.lviii Thus historians who take language seriously need to search out the emergence of new languages, which must represent transformations in what people can think and how they can conceptualize their world.lix It is important here to distinguish this claim from the argument with which this chapter started. The historian has always to learn the language which people in the past used, and must always be alert to changes in that language; that does not mean they need always use that language when writing about the past.


Top 10 Prague by Schwinke, Theodore.

centre right, Defenestration of Prague, G4S, Johannes Kepler, New Urbanism

@ Mordecai Maisel’s Grave Mordecai Maisel (1528– 1601) was ghetto mayor during the reign of Rudolf II, and funded the synagogue that bears his name (see p100). £ Rabbi Loew’s Grave The burial site of one of Prague’s major Jewish figures, Rabbi Jehuda Loew ben Bezalel (1520– 1609), and creator of the Golem (see p52). Gans’s $ David Tombstone A pupil of Rabbi Loew, Gans (1541–1613) was the author of a seminal two-volume history of the Jewish people. He was also an accomplished astronomer during the time of Johannes Kepler (see p35). His headstone (right) is marked with the Star of David, after his name and his faith. Synagogue % Klausen Mordechai Maisel also commissioned the building of the Klausen Synagogue (left) on the cemetery’s northern edge. It now houses exhibitions on Jewish festivals and traditions. Sign up for DK’s email newsletter on traveldk.com Oppenheim’s ^ Rabbi Grave 8 5 3 2 Entrance 6 9 7 0 1 4 Plan of the Old Jewish Cemetery Graves ( Zemach Next to the Pinkas Prague’s Top 10 Rabbi David Oppenheim (left) was the first chief rabbi of Moravia, and later chief rabbi of Bohemia and finally of Prague, where he died in 1736.

Wars £ Hussite After the Church Council at Constance burned Catholic reformer Jan Hus at the stake in 1415 (see p15), his followers literally beat their ploughshares into swords and rebelled against both church and crown. The resulting animosity between Protestant Czechs and German Catholics would rage for centuries. of Rudolph II $ Reign The melancholy emperor (1576–1611) was not much good as a statesman and was under threat from his ambitious brother, Matthias, but he was a liberal benefactor of the arts and sciences. Among his achievements were the support of Johannes Kepler’s studies of planetary motion. He also promoted religious freedom. of White Mountain % Battle The Protestant nobility and the emperor continued to provoke each other until hostilities broke into open war. Imperial forces devastated the Czechs in the first battle of the Thirty Years’ War in 1620. Czech lands were re-Catholicized, but resentment against Vienna and Rome continued to smoulder. ^ Independence While World Battle of White Mountain 34 War I raged, National Revival leaders such as Tomáš Masaryk turned to the United States for support for an independent Czechoslovakia.

Top 10 Historical Figures Maisel $ Mordecai The Jewish mayor (1528– 1601) was one of the richest men in Europe (see p22). de Brahe % Tycho Astronomer at Rudolph’s court, Brahe (1546–1601) suffered a burst bladder when he refused to leave the emperor’s side at a banquet. Kelley and ^ Edward John Dee The English charlatans gained Rudolph II’s trust by converting lead into gold, but were more interested in necromancy. & Johannes Kepler The German astronomer (1571–1630) pioneered studies of planetary motion. von * Albrecht Wallenstein Leader of the Catholics during the Thirty Years’ War, Wallenstein (1583–1634) built a vast palace in Prague (see p86). ( Franz Kafka Prague’s best-known author (1883–1924) was largely unpublished in his lifetime (see p44). ) Emil Zátopek “The Locomotive” (1922– 2000) won three long-distance gold medals at the 1952 Olympic Games.


pages: 406 words: 109,794

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

Martinez, “Giordano Bruno and the Heresy of Many Worlds,” Annals of Science 73, no. 4 (2016): 345–74. Johannes Kepler inherited: Sources that give excellent background on the worldviews that Kepler inherited, and his transformative analogies, are: D. Gentner et al., “Analogical Reasoning and Conceptual Change: A Case Study of Johannes Kepler,” Journal of the Learning Sciences 6, no. 1 (1997): 3–40; D. Gentner, “Analogy in Scientific Discovery: The Case of Johannes Kepler,” in Model-Based Reasoning: Science, Technology, Values, ed. L. Magnani and N. J. Nersessian (New York: Kluwer Academic/Plenum Publishers, 2002), 21–39; D. Gentner et al., “Analogy and Creativity in the Works of Johannes Kepler,” in Creative Thought: An Investigation of Conceptual Structures and Processes, ed. T. B. Ward et al.

Their spirits may have been driving, but the planets also needed a vehicle for motion, so they were assumed to be riding on pure crystalline spheres. The spheres were invisible from Earth and interlocked, like the gears of a clock, to produce collective motion at a constant speed for all eternity. Plato and Aristotle had laid the foundation for the accepted model, and it dominated for two thousand years. That clockwork universe was the one German astronomer Johannes Kepler inherited. He accepted it, at first. When the constellation Cassiopeia suddenly gained a new star (it was actually a supernova, the bright explosion at the end of a star’s life), Kepler recognized that the idea of the unchanging heavens could not be correct. A few years later, a comet tracked across the European sky. Shouldn’t it have cracked the crystalline spheres as it traveled, Kepler wondered?

Koestler, The Sleepwalkers: A History of Man’s Changing Vision of the Universe (New York: Penguin Classics, 2017). “I especially love analogies”: B. Vickers, “Analogy Versus Identity,” in: Occult and Scientific Mentalities in the Renaissance, ed. B. Vickers (Cambridge: Cambridge University Press, 1984). “action at a distance”: Gentner et al., “Analogy and Creativity in the Works of Johannes Kepler.”; E. McMullin, “The Origins of the Field Concept in Physics,” Physics in Perspective 4, no. 1 (2002): 13–39. Suppose you are a doctor: M. L. Gick and K. J. Holyoak, “Analogical Problem Solving,” Cognitive Psychology 12 (1980): 306–55. There once was a general; small-town fire chief; “might well have supposed”; “ill-defined” problems: M. L. Gick and K. J. Holyoak, “Schema Induction and Analogical Transfer,” Cognitive Psychology 15 (1983): 1–38.


pages: 190 words: 52,570

The Planets by Dava Sobel

Albert Einstein, Colonization of Mars, Dava Sobel, Edmond Halley, Eratosthenes, friendly fire, Isaac Newton, Johannes Kepler, Kuiper Belt, music of the spheres, Norman Mailer, Thales of Miletus

None of those individuals, however, had sighted Mercury often enough or precisely enough to help Copernicus establish its orbit as he had hoped. The Danish perfectionist Tycho Brahe, born in 1546, just three years after Copernicus’s death, amassed a great number of Mercury observations—at least eighty-five—from his astronomical castle on the island of Hven, where he used instruments of his own design to measure the positions of each planet at accurately noted times. Inheriting this trove of information, Brahe’s German associate Johannes Kepler determined the correct orbits of all the wanderers in 1609—“even Mercury itself.” It later occurred to Kepler that although Mercury remained hard to see at the horizon, he might catch it high overhead on one of those special occasions, called a “transit,” when the planet must cross directly in front of the Sun. Then, by projecting the Sun’s image through a telescope onto a sheet of paper, where he could view it safely, he would track Mercury’s dark form as it traveled from one edge of the Sun’s disk to the other over a period of several hours.

By the final hour of Galileo’s odyssey, the spacecraft’s horoscope showed Saturn, the planet of endings, well inside the eighth house, the mansion of death. *Two horoscopes drawn for Galileo during his lifetime (1564–1642) show his Sun near six degrees in Pisces. While his birth in Pisa on February 15 would seem to make him an Aquarian (since Aquarius is the Sun sign of those born January 20–February 18), the calendar reforms of 1582 moved his birthday to the 25th. *Johannes Kepler (1571–1630), court astronomer and astrologer in Prague, first referred to the “Medicean stars” as “Galilean satellites” in 1610. Simon Marius, a contemporary of Galileo and Kepler, gave the moons their enduring individual names by selecting four favored lovers of the mythological Zeus/Jupiter. MUSIC of the SPHERES Between 1914 and 1916, the English composer Gustav Holst created the only known example of a symphonic tribute to the Solar System, his Opus 32, The Planets, Suite for Orchestra.

Giovanni Schiaparelli found what he called canali on Mars in 1877, eight years after the completion of the Suez Canal. Schiaparelli, trained as a hydraulic engineer, thought the straight lines no more the product of artificial intelligence than the English Channel, but later changed his mind. When Schiaparelli’s sight failed, Percival Lowell took over observations—and interpretations—of the canals. Johannes Kepler first imagined two moons for Mars in 1610, but the moons were not seen until August 1877, when Asaph Hall, working at the U.S. Naval Observatory in Washington, D.C., found them orbiting so close to the planet as to be nearly lost in its glare. He named them after two characters from Greek mythology, Phobos and Deimos, who were variously described by Homer as the sons of the war god Ares, or his attendants—or the horses that pulled his chariot.


pages: 523 words: 143,139

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths

4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, algorithmic trading, anthropic principle, asset allocation, autonomous vehicles, Bayesian statistics, Berlin Wall, Bill Duvall, bitcoin, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, David Heinemeier Hansson, delayed gratification, dematerialisation, diversification, Donald Knuth, double helix, Elon Musk, fault tolerance, Fellow of the Royal Society, Firefox, first-price auction, Flash crash, Frederick Winslow Taylor, George Akerlof, global supply chain, Google Chrome, Henri Poincaré, information retrieval, Internet Archive, Jeff Bezos, Johannes Kepler, John Nash: game theory, John von Neumann, Kickstarter, knapsack problem, Lao Tzu, Leonard Kleinrock, linear programming, martingale, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, Pierre-Simon Laplace, prediction markets, race to the bottom, RAND corporation, RFC: Request For Comment, Robert X Cringely, Sam Altman, sealed-bid auction, second-price auction, self-driving car, Silicon Valley, Skype, sorting algorithm, spectrum auction, Stanford marshmallow experiment, Steve Jobs, stochastic process, Thomas Bayes, Thomas Malthus, traveling salesman, Turing machine, urban planning, Vickrey auction, Vilfredo Pareto, Walter Mischel, Y Combinator, zero-sum game

Ultimately, what we can gain is not only a set of concrete takeaways for the problems around us, not only a new way to see the elegant structures behind even the hairiest human dilemmas, not only a recognition of the travails of humans and computers as deeply conjoined, but something even more profound: a new vocabulary for the world around us, and a chance to learn something truly new about ourselves. 1 Optimal Stopping When to Stop Looking Though all Christians start a wedding invitation by solemnly declaring their marriage is due to special Divine arrangement, I, as a philosopher, would like to talk in greater detail about this … —JOHANNES KEPLER If you prefer Mr. Martin to every other person; if you think him the most agreeable man you have ever been in company with, why should you hesitate? —JANE AUSTEN, EMMA It’s such a common phenomenon that college guidance counselors even have a slang term for it: the “turkey drop.” High-school sweethearts come home for Thanksgiving of their freshman year of college and, four days later, return to campus single.

So when he found a woman who was a better match than all those he had dated so far, he knew exactly what to do. He leapt. “I didn’t know if she was Perfect (the assumptions of the model don’t allow me to determine that), but there was no doubt that she met the qualifications for this step of the algorithm. So I proposed,” he writes. “And she turned me down.” Mathematicians have been having trouble with love since at least the seventeenth century. The legendary astronomer Johannes Kepler is today perhaps best remembered for discovering that planetary orbits are elliptical and for being a crucial part of the “Copernican Revolution” that included Galileo and Newton and upended humanity’s sense of its place in the heavens. But Kepler had terrestrial concerns, too. After the death of his first wife in 1611, Kepler embarked on a long and arduous quest to remarry, ultimately courting a total of eleven women.

analogy to a human mathematician: In section 9 of Turing, “On Computable Numbers,” Turing justifies the choices made in defining what we now call a Turing machine by comparing them to operations that a person might carry out: a two-dimensional piece of paper becomes a one-dimensional tape, the person’s state of mind becomes the state of the machine, and symbols are written and read as the person or machine moves around on the paper. Computation is what a computer does, and at the time the only “computers” were people. we are irrational and error-prone: For example, see Gilovich, How We Know What Isn’t So; Ariely and Jones, Predictably Irrational; and Marcus, Kluge. 1. OPTIMAL STOPPING “Though all Christians start”: From Kepler’s letter to “an unknown nobleman” on October 23, 1613; see, e.g., Baumgardt, Johannes Kepler. such a common phenomenon: The turkey drop is mentioned, among many other places, in http://www.npr.org/templates/story/story.php?storyId=120913056 and http://jezebel.com/5862181/technology-cant-stop-the-turkey-drop. In any optimal stopping problem: For more about the mathematics of optimal stopping, Ferguson, Optimal Stopping and Applications, is a wonderful reference. optimal stopping’s most famous puzzle: A detailed treatment of the nature and origins of the secretary problem appears in Ferguson, “Who Solved the Secretary Problem?”


pages: 233 words: 62,563

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

The same year, Copernicus’s De Revolutionibus was placed on the Index of forbidden books. An attack on Aristotle was considered an attack upon the church. Despite the church’s Counter-Reformation, the new philosophy wasn’t easily destroyed. It got stronger as time went on, thanks to the investigations of Copernicus’s successors. In the beginning of the seventeenth century, another astrologer-monk, Johannes Kepler, refined Copernicus’s theory, making it even more accurate than the Ptolemaic system. Instead of moving in circles, the planets, including Earth, moved in ellipses around the sun. This explained the motion of the planets in the heavens with incredible accuracy; no longer could astronomers object that the heliocentric system was inferior to the geocentric one. Kepler’s model was simpler than Ptolemy’s, and it was more accurate.

And an infinite sum of zeros can equal anything at all—and everything at the same time. Something very bizarre was going on; nobody knew quite how to handle the infinite. Luckily the physical world made a little more sense than the mathematical one. Adding infinite things to each other seems to work out most of the time, so long as you are dealing with something in real life, like finding the volume of a barrel of wine. And 1612 was a banner year for wine. Johannes Kepler—the man who figured out that planets move in ellipses—spent that year gazing into wine barrels, since he realized that the methods that vintners and coopers used to estimate the size of barrels were extremely crude. To help the wine merchants out, Kepler chopped up the barrels—in his mind—into an infinite number of infinitely tiny pieces, and then added them back together again to yield their volumes.

Poncelet’s mathematics was the culmination of the work begun by the artists and architects of the fifteenth century, like Filippo Brunelleschi and Leonardo da Vinci, who discovered how to draw realistically—in perspective. When “parallel” lines converge at the vanishing point in a painting, observers are tricked into believing that the lines never meet. Squares on the floor become trapezoids in a painting; everything gets gently distorted, but it looks perfectly natural to the viewer. This is the property of an infinitely distant point—a zero at infinity. Johannes Kepler, the man who discovered that planets travel in ellipses, took this idea—the infinitely distant point—one step further. Ellipses have two centers, or foci; the more elongated the ellipse, the farther apart these foci are. And all ellipses have the same property: if you had a mirror in the shape of an ellipse and you placed a lightbulb at one focus, all the beams of light would converge at the other focus, no matter how stretched-out the ellipses are (Figure 29).


The Rough Guide to Prague by Humphreys, Rob

active transport: walking or cycling, Albert Einstein, anti-communist, Berlin Wall, centre right, clean water, Fall of the Berlin Wall, Frank Gehry, Johannes Kepler, land reform, Live Aid, Mikhail Gorbachev, Peace of Westphalia, sexual politics, sustainable-tourism, trade route, upwardly mobile

Bad-tempered, paranoid and probably insane, Rudolf had little interest in the affairs of state – instead, he holed up in the Hrad and indulged his own personal passions of alchemy, astrology and art. Thus, Rudolfine Prague played host to an impressive array of international artists, including the idiosyncratic Giuseppe Arcimboldo, whose surrealist portrait heads were composed entirely of objects. The astronomers Johannes Kepler and Tycho Brahe were summoned to Rudolf’s court to chart the planetary movements and assuage Rudolf’s superstitions, and the English alchemists Edward Kelley and John Dee were employed in order to discover the secret of the philosopher’s stone, the mythical substance that would transmute base metal into gold. Accompanied by his pet African lion, Otakar, Rudolf spent less and less time in public, hiding out in the Hrad, where he “loved to paint, weave and dabble in inlaying and watchmaking”, according to modern novelist Angelo Maria Ripellino.

The focus of the gardens is the gigantic Italianate sala terrena, a monumental loggia decorated with frescoes of the Trojan Wars, which stands at the end of an avenue of bronze sculptures by Adriaen de Vries. The originals, which Waldstein 70 Albrecht von Waldstein (known to the Czechs as Albrecht z Valdštejna, and to the English as Wallenstein – the name given to him by the German playwright Schiller in his tragic trilogy) was the most notorious warlord of the Thirty Years’ War. If the imperial astrologer Johannes Kepler is to be believed, this is all because he was born at four in the afternoon on September 14, 1583. According to Kepler’s horoscope, Waldstein was destined to be greedy, deceitful, unloved and unloving. Sure enough, at an early age he tried to kill a servant, for which he was expelled from his Lutheran school. Recuperating in Italy, he converted to Catholicism (an astute career move) and married a wealthy widow who conveniently died shortly after the marriage.

At roughly the centre of the Klementinum complex, is the Jesuits’ Astronomická věž (Astonomical Tower), from which you can enjoy a superb view over the centre of Prague. The tower is also the only place in the world that has been monitoring and recording meteorological data since 1775. Until 1928, the tower was also used to signal noon to the citizens of Prague: a man would wave a flag from the tower and a cannon would be fired from Petřín Hill. Incidentally, Prague’s most illustrious visiting scientist, Johannes Kepler (1571–1630), who succeeded Tycho Brahe as court astronomer to Rudolf II, lived at Karlova 4 for a number of years. A Protestant exile from his native Germany, Kepler drew up the first heliocentric laws on the movement of the planets while in Prague, though he did his planet-gazing in the Belvedér, not in the Klementinum. Malé náměstí After a couple more shops, boutiques, hole-in-the-wall bars and a final twist in Karlova, you emerge onto Malé náměstí, originally settled by French merchants in the twelfth century.


pages: 532 words: 133,143

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

Gingerich, “Giovanni Antonio Magini’s ‘Keplerian’ Tables of 1614 and Their Implications for the Reception of Keplerian Astronomy in the Seventeenth Century,” Journal for the History of Astronomy 32, 237 (2001). 16. Quoted in Robert S. Westfall, The Construction of Modern Science—Mechanism and Mechanics (Cambridge University Press, Cambridge, 1977), p. 10. 17. This is the translation of William H. Donahue, in Johannes Kepler—New Astronomy (Cambridge University Press, Cambridge, 1992), p. 65. 18. Johannes Kepler, Epitome of Copernican Astronomy and Harmonies of the World, trans. Charles Glenn Wallis (Prometheus, Amherst, N.Y., 1995), p. 180. 19. Quoted by Owen Gingerich in Tribute to Galileo in Padua, International Symposium a cura dell’Universita di Padova, 2–6 dicembre 1992, Volume 4 (Edizioni LINT, Trieste, 1995). 20. Quotations from Galileo Galilei, Siderius Nuncius, or The Sidereal Messenger, trans.

This was not what one would expect if the Sun goes around the Earth (or the Earth around the Sun) in a circle at constant speed, with the Earth (or the Sun) at the center, in which case the seasons would be of equal length. Astronomers tried for centuries to understand the inequality of the seasons, but the correct explanation of this and other anomalies was not found until the seventeenth century, when Johannes Kepler realized that the Earth moves around the Sun on an orbit that is elliptical rather than circular, with the Sun not at the center of the orbit but off to one side at a point called a focus, and moves at a speed that increases and decreases as the Earth approaches closer to and recedes farther from the Sun. The Moon also seems to revolve like the stars each night from east to west around the north celestial pole; and over longer times it moves, like the Sun, through the zodiac from west to east, but taking a little more than 27 days instead of a year to make a full circle against the background of stars.

He was succeeded by Christian IV, whom Danes today regard as one of their greatest kings, but who unfortunately had little interest in supporting work on astronomy. Tycho’s last observations from Hven were made in 1597; he then left on a journey that took him to Hamburg, Dresden, Wittenberg, and Prague. In Prague, he became the imperial mathematician to the Holy Roman Emperor Rudolph II and started work on a new set of astronomical tables, the Rudolphine Tables. After Tycho’s death in 1601, this work was continued by Kepler. Johannes Kepler was the first to understand the nature of the departures from uniform circular motion that had puzzled astronomers since the time of Plato. As a five-year-old he was inspired by the sight of the comet of 1577, the first comet that Tycho had studied from his new observatory on Hven. Kepler attended the University of Tübingen, which under the leadership of Melanchthon had become eminent in theology and mathematics.


pages: 393 words: 115,217

Loonshots: How to Nurture the Crazy Ideas That Win Wars, Cure Diseases, and Transform Industries by Safi Bahcall

accounting loophole / creative accounting, Albert Einstein, Apple II, Apple's 1984 Super Bowl advert, Astronomia nova, British Empire, Cass Sunstein, Charles Lindbergh, Clayton Christensen, cognitive bias, creative destruction, disruptive innovation, diversified portfolio, double helix, Douglas Engelbart, Douglas Engelbart, Edmond Halley, Gary Taubes, hypertext link, invisible hand, Isaac Newton, Johannes Kepler, Jony Ive, knowledge economy, lone genius, Louis Pasteur, Mark Zuckerberg, Menlo Park, Mother of all demos, Murray Gell-Mann, PageRank, Peter Thiel, Philip Mirowski, Pierre-Simon Laplace, prediction markets, pre–internet, Ralph Waldo Emerson, RAND corporation, random walk, Richard Feynman, Richard Thaler, side project, Silicon Valley, six sigma, Solar eclipse in 1919, stem cell, Steve Jobs, Steve Wozniak, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Tim Cook: Apple, tulip mania, Wall-E, wikimedia commons, yield management

STEVE JOBS: A BRIEF INTERLUDE Stories of great breakthroughs tend to coalesce around one person, one genius, and often one moment. Those stories are fun to tell and easy to digest. Occasionally they are true. More often, they contain a kernel of truth, but omit a much richer and more interesting picture. Isaac Newton, for example, is often celebrated for discovering universal gravity, explaining the motion of the planets, and inventing calculus. But well before Newton’s Principia, it was Johannes Kepler who first suggested the idea of a force from the sun driving the motion of the planets, Robert Hooke who first suggested a principle of universal gravity, Christiaan Huygens who showed that circular motion generates a centrifugal force, many who used Huygens’s law to derive the now-familiar form of gravity, Giovanni Borelli who explained the elliptical motion of Jupiter’s moons using gravitational forces, John Wallis and others who created the differential mathematics Newton used, and Gottfried Leibniz who invented calculus in the form we use today.

In 1589, the most prominent Italian astronomer, Giovanni Magini, wrote of Copernicus’s ideas: “His hypotheses are rejected by practically everybody as being absurd.” One historian identified only five scholars across all Europe around that time, five decades after Copernicus’s death, who believed in his sun-centered world. One of those five was a teacher at the University of Tübingen in Germany named Michael Maestlin, whose lectures on planetary motion impressed a 17-year-old student named Johannes Kepler. This is Kepler describing himself in his diary: His appearance is that of a little lap-dog. His body is agile, wiry and well-proportioned. Even his appetites were alike: he liked gnawing bones and dry crusts of bread.… He is bored with conversation, but greets visitors just like a little dog; yet when the last thing is snatched away from him, he flares up and growls.… He hates many people exceedingly and they avoid him, but his masters are fond of him.

(His theory of general relativity explained those forces by showing how matter curves the space around it.) Einstein saw in Kepler a “kindred spirit” who overcame religious persecution, poverty, personal tragedies, disbelieving audiences, and a heritage of mystical thinking. “Kepler’s lifework was possible,” Einstein wrote, “only once he succeeded in freeing himself to a great extent of the intellectual traditions into which he was born.” Kindred spirits: Albert Einstein and Johannes Kepler Unlike Kepler, Einstein benefited from a large and well-established scientific community. As mentioned earlier, the eclipse of 1919 confirmed Einstein’s theory of gravity four years after he published it. Confirmation of Kepler’s ideas proceeded much more gradually. In the decades after Kepler published his “War on Mars,” astronomers and astrologers and navigators slowly realized Kepler’s system worked far better than any earth-centric theory.


pages: 467 words: 114,570

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

To most people in the West, and indeed in the Muslim world, Isaac Newton is the undisputed father of modern optics; at least, that is what we are told at school, where our textbooks abound with his famous experiments with lenses and prisms, his study of the nature of light and its reflection, refraction and decomposition into the colours of the rainbow. Even historians of science who acknowledge that work on optics predates Newton often do not go back any earlier than other notables from the European scientific revolution of the seventeenth century such as René Descartes, Willebrord Snell and Johannes Kepler. But studies of the properties of light, particularly catoptrics (reflection of light by mirrors) and dioptrics (refraction of light through lenses) go back all the way to the Greeks. An interest in optics began in antiquity, with the Babylonians, Egyptians and Assyrians all making use of polished quartz to make rudimentary lenses. The basic principles of geometric optics were laid down by Plato and Euclid and included ideas such as the propagation of light in straight lines and the simple laws of reflection from plane mirrors, while the earliest serious contribution to the field in the Islamic world came from al-Kindi.

Through the use of simple geometric ideas and a value for the size of the earth provided by al-Ma’mūn’s astronomers, Ibn Mu’ādh calculated the height of the atmosphere to be around 52 miles. His work found wide interest in the Latin Middle Ages and in the Renaissance. His method and understanding of atmospheric optics was improved upon only when the Danish astronomer Tycho Brahe raised the issue of atmospheric refraction at the end of the sixteenth century and the subsequent optical work of the great Johannes Kepler was published in 1604. But Ibn Mu’ādh’s value for the height of the atmosphere is still pretty good. Indeed, the boundary between the earth’s atmosphere and outer space, known as the Kármán line, is at an altitude of 62 miles. Ibn Mu’ādh’s method for calculating the height of the atmosphere. If an observer at A catches the last glimpse of twilight on the horizon along his line of sight, at point B, this means there should be matter at B that is still illuminated by the sun.

Among the European scholars influenced by their Islamic counterparts before them were Roger Bacon, whose work on lenses relied heavily on his study of Ibn al-Haytham’s Optics, and Leonardo of Pisa (Fibonacci), who introduced algebra and the Arabic numeral characters after being strongly influenced by the work of al-Khwārizmi. Some historians have even argued that the great German astronomer Johannes Kepler may have been inspired to develop his groundbreaking work on elliptical orbits after studying the work of the twelfth-century Andalusian astronomer al-Bitrūji (Alpetragius), who had tried and failed to modify the Ptolemaic model. While far from the most important of Islamic astronomers, al-Bitrūji’s Principles of Astronomy (Kitab al-Hay’a) became very popular in Europe.3 Of course, the influence of Arabic scientists on the rest of the world, and Western Europe in the Middle Ages in particular, extended far beyond their achievements in the pure sciences.


pages: 298 words: 81,200

Where Good Ideas Come from: The Natural History of Innovation by Steven Johnson

Ada Lovelace, Albert Einstein, Alfred Russel Wallace, carbon-based life, Cass Sunstein, cleantech, complexity theory, conceptual framework, cosmic microwave background, creative destruction, crowdsourcing, data acquisition, digital Maoism, digital map, discovery of DNA, Dmitri Mendeleev, double entry bookkeeping, double helix, Douglas Engelbart, Douglas Engelbart, Drosophila, Edmond Halley, Edward Lloyd's coffeehouse, Ernest Rutherford, Geoffrey West, Santa Fe Institute, greed is good, Hans Lippershey, Henri Poincaré, hive mind, Howard Rheingold, hypertext link, invention of air conditioning, invention of movable type, invention of the printing press, invention of the telephone, Isaac Newton, Islamic Golden Age, James Hargreaves, James Watt: steam engine, Jane Jacobs, Jaron Lanier, Johannes Kepler, John Snow's cholera map, Joseph Schumpeter, Joseph-Marie Jacquard, Kevin Kelly, lone genius, Louis Daguerre, Louis Pasteur, Mason jar, mass immigration, Mercator projection, On the Revolutions of the Heavenly Spheres, online collectivism, packet switching, PageRank, patent troll, pattern recognition, price mechanism, profit motive, Ray Oldenburg, Richard Florida, Richard Thaler, Ronald Reagan, side project, Silicon Valley, silicon-based life, six sigma, Solar eclipse in 1919, spinning jenny, Steve Jobs, Steve Wozniak, Stewart Brand, The Death and Life of Great American Cities, The Great Good Place, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, transaction costs, urban planning

Concepts from one domain migrate to another as a kind of structuring metaphor, thereby unlocking some secret door that had long been hidden from view. In his memoirs, Francis Crick reports that he first hit upon the complementary replication system of DNA—each base A matched with a T, and each C with a G—by thinking of the way a work of sculpture can be reproduced by making an impression in plaster, and then using that impression, when dry, as a mold to create copies. Johannes Kepler credited his laws of planetary motion to a generative metaphor imported from religion; he imagined the sun, stars, and the dark space between them as the celestial equivalents of the Father, Son, and Holy Ghost. When computer science pioneers like Doug Engelbart and Alan Kay invented the graphical interface, they imported a metaphor from the real-world environment of offices: instead of organizing information on the screen as a series of command-line inputs, the way a programmer would, they borrowed the iconography of a desktop with pieces of paper stacked on it.

