Eratosthenes

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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

Columbus’ first voyage is connected in the most straightforward way with the calculations of Eratosthenes. Columbus was fascinated by what he called “the Enterprise of the Indies,” a project to reach Japan, China and India not by following the coastline of Africa and sailing East but rather by plunging boldly into the unknown Western ocean—or, as Eratosthenes had said with startling prescience, “to pass by sea from Iberia to India.” Columbus had been an itinerant peddler of old maps and an assiduous reader of the books by and about the ancient geographers, including Eratosthenes, Strabo and Ptolemy. But for the Enterprise of the Indies to work, for ships and crews to survive the long voyage, the Earth had to be smaller than Eratosthenes had said. Columbus therefore cheated on his calculations, as the examining faculty of the University of Salamanca quite correctly pointed out.

Human beings, born ultimately of the stars and now for a while inhabiting a world called Earth, have begun their long voyage home. The discovery that the Earth is a little world was made, as so many important human discoveries were, in the ancient Near East, in a time some humans call the third century B.C., in the greatest metropolis of the age, the Egyptian city of Alexandria. Here there lived a man named Eratosthenes. One of his envious contemporaries called him “Beta,” the second letter of the Greek alphabet, because, he said, Eratosthenes was second best in the world in everything. But it seems clear that in almost everything Eratosthenes was “Alpha.” He was an astronomer, historian, geographer, philosopher, poet, theater critic and mathematician. The titles of the books he wrote range from Astronomy to On Freedom from Pain. He was also the director of the great library of Alexandria, where one day he read in a papyrus book that in the southern frontier outpost of Syene, near the first cataract of the Nile, at noon on June 21 vertical sticks cast no shadows.

A reflection of the Sun could then be seen in the water at the bottom of a deep well. The Sun was directly overhead. It was an observation that someone else might easily have ignored. Sticks, shadows, reflections in wells, the position of the Sun—of what possible importance could such simple everyday matters be? But Eratosthenes was a scientist, and his musings on these commonplaces changed the world; in a way, they made the world. Eratosthenes had the presence of mind to do an experiment, actually to observe whether in Alexandria vertical sticks cast shadows near noon on June 21. And, he discovered, sticks do. Eratosthenes asked himself how, at the same moment, a stick in Syene could cast no shadow and a stick in Alexandria, far to the north, could cast a pronounced shadow. Consider a map of ancient Egypt with two vertical sticks of equal length, one stuck in Alexandria, the other in Syene.


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

The size of the Earth was measured a few decades after the work of Aristarchus by Eratosthenes. Eratosthenes was born in 273 BC at Cyrene, a Greek city on the Mediterranean coast of today’s Libya, founded around 630 BC, that had become part of the kingdom of the Ptolemies. He was educated in Athens, partly at the Lyceum, and then around 245 BC was called by Ptolemy III to Alexandria, where he became a fellow of the Museum and tutor to the future Ptolemy IV. He was made the fifth head of the Library around 234 BC. His main works—On the Measurement of the Earth, Geographic Memoirs, and Hermes—have all unfortunately disappeared, but were widely quoted in antiquity. The measurement of the size of the Earth by Eratosthenes was described by the Stoic philosopher Cleomedes in On the Heavens,16 sometime after 50 BC. Eratosthenes started with the observations that at noon at the summer solstice the Sun is directly overhead at Syene, an Egyptian city that Eratosthenes supposed to be due south of Alexandria, while measurements with a gnomon at Alexandria showed the noon Sun at the solstice to be one-fiftieth of a full circle, or 7.2°, away from the vertical.

We don’t know the length of the stadion as used by Eratosthenes, and Cleomedes probably didn’t know it either, since (unlike our mile or kilometer) it had never been given a standard definition. But without knowing the length of the stadion, we can judge the accuracy of Eratosthenes’ use of astronomy. The Earth’s circumference is actually 47.9 times the distance from Alexandria to Syene (modern Aswan), so the conclusion of Eratosthenes that the Earth’s circumference is 50 times the distance from Alexandria to Syene was actually quite accurate, whatever the length of the stadion.* In his use of astronomy, if not of geography, Eratosthenes had done quite well. 8 The Problem of the Planets The Sun and Moon are not alone in moving from west to east through the zodiac while they share the quicker daily revolution of the stars from east to west around the north celestial pole. In several ancient civilizations it was noticed that over many days five “stars” travel from west to east through the fixed stars along pretty much the same path as the Sun and Moon.

Eratosthenes started with the observations that at noon at the summer solstice the Sun is directly overhead at Syene, an Egyptian city that Eratosthenes supposed to be due south of Alexandria, while measurements with a gnomon at Alexandria showed the noon Sun at the solstice to be one-fiftieth of a full circle, or 7.2°, away from the vertical. From this he could conclude that the Earth’s circumference is 50 times the distance from Alexandria to Syene. (See Technical Note 12.) The distance from Alexandria to Syene had been measured (probably by walkers, trained to make each step the same length) as 5,000 stadia, so the circumference of the Earth must be 250,000 stadia. How good was this estimate? We don’t know the length of the stadion as used by Eratosthenes, and Cleomedes probably didn’t know it either, since (unlike our mile or kilometer) it had never been given a standard definition.


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

The centre of the Earth supposedly coincided with the hypothetical universal centre, so the Earth itself was static and everything on its surface was pulled towards the centre. Hence, the Greeks would be held on the ground by this force, as would everybody else on the globe, even if they lived down under. The feat of measuring the size of the Earth was first accomplished by Eratosthenes, born in about 276 BC in Cyrene, in modern-day Libya. Even when he was a little boy it was clear that Eratosthenes had a brilliant mind, one that he could turn to any discipline, from poetry to geography. He was even nicknamed Pentathlos, meaning an athlete who participates in the five events of the pentathlon, hinting at the breadth of his talents. Eratosthenes spent many years as the chief librarian at Alexandria, arguably the most prestigious academic post in the ancient world. Cosmopolitan Alexandria had taken over from Athens as the intellectual hub of the Mediterranean, and the city’s library was the most respected institution of learning in the world.

Forget any notion of strait-laced librarians stamping books and whispering to each other, because this was a vibrant and exciting place, full of inspiring scholars and dazzling students. While at the library, Eratosthenes learned of a well with remarkable properties, situated near the town of Syene in southern Egypt, near modern-day Aswan. At noon on 21 June each year, the day of the summer solstice, the Sun shone directly into the well and illuminated it all the way to the bottom. Eratosthenes realised that on that particular day the Sun must be directly overhead, something that never happened in Alexandria, which was several hundred kilometres north of Syene. Today we know that Syene lies close to the Tropic of Cancer, the most northerly latitude from which the Sun can appear overhead. Aware that the Earth’s curvature was the reason why the Sun could not be overhead at both Syene and Alexandria simultaneously, Eratosthenes wondered if he could exploit this to measure the circumference of the Earth.

The rest of the calculation is straightforward. Eratosthenes measured the distance between the two towns, which turned out to be 5,000 stades. If this represents 1/50 of the total circumference of the Earth, then the total circumference must be 250,000 stades. But you might well be wondering, how far is 250,000 stades? One stade was a standard distance over which races were held. The Olympic stade was 185 metres, so the estimate for the circumference of the Earth would be 46,250 km, which is only 15% bigger than the actual value of 40,100 km. In fact, Eratosthenes may have been even more accurate. The Egyptian stade differed from the Olympic stade and was equal to just 157 metres, which gives a circumference of 39,250 km, accurate to 2%. Whether he was accurate to 2% or 15% is irrelevant. The important point is that Eratosthenes had worked out how to reckon the size of the Earth scientifically.


Prime Obsession:: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire

Albert Einstein, Andrew Wiles, Colonization of Mars, Eratosthenes, Ernest Rutherford, four colour theorem, Georg Cantor, Henri Poincaré, Isaac Newton, John Conway, John von Neumann, Paul Erdős, Richard Feynman, Turing machine, Turing test

In fact, by yoking the two concepts together in a certain way, by turning the Golden Key, Riemann opened up the whole field of analytic number theory. But how did he do that? What’s the connection? What is the Golden Key? In this chapter I aim to answer that question—to show you the Golden Key. Then I shall begin preparations for turning the Golden Key by offering an improved version of the PNT. 99 PRIME OBSESSION 100 II. It begins with the “sieve of Eratosthenes.” The Golden Key is, in fact, just a way that Leonhard Euler found to express the sieve of Eratosthenes in the language of analysis.34 Eratosthenes of Cyrene (nowadays the little town of Shahhat in Libya) was one of the librarians at the great library of Alexandria. Around 230 B.C.E.—70 years or so after Euclid—he developed his famous sieve method for finding prime numbers. It works like this. First, write down all the whole numbers, starting with 2. Of course, you can’t write them all, so let’s make do with 100 or so. 2 16 30 44 58 72 86 100 3 17 31 45 59 73 87 101 4 18 32 46 60 74 88 102 5 19 33 47 61 75 89 103 6 20 34 48 62 76 90 104 7 8 21 22 35 36 49 50 63 64 77 78 91 92 104 106 9 10 23 24 37 38 51 52 65 66 79 80 93 94 107 108 11 25 39 53 67 81 95 109 12 13 26 27 40 41 54 55 68 69 82 83 96 97 110 111 14 15 28 29 42 43 56 57 70 71 84 85 98 99 112 113 Now, starting from 2, and leaving 2 untouched, remove every second number from 2 on.

The next step would be to leave 7 untouched, but remove every seventh number from 7 on, if it hasn’t already been removed. The first number left unscathed after 7 would then be 11, and so on. If you keep doing this for ever, the numbers you are left with are all the primes. That is the sieve of Eratosthenes. If you stop just before processing prime p—that is, just before removing every pth number that wasn’t already removed—you have all the primes less than p2. Since I stopped before processing 7, I have all the primes up to 72, which is 49. After that you see some numbers, like 77, that are not prime. PRIME OBSESSION 102 III. The sieve of Eratosthenes is pretty straightforward, and 2,230 years old. How does it get us into the middle of the nineteenth century, and deep results in function theory? Here’s how. I am going to repeat the process I went through above. (That’s why I went through it so painstakingly.)