TELESCOPE (1600--1610) A classic example of collective invention, the first telescopes and spyglasses began to appear in Europe in the first decade of the seventeenth century. Two patent applications were filed on designs in the Netherlands in 1608, and by 1609 Galileo was using a device he built with 20x magnification to gaze at the stars, discovering Jupiter’s moons in the process. ELLIPTICAL ORBITS (1605--1609) The German astronomer and mathematician Johannes Kepler was the first to document the elliptical orbit that the planets took around the sun, though he built his equations by analyzing data collected by Tycho Brahe, his friend and occasional employer. JUPITER’S MOONS (1610) With the aid of a telescope, Galileo Galilei first observed the orbiting moons of Jupiter, thus proving the fundamental principle of the Copernican system, that the universe did not revolve around earth.

BLOOD CIRCULATION (1628) English physician William Harvey correctly theorized the movement of blood through the human body as pumped by the heart and cycled perpetually, dispelling earlier arguments for the existence of two separate circulation systems. VERNIER SCALE (1631) The Vernier scale, invented by French mathematician Pierre Vernier, can be used in conjunction with a larger scale to precisely measure extremely small units of space. It became widely employed in navigation systems. OCEAN TIDES (1632) Following in the steps of the ancients, Galileo Galilei ventured an explanation of ocean tides in relation to the sun. Johannes Kepler correctly theorized that it was the earth’s relation to the moon that created the phenomenon, and Isaac Newton furnished the scientific community with a fully developed explanation in 1687. SLIDE RULE (1632) William Oughtred is commonly credited with inventing the earliest version of the slide rule, two parallel logarithmic scales that one could slide in relation to each other to conduct advanced calculations easily and quickly.


pages: 315 words: 93,628

Is God a Mathematician? by Mario Livio

Albert Einstein, Antoine Gombaud: Chevalier de Méré, Brownian motion, cellular automata, correlation coefficient, correlation does not imply causation, cosmological constant, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Georg Cantor, Gerolamo Cardano, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, music of the spheres, Myron Scholes, probability theory / Blaise Pascal / Pierre de Fermat, Russell's paradox, Thales of Miletus, The Design of Experiments, the scientific method, traveling salesman

The seven subjects taught in those universities were divided into the trivium, which included dialectic, grammar, and rhetoric, and the quadrivium, which included the favorite topics of the Pythagoreans—geometry, arithmetic, astronomy, and music. The celestial “harmony of the spheres”—the music supposedly performed by the planets in their orbits, which, according to his disciples, only Pythagoras could hear—has inspired poets and scientists alike. The famous astronomer Johannes Kepler (1571–1630), who discovered the laws of planetary motion, chose the title of Harmonice Mundi (Harmony of the World) for one of his most seminal works. In the Pythagorean spirit, he even developed little musical “tunes” for the different planets (as did the composer Gustav Holst three centuries later). From the perspective of the questions that are at the focus of the present book, once we strip the Pythagorean philosophy of its mystical clothing, the skeleton that remains is still a powerful statement about mathematics, its nature, and its relation to both the physical world and the human mind.

Galileo’s father died in 1591, prompting the young man, who had now to support his family, to take an appointment in Padua, where his salary was tripled. The next eighteen years proved to be the happiest in Galileo’s life. In Padua he also began his long-term relationship with Marina Gamba, whom he never married, but who bore him three children—Virginia, Livia, and Vincenzio. On August 4, 1597, Galileo wrote a personal letter to the great German astronomer Johannes Kepler in which he admitted that he had been a Copernican “for a long time,” adding that he found in the Copernican heliocentric model a way to explain a number of natural events that could not be explained by the geocentric doctrine. He lamented the fact, however, that Copernicus “appeared to be ridiculed and hissed off the stage.” This letter marked the widening of the momentous rift between Galileo and the Aristotelian cosmology.

No wonder, then, that they, and Euclid (who documented this tradition), invented the concept of the golden ratio that was involved in these constructions, and gave it a name. Unlike any other arbitrary ratio, the number 1.618…now became the focus of an intense and rich history of investigation, and it continues to pop up even today in the most unexpected places. For instance, two millennia after Euclid, the German astronomer Johannes Kepler discovered that this number appears, miraculously as it were, in relation to a series of numbers known as the Fibonacci sequence. The Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,…is characterized by the fact that, starting with the third, each number is the sum of the previous two (e.g., 2 = 1 + 1;3 = 1 + 2;5 = 2 + 3; and so on). If you divide each number in the sequence by the one immediately preceding it (e.g., 144 ÷ 89; 233 ÷ 144;…), you find that the ratios oscillate about, but come closer and closer to the golden ratio the farther you go in the sequence.


pages: 310 words: 89,653

The Interstellar Age: Inside the Forty-Year Voyager Mission by Jim Bell

Albert Einstein, crowdsourcing, dark matter, Edmond Halley, Edward Charles Pickering, en.wikipedia.org, Eratosthenes, gravity well, Isaac Newton, Johannes Kepler, Kuiper Belt, Mars Rover, Pierre-Simon Laplace, planetary scale, Pluto: dwarf planet, polynesian navigation, Ronald Reagan, Saturday Night Live, Search for Extraterrestrial Intelligence, Stephen Hawking

Science, perhaps especially astronomical science, generally begins with highly motivated individuals making careful observations, or working out interactive theories, essentially on their own or with just a few select others. Notable examples from the history of Western astronomy include pioneers like the sixteenth-century Polish astronomer Nicolaus Copernicus; Danish observer Tycho Brahe and German astronomer Johannes Kepler working together in the late sixteenth century; the late-seventeenth-century English physicist Isaac Newton; and of course the first loner at the telescope, Galileo Galilei, in the early 1600s. But the history of individual, or “small,” science pushed forward mostly by key individuals goes much farther back in time and crosses many cultures, including notable Greek, Arab, Persian, Chinese, Indian, and other thinkers.

Now that it was possible to accurately track the positions of Uranus and the other planets against the background stars with unprecedented precision, it was also possible to search for tiny deviations in their positions that could arise from the gravitational attraction that might be exerted by some new, as-yet-undiscovered planet. In some sense, just like the Voyagers, all of the planets, moons, asteroids, and comets in the solar system are constantly going through mini gravity-assist flybys with one another, slightly tweaking their positions relative to what would otherwise be the kinds of perfectly predictable orbital motions that Johannes Kepler and Isaac Newton had long ago described. When my colleagues on the navigation team at JPL, for example, want to study a possible trajectory for a new space mission, they load their computers with the positions and masses of the sun, all the planets and their fifty or so large moons, and more than a half million asteroids, to make sure that every single possible “perturber” of the spacecraft is taken into consideration in their calculations.

Transits are rare events, but they do happen if you’re in the right place at the right time, and if you were to observe huge numbers of nearby stars, then even rare events like that should happen to some of those stars now and then. That was exactly the philosophy that Bill Borucki had in mind when he and colleagues pitched the Kepler space telescope mission (named after the planetary-orbit discoverer Johannes Kepler) to NASA in 2001. Bill’s idea was to launch a very sensitive camera and telescope—so sensitive that they could detect a 0.002 percent change in the light of a star corresponding to the dimming caused by transiting Earth-sized or smaller planets—and to literally stare at the same 150,000 stars or so for years to detect such transits. On the one hand, the Kepler mission has got to represent the most boring mission ever conducted, as it would orbit far beyond the Earth, and simply stare at the same region of space (a random patch of sky about as big as your fist held out at arm’s length, in the northern constellations Cygnus and Lyra) over and over and over, radioing the same picture back to Earth again and again and again.


pages: 361 words: 97,787

The Curse of Cash by Kenneth S Rogoff

Andrei Shleifer, Asian financial crisis, bank run, Ben Bernanke: helicopter money, Berlin Wall, bitcoin, blockchain, Boris Johnson, Bretton Woods, business cycle, capital controls, Carmen Reinhart, cashless society, central bank independence, cryptocurrency, debt deflation, disruptive innovation, distributed ledger, Edward Snowden, Ethereum, ethereum blockchain, eurozone crisis, Fall of the Berlin Wall, fiat currency, financial exclusion, financial intermediation, financial repression, forward guidance, frictionless, full employment, George Akerlof, German hyperinflation, illegal immigration, inflation targeting, informal economy, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, Johannes Kepler, Kenneth Rogoff, labor-force participation, large denomination, liquidity trap, money market fund, money: store of value / unit of account / medium of exchange, moral hazard, moveable type in China, New Economic Geography, offshore financial centre, oil shock, open economy, payday loans, price stability, purchasing power parity, quantitative easing, RAND corporation, RFID, savings glut, secular stagnation, seigniorage, The Great Moderation, the payments system, The Rise and Fall of American Growth, transaction costs, unbanked and underbanked, unconventional monetary instruments, underbanked, unorthodox policies, Y2K, yield curve

“The Financial Flows of Transnational Crime and Tax Fraud in OECD Countries: What Do We (Not) Know?” Public Finance Review 41 (3): 677–707. ———. 2015. “The Financial Flows of Transnational Crime and Tax Fraud: How Much Cash Is Used and What We Do (Not) Know.” Talk presented at Johannes Kepler Universität Linz, November. Slides available at www.libinst.ch/presentationen/LI-FSchneider-Bargeldtrial.pdf. ———. 2016. “Size and Development of the Shadow Economy of 31 European and 5 Other OECD Countries” (January). Mimeo, Department of Economics, Johannes Kepler University Linz, Austria. Schneider, Friedrich, and Andreas Buehn. 2012. “Size and Development of Tax Evasion in 38 OECD Countries: What Do We (Not) Know?” CESifo Working Paper 4004 (November). University of Munich, Germany. Schneider, Friedrich, Andreas Buehn, and Claudio E.

Schneider, Friedrich, Andreas Buehn, and Claudio E. Montenegro. 2010. “New Estimates for the Shadow Economies All Over the World.” International Economic Journal 24 (December): 443–61. Schneider, Friedrich, and Alexandra Rudolph. 2013. “International Human Trafficking: Measuring Clandestinity by the Structural Equation Approach.” Working Paper 1325 (December). Department of Economics, Johannes Kepler University Linz, Austria. Schneider, Friedrich, and Colin Williams. 2013. The Shadow Economy. London: Profile Books and Institute for International Affairs. Schuh, Scott, and Joanna Stavins. 2015. “The 2013 Survey of Consumer Payment Choice: Summary Results.” Federal Reserve Bank of Boston Research Data Report 15-4 (July 27). Seitz, Franz. 1995. “The Circulation of the Deutschmark Abroad.” Deutsche Bank Discussion Paper 1/95.


pages: 492 words: 149,259

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

Fortunately, Tycho’s instruments had been designed to be transportable, because he had shrewdly realised: ‘An astronomer must be cosmopolitan, because ignorant statesmen cannot be expected to value their services.’ Tycho Brahe migrated to Prague, where Emperor Rudolph II appointed him Imperial Mathematician and allowed him to establish a new observatory in Benatky Castle. The move turned out to have a silver lining, because it was in Prague that Tycho teamed up with a new assistant, Johannes Kepler, who would arrive in the city a few months later. The Lutheran Kepler had been forced to flee his previous home in Graz when the fiercely Catholic Archduke Ferdinand had threatened to execute him, in keeping with his stated declaration that he would rather ‘make a desert of the country than rule over heretics’. Fittingly, Kepler set out on his journey to Prague on 1 January 1600. The start of a new century would mark the start of a new collaboration that would lead to a reinvention of the universe.

Together their achievements illustrate a key feature of scientific progress, namely how theories and models are developed and refined over time by several scientists building on each other’s work. Copernicus was prepared to make the theoretical leap that relegated the Earth to a mere satellite and promoted the Sun to the central role. Tycho Brahe, despite his brass nose, provided the observational evidence that would later help Johannes Kepler to identify the outstanding flaw in Copernicus’s model, namely that the planetary orbits are slightly elliptical, not perfectly circular. Finally, Galileo used a telescope to discover the key evidence that should have convinced doubters. He showed that the Earth is not at the centre of everything, because Jupiter has its own satellites. Also, he showed that the phases of Venus are only compatible with a Sun-centred universe.

Scholars trawled through the lists of Biblical begats from Genesis onwards, adding up the years between each birth, taking into account Adam, the prophets, the reigns of the kings, and so on, keeping a careful running total as they went along. There were sufficient uncertainties for the estimated date of creation to vary by up to three thousand years, depending on who was doing the reckoning. Alfonso X of Castile and León, for instance, the king responsible for the Alphonsine Tables, quoted the oldest date for creation, 6904 BC, while Johannes Kepler preferred a date at the lower end of the range, 3992 BC. The most fastidious calculation was by James Ussher, who became the Archbishop of Armagh in 1624. He employed an agent in the Middle East to seek out the oldest known Biblical texts, to make his estimate less susceptible to errors in transcription and translation. He also put an enormous effort into anchoring the Old Testament chronology to an event in recorded history.


pages: 363 words: 108,670

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

For the virtue of these new planets must needs vary the judicial part, and why may there not yet be more? These things I have been bold thus to discourse unto your Lordship, whereof here all corners are full. And the author runneth a fortune to be either exceeding famous or exceeding ridiculous. By the next ship your Lordship shall receive from me one of the above instruments, as it is bettered by this man. In Prague, the highly respected Johannes Kepler, imperial astronomer to Rudolf II, read the emperor’s copy of the book and leaped to judgment—despite the lack of a good telescope that could confirm Galileo’s findings. “I may perhaps seem rash in accepting your claims so readily with no support of my own experience,” Kepler wrote to Galileo. “But why should I not believe a most learned mathematician, whose very style attests the soundness of his judgment?”

Tycho Brahe dies. 1603 Prince Federico Cesi founds Lyncean Academy in Rome. 1604 New star appears in the heavens, generating debate and three public lectures by Galileo. 1605 Prince Cosimo de’ Medici takes instruction from Galileo. 1606 Galileo publishes treatise on geometric and military compass; Vincenzio Galilei (son) is born in Padua. 1607 Baldessar Capra publishes pirated Latin edition of Galileo’s instructions for geometric and military compass. 1608 Hans Lippershey invents a refracting telescope in Holland. Prince Cosimo marries Maria Maddalena, archduchess of Austria. 1609 Grand Duke Ferdinando I dies; Cosimo II succeeds him. Galileo improves telescope, observes and measures mountains on the Moon. Johannes Kepler (1571-1630) publishes first two laws of planetary motion. 1610 Galileo discovers the moons of Jupiter. The Starry Messenger is published. Galileo is appointed chief mathematician and philosopher to the grand duke of Tuscany, Cosimo II. 1611 Galileo visits Rome, is elected to membership in the Lyncean Academy. 1612 Bodies That Stay Atop Water or Move Within It is published in Florence. 1613 Prince Cesi publishes Galileo’s Sunspot Letters; Virginia and Livia Galilei (daughters) enter the Convent of San Matteo in Arcetri. 1614 Virginia and Livia Galilei assume religious habit. 1616 Galileo writes his “Theory on the Tides.”

The Galileo Affair: A Documentary History. Berkeley: University of California Press, 1989. ----------. Galileo on the World Systems. Berkeley: University of California Press, 1997. Galilei, Celeste. Lettere al Padre. Edited by Giovanni Ansaldo (1927). Genoa: Blengino, 1992. Galilei, Galileo. The Assayer. In The Controversy on the Comets of 1618, by Galileo Galilei, Horatio Grassi, Mario Guiducci, and Johannes Kepler. Translated by Stillman Drake and C. D. O’Malley. Philadelphia: University of Pennsylvania Press, i960. alogo di Galileo Galilei Linceo. Florence: Gio: Batista Landini, 1632. ----------. Dialogue Concerning the Two Chief World Systems. Translated by Stillman Drake. Berkeley: University of California Press, 1967. ----------. Dialogues Concerning Two New Sciences. Translated by Henry Crew and Alfonso de Salvio.


pages: 221 words: 61,146

The Crowded Universe: The Search for Living Planets by Alan Boss

Albert Einstein, Dava Sobel, diversified portfolio, full employment, if you build it, they will come, Johannes Kepler, Kuiper Belt, low earth orbit, Mars Rover, Pluto: dwarf planet, Silicon Valley, wikimedia commons, zero-sum game

Borucki gave a talk at the Baltimore meeting about the Kepler Mission, the new name for FRESIP. Rather than choose a new acronym, Borucki went with the rage at the time of naming missions after famous scientists, as had been the case when NASA’s Space Telescope was named after the Carnegie Institution astronomer, Edwin P. Hubble, who had discovered the fact that the universe is expanding. Johannes Kepler (1571-1630) was a German astronomer who built on the work of previous astronomers, such as the Polish astronomer Nicolas Copernicus, who proposed in 1530 that the planets orbited the Sun, not the other way around, and the Danish astronomer Tycho Brahe, who could not quite take the leap to believe in Copernicus’s heliocentric, or Sun-centered, universe but nevertheless made sufficiently precise measurements of the locations of the planets in the sky to allow his successor, Kepler, to take the next logical steps.

Kepler’s Third Law of planetary motion showed how the orbital periods of planets are related to their distances from the Sun, a fact that is used routinely to determine the sizes of the orbits of extrasolar planets where only the orbital period is determined directly. Kepler also founded the field of astrometry, which Peter van de Kamp would use over three centuries later to search for a planet around Barnard’s star. And Kepler accomplished all of this during an era when he had to spend time defending his mother against charges of witchcraft. FIGURE 10. Johannes Kepler [1571-1630], the German astronomer who first understood the elliptical nature and basic laws of planetary orbits. [Courtesy of NASA’s Kepler Mission and the Sternwarte Kremsmunster, Upper-Austria.] Borucki estimated at the Baltimore meeting that if the Solar System was typical of planetary systems, the Kepler Mission would discover not just one or two but hundreds of Earth-like planets.


pages: 186 words: 64,267

A Brief History of Time by Stephen Hawking

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, bet made by Stephen Hawking and Kip Thorne, Brownian motion, cosmic microwave background, cosmological constant, dark matter, Edmond Halley, Ernest Rutherford, Henri Poincaré, Isaac Newton, Johannes Kepler, Magellanic Cloud, Murray Gell-Mann, Richard Feynman, Stephen Hawking

FIGURE 1.1 A simpler model, however, was proposed in 1514 by a Polish priest, Nicholas Copernicus. (At first, perhaps for fear of being branded a heretic by his church, Copernicus circulated his model anonymously.) His idea was that the sun was stationary at the center and that the earth and the planets moved in circular orbits around the sun. Nearly a century passed before this idea was taken seriously. Then two astronomers—the German, Johannes Kepler, and the Italian, Galileo Galilei—started publicly to support the Copernican theory, despite the fact that the orbits it predicted did not quite match the ones observed. The death blow to the Aristotelian/Ptolemaic theory came in 1609. In that year, Galileo started observing the night sky with a telescope, which had just been invented. When he looked at the planet Jupiter, Galileo found that it was accompanied by several small satellites or moons that orbited around it.

This implied that everything did not have to orbit directly around the earth, as Aristotle and Ptolemy had thought. (It was, of course, still possible to believe that the earth was stationary at the center of the universe and that the moons of Jupiter moved on extremely complicated paths around the earth, giving the appearance that they orbited Jupiter. However, Copernicus’s theory was much simpler.) At the same time, Johannes Kepler had modified Copernicus’s theory, suggesting that the planets moved not in circles but in ellipses (an ellipse is an elongated circle). The predictions now finally matched the observations. As far as Kepler was concerned, elliptical orbits were merely an ad hoc hypothesis, and a rather repugnant one at that, because ellipses were clearly less perfect than circles. Having discovered almost by accident that elliptical orbits fit the observations well, he could not reconcile them with his idea that the planets were made to orbit the sun by magnetic forces.


pages: 203 words: 63,257

Neutrino Hunters: The Thrilling Chase for a Ghostly Particle to Unlock the Secrets of the Universe by Ray Jayawardhana

Albert Einstein, Alfred Russel Wallace, anti-communist, Arthur Eddington, cosmic microwave background, dark matter, Ernest Rutherford, invention of the telescope, Isaac Newton, Johannes Kepler, Magellanic Cloud, New Journalism, race to the bottom, random walk, Richard Feynman, Schrödinger's Cat, Skype, Solar eclipse in 1919, South China Sea, Stephen Hawking, undersea cable, uranium enrichment

By midmorning of February 24, scientists around the world learned about the discovery, tipped off by phone calls from giddy colleagues and a telegram from the International Astronomical Union. Their delight had to do with the fact that Supernova 1987A (as it came to be known) was the first one observed in our galactic neighborhood since the invention of the telescope nearly four centuries earlier. It was the nearest and the brightest supernova seen in 383 years—since Johannes Kepler observed a supernova in our own galaxy with his naked eye in 1604—and as such, it offered astronomers an unprecedented opportunity to witness a massive star’s last hurrah. Over the next hours and days, the star’s debris would expand outward from the site of the initial explosion, colliding with dust and gas in the space around it. Meanwhile, the supernova would appear dimmer and dimmer in our sky.

Particle physicists are also interested in neutrinos from supernovae, because they provide a rare opportunity to understand how these elusive particles behave under extreme conditions that can’t be replicated in a laboratory. What both sets of scientists need to achieve their goals is a core collapse supernova in our own galaxy. However, no supernova has been seen in the Milky Way since 1604, when stargazers including the German mathematician Johannes Kepler noticed a “new star” in the constellation Ophiuchus. At its peak, this supernova was so bright that it was visible during the daytime. Modern radio, optical, and X-ray telescopes have observed the remnant it left behind in the form of a shell of hot gas. Just three decades before Kepler saw the 1604 supernova, observers in Europe had seen one. The legendary Danish astronomer Tycho Brahe, who saw the earlier supernova in 1572, wrote that upon spotting “a new and unusual star, surpassing all others in brilliance” in the constellation Cassiopeia, “I was so astonished at this sight that I was not ashamed to doubt the trustworthiness of my own eyes.


pages: 240 words: 60,660

Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life by Emanuel Derman

Albert Einstein, Asian financial crisis, Augustin-Louis Cauchy, Black-Scholes formula, British Empire, Brownian motion, capital asset pricing model, Cepheid variable, creative destruction, crony capitalism, diversified portfolio, Douglas Hofstadter, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Henri Poincaré, I will remember that I didn’t make the world, and it doesn’t satisfy my equations, Isaac Newton, Johannes Kepler, law of one price, Mikhail Gorbachev, Myron Scholes, quantitative trading / quantitative finance, random walk, Richard Feynman, riskless arbitrage, savings glut, Schrödinger's Cat, Sharpe ratio, stochastic volatility, the scientific method, washing machines reduced drudgery, yield curve

It postulates that the force between any two masses (the moon and the Earth, the Earth and an apple) is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Newton’s Second Law of Motion, a theory too, dictates that the gravitational force accelerates each particle inversely proportional to its mass. Solving these equations, Newton deduced that planets must traverse elliptical paths around the sun, thereby justifying Johannes Kepler’s empirical laws of planetary motion. Newton’s theory is general and precise. The gravitational force is inversely proportional to exactly the square of the distance between the planets; Newton was confident that the power of the distance is precisely 2. Had he been a social scientist performing statistical regressions in psychology, economics, or finance, he would probably have proposed a power of 2.05 ± 0.31.

Things made out of Substance obey the deterministic laws of the universe, but it’s not easy to deduce those general laws when you observe only particulars. Lest you think it naïve to assume that there are laws behind everything, recall how many centuries of observing the lights in the night sky it took to discover that Newton’s three laws of motion and his law of gravity could explain the motions of the planets, the stars, and objects on earth. Tycho Brahe had to map the planetary motions and Johannes Kepler had to intuit that they described mathematical ellipses, each planet sweeping out equal areas in equal times; only then could Newton step into the picture with dynamics. With time, what more may we still discover? Mysterious Materialism Spinoza is a materialist, but not a naïve materialist. Since Newton we think of matter as dull, inanimate stuff that must obey laws. But Spinoza points out that the matter we inhabit is full of mysterious possibilities: However, no one has hitherto laid down the limits to the powers of the body, that is, no one has as yet been taught by experience what the body can accomplish solely by the laws of nature. . . .


pages: 208 words: 67,288

The Magic of Reality: How We Know What's Really True by Richard Dawkins

Any sufficiently advanced technology is indistinguishable from magic, Buckminster Fuller, double helix, Ernest Rutherford, false memory syndrome, Fellow of the Royal Society, gravity well, if you see hoof prints, think horses—not zebras, Isaac Newton, Johannes Kepler, phenotype, Richard Feynman, the scientific method

I hope that gives you a feel for the difference between weight and mass. In the space station, a cannon ball has much more mass than a balloon, although both have the same weight – zero. Eggs, ellipses and escaping gravity Let’s go back to our cannon on the mountain-top, and make it more powerful still. What will happen? Well, now we need to acquaint ourselves with the discovery of the great German scientist Johannes Kepler, who lived just before Newton. Kepler showed that the graceful curve by which things orbit other things in space is not really a circle but something known to mathematicians since ancient Greek times as an ‘ellipse’. An ellipse is sort of egg-shaped (only ‘sort of’: eggs are not perfect ellipses). A circle is a special case of an ellipse; think of a very blunt egg, an egg so short and squat that it looks like a ping-pong ball.

But don’t worry: we wouldn’t know about it for another 8,000 years, which is how long it takes light to travel the vast distance between Eta Carinae and us (and nothing travels faster than light). What, then, if Eta Carinae exploded 8,000 years ago? Well, in that case the light and other radiation from the explosion really could reach us any day now. The moment we see it, we’ll know that Eta Carinae blew up 8,000 years ago. Only about 20 supernovas have been seen in recorded history. The great German scientist Johannes Kepler saw one on 9 October 1604: the debris has expanded since he first saw it. The explosion itself actually occurred some 20,000 years earlier, roughly the time the Neanderthal people went extinct. Supernovas, unlike ordinary stars, can create elements even heavier than iron: lead, for example, and uranium. The titanic explosion of a supernova scatters all the elements that the star, and then the supernova, have made, including the elements necessary for life, far and wide through space.


pages: 208 words: 70,860

Paradox: The Nine Greatest Enigmas in Physics by Jim Al-Khalili

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, butterfly effect, clockwork universe, complexity theory, dark matter, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Henri Poincaré, invention of the telescope, Isaac Newton, Johannes Kepler, Laplace demon, luminiferous ether, Magellanic Cloud, Olbers’ paradox, Pierre-Simon Laplace, Schrödinger's Cat, Search for Extraterrestrial Intelligence, The Present Situation in Quantum Mechanics, Wilhelm Olbers

In 1952 the great Anglo-Austrian cosmologist Hermann Bondi published an influential textbook in which the term “Olbers’ Paradox” was coined for the first time. But as we shall see, the attribution was misplaced, for Olbers was not the first to pose the problem, nor was his contribution to its resolution particularly original or enlightening. A century before him Edmond Halley had already stated it, and a century before him Johannes Kepler had posed it in 1610. And even he wasn’t the first to record it: for that, we have to go back to 1576 and the very first English translation of De revolutionibus, the great work of Copernicus, written a few decades earlier. Any account of the history of astronomy begins with the same few key individuals in the leading roles. First up is Ptolemy, the second-century Greek who, despite writing one of the most important scientific textbooks in history (known as the Almagest), believed erroneously that the Sun revolved around the Earth.

As he contemplated the idea of an infinite space with an infinite number of stars, Digges was inevitably led to ask the crucial question: why is the night sky dark? For Digges, however, there was no paradox. He just assumed that the distant stars were simply too faint to contribute any light. What Digges was missing was a vital mathematical calculation that would have shown the error in his reasoning about the darkness of the night sky. But that was to come later. In 1610 Johannes Kepler revisited the problem, arguing the reason it was dark at night was simply because the Universe was finite in extent: the darkness between the stars was the dark outer wall enclosing the Universe. Over a century after Kepler, another astronomer, the Englishman Edmond Halley, looked at the problem again and came out in support of Digges’ original solution: that the Universe is infinite, but that the distant stars are too faint to be seen.


pages: 212 words: 68,754

Thinking in Numbers by Daniel Tammet

Albert Einstein, Alfred Russel Wallace, Anton Chekhov, computer age, dematerialisation, Edmond Halley, Georg Cantor, index card, Isaac Newton, Johannes Kepler, Paul Erdős, Searching for Interstellar Communications, Vilfredo Pareto

But from out of it, patterns, forms, identities that every culture can perceive and understand. I have read, for instance, that the ancient Chinese called snowflakes blossoms and that the Scythians compared them to feathers. In the Psalms (147:16), snow is a ‘white fleece’ while in parts of Africa it is likened to cotton. The Romans called snow nix, a synonym – the seventeenth-century mathematician and astronomer Johannes Kepler would later point out – of his Low German word for ‘nothing’. Kepler was the first scientist to describe snow. Not as flowers or fleece or feathers, snowflakes were at last perceived as being the product of complexity. The reason behind the snowflake’s regular hexagonal shape was ‘not to be looked for in the material, for vapour is formless’. Instead, Kepler suggested some dynamic organising process, by which frozen water ‘globules’ packed themselves together methodically in the most efficient way.

For this and other ‘theological errors’, the authorities denounced the heretic and burned him at the stake. The Inquisitors’ heavy footsteps dissuaded Bruno’s contemporary, Galileo Galilei, from seeing any evidence for extraterrestrial life in the rugged lunar landscape revealed by his telescope. All the same, since the valleys and mountains that corrugated the moon’s surface seemed at least comparable to those on Earth, might not the moon also have people to dwell among them? His friend Johannes Kepler, the seventeenth-century mathematician and astronomer, thought so. Jupiter, too, he deduced ‘with the highest degree of probability’, though its inhabitants were undoubtedly inferior to humans. Probability: this word became the cornerstone of the argument for life on other planets. ‘As for mind beyond the confines of our tiny globe,’ wrote the American astronomer Percival Lowell in 1895, ‘modesty, backed by a probability little short of demonstration, forbids the thought that we are the sole thinkers in this great universe.’


pages: 437 words: 126,860

Case for Mars by Robert Zubrin

Charles Lindbergh, Colonization of Mars, gravity well, Johannes Kepler, Kevin Kelly, low earth orbit, Mars Rover, orbital mechanics / astrodynamics, planetary scale, skunkworks, spice trade, telerobotics, uranium enrichment

It took another four months of travel for Amundsen to reach an outpost where he could telegraph news of his success to his main backer in Norway, which he did, charges reversed. Six years later Amundsen would use what he had learned on King William to become the first to reach the South Pole. 2: FROM KEPLER TO THE SPACE AGE Ships and sails proper for the heavenly air should be fashioned. Then there willand o be people, who do not shrink from the dreary vastness of space. —Johannes Kepler to Galileo Galilei, 1609 We’ve been to Mars before. On the morning of July 20, 1976, an American spacecraft, Viking 1, settled down onto the Chryse Planitia—the Plains of Gold on the red planet Mars. At the moment of touchdown, though, with Viking resting on the surface of a planet nearly 330 million kilometers distant, no one at NASA’s Jet Propulsion Laboratory in Pasadena, California, knew if the unmanned spacecraft had arrived safely or burrowed into the ground.

The action started with the work of Nicholas Copernicus, who between 1510 and 1514 redeveloped a long-forgotten heliocentric (Sun-centered) theory of the universe first posited by the third century B.C. Greek thinker Aristarchus of Samos. Under the heliocentric system, the planets traveled about the Sun in circular orbits. This concept was revolutionary, heretical even, and could not precisely match the observed planetary motions, yet some scholars of the time saw beauty in the fundamental simplicity of Copernicus’ system. Chief among them was Johannes Kepler. Born in 1571, Kepler grew to be a devout Lutheran, yet also a diehard Platonist with a passion for seeking the true nature of the universe in the rational laws of geometry. He would write, “Geometry is one and eternal, a reflection out of the mind of God. That mankind shares in it is one of the reasons to call man an image of God.” This quote is the key to the whole affair. If the human mind can understand the universe, it means that the human mind is fundamentally of the same order as the divine mind.

Electric ion thrusters already exist in kilowatt-sized units, and bulking them up to the megawatt sizes needed for NEP transportation systems offers no fundamental challenges. The real problem in enabling NEP propulsion systems to date has been to obtain the funds and sustained commitment required to develop a multi-megawatt space nuclear reactor. SOLAR SAILS Ships and sails proper for heavenly breezes should be fashioned ... —Johannes Kepler, 1609 Nearly four hundred years ago our old friend Kepler observed that regardless of whether a comet is moving toward or away from the Sun, its tail always points away from the Sun. This caused him to guess that light emanating from the Sun exerts a force that pushes the comet’s tail away. He was right, although the fact that light exerts force had to wait till 1901 to be proven. Well, if sunlight can push comet tails around, why can’t we use it to move spaceships around?


pages: 52 words: 16,113

The Laws of Medicine: Field Notes From an Uncertain Science by Siddhartha Mukherjee

Atul Gawande, cognitive dissonance, Johannes Kepler, medical residency, randomized controlled trial, retrograde motion, stem cell, Thomas Bayes

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. Perhaps Kepler, too, would be stuck cycling two steps forward and five steps back, leaving Brahe to ponder real questions of cosmological importance. 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.


Wonders of the Universe by Brian Cox, Andrew Cohen

a long time ago in a galaxy far, far away, Albert Einstein, Albert Michelson, Arthur Eddington, California gold rush, Cepheid variable, cosmic microwave background, dark matter, Dmitri Mendeleev, Isaac Newton, James Watt: steam engine, Johannes Kepler, Karl Jansky, Magellanic Cloud, Mars Rover, Solar eclipse in 1919, Stephen Hawking, the scientific method, trade route

So astronomy began a virtuous cycle through which the quest to understand the heavens and their meaning lead to practical and intellectual riches beyond the imagination of the ancients. The step from observing the regularity in the movement of the heavenly lights to modern science took much of recorded human history. The ancient Greeks began the work, but the correct description of the motion of the Sun, Moon and planets across the sky was discovered in the seventeenth century by Johannes Kepler. Removing the veil of the divine to reveal the true beauty of the cosmos was a difficult process, but the rewards that stem from that innate human fascination with the lights in the sky have proved to be incalculable * * * By following the light we have mapped our place among the hundreds of billions of stars that make up the Milky Way Galaxy. We have visited our nearest star, Proxima Centauri, and measured its chemical compositions, and those of thousands of other stars in the sky.

In these cases, Einstein’s more accurate theory of General Relativity is required. For planetary orbits around stars, orbits of stars around galaxies and the movements of the galaxies themselves, it is more than accurate enough. It has also applied at all times in the Universe’s history beyond the first instants after the Big Bang. This is not to be taken for granted, because the law was derived based on the work of Johannes Kepler and the observations of Tycho Brahe, who were concerned only with the motion of the planets around the Sun. The fact that a law that governs the clockwork of our solar system is the same law that governs the motion of the galaxies is interesting and important. It is the statement that the same laws of physics govern our whole universe, and Newton’s law of gravitation was the first example of such a universal law.


Exoplanets by Donald Goldsmith

Albert Einstein, Albert Michelson, Carrington event, Colonization of Mars, cosmic abundance, dark matter, Dava Sobel, en.wikipedia.org, Isaac Newton, Johannes Kepler, Kickstarter, Kuiper Belt, Magellanic Cloud, Mars Rover, megastructure, Pluto: dwarf planet, race to the bottom, Ralph Waldo Emerson, Search for Extraterrestrial Intelligence, Solar eclipse in 1919, Stephen Hawking

The amount of the elongation of the star’s orbit, which astronomers denote as the orbital eccentricity, exactly equals the eccentricity of the planet’s much larger orbit, whose shape and orbital period must match the star’s.1 In addition to furnishing us with the planet’s orbital period and eccentricity, radial-­velocity observations provide a third key property of the planet’s orbit: its mass. As Johannes Kepler realized four centuries ago from his studies of the planets in the solar system, and as Isaac Newton showed how to generalize to other objects in orbit, the length of time required for a less massive object to complete an orbit around a more massive one depends on the average distance between the two objects. More distant objects, which feel less gravitational force, move more slowly in orbit and 37 EXOPLANETS must travel farther to complete an orbit.

Created by the French Space Agency and the Eu­ro­pean Space Agency, CoRoT, which stands for COnvection, ROtation et Transits planétaires, (or, in En­glish, COnvection, ROtation, and planetary Transits), was launched from the Baikonur Cosmodrome in Kazakhstan and entered an orbit around the Earth at the end of 2006. CoROT proceeded to discover transiting exoplanets ­until its computers failed in November 2012. During its five years of operation, CoRoT, which could mea­sure brightness variations by 1 part in 10,000, detected about three dozen exoplanets, opening the path to spaceborne planetary discovery.1 NASA’s Kepler spacecraft, named a­ fter the famous seventeenth-­ century astronomer Johannes Kepler and launched in March 2009, built upon CoRoT’s success and embodied a more ambitious plan: to include a telescope with a mirror mea­sur­ing 1.4 meters in dia­ meter (far larger than CoRoT’s 27 centimeters), and to observe the heavens far from Earth’s interference. Kepler passed long years in design and preparation as the technological child of William Borucki, an astronomer at the Ames Research Center in California who emphasized to NASA that a g ­ reat advantage would be gained from placing a telescope outside the atmosphere to search for exoplanets’ transits. 51 EXOPLANETS All Earthbound observers, submerged within their life-­giving, mobile blanket of air, remain forever barred from a completely clear view of any celestial object, no ­matter how large their telescopes.


The Card Catalog: Books, Cards, and Literary Treasures by Library Of Congress, Carla Hayden

In Cold Blood by Truman Capote, index card, information retrieval, Johannes Kepler, late fees

The rediscovery of ancient Greek literature and history was the driving force in the early Renaissance, and the resulting abundance of new humanistic works unnerved the Catholic Church. The church moved quickly to blacklist certain titles and created an Index of Prohibited Books it found heretical, seditious, or scandalous. Subsequent editions included major works by Machiavelli, John Calvin, Voltaire, and Johannes Kepler. The indexes were not officially abolished until 1966. VIVE LA REVOLUTION . . . AND CARD CATALOGS Throughout most of the seventeenth and eighteenth centuries, national and university libraries continued experimenting with the feasibility of different cataloging techniques, with relatively few innovations. Ironically, it wasn’t until France descended headlong into the chaos of the French Revolution in 1789 that there was a concerted effort to codify cataloging rules and settle on a uniform format that would eventually lead to the standard index card.


pages: 360 words: 85,321

The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling by Adam Kucharski

Ada Lovelace, Albert Einstein, Antoine Gombaud: Chevalier de Méré, beat the dealer, Benoit Mandelbrot, butterfly effect, call centre, Chance favours the prepared mind, Claude Shannon: information theory, collateralized debt obligation, correlation does not imply causation, diversification, Edward Lorenz: Chaos theory, Edward Thorp, Everything should be made as simple as possible, Flash crash, Gerolamo Cardano, Henri Poincaré, Hibernia Atlantic: Project Express, if you build it, they will come, invention of the telegraph, Isaac Newton, Johannes Kepler, John Nash: game theory, John von Neumann, locking in a profit, Louis Pasteur, Nash equilibrium, Norbert Wiener, p-value, performance metric, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Richard Feynman, Ronald Reagan, Rubik’s Cube, statistical model, The Design of Experiments, Watson beat the top human players on Jeopardy!, zero-sum game

In 1525, he was playing cards in Venice and realized his opponent was cheating. “When I observed that the cards were marked, I impetuously slashed his face with my poniard,” Cardano said, “though not deeply.” In the decades that followed, other researchers chipped away at the mysteries of probability, too. At the request of a group of Italian nobles, Galileo investigated why some combinations of dice faces appeared more often than others. Astronomer Johannes Kepler also took time off from studying planetary motion to write a short piece on the theory of dice and gambling. The science of chance blossomed in 1654 as the result of a gambling question posed by a French writer named Antoine Gombaud. He had been puzzled by the following dice problem. Which is more likely: throwing a single six in four rolls of a single die, or throwing double sixes in twenty-four rolls of two dice?

“Some Laws and Problems of Classical Probability and How Cardano Anticipated Them.” Chance Magazine 25, no. 4 (2012): 13–20. xii“When I observed that the cards were marked”: Cardan, Jerome. Book of My Life (New York: Dutton, 1930). xiiAt the request of a group of Italian nobles: Ore, Oystein. “Pascal and the Invention of Probability Theory.” American Mathematical Monthly 67, no. 5 (May 1960): 409–419. xiiAstronomer Johannes Kepler also took time: Epstein, Richard. The Theory of Gambling and Statistical Logic (Waltham, MA: Academic Press, 2013). xiiThe science of chance blossomed: Ore, “Pascal and the Invention.” xiihe was more likely to get a six: It’s easiest to start by calculating the probability of not getting a six in four rolls, which is (5/6)4. It therefore follows that the probability of getting at least one six is 1–(5/6)4 = 51.8 percent.


pages: 294 words: 87,986

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

Legend has it that one day he became so frustrated that he begged the spirits to help him. An apparition appeared and violently threw Rheticus about, smashing his head first on the ceiling and then on the floor, with a parting roar: ‘These are the motions of Mars!’ The Mars story involves a great many of the leading names and figures in the history of astronomy. Mars’s motions also preoccupied Danish astronomer Tycho Brahe and his German colleague Johannes Kepler, both active in the 1500s and 1600s. Brahe’s career began a few years after Copernicus’s death. Despite his work still taking place in a pre-telescopic era, Brahe made strikingly accurate observations of Mars and its position in the sky. These data were later used by Kepler to prove that Mars didn’t orbit on a circular path, but an elliptical one. Although Brahe’s theories and ideas were not always correct, he was revered for gathering meticulous and incredibly accurate observations.

Brahe compiled all his thoughts into his own theory of the Universe and produced a geo-heliocentric model, in which the Moon and Sun orbited the Earth and all other planets orbited the Sun. In a way, Brahe’s model was an intermediary between Ptolemy and Copernicus – it maintained the Earth’s importance, removed the solid planetary shells but kept circular orbits, scrapped the immutable stars and heavens, and kept the stars relatively close to the outermost planet (at the time, Saturn). In the late 1500s, Brahe met Johannes Kepler (1571–1630), who subsequently became his assistant. Brahe tasked Kepler with understanding Mars’s orbit, a task that was readily accepted. Sadly, Brahe died in 1601 before he could see his assistant’s conclusions, but Kepler continued his work in earnest and some eight years later published his Astronomia Nova (New Astronomy). Kepler’s big breakthrough was to picture planetary orbits as ellipses, not circles, with the Sun at one of the foci (essentially the ‘centres’ of the ellipse – a circle has just one focus, its centre, but ellipses have two due to their elongated shape along one axis).


The Fractalist by Benoit Mandelbrot

Albert Einstein, Benoit Mandelbrot, Brownian motion, business cycle, Claude Shannon: information theory, discrete time, double helix, Georg Cantor, Henri Poincaré, Honoré de Balzac, illegal immigration, Isaac Newton, iterative process, Johannes Kepler, John von Neumann, linear programming, Louis Bachelier, Louis Blériot, Louis Pasteur, mandelbrot fractal, New Journalism, Norbert Wiener, Olbers’ paradox, Paul Lévy, Richard Feynman, statistical model, urban renewal, Vilfredo Pareto

This is a memoir of an ardent but bumpy pursuit of order and beauty in roughness— through mathematics and economics, the sciences, engineering, and the arts. It led me to encounter more than my share of unusually diverse and forceful persons along the way. Many were warm and welcoming; many were indifferent, dismissive, hostile—even beastly. This book cannot possibly mention them all, but every one taught me something and to all I owe a great deal. To the memory of Johannes Kepler, who brought ancient data and ancient toys together and founded science. Contents Cover Title Page Copyright Dedication Acknowledgments by Aliette Mandelbrot Beauty and Roughness: Introduction Part One: How I Came to Be a Scientist 1. Roots: Of Flesh and the Mind 2. Child in Warsaw, 1924–36 3. Adolescent in Paris, 1936–39 4. Dirt-Poor Hills of Unoccupied Vichy France, 1939–43 5.

Can geometry deliver what the Greek root of its name seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth? These questions, as well as a host of others, are scattered across a multitude of sciences and have been faced only recently … by me. As an adolescent during World War II, I came to worship a major achievement of a mathematician and astronomer of long ago, Johannes Kepler (1571–1630). Kepler combined the ellipses of ancient Greek geometers with a failure of ancient Greek astronomers, who mistakenly believed that persistent “anomalies” existed in the motion of planets. Kepler used his knowledge of two different fields—mathematics and astronomy—to calculate that this motion of the planets was not an anomaly. It was, in fact, an elliptical orbit. To discover something like this became my childhood dream.


The Map of Knowledge: How Classical Ideas Were Lost and Found: A History in Seven Cities by Violet Moller

Book of Ingenious Devices, British Empire, double entry bookkeeping, Johannes Kepler, Murano, Venice glass, Republic of Letters, spice trade, the market place, trade route, wikimedia commons

Al-Zarqali studied in Córdoba, but returned to Toledo, where he wrote several books, including one called The Canones (rules) that explained how to use the Toledan Tables. Gerard of Cremona translated this work into Latin and it went on to influence European astronomy for centuries. Al-Zarqali also wrote an astronomical treatise in which he made the groundbreaking claim that Mercury’s orbit was elliptical, not circular, as was commonly thought. In the sixteenth century, Johannes Kepler drew on al-Zarqali’s visionary work to prove that the orbit of Mars was also elliptical. Toledo fell to Alfonso of Castile in 1085, and al-Zarqali left the city, but his ideas were taken up by Christian scholars and thus shared throughout Europe. 15. An astrolabe made in Toledo in 1029 when the city was still under Muslim rule. Al-Zarqali moved south, possibly to Granada or another Andalusian city still under Muslim control, as did many of his fellow Arabs.

Unlike Vesalius’ work on anatomy, De revolutionibus did not contain much new observational data, but, in the following century, Tycho Brahe, a Danish nobleman, built himself an observatory on the island of Hven, in the Kattegat, between the coasts of Denmark and Sweden. He filled it with sophisticated instruments, capable of making far more accurate astronomical observations than had previously been possible. Applying these to Copernicus’ new cosmos, he did away with Ptolemy’s system of spheres, opening up the possibility of a far more complex and exact representation of the universe. The next step was taken by Johannes Kepler, who, using Brahe’s data, reluctantly rejected Ptolemy’s theory that the planets moved with regular motion in circular orbits, in favour of elliptical movement – another huge step forward in our understanding of the solar system. Each of the cities we have visited in this book had its own particular topography and character, but they all shared the conditions that allowed scholarship to flourish: political stability, a regular supply of funding and of texts, a pool of talented, interested individuals and, most striking of all, an atmosphere of tolerance and inclusivity towards different nationalities and religions.


pages: 81 words: 28,120

Illustrated Theory of Everything: The Origin and Fate of the Universe by Stephen Hawking

anthropic principle, cosmological constant, dark matter, Johannes Kepler

A much simpler model, however, was proposed in 1514 by a Polish priest,Nicholas Copernicus. At first, for fear of being accused of heresy, Copernicuspublished his model anonymously. His idea was that the sun was stationary atthe center and that the Earth and the planets moved in circular orbits aroundthe sun. Sadly for Copernicus, nearly a century passed before this idea was tobe taken seriously. Then two astronomers-the German, Johannes Kepler, andthe Italian, Galileo Galilei-started publicly to support the Copernican theo-ry, despite the fact that the orbits it predicted did not quite match the onesobserved. The death of the Aristotelian-Ptolemaic theory came in 1609. Inthat year Galileo started observing the night sky with a telescope, which hadjust been invented. When he looked at the planet Jupiter, Galileo found that it was accompa-nied by several small satellites, or moons, which orbited around it.


pages: 400 words: 94,847

Reinventing Discovery: The New Era of Networked Science by Michael Nielsen

Albert Einstein, augmented reality, barriers to entry, bioinformatics, Cass Sunstein, Climategate, Climatic Research Unit, conceptual framework, dark matter, discovery of DNA, Donald Knuth, double helix, Douglas Engelbart, Douglas Engelbart, en.wikipedia.org, Erik Brynjolfsson, fault tolerance, Fellow of the Royal Society, Firefox, Freestyle chess, Galaxy Zoo, Internet Archive, invisible hand, Jane Jacobs, Jaron Lanier, Johannes Kepler, Kevin Kelly, Magellanic Cloud, means of production, medical residency, Nicholas Carr, P = NP, publish or perish, Richard Feynman, Richard Stallman, selection bias, semantic web, Silicon Valley, Silicon Valley startup, Simon Singh, Skype, slashdot, social intelligence, social web, statistical model, Stephen Hawking, Stewart Brand, Ted Nelson, The Death and Life of Great American Cities, The Nature of the Firm, The Wisdom of Crowds, University of East Anglia, Vannevar Bush, Vernor Vinge

But I should perhaps have put “Ptolemy” in quotes, because many historians of science—not all, but many—believe that Ptolemy plagiarized many of the star positions in his catalog from the astronomer Hipparchus, who had done his own sky survey nearly 300 years earlier. In fact, the history of science is full of examples of scientists stealing data from one another. Back at the dawn of modern science the astronomer Johannes Kepler discovered that planets move in ellipses around the sun using data he stole from his deceased mentor, the astronomer Tycho Brahe. James Watson and Francis Crick discovered the structure of DNA with the aid of data they borrowed from one of the world’s leading crystallographers, Rosalind Franklin. I say borrowed, because this was done without her knowledge, although with the aid of a colleague of Franklin’s who was arguably within his rights.

Unfortunately for Galileo, his telescope wasn’t quite good enough to clearly resolve the rings. That would have to wait for the Dutch scientist Christiaan Huygens, in 1655. Still, this was another momentous discovery, and Galileo is often credited, along with Huygens, as the discoverer of the rings. Eager to claim the credit for his new discovery, Galileo immediately sent out letters to several of his colleagues, including his great colleague and rival, the astronomer Johannes Kepler. Galileo’s letter to Kepler (and his other colleagues) was peculiar. Instead of explaining forthrightly what he had seen, Galileo explained that he would describe his latest discovery in the form of an anagram: smaismrmilmepoetaleumibunenugttauiras By sending this anagram, Galileo avoided revealing the details of his discovery, but at the same time ensured that if someone else—such as Kepler—later made the same discovery, Galileo could reveal the anagram and claim the credit.


pages: 356 words: 102,224

Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan

Albert Einstein, anthropic principle, cosmological principle, dark matter, Dava Sobel, Francis Fukuyama: the end of history, germ theory of disease, invention of the telescope, Isaac Newton, Johannes Kepler, Kuiper Belt, linked data, low earth orbit, nuclear winter, planetary scale, profit motive, scientific worldview, Search for Extraterrestrial Intelligence, Stephen Hawking, telepresence

We are right to rejoice in our accomplishments, to be proud that our species has been able to see so far, and to judge our merit in part by the very science that has so deflated our pretensions. To our ancestors there was much in Nature to be afraid of—lightning, storms, earthquakes, volcanos, plagues, drought, long winters. Religions arose in part as attempts to propitiate and control, if not much to understand, the disorderly aspect of Nature. The scientific revolution permitted us to glimpse an underlying ordered Universe in which there was a literal harmony of the worlds (Johannes Kepler's phrase). If we understand Nature, there is a prospect of controlling it or at least mitigating the harm it may bring. In this sense, science brought hope. Most of the great deprovincializing debates were entered into with no thought for their practical implications. Passionate and curious humans wished to understand their actual circumstances, how unique or pedestrian they and their world are, their ultimate origins and destinies, how the Universe works.

Perhaps it will actually come about. Perhaps winging across the billion miles of intervening interplanetary space will be, in the not too distant future. news about how far along the path to life Titan has come. 61 C H A P T E R 8 THE FIRST NEW PLANET 1 implore you, you do not hope to be able to give the reasons for the number of planets, do you? This worry has been resolved . . . — JOHANNES KEPLER, EPITOME OF COPERNICAN ASTRONOMY, BOOK 4 / 1621 Before we invented civilization, our ancestors lived mainly in the open, out under the sky. Before we devised artificial lights and atmospheric pollution and modern forms of nocturnal entertainment, we watched the stars. There were practical calendrical reasons, of course, but there was more to it than that. Even today, the most jaded city dweller can be unexpectedly moved upon encountering a clear night sky studded with thousands of twinkling stars.


pages: 400 words: 99,489

The Sirens of Mars: Searching for Life on Another World by Sarah Stewart Johnson

Albert Einstein, Alfred Russel Wallace, Astronomia nova, back-to-the-land, cuban missile crisis, dark matter, Drosophila, Elon Musk, invention of the printing press, Isaac Newton, Johannes Kepler, low earth orbit, Mars Rover, Mercator projection, Pierre-Simon Laplace, Ronald Reagan, scientific mainstream, sensible shoes

. | Mars (Planet) Classification: LCC QB641 .J64 2020 (print) | LCC QB641 (ebook) | DDC 576.8/39099923—dc23 LC record available at https://lccn.loc.gov/​2020007280 LC ebook record available at https://lccn.loc.gov/​2020007281 Ebook ISBN 9781101904824 randomhousebooks.com Cover design: Elena Giavaldi Cover images: Sand dunes lie next to a hill within an unnamed crater in eastern Arabia on Mars. This false-color mosaic, in which bluish tints indicate fine sand and reddish tints indicate outcrops of rock, was made from images taken at visible and infrared wavelengths by the Thermal Emission Imaging System on NASA’s 2001 Mars Odyssey mission. (NASA/JPL-Caltech/ASU); Fol 36-37 “Astronomia nova Aitiologetos,” by Johannes Kepler (engraving), Bridgeman Images (top right); August 20, 1982, “Professor Pickering’s Observation of Mars,” Scientific American (center left); Morphart Creation/Shutterstock (bottom right) ep_prh_5.5.0_c0_r0 Contents Cover Title Page Copyright Prologue Part 1: A Point Is That Which Has No Part. Chapter 1: Into the Silent Sea Chapter 2: The Light That Shifts Chapter 3: Red Smoke Part 2: A Line Is Breadthless Length.

Mars rode on a large epicycle, which was needed to explain the large loops backward that it underwent every two years, and since the size of its loops varied, the center of its epicycle had to be placed off-center to the Earth. By the sixteenth century, Copernicus decided to put the sun at the center of his system, and Mars’s largest epicycle was no longer needed—since it was now evident that it was merely an illusion of perspective, created as the Earth, following its own orbit around the sun, caught up with and passed the slower-moving Mars. In 1609, Johannes Kepler worked out the elliptic shape of the planetary orbits, using the orbit of Mars, which is highly elliptical, as the basis of his protracted and difficult calculations. This was one of the great discoveries of modern astronomy—and we owe it all to Mars. PLATO CONCLUDED THAT Plato, “Book X,” The Republic, trans. Benjamin Jowett (Cambridge: Internet Classics Archive, MIT, 2008). See also the claim that, based on the planets’ observed “retrogradation” and “wobbling,” “it almost seemed (for example, to Plato when the Timaeus was being written) that nothing less than an exercise of free will could account for their reversals of direction”: Robert Sherrick Brumbaugh, Plato for the Modern Age (Lanham, Md.: University Press of America, 1991).


pages: 615 words: 189,720

Galileo's Dream by Kim Stanley Robinson

clockwork universe, dark matter, Dava Sobel, gravity well, Johannes Kepler, Murano, Venice glass, music of the spheres

The stranger came up to Galileo, stopped and bowed stiffly, then held out his right hand. Galileo bowed in return, took the offered hand, and squeezed; it was narrow and long, like the man’s face. In guttural Latin, very strangely accented, the stranger croaked, “Are you Domino Signor Galileo Galilei, professor of mathematics at the University of Padua?” “I am. Who are you?” The man let go of his hand. “I am a colleague of Johannes Kepler. He and I recently examined one of your very useful military compasses.” “I am glad to hear it,” Galileo said, surprised. “I have corresponded with Signor Kepler, as he probably told you, but he did not write to me about this. When and where did you meet him?” “Last year, in Prague.” Galileo nodded. Kepler’s places of residence had shifted through the years in ways Galileo had not tried to keep track of.

As Galileo straightened up, he said, “God bless you, Father. I was quite sure that you would see them, they are so prominent, and you such an experienced astronomer. And I can tell you that on my journey to Rome I have made good progress in determining the period of orbit of all four of these new moons.” Grienberger and Maelcote raised their eyebrows and exchanged glances, but Clavius only smiled. “I think here we are in rare agreement with Johannes Kepler, that establishing their periods of rotation will be very difficult.” “But …” Galileo hesitated, then realized he had made a mistake, and dropped the matter with a wave of the hand. There was no point in making announcements in advance of results; indeed, since he was intent on being the first to make every discovery having to do with the new stars, he should not be inciting competitors to further effort.