Here is the zeta function for some number s bigger than 1. 1 1 1 1 1 1 1 1 1 1 + s + s + s + s + s + s + s + s + s +K s 2 3 4 5 6 7 8 9 10 11 Note that writing it in this way involves writing out all the positive whole numbers—which is how we started off the sieve of Eratosthenes (except that this time I included 1). What I’m going to do is multiply both sides of the equals sign by 1 2s . This gives me ζ (s ) = 1 + 1 1 1 1 1 1 1 1 1 1 ζ (s ) = s + s + s + s + s + s + s + s + s + K s 2 2 4 6 8 10 12 14 16 18 because of Power Rule 7 (which, for example, makes 2s times 7s equal to 14s). Now I’ll subtract the second of these expressions from the 1 first. On the left-hand sides I have one of ζ (s), and I have 2s of it. Subtracting 1 1 1 1 1 1 1 1 1 1  1 − s  ζ (s ) = 1 + s + s + s + s + s + s + s + s + s + K  2  3 5 7 9 11 13 15 17 19 The subtraction eliminated all the even-numbered terms from the infinite sum. I’m left with just the odd-numbered terms. Remembering the sieve of Eratosthenes, I’ll now multiply both 1 sides of this equals sign by 3s , 3 being the first unscathed number on the right-hand side. 1 3s 1 3s 1  1 − s  ζ (s ) =  2  + 1 1 1 1 1 1 1 1 K + + + + + + + + 9s 15s 21s 27s 33s 39s 45s 51s THE GOLDEN KEY, AND AN IMPROVED PRIME NUMBER THEOREM 103 Now subtract this expression from the one before.


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

Lastly, we do not know the exact length of his unit of distance (the stadion); I said ‘a tenth of a mile’, but this is rather approximate. In any case, the fact that the number of paces came to exactly 5,000 stadia is suspicious and most modern historians do not believe Eratosthenes ever did have the distance measured in this way but had unwittingly used instead a value for the distance that itself had been calculated from an even earlier estimate of the earth’s circumference;10 a sort of circular logic whereby an estimate of the earth’s circumference is used to deduce a distance that is then itself used to recalculate the circumference. And so we move forward in time a thousand years to Abbāsid Baghdad and the band of astronomers working for al-Ma’mūn. They knew about Eratosthenes’ method from the writings of Ptolemy. In fact, Ptolemy quoted a later, revised but incorrect value for the circumference of the earth of just 180,000 stadia by another Greek astronomer, by the name of Posidonius.11 Ten years after his arrival in Baghdad, al-Ma’mūn wished to know what all this meant: exactly how long was one Greek stadion?

Multiplying this number by 360 gives a figure of 24,500 miles, which is a more reliable figure than the one arrived at a thousand years earlier by Eratosthenes. Good scientist that he was, al-Ma’mūn then commissioned another expedition to carry out a second measurement, this time in the Syrian desert. Starting from the city of Palmyra in central Syria, his astronomers measured the distance to the city of Raqqah to its north. They found the two cities separated by 1 degree of latitude and 66.6 mīl, giving a larger circumference of 24,000 mīl, or 28,700 statute miles. Of course, while the whole project is admirable, all these numbers just added to the confusion. Everyone seems to have been in the right ballpark and it is probably pointless trying to credit those who arrived at the closest value. Al-Ma’mūn’s astronomers will have had to contend with the same issues as Eratosthenes. For instance, al-Raqqah is in fact about 1.5 degrees of latitude north of Palmyra as well as being about a degree of longitude to the east.

Even Plato, whom I do not regard as having been as good a scientist as either Aristotle or Archimedes, provides a remarkable description of our planet as a large sphere floating in space: ‘First of all the true earth, if one views it from above, is said to look like those twelve-piece leather balls, variegated, a patchwork of colours, of which our colours here are, as it were, samples that painters use.’9 Not only did Plato know that the earth was spherical but his description of its surface as having a ‘patchwork of colours’ evokes the images we are so familiar with today of our planet viewed from space with its weather patterns swirling above seas, deserts and snow-capped mountains. As for its size, another Greek scholar decided he could go one better than educated guesswork. He believed he could actually measure it. His name was Eratosthenes (c. 275–195 BCE) and he was the chief librarian of Alexandria, as well as being a brilliant astronomer and mathematician. His method for working out the size of the world was, like so many great ideas in science, beautifully simple: if he could measure the distance along the surface of the earth corresponding to just one of the 360 degrees around its circumference, then all he would have to do is multiply this distance by 360.


pages: 197 words: 35,256

NumPy Cookbook by Ivan Idris

business intelligence, cloud computing, computer vision, Debian, en.wikipedia.org, Eratosthenes, mandelbrot fractal, p-value, sorting algorithm, statistical model, transaction costs, web application

See also The Installing Matplotlib recipe in Chapter 1, Winding Along with IPython Sieving integers with the Sieve of Erasthothenes The Sieve of Eratosthenes (http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes) is an algorithm that filters out prime numbers. It iteratively identifies multiples of found primes. This sieve is efficient for primes smaller than 10 million. Let's now try to find the 10001st prime number. How to do it... The first mandatory step is to create a list of natural numbers. Create a list of consecutive integers.NumPy has the arange function for that: a = numpy.arange(i, i + LIM, 2) Sieve out multiples of p.We are not sure if this is what Eratosthenes wanted us to do, but it works. In the following code, we are passing a NumPy array and getting rid of all the elements that have a zero remainder, when divided by p: a = a[a % p !

Get to Grips with Commonly Used Functions In this chapter, we will cover a number of commonly used functions: sqrt, log, arange, astype, and sum ceil, modf, where, ravel, and take sort and outer diff, sign, eig histogram and polyfit compress and randint We will be discussing these functions through the following recipes: Summing Fibonacci numbers Finding prime factors Finding palindromic numbers The steady state vector determination Discovering a power law Trading periodically on dips Simulating trading at random Sieving integers with the Sieve of Eratosthenes Introduction This chapter is about the commonly used functions. These are the functions that you will be using on a daily basis. Obviously, the usage may differ for you. There are so many NumPy functions that it is virtually impossible to know all of them, but the functions in this chapter will be the bare minimum with which we must be familiar. You can download source code for this chapter from the book website http://www.packtpub.com.


pages: 295 words: 92,670

1494: How a Family Feud in Medieval Spain Divided the World in Half by Stephen R. Bown

Atahualpa, Bartolomé de las Casas, British Empire, charter city, Eratosthenes, European colonialism, Francisco Pizarro, Hernando de Soto, Peace of Westphalia, spice trade, The Wealth of Nations by Adam Smith, trade route, UNCLOS

Socrates propounded no precise opinion of the earth’s size—only that it was surely larger than most people surmised. The most accurate estimate of the earth’s circumference came from the Hellenic-Egyptian scholar Eratosthenes, using a simple method of calculating the angle of the shadows produced by a wooden pole of a specific height at midday in two locations. Although his equation was considerably more sophisticated than this brief description, his premise was clear and simple and his accuracy quite remarkable: he calculated that the earth was about 25,000 miles in circumference. The correct figure is about 24,862 miles, so Eratosthenes was only off by a mere 200 miles or so. But although he was accurate, his reasoning was not accepted by his peers. Speculating on the size of the world was one of the most fashionable and popular fields of inquiry for the Greek philosophers, and they collectively produced a great many estimates for the circumference of the earth.

Thus, for cosmographers and geographers, the world according to Ptolemy became the accepted truth. But Ptolemy’s conceptualization of the world contained a major and fundamental error, an error that was introduced into the European world view of the fifteenth century. Regarding the size of the earth, Ptolemy preferred the erroneous calculations of one of Eratosthenes’s near-contemporaries, Posidonius, who argued that the earth was only about eighteen thousand miles in circumference—two-thirds of the distance propounded by Eratosthenes. Ptolemy relied exclusively on this smaller figure when he produced the coordinates of his famous atlas, a work that came to define the known world for centuries. The rediscovery of Ptolemy’s ancient global atlas in the mid-fifteenth century, complete with its erroneous depiction of the continents and its vastly smaller estimation of the circumference of the earth, had initially given the idea to cosmographers and cartographers that on a spherical world you could reach the east by sailing west—it was basic common sense.

From this knowledge base, he required only a few further “adjustments” to produce an astonishing and fanciful picture of the geography of the world, a picture that completely supported his ambitious scheme. By choosing the erroneous calculations of an Islamic geographer named Alfragan, Columbus then presented the distance of a degree of longitude, theoretically one-360th of the circumference of the earth, a full 25 per cent less than Eratosthenes had calculated, and 10 per cent less than Ptolemy. He then adjusted Alfragan’s calculations by claiming that the speculative geographer had used the shorter Italian mile for his calculations and that therefore the distance was even less because the miles then accepted in Portugal were slightly longer. Finally, Columbus claimed that these figures were based on a degree of longitude at the equator, but since his proposed route across the Atlantic was at 28 degrees latitude, the width of the Atlantic was yet another 10 per cent shorter.


pages: 434 words: 135,226

The Music of the Primes by Marcus Du Sautoy

Ada Lovelace, Andrew Wiles, Arthur Eddington, Augustin-Louis Cauchy, computer age, Dava Sobel, Dmitri Mendeleev, Eratosthenes, Erdős number, Georg Cantor, German hyperinflation, global village, Henri Poincaré, Isaac Newton, Jacquard loom, lateral thinking, music of the spheres, New Journalism, P = NP, Paul Erdős, Richard Feynman, Rubik’s Cube, Search for Extraterrestrial Intelligence, Simon Singh, Solar eclipse in 1919, Stephen Hawking, Turing machine, William of Occam, Wolfskehl Prize, Y2K

He then stuck off every third number after 3. Since these were all divisible by 3, they weren’t prime either. He kept doing this, just picking up the next number which hadn’t already been struck from the list and striking off all the numbers divisible by the new prime. By this systematic process he produced tables of primes. The procedure was later christened the sieve of Eratosthenes. Each new prime creates a ‘sieve’ which Eratosthenes uses to eliminate non-primes. The size of the sieve changes at each stage, but by the time he reaches 1,000 the only numbers to have made it through all the sieves are prime numbers. When Gauss was a young boy he was given a present – a book containing a list of the first several thousand prime numbers which had probably been constructed using these ancient number sieves.

Solving one of Clay’s problems may earn you a million dollars, but that is nothing compared with carving your name on civilisation’s intellectual map. The Riemann Hypothesis, Fermat’s Last Theorem, Goldbach’s Conjecture, Hilbert space, the Ramanujan tau function, Euclid’s algorithm, the Hardy—Littlewood Circle Method, Fourier series, Gödel numbering, a Siegel zero, the Selberg trace formula, the sieve of Eratosthenes, Mersenne primes, the Euler product, Gaussian integers – these discoveries have all immortalised the mathematicians who have been responsible for unearthing these treasures in our exploration of the primes. Those names will live on long after we have forgotten the likes of Aeschylus, Goethe and Shakespeare. As G.H. Hardy explained, ‘languages die and mathematical ideas do not. “Immortality” may be a silly word, but probably a mathematician has the best chance of whatever it may mean.’