Or grieving.” “But why?” “Because!” Galileo glanced at her in surprise; she was staring wildly at him. “Because we killed its daughter,” he suggested. CHAPTER FIFTEEN The Two Worlds The die is cast, and I am writing the book to be read either now or by posterity, it matters not. It can wait a century for a reader, as God himself has waited six thousand years for a witness. —JOHANNES KEPLER, Harmonies of the World HE WOKE SO STIFF HE COULD NOT MOVE, feeling the pressure of full bowel and full bladder, which seemed to be in competition with each other to shove their way out of his second asshole. He was in his bed. Cartophilus was staring him in the face with his peculiar look—either knowing or intensely curious, it was impossible for Galileo to say. “What?” Galileo croaked.


pages: 687 words: 189,243

A Culture of Growth: The Origins of the Modern Economy by Joel Mokyr

"Robert Solow", Andrei Shleifer, barriers to entry, Berlin Wall, business cycle, clockwork universe, cognitive dissonance, Copley Medal, creative destruction, David Ricardo: comparative advantage, delayed gratification, deliberate practice, Deng Xiaoping, Edmond Halley, epigenetics, Fellow of the Royal Society, financial independence, framing effect, germ theory of disease, Haber-Bosch Process, hindsight bias, income inequality, information asymmetry, invention of movable type, invention of the printing press, invisible hand, Isaac Newton, Jacquard loom, Jacques de Vaucanson, James Watt: steam engine, Johannes Kepler, John Harrison: Longitude, Joseph Schumpeter, knowledge economy, labor-force participation, land tenure, law of one price, Menlo Park, moveable type in China, new economy, phenotype, price stability, principal–agent problem, rent-seeking, Republic of Letters, Ronald Reagan, South Sea Bubble, statistical model, survivorship bias, the market place, The Structural Transformation of the Public Sphere, The Wealth of Nations by Adam Smith, transaction costs, ultimatum game, World Values Survey, Wunderkammern

Science and religion in the sixteenth century were deeply intertwined in complex fashions, far more than was the case, say, in the eighteenth century. An example is the Spanish physician Miguel Servetus, who had decided at an early age that the doctrine of Trinity was false, and after he studied medicine this led him to reject, as a parallel, the triadic structure of body functions (nutrition, muscular activity, and mental activity) that was part of the Galenian medical orthodoxy of his time (Mason, 1992, p. 8). Such astronomers as Johannes Kepler and physicists as William Gilbert, after accepting the heliocentric hypothesis, suggested that God might be living in the sun, the center of the Universe.22 All over seventeenth-century Europe, science and religion discovered a range of possible symbiotic relations. In England this was expressed in the deep Anglican beliefs of Robert Boyle and the somewhat eccentric but deeply felt religious sentiments of Newton.

Patronage could take different forms. Much of it was handed out by the princes and kings of Europe who collected intellectuals at their courts in part just for prestige reasons. The otherwise rather inept Habsburg Emperor Rudolf II (ruled 1572–1612) collected a large number of scientists and artists at his court in Prague (at that time the Imperial capital). The astronomers Tycho Brahe and Johannes Kepler were both members of the Habsburg court, as was Carolus Clusius, né Charles de l’Écluse (1526–1609). Clusius, one of the founders of modern botany, was by all accounts a paradigmatic member of the sixteenth-century Republic of Letters: cosmopolitan, widely traveled, extremely well connected, he worked for both Rudolf II and Rudolf’s father Maximilian II (Evans, 1973, pp. 119–20).43 Galileo was perhaps the most famous case: in 1610 he was appointed as court mathematician and philosopher by Grand Duke Cosimo II of Florence, and as such he was free to pursue his research (as long as it did not conflict too much with religious doctrine—but that is another story).

The Republic of Letters was a pan-European institution, and while British intellectuals played an important role it, they did not dominate it in any sense. Yet, as we have already seen, Britain gave as good as it got. While Puritanism was a very British phenomenon, the science that it created easily disseminated abroad, and the irrelevance of national boundaries marks the scientific contributions of scholars from Boyle and Wallis to Kepler and Leeuwenhoek. Johannes Kepler was a pious Lutheran, as was Tycho Brahe. Catholic scholars contributed much to the development of science and its practical applications in this age. This is not just true for lay Catholics such as Galileo, Cassini, and Descartes, but also of Jesuits, who played an important role in early modern science. Puritanism is unlikely to have influenced a figure such as the Jesuit Athanasius Kircher, a German-born polymath of prodigious scholarly productivity who wrote important books on topics as different as natural history, mathematics, geology, and the history of ancient Egypt (Findlen, 2004), or his equally prodigious predecessor and fellow German, the eminent Jesuit mathematician Christopher Clavius (1538–1612), who single-handedly imposed the study of mathematics in Jesuit education and helped Pope Gregory XIII reform the calendar to what is now named after him.11 French Catholic clerics were able to combine a life of serious research and scientific activity with unwavering piety.


pages: 124 words: 40,697

The Grand Design by Stephen Hawking, Leonard Mlodinow

airport security, Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, Buckminster Fuller, conceptual framework, cosmic microwave background, cosmological constant, dark matter, fudge factor, invention of the telescope, Isaac Newton, Johannes Kepler, John Conway, John von Neumann, luminiferous ether, Mercator projection, Richard Feynman, Stephen Hawking, Thales of Miletus, the scientific method, Turing machine

In the thirteenth century the early Christian philosopher Thomas Aquinas (ca. 1225–1274) adopted this view and used it to argue for the existence of God, writing, “It is clear that [inanimate bodies] reach their end not by chance but by intention…. There is therefore, an intelligent personal being by whom everything in nature is ordered to its end.” Even as late as the sixteenth century, the great German astronomer Johannes Kepler (1571–1630) believed that planets had sense perception and consciously followed laws of movement that were grasped by their “mind.” The notion that the laws of nature had to be intentionally obeyed reflects the ancients’ focus on why nature behaves as it does, rather than on how it behaves. Aristotle was one of the leading proponents of that approach, rejecting the idea of science based principally on observation.


pages: 452 words: 126,310

The Case for Space: How the Revolution in Spaceflight Opens Up a Future of Limitless Possibility by Robert Zubrin

Ada Lovelace, Albert Einstein, anthropic principle, battle of ideas, Charles Lindbergh, Colonization of Mars, complexity theory, cosmic microwave background, cosmological principle, discovery of DNA, double helix, Elon Musk, en.wikipedia.org, flex fuel, Francis Fukuyama: the end of history, gravity well, if you build it, they will come, Internet Archive, invisible hand, Jeff Bezos, Johannes Kepler, John von Neumann, Kuiper Belt, low earth orbit, Mars Rover, Menlo Park, more computing power than Apollo, Naomi Klein, nuclear winter, off grid, out of africa, Peter H. Diamandis: Planetary Resources, Peter Thiel, place-making, Pluto: dwarf planet, private space industry, rising living standards, Search for Extraterrestrial Intelligence, self-driving car, Silicon Valley, telerobotics, Thomas Malthus, transcontinental railway, uranium enrichment

As discussed above, the effective exhaust velocity of an antimatter photon rocket would be about 50 percent the speed of light, making flights at up to 90 percent of light speed theoretically possible. This would get a ship to Alpha Centauri in about five years, which would seem like three to the crew due to the effects of relativistic time dilation. But the society that launched such a mission would have to be one that was so rich that cost was simply not an issue. LIGHT SAILS Nearly four hundred years ago, the famous German astronomer Johannes Kepler observed that regardless of whether a comet is moving toward or away from the sun, its tail always points away from the sun. This caused him to guess that light emanating from the sun exerts a force that pushes the comet's tail away. He was right, although the fact that light exerts force had to wait till 1901 to be proven by Russian physicist Peter N. Lebedev, who made mirrors suspended on thin fibers in vacuum jars turn by shining light upon them.

It is also the basis of our highest notions of law—the natural law determinable as justice by human conscience and reason, put forth, for example, in the US Declaration of Independence (“We hold these truths to be self-evident…”)—from which we draw our belief that the fundamental rights of humans exist independent of any laws that may or may not be on the books or existing accepted customs. It is also the basis for science, our search for universal truth through the tools of reason. As the great Renaissance scientist Johannes Kepler, the discoverer of the laws of planetary motion, put it, “Geometry is one and eternal, a reflection out of the mind of God. That mankind shares in it is one reason to call man the image of God.” In other words, the human mind, because it is the image of God, is able to understand the laws of the universe. It was the forceful demonstration of this proposition by Kepler, Galileo, and others that let loose the scientific revolution in the West.


pages: 159 words: 45,073

GDP: A Brief but Affectionate History by Diane Coyle

"Robert Solow", Asian financial crisis, Berlin Wall, big-box store, Bretton Woods, BRICs, business cycle, clean water, computer age, conceptual framework, crowdsourcing, Diane Coyle, double entry bookkeeping, en.wikipedia.org, endogenous growth, Erik Brynjolfsson, Fall of the Berlin Wall, falling living standards, financial intermediation, global supply chain, happiness index / gross national happiness, hedonic treadmill, income inequality, income per capita, informal economy, Johannes Kepler, John von Neumann, Kevin Kelly, Long Term Capital Management, mutually assured destruction, Nathan Meyer Rothschild: antibiotics, new economy, Occupy movement, purchasing power parity, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, Silicon Valley, Simon Kuznets, The Wealth of Nations by Adam Smith, Thorstein Veblen, University of East Anglia, working-age population

Ehrlich, The Population Bomb (New York: Ballantine, 1968). 24. Clyde Haberman, “For Italy’s Entrepreneurs, the Figures Are Bella,” New York Times, 16 July 1989, http://www.nytimes.com/1989/07/16/magazine/for-italy-s-entrepreneurs-the-figures-are-bella.html?pagewanted=all&src=pm. 25. Friedrich Schneider, “Size and Development of the Shadow Economy of 31 European and 5 Other OECD Countries from 2003 to 2012: Some New Facts,” Johannes Kepler University, December 2011, http://www.econ.jku.at/members/Schneider/files/publications/2012/ShadEcEurope31.pdf. See also Friedrich Schneider with Dominik Enste, “Hiding in the Shadows: The Growth of the Underground Economy,” International Monetary Fund, March 2002, http://www.imf.org/external/pubs/ft/issues/issues30/index.htm#3. 26. http://www-2009.timeuse.org/information/studies/. 27. Jonathan Gershuny, “Time-Use Surveys and the Measurement of National Well-Being,” Centre for Time-Use Research, Department of Sociology, University of Oxford, September 2011, http://www.ons.gov.uk/ons/rel/environmental/time-use-surveys-and-the-measurement-of-national-well-being/article-by-jonathan-gershuny/index.html. 28.


pages: 437 words: 132,041

Alex's Adventures in Numberland by Alex Bellos

Andrew Wiles, Antoine Gombaud: Chevalier de Méré, beat the dealer, Black Swan, Black-Scholes formula, Claude Shannon: information theory, computer age, Daniel Kahneman / Amos Tversky, Edward Thorp, family office, forensic accounting, game design, Georg Cantor, Henri Poincaré, Isaac Newton, Johannes Kepler, lateral thinking, Myron Scholes, pattern recognition, Paul Erdős, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Feynman, Rubik’s Cube, SETI@home, Steve Jobs, The Bell Curve by Richard Herrnstein and Charles Murray, traveling salesman

Using Napier’s invention, not only could multiplication be made into the addition of logs, but division was made into the subtraction of logs; calculating of square roots was made into the division of logs by two; and calculating cube roots, into the division of logs by three. The convenience that logarithms brought made them the most significant mathematical invention of Napier’s time. Science, commerce and industry benefited massively. The German astronomer Johannes Kepler, for example, used logs almost immediately to calculate the orbit of Mars. It has recently been suggested that he might not have discovered his three laws of celestial mechanics without the ease of calculation offered by Napier’s new numbers. In his 1614 book A Description of the Admirable Table of Logarithmes, Napier used a slightly different version of logarithms than those used in modern mathematics.

The trick is explained by the fact that the shapes are not a perfect fit. Though it is not that obvious to the naked eye, there is a long thin gap along the middle diagonal with an area of one unit. It follows that a square of 169 unit squares (13 × 13) can be rearranged to ‘make’ a rectangle of 168 squares (8 × 21). In this case the segments overlap slightly along the middle diagonal. In the early seventeenth century, the German astronomer Johannes Kepler wrote that: ‘As 5 is to 8, so 8 is to 13, approximately, and as 8 to 13, so 13 is to 21, approximately.’ In other words, he noticed that the ratios of consecutive F-numbers were similar. A century later the Scottish mathematician Robert Simson saw something even more incredible. If you take the ratios of consecutive F-numbers and put them in the sequence: which is: or (to three decimal places): 1, 2, 1.5, 1.667, 1.6, 1.625, 1.615, 1.619, 1.618… then the values of these terms get closer and closer to phi, the golden ratio.


pages: 236 words: 50,763

The Golden Ticket: P, NP, and the Search for the Impossible by Lance Fortnow

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Claude Shannon: information theory, cloud computing, complexity theory, Donald Knuth, Erdős number, four colour theorem, Gerolamo Cardano, Isaac Newton, Johannes Kepler, John von Neumann, linear programming, new economy, NP-complete, Occam's razor, P = NP, Paul Erdős, Richard Feynman, Rubik’s Cube, smart grid, Stephen Hawking, traveling salesman, Turing machine, Turing test, Watson beat the top human players on Jeopardy!, William of Occam

And as I observed that in the words “I think, therefore I am”, there is nothing at all which gives me assurance of their truth beyond this, that I see very clearly that in order to think it is necessary to exist, I concluded that I might take, as a general rule, the principle, that all the things which we very clearly and distinctly conceive are true, only observing, however, that there is some difficulty in rightly determining the objects which we distinctly conceive. Descartes, Discourse, Part IV A contemporary of Descartes, Johannes Kepler, examined planetary motion and derived a set of rules that described the path and speed of planets in their orbits. Kepler had no simple description of why planets followed these rules. Isaac Newton applied the principle of Occam’s razor to the physical world. Newton’s famous laws of motion gave very simple rules on how objects react. 1. If no force is applied to an object, an object at rest remains at rest and one in motion remains at a constant velocity. 2.


pages: 193 words: 51,445

On the Future: Prospects for Humanity by Martin J. Rees

23andMe, 3D printing, air freight, Alfred Russel Wallace, Asilomar, autonomous vehicles, Benoit Mandelbrot, blockchain, cryptocurrency, cuban missile crisis, dark matter, decarbonisation, demographic transition, distributed ledger, double helix, effective altruism, Elon Musk, en.wikipedia.org, global village, Hyperloop, Intergovernmental Panel on Climate Change (IPCC), Internet of things, Jeff Bezos, job automation, Johannes Kepler, John Conway, life extension, mandelbrot fractal, mass immigration, megacity, nuclear winter, pattern recognition, quantitative hedge fund, Ray Kurzweil, Rodney Brooks, Search for Extraterrestrial Intelligence, sharing economy, Silicon Valley, smart grid, speech recognition, Stanford marshmallow experiment, Stanislav Petrov, stem cell, Stephen Hawking, Steven Pinker, Stuxnet, supervolcano, technological singularity, the scientific method, Tunguska event, uranium enrichment, Walter Mischel, Yogi Berra

A star would appear to dim slightly when a planet was ‘in transit’ in front of it; these dimmings would repeat at regular intervals. Such data reveal two things: the interval between successive dimmings tells us the length of the planet’s year, and the amplitude of the dimming tells us what fraction of the star’s light a planet blocks out during the transit, and therefore how big it is. The most important search (so far) for transiting planets was carried out by a NASA spacecraft named after astronomer Johannes Kepler,4 which spent more than three years measuring the brightness of 150,000 stars, to a precision of one part in 100,000—it did this once or more times an hour for each star. Kepler found thousands of transiting planets, some no bigger than Earth. The prime mover behind the Kepler project was Bill Borucki, an American engineer who had worked for NASA since 1964. He conceived the concept in the 1980s and doggedly pursued it despite funding setbacks and initial scepticism from many in the community of ‘established’ astronomers.


pages: 189 words: 49,386

Letters From an Astrophysicist by Neil Degrasse Tyson

dark matter, Isaac Newton, Johannes Kepler, Pluto: dwarf planet, The Wealth of Nations by Adam Smith, unbiased observer

‡ James McGaha (USAF Retired) is an acquaintance and fellow skeptic, with a long history of debunking claims that UFOs are visiting aliens. Here, I rein in his skepticism . . . just a bit. § The US military budget for 2004 was $400 billion. Since then, the budget has increased to $600 billion, by far the largest in the world. Three times that of the next country (China) and more than the next ten countries combined. ¶ Johannes Kepler, a German astronomer and mathematician (1571–1630). # Sir Francis Bacon (1561–1626), English scientist, philosopher, and statesman. ** M. Griaule and G. Dieterlen, The Pale Fox (Baltimore, MD: Afrikan World Books, 1986). †† Ivan Van Sertima, Blacks in Science: Ancient and Modern (Abingdon-on-Thames, UK: Transaction Books [now Routledge], 1991). ‡‡ Of course natural history as a topic of interest goes way back.


pages: 168 words: 56,211

The Pleasures and Sorrows of Work by Alain de Botton

Donald Trump, Isaac Newton, Johannes Kepler, Malacca Straits, mass immigration, Ralph Waldo Emerson, spice trade, supply-chain management, Vilfredo Pareto

Some of the technical properties of WOWOW TV’s new machine were the result of research done in the early 1980s by a team of scientists from Milan Polytechnic, who, in investigating the use of the upper reaches of the electromagnetic spectrum in communications satellites, had found a way around the interference caused by low cloud and misty rain at microwave frequencies above 10 gigahertz – slow and unheroic work that now, a quarter of a century later, ensured that Japanese viewers would be able to enjoy the uncut version of the anime film Cowboy Bebop even during the worst downpours in Japan’s rainy season. Though there had certainly been a loss of colour and novelistic detail in the passing of the age of geniuses, there was perhaps something greater and more reassuring in our graduation to a time of collective effort, for it meant that never again would the fate of planetary exploration depend to a hazardous degree on such unpredictable variables as the mood of Johannes Kepler’s wife, Barbara, or the inclinations of his patron Emperor Rudolf II – though the German astronomer, like many of his fellow geniuses, had at least provided Kourou with a name for one of its dispiriting streets, a rectangle of waste ground bordered by a dry cleaner at one end and a burnt-out Internet café at the other, a matter in which the collated proponents of later discoveries would perhaps never be quite so obliging. 6.


pages: 807 words: 154,435

Radical Uncertainty: Decision-Making for an Unknowable Future by Mervyn King, John Kay

"Robert Solow", Airbus A320, Albert Einstein, Albert Michelson, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, autonomous vehicles, availability heuristic, banking crisis, Barry Marshall: ulcers, battle of ideas, Benoit Mandelbrot, bitcoin, Black Swan, Bonfire of the Vanities, Brownian motion, business cycle, business process, capital asset pricing model, central bank independence, collapse of Lehman Brothers, correlation does not imply causation, credit crunch, cryptocurrency, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, Donald Trump, easy for humans, difficult for computers, Edmond Halley, Edward Lloyd's coffeehouse, Edward Thorp, Elon Musk, Ethereum, Eugene Fama: efficient market hypothesis, experimental economics, experimental subject, fear of failure, feminist movement, financial deregulation, George Akerlof, germ theory of disease, Hans Rosling, Ignaz Semmelweis: hand washing, income per capita, incomplete markets, inflation targeting, information asymmetry, invention of the wheel, invisible hand, Jeff Bezos, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Snow's cholera map, John von Neumann, Kenneth Arrow, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, market bubble, market fundamentalism, Moneyball by Michael Lewis explains big data, Nash equilibrium, Nate Silver, new economy, Nick Leeson, Northern Rock, oil shock, Paul Samuelson, peak oil, Peter Thiel, Philip Mirowski, Pierre-Simon Laplace, popular electronics, price mechanism, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, railway mania, RAND corporation, rent-seeking, Richard Feynman, Richard Thaler, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Coase, sealed-bid auction, shareholder value, Silicon Valley, Simon Kuznets, Socratic dialogue, South Sea Bubble, spectrum auction, Steve Ballmer, Steve Jobs, Steve Wozniak, Tacoma Narrows Bridge, Thales and the olive presses, Thales of Miletus, The Chicago School, the map is not the territory, The Market for Lemons, The Nature of the Firm, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, Thomas Davenport, Thomas Malthus, Toyota Production System, transaction costs, ultimatum game, urban planning, value at risk, World Values Survey, Yom Kippur War, zero-sum game

Although Mercury is on average ‘only’ 60 million miles from Earth, 2 the rocket travelled 4.9 billion miles at a speed of 84,500 mph before it finally entered its investigative orbit of the planet, according to plan, in March 2011. 3 This remarkable feat of computation was possible because: the equations of planetary motion have been comprehensively understood since the seventeenth century, thanks to Johannes Kepler and his successors; the equations of planetary motion are stationary, in the sense that those equations governed their motion for millions of years before Kepler’s discoveries and have continued to govern them since (‘stationary’ is a technical term in mathematics and statistics and does not relate to the movements of the planets themselves but to the underlying determinants of planetary motion, which do not change over time: we will make frequent use of the word ‘stationary’ in this sense); 4 the motion of the planets is not significantly affected by human actions 5 or at all by human beliefs about their motion.

Economics demands data The American historian of economic thought Philip Mirowski popularised the term ‘physics envy’ to describe the longing of many economists to emulate Max Planck rather than Keynes’ dentist. And while Keynes’ description of Planck’s deductive reasoning is accurate, the knowledge of the solar system which lies behind NASA’s success originates not in axiomatic reasoning but in the careful and extensive observation of the planets undertaken in the sixteenth century by the Danish nobleman Tycho Brahe. His data collection was subsequently analysed by the German mathematician Johannes Kepler, with whom Brahe collaborated at the end of his life. Physics is inductive as well as deductive. But the underlying stationarity of physical processes reduces the need for abductive reasoning. Economists, however, face unique situations, such as the one encountered in the last months of 2008, and must make ‘inference to best explanation’. Like physics, economics demands data, and the world of business and finance provides plentiful data.


pages: 661 words: 169,298

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

His chief contribution to theoretical cosmology—a compromise geocentric model in which the planets orbit the sun, which in turn orbits the earth—created as many problems as it solved. Needed was someone with the ingenuity and perservance to compose Tycho’s tables into a single, accurate and simple theory. Tycho proposed a compromise between the Copernican and Ptolemaic models in which the sun orbited the earth, and was in turn orbited by the other planets. (Not to scale.) Amazingly, just such a man turned up. He was Johannes Kepler, and on February 4, 1600, he arrived at Benatek Castle near Prague, where Tycho had moved his observatory and retinue after his benefactor King Frederick drank himself to death. Tycho and Kepler made for unlikely collaborators, with each other or anybody else. Tycho was an expansive, despotic giant of a man, who sported a belly of Jovian proportions and a gleaming, metal-alloy nose (the bridge of his original nose having been cut off in a youthful duel).

New York: Sloane, 1948. Venerable popularization of relativity theory. Barrow, John D., and Frank Tipler. The Anthropic Cosmological Principle. London: Oxford University Press, 1986. Barut, Asim O., Alwyn van der Merwe, and Jean-Pierre Vigier, eds. Quantum, Space, and Time—The Quest Continues. London: Cambridge University Press, 1984. Essays in honor of de Broglie, Dirac, and Wigner. Baumgardt, Carola. Johannes Kepler, Life and letters. New York: Philosophical Library, 1951. Beaglehole, J.C. The Exploration of the Pacific. London: Black, 1966. Beazley, Charles Raymond. Prince Henry the Navigator. New York: Putnam’s, 1904. Beer, Arthur, and K.A. Strand, eds. Copernicus: Yesterday and Today. New York: Pergamon, 1975, Beiser, Arthur. Concepts of Modem Physics. New York: McGraw-Hill, 1981. College-level textbook.


pages: 238 words: 46

When Things Start to Think by Neil A. Gershenfeld

3D printing, Ada Lovelace, Bretton Woods, cellular automata, Claude Shannon: information theory, Dynabook, Hedy Lamarr / George Antheil, I think there is a world market for maybe five computers, invention of movable type, Iridium satellite, Isaac Newton, Jacquard loom, Johannes Kepler, John von Neumann, low earth orbit, means of production, new economy, Nick Leeson, packet switching, RFID, speech recognition, Stephen Hawking, Steve Jobs, telemarketer, the medium is the message, Turing machine, Turing test, Vannevar Bush

He had found that apparently innocuous equations can contain solutions of unimaginable complexity. This raised the striking possibility that weather forecasts are so bad because it's fundamentally not possible to predict the weather, rather than because the forecasters are not clever enough. Like all good scientific discoveries, the seeds of Lorenz's observation can be found much earlier. Around 1600 Johannes Kepler (a devout Lutheran) was trying to explain the observations of the orbits of the planets. His first attempt, inspired by Copernicus, matched them to the diameters of nested regular polyhedra (a pyramid inside a cube ... ). He published this analysis in the Mysterium Cosmographicum, an elegant and entirely incorrect little book. While he got the explanation wrong, this book did have all of the elements of modern science practice, including a serious comparison between theoretical predictions and experimental observations, and a discussion of the measurement errors.


pages: 244 words: 68,223

Isaac Newton by James Gleick

Albert Einstein, Astronomia nova, complexity theory, dark matter, Edmond Halley, Fellow of the Royal Society, fudge factor, Isaac Newton, Johannes Kepler, On the Revolutions of the Heavenly Spheres, Richard Feynman, Thomas Kuhn: the structure of scientific revolutions

Just a few bright objects caused a puzzle—the planets, wanderers, like gods or messengers, moving irregularly against the fixed backdrop of stars. In 1543, just before his death, Nicolaus Copernicus, Polish astronomer, astrologer, and mathematician, published the great book De Revolutionibus Orbium Coelestium (“On the Revolutions of the Heavenly Spheres”). In it he gave order to the planets’ paths, resolving them into perfect circles; he set the earth in motion and placed an immobile sun at the center of the universe.4 Johannes Kepler, looking for more order in a growing thicket of data, thousands of painstakingly recorded observations, declared that the planets could not be moving in circles. He suspected the special curves known to the ancients as ellipses. Having thus overthrown one kind of celestial perfection, he sought new kinds, believing fervently in a universe built on geometrical harmony. He found an elegant link between geometry and motion by asserting that an imaginary line from a planet to the sun sweeps across equal areas in equal times.5 Galileo Galilei took spy-glasses—made by inserting spectacle makers’ lenses into a hollow tube—and pointed them upward toward the night sky.


pages: 274 words: 66,721

Double Entry: How the Merchants of Venice Shaped the Modern World - and How Their Invention Could Make or Break the Planet by Jane Gleeson-White

Affordable Care Act / Obamacare, Bernie Madoff, Black Swan, British Empire, business cycle, carbon footprint, corporate governance, credit crunch, double entry bookkeeping, full employment, Gordon Gekko, income inequality, invention of movable type, invention of writing, Islamic Golden Age, Johann Wolfgang von Goethe, Johannes Kepler, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, means of production, Naomi Klein, Nelson Mandela, Ponzi scheme, shareholder value, Silicon Valley, Simon Kuznets, source of truth, spice trade, spinning jenny, The Wealth of Nations by Adam Smith, Thomas Malthus, trade route, traveling salesman, upwardly mobile

Journals Achenbach, Joel, ‘All the president’s pennies: Washington, the meticulous businessman’, Sydney Morning Herald, 17–18 October 2009. Ahrens, Frank, ‘For Wall Street’s math brains, miscalculations’, Washington Post, 21 August 2007. Bushaw, Donald W., ‘Rediscovering the Archimedean Polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro and Johannes Kepler’, The College of Mathematicians Journal, Washington, vol. 29, issue 2, March 1998, pp. 176–88. Calhoun, Ada, ‘Count her in: Denise Schmandt-Besserat’s new way of seeing’, The Austin Chronicle, 10 December 1999. Carruthers, Bruce G. and Wendy Nelson Espeland, ‘Accounting for rationality: Double-entry bookkeeping and the rhetoric of economic rationality’, American Journal of Sociology, vol. 97, no. 1, July 1991, pp. 31–69.


pages: 239 words: 70,206

Data-Ism: The Revolution Transforming Decision Making, Consumer Behavior, and Almost Everything Else by Steve Lohr

"Robert Solow", 23andMe, Affordable Care Act / Obamacare, Albert Einstein, big data - Walmart - Pop Tarts, bioinformatics, business cycle, business intelligence, call centre, cloud computing, computer age, conceptual framework, Credit Default Swap, crowdsourcing, Daniel Kahneman / Amos Tversky, Danny Hillis, data is the new oil, David Brooks, East Village, Edward Snowden, Emanuel Derman, Erik Brynjolfsson, everywhere but in the productivity statistics, Frederick Winslow Taylor, Google Glasses, impulse control, income inequality, indoor plumbing, industrial robot, informal economy, Internet of things, invention of writing, Johannes Kepler, John Markoff, John von Neumann, lifelogging, Mark Zuckerberg, market bubble, meta analysis, meta-analysis, money market fund, natural language processing, obamacare, pattern recognition, payday loans, personalized medicine, precision agriculture, pre–internet, Productivity paradox, RAND corporation, rising living standards, Robert Gordon, Second Machine Age, self-driving car, Silicon Valley, Silicon Valley startup, six sigma, skunkworks, speech recognition, statistical model, Steve Jobs, Steven Levy, The Design of Experiments, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbanked and underbanked, underbanked, Von Neumann architecture, Watson beat the top human players on Jeopardy!

“But to be clear,” Norvig wrote in an explanatory blog post, “the methodology still involves models. Theory has not ended, it is expanding into new forms.” The virtue of the measurements-plus-models approach was evident well before there were computers. In his “Measurement Without Theory” essay, Koopmans cited the collaboration, starting in 1600, between the early astronomers Tycho Brahe and Johannes Kepler. They were exploring the movements of the planets, and Koopmans pointed to their work together as an ideal example of “a case where the empirical approach paved the way for the discovery of fundamental laws.” When they began, the prevailing theory, firmly held by Kepler and others, was that the planets orbited the sun in circular paths. In their partnership, Tycho was the data expert, accumulating careful measurements from his state-of-the-art seventeenth-century observatory.


pages: 226 words: 66,188

Adventures in Human Being (Wellcome) by Gavin Francis

Atul Gawande, Isaac Newton, Johannes Kepler, meta analysis, meta-analysis, Ralph Waldo Emerson, stem cell, traveling salesman

In the thirteenth century the English philosopher Roger Bacon hedged his bets: the soul reaches out from the lens in a projection which ‘ennobles’ our environment, but that environment projects itself back into the eyes. By the seventeenth century, classical perspectives on vision were giving way. Astronomers, whose very business was the elucidation and understanding of light, were peering into the eye in order to better comprehend the stars. The astronomer-mystic Johannes Kepler was the first to write about how an image of the world was projected upside down and back to front onto the retina. When Isaac Newton was working out the motion of the planets around the sun he embarked on dramatic experiments to test the reliability of his own vision. Inserting a long blunt needle (a ‘bodkin’) into his own eye socket between the bone and the eyeball, he described how wiggling it around distorted his vision.


pages: 257 words: 66,480

Strange New Worlds: The Search for Alien Planets and Life Beyond Our Solar System by Ray Jayawardhana

Albert Einstein, Albert Michelson, Arthur Eddington, cosmic abundance, dark matter, Donald Davies, Edmond Halley, invention of the telescope, Isaac Newton, Johannes Kepler, Kuiper Belt, Louis Pasteur, Pierre-Simon Laplace, planetary scale, Pluto: dwarf planet, Search for Extraterrestrial Intelligence, Solar eclipse in 1919

As Venus passes in front of the Sun, taking several hours to do so, it appears as a black dot about one-thirtieth the solar diameter. It’s big enough to be seen with the (properly protected) naked eye, but there are no records of a transit being observed before the invention of the telescope early in the seventeenth century. That’s not too surprising given the rarity of the event. In 1629 Johannes Kepler, as he investigated the laws of planetary motion, realized that transits of both Venus and Mercury would occur two years later. Unfortunately, he didn’t live to see either, and the Venus transit of 1631 was not visible from Europe in any case. But European astronomers were able to observe the transit of Mercury in November that year, vindicating Kepler’s prediction. Eight years later, Englishmen Jeremiah Horrocks and William Crabtree, friends living thirty miles apart, made the frst recorded observations of a Venus transit by projecting the Sun’s image with small telescopes.


pages: 270 words: 71,659

The Right Side of History by Ben Shapiro

Bernie Sanders, Donald Trump, Filter Bubble, illegal immigration, income inequality, Internet Archive, Isaac Newton, Johannes Kepler, labor-force participation, longitudinal study, means of production, Peace of Westphalia, Ronald Reagan, Steven Pinker, the scientific method, The Wealth of Nations by Adam Smith, Thomas L Friedman, white picket fence, women in the workforce

[Yet] when I consider what marvelous things and how many of them men have understood, inquired into, and contrived, I recognize and understand only too clearly that the human mind is a work of God’s, and one of the most excellent.”4 Galileo was no exception. He was a representative of the rule: religious men saw a duty to examine the universe, and to do so with the best possible methodology. This philosophy permeated the wisdom of the Enlightenment’s greatest scientists. Johannes Kepler (1571–1630), the discoverer of the laws of planetary motion, explained: “The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.”5 Kepler routinely described his own physics as part and parcel of Aristotelian metaphysics, and explained that the laws of nature “are within the grasp of the human mind.


pages: 226 words: 75,783

In the Land of Invented Languages: Adventures in Linguistic Creativity, Madness, and Genius by Arika Okrent

British Empire, centre right, global village, Johannes Kepler, Sapir-Whorf hypothesis, slashdot, software patent, Stephen Hawking

It is possible to do mathematics like this, but the text really gets in the way. Wait, which sides are squared? What is taken out of what? What was that thing three clauses ago that I'm now supposed to add to this thing? Late-sixteenth-century scientists who were engaged in calculating the facts of the universe had a sense that the important ideas, the truths behind the calculations, were struggling against the language in which they were trapped. The astronomer Johannes Kepler had turned to musical notation (already well developed at that time) in an effort to better express his discoveries about the motions of the planets, yielding “the harmony of the spheres.” But musical notation could only go so far. The development of mathematical notation in this context was nothing short of revolutionary. The notational innovations of the seventeenth century—symbols and variables instead of words, equations instead of sentences—not only made it easier to keep track of which thing was which in a particular calculation; they also made it easier to see fundamental similarities and differences, and to draw generalizations that hadn't been noticed before.


pages: 260 words: 77,007

Are You Smart Enough to Work at Google?: Trick Questions, Zen-Like Riddles, Insanely Difficult Puzzles, and Other Devious Interviewing Techniques You ... Know to Get a Job Anywhere in the New Economy by William Poundstone

affirmative action, Albert Einstein, big-box store, Buckminster Fuller, car-free, cloud computing, creative destruction, en.wikipedia.org, full text search, hiring and firing, index card, Isaac Newton, Johannes Kepler, John von Neumann, lateral thinking, loss aversion, mental accounting, new economy, Paul Erdős, RAND corporation, random walk, Richard Feynman, rolodex, Rubik’s Cube, Silicon Valley, Silicon Valley startup, sorting algorithm, Steve Ballmer, Steve Jobs, The Spirit Level, Tony Hsieh, why are manhole covers round?, William Shockley: the traitorous eight

You’ll notice that many Fermi questions involve spherical sports equipment filling a bus, swimming pool, jet plane, or sports stadium. You can score a bonus by mentioning Kepler’s conjecture. In the late 1500s, Sir Walter Raleigh asked the English mathematician Thomas Harriot to devise the best way to stack cannonballs on British navy ships. Harriot mentioned the problem to his friend, the astronomer Johannes Kepler. Kepler in turn supposed that the densest way of packing spheres was the one already used for cannonballs and fruit. Start with a flat layer of spheres in a hexagonal array; then put another layer on top of that, fitting each new sphere into the depressions between three spheres on the lower layer. In a large crate, this arrangement approaches a maximum density of about 74 percent. That’s the space occupied by the cannonballs or oranges, as a fraction of total space.


pages: 257 words: 76,785

Shorter by Alex Soojung-Kim Pang

8-hour work day, airport security, Albert Einstein, Bertrand Russell: In Praise of Idleness, business process, call centre, carbon footprint, centre right, cloud computing, colonial rule, disruptive innovation, Erik Brynjolfsson, future of work, game design, gig economy, Henri Poincaré, IKEA effect, iterative process, job automation, job satisfaction, job-hopping, Johannes Kepler, Kickstarter, labor-force participation, longitudinal study, means of production, neurotypical, performance metric, race to the bottom, remote working, Second Machine Age, side project, Silicon Valley, Steve Jobs, telemarketer, The Wealth of Nations by Adam Smith, women in the workforce, young professional, zero-sum game

New Data Show American Commute Times Are Longer,” Here and Now, September 20, 2018, www.npr.org/2018/09/20/650061560/stuck-in-traffic-youre-not-alone-new-data-show-american-commute-times-are-longer; Helen Flores, “Government Urged to Try 4-Day Work Week Amid Traffic,” Philippine Star, August 20, 2018, www.philstar.com/headlines/2018/08/20/1844163/government-urged-try-4-day-work-week-amid-traffic; “4-Day Workweek Possible in BPO, Say Stakeholders,” Business Mirror, September 25, 2018, https://businessmirror.com.ph/2018/09/25/4-day-workweek-possible-in-bpo-say-stakeholders/. Environmental Impacts. See Juliet Schor, “Sustainable Consumption and Worktime Reduction,” Working Paper No. 0406, Johannes Kepler University of Linz, Department of Economics (2004), www.econstor.eu/bitstream/10419/73279/1/wp0406.pdf; Anders Hayden and John M. Shandra, “Hours of Work and the Ecological Footprint of Nations: An Exploratory Analysis,” Local Environment 14, no. 6 (2009): 575–600, https://doi.org/10.1080/13549830902904185; François-Xavier Devetter and Sandrine Rousseau, “Working Hours and Sustainable Development,” Review of Social Economy 69, no. 3 (2011): 333–355, https://doi.org/10.1080/00346764.2011.563507; Carlo Aall et al., “Leisure and Sustainable Development in Norway: Part of the Solution and the Problem,” Leisure Studies 30, no. 4 (2011): 453–476, https://doi.org/10.1080/02614367.2011.589863; Kyle W.


pages: 789 words: 207,744

The Patterning Instinct: A Cultural History of Humanity's Search for Meaning by Jeremy Lent

"Robert Solow", Admiral Zheng, agricultural Revolution, Albert Einstein, Alfred Russel Wallace, Atahualpa, Benoit Mandelbrot, Bretton Woods, British Empire, Buckminster Fuller, Capital in the Twenty-First Century by Thomas Piketty, cognitive dissonance, commoditize, complexity theory, conceptual framework, dematerialisation, demographic transition, different worldview, Doomsday Book, en.wikipedia.org, European colonialism, failed state, Firefox, Francisco Pizarro, Georg Cantor, happiness index / gross national happiness, hedonic treadmill, income inequality, Intergovernmental Panel on Climate Change (IPCC), Internet of things, invention of gunpowder, invention of writing, Isaac Newton, Johann Wolfgang von Goethe, Johannes Kepler, Lao Tzu, Law of Accelerating Returns, mandelbrot fractal, mass immigration, megacity, Metcalfe's law, Mikhail Gorbachev, Nicholas Carr, Norbert Wiener, oil shale / tar sands, out of africa, peak oil, Pierre-Simon Laplace, QWERTY keyboard, Ray Kurzweil, Sapir-Whorf hypothesis, Scientific racism, scientific worldview, shareholder value, sharing economy, Silicon Valley, Simon Kuznets, social intelligence, South China Sea, Stephen Hawking, Steven Pinker, technological singularity, the scientific method, theory of mind, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Thorstein Veblen, Turing test, ultimatum game, urban sprawl, Vernor Vinge, wikimedia commons

Nicholas Oresme in the fourteenth century was the first to conceive of the world as a vast clock; he referred to God as having created the heavens with its functions “so tempered, and so harmonized that…the situation is much like that of a man making a clock and letting it run and continue its own motion by itself.”19 For the pioneers of the Scientific Revolution, the image of nature as a machine proved irresistibly attractive. Johannes Kepler framed his entire life's work on the metaphor, writing to a friend in 1605, “My aim is to show that the celestial machine is to be likened not to a divine organism but to a clockwork.” The metaphor became so entrenched in the burgeoning scientific worldview that it began to lose its metaphoric character and be used as if it were reality. It was Descartes who transformed the NATURE AS MACHINE metaphor into a pseudoscientific theory that nature actually is a machine, boldly declaring, “I do not recognize any difference between the machines made by craftsmen and the various bodies that nature alone composes.”

The Renaissance, which is conventionally viewed as a drastic break from the past, was, rather, a flowering of the growth in learning that had been accumulating over centuries.28 The vision of God's laws as a geometric harmony, and the ambition of tapping into divine consciousness by understanding them, drove the intellectual breakthroughs that created the modern scientific conception of the universe. Johannes Kepler based a radical new theory of planetary motion on this belief. Kepler was an ardent Platonist with a mystical vision of divine geometry. He wrote in the preface of his first major work that he would demonstrate that God did, in fact, create his universe on the basis of geometry, exactly as Plato had speculated. In a tour de force of mathematical wishful thinking, Kepler proposed that each of the five planets (known in his era) traveled in an orbit defined by a sphere, each of which contained one of the “regular solids” or polyhedra, which had remained a source of fascination since Pythagoras (figure 18.1).29 Figure 18.1: Kepler's illustration of the geometric “Secret of the Universe.”


pages: 369 words: 80,355

Too Big to Know: Rethinking Knowledge Now That the Facts Aren't the Facts, Experts Are Everywhere, and the Smartest Person in the Room Is the Room by David Weinberger

airport security, Alfred Russel Wallace, Amazon Mechanical Turk, Berlin Wall, Black Swan, book scanning, Cass Sunstein, commoditize, corporate social responsibility, crowdsourcing, Danny Hillis, David Brooks, Debian, double entry bookkeeping, double helix, en.wikipedia.org, Exxon Valdez, Fall of the Berlin Wall, future of journalism, Galaxy Zoo, Hacker Ethic, Haight Ashbury, hive mind, Howard Rheingold, invention of the telegraph, jimmy wales, Johannes Kepler, John Harrison: Longitude, Kevin Kelly, linked data, Netflix Prize, New Journalism, Nicholas Carr, Norbert Wiener, openstreetmap, P = NP, Pluto: dwarf planet, profit motive, Ralph Waldo Emerson, RAND corporation, Ray Kurzweil, Republic of Letters, RFID, Richard Feynman, Ronald Reagan, semantic web, slashdot, social graph, Steven Pinker, Stewart Brand, technological singularity, Ted Nelson, the scientific method, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Whole Earth Catalog, X Prize

There are many fewer universals than particulars, and you can often figure out the particulars if you know the universals: If you know the universal theorems that explain the orbits of planets, you can figure out where Mars will be in the sky on any particular day on Earth. Aiming at universals is a simplifying tactic within our broader traditional strategy for dealing with a world that is too big to know by reducing knowledge to what our brains and our technology enable us to deal with. We therefore stared at tables of numbers until their simple patterns became obvious to us. Johannes Kepler examined the star charts carefully constructed by his boss, Tycho Brahe, until he realized in 1605 that if the planets orbit the Sun in ellipses rather than perfect circles, it all makes simple sense. Three hundred fifty years later, James Watson and Francis Crick stared at x-rays of DNA until they realized that if the molecule were a double helix, the data about the distances among its atoms made simple sense.


pages: 291 words: 81,703

Average Is Over: Powering America Beyond the Age of the Great Stagnation by Tyler Cowen

Amazon Mechanical Turk, Black Swan, brain emulation, Brownian motion, business cycle, Cass Sunstein, choice architecture, complexity theory, computer age, computer vision, computerized trading, cosmological constant, crowdsourcing, dark matter, David Brooks, David Ricardo: comparative advantage, deliberate practice, Drosophila, en.wikipedia.org, endowment effect, epigenetics, Erik Brynjolfsson, eurozone crisis, experimental economics, Flynn Effect, Freestyle chess, full employment, future of work, game design, income inequality, industrial robot, informal economy, Isaac Newton, Johannes Kepler, John Markoff, Khan Academy, labor-force participation, Loebner Prize, low skilled workers, manufacturing employment, Mark Zuckerberg, meta analysis, meta-analysis, microcredit, Myron Scholes, Narrative Science, Netflix Prize, Nicholas Carr, P = NP, pattern recognition, Peter Thiel, randomized controlled trial, Ray Kurzweil, reshoring, Richard Florida, Richard Thaler, Ronald Reagan, Silicon Valley, Skype, statistical model, stem cell, Steve Jobs, Turing test, Tyler Cowen: Great Stagnation, upwardly mobile, Yogi Berra

When it comes to Google, the right magic keys can get you to many new places, and those keys consist in the relatively manageable art of knowing the right search words. Google is the successful embodiment, through technology, of the earlier dream of the memory palace. For many centuries the idea of an algorithmic path toward greater knowledge was an obsession in Western thought and religion; it infused the Kabbalah, many of the medieval scholastics, and scientists such as Isaac Newton and Johannes Kepler. It fell out of favor as it was increasingly regarded as ridiculous, but guess what? These visions made perfect sense but just didn’t yet have the right technologies to make them work. For a long time the memory tradition in Western thought appeared to be a dead end and indeed few people today use memory theatres or other memory tricks; the technology never seemed practical for most of us.


pages: 313 words: 84,312

We-Think: Mass Innovation, Not Mass Production by Charles Leadbeater

1960s counterculture, Andrew Keen, barriers to entry, bioinformatics, c2.com, call centre, citizen journalism, clean water, cloud computing, complexity theory, congestion charging, death of newspapers, Debian, digital Maoism, disruptive innovation, double helix, Douglas Engelbart, Edward Lloyd's coffeehouse, frictionless, frictionless market, future of work, game design, Google Earth, Google X / Alphabet X, Hacker Ethic, Hernando de Soto, hive mind, Howard Rheingold, interchangeable parts, Isaac Newton, James Watt: steam engine, Jane Jacobs, Jaron Lanier, Jean Tirole, jimmy wales, Johannes Kepler, John Markoff, John von Neumann, Joi Ito, Kevin Kelly, knowledge economy, knowledge worker, lateral thinking, lone genius, M-Pesa, Mark Shuttleworth, Mark Zuckerberg, Marshall McLuhan, Menlo Park, microcredit, Mitch Kapor, new economy, Nicholas Carr, online collectivism, planetary scale, post scarcity, Richard Stallman, Shoshana Zuboff, Silicon Valley, slashdot, social web, software patent, Steven Levy, Stewart Brand, supply-chain management, The Death and Life of Great American Cities, the market place, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Whole Earth Catalog, Zipcar

The EOL plans to engage citizen scientists with tools developed with Google Earth to allow people to log observations of specimens. Science in future will not be solely a collaboration among scientists across disciplines and time zones. More sciences will acquire a following of citizen scientists who will work alongside the professionals. Astronomy is a prime example. Like most sciences, astronomy started with amateurs. When Copernicus moved the sun to the centre of the universe he was only a part-time astronomer. Johannes Kepler, who discovered that planets orbit in ellipses, made most of his money from horoscopes. Yet by the 20th century the pendulum had swung decisively in favour of professional astronomers who had access to huge telescopes – like Jodrell Bank in the UK, or the Mount Wilson Observatory near Pasadena, California, where Edwin Hubble determined that the galaxies are being carried away from one another.


pages: 287 words: 87,204

Erwin Schrodinger and the Quantum Revolution by John Gribbin

Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Arthur Eddington, British Empire, Brownian motion, double helix, Drosophila, Edmond Halley, Ernest Rutherford, Fellow of the Royal Society, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, lateral thinking, Richard Feynman, Schrödinger's Cat, Solar eclipse in 1919, The Present Situation in Quantum Mechanics, the scientific method, trade route, upwardly mobile

The purpose of his visit was to ask if Newton could help with a problem that had been puzzling Halley, Hooke, and another Fellow of the Royal Society, Christopher Wren (1632–1723). The three scientists had realized that the orbits of the planets around the Sun could be explained by a force which falls off in proportion to the square of the distance of a planet from the Sun (an inverse-square law), but they could not prove that all of the laws of planetary motion, described by Johannes Kepler (1571–1630), must result from such a law. Newton, never one for false modesty, told Halley that he had solved that puzzle long ago, but claimed he could not find the relevant document among his papers, and promised to send a copy to Halley later. It is clear from Newton’s surviving papers that this claim was a lie intended to buy time while Newton, confident in his own abilities, actually did solve the problem.


pages: 246 words: 81,625

On Intelligence by Jeff Hawkins, Sandra Blakeslee

airport security, Albert Einstein, computer age, conceptual framework, Johannes Kepler, Necker cube, pattern recognition, Paul Erdős, Ray Kurzweil, Silicon Valley, Silicon Valley startup, speech recognition, superintelligent machines, the scientific method, Thomas Bayes, Turing machine, Turing test

To this day I still hear people claim that computers should adapt to users. This isn't always true. Our brains prefer systems that are consistent and predictable, and we like learning new skills. Can Creativity Lead Me Astray? Can I Fool Myself? False analogy is always a danger. The history of science is rife with examples of beautiful analogies that turned out to be wrong. For example, the celebrated astronomer Johannes Kepler convinced himself that the orbits of the six known planets were defined by the Platonic solids. The Platonic solids are the only three-dimensional shapes that can be constructed entirely out of regular polygons. There are exactly five of them: tetrahedron (four equilateral triangles), sextahedron (six squares, aka a cube), octahedron (eight equilateral triangles), dodecahedron (twelve regular pentagons), and icosahedron (twenty equilateral triangles).


pages: 432 words: 85,707

QI: The Third Book of General Ignorance (Qi: Book of General Ignorance) by John Lloyd, John Mitchinson

Albert Einstein, Boris Johnson, British Empire, California gold rush, cognitive dissonance, dark matter, double helix, epigenetics, Johann Wolfgang von Goethe, Johannes Kepler, Kickstarter, music of the spheres, Nelson Mandela, out of africa, Ronald Reagan, The Wisdom of Crowds, trade route

It’s not even symmetrical. The next time it snows, go outside and try to find a six-sided flake. You’ll be remarkably lucky if you do. The vast majority of snowflakes found on the ground are irregularly shaped crystals, which look nothing like the ones children make with white paper and scissors. The first person to research the shape of snowflakes scientifically was the German astronomer Johannes Kepler (1571–1630). In 1611, two years after publishing the laws that govern the movement of the planets, he wrote On the Six-cornered Snowflake, which he hoped would provide him with funds to buy a Christmas present for a friend. Kepler’s essay, which also looked at the shapes of beehives and pomegranates, didn’t quite manage to explain how snowflakes are made. But it did contain an important mathematical statement, the ‘Kepler Conjecture’, which states that the most efficient way of packing spheres is in a pyramid.


Germany by Andrea Schulte-Peevers

Albert Einstein, bank run, Berlin Wall, call centre, car-free, carbon footprint, centre right, computer age, credit crunch, Donald Trump, Fall of the Berlin Wall, Frank Gehry, glass ceiling, Google Earth, haute couture, haute cuisine, Honoré de Balzac, Johann Wolfgang von Goethe, Johannes Kepler, Kickstarter, low cost airline, low cost carrier, Mikhail Gorbachev, New Urbanism, Peace of Westphalia, Peter Eisenman, place-making, post-work, ride hailing / ride sharing, sensible shoes, Skype, trade route, urban planning, urban renewal, V2 rocket, white picket fence

Dating from AD 179 the rough-hewn Porta Praetoria arch is a key reminder of the city’s heritage. The Historisches Museum ( 507 2448; Dachauplatz 2-4; adult/concession €2.20/1.10; 10am-4pm Tue-Sun, additionally 4-8pm Thu) has exhibits ranging from the Stone Age to the 19th century, with an emphasis on the Roman period and the city’s medieval glory days. Other worthwhile attractions include the house of astronomer and mathematician Johannes Kepler, now the Kepler-Gedächtnishaus (Kepler Memorial House; 507 3442; Keplerstrasse 5; adult/concession €2.20/1.10; 10.30am-4pm Sat & Sun), and the unexpected Schnupftabak Fabrik (Snuff Factory; 507 3442; Gesandtenstrasse 3; adult/concession €5/2.50; tours 2.30pm Fri, 11am & 2.30pm Sat & Sun), a museum in the old Bernard snuff works packed full of old machines and tobacco-related knick-knacks. Return to beginning of chapter Tours City walking tours (adult/child €8/5; in English 1.30pm Wed & Sat May-Oct) Groups meet in front of the Altes Rathaus.

Return to beginning of chapter KLOSTER MAULBRONN Billed as the best-preserved medieval monastery north of the Alps, this one-time Cistercian monastery ( 07043-926 610; www.schloesser-und-gaerten.de; adult/concession/family €6/3/15; 9am-5.30pm Mar-Oct, 9.30am-5pm Tue-Sun Nov-Feb) was founded by Alsatian monks in 1147, born again as a Protestant school in 1556 and designated a Unesco World Heritage Site in 1993. Its famous graduates include the astronomer Johannes Kepler. Aside from the Romanesque-Gothic portico in the monastery church and the weblike vaulting of the cloister, it’s the insights into monastic life that make this place so culturally stimulating. Maulbronn is 30km east of Karlsruhe and 33km northwest of Stuttgart, near the Pforzheim Ost exit on the A8. From Karlsruhe, take the S4 to Bretten Bahnhof and from there bus 700 (€4, one hour); from Stuttgart, take the train to Mühlacker and then bus 700.

Return to beginning of chapter TÜBINGEN 07071 / pop 83,800 Liberal students and deeply traditional Burschenschaften (fraternities) singing ditties for beloved Germania, eco-warriors and punks – all have a soft spot for this bewitchingly pretty Swabian city, where cobbled alleys lined with gabled town houses twist up to a perkily turreted castle. As did some of the country’s biggest brains. It was here that Joseph Ratzinger, now Pope Benedict XVI, lectured theology in the late 1960s before fleeing to Bavaria, scandalised by Marxist-inspired student radicalism; and here that Friedrich Hölderlin studied stanzas, Johannes Kepler planetary motions and Goethe the bottom of a beer glass. Today the hybrid-driving mayor, Boris Palmer, is on his own green mission to cut emissions with clean transport and renewable energy policies. The finest days unfold slowly in Tübingen, with leisurely brunches in Altstadt cafes, punting on the willow-lined Neckar River and pretending, as the students so diligently do, to work your brain cells in a chestnut-shaded beer garden.


pages: 340 words: 91,387

Stealth of Nations by Robert Neuwirth

accounting loophole / creative accounting, big-box store, British Empire, call centre, collective bargaining, corporate governance, full employment, Hernando de Soto, illegal immigration, income inequality, informal economy, invisible hand, Jane Jacobs, jitney, Johannes Kepler, joint-stock company, Joseph Schumpeter, megacity, microcredit, New Urbanism, Pepto Bismol, pirate software, profit motive, Shenzhen was a fishing village, Simon Kuznets, special economic zone, The Wealth of Nations by Adam Smith, thinkpad, upwardly mobile, Vilfredo Pareto, yellow journalism

Squatter communities may be growing, but System D is bringing commerce and opportunity to these neighborhoods that are off the governmental grid. System D is distributing products more equitably and cheaply than any big company can. And, even as governments around the world are looking to privatize agencies and get out of the business of providing for people, System D is running public services—trash pickup, recycling, transportation, and even utilities. Friedrich Schneider, chair of the economics department at Johannes Kepler University in Linz, Austria, has spent decades calculating the dollar value of what he calls the shadow economies of the world. He admits his projections are imprecise, in part because, like privately held businesses everywhere, businesspeople who engage in trade off the books don’t want to open their books (most successful System D merchants are obsessive about profit and loss and keep detailed accounts of their revenues and expenses in old-fashioned ledger books) to anyone who will write anything in a book.


pages: 310 words: 89,838

Massive: The Missing Particle That Sparked the Greatest Hunt in Science by Ian Sample

Albert Einstein, Arthur Eddington, cuban missile crisis, dark matter, Donald Trump, double helix, Ernest Rutherford, Gary Taubes, Isaac Newton, Johannes Kepler, John Conway, John von Neumann, Kickstarter, Menlo Park, Murray Gell-Mann, Richard Feynman, Ronald Reagan, Stephen Hawking, uranium enrichment, Yogi Berra

The observation, which surely made for lively theological discussions about the Trinity, mirrors the modern definitions of volume and mass. In the early fourteenth century, the Parisian philosopher Jean Buridan drew on the concept of mass when he described how throwing an object gave it an impetus that depended on how much matter it contained and the speed at which it was lobbed.3 The sixteenth-century German astronomer Johannes Kepler took things further, arguing that planets stayed true to their orbits and didn’t hurtle around space like scattered snooker balls thanks to the inertia arising from their enormous masses. Despite the valuable work of early philosophers and astronomers, the term “mass” was not used systematically until 1687, when Isaac Newton laid the foundations of classical mechanics in a great but wholly impenetrable work, the Principia.4 Newton said mass was a quantity of matter that arose from an object’s volume and density.


pages: 339 words: 94,769

Possible Minds: Twenty-Five Ways of Looking at AI by John Brockman

AI winter, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, artificial general intelligence, Asilomar, autonomous vehicles, basic income, Benoit Mandelbrot, Bill Joy: nanobots, Buckminster Fuller, cellular automata, Claude Shannon: information theory, Daniel Kahneman / Amos Tversky, Danny Hillis, David Graeber, easy for humans, difficult for computers, Elon Musk, Eratosthenes, Ernest Rutherford, finite state, friendly AI, future of work, Geoffrey West, Santa Fe Institute, gig economy, income inequality, industrial robot, information retrieval, invention of writing, James Watt: steam engine, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, Kickstarter, Laplace demon, Loebner Prize, market fundamentalism, Marshall McLuhan, Menlo Park, Norbert Wiener, optical character recognition, pattern recognition, personalized medicine, Picturephone, profit maximization, profit motive, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Rodney Brooks, self-driving car, sexual politics, Silicon Valley, Skype, social graph, speech recognition, statistical model, Stephen Hawking, Steven Pinker, Stewart Brand, strong AI, superintelligent machines, supervolcano, technological singularity, technoutopianism, telemarketer, telerobotics, the scientific method, theory of mind, Turing machine, Turing test, universal basic income, Upton Sinclair, Von Neumann architecture, Whole Earth Catalog, Y2K, zero-sum game

Neither of these developments would Wiener have anticipated, said David, prompting him to ask, “Do we need a new set of guiding metaphors?” In The Sleepwalkers, a sweeping history of scientific thought from ancient times through the Renaissance, Arthur Koestler identified a tension that has marked the most dramatic leaps of our cosmological imagination. In reading the great works of Nicolaus Copernicus and Johannes Kepler today, Koestler argued, we are struck as much by their strange unfamiliarity—their embeddedness in the magic or mysticism of an earlier age—as by their modern-sounding insights. I detect that same doubleness—the zigzag origami folds of old and new—in Norbert Wiener’s classic The Human Use of Human Beings. First published in 1950 and revised in 1954, the book is in many ways extraordinarily prescient.