For many centuries, chemists strove to identify the basic constituents of their subject, and the Greeks’ intuition finally culminated in Dmitri Mendeleev’s Periodic Table, a complete description of the elements of chemistry. In contrast to the Greeks’ head start in identifying the building blocks of arithmetic, mathematicians are still floundering in their attempts to understand their own table of prime numbers. The librarian of the great ancient Greek research institute in Alexandria was the first person we know of to have produced tables of primes. Like some ancient mathematical Mendeleev, Eratosthenes in the third century BC discovered a reasonably painless procedure for determining which numbers are prime in a list of, say, the first 1,000 numbers. He began by writing out all the numbers from 1 to 1,000. He then took the first prime, 2, and struck off every second number in the list. Since all these numbers were divisible by 2, they weren’t prime. He then moved to the next number that hadn’t been struck off, namely 3.


The Haskell Road to Logic, Maths and Programming by Kees Doets, Jan van Eijck, Jan Eijck

Albert Einstein, Eratosthenes, Georg Cantor, P = NP, Russell's paradox

CORECURSION The process on Fibonacci numbers that was defined in Exercise 7.17 can be defined with corecursion, as follows: pr (x1:x2:x3:xs) = x1*x3 - x2*x2 : pr (x2:x3:xs) As we proved in Exercise 7.17, applying this process to theFibs gives the list λn.(−1)n+1 : COR> take 20 (pr theFibs) [-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1] The definition of the sieve of Eratosthenes (page 106) also uses corecursion: sieve :: [Integer] -> [Integer] sieve (0 : xs) = sieve xs sieve (n : xs) = n : sieve (mark xs 1 n) where mark (y:ys) k m | k == m = 0 : (mark ys 1 m) | otherwise = y : (mark ys (k+1) m) What these definitions have in common is that they generate infinite objects, and that they look like recursive definitions, except for the fact that there is no base case. Here is a faster way to implement the Sieve of Eratosthenes. This time, we actually remove multiples of x from the list on encountering x in the sieve. The counting procedure now has to be replaced by a calculation, for the removals affect the distances in the list.

Thanks to Johan van Benthem, Jan Bergstra, Jacob Brunekreef, Thierry Coquand (who found the lecture notes on the internet and sent us his comments), Tim van Erven, Wan Fokkink, Evan Goris, Robbert de Haan, Sandor Heman, Eva Hoogland, Rosalie Iemhoff, Dick de Jongh, Anne Kaldewaij, Breanndán Ó Nualláin, Alban Ponse, Vincent van Oostrom, Piet Rodenburg, Jan Rutten, Marco Swaen, Jan Terlouw, John Tromp, Yde Venema, Albert Visser and Stephanie Wehner for suggestions and criticisms. The beautiful implementation of the sieve of Eratosthenes in Section 3.7 was suggested to us by Fer-Jan de Vries. The course on which this book is based was developed at ILLC (the Institute of Logic, Language and Computation of the University of Amsterdam) with financial support from the Spinoza Logic in Action initiative of Johan van Benthem, which is herewith gratefully acknowledged. We also wish to thank ILLC and CWI (Centrum voor Wiskunde en Informatica, or Centre for Mathematics and Computer Science, also in Amsterdam), the home institute of the second author, for providing us with a supportive working environment.

Next, we use ^ for exponentiation to make a new Mersenne guess, as follows: TUOLP> prime 5 True TUOLP> prime (2^5-1) True TUOLP> 2^5-1 31 TUOLP> prime (2^31-1) True TUOLP> 2^31-1 2147483647 TUOLP> It may interest you to know that the fact that 231 − 1 is a prime was discovered by Euler in 1750. Using a computer, this fact is a bit easier to check. We have already seen how to generate prime numbers in Haskell (Examples 1.22 and 1.23). We will now present an elegant alternative: a lazy list implementation of the Sieve of Eratosthenes. The idea of the sieve is this. Start with the list of all natural numbers > 2: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, . . . In the first round, mark 2 (the first number in the list) as prime, and mark all multiples of 2 for removal in the remainder of the list (marking for removal indicated by over-lining): 2 , 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, . . .


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

His evidence was indirect: Greek sailors saw southern constellations rising higher as they sailed south; when they got really far south, the sun shone from the north instead of the south (as it does north of the equator); and when the full moon passed into the Earth’s shadow during a rare lunar eclipse, the outline of the Earth’s shadow appears curved. It seemed obvious to Pythagoras. It would take more than 250 years, however, for another famous Greek mathematician and astronomer, Eratosthenes, to prove it and to accurately estimate our planet’s size. He performed one of the most simple and famous scientific experiments of all time, and one that is easy for schoolkids to reproduce today, using just two sticks and a sunny day. One stick was in the southern Egyptian city of Syene (modern-day Aswan), on a day when, at noon, the sun was directly overhead and that stick did not cast a shadow. The other stick was in his own northern Egyptian city of Alexandria (Eratosthenes was the head of the Library of Alexandria, an amazing collection of all of the then-known books of the world—the equivalent of the Internet on Planet Earth in the third century BCE), where, on the same day, a stick would indeed cast a short shadow at noon.

This is, in fact, the same philosophy that Jon and I, along with Steve Squyres, Bill Nye, and other colleagues, had taken when we devised the design, messages, and other “furniture” that turned an esoteric camera calibration target on the Mars rovers Spirit, Opportunity, and Curiosity into Martian sundials, or “MarsDials.” The idea was to be able to calibrate the cameras using swatches of colored and gray-scale materials, but the bigger-picture idea was also to help teach kids about timekeeping and understanding our place in space using only sticks and shadows—much like the third-century BCE Greek mathematician and astronomer Eratosthenes had done to accurately estimate the size of our planet. We figured, apparently as Carl Sagan did for the Voyager Golden Record, let’s keep this under the radar, lest it get killed by committee. The Voyager’s two-sided gold-anodized copper LP contains an hour and a half of music (27 pieces in all), 116 digitized photographs, and a catalogue of terrestrial sounds (such as the chirping of crickets) and voices (such as short greetings in fifty-five languages, including a “hello from the children of Planet Earth” in English from Carl Sagan’s six-year-old son, Nick).

He knew that the angle between the sticks was the result of being at different places on a sphere, so he had an assistant (a graduate student, no doubt) walk off and measure the distance between Alexandria and Syene. His predecessors Plato and Archimedes, not mathematical slouches, to be sure, used their best reasoning to estimate the diameter of the Earth as 14,000 and 11,000 miles, respectively. Eratosthenes, armed with data from his simple measurements, came up with around 9,000 miles, or within about 15 percent of the correct modern answer (7,918 miles). Not bad for sticks and shadows. Fast-forward almost 2,200 years and we’ve entered an era when we can, in fact, just leave our planet, turn around, and take a look. The first time this was actually done was in the late 1940s, with cameras on suborbital German V-2 rockets that had been captured by the US Army after World War II and transported to the White Sands Missile Range in New Mexico.


pages: 184 words: 13,957

Programming in Haskell by Graham Hutton

Eratosthenes, John Conway, Simon Singh, type inference

Hence, by using factors , a simple function that decides if an integer is prime can be defined as follows: prime :: prime n = Int → Bool factors n == [1, n ] For example: > prime 15 False > prime 7 True Note that deciding that a number such as 15 is not prime does not require the function prime to produce all of its factors, because under lazy evaluation the result False is returned as soon as any factor other than one or the number itself is produced, which for this example is given by the factor 3. Returning to list comprehensions, using prime we can now define a function that produces the list of all prime numbers up to a given limit: primes :: primes n = Int → [Int ] [x | x ← [2 . . n ], prime x ] For example: > primes 40 [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37] In chapter 12 we will present a more efficient program to generate prime numbers using the famous “sieve of Eratosthenes”, which has a particularly clear and concise implementation in Haskell. As a final example concerning guards, suppose that we represent a lookup table by a list of pairs comprising keys and values. Then for any type of keys that is an equality type, a function find that returns the list of all values that are associated with a given key in a table can be defined as follows: find :: find k t = Eq a ⇒ a → [(a, b)] → [b ] [v | (k , v ) ← t, k == k ] For example: > find ’b’ [(’a’, 1), (’b’, 2), (’c’, 3), (’b’, 4)] [2, 4] 5.3 The zip function The library function zip produces a new list by pairing successive elements from two existing lists until either or both are exhausted.

The first few iterations of this procedure can be illustrated as follows: 2 3 3 4 5 6 7 5 7 5 8 9 9 10 11 12 13 14 15 ··· 15 ··· 11 13 7 11 13 ··· 7 11 13 ··· 11 13 ··· 13 ··· Each row corresponds to one iteration, with the first row being the initial sequence (step one), the first number in each row being written in bold to indicate its primality (step two), and all multiples of this number being underlined to indicate their deletion (step three) prior to the next iteration. In this manner, we can imagine the initial sequence of numbers falling downwards, with cer- 133 134 L A Z Y E VA L UAT I O N tain numbers being sieved out at each stage by the underlining, and the bold numbers forming the infinite sequence of primes: 2, 3, 5, 7, 11, 13, · · · The above procedure for generating prime numbers is known as the sieve of Eratosthenes, after the Greek mathematician who first described it. This procedure can be translated directly into Haskell: primes primes :: [Int ] = sieve [2 . .] sieve :: [Int ] → [Int ] sieve (p : xs) = p : sieve [x | x ← xs, x ‘mod ‘ p = 0] That is, starting with the infinite list [2 . .] (step one), we apply the function sieve that retains the first number p as being prime (step two), and then calls itself recursively with a new list obtained by filtering all multiples of p from this list (steps three and four).