pages: 321 words: 89,109

The New Gold Rush: The Riches of Space Beckon! by Joseph N. Pelton

3D printing, Any sufficiently advanced technology is indistinguishable from magic, Buckminster Fuller, Carrington event, Colonization of Mars, disruptive innovation, Donald Trump, Elon Musk, en.wikipedia.org, full employment, global pandemic, Google Earth, gravity well, Iridium satellite, Jeff Bezos, job automation, Johannes Kepler, John von Neumann, life extension, low earth orbit, Lyft, Mark Shuttleworth, Mark Zuckerberg, megacity, megastructure, new economy, Peter H. Diamandis: Planetary Resources, post-industrial society, private space industry, Ray Kurzweil, Silicon Valley, skunkworks, Stephen Hawking, Steve Jobs, Thomas Malthus, Tim Cook: Apple, Tunguska event, uber lyft, urban planning, urban sprawl, wikimedia commons, X Prize

© Springer International Publishing Switzerland 2017 Joseph N. PeltonThe New Gold Rushhttps://doi.org/10.1007/978-3-319-39273-8_1 1. Why This Gold Rush Is Different Joseph N. Pelton1 (1)Executive Board, International Association for the Advancement of Space Safety, Arlington, VA, USA “Ships and sails proper for the heavenly air should be fashioned. Then there will also be people, who do not shrink from the dreary vastness of space.” —Johannes Kepler, Letter to Galileo Galilei, 1609 “In spite of the opinions of certain narrow-minded people, who would shut up the human race upon this globe, as within some magic circle which it must never outstep, we shall 1 day travel to the moon, the planets, and the stars, with the same facility, rapidity, and certainty as we now make the voyage from Liverpool to New York!” —Jules Verne, From the Earth to the Moon, 1865 “The choice, as Wells once said, is the Universe—or nothing… The challenge of the great spaces between the worlds is a stupendous one; but if we fail to meet it, the story of our race will be drawing to its close.


pages: 294 words: 96,661

The Fourth Age: Smart Robots, Conscious Computers, and the Future of Humanity by Byron Reese

agricultural Revolution, AI winter, artificial general intelligence, basic income, Buckminster Fuller, business cycle, business process, Claude Shannon: information theory, clean water, cognitive bias, computer age, crowdsourcing, dark matter, Elon Musk, Eratosthenes, estate planning, financial independence, first square of the chessboard, first square of the chessboard / second half of the chessboard, full employment, Hans Rosling, income inequality, invention of agriculture, invention of movable type, invention of the printing press, invention of writing, Isaac Newton, Islamic Golden Age, James Hargreaves, job automation, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, lateral thinking, life extension, Louis Pasteur, low skilled workers, manufacturing employment, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Mary Lou Jepsen, Moravec's paradox, On the Revolutions of the Heavenly Spheres, pattern recognition, profit motive, Ray Kurzweil, recommendation engine, Rodney Brooks, Sam Altman, self-driving car, Silicon Valley, Skype, spinning jenny, Stephen Hawking, Steve Wozniak, Steven Pinker, strong AI, technological singularity, telepresence, telepresence robot, The Future of Employment, the scientific method, Turing machine, Turing test, universal basic income, Von Neumann architecture, Wall-E, Watson beat the top human players on Jeopardy!, women in the workforce, working poor, Works Progress Administration, Y Combinator

Shortly thereafter, a French philosopher named Jean Bodin was one of a group of people who saw science as the way forward. Bodin didn’t believe in some golden age of the past; rather, he believed that the power of print would launch the world forward and that the sciences “contain in themselves treasure that no future ages will ever be able to exhaust.” By 1600, things were really getting under way. In 1609, Johannes Kepler wrote a letter to Galileo Galilei talking about a future with spaceships: “Ships and sails proper for the heavenly air should be fashioned. Then there will also be people who do not shrink from the dreary vastness of space.” In 1620, Sir Francis Bacon published a book called Novum Organum (The New Method), which is regarded as the beginning of what we now call the scientific method. Bacon emphasized the firsthand study of nature along with careful observations and the recording of data.


pages: 315 words: 92,151

Ten Billion Tomorrows: How Science Fiction Technology Became Reality and Shapes the Future by Brian Clegg

Albert Einstein, anthropic principle, Brownian motion, call centre, Carrington event, combinatorial explosion, don't be evil, Ernest Rutherford, experimental subject, game design, gravity well, hive mind, invisible hand, Isaac Newton, Johannes Kepler, John von Neumann, Kickstarter, nuclear winter, pattern recognition, RAND corporation, Ray Kurzweil, RFID, Richard Feynman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, silicon-based life, speech recognition, stem cell, Stephen Hawking, Steve Jobs, Turing test

Godwin doesn’t even attempt a reasonable mechanism for getting to the Moon, putting the transport in the hand of gansas, an imaginary breed of swan that he described as migrating to the Moon each year. On the other hand Godwin (more precisely his narrator Gonsales) is more scientific in describing the way that he lost weight as he flew away from the Earth. If hitching a ride with a flock of lunar migrating birds seems an unlikely mode of transport, it is as nothing compared with the strange work Somnium, written by astronomer Johannes Kepler in 1634. In this, Kepler has his fictional hero cross an insubstantial bridge of darkness, used by lunar demons to make the journey over to the Earth during eclipses. Despite this, Kepler too throws in some interesting thinking about the experience of being on the Moon. He seems to have been one of the first to realize that when looking back at the Earth he would see it in the lunar sky as a huge, dramatic moon.


pages: 330 words: 99,226

Extraterrestrial Civilizations by Isaac Asimov

Albert Einstein, Cepheid variable, Columbine, Edward Charles Pickering, Harvard Computers: women astronomers, invention of radio, invention of the telescope, invention of writing, Isaac Newton, Johannes Kepler, Louis Pasteur, Magellanic Cloud, Search for Extraterrestrial Intelligence

For the first time in history, the Moon was seen magnified, and more clearly detailed than was possible with the unaided eye. Galileo saw mountain ranges on the Moon, together with what looked like volcanic craters. He saw dark, smooth patches that looked like seas. Quite plainly and simply, he was seeing another world. This stimulated the further production of fictional flights to the Moon. The first was written by Johannes Kepler (1571–1630), an astronomer of the first rank* and was published posthumously in 1633. It was entitled Somnium because the hero reached the Moon in a dream. The book was remarkable in that it was the first to take into account the actual known facts about the Moon, which until then had been treated as in no way different from any Earthly piece of real estate. Kepler was aware that on the Moon the nights and days were each 14 Earth days long.


pages: 326 words: 97,089

Five Billion Years of Solitude: The Search for Life Among the Stars by Lee Billings

addicted to oil, Albert Einstein, Arthur Eddington, California gold rush, Colonization of Mars, cosmological principle, cuban missile crisis, dark matter, Dava Sobel, double helix, Edmond Halley, full employment, hydraulic fracturing, index card, Isaac Newton, Johannes Kepler, Kuiper Belt, low earth orbit, Magellanic Cloud, music of the spheres, out of africa, Peter H. Diamandis: Planetary Resources, planetary scale, profit motive, quantitative trading / quantitative finance, Ralph Waldo Emerson, RAND corporation, random walk, Search for Extraterrestrial Intelligence, Searching for Interstellar Communications, selection bias, Silicon Valley, Solar eclipse in 1919, technological singularity, the scientific method, transcontinental railway

This was the crucial evidence for heliocentrism, as geocentric models predicted that Venus, closer to the Sun but still circling Earth, would consequently always be backlit by the Sun’s radiance and would display only a crescent phase as viewed from our world. Yet the Copernican model was still imperfect: it failed to replicate the exact motions of the planets in the sky. In making his model, Copernicus had implicitly relied upon the old Pythagorean notion, extended by Plato, Aristotle, and others, that planets moved in perfect circles. Around the same time that Galileo began using his telescope, a German astronomer, Johannes Kepler, announced a discovery that would mark the true beginning of modern astronomy, one that ironically came to him while he worked to create a table for casting more accurate horoscopes. Kepler had been grappling with the orbit of Mars, trying to integrate historical records of the planet’s motions into Copernicus’s heliocentric model. He had painstakingly considered circular orbits, even spiraling orbits, but his results did not align with observations.


pages: 319 words: 100,984

The Moon: A History for the Future by Oliver Morton

Charles Lindbergh, commoditize, Dava Sobel, Donald Trump, Elon Musk, facts on the ground, gravity well, Isaac Newton, Jeff Bezos, Johannes Kepler, low earth orbit, Mark Zuckerberg, Menlo Park, multiplanetary species, Norman Mailer, Pierre-Simon Laplace, planetary scale, Pluto: dwarf planet, plutocrats, Plutocrats, Silicon Valley, South China Sea, Steve Jobs, Stewart Brand, UNCLOS, Whole Earth Catalog, X Prize

Galileo assured his readers they could easily see the effect for themselves if, when the crescent Moon was low in the sky, they so positioned themselves that the sunlit sliver was hidden by a chimney or wall. Once thus seen, the ashen light was easily, even naturally, understood as light that had bounced first off the Earth and then off the Moon, like sunlight reaching an inner room. For most of his readers, this must have been a strange new thought. For Michael Maestlin, an astronomer at the University of Tübingen, and his pupil Johannes Kepler, then the court astronomer to Holy Roman Emperor Rudolph II, this part of “The Starry Messenger” came as no surprise. They had come to the same conclusions about how the Moon was lit with no need of telescopes. So had Paolo Sarpi, a priest and statesman in Venice whom Galileo knew and with whom he may have discussed the matter. It is no coincidence that these men were, like Galileo, members of the small band of Moonwatchers which took seriously the idea that Nicolaus Copernicus, a Polish cleric, had published more than half a century before: that the Earth orbited the Sun.


pages: 282 words: 89,436

Einstein's Dice and Schrödinger's Cat: How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics by Paul Halpern

Albert Einstein, Albert Michelson, Arthur Eddington, Brownian motion, clockwork universe, cosmological constant, dark matter, double helix, Ernest Rutherford, Fellow of the Royal Society, Isaac Newton, Johannes Kepler, John von Neumann, lone genius, Murray Gell-Mann, New Journalism, orbital mechanics / astrodynamics, Richard Feynman, Schrödinger's Cat, Solar eclipse in 1919, The Present Situation in Quantum Mechanics

In that case a researcher could anticipate the brain patterns, nerve signals, and muscle contractions triggering the toss, making its outcome even more predictable. In short, believers in the standpoint that the entire universe runs like a perfect clock dismiss the notion that anything is fundamentally random. Indeed, on astronomical scales, such as the domain of the solar system, Newton’s laws are remarkably accurate. They wonderfully reproduce German astronomer Johannes Kepler’s laws describing how planets orbit the Sun. Our capacity to anticipate celestial events, such as solar eclipses and planetary conjunctions, and to launch spacecraft precisely toward faraway targets are testimony to the clockwork predictability of Newtonian mechanics, particularly as applied to gravitation. Maxwell’s equations brought unity to another natural force, electromagnetism. Before the nineteenth century, science treated electricity and magnetism as separate phenomena.


pages: 366 words: 100,602

Sextant: A Young Man's Daring Sea Voyage and the Men Who ... by David Barrie

centre right, colonial exploitation, Edmond Halley, Eratosthenes, Fellow of the Royal Society, Isaac Newton, Johannes Kepler, John Harrison: Longitude, lone genius, Maui Hawaii, Nicholas Carr, polynesian navigation, South China Sea, trade route

The observer’s longitude could then be derived by converting the time difference in hours and minutes into a spatial displacement measured in degrees and minutes east or west—one hour being equal to 15 degrees of longitude (360 divided by 24). It was not until the early seventeenth century that Copernican theory was firmly established on the basis of the observations of Tycho Brahe (1546–1601), Galileo Galilei (1564–1642), and Johannes Kepler (1571–1630). Galileo’s momentous discovery of the moons of Jupiter and, soon afterward, of the changing phases of the planet Venus, not only provided overwhelming evidence that the earth was not the center of the universe but also opened the way to a proper understanding of planetary motion.3 The invention of the first pendulum clock in the 1650s by Christiaan Huygens (1629–95) also marked a great advance.


pages: 370 words: 97,138

Beyond: Our Future in Space by Chris Impey

3D printing, Admiral Zheng, Albert Einstein, Alfred Russel Wallace, AltaVista, Berlin Wall, Buckminster Fuller, butterfly effect, California gold rush, carbon-based life, Charles Lindbergh, Colonization of Mars, cosmic abundance, crowdsourcing, cuban missile crisis, dark matter, discovery of DNA, Doomsday Clock, Edward Snowden, Elon Musk, Eratosthenes, Haight Ashbury, Hyperloop, I think there is a world market for maybe five computers, Isaac Newton, Jeff Bezos, Johannes Kepler, John von Neumann, Kickstarter, life extension, low earth orbit, Mahatma Gandhi, Marc Andreessen, Mars Rover, mutually assured destruction, Oculus Rift, operation paperclip, out of africa, Peter H. Diamandis: Planetary Resources, phenotype, private space industry, purchasing power parity, RAND corporation, Ray Kurzweil, RFID, Richard Feynman, Richard Feynman: Challenger O-ring, risk tolerance, Rubik’s Cube, Search for Extraterrestrial Intelligence, Searching for Interstellar Communications, Silicon Valley, skunkworks, Skype, Stephen Hawking, Steven Pinker, supervolcano, technological singularity, telepresence, telerobotics, the medium is the message, the scientific method, theory of mind, There's no reason for any individual to have a computer in his home - Ken Olsen, wikimedia commons, X Prize, Yogi Berra

One of their ideas was a strong but lightweight spacesuit that could repair itself with protein-dispensing nanounits built into the layers of fabric. The same suit could also monitor the vital signs of astronauts and carry emergency drugs. When there’s room at the bottom, the sky’s the limit.14 Solar Sailing The cost and difficulty of space travel is rooted in dependence on the way rockets work. Sunlight is used to generate electricity and power on Earth and in space. What if it could be used for propulsion as well? It can. Johannes Kepler noticed that comet tails point away from the Sun, and in a 1610 letter to Galileo, he suggested: “Provide ships or sails adapt to the heavenly breeze, and there will be some who brave even that void.” Jules Verne was the first to outline the concept of the solar sail in 1865, seizing on James Clerk Maxwell’s theory that light has momentum as well as energy so it can exert pressure on objects.


pages: 349 words: 98,868

Nervous States: Democracy and the Decline of Reason by William Davies

active measures, Affordable Care Act / Obamacare, Amazon Web Services, bank run, banking crisis, basic income, business cycle, Capital in the Twenty-First Century by Thomas Piketty, citizen journalism, Climategate, Climatic Research Unit, Colonization of Mars, continuation of politics by other means, creative destruction, credit crunch, decarbonisation, deindustrialization, discovery of penicillin, Dominic Cummings, Donald Trump, drone strike, Elon Musk, failed state, Filter Bubble, first-past-the-post, Frank Gehry, gig economy, housing crisis, income inequality, Isaac Newton, Jeff Bezos, Johannes Kepler, Joseph Schumpeter, knowledge economy, loss aversion, low skilled workers, Mahatma Gandhi, Mark Zuckerberg, mass immigration, meta analysis, meta-analysis, Mont Pelerin Society, mutually assured destruction, Northern Rock, obamacare, Occupy movement, pattern recognition, Peace of Westphalia, Peter Thiel, Philip Mirowski, planetary scale, post-industrial society, quantitative easing, RAND corporation, Ray Kurzweil, Richard Florida, road to serfdom, Robert Mercer, Ronald Reagan, sentiment analysis, Silicon Valley, Silicon Valley startup, smart cities, statistical model, Steve Jobs, the scientific method, Turing machine, Uber for X, universal basic income, University of East Anglia, Valery Gerasimov, We are the 99%, WikiLeaks, women in the workforce, zero-sum game

Battles were being fought in the name of one truth versus another. Hobbes held nothing but scorn for the “schoolmen” who fueled these retrograde disputes. Above all, he believed that philosophy and science ought to provide a basis of peaceful consensus rather than of violent conflict. This is one reason to take his ideas seriously today. Hobbes was deeply impressed by the advances of anatomists such as Harvey and of astronomers such as Johannes Kepler and Galileo. What underpinned this scientific progress, as Hobbes saw it, was an emphasis on mathematics and geometry, and not on idle and often moralistic speculation as the basis of all truth. Whether it be the circulation of the planets or of the blood (or, as we will see, of money), the underlying reality was always the same, namely the mathematical laws that governed bodies in motion. Geometry revealed the basic rules of physical existence.


pages: 416 words: 106,582

This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking by John Brockman

23andMe, Albert Einstein, Alfred Russel Wallace, banking crisis, Barry Marshall: ulcers, Benoit Mandelbrot, Berlin Wall, biofilm, Black Swan, butterfly effect, Cass Sunstein, cloud computing, congestion charging, correlation does not imply causation, Daniel Kahneman / Amos Tversky, dark matter, data acquisition, David Brooks, delayed gratification, Emanuel Derman, epigenetics, Exxon Valdez, Flash crash, Flynn Effect, hive mind, impulse control, information retrieval, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Jaron Lanier, Johannes Kepler, John von Neumann, Kevin Kelly, lifelogging, mandelbrot fractal, market design, Mars Rover, Marshall McLuhan, microbiome, Murray Gell-Mann, Nicholas Carr, open economy, Pierre-Simon Laplace, place-making, placebo effect, pre–internet, QWERTY keyboard, random walk, randomized controlled trial, rent control, Richard Feynman, Richard Feynman: Challenger O-ring, Richard Thaler, Satyajit Das, Schrödinger's Cat, security theater, selection bias, Silicon Valley, Stanford marshmallow experiment, stem cell, Steve Jobs, Steven Pinker, Stewart Brand, the scientific method, Thorstein Veblen, Turing complete, Turing machine, twin studies, Vilfredo Pareto, Walter Mischel, Whole Earth Catalog, WikiLeaks, zero-sum game

At first he put the fence up only when facing a team full of power hitters, but eventually he took it to the limit, putting the fence up when the visitors were at bat and taking it down when his team was. The history of science is littered with flexible fences. The phlogiston theory predicted that phlogiston would be released when magnesium burned. It looked bad for that theory when experiments showed that burning magnesium became heavier—but its supporters happily explained that phlogiston had negative weight. Consider Johannes Kepler. He came up with the idea that the distances of the six (known) planets could be explained by nesting the five Platonic solids. It almost worked for Earth, Mars, and Venus but clearly failed for Jupiter. He dismissed the trouble with Jupiter, saying, “Nobody will wonder at it, considering the great distance.” The theory certainly wouldn’t have worked with any extra planets, but fortunately for Kepler’s peace of mind, Uranus was discovered well after his death.


pages: 442 words: 110,704

The Glass Universe: How the Ladies of the Harvard Observatory Took the Measure of the Stars by Dava Sobel

Albert Einstein, card file, Cepheid variable, crowdsourcing, dark matter, Dava Sobel, Edmond Halley, Edward Charles Pickering, Ernest Rutherford, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, index card, invention of the telescope, Isaac Newton, Johannes Kepler, John Harrison: Longitude, luminiferous ether, Magellanic Cloud, pattern recognition, QWERTY keyboard, Ralph Waldo Emerson, Solar eclipse in 1919

When the legendary Tycho Brahe of Denmark glanced skyward one night and beheld such a sight, he declared it “the greatest wonder that has ever shown itself in the whole of nature since the beginning of the world.” De nova stella, Tycho’s eyewitness account of the 1572 marvel, argued that Aristotle had been wrong to call the heavens immutable. Surely the abrupt appearance of the new star and its subsequent disappearance a year later proved that change could occur in the realm beyond the Moon. Not long after Tycho died in 1601, another nova burst into splendor. Both Galileo in Padua and Johannes Kepler in Prague observed the brilliant new star of 1604, which was so bright as to be visible in the daytime for more than three weeks. Although no comparable naked-eye nova ever materialized over the following centuries, a few fortunate astronomers who happened to be pointing their telescopes to the right place at the right time discovered seven more novae between 1670 and 1892. Then Mina Fleming found one.


pages: 460 words: 108,654

Time Travelers Never Die by Jack McDevitt

Albert Einstein, index card, indoor plumbing, Johannes Kepler, life extension, orbital mechanics / astrodynamics, Ralph Waldo Emerson, rolodex, Rosa Parks, Thales of Miletus, walking around money, white picket fence, Winter of Discontent

“Dad—” “Adrian, I’m on the edge of the Enlightenment. And I know who the players are.” “But people always know who the players are.” “No, they don’t. It usually takes a couple of generations to figure that out. Contemporaries only know the authority figures and the loudmouths. And the people born into power. But it takes perspective to know who’s carrying the load. Nobody here has a clue who Johannes Kepler is. All they know about Galileo is that he’s a teacher who got in trouble with the Inquisition. I doubt anyone’s heard of Francis Bacon. Even in Britain, nobody really knows him. He’s just a guy with a funny name.” “How’ve you managed to live?” asked Shel. “In the beginning, I became a field hand. I worked in shops. Been a waiter. When I came here, Santo Pietro took me in. Eventually, I founded a company that promoted the use of table utensils.”


pages: 332 words: 109,213

The Scientist as Rebel by Freeman Dyson

Albert Einstein, Asilomar, British Empire, Claude Shannon: information theory, dark matter, double helix, Edmond Halley, Ernest Rutherford, experimental subject, Fellow of the Royal Society, From Mathematics to the Technologies of Life and Death, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, kremlinology, Mikhail Gorbachev, Norbert Wiener, Paul Erdős, Richard Feynman, Ronald Reagan, Silicon Valley, Stephen Hawking, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, undersea cable

Another factor favoring the amateur observer is the change in our view of the universe caused by recent discoveries. The traditional Aristotelian view imagined the astronomical universe to be a sphere of unchanging peace and harmony. The earth alone was perishable and violent, while the heavenly bodies were perfect and quiescent. This view was contradicted by a multitude of discoveries during the last four hundred years, beginning with the two exploding stars observed by Tycho Brahe and Johannes Kepler and with the mountains and valleys discovered by Galileo on the moon. In the last fifty years it became clear that we live in a violent universe, full of explosions, collapses, and collisions. The Earth now appears to be a comparatively quiet corner in a universe of cosmic mayhem. The 1994 bombardment of Jupiter demonstrated that our own solar system is not immune to cosmic violence. After this replacement of the old static view of the universe by a new dynamic view, the subject matter of astronomy is also transformed.


pages: 325 words: 110,330

Creativity, Inc.: Overcoming the Unseen Forces That Stand in the Way of True Inspiration by Ed Catmull, Amy Wallace

Albert Einstein, business climate, buy low sell high, complexity theory, fear of failure, Golden Gate Park, iterative process, Johannes Kepler, Menlo Park, rolodex, Rubik’s Cube, Sand Hill Road, Silicon Valley, Silicon Valley startup, Steve Jobs, Wall-E

On the most basic level, it says that if there are competing explanations for why something occurs the way it does, you should pick the one that relies on the fewest assumptions and is thus the simplest. When Renaissance astronomers were trying to explain the movement of the planets, for example, there were many complex theories. The prevailing belief was that orbits were perfect circles, or epicycles, but as planetary observation improved, the models based on circles had to be made extremely complex in order to work. Then, Johannes Kepler hit upon the comparatively simple idea that the orbit of every planet is an ellipse, with the sun at one of two foci within it. The explanation’s simplicity seemed proof that it was the right one—and with that simplicity came great power. Unlike some theoretical ideas, Occam’s Razor accords easily with human nature. In general, we seek what we think are simple explanations for events in our lives because we believe the simpler something is, the more fundamental—the more true—it is.


pages: 476 words: 118,381

Space Chronicles: Facing the Ultimate Frontier by Neil Degrasse Tyson, Avis Lang

Albert Einstein, Arthur Eddington, asset allocation, Berlin Wall, carbon-based life, centralized clearinghouse, cosmic abundance, cosmic microwave background, dark matter, Gordon Gekko, informal economy, invention of movable type, invention of the telescope, Isaac Newton, Johannes Kepler, Karl Jansky, Kuiper Belt, Louis Blériot, low earth orbit, Mars Rover, mutually assured destruction, orbital mechanics / astrodynamics, Pluto: dwarf planet, RAND corporation, Ronald Reagan, Search for Extraterrestrial Intelligence, SETI@home, space pen, stem cell, Stephen Hawking, Steve Jobs, the scientific method, trade route

In his 1543 magnum opus, De Revolutionibus, Nicolaus Copernicus placed the Sun in the center of the known universe and asserted that Earth plus the five known planets—Mercury, Venus, Mars, Jupiter, and Saturn—executed perfect circular orbits around it. Unknown to Copernicus, a circle is an extremely rare shape for an orbit and does not describe the path of any planet in our solar system. The actual shape was deduced by German mathematician and astronomer Johannes Kepler, who published his calculations in 1609. The first of his laws of planetary motion asserts that planets orbit the Sun in ellipses. An ellipse is a flattened circle, and the degree of flatness is indicated by a numerical quantity called eccentricity, abbreviated e. If e equals zero, you get a perfect circle. As e increases from zero to one, your ellipse gets more and more elongated. Of course, the greater your eccentricity, the more likely you are to cross somebody else’s orbit.


pages: 515 words: 117,501

Miracle Cure by William Rosen

Affordable Care Act / Obamacare, availability heuristic, biofilm, cognitive bias, cognitive dissonance, conceptual framework, Copley Medal, creative destruction, demographic transition, discovery of penicillin, Ernest Rutherford, experimental subject, Fellow of the Royal Society, Frederick Winslow Taylor, friendly fire, functional fixedness, germ theory of disease, global supply chain, Haber-Bosch Process, Ignaz Semmelweis: hand washing, Isaac Newton, James Watt: steam engine, Johannes Kepler, John Snow's cholera map, Joseph Schumpeter, Louis Pasteur, medical malpractice, meta analysis, meta-analysis, microbiome, New Journalism, obamacare, out of africa, pattern recognition, Pepto Bismol, randomized controlled trial, selection bias, stem cell, transcontinental railway, working poor

Although what was left behind when penicillin was broken down to simpler compounds—formally “degradation products”—weren’t of any therapeutic value, they did have one extremely important aspect: The degradation products, primarily penicillamine, penillic acid, and the penilloaldehydes, were all crystals. Crystals could be analyzed. As far back as the seventeenth century, the polymaths Robert Hooke and Johannes Kepler were independently speculating that crystals like gemstones, common salt, and even snowflakes were structurally similar, each with visibly flat faces meeting at regular angles, all in a repeating series. As scientists realized that all matter is composed of atoms, they also concluded that macroscopic crystals reflected a microscopic structural similarity: The atoms that composed them had to be organized in some regular, and therefore decipherable, structure.


pages: 410 words: 114,005

Black Box Thinking: Why Most People Never Learn From Their Mistakes--But Some Do by Matthew Syed

Airbus A320, Alfred Russel Wallace, Arthur Eddington, Atul Gawande, Black Swan, British Empire, call centre, Captain Sullenberger Hudson, Checklist Manifesto, cognitive bias, cognitive dissonance, conceptual framework, corporate governance, creative destruction, credit crunch, crew resource management, deliberate practice, double helix, epigenetics, fear of failure, fundamental attribution error, Henri Poincaré, hindsight bias, Isaac Newton, iterative process, James Dyson, James Hargreaves, James Watt: steam engine, Johannes Kepler, Joseph Schumpeter, Kickstarter, Lean Startup, mandatory minimum, meta analysis, meta-analysis, minimum viable product, publication bias, quantitative easing, randomized controlled trial, selection bias, Shai Danziger, Silicon Valley, six sigma, spinning jenny, Steve Jobs, the scientific method, Thomas Kuhn: the structure of scientific revolutions, too big to fail, Toyota Production System, US Airways Flight 1549, Wall-E, Yom Kippur War

But when Galileo invited Christian scholars to look through his telescope in order to see the new evidence, they flatly refused. They didn’t want to see any data that might count against the earth-centric view of the universe. It is difficult to think of a more revelatory episode of cognitive dissonance. They simply shut their eyes. As Galileo said in a letter to the German mathematician Johannes Kepler: My dear Kepler, I wish that we might laugh at the remarkable stupidity of the common herd. What do you have to say about the principal philosophers of this academy who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times? Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth.


pages: 437 words: 113,173

Age of Discovery: Navigating the Risks and Rewards of Our New Renaissance by Ian Goldin, Chris Kutarna

2013 Report for America's Infrastructure - American Society of Civil Engineers - 19 March 2013, 3D printing, Airbnb, Albert Einstein, AltaVista, Asian financial crisis, asset-backed security, autonomous vehicles, banking crisis, barriers to entry, battle of ideas, Berlin Wall, bioinformatics, bitcoin, Bonfire of the Vanities, clean water, collective bargaining, Colonization of Mars, Credit Default Swap, crowdsourcing, cryptocurrency, Dava Sobel, demographic dividend, Deng Xiaoping, Doha Development Round, double helix, Edward Snowden, Elon Musk, en.wikipedia.org, epigenetics, experimental economics, failed state, Fall of the Berlin Wall, financial innovation, full employment, Galaxy Zoo, global pandemic, global supply chain, Hyperloop, immigration reform, income inequality, indoor plumbing, industrial cluster, industrial robot, information retrieval, Intergovernmental Panel on Climate Change (IPCC), intermodal, Internet of things, invention of the printing press, Isaac Newton, Islamic Golden Age, Johannes Kepler, Khan Academy, Kickstarter, low cost airline, low cost carrier, low skilled workers, Lyft, Malacca Straits, mass immigration, megacity, Mikhail Gorbachev, moral hazard, Nelson Mandela, Network effects, New Urbanism, non-tariff barriers, Occupy movement, On the Revolutions of the Heavenly Spheres, open economy, Panamax, Pearl River Delta, personalized medicine, Peter Thiel, post-Panamax, profit motive, rent-seeking, reshoring, Robert Gordon, Robert Metcalfe, Search for Extraterrestrial Intelligence, Second Machine Age, self-driving car, Shenzhen was a fishing village, Silicon Valley, Silicon Valley startup, Skype, smart grid, Snapchat, special economic zone, spice trade, statistical model, Stephen Hawking, Steve Jobs, Stuxnet, The Future of Employment, too big to fail, trade liberalization, trade route, transaction costs, transatlantic slave trade, uber lyft, undersea cable, uranium enrichment, We are the 99%, We wanted flying cars, instead we got 140 characters, working poor, working-age population, zero day

Copernicus’s heliocentric theory had its own flaws—the sun is no more the center of the universe than the Earth is—but it took astronomy past Ptolemy and raised many new avenues of productive inquiry. How might we prove that the planets orbit the sun and not the Earth? In 1610, this question prompted Galileo Galilei (1564–1642) to point a recent Dutch invention (the telescope) skywards and gather fresh evidence from the phases of Venus and the moons of Jupiter. How best to describe a planet’s orbit? As an ellipse, Johannes Kepler (1571–1630) discovered. He derived three laws of planetary motion that made new almanacs accurate to within two-tenths of a degree.* And why, if the Earth really were spinning through space, could no one feel it? Inertia, answered Sir Isaac Newton (1642–1727)—and the answer became the first of his Three Laws of Motion. The impact of Copernicus’s work extended far beyond the time horizon of the Renaissance and far beyond astronomy.


Time of the Magicians: Wittgenstein, Benjamin, Cassirer, Heidegger, and the Decade That Reinvented Philosophy by Wolfram Eilenberger

Albert Einstein, Charles Lindbergh, Johann Wolfgang von Goethe, Johannes Kepler, liberation theology, precariat, scientific worldview, side project, traveling salesman, wikimedia commons

The pinnacle was the large ellipse of its reading room, where Cassirer now stepped onto the podium to deliver a lecture about “freedom and necessity in the philosophy of the Renaissance.” In the face of the reservations of his engineers, Warburg, in whose intellectual world every geometric shape had a specific symbolic, indeed philosophical, significance, had insisted that the largest, most important room in the building be elliptical. Cassirer was not entirely innocent. In particular their discussion in Kreuzlingen about the significance of the ellipse in Johannes Kepler’s astronomical calculations had restored Warburg’s intellectual resilience as a researcher. For Warburg, Kepler’s discovery that the orbit of Mars was elliptical—and not circular—represented the actual breakthrough from mythical, medieval thinking into the freedom of modern, scientific thought. The ellipse, as a circular form with two focal points, did not appear among the ideal geometric bodies set out by Plato in his dialogue Timaeus, which were fixtures in the geometric study of nature well into Kepler’s time.


pages: 389 words: 112,319

Think Like a Rocket Scientist by Ozan Varol

Affordable Care Act / Obamacare, Airbnb, airport security, Albert Einstein, Amazon Web Services, Andrew Wiles, Apple's 1984 Super Bowl advert, Arthur Eddington, autonomous vehicles, Ben Horowitz, Cal Newport, Clayton Christensen, cloud computing, Colonization of Mars, dark matter, delayed gratification, different worldview, discovery of DNA, double helix, Elon Musk, fear of failure, functional fixedness, Gary Taubes, George Santayana, Google Glasses, Google X / Alphabet X, Inbox Zero, index fund, Isaac Newton, James Dyson, Jeff Bezos, job satisfaction, Johannes Kepler, Kickstarter, knowledge worker, late fees, lateral thinking, lone genius, longitudinal study, Louis Pasteur, low earth orbit, Marc Andreessen, Mars Rover, meta analysis, meta-analysis, move fast and break things, move fast and break things, multiplanetary species, obamacare, Occam's razor, out of africa, Peter Thiel, Pluto: dwarf planet, Ralph Waldo Emerson, Richard Feynman, Richard Feynman: Challenger O-ring, Ronald Reagan, Sam Altman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, self-driving car, Silicon Valley, Simon Singh, Steve Ballmer, Steve Jobs, Steven Levy, Stewart Brand, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Upton Sinclair, Vilfredo Pareto, We wanted flying cars, instead we got 140 characters, Whole Earth Catalog, women in the workforce, Yogi Berra

The theory is the brainchild of Alfred Wegener—a meteorologist and an outsider to geology.83 Continental drift was initially declared absurd by geological experts who assumed that continents were stable and didn’t move. Geologist R. Thomas Chamberlain summed up the collective sentiments of the insiders: “If we are to believe in Wegener’s hypothesis we must forget everything which has been learned in the past 70 years and start all over again.”84 Wegener’s theory would upend the foundations of the insiders’ reputation in the field, so they stuck to their guns. For similar reasons, when Johannes Kepler discovered that planets had elliptical—rather than circular—orbits, Galileo balked. As astrophysicist Mario Livio observes, “Galileo was still prisoner to the aesthetic ideals of antiquity, which assumed that the orbits had to be perfectly symmetrical.”85 Einstein’s secret to success was escaping the intellectual prison that confined other physicists. When he published his paper on special relativity, he was an unknown clerk in a Swiss patent office.


Germany Travel Guide by Lonely Planet

Airbnb, Albert Einstein, bank run, Berlin Wall, bike sharing scheme, British Empire, call centre, car-free, carbon footprint, centre right, double helix, eurozone crisis, Fall of the Berlin Wall, Frank Gehry, glass ceiling, haute couture, haute cuisine, Honoré de Balzac, Johann Wolfgang von Goethe, Johannes Kepler, Kickstarter, low cost airline, low cost carrier, Mikhail Gorbachev, New Urbanism, oil shale / tar sands, Peace of Westphalia, Peter Eisenman, post-work, ride hailing / ride sharing, Ronald Reagan, Ronald Reagan: Tear down this wall, sensible shoes, Skype, starchitect, trade route, upwardly mobile, urban planning, urban renewal, V2 rocket, white picket fence

The subterranean Document Neupfarrplatz only provides access to a small portion of the excavated area, but tours feature a nifty multimedia presentation (in German) about the square’s history. Back up above, on the square itself, a work by renowned Israeli artist Dani Karavan graces the site of the former synagogue. Tickets are purchased from Tabak Götz at Neupfarrplatz 3. Kepler-Gedächtnishaus MUSEUM Offline map Google map (Kepler Memorial House; Keplerstrasse 5; adult/concession €2.20/1.10; 10.30am-4pm Sat & Sun) Disciples of astronomer and mathematician Johannes Kepler should visit the house he lived in while resident in Regensburg. Alte Kapelle CHURCH Offline map Google map (Alter Kornmarkt 8) South of the Dom, the humble exterior of the graceful Alte Kapelle belies the stunning interior with its rich rococo decorations. The core of the church, however, is about 1000 years old, although the Gothic vaulted ceilings were added in the Middle Ages. The church is open only during services but you can always peek through the wrought-iron grill.

MAULBRONN Billed as the best-preserved medieval monastery north of the Alps, the one-time Cistercian monastery Kloster Maulbronn (07043-926 610; www.schloesser-und-gaerten.de; adult/concession/family €6/3/15; 9am-5.30pm Mar-Oct, 9.30am-5pm Tue-Sun Nov-Feb) was founded by Alsatian monks in 1147, born again as a Protestant school in 1556 and designated a Unesco World Heritage Site in 1993. Its famous graduates include the astronomer Johannes Kepler. Aside from the Romanesque-Gothic portico in the monastery church and the weblike vaulting of the cloister, it’s the insights into monastic life that make this place so culturally stimulating. Maulbronn is 30km east of Karlsruhe and 33km northwest of Stuttgart, near the Pforzheim Ost exit on the A8. From Karlsruhe, take the S4 to Bretten Bahnhof and from there bus 700; from Stuttgart, take the train to Mühlacker and then bus 700.

SWABIAN ALPS & AROUND Tübingen 07071 / POP 88,360 Liberal students and deeply traditional Burschenschaften (fraternities) singing ditties for beloved Germania, eco-warriors, artists and punks – all have a soft spot for this bewitchingly pretty Swabian city, where cobbled lanes lined with half-timbered town houses twist up to a turreted castle. It was here that Joseph Ratzinger, now Pope Benedict XVI, lectured theology in the late 1960s; and here that Friedrich Hölderlin studied stanzas; Johannes Kepler planetary motions; and Goethe, the bottom of a beer glass. The finest days unfold slowly in Tübingen: lingering in Altstadt cafes, punting on the plane-tree-lined Neckar River and pretending, as the students so diligently do, to work your brain cells in a chestnut-shaded beer garden. Sights & Activities Schloss Hohentübingen CASTLE (Burgsteige 11; museum adult/concession €5/3; castle 7am-8pm daily, museum 10am-5pm Wed-Sun, to 7pm Thu) On its perch above Tübingen, this turreted 16th-century castle has a terrace overlooking the Neckar and the Altstadt’s triangular rooftops to the vine-streaked hills beyond.


pages: 423 words: 126,096

Our Own Devices: How Technology Remakes Humanity by Edward Tenner

A. Roger Ekirch, Bonfire of the Vanities, card file, Douglas Engelbart, Douglas Engelbart, Frederick Winslow Taylor, future of work, indoor plumbing, informal economy, invention of the telephone, invisible hand, Johannes Kepler, John Markoff, Joseph-Marie Jacquard, Network effects, optical character recognition, QWERTY keyboard, Shoshana Zuboff, Stewart Brand, women in the workforce

For the first time, investigators were beginning to understand the physics of vision and the effects of lenses. The most common explanation in antiquity and the Middle Ages had been that the eye sent out rays. Three stunning accomplishments of the early seventeenth century changed this model. Galileo’s construction of the telescope and his observation of the earthlike contours of the moon suggested that lenses could multiply the powers of human vision to a previously unimagined degree. Johannes Kepler (1571–1630), in his work Dioptrice (1611), showed that images are formed by rays of light on the retina passing through the eye’s lens, and René Descartes (1596–1650) presented the law of refraction in his own Dioptrique (1637). These discoveries (and the development of the microscope) meant that the grinding of lenses, once exclusively a craft, was on its way to being a science. Glasses lost their former stigma as suspect devices that distorted as they clarified.


pages: 561 words: 120,899

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy by Sharon Bertsch McGrayne

Bayesian statistics, bioinformatics, British Empire, Claude Shannon: information theory, Daniel Kahneman / Amos Tversky, double helix, Edmond Halley, Fellow of the Royal Society, full text search, Henri Poincaré, Isaac Newton, Johannes Kepler, John Markoff, John Nash: game theory, John von Neumann, linear programming, longitudinal study, meta analysis, meta-analysis, Nate Silver, p-value, Pierre-Simon Laplace, placebo effect, prediction markets, RAND corporation, recommendation engine, Renaissance Technologies, Richard Feynman, Richard Feynman: Challenger O-ring, Robert Mercer, Ronald Reagan, speech recognition, statistical model, stochastic process, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, Turing machine, Turing test, uranium enrichment, Yom Kippur War

And for that to happen, he needed to make a spectacular impact. D’Alembert, who had made Newton’s revolution the focus of French mathematics, urged Laplace to concentrate on astronomy. D’Alembert had a clear problem in mind. Over the previous two centuries mathematical astronomy had made great strides. Nicolaus Copernicus had moved Earth from the center of the solar system to a modest but accurate position among the planets; Johannes Kepler had connected the celestial bodies by simple laws; and Newton had introduced the concept of gravity. But Newton had described the motions of heavenly bodies roughly and without explanation. His death in 1727 left Laplace’s generation an enormous challenge: showing that gravitation was not a hypothesis but a fundamental law of nature. Astronomy was the era’s most quantified and respected science, and only it could test Newton’s theories by explaining precisely how gravitation affects the movements of tides, interacting planets and comets, our moon, and the shape of Earth and other planets.


pages: 481 words: 125,946

What to Think About Machines That Think: Today's Leading Thinkers on the Age of Machine Intelligence by John Brockman

agricultural Revolution, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic trading, artificial general intelligence, augmented reality, autonomous vehicles, basic income, bitcoin, blockchain, clean water, cognitive dissonance, Colonization of Mars, complexity theory, computer age, computer vision, constrained optimization, corporate personhood, cosmological principle, cryptocurrency, cuban missile crisis, Danny Hillis, dark matter, discrete time, Douglas Engelbart, Elon Musk, Emanuel Derman, endowment effect, epigenetics, Ernest Rutherford, experimental economics, Flash crash, friendly AI, functional fixedness, global pandemic, Google Glasses, hive mind, income inequality, information trail, Internet of things, invention of writing, iterative process, Jaron Lanier, job automation, Johannes Kepler, John Markoff, John von Neumann, Kevin Kelly, knowledge worker, loose coupling, microbiome, Moneyball by Michael Lewis explains big data, natural language processing, Network effects, Norbert Wiener, pattern recognition, Peter Singer: altruism, phenotype, planetary scale, Ray Kurzweil, recommendation engine, Republic of Letters, RFID, Richard Thaler, Rory Sutherland, Satyajit Das, Search for Extraterrestrial Intelligence, self-driving car, sharing economy, Silicon Valley, Skype, smart contracts, social intelligence, speech recognition, statistical model, stem cell, Stephen Hawking, Steve Jobs, Steven Pinker, Stewart Brand, strong AI, Stuxnet, superintelligent machines, supervolcano, the scientific method, The Wisdom of Crowds, theory of mind, Thorstein Veblen, too big to fail, Turing machine, Turing test, Von Neumann architecture, Watson beat the top human players on Jeopardy!, Y2K

More profoundly, you can generalize from this kind of statistical learning only in a limited way, whether you’re a baby or a computer or a scientist. A more powerful way to learn is to formulate hypotheses about what the world is like and test them against the data. Tycho Brahe, the Google Scholar of his day, amalgamated an immense data set of astronomical observations and could use them to predict star positions in the future. But Johannes Kepler’s theory allowed him to make unexpected, wide-ranging, entirely novel predictions well beyond Brahe’s ken. Preschoolers can do the same. One of the other big advances in machine learning has been to formalize and automate this kind of hypothesis testing. Introducing Bayesian probability theory into the learning process has been particularly important. We can mathematically describe a particular causal hypothesis—for example, about how temperature changes in the ocean will influence hurricanes—and then calculate just how likely that hypothesis is to be true, given the data we see.


pages: 571 words: 124,448

Building Habitats on the Moon: Engineering Approaches to Lunar Settlements by Haym Benaroya

3D printing, biofilm, Black Swan, Brownian motion, Buckminster Fuller, carbon-based life, centre right, clean water, Colonization of Mars, Computer Numeric Control, conceptual framework, data acquisition, Elon Musk, fault tolerance, gravity well, inventory management, Johannes Kepler, low earth orbit, orbital mechanics / astrodynamics, performance metric, RAND corporation, risk tolerance, Ronald Reagan, stochastic process, telepresence, telerobotics, the scientific method, urban planning, X Prize, zero-sum game

“Here Men From The Planet Earth First Set Foot Upon the Moon, July 1969 A.D. We Came in Peace For All Mankind.” The inscription on a plaque left behind. “As soon as somebody demonstrates the art of flying, settlers from our species of man will not be lacking [on the Moon and Jupiter]. ... Given ships or sails adapted to the breezes of heaven, there will be those who will not shrink from even that vast expanse.” Johannes Kepler, letter to Galileo, 1610. “I think there’s a supreme power behind the whole thing, an intelligence. Look at all of the instincts of nature, both animals and plants, the very ingenious ways they survive. If you cut yourself, you don’t have to think about it.” Clyde Tombaugh. “Space flights are merely an escape, a fleeing away from oneself, because it is easier to go to Mars or to the Moon than it is to penetrate one’s own being.”


pages: 677 words: 121,255

Giving the Devil His Due: Reflections of a Scientific Humanist by Michael Shermer

Alfred Russel Wallace, anthropic principle, anti-communist, barriers to entry, Berlin Wall, Boycotts of Israel, Chelsea Manning, clean water, clockwork universe, cognitive dissonance, Colonization of Mars, Columbine, cosmological constant, cosmological principle, creative destruction, dark matter, Donald Trump, Edward Snowden, Elon Musk, Flynn Effect, germ theory of disease, gun show loophole, Hans Rosling, hedonic treadmill, helicopter parent, hindsight bias, illegal immigration, income inequality, invisible hand, Johannes Kepler, Joseph Schumpeter, laissez-faire capitalism, Laplace demon, luminiferous ether, McMansion, means of production, mega-rich, Menlo Park, moral hazard, moral panic, More Guns, Less Crime, Peter Singer: altruism, phenotype, positional goods, race to the bottom, Richard Feynman, Ronald Coase, Silicon Valley, Skype, social intelligence, stem cell, Stephen Hawking, Steve Jobs, Steven Pinker, the scientific method, The Wealth of Nations by Adam Smith, transaction costs, WikiLeaks, working poor, Yogi Berra

Since Professor Ellis is a physicist, let me approach this defense of moral realism from the perspective of a physical scientist. It is my hypothesis that, in the same way that Galileo and Newton discovered physical laws and principles about the natural world that really are out there, so too have social scientists discovered moral laws and principles about human nature and society that really do exist. Just as it was inevitable that the astronomer Johannes Kepler would discover that planets have elliptical orbits – given that he was making accurate astronomical measurements and given that planets really do travel in elliptical orbits, he could hardly have discovered anything else – scientists studying political, economic, social, and moral subjects will discover certain things that are true in these fields of inquiry. For example, that democracies are better than autocracies, that market economies are superior to command economies, that torture and the death penalty do not curb crime, that burning women as witches is a fallacious idea, that women are not too weak and emotional to run companies or countries, and, most poignantly here, that blacks do not like being enslaved and that the Jews do not want to be exterminated.


pages: 1,773 words: 486,685

Global Crisis: War, Climate Change and Catastrophe in the Seventeenth Century by Geoffrey Parker

agricultural Revolution, British Empire, Climatic Research Unit, colonial rule, creative destruction, currency manipulation / currency intervention, Defenestration of Prague, Edmond Halley, en.wikipedia.org, European colonialism, failed state, Fellow of the Royal Society, financial independence, friendly fire, Google Earth, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Johannes Kepler, Joseph Schumpeter, Khyber Pass, mass immigration, Mercator projection, moral hazard, mortgage debt, Peace of Westphalia, Peter Thiel, Republic of Letters, sexual politics, South China Sea, the market place, trade route, transatlantic slave trade, unemployed young men, University of East Anglia, World Values Survey, zero-sum game

Contemporaries saw each eruption as a harbinger of disaster.29 The mid-seventeenth century witnessed not only a peak of seismic activity but also a rare ‘fireball flux’. The English astronomer John Bainbridge was apparently the first to comment, in 1619, on the ‘many new stars and comets, which have been more [numerous] this last century of the world than in many ages before’. He wrote just after the appearance of three comets in 1618, which excited widespread anxiety. Even before they appeared, Johannes Kepler, the foremost mathematician of his day, warned in his Astrological Almanac for 1618 that the conjunction of five planets in May would cause extreme climatic events; and if a comet appeared as well everyone should ‘sharpen their pens’, because it would presage a major political upheaval. Over the winter of 1618–19, a multitude of books and pamphlets in Europe reminded readers that comets ‘signify wars’ and brought in their wake ‘discord, irritations, deaths, upheavals, robberies, rape, tyranny and the change of kingdoms’, and they predicted dire consequences for humanity following the three ‘blazing stars’ of 1618.30 Some observers were more precise: a Spanish friar argued that the comets would prove especially dangerous for the Habsburg dynasty ‘because they have touched us to the quick with the deaths of the empress, the Archduke Maximilian, and most recently the emperor [Matthias] … May God preserve those members of the House of Austria who are left!

Thomas Hobbes left England for Paris in 1641, just before the Civil War, and did not return until it became clear that Parliament had won (and he had provided, in his Leviathan, a rationale for its rule that secured him a state pension); three years later, the marquis of Newcastle joined him, following the annihilation of his army at Marston Moor; and many other English royalists followed. Most of them remained in Europe until the Restoration in 1660 – when several of the leading British Republicans took their place. ‘Bloodthirsty Mars’ forced far more men and women to flee from central Europe. Some were intellectuals at the height of their powers (like the musician Heinrich Schütz, the poet Martin Opitz, the mathematician and astronomer Johannes Kepler); others were country folk who could not protect their families, like the village shoemaker Hans Heberle, who had to flee with his family to Ulm 30 times during the Thirty Years War. Some went into exile alone, like Hugo Grotius after the execution of Oldenbarnevelt; others moved as a group, like the thousands of ‘Masanielli’, the unsuccessful Neapolitan rebels against Philip IV, who in 1648 took refuge in Rome, and the malvizzi from Messina 30 years later, hundreds of whom left for France on the fleet that evacuated the city's garrison.17 Escape was even more common in eastern Europe, where peasants could flee misery at home by joining the Cossacks or the Tartars to the south, or (in the case of Russian peasants) by crossing the Urals into Siberia.

., Oeuvres de Jean-Jacques Bouchard: Journal, 2 vols (Turin, 1976–7) Kâtib Çelebi, Fezleke-i Tarih, 2 vols (Istanbul, 1870) Kâtib Çelebi, The balance of truth (1656: ed. and tr. G. L. Lewis, London, 1957) Kenyon, J. P., ed., The Stuart Constitution, 1603–1688: Documents and commentary (Cambridge, 1966) Kepler, Johannes, Prognosticum astrologicum auff das Jahr … 1618 (Linz, 1618), reprinted in V. Bialas and H. Grüssing, eds, Johannes Kepler Gesammelte Werke, XI part 2 (Munich, 1993) Kingsbury, S. M., The records of the Virginia Company of London, 4 vols (Washington, DC, 1906–35) Knowler, W., ed., The earl of Strafforde's letters and dispatches, 2 vols (London, 1739) Kodama Kōta and Ōishi Shinzaburo, Kinsei nōsei shiryōshû. I. Edo bakufu horei (Tokyo, 1966) Kolff, D. H. A., and H. W. van Santen, eds, De geschriften van Francisco Pelsaert over Mughal Indië, 1627.


pages: 461 words: 139,924

The Habsburgs by Martyn Rady

Isaac Newton, Johannes Kepler, night-watchman state, Peace of Westphalia, Potemkin village, spice trade, the market place, trade route, transatlantic slave trade, éminence grise

Among these we may count the drunken medium Edward Kelley, who by the time he arrived in Prague had already had his ears cropped for the crime of counterfeiting. At the other end were genuine practitioners whose rigour in observation and experimental method provided the foundation of modern science. These included Tycho Brahe, who during his short stay in Prague (1599–1601) built an observatory to plot the movement of the stars, and Johannes Kepler, who worked as Rudolf’s principal astrologer between 1600 and 1612. Kepler’s observations yielded the earliest insights into how the planets moved within the sun’s gravitational field, and with his improved telescope he detected that Jupiter also had its own moons. Others added their own arcane knowledge to the mysteries of Hermetic magic. The English wizard John Dee, who had previously dedicated his treatise on the celestial symbol of the monad to Maximilian II, sought Rudolf’s favour in the 1580s, but Rudolf confessed that he did not understand Dee’s work.


How to Make a Spaceship: A Band of Renegades, an Epic Race, and the Birth of Private Spaceflight by Julian Guthrie

Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, Ayatollah Khomeini, Berlin Wall, Charles Lindbergh, cosmic microwave background, crowdsourcing, Doomsday Book, Elon Musk, fear of failure, Frank Gehry, gravity well, high net worth, Iridium satellite, Isaac Newton, Jacquard loom, Jeff Bezos, Johannes Kepler, Leonard Kleinrock, life extension, low earth orbit, Mark Shuttleworth, Menlo Park, meta analysis, meta-analysis, Murray Gell-Mann, Oculus Rift, orbital mechanics / astrodynamics, packet switching, Peter H. Diamandis: Planetary Resources, pets.com, private space industry, Richard Feynman, Richard Feynman: Challenger O-ring, Ronald Reagan, side project, Silicon Valley, South of Market, San Francisco, stealth mode startup, stem cell, Stephen Hawking, Steve Jobs, urban planning

Sitting in the Deli Haus diner, Peter poked at his cheesecake. It was after two A.M., and he and John were still talking about faith and truth seeking. John pointed out that many great scientists and engineers, including Einstein and Nikola Tesla, recognized “different kinds of truth and shifting levels of consciousness.” Famous founders of science held Christian beliefs, including Blaise Pascal (who was a Jansenist), Galileo, and Johannes Kepler. It was Einstein, John noted, who said, “Whether you can observe a thing or not depends on the theory which you use. It is the theory which decides what can be observed.” And Tesla, John continued, wrote about the relationship between matter and energy, saying: “If you want to find the secrets of the universe, think in terms of energy, frequency and vibration. What one man calls God, another calls the laws of physics.”


pages: 609 words: 159,043

Come Fly With Us: NASA's Payload Specialist Program by Melvin Croft, John Youskauskas, Don Thomas

active measures, active transport: walking or cycling, Berlin Wall, Elon Musk, gravity well, Johannes Kepler, Kickstarter, low earth orbit, orbital mechanics / astrodynamics, Ronald Reagan, X Prize, Yom Kippur War

The incredible detailed editing and challenges by Jeremy Hall improved the manuscript tremendously. Lastly, while many of the stories told here are based on the recollections of those involved, any factual errors are ours alone. Introduction Ships and sails proper for the heavenly air should be fashioned. Then there will also be people, who do not shrink from the dreary vastness of space. Johannes Kepler At the conclusion of space shuttle Columbia’s fourth mission in July of 1982, NASA’s orbital flight test program was deemed complete and the Space Transportation System was declared operational. The crew of STS-4, commander Thomas “Ken” Mattingly and pilot Henry “Hank” Hartsfield, undertook a worldwide tour to celebrate the important milestone and to begin the outright promotion of the shuttle as a commercial, profit-making vehicle for the rapidly expanding world launch market of military, communication, weather, and Earth-monitoring satellites.