assignment, 3, 125 associativity, 11, 66, 140 for addition, 67, 82, 139, 143 for append, 146 for application, 22 for composition, 68 for cons, 33 for function types, 22 for multiplication, 82 binary trees, 103 Bool, 17, 18, 157 case, 76 category theory, 114 Char , 18, 158 characters, see Char chr , 43, 158 class, 111 classes, 24, 111, 156 constraints, 23, 111 default definitions, 111 derived instances, 112 instances, 24, 111 methods, 24 clearing the screen, 91 comments, 15 commutativity, 122 for addition, 122, 154 for multiplication, 122, 139 composition, see ◦ comprehensions list, 4, 38 set, 38, 46 string, 42 concat, 39, 163 concatenation, see concat conditions, 31 conjunction, see ∧, and cons, see : const, 35, 164 control characters, 19, 91 curry, 164 cursor, 91 dangling else, 31 data, 100 deriving, 112 digitToInt, 158 disjunction, see ∨, or distributivity, 139, 146, 152 div , 10, 14, 27, 71, 157 division, see div , / do, 77, 89, 114 domain-specific languages, 5, 62 domino effect, 143 Dr Seuss, 75 drop, 11, 53, 56, 162 dropWhile, 64, 162 elem, 160 Eq, 24, 40, 156 equality, see == equational reasoning, 5, 139 error , 84, 165 error messages, 12, see error evaluation, 10, 17, 84, 117, 124 call-by-name, 127, 128 call-by-value, 126, 128 innermost, 126 lazy, 5, 20, 32, 40, 70, 130 outermost, 126 top-level, 134 even, 30, 53, 159 examples 170 INDEX abstract machine, 109 base conversion, 70 Caesar cipher, 42 calculator, 91 chi-square, 45 compiler, 150 countdown, 116 expression parser, 82 factorial, 14, 48 fast reverse, 147 Fibonacci sequence, 53, 137 game of life, 94 insertion sort, 52 permutations, 118 prime numbers, 40, 133 quicksort, 7, 53 sieve of Eratosthenes, 134 string transmitter, 69 subsequences, 118 tautology checker, 105 exception handling, 97 exponentiation, see ↑ expressions, 1 arithmetic, 82, 109, 116, 150 conditional, see if impure, 89 lambda, see λ logical, 105 pure, 89 reducible, 125 False, 17, 18 file handling, 97 filter , 63, 161 Float, 19, 44, 159 foldl, 56, 67, 136, 162 foldl1 , 162 foldr , 56, 64, 72, 162 foldr1 , 162 FP, 6 Fractional, 28, 157 fromInt, 44 fst, 33, 160 functions, 1, 12, 21, 164 combinatorial, 118 composite, see ◦ constant, see const constructor, 101 curried, 22, 35, 61, 127, 135 higher-order, 5, 62 identity, see id nameless, see λ overloaded, 4, 24 polymorphic, 4, 23, 42, 62 recursive, 7, 48 strict, 127, 134 total, 21 generators, see ← getCh, 90 getChar , 88, 90, 165 getLine, 90, 165 GHC, 10, 120 grammars, 82 ambiguous, 84 guards, 5, 31, 39, 58 head, 11, 34, 161 Hugs, 10, 13 commands, 14 id, 69, 164 identifiers, 14, 80 identities, 122 for addition, 7 for append, 147 for composition, 68 for division, 122 for multiplication, 49, 55, 122 if, 18, 31 indentation, 4, see layout rule induction, 5, 142 hypothesis, 142 on expressions, 151 on lists, 145 on numbers, 142, 144 on trees, 149 inequality, see = infinity, 128, 142 infix notation, 14 init, 58, 162 input/output, see IO instance, 111 Int, 19, 159 Integer , 19, 137, 159 Integral, 27, 57, 157 intToDigit, 159 IO, 88, 164 isAlpha, 78, 158 isAlphaNum, 78, 158 isDigit, 30, 78, 158 isLower , 78, 158 isSpace, 80, 158 isUpper , 78, 158 ISWIM, 6 iterate, 70, 163 keywords, 4, 15 lambda calculus, 6, 36 layout rule, 15, 77 length, 12, 39, 50, 65, 67, 163 lexicographic ordering, 25 Lisp, 6 lists, 4, 6, 11, 20, 38, 160 elements, 20, 33 empty, see [ ] indexing, see !!


pages: 329 words: 102,469

Free World: America, Europe, and the Surprising Future of the West by Timothy Garton Ash

Albert Einstein, battle of ideas, Berlin Wall, BRICs, British Empire, call centre, centre right, clean water, Columbine, continuation of politics by other means, cuban missile crisis, demographic transition, Deng Xiaoping, Doha Development Round, Eratosthenes, European colonialism, failed state, Fall of the Berlin Wall, Francis Fukuyama: the end of history, illegal immigration, income inequality, Intergovernmental Panel on Climate Change (IPCC), James Watt: steam engine, Kickstarter, Mikhail Gorbachev, Nelson Mandela, Peace of Westphalia, postnationalism / post nation state, Project for a New American Century, purchasing power parity, reserve currency, Ronald Reagan, shareholder value, Silicon Valley, Thomas Malthus, trade liberalization, Washington Consensus, working poor, working-age population, World Values Survey

The lifting of the Iron Curtain has therefore revealed a stage on which Europe must confront its own radical indeterminacy. In a sense, Europeans are now face-to-face with Eratosthenes, the Greek geographer who in about 220 bce drew Europe on a map, covering roughly the area we still know as Europe today.17 This purely geographical delineation, though arbitrary, has at least the sanction of great antiquity. Yet according to Eratosthenes, Europe stopped at the Bosporus. In the Roman and Byzantine periods, what is now western Turkey was part of a single Mediterranean world; but when Europeans started to draw proper maps again, in the fifteenth century, they followed Eratosthenes and drew the frontier on the Bosporus. Now, partly as a result of promises made during the Cold War, the European Union has crossed even that ancient line, explicitly recognizing Turkey as a European country.

The preamble, drafted by Valéry Giscard d’Estaing, refers only to “the cultural, religious and humanist inheritance of Europe,” see Draft Treaty Establishing a Constitution for Europe (Brussels: European Convention, 2003), p. 5. 16. Estimates from The Economist, March 6, 2004. 17. See the reconstruction of his map in John Goss, The Mapmaker’s Art: An Illustrated History of Cartography (New York: Rand McNally, 1993), p. 24. Eratosthenes appears to have placed the eastern frontier of Europe on the Don River. Only in the eighteenth century did the Urals come to be accepted as the conventional eastern frontier of the geographer’s Europe. 18. Quoted by Giuliano Amato in Mark Leonard (ed.), The Future Shape of Europe (London: Foreign Policy Centre, 2000), p. 32. 19. Quoted in Jeremy Black, Convergence or Divergence? Britain and the Continent (London: Macmillan, 1994), p. 164. 20.


Programming in Haskell by Graham Hutton

domain-specific language, Eratosthenes, first-past-the-post, type inference

Hence, by using factors, a simple function that decides if an integer is prime can be defined as follows: prime :: Int -> Bool prime n = factors n == [1,n] For example: > prime 15 False > prime 7 True Note that deciding that a number such as 15 is not prime does not require the function prime to produce all of its factors, because under lazy evaluation the result False is returned as soon as any factor other than one or the number itself is produced, which for this example is given by the factor 3. Returning to list comprehensions, using prime we can now define a function that produces the list of all prime numbers up to a given limit: primes :: Int -> [Int] primes n = [x | x <- [2..n], prime x] For example: > primes 40 [2,3,5,7,11,13,17,19,23,29,31,37] In chapter 15 we will present a more efficient program to generate prime numbers using the famous sieve of Eratosthenes, which has a particularly clear and concise implementation in Haskell using the idea of lazy evaluation. As a final example concerning guards, suppose that we represent a lookup table by a list of pairs of keys and values. Then for any type of keys that supports equality, a function find that returns the list of all values that are associated with a given key in a table can be defined as follows: find :: Eq a => a -> [(a,b)] -> [b] find k t = [v | (k’,v) <- t, k == k’] For example: > find ’b’ [(’a’,1),(’b’,2),(’c’,3),(’b’,4)] [2,4] 5.3The zip function The library function zip produces a new list by pairing successive elements from two existing lists until either or both lists are exhausted.

The first few iterations of this procedure can be illustrated as follows: Each row corresponds to one iteration of the procedure, with the first row being the initial sequence (step one), the first number in each row being circled to indicate its primality (step two), and all multiples of this number being underlined to indicate their deletion (step three) prior to the next iteration. In this manner, we can imagine the initial sequence of numbers falling downwards, with certain numbers being sieved out at each stage by the underlining, and the circled numbers forming the infinite sequence of primes: 2, 3, 5, 7, 11, 13, ... The above procedure for generating prime numbers is known as the sieve of Eratosthenes, after the Greek mathematician who first described it. This procedure can be translated directly into Haskell: primes :: [Int] primes = sieve [2..] sieve :: [Int] -> [Int] sieve (p:xs) = p : sieve [x | x <- xs, x ‘mod‘ p /= 0] That is, starting with the infinite list [2..] (step one), we apply the function sieve that retains the first number p as being prime (step two), and then calls itself recursively with a new list obtained by filtering all multiples of p from this list (steps three and four).

comprehensions list, 7, 47 set, 47, 56 string, 51 concat, 48, 206, 296 concatenation, see concat conjunction, see &&, and cons, see : const, 43, 287 continuation-passing style, 252 control characters, 24, 134 Control.Applicative, 179, 290 Control.Monad, 172, 183, 291 crush operators, 210 curry, 284 data, 93 Data.Char, 132, 140, 179, 282 Data.Foldable, 200, 205, 225, 294 Data.List, 35, 87, 140 Data.Monoid, 197, 292 defunctionalisation, 254 deriving, 100 digitToInt, 132, 282 disjunction, see ||, or distributivity, 156, 228, 243 contravariant, 235 div, 18, 35, 84, 281 division, see div, / do, 126, 166, 181 domain-specific languages, 7, 74 Double, 25, 283 Dr Seuss, 178 drop, 16, 64, 68, 286 dropWhile, 76, 286 effects, 7, 124, 162 elem, 202, 294 empty, 181, 291 Eq, 31, 49, 280 equality, see == equational reasoning, 8, 228, 257 error, 90, 190, 288 Euclid’s algorithm, 71 evaluation, 15, 22, 113, 212 call-by-name, 215, 216 call-by-value, 214, 216 innermost, 214 lazy, 7, 26, 40, 49, 51, 148, 150, 219 outermost, 214 top-level, 223 even, 38, 65, 283 examples abstract machine, 106, 261 base conversion, 83 binary string transmitter, 82 Caesar cipher, 52 calculator, 191 compiler, 241, 249 countdown problem, 111 expression parser, 187 fast reverse, 238 Fibonacci sequence, 64, 226 game of life, 133 game of nim, 129 hangman, 128 insertion sort, 63 Newton’s method, 227 prime numbers, 49, 222 quicksort, 10, 65 sieve of Eratosthenes, 222 tautology checker, 101 tic-tac-toe, 139 tree relabelling, 171 virtual machine, 256 voting algorithms, 86 exceptions, 160, 261 exponentiation, see ^ expressions, 3 arithmetic, 106, 111, 187, 241 conditional, see if impure, 125 lambda, see \ logical, 101 pure, 125 reducible, 213 False, 22, 24 filter, 75, 211, 285 filterM, 173 flip, 287 Float, 24, 54, 283 fmap, 154, 288 fold, 200, 294 Foldable, 200, 294 foldables, 7, 200 Maybe, 210 Tree, 202, 210 list, 201, 295 foldl, 68, 80, 200, 225, 294 foldl’, 225 foldl1, 203, 294 foldMap, 200, 294 foldr, 68, 77, 89, 200, 294 foldr1, 143, 203, 294 FP, 8 Fractional, 35, 281 fromIntegral, 54 fst, 41, 284 functions, 3, 16, 27, 287 combinator, 254 combinatorial, 114 composite, see .


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

(I’m using the present tense here because the essay is so intimate, it feels like he’s speaking to us today.) He shares his private intuition, a vulnerable, soft-bellied thing, and says he hopes that future mathematicians will use it to solve problems that eluded him. Today this secret is known as the Method. I never heard of it in calculus class. We don’t teach it anymore. But I found the story of it and the idea behind it enthralling and astounding. He writes about it in a letter to his friend Eratosthenes, the librarian at Alexandria and the only mathematician of his era who could understand him. He confesses that even though his Method “does not furnish an actual demonstration” of the results he’s interested in, it helps him figure out what’s true. It gives him intuition. As he says, “It is easier to supply the proof when we have previously acquired, by the method, some knowledge of the questions than it is to find it without any previous knowledge.”

He’s openly thinking of the triangle as a completed infinity of ribs. In doing so, he’s unleashing the golem. Likewise he describes the parabolic segment as being “made up of all the parallel lines drawn inside the curve.” Dallying with completed infinity lowers the status of this reasoning, in his estimation, to a heuristic—a means of finding an answer, not a proof of its correctness. In his letter to Eratosthenes, he downplays the Method as giving nothing more than “a sort of indication” that the conclusion is true. Whatever its logical status, Archimedes’s Method has an e pluribus unum quality to it. This Latin phrase, the motto of the United States, means “out of many, one.” Out of the infinitely many straight lines making up the parabola, one area emerges. Thinking of that area as a mass, Archimedes shifts it, line by line, to the far left seat on the seesaw.

Or, rather, that he was feeling the same things I feel and that all of my colleagues feel when we do mathematics. Although we are told that the past is a foreign country, it may not be foreign in every respect. People we read about in Homer and the Bible seem a lot like us. And the same appears to be true of ancient mathematicians, or at least of Archimedes, the only one who let us into his heart. Twenty-two centuries ago, Archimedes wrote a letter to his friend Eratosthenes, the librarian at Alexandria, essentially sending him a mathematical message in a bottle that virtually no one could appreciate but that he hoped might somehow sail safely across the seas of time. He had shared his private intuition, his Method, in the wish that it might enable future generations of mathematicians “to find other theorems which have not yet fallen to our share.” The odds were against him.


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

Needless to say, writing programs that depend on such subtleties is odious programming style. Part of the power of stream processing is that it lets us ignore the order in which events actually happen in our programs. Unfortunately, this is precisely what we cannot afford to do in the presence of assignment, which forces us to be concerned with time and change. 60 Eratosthenes, a third-century B.C. Alexandrian Greek philosopher, is famous for giving the first accurate estimate of the circumference of the Earth, which he computed by observing shadows cast at noon on the day of the summer solstice. Eratosthenes's sieve method, although ancient, has formed the basis for special-purpose hardware “sieves” that, until recently, were the most powerful tools in existence for locating large primes. Since the 70s, however, these methods have been superseded by outgrowths of the probabilistic techniques discussed in section 1.2.6. 61 We have named these figures after Peter Henderson, who was the first person to show us diagrams of this sort as a way of thinking about stream processing.

x 7))) integers)) Then we can find integers not divisible by 7 simply by accessing elements of this stream: (stream-ref no-sevens 100) 117 In analogy with integers, we can define the infinite stream of Fibonacci numbers: (define (fibgen a b) (cons-stream a (fibgen b (+ a b)))) (define fibs (fibgen 0 1)) Fibs is a pair whose car is 0 and whose cdr is a promise to evaluate (fibgen 1 1). When we evaluate this delayed (fibgen 1 1), it will produce a pair whose car is 1 and whose cdr is a promise to evaluate (fibgen 1 2), and so on. For a look at a more exciting infinite stream, we can generalize the no-sevens example to construct the infinite stream of prime numbers, using a method known as the sieve of Eratosthenes.60 We start with the integers beginning with 2, which is the first prime. To get the rest of the primes, we start by filtering the multiples of 2 from the rest of the integers. This leaves a stream beginning with 3, which is the next prime. Now we filter the multiples of 3 from the rest of this stream. This leaves a stream beginning with 5, which is the next prime, and so on. In other words, we construct the primes by a sieving process, described as follows: To sieve a stream S, form a stream whose first element is the first element of S and the rest of which is obtained by filtering all multiples of the first element of S out of the rest of S and sieving the result.

environment model of evaluation, [2] environment structure internal definitions local state message passing metacircular evaluator and procedure-application example rules for evaluation tail recursion and eq? (primitive procedure) for arbitrary objects as equality of pointers, [2] implementation for symbols numerical equality and equ? (generic predicate) equal-rat? equal? equality in generic arithmetic system of lists of numbers, [2], [3] referential transparency and of symbols equation, solving, see half-interval method; Newton's method; solve Eratosthenes error (primitive procedure) error handling in compiled code in explicit-control evaluator, [2] Escher, Maurits Cornelis estimate-integral estimate-pi, [2] Euclid's Algorithm, [2], see also greatest common divisor order of growth for polynomials Euclid's Elements Euclid's proof of infinite number of primes Euclidean ring Euler, Leonhard proof of Fermat's Little Theorem series accelerator euler-transform ev-application ev-assignment ev-begin ev-definition ev-if ev-lambda ev-quoted ev-self-eval ev-sequence with tail recursion without tail recursion ev-variable eval (lazy) eval (metacircular), [2] analyzing version data-directed primitive eval vs.


pages: 304 words: 82,395

Big Data: A Revolution That Will Transform How We Live, Work, and Think by Viktor Mayer-Schonberger, Kenneth Cukier

23andMe, Affordable Care Act / Obamacare, airport security, barriers to entry, Berlin Wall, big data - Walmart - Pop Tarts, Black Swan, book scanning, business intelligence, business process, call centre, cloud computing, computer age, correlation does not imply causation, dark matter, double entry bookkeeping, Eratosthenes, Erik Brynjolfsson, game design, IBM and the Holocaust, index card, informal economy, intangible asset, Internet of things, invention of the printing press, Jeff Bezos, Joi Ito, lifelogging, Louis Pasteur, Mark Zuckerberg, Menlo Park, Moneyball by Michael Lewis explains big data, Nate Silver, natural language processing, Netflix Prize, Network effects, obamacare, optical character recognition, PageRank, paypal mafia, performance metric, Peter Thiel, post-materialism, random walk, recommendation engine, self-driving car, sentiment analysis, Silicon Valley, Silicon Valley startup, smart grid, smart meter, social graph, speech recognition, Steve Jobs, Steven Levy, the scientific method, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, Thomas Davenport, Turing test, Watson beat the top human players on Jeopardy!

To datafy location requires a few prerequisites. We need a method to measure every square inch of area on Earth. We need a standardized way to note the measurements. We need an instrument to monitor and record the data. Quantification, standardization, collection. Only then can we store and analyze location not as place per se, but as data. In the West, quantification of location began with the Greeks. Around 200 B.C. Eratosthenes invented a system of grid lines to demarcate location, akin to latitude and longitude. But like so many good ideas from antiquity, the practice faded away over time. A millennium and a half later, around 1400 A.D., a copy of Ptolemy’s Geographia arrived in Florence from Constantinople just as the Renaissance and the shipping trade were igniting interest in science and in know-how from the ancients.

Its precision was enhanced for commercial applications a decade later. Accurate to one meter, GPS marked the moment when a method to measure location, the dream of navigators, mapmakers, and mathematicians since antiquity, was finally fused with the technical means to achieve it quickly, (relatively) cheaply, and without requiring any specialized knowledge. Yet the information must actually be generated. There was nothing to prevent Eratosthenes and Mercator from estimating their whereabouts every minute of the day, had they cared to. While feasible, that was impractical. Likewise, early GPS receivers were complex and costly, suitable for a submarine but not for everyone at all times. But this would change, thanks to the ubiquity of inexpensive chips embedded in digital gadgets. The cost of a GPS module tumbled from hundreds of dollars in the 1990s to about a dollar today at high volume.

See also books Amazon and, [>]–[>] and datafication, [>]–[>] and data-reuse, [>]–[>], [>]–[>] e-commerce: big data in, [>]–[>] economic development: big data in, [>]–[>] education: misuse of data in, [>] online, [>] edX, [>] Eisenstein, Elizabeth, [>] Elbaz, Gil, [>] election of 2008: data-gathering in, [>] electrical meters: data-gathering by, [>]–[>] energy: data compared to, [>] Equifax, [>], [>], [>] Eratosthenes, [>], [>] ergonomic data: Koshimizu analyzes, [>], [>], [>], [>]–[>] ethics: of big data, [>]–[>] Etzioni, Oren, [>], [>], [>], [>] analyzes airline fare pricing patterns, [>]–[>], [>], [>], [>], [>], [>], [>], [>], [>] Euclid, [>] European Union: open data in, [>] Evans, Philip, [>] exactitude. See also imprecision and big data, [>]–[>], [>], [>], [>], [>] in database design, [>]–[>], [>] and measurement, [>]–[>], [>] necessary in sampling, [>], [>]–[>] Excite, [>] Experian, [>], [>], [>], [>], [>] expertise, subject-area: role in big data, [>]–[>] explainability: big data and, [>]–[>] Facebook, [>], [>], [>]–[>], [>]–[>], [>], [>], [>], [>] data processing by, [>] datafication by, [>], [>] IPO by, [>]–[>] market valuation of, [>]–[>] uses “data exhaust,” [>] Factual, [>] Fair Isaac Corporation (FICO), [>], [>] Farecast, [>]–[>], [>], [>], [>], [>], [>], [>], [>], [>] finance: big data in, [>]–[>], [>], [>] Fitbit, [>] Flickr, [>]–[>] FlightCaster.com, [>]–[>] floor covering, touch-sensitive: and datafication, [>] Flowers, Mike: and government use of big data, [>]–[>], [>] flu: cell phone data predicts spread of, [>]–[>] Google predicts spread of, [>]–[>], [>], [>], [>], [>], [>], [>], [>] vaccine shots, [>]–[>] FlyOnTime.us, [>]–[>], [>]–[>] Ford, Henry, [>] Ford Motor Company, [>]–[>] Foursquare, [>], [>] Freakonomics (Leavitt), [>]–[>] free will: justice based on, [>]–[>] vs. predictive analytics, [>], [>], [>], [>]–[>] Galton, Sir Francis, [>] Gasser, Urs, [>] Gates, Bill, [>] Geographia (Ptolemy), [>] geospatial location: cell phone data and, [>]–[>], [>]–[>] commercial data applications, [>]–[>] datafication of, [>]–[>] insurance industry uses data, [>] UPS uses data, [>]–[>] Germany, East: as police state, [>], [>], [>] Global Positioning System (GPS) satellites, [>]–[>], [>], [>], [>] Gnip, [>] Goldblum, Anthony, [>] Google, [>], [>], [>], [>], [>], [>], [>], [>] artificial intelligence at, [>] as big-data company, [>] Books project, [>]–[>] data processing by, [>] data-reuse by, [>]–[>], [>], [>] Flu Trends, [>], [>], [>], [>], [>], [>] gathers GPS data, [>], [>], [>] Gmail, [>], [>] Google Docs, [>] and language translation, [>]–[>], [>], [>], [>], [>] MapReduce, [>], [>] maps, [>] PageRank, [>] page-ranking by, [>] predicts spread of flu, [>]–[>], [>], [>], [>], [>], [>], [>], [>] and privacy, [>]–[>] search-term analytics by, [>], [>], [>], [>], [>], [>] speech-recognition at, [>]–[>] spell-checking system, [>]–[>] Street View vehicles, [>], [>]–[>], [>], [>] uses “data exhaust,” [>]–[>] uses mathematical models, [>]–[>], [>] government: and open data, [>]–[>] regulation and big data, [>]–[>], [>] surveillance by, [>]–[>], [>]–[>] Graunt, John: and sampling, [>] Great Britain: open data in, [>] guilt by association: profiling and, [>]–[>] Gutenberg, Johannes, [>] Hadoop, [>], [>] Hammerbacher, Jeff, [>] Harcourt, Bernard, [>] health care: big data in, [>]–[>], [>], [>] cell phone data in, [>], [>]–[>] predictive analytics in, [>]–[>], [>] Health Care Cost Institute, [>] Hellend, Pat: “If You Have Too Much Data, Then ‘Good Enough’ Is Good Enough,” [>] Hilbert, Martin: attempts to measure information, [>]–[>] Hitwise, [>], [>] Hollerith, Herman: and punch cards, [>], [>] Hollywood films: profits predicted, [>]–[>] Honda, [>] Huberman, Bernardo: and social networking analysis, [>] human behavior: datafication and, [>]–[>], [>]–[>] human perceptions: big data changes, [>] IBM, [>] and electric automobiles, [>]–[>] founded, [>] and language translation, [>]–[>], [>] Project Candide, [>]–[>] ID3, [>] “If You Have Too Much Data, Then ‘Good Enough’ Is Good Enough” (Hellend), [>] Import.io, [>] imprecision.


pages: 566 words: 122,184

Code: The Hidden Language of Computer Hardware and Software by Charles Petzold

Bill Gates: Altair 8800, Claude Shannon: information theory, computer age, Donald Knuth, Douglas Engelbart, Douglas Engelbart, Dynabook, Eratosthenes, Grace Hopper, invention of the telegraph, Isaac Newton, Jacquard loom, James Watt: steam engine, John von Neumann, Joseph-Marie Jacquard, Louis Daguerre, millennium bug, Norbert Wiener, optical character recognition, popular electronics, Richard Feynman, Richard Stallman, Silicon Valley, Steve Jobs, Turing machine, Turing test, Vannevar Bush, Von Neumann architecture

I make use of a Boolean array (and almost every other feature we've learned about so far) in the final program of this chapter—a program that implements a famous algorithm for finding prime numbers called the Sieve of Eratosthenes. Eratosthenes (circa 276–196 BCE) was the librarian of the legendary library at Alexandria and is best remembered today for accurately calculating the circumference of the earth. Prime numbers are those whole numbers that are divisible without a remainder only by themselves and 1. The first prime number is 2 (the only even prime number), and the primes continue with 3, 5, 7, 11, 13, 17, and so forth. Eratosthenes' technique begins with a list of the positive whole numbers beginning with 2. Because 2 is a prime number, cross out all the numbers that are multiples of 2. (That's all the even numbers except 2.)

On the one hand, you have college curricula in Computer Science, and on the other hand, you have books such as Donald Knuth's famous The Art of Computer Programming series. "Rather," wrote physicist Richard Feynman, "computer science is like engineering—it is all about getting something to do something." If you ask 100 different people to write a program that prints out prime numbers, you'll get 100 different solutions. Even those programmers who use the Sieve of Eratosthenes won't implement it in precisely the same way that I did. If programming truly were a science, there wouldn't be so many possible solutions, and incorrect solutions would be more obvious. Occasionally, a programming problem incites flashes of creativity and insight, and that's the "art" part. But programming is mostly a designing and building process not unlike erecting a bridge. Many of the early programmers were scientists and engineers who could be expected to formulate their problems in the mathematical algorithms required by FORTRAN and ALGOL.


pages: 202 words: 58,823

Willful: How We Choose What We Do by Richard Robb

activist fund / activist shareholder / activist investor, Alvin Roth, Asian financial crisis, asset-backed security, Bernie Madoff, capital asset pricing model, cognitive bias, collapse of Lehman Brothers, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, delayed gratification, diversification, diversified portfolio, effective altruism, endowment effect, Eratosthenes, experimental subject, family office, George Akerlof, index fund, information asymmetry, job satisfaction, John Maynard Keynes: Economic Possibilities for our Grandchildren, lake wobegon effect, loss aversion, market bubble, market clearing, money market fund, Pareto efficiency, Paul Samuelson, Peter Singer: altruism, principal–agent problem, profit maximization, profit motive, Richard Thaler, Silicon Valley, sovereign wealth fund, survivorship bias, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, Thorstein Veblen, transaction costs, ultimatum game

People flourish not only in terms of consumption, but also because “a good economy promotes lives of vitality.”22 Phelps shows that this dynamism comes not from breakthroughs in basic science, the accumulation of physical capital, human capital (education and training), or the emergence of business geniuses like Bill Gates. If science were enough, dynamic economies would have sprung up at various points in the ancient world. The Greeks, for instance, achieved little by way of business or commercial innovation in spite of their astonishing scientific achievements. Not only did they know that the earth is round, around 240 BCE Eratosthenes calculated its circumference within a few thousand miles. They understood the causes of lunar and solar eclipses and accurately predicted when they would occur. Anaximander, born two hundred years before Aristotle, speculated that life first formed in water. Ancient Romans surmised that disease is caused by invisible little animals—an idea that could have made the Middle Ages considerably more pleasant, if only they had run with it.23 But unfortunately, most of this science never made it to the shop room floor.24 Having examined when commercial activity thrives and when it does not, Phelps concludes in Mass Flourishing, daringly for an economist, that values play a central role.

See also mercy ambiguity effect, 24 American Work-Sports (Zarnowski), 191 Anaximander, 190 anchoring, 168 angel investors, 212–213n1 “animal spirits,” 169 Antipater of Tarsus, 134–135, 137 “anxious vigilance,” 73, 82 arbitrage, 70, 78 Aristotle, 200, 220n24 Asian financial crisis (1997–1998), 13 asset-backed securities, 93–95 asset classes, 75 astrology, 67 asymmetric information, 96, 210n2 authenticity, 32–37, 114 of challenges, 176–179 autism, 58, 59 auto safety, 139 Bank of New York Mellon, 61 Battle of Waterloo, 71, 205 Bear Stearns, 85 Becker, Gary, 33, 108–109 behavioral economics, 4, 10, 198–199 assumptions underlying, 24 insights of, 24–25 rational choice complemented by, 6 Belgium, 191 beliefs: attachment to, 51 defined, 50 evidence inconsistent with, 54, 57–58 formation of, 53, 92 persistence of, 26–28, 54 transmissibility of, 92–93, 95–96 Bentham, Jeremy, 127, 197–198 “black swans,” 62–64 blame aversion, 57, 72 brain hemispheres, 161 Brexit, 181–185 “bull markets,” 78 capital asset pricing model, 64 care altruism, 38, 104, 108–114, 115, 120, 135, 201 Casablanca (film), 120, 125 The Cask of Amontillado (Poe), 126–127 challenges, 202–203 authenticity of, 176–179 staying in the game linked to, 179–181 changes of mind, 147–164 charity, 40, 45–46, 119, 128 choice: abundance of, 172–174 intertemporal, 149–158, 166 purposeful vs. rational, 22–23 Christofferson, Johan, 83, 86, 87, 88 Cicero, 133–134 Clark, John Bates, 167 cognitive bias, 6, 23, 51, 147–148, 167, 198–199 confirmation bias, 200 experimental evidence of, 10–11, 24 for-itself behavior disguised as, 200–201 gain-loss asymmetry, 10–11 hostile attribution bias, 59 hyperbolic discounting as, 158 lawn-mowing paradox and, 33–34 obstinacy linked to, 57 omission bias, 200 rational choice disguised as, 10–11, 33–34, 199–200 salience and, 29, 147 survivor bias, 180 zero risk bias, 24 Colbert, Claudette, 7 Columbia University, 17 commitment devices, 149–151 commodities, 80, 86, 89 commuting, 26, 38–39 competitiveness, 11, 31, 41, 149, 189 complementary skills, 71–72 compound interest, 79 confirmation bias, 57, 200 conspicuous consumption, 31 consumption planning, 151–159 contrarian strategy, 78 cooperation, 104, 105 coordination, 216n15 corner solutions, 214n8 cost-benefit analysis: disregard of, in military campaigns, 117 of human life, 138–143 credit risk, 11 crime, 208 Dai-Ichi Kangyo Bank (DKB), 12–14, 15, 17, 87, 192–193 Darwin, Charles, 62–63 depression, psychological, 62 de Waal, Frans, 118 Diogenes of Seleucia, 134–135, 137 discounting of the future, 10, 162–164 hyperbolic, 158, 201 disjunction effect, 174–176 diversification, 64–65 divestment, 65–66 Dostoevsky, Fyodor, 18 drowning husband problem, 6–7, 110, 116, 123–125 effective altruism, 110–112, 126, 130, 135–136 efficient market hypothesis, 69–74, 81–82, 96 Empire State Building, 211–212n12 endowment effect, 4 endowments, of universities, 74 entrepreneurism, 27, 90, 91–92 Eratosthenes, 190 ethics, 6, 104, 106–108, 116, 125 European Union, 181–182 experiential knowledge, 59–61 expert opinion, 27–28, 53, 54, 56–57 extreme unexpected events, 61–64 fairness, 108, 179 family offices, 94 Fear and Trembling (Kierkegaard), 53–54 “felicific calculus,” 197–198 financial crisis of 2007–2009, 61, 76, 85, 93–94, 95 firemen’s muster, 191 flow, and well-being, 201–202 Foot, Philippa, 133–134, 135 for-itself behavior, 6–7, 19, 21, 27, 36, 116, 133–134, 204–205, 207–208 acting in character as, 51–53, 55–56, 94–95, 203 acting out of character as, 69, 72 analyzing, 20 authenticity and, 33–35 charity as, 39–40, 45–46 comparison and ranking lacking from, 19, 24, 181 consequences of, 55–64 constituents of, 26–31 defined, 23–24 difficulty of modeling, 204 expert opinion and, 57 extreme unexpected events and, 63–64 flow of time and, 30 free choice linked to, 169–172 in groups, 91–100 incommensurability of, 140–143 in individual investing, 77–78 in institutional investing, 76 intertemporal choice and, 168, 175, 176 job satisfaction as, 189 mercy as, 114 misclassification of, 42, 44, 200–201 out-of-character trading as, 68–69 purposeful choice commingled with, 40–43, 129, 171 rationalizations for, 194–195 in trolley problem, 137 unemployment and, 186 France, 191 Fuji Bank, 14 futures, 80–81 gain-loss asymmetry, 10–11 Galperti, Simone, 217n1 gambler’s fallacy, 199 gamifying, 177 Garber, Peter, 212n1 Germany, 191 global equity, 75 Good Samaritan (biblical figure), 103, 129–130, 206 governance, of institutional investors, 74 Great Britain, 191 Great Depression, 94 Greek antiquity, 190 guilt, 127 habituation, 201 happiness research (positive psychology), 25–26, 201–202 Hayek, Friedrich, 61, 70 hedge funds, 15–17, 65, 75, 78–79, 93, 95 herd mentality, 96 heroism, 6–7, 19–20 hindsight effect, 199 holding, of investments, 79–80 home country bias, 64–65 Homer, 149 Homo ludens, 167–168 hostile attribution bias, 59 housing market, 94 Huizinga, Johan, 167–168 human life, valuation of, 138–143 Hume, David, 62, 209n5 hyperbolic discounting, 158, 201 illiquid markets, 74, 94 index funds, 75 individual investing, 76–82 Industrial Bank of Japan, 14 information asymmetry, 96, 210n2 innovation, 190 institutional investing, 74–76, 82, 93–95, 205 intergenerational transfers, 217n1, 218n4 interlocking utility, 108 intertemporal choice, 149–159, 166 investing: personal beliefs and, 52–53 in start-ups, 27 Joseph (biblical figure), 97–99 Kahneman, Daniel, 168 Kantianism, 135–136 Keynes, John Maynard, 12, 58, 167, 169, 188–189 Kierkegaard, Søren, 30, 53, 65, 88 Knight, Frank, 145, 187 Kranton, Rachel E., 210–211n2 labor supply, 185–189 Lake Wobegon effect, 4 lawn-mowing paradox, 33–34, 206 Lehman Brothers, 61, 86, 89, 184 leisure, 14, 17, 41, 154, 187 Libet, Benjamin, 161 life, valuation of, 138–143 Life of Alexander (Plutarch), 180–181 Locher, Roger, 117, 124 long-term vs. short-term planning, 148–149 loss aversion, 70, 199 lottery: as rational choice, 199–200 Winner’s Curse, 34–36 love altruism, 104, 116, 123–125, 126, 203 lying, vs. omitting, 134 Macbeth (Shakespeare), 63 MacFarquhar, Larissa, 214n6 Madoff, Bernard, 170 malevolence, 125–127 Malthus, Thomas, 212n2 manners, in social interactions, 104, 106, 107, 116, 125 market equilibrium, 33 Markowitz, Harry, 65 Marshall, Alfred, 41, 167 Mass Flourishing (Phelps), 189–191 materialism, 5 merchant’s choice, 133–134, 137–138 mercy, 104, 114–116, 203 examples of, 116–120 inexplicable, 45–46, 120–122 uniqueness of, 119, 129 mergers and acquisitions, 192 “money pump,” 159 monks’ parable, 114, 124 Montaigne, Michel de, 114, 118 mortgage-backed securities, 93 Nagel, Thomas, 161 Napoleon I, emperor of the French, 71 neoclassical economics, 8, 10, 11, 22, 33 Nietzsche, Friedrich, 21, 43, 209n5 norms, 104, 106–108, 123 Norway, 66 Nozick, Robert, 162 observed care altruism, 108–112 Odyssey (Homer), 149–150 omission bias, 200 On the Fourfold Root of the Principle of Sufficient Reason (Schopenhauer), 209n5 “on the spot” knowledge, 61, 70, 80, 94, 205 Orico, 13 overconfidence, 57, 200 “overearning,” 44–45 The Palm Beach Story (film), 7 The Paradox of Choice (Schwartz), 172 parenting, 108, 141, 170–171 Pareto efficiency, 132–133, 136, 139–140 Peirce, Charles Sanders, 53–54, 67, 94 pension funds, 66, 74–75, 93, 95 permanent income hypothesis, 179 Pharaoh (biblical figure), 97–99 Phelps, Edmund, 17, 189–191 Philip II, king of Macedonia, 181 planning, 149–151 for consumption, 154–157 long-term vs. short-term, 148–149 rational choice applied to, 152–158, 162 play, 44–45, 167, 202 pleasure-pain principle, 18 Plutarch, 180–181 Poe, Edgar Allan, 126 pollution, 132–133 Popeye the Sailor Man, 19 portfolio theory, 64–65 positive psychology (happiness research), 25–26, 201–202 preferences, 18–19, 198 aggregating, 38–39, 132, 164 altruism and, 28, 38, 45, 104, 110, 111, 116 in behavioral economics, 24, 168 beliefs’ feedback into, 51, 55 defined, 23 intransitive, 158–159 in purposeful behavior, 25, 36 risk aversion and, 51 stability of, 33, 115, 147, 207, 208 “time-inconsistent,” 158, 159, 166, 203 present value, 7, 139 principal-agent problem, 72 Principles of Economics (Marshall), 41 prisoner’s dilemma, 105 private equity, 75 procrastination, 3, 4, 19, 177–178 prospect theory, 168 protectionism, 185–187 Prussia, 191 public equities, 75 punishment, 109 purposeful choice, 22–26, 27, 34, 36, 56, 133–134, 204–205 altruism compatible with, 104, 113–114, 115–116 commensurability and, 153–154 as default rule, 43–46 expert opinion and, 57 extreme unexpected events and, 62–63 flow of time and, 30 for-itself behavior commingled with, 40–43, 129, 171 mechanistic quality of, 68 in merchant’s choice, 135, 137–138 Pareto efficiency linked to, 132 rational choice distinguished from, 22–23 regret linked to, 128 social relations linked to, 28 stable preferences linked to, 33 in trolley problem, 135–136 vaccination and, 58–59 wage increases and, 187.


pages: 462 words: 172,671

Clean Code: A Handbook of Agile Software Craftsmanship by Robert C. Martin

continuous integration, database schema, domain-specific language, don't repeat yourself, Donald Knuth, en.wikipedia.org, Eratosthenes, finite state, G4S, Ignaz Semmelweis: hand washing, iterative process, place-making, Rubik’s Cube, web application

Later I adapted the example for my book Agile Software Development, Principles, Patterns, and Practices and the first of my Craftsman articles published in Software Development magazine. What I find fascinating about this module is that there was a time when many of us would have considered it “well documented.” Now we see it as a small mess. See how many different comment problems you can find. Listing 4-7 GeneratePrimes.java /** * This class Generates prime numbers up to a user specified * maximum. The algorithm used is the Sieve of Eratosthenes. * <p> * Eratosthenes of Cyrene, b. c. 276 BC, Cyrene, Libya -- * d. c. 194, Alexandria. The first man to calculate the * circumference of the Earth. Also known for working on * calendars with leap years and ran the library at Alexandria. * <p> * The algorithm is quite simple. Given an array of integers * starting at 2. Cross out all multiples of 2. Find the next * uncrossed integer, and cross out all of its multiples

int count = 0; for (i = 0; i < s; i++) { if (f[i]) count++; // bump count. } int[] primes = new int[count]; // move the primes into the result for (i = 0, j = 0; i < s; i++) { if (f[i]) // if prime primes[j++] = i; } return primes; // return the primes } else // maxValue < 2 return new int[0]; // return null array if bad input. } } In Listing 4-8 you can see a refactored version of the same module. Note that the use of comments is significantly restrained. There are just two comments in the whole module. Both comments are explanatory in nature. Listing 4-8 PrimeGenerator.java (refactored) /** * This class Generates prime numbers up to a user specified * maximum. The algorithm used is the Sieve of Eratosthenes. * Given an array of integers starting at 2: * Find the first uncrossed integer, and cross out all its * multiples. Repeat until there are no more multiples * in the array. */ public class PrimeGenerator { private static boolean[] crossedOut; private static int[] result; public static int[] generatePrimes(int maxValue) { if (maxValue < 2) return new int[0]; else { uncrossIntegersUpTo(maxValue); crossOutMultiples(); putUncrossedIntegersIntoResult(); return result; } } private static void uncrossIntegersUpTo(int maxValue) { crossedOut = new boolean[maxValue + 1]; for (int i = 2; i < crossedOut.length; i++) crossedOut[i] = false; } private static void crossOutMultiples() { int limit = determineIterationLimit(); for (int i = 2; i <= limit; i++) if (notCrossed(i)) crossOutMultiplesOf(i); } private static int determineIterationLimit() { // Every multiple in the array has a prime factor that // is less than or equal to the root of the array size, // so we don’t have to cross out multiples of numbers // larger than that root.


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

And every speculation begins with a problem: problems in regard to the future can reach beyond the horizon of prediction too – and problems have solutions. In regard to understanding the physical world, we are in much the same position as Eratosthenes was in regard to the Earth: he could measure it remarkably accurately, and he knew a great deal about certain aspects of it – immensely more than his ancestors had known only a few centuries before. He must have known about such things as seasons in regions of the Earth about which he had no evidence. But he also knew that most of what was out there was far beyond his theoretical knowledge as well as his physical reach. We cannot yet measure the universe as accurately as Eratosthenes measured the Earth. And we, too, know how ignorant we are. For instance, we know from universality that AI is attainable by writing computer programs, but we have no idea how to write (or evolve) the right one.

Not the eternal and only home of mankind, but only a starting point of an infinite adventure. All you need do is make the decision [to end your static society]. It is yours to make.’ [With that decision] came the end, the final end of Eternity.– And the beginning of Infinity. Isaac Asimov, The End of Eternity (1955) The first person to measure the circumference of the Earth was the astronomer Eratosthenes of Cyrene, in the third century BCE. His result was fairly close to the actual value, which is about 40,000 kilometres. For most of history this was considered an enormous distance, but with the Enlightenment that conception gradually changed, and nowadays we think of the Earth as small. That was brought about mainly by two things: first, by the science of astronomy, which discovered titanic entities compared with which our planet is indeed unimaginably tiny; and, second, by technologies that have made worldwide travel and communication commonplace.

What is the difference between a computer simulation of a person (which must be a person, because of universality) and a recording of that simulation (which cannot be a person)? When there are two identical simulations under way, are there two sets of qualia or one? Double the moral value or not? Our world, which is so much larger, more unified, more intricate and more beautiful than that of Eratosthenes, and which we understand and control to an extent that would have seemed godlike to him, is nevertheless just as mysterious, yet open, to us now as his was to him then. We have lit only a few candles here and there. We can cower in their parochial light until something beyond our ken snuffs us out, or we can resist. We already see that we do not live in a senseless world. The laws of physics make sense: the world is explicable.


pages: 408 words: 114,719

The Swerve: How the Renaissance Began by Stephen Greenblatt

Albert Einstein, Bonfire of the Vanities, complexity theory, Eratosthenes, George Santayana, invention of movable type, invention of the printing press, Isaac Newton

That moment was the culmination of a lengthy process that braided together Greek and Roman high culture. The two cultures had not always been comfortably intertwined. Among the Greeks, Romans had long held the reputation of tough, disciplined people, with a gift for survival and a hunger for conquest. But they were also regarded as barbarians—“refined barbarians,” in the moderate view of the Alexandrian scientist Eratosthenes, crude and dangerous barbarians in the view of many others. When their independent city-states were still flourishing, Greek intellectuals collected some arcane lore about the Romans, as they did about the Carthaginians and Indians, but they did not find anything in Roman cultural life worthy of their notice. The Romans of the early republic might not altogether have disagreed with this assessment.

Starting as early as 300 BCE, the Ptolomaic kings who ruled Alexandria had the inspired idea of luring leading scholars, scientists, and poets to their city by offering them life appointments at the Museum, with handsome salaries, tax exemptions, free food and lodging, and the almost limitless resources of the library. The recipients of this largesse established remarkably high intellectual standards. Euclid developed his geometry in Alexandria; Archimedes discovered pi and laid the foundation for calculus; Eratosthenes posited that the earth was round and calculated its circumference to within 1 percent; Galen revolutionized medicine. Alexandrian astronomers postulated a heliocentric universe; geometers deduced that the length of a year was 365¼ days and proposed adding a “leap day” every fourth year; geographers speculated that it would be possible to reach India by sailing west from Spain; engineers developed hydraulics and pneumatics; anatomists first understood clearly that the brain and the nervous system were a unit, studied the function of the heart and the digestive system, and conducted experiments in nutrition.

Angelo, 20, 161 catasto (official inventory), 22 Catherine of Siena, Saint, 293n Catherine von Gebersweiler, 108 Catholic Church: apologetics of, 23–24, 47–48, 53–54, 97–108, 101, 208, 285n bureaucracy of, 85, 135–38, 157 corruption in, 136–41, 151–52, 165–66, 170–71, 181 Epicureanism opposed to, 7, 97–109, 182–84, 219–41, 249–62, 284n, 285n, 302n fundamentalism in, 89–108, 219–21, 227, 236, 239–40, 254–56 legal system of, 136–37, 158 literature of, 42, 43, 46–47 national factions in, 160, 163, 164, 176, 178, 205 as official religion, 89–108 paganism suppressed by, 10, 13, 19, 53–54, 75–78, 86–108, 117–18, 123, 129, 150, 222–24, 258, 283n, 284n, 286n papacy of, see specific popes schism in, 142–43, 155, 160, 161–78, 205 spiritual authority of, 100–109, 136–37, 149–50, 164–65, 168–69, 227, 230, 232 temporal authority of, 36, 135–37, 149–50, 157–58, 161–62, 239–40 theology of, 16, 17, 27, 75–76, 94–108, 120, 136–37, 163, 208, 252–54, 282n–83n, 285n Catullus, 53 celestial spheres, 5–6 Ceres, 183 Cervantes, 9, 142 Cervini, Marcello, 227 Cesena, 293n–94n chancery courts, 137 change, 5–7, 10, 186–87, 243–45, 259–60, 263 Charlemagne, 12, 47, 121 Chaucer, Geoffrey, 277n–78n children, 127, 137, 193, 194, 210, 212–13, 215 Chloris, 267n Chronicles of Herculaneum, 65 Chrysippus, 82 Chrysolaras, Manuel, 126 Church Fathers, 23–24, 47–48, 53–54, 99–100, 101, 208, 284n, 285n Cicero, Marcus Tullius, 23, 24, 43, 49, 53, 65, 69–70, 71, 72, 76, 85, 94–95, 96, 119, 120, 121–22, 123 138, 155–56, 176–77, 208, 273n, 274n, 283n, 289n, 296n, 300n Cicero, Quintus Tullius, 51 Ciompi (working-class revolutionaries), 114–15 city-states, 59, 122–24 Clare of Assisi, Saint, 108 Clement of Alexandria, 285n Clement VII, Pope, 293n, 294n Cleopatra, 281n clinamen (swerve) principle, 7–13, 188–89, 297n Cluny abbey, 176–77 codices, 39–40, 42–43, 62, 82–83, 89, 176–77 Colonna, Oddo, 205–6, 211, 269n Colonna family, 135 Colosseum, 63, 129 Columbanus, Saint, 27–28, 272n commentaries, 46, 221–41 conclaves, papal, 205–6 confession, 65, 143, 173, 255 Constance, 15, 19–20, 31, 35–36, 102, 162–78, 180, 206, 294n Constantine I, Emperor of Rome, 89, 102, 149–50, 224 Constantinople, 113, 169, 216 convents, 106, 108 Copernicus, Nicolaus, 10, 238, 254 Coptics, 24–25 copyists (librari), 85–86 copyright, 85 corporale supplicium (bodily punishments), 106 corporal punishment, 104–6 Correr, Angelo, 160, 180, 205 Cossa, Baldassare, see John XXIII (Baldassare Cossa), Antipope Cotta, Gaius Aurelius, 69–70 Council of Constance (1414–18), 15, 19–20, 31, 35–36, 102, 162–78, 180, 206, 294n Council of Trent (1545–63), 252, 253, 255 Counter-Reformation, 237–38, 253 courtiers, 8, 14, 15 Creech, Thomas, 257, 267n crime, 38, 104, 140, 228 crucifixions, 104, 112, 194, 241 cruelty, 194, 195, 198, 246, 298n cult objects, 90–91, 92 cults, 89–90 Cupid, 267n cyclical patterns, 10 Cyril, Saint, 91, 92–93 Damian, Peter, 107 Danae, 175 Dante Alighieri, 123, 132–33, 288n Darwin, Charles, 262 Darwin, Erasmus, 262 David, King, 43 day laborers (populo minuto), 114–15 Day of Judgment, 100 De aquaeductu urbis (Frontius), 152 death, fear of, 2–5, 9, 75–76, 112, 152, 180, 192–94, 196, 199, 220, 248 death sentences, 104, 158, 164, 172–73, 177–79, 213, 219, 228, 240–41, 255, 286n, 296n, 297n debate, 27–28 Decembrio, Pier Candido, 226 Declaration of Independence, 263 declinatio (swerve) principle, 7–13, 188–89, 297n della Robbia, Luca, 218 delusion, 195–97 Democritus, 74–75, 82 demons, 8, 10, 26, 89, 105, 194–95 De rerum natura (Lucretius), 182–202, 219–41 adaptation principle in, 189–90 afterlife denied in, 171, 183, 192–94, 195, 196–97, 220, 223, 230–32, 244, 260 Aldine edition of, 226 atheism in, 183–84, 221, 239, 259, 261 atomist theory in, 5–6, 8, 46, 73–75, 82, 99, 101, 185–89, 198–201, 220–21, 237, 239, 242–43, 244, 249, 250–53, 254, 255–56, 258, 260, 261, 297n, 306n author’s reading of, 1–13 beauty in, 1–2, 8–10, 11, 201–2, 228, 251, 260–61, 299n books and sections of, 65 Catholic doctrine opposed to, 7, 97–109, 182–84, 219–41, 249–62, 284n, 285n, 302n change and transition in, 5–7, 10, 186–87, 243–45, 259–60, 263 Cicero’s revision of, 53 classical references to, 49–52 commentaries on, 221–41 creation vs. destruction in, 186–89, 220, 249, 250–52, 261 cultural influence of, 11–13, 49–52, 182–83, 185, 204–5, 209–10, 218, 219–63, 302n cyclical patterns in, 10 dedication written for, 53 delusion in, 195–97 description of, 182–202 desire in, 197–98 detachment in, 195–97 disappearance of, 12–13, 49–52, 88–89, 209–10, 272n divine will in, 71, 74, 75, 102–3, 105, 187, 194–95, 220, 230–36, 249, 251, 285n emendations of, 226 English translations of, 184, 198, 201, 257–62, 267n, 297n–98n, 299n, 305n Epicurean philosophy of, 1–5, 58–59, 72–80, 88–89, 103, 104, 109, 182–202, 220–21, 222, 228–32, 244–46, 252–54, 256, 262–63, 303n eroticism in, 197–98, 201–2 ethics and morality in, 195–96 fear of death in, 2–5, 9, 192–94, 196, 199, 220, 248 free will in, 71, 74–75, 189 French translations of, 243–44, 247, 257, 262 gods and goddesses in, 1–2, 10, 183, 184, 193–94, 195, 197, 198, 199, 201–2, 228, 231–32, 251, 260–61, 298n, 299n as grammatical source, 12 happiness in, 195–97, 199 Herculaneum fragments of, 54–59, 64–65, 70–72, 81 hexameters of, 2, 182 historical influence of, 11–13 human existence in, 190–92 hymn to Venus in, 1–2, 10, 201–2, 228, 251, 260–61, 299n illusion in, 198–99 imagination in, 196–97 infinity in, 186, 187, 189, 196–97, 237, 239, 244, 256 “intelligent design” discredited by, 187–88, 220, 297n Italian translation of, 257, 262 language of, 2–3 Latin language of, 2–3, 12, 50, 182, 202, 225, 243, 247, 256 Machiavelli’s copy of, 221 manuscripts of, 11–13, 49–50, 88–89, 181, 182–85, 202, 203–5, 208–10, 218, 221–22, 225, 226, 231, 244, 256, 262, 272n, 300n materialism in, 9–10, 184–86, 190–91, 193, 198–201, 243, 244, 249, 259–63, 297n metaphors in, 201 in Middle Ages, 52–53, 88–89, 209–10, 272n modern influence of, 6–7, 8, 13, 185, 242–63 Montaigne’s copy of, 248–49, 256, 306n mythology in, 193–95 natural world in, 6, 10–11, 188–90, 262, 298n Niccoli’s transcription of, 203–4 “Oblongus” manuscript of, 204 paradise in, 191–92, 193 pleasure principle in, 8–10, 11, 75–80, 82, 102, 103–9, 195–98, 222–26, 228, 231 as poetry, 2–3, 50, 54, 80, 198, 200, 201–2, 221, 247, 259–60 Poggio’s copy of, 49–50, 203–5, 208–10, 225, 300n Poggio’s discovery of, 11–13, 22, 23–24, 49–50, 62, 65, 88–89, 93, 109, 181, 182–85, 202, 203–5, 218, 221–22, 225, 226, 231, 244, 256, 262 printed editions of, 204, 219, 248–50, 256, 262 Providence in, 187, 230–36, 251 “Quadratus” manuscript of, 204 readership of, 65–67, 70–72, 182, 209–10, 219–63 readings of, 71–72, 