What We Cannot Know: Explorations at the Edge of Knowledge by Marcus Du Sautoy

Albert Michelson, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, banking crisis, bet made by Stephen Hawking and Kip Thorne, Black Swan, Brownian motion, clockwork universe, cosmic microwave background, cosmological constant, dark matter, Dmitri Mendeleev, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Georg Cantor, Hans Lippershey, Harvard Computers: women astronomers, Henri Poincaré, invention of the telescope, Isaac Newton, Johannes Kepler, Magellanic Cloud, mandelbrot fractal, MITM: man-in-the-middle, Murray Gell-Mann, music of the spheres, Necker cube, Paul Erdős, Pierre-Simon Laplace, Richard Feynman, Skype, Slavoj Žižek, Solar eclipse in 1919, stem cell, Stephen Hawking, technological singularity, Thales of Miletus, Turing test, wikimedia commons

And it did indeed allow Galileo and subsequent generations of astronomers to see further than ever before. Galileo discovered moons orbiting Jupiter and sunspots that rotated, implying that the Sun was spinning on its axis – phenomena that helped to confirm Copernicus’s model of a Sun-centred solar system. In 1663 the Scottish mathematician James Gregory realized that the telescope could also be used to make new calculations of just how far away the Sun was from the Earth. Johannes Kepler had already observed the time it takes each planet to orbit the Sun and deduced, using his laws of planetary motion, the relative distance of each planet from the Sun. His third law states that the square of the time a planet takes to complete one orbit of the Sun is proportional to the cube of the distance from the Sun. For example, Venus completes an orbit in ⅗ of the time it takes the Earth to go round the Sun, which means that Venus’s distance from the Sun is about 7⁄10 (approximately (3⁄5)⅔) of the distance of the Earth to the Sun.


pages: 855 words: 178,507

The Information: A History, a Theory, a Flood by James Gleick

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, AltaVista, bank run, bioinformatics, Brownian motion, butterfly effect, citation needed, Claude Shannon: information theory, clockwork universe, computer age, conceptual framework, crowdsourcing, death of newspapers, discovery of DNA, Donald Knuth, double helix, Douglas Hofstadter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Gödel, Escher, Bach, Henri Poincaré, Honoré de Balzac, index card, informal economy, information retrieval, invention of the printing press, invention of writing, Isaac Newton, Jacquard loom, Jaron Lanier, jimmy wales, Johannes Kepler, John von Neumann, Joseph-Marie Jacquard, lifelogging, Louis Daguerre, Marshall McLuhan, Menlo Park, microbiome, Milgram experiment, Network effects, New Journalism, Norbert Wiener, Norman Macrae, On the Economy of Machinery and Manufactures, PageRank, pattern recognition, phenotype, Pierre-Simon Laplace, pre–internet, Ralph Waldo Emerson, RAND corporation, reversible computing, Richard Feynman, Rubik’s Cube, Simon Singh, Socratic dialogue, Stephen Hawking, Steven Pinker, stochastic process, talking drums, the High Line, The Wisdom of Crowds, transcontinental railway, Turing machine, Turing test, women in the workforce

The new technology was a watershed: “It may be here also noted that the use of a 100 pound for a day at the rate of 8, 9, 10, or the like for a yeare hath beene scarcely known, till by Logarithms it was found out: for otherwise it requires so many laborious extractions of roots, as will cost more paines than the knowledge of the thing is accompted to be worth.”♦ Knowledge has a value and a discovery cost, each to be counted and weighed. Even this exciting discovery took several years to travel as far as Johannes Kepler, who employed it in perfecting his celestial tables in 1627, based on the laboriously acquired data of Tycho Brahe. “A Scottish baron has appeared on the scene (his name I have forgotten) who has done an excellent thing,” Kepler wrote a friend, “transforming all multiplication and division into addition and subtraction.”♦ Kepler’s tables were far more accurate—perhaps thirty times more—than any of his medieval predecessors, and the accuracy made possible an entirely new thing, his harmonious heliocentric system, with planets orbiting the sun in ellipses.


pages: 551 words: 174,280

The Beginning of Infinity: Explanations That Transform the World by David Deutsch

agricultural Revolution, Albert Michelson, anthropic principle, artificial general intelligence, Bonfire of the Vanities, conceptual framework, cosmological principle, dark matter, David Attenborough, discovery of DNA, Douglas Hofstadter, Eratosthenes, Ernest Rutherford, first-past-the-post, Georg Cantor, global pandemic, Gödel, Escher, Bach, illegal immigration, invention of movable type, Isaac Newton, Islamic Golden Age, Jacquard loom, Johannes Kepler, John Conway, John von Neumann, Joseph-Marie Jacquard, Kenneth Arrow, Loebner Prize, Louis Pasteur, pattern recognition, Pierre-Simon Laplace, Richard Feynman, Search for Extraterrestrial Intelligence, Stephen Hawking, supervolcano, technological singularity, Thales of Miletus, The Coming Technological Singularity, the scientific method, Thomas Malthus, Thorstein Veblen, Turing test, Vernor Vinge, Whole Earth Review, William of Occam, zero-sum game

Successive scientific explanations are occasionally dissimilar in the way they explain their predictions, even in the domain where the predictions themselves are similar or identical. For instance, Einstein’s explanation of planetary motion does not merely correct Newton’s: it is radically different, denying, among many other things, the very existence of central elements of Newton’s explanation, such as the gravitational force and the uniformly flowing time with respect to which Newton defined motion. Likewise the astronomer Johannes Kepler’s theory which said that the planets move in ellipses did not merely correct the celestial-sphere theory, it denied the spheres’ existence. And Newton’s did not substitute a new shape for Kepler’s ellipses, but a whole new way for laws to specify motion – through infinitesimally defined quantities like instantaneous velocity and acceleration. Thus each of those theories of planetary motion was ignoring or denying its predecessor’s basic means of explaining what was happening out there.


pages: 634 words: 185,116

From eternity to here: the quest for the ultimate theory of time by Sean M. Carroll

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, Brownian motion, cellular automata, Claude Shannon: information theory, Columbine, cosmic microwave background, cosmological constant, cosmological principle, dark matter, dematerialisation, double helix, en.wikipedia.org, gravity well, Harlow Shapley and Heber Curtis, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, Lao Tzu, Laplace demon, lone genius, low earth orbit, New Journalism, Norbert Wiener, pets.com, Pierre-Simon Laplace, Richard Feynman, Richard Stallman, Schrödinger's Cat, Slavoj Žižek, Stephen Hawking, stochastic process, the scientific method, wikimedia commons

But it won’t be because modern cosmologists had abandoned the true path of science; it will (if that’s how things turn out) simply be because the theory wasn’t correct. Two points deserve to be emphasized concerning the role of unobservable things in science. First, it’s wrong to think of the goal of science as simply to fit the data. The goal of science goes much deeper than that: It’s to understand the behavior of the natural world.299 In the early seventeenth century, Johannes Kepler proposed his three laws of planetary motion, which correctly accounted for the voluminous astronomical data that had been collected by his mentor, Tycho Brahe. But we didn’t really understand the dynamics of planets within the Solar System until Isaac Newton showed that they could all be explained in terms of a simple i nverse-square law for gravity. Similarly, we don’t need to look beyond the Big Bang to understand the evolution of our observable universe; all we have to do is specify what conditions were like at early times, and leave it at that.


pages: 893 words: 199,542

Structure and interpretation of computer programs by Harold Abelson, Gerald Jay Sussman, Julie Sussman

Andrew Wiles, conceptual framework, Donald Knuth, Douglas Hofstadter, Eratosthenes, Fermat's Last Theorem, Gödel, Escher, Bach, industrial robot, information retrieval, iterative process, Johannes Kepler, loose coupling, probability theory / Blaise Pascal / Pierre de Fermat, Richard Stallman, Turing machine

Chapter 5 Computing with Register Machines My aim is to show that the heavenly machine is not a kind of divine, live being, but a kind of clockwork (and he who believes that a clock has soul attributes the maker's glory to the work), insofar as nearly all the manifold motions are caused by a most simple and material force, just as all motions of the clock are caused by a single weight. Johannes Kepler (letter to Herwart von Hohenburg, 1605) We began this book by studying processes and by describing processes in terms of procedures written in Lisp. To explain the meanings of these procedures, we used a succession of models of evaluation: the substitution model of chapter 1, the environment model of chapter 3, and the metacircular evaluator of chapter 4. Our examination of the metacircular evaluator, in particular, dispelled much of the mystery of how Lisp-like languages are interpreted.


pages: 1,387 words: 202,295

Structure and Interpretation of Computer Programs, Second Edition by Harold Abelson, Gerald Jay Sussman, Julie Sussman

Andrew Wiles, conceptual framework, Donald Knuth, Douglas Hofstadter, Eratosthenes, Gödel, Escher, Bach, industrial robot, information retrieval, iterative process, Johannes Kepler, loose coupling, probability theory / Blaise Pascal / Pierre de Fermat, Richard Stallman, Turing machine, wikimedia commons

Next: Chapter 5, Prev: 4.3, Up: 4.4.4 [Contents] Next: 5.1, Prev: 4.4, Up: Top [Contents] 5Computing with Register Machines My aim is to show that the heavenly machine is not a kind of divine, live being, but a kind of clockwork (and he who believes that a clock has soul attributes the maker’s glory to the work), insofar as nearly all the manifold motions are caused by a most simple and material force, just as all motions of the clock are caused by a single weight. —Johannes Kepler (letter to Herwart von Hohenburg, 1605) We began this book by studying processes and by describing processes in terms of procedures written in Lisp. To explain the meanings of these procedures, we used a succession of models of evaluation: the substitution model of Chapter 1, the environment model of Chapter 3, and the metacircular evaluator of Chapter 4. Our examination of the metacircular evaluator, in particular, dispelled much of the mystery of how Lisp-like languages are interpreted.


pages: 915 words: 232,883

Steve Jobs by Walter Isaacson

air freight, Albert Einstein, Apple II, Apple's 1984 Super Bowl advert, big-box store, Bob Noyce, Buckminster Fuller, Byte Shop, centre right, Clayton Christensen, cloud computing, commoditize, computer age, computer vision, corporate governance, death of newspapers, don't be evil, Douglas Engelbart, Dynabook, El Camino Real, Electric Kool-Aid Acid Test, fixed income, game design, Golden Gate Park, Hacker Ethic, hiring and firing, Jeff Bezos, Johannes Kepler, John Markoff, Jony Ive, lateral thinking, Mark Zuckerberg, Menlo Park, Mitch Kapor, Mother of all demos, Paul Terrell, profit maximization, publish or perish, Richard Feynman, Robert Metcalfe, Robert X Cringely, Ronald Reagan, Silicon Valley, skunkworks, Steve Ballmer, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, supply-chain management, thinkpad, Tim Cook: Apple, Wall-E, Whole Earth Catalog

His quest for perfection led to his compulsion for Apple to have end-to-end control of every product that it made. He got hives, or worse, when contemplating great Apple software running on another company’s crappy hardware, and he likewise was allergic to the thought of unapproved apps or content polluting the perfection of an Apple device. This ability to integrate hardware and software and content into one unified system enabled him to impose simplicity. The astronomer Johannes Kepler declared that “nature loves simplicity and unity.” So did Steve Jobs. This instinct for integrated systems put him squarely on one side of the most fundamental divide in the digital world: open versus closed. The hacker ethos handed down from the Homebrew Computer Club favored the open approach, in which there was little centralized control and people were free to modify hardware and software, share code, write to open standards, shun proprietary systems, and have content and apps that were compatible with a variety of devices and operating systems.


pages: 1,014 words: 237,531

Escape From Rome: The Failure of Empire and the Road to Prosperity by Walter Scheidel

agricultural Revolution, barriers to entry, British Empire, colonial rule, conceptual framework, creative destruction, currency manipulation / currency intervention, dark matter, disruptive innovation, Eratosthenes, European colonialism, financial innovation, financial intermediation, Intergovernmental Panel on Climate Change (IPCC), invisible hand, Isaac Newton, Johann Wolfgang von Goethe, Johannes Kepler, joint-stock company, Joseph Schumpeter, knowledge economy, mandelbrot fractal, means of production, Network effects, out of africa, Peace of Westphalia, peer-to-peer lending, plutocrats, Plutocrats, principal–agent problem, purchasing power parity, rent-seeking, Republic of Letters, secular stagnation, South China Sea, spinning jenny, The Rise and Fall of American Growth, The Wealth of Nations by Adam Smith, trade route, transaction costs, zero-sum game

Their Turkic overlords demonstrated commitment to their religious obligations, not just in waging war against infidels but also in curbing contact with Christian Europe: travel to and trade with Europe as well as engagement with European scholarship generally met with disapproval. Except for Jews and Christians, printing was banned until the early eighteenth century. Just as in imperial China, the potential for random intervention was significant. In 1580 the religious leadership persuaded the sultan to destroy a newly built observatory in Istanbul—in the same year that the king of Denmark had built one for Tycho Brahe, which was to provide Johannes Kepler with valuable data that in turn contributed to Isaac Newton’s discovery of the laws of gravity and motion. And all of these European scholars accessed information in printed works. Restraints loosened only after Napoleon’s invasion of the Middle East, as Ottoman hegemony began to erode.33 This was not a unique outcome. In India, Mughal rulers such as Aurangzeb had championed adherence to orthodox Islam.


pages: 1,799 words: 532,462

The Codebreakers: The Comprehensive History of Secret Communication From Ancient Times to the Internet by David Kahn

anti-communist, British Empire, Claude Shannon: information theory, computer age, cuban missile crisis, Fellow of the Royal Society, Honoré de Balzac, index card, interchangeable parts, invention of the telegraph, Isaac Newton, Johannes Kepler, John von Neumann, Louis Daguerre, Maui Hawaii, Norbert Wiener, out of africa, pattern recognition, place-making, popular electronics, positional goods, Republic of Letters, Searching for Interstellar Communications, stochastic process, the scientific method, trade route, Turing machine, union organizing, yellow journalism, zero-sum game

Porta’s Accademia dei Lincei corresponded in cipher with Johann Eck. When Galileo Galilei discovered with his new telescope that Venus went through phases like the moon, thereby powerfully supporting the Copernican theory, he risked getting into serious trouble with the Catholic Church, which was soon to declare that theory heretical. Consequently he recorded his discovery as an anagram in a letter to Johannes Kepler: HAEC IMMATURA A ME JAM FRUSTRA LEGUNTUR O.Y. (“These unripe things are now read by me in vain”), with the O.Y. two letters that he could not fit in. The plaintext further hid the names of the celestial bodies under mythological allusions, referring to Venus’ character as the goddess of love, and Cynthia’s as the goddess of the moon: Cynthiae figuras aemulatur mater amorum (“The mother of love imitates the phases of Cynthia”).

Accept now this token, such as it is and long overdue though it be, of my affection for you, and burst through its bars, if any there be, with your wonted success.” Bars there were, but Kircher, who never shrank from bragging of what he thought were his successes, did not burst through them, for his silence on this point is eloquent. Marci wrote that the manuscript had been bought for 600 ducats by the Holy Roman Emperor Rudolf II. More of a scholar than a ruler, Rudolf founded observatories for Tycho Brahe and Johannes Kepler, established a botanical garden, and set up an alchemical laboratory to which he invited numberless scientists. The presence of the manuscript at his court in Prague was later proved by the discovery in a margin of the autograph of Johannes de Tepenecz, a Bohemian scientist who was a favorite of Rudolf. A page of the Voynich manuscript Marci also reported the belief that the author of the manuscript was Roger Bacon, the English Franciscan friar who lived from about 1214 to 1294.


pages: 796 words: 242,660

This Sceptred Isle by Christopher Lee

agricultural Revolution, Berlin Wall, British Empire, colonial rule, Corn Laws, cuban missile crisis, Edward Lloyd's coffeehouse, failed state, financial independence, glass ceiling, half of the world's population has never made a phone call, James Hargreaves, James Watt: steam engine, Johannes Kepler, Khartoum Gordon, Khyber Pass, mass immigration, Mikhail Gorbachev, Monroe Doctrine, Nelson Mandela, new economy, Northern Rock, Ronald Reagan, sceptred isle, spice trade, spinning jenny, The Wealth of Nations by Adam Smith, trade route, urban decay

That is because Britain does not yet know where it wants to position itself in, say, the coming thirty or forty years and into the second half of the twenty-first century. The people who ran the Empire knew what they wanted for the coming half century. But then they knew who they were, and so did everyone else. ENDNOTES 1. Professor Chris Stringer, Department of Palaeontology, Natural History Museum, London, in Nature, 2005. 2. This has been known since the seventeenth century largely due to the work of Johannes Kepler (1571–1630). 3. Stephen Oppenheimer, The Origins of the British (London: Robinson, 2007), 197. 4. The Skara Brae settlement is an exceptional example of preserved Neolithic society. 5. Oppenheimer, The Origins of the British, 272. 6. Barry Cunliffe, Facing the Ocean: The Atlantic and Its Peoples (Oxford: OUP, 2004), 218–19. 7. Gildas Badonicus, a Celtic monk writing in the 540s to denounce the wickedness of his times. 8.


pages: 1,034 words: 241,773

Enlightenment Now: The Case for Reason, Science, Humanism, and Progress by Steven Pinker

3D printing, access to a mobile phone, affirmative action, Affordable Care Act / Obamacare, agricultural Revolution, Albert Einstein, Alfred Russel Wallace, anti-communist, Anton Chekhov, Arthur Eddington, artificial general intelligence, availability heuristic, Ayatollah Khomeini, basic income, Berlin Wall, Bernie Sanders, Black Swan, Bonfire of the Vanities, business cycle, capital controls, Capital in the Twenty-First Century by Thomas Piketty, carbon footprint, clean water, clockwork universe, cognitive bias, cognitive dissonance, Columbine, conceptual framework, correlation does not imply causation, creative destruction, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, dark matter, decarbonisation, deindustrialization, dematerialisation, demographic transition, Deng Xiaoping, distributed generation, diversified portfolio, Donald Trump, Doomsday Clock, double helix, effective altruism, Elon Musk, en.wikipedia.org, end world poverty, endogenous growth, energy transition, European colonialism, experimental subject, Exxon Valdez, facts on the ground, Fall of the Berlin Wall, first-past-the-post, Flynn Effect, food miles, Francis Fukuyama: the end of history, frictionless, frictionless market, germ theory of disease, Gini coefficient, Hans Rosling, hedonic treadmill, helicopter parent, Hobbesian trap, humanitarian revolution, Ignaz Semmelweis: hand washing, income inequality, income per capita, Indoor air pollution, Intergovernmental Panel on Climate Change (IPCC), invention of writing, Jaron Lanier, Joan Didion, job automation, Johannes Kepler, John Snow's cholera map, Kevin Kelly, Khan Academy, knowledge economy, l'esprit de l'escalier, Laplace demon, life extension, long peace, longitudinal study, Louis Pasteur, Martin Wolf, mass incarceration, meta analysis, meta-analysis, Mikhail Gorbachev, minimum wage unemployment, moral hazard, mutually assured destruction, Naomi Klein, Nate Silver, Nathan Meyer Rothschild: antibiotics, Nelson Mandela, New Journalism, Norman Mailer, nuclear winter, obamacare, open economy, Paul Graham, peak oil, Peter Singer: altruism, Peter Thiel, precision agriculture, prediction markets, purchasing power parity, Ralph Nader, randomized controlled trial, Ray Kurzweil, rent control, Republic of Letters, Richard Feynman, road to serfdom, Robert Gordon, Rodney Brooks, rolodex, Ronald Reagan, Rory Sutherland, Saturday Night Live, science of happiness, Scientific racism, Second Machine Age, secular stagnation, self-driving car, sharing economy, Silicon Valley, Silicon Valley ideology, Simon Kuznets, Skype, smart grid, sovereign wealth fund, stem cell, Stephen Hawking, Steven Pinker, Stewart Brand, Stuxnet, supervolcano, technological singularity, Ted Kaczynski, The Rise and Fall of American Growth, the scientific method, The Signal and the Noise by Nate Silver, The Spirit Level, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, total factor productivity, union organizing, universal basic income, University of East Anglia, Unsafe at Any Speed, Upton Sinclair, uranium enrichment, urban renewal, War on Poverty, We wanted flying cars, instead we got 140 characters, women in the workforce, working poor, World Values Survey, Y2K

The other explanation is that our universe is just one region in a vast, possibly infinite landscape of universes—a multiverse—each with different values of the fundamental constants.36 We find ourselves in a universe compatible with life not because it was tuned to allow us to exist but because the very fact that we exist implies that it is that kind of universe, and not one of the vastly more numerous inhospitable ones, that we find ourselves in. Fine-tuning is a fallacy of post hoc reasoning, like the Megabucks winner who wonders what made him win against all odds. Someone had to win, and it’s only because it happened to be him that he’s wondering in the first place. It’s not the first time that a selection artifact has fooled thinkers into searching for a nonexistent deep explanation for a physical constant. Johannes Kepler agonized over why the Earth was 93 million miles away from the sun, just right for water to fill our lakes and rivers without freezing solid or boiling away. Today we know that the Earth is just one of many planets, each at a different distance from our sun or another star, and we are unsurprised to learn that we find ourselves on that planet rather than on Mars. The theory of the multiverse would itself be a post hoc excuse for an explanation if it were not consistent with other theories in physics—in particular, that the vacuum of space can spawn big bangs which grow into new universes, and that the baby universes can be born with different fundamental constants.37 Still, the very idea repels many people (not least some physicists) because of its mind-boggling profligacy.


pages: 904 words: 246,845

A History of the Bible: The Story of the World's Most Influential Book by John Barton

complexity theory, feminist movement, invention of the printing press, Johannes Kepler, lateral thinking, liberation theology, Republic of Letters, source of truth, the market place, trade route

Israel (ed.), Spinoza: Theological-Political Treatise, pp. 33–4. 8. ‘He contends that reconstructing the historical context and especially the belief system of a given era is always the essential first and most important step to a correct understanding of any text’: Jonathan Israel, Introduction to Israel (ed.), Spinoza: Theological-Political Treatise, p. x. 9. Though it was anticipated by Johannes Kepler (1571–1630), who regarded the biblical texts as reflecting the thought-world of the time (and hence as offering no objection to a modern scientific understanding of the universe): see Charlotte Methuen, ‘On the Threshold of a New Age: Expanding Horizons as the Broader Context of Scriptural Interpretation’, in Sæbø (ed.), Hebrew Bible/Old Testament, vol. 2, pp. 665–90, at p. 672. 10. Israel (ed.), Spinoza: Theological-Political Treatise, p. 65. 11.


pages: 913 words: 265,787

How the Mind Works by Steven Pinker

affirmative action, agricultural Revolution, Alfred Russel Wallace, Buckminster Fuller, cognitive dissonance, Columbine, combinatorial explosion, complexity theory, computer age, computer vision, Daniel Kahneman / Amos Tversky, delayed gratification, double helix, experimental subject, feminist movement, four colour theorem, Gordon Gekko, greed is good, hedonic treadmill, Henri Poincaré, income per capita, information retrieval, invention of agriculture, invention of the wheel, Johannes Kepler, John von Neumann, lake wobegon effect, lateral thinking, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, Mikhail Gorbachev, Murray Gell-Mann, mutually assured destruction, Necker cube, out of africa, pattern recognition, phenotype, plutocrats, Plutocrats, random walk, Richard Feynman, Ronald Reagan, Rubik’s Cube, Saturday Night Live, scientific worldview, Search for Extraterrestrial Intelligence, sexual politics, social intelligence, Steven Pinker, theory of mind, Thorstein Veblen, Turing machine, urban decay, Yogi Berra

But add a second mark, and their retinal images can be matched in two ways: spot 1 in the left eye with spot 1 in the right eye, and spot 2 in the left eye with spot 2 in the right eye—the correct matchup—or spot 1 in the left eye with spot 2 in the right eye, and spot 2 in the left eye with spot 1 in the right eye—a mismatch that would lead to the hallucination of two ghost marks instead. Add more marks, and the matching problems multiply. With three marks, there are six ghost matches; with ten marks, ninety; with a hundred marks, almost ten thousand. This “correspondence problem” was noticed in the sixteenth century by the astronomer Johannes Kepler, who thought about how stargazing eyes match up their thousands of white dots and how an object’s position in space could be determined from its multiple projections. The wallpaper stereogram works by coaxing the brain to accept a plausible but false solution to the correspondence problem. Until recently, everyone thought that the brain solved the correspondence problem in everyday scenes by first recognizing the objects in each eye and then matching up images of the same object.


EuroTragedy: A Drama in Nine Acts by Ashoka Mody

"Robert Solow", Andrei Shleifer, asset-backed security, availability heuristic, bank run, banking crisis, Basel III, Berlin Wall, book scanning, Bretton Woods, call centre, capital controls, Carmen Reinhart, Celtic Tiger, central bank independence, centre right, credit crunch, Daniel Kahneman / Amos Tversky, debt deflation, Donald Trump, eurozone crisis, Fall of the Berlin Wall, financial intermediation, floating exchange rates, forward guidance, George Akerlof, German hyperinflation, global supply chain, global value chain, hiring and firing, Home mortgage interest deduction, income inequality, inflation targeting, Irish property bubble, Isaac Newton, job automation, Johann Wolfgang von Goethe, Johannes Kepler, Kenneth Rogoff, Kickstarter, liberal capitalism, light touch regulation, liquidity trap, loadsamoney, London Interbank Offered Rate, Long Term Capital Management, low-wage service sector, Mikhail Gorbachev, mittelstand, money market fund, moral hazard, mortgage tax deduction, neoliberal agenda, offshore financial centre, oil shock, open borders, pension reform, premature optimization, price stability, purchasing power parity, quantitative easing, rent-seeking, Republic of Letters, Robert Gordon, Robert Shiller, Robert Shiller, short selling, Silicon Valley, The Great Moderation, The Rise and Fall of American Growth, too big to fail, total factor productivity, trade liberalization, transaction costs, urban renewal, working-age population, Yogi Berra

In April 2010, in a lecture to the Royal Society in London, I recalled that we owe our “contemporary way of life” to the astonishing scientific progress made during Europe’s Age of Enlightenment in the seventeenth and early-​eighteenth centuries.40 That progress occurred, as economic historians have reminded us, within a politically fragmented Europe but one that was united in the marketplace of ideas.41 Indeed, political fragmentation was a source of creative energy as nations sought to gain the intellectual and scientific lead. Nations promoted and competed for the best minds. Galileo Galilei, Johannes Kepler, and Isaac Newton were among the intellectual giants. Universities, academies, and learned societies “sprang up all over Europe,” which created a ferment of innovative excitement.42 Europe was successful then as a republic of letters, not as a political organization that tried to coordinate European nations through rules and committees. Europe must again be a republic of letters invigorated by competition among its nation-​states.


The Art of Computer Programming: Fundamental Algorithms by Donald E. Knuth

discrete time, distributed generation, Donald Knuth, fear of failure, Fermat's Last Theorem, G4S, Gerard Salton, Isaac Newton, Jacquard loom, Johannes Kepler, John von Neumann, linear programming, linked data, Menlo Park, probability theory / Blaise Pascal / Pierre de Fermat, sorting algorithm, stochastic process, Turing machine

Before Fibonacci wrote his work, the sequence Fn had already been discussed by Indian scholars, who had long been interested in rhythmic patterns that are formed from one-beat and two-beat notes or syllables. The number of such rhythms having n beats altogether is Fn+i; therefore both Gopala (before 1135) and Hemachandra (c. 1150) mentioned the numbers 1, 2, 3, 5, 8, 13, 21, ... explicitly. [See P. Singh, Historia Math. 12 A985), 229-244; see also exercise 4.5.3-32.] The same sequence also appears in the work of Johann Kepler, 1611, who was musing about the numbers he saw around him [J. Kepler, The Six-Cornered SnowBake (Oxford: Clarendon Press, 1966), 21]. Kepler was presumably unaware of Fibonacci's brief mention of the sequence. Fibonacci numbers have often been observed in nature, probably for reasons similar to the original assumptions of the rabbit problem. [See Conway and Guy, The Book of Numbers (New York: Copernicus, 1996), 113-126, for an especially lucid explanation.]


God Created the Integers: The Mathematical Breakthroughs That Changed History by Stephen Hawking

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Antoine Gombaud: Chevalier de Méré, Augustin-Louis Cauchy, British Empire, Edmond Halley, Eratosthenes, Fellow of the Royal Society, G4S, Georg Cantor, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, p-value, Pierre-Simon Laplace, Richard Feynman, Stephen Hawking, Turing machine

This episode in the scientist’s life has been a source of embarrassment to many Newton scholars. Only long after Newton died did it become apparent that his interest in chemical experiments was related to his later research in celestial mechanics and gravitation. Newton had already begun forming theories about motion by 1666, but he was as yet unable to adequately explain the mechanics of circular motion. Some fifty years earlier, the German mathematician and astronomer Johannes Kepler had proposed three laws of planetary motion, which accurately described how the planets moved in relation to the sun, but he could not explain why the planets moved as they did. The closest Kepler came to understanding the forces involved was to say that the sun and the planets were “magnetically” related. Newton set out to discover the cause of the planets’ elliptical orbits. By applying his own law of centripetal force to Kepler’s third law of planetary motion, (the law of harmonies) he deduced the inverse-square law, which states that the force of gravity between any two objects is inversely proportional to the square of the distance between the object’s centers.


Europe: A History by Norman Davies

agricultural Revolution, Albert Einstein, anti-communist, Berlin Wall, Bretton Woods, British Empire, business climate, centre right, charter city, clean water, Columbian Exchange, conceptual framework, continuation of politics by other means, Corn Laws, cuban missile crisis, Defenestration of Prague, discovery of DNA, double entry bookkeeping, Edmond Halley, Edward Lloyd's coffeehouse, equal pay for equal work, Eratosthenes, Etonian, European colonialism, experimental economics, financial independence, finite state, Francis Fukuyama: the end of history, Francisco Pizarro, full employment, global village, Honoré de Balzac, Index librorum prohibitorum, interchangeable parts, invention of agriculture, invention of movable type, Isaac Newton, James Hargreaves, James Watt: steam engine, Johann Wolfgang von Goethe, Johannes Kepler, John Harrison: Longitude, joint-stock company, Joseph-Marie Jacquard, land reform, liberation theology, long peace, Louis Blériot, Louis Daguerre, Mahatma Gandhi, mass immigration, Mikhail Gorbachev, Monroe Doctrine, Murano, Venice glass, music of the spheres, New Urbanism, North Sea oil, offshore financial centre, Peace of Westphalia, popular capitalism, Potemkin village, purchasing power parity, Ralph Waldo Emerson, road to serfdom, sceptred isle, Scramble for Africa, spinning jenny, Thales of Miletus, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, trade route, transatlantic slave trade, Transnistria, urban planning, urban sprawl

Its immediate impact was much reduced because a fearful editor replaced Copernicus’s introduction with a misleading preface of his own. The Copernican theory gestated for almost a century. The Dane Tycho Brahe (1546–1601) rejected heliocentrism; but through observing the pathways of comets he destroyed another ancient misconception, namely that the cosmos consists of onion-like crystalline spheres. Brahe’s colleague in Prague, Johann Kepler (1571–1630), established the elliptical shape of planetary orbits, and enunciated the laws of motion underlying Copernicus. But it was the Florentine, Galileo Galilei (1564–1642), one of the first to avail himself of the newly invented telescope, who really brought Copernicus to the wider public. Fortunately for posterity, Galileo was as rash as he was perceptive. Having discovered that ‘the moon is not smooth or uniform, but rough and full of cavities, like the earth’, he exploded the prevailing theory of ‘perfect spheres’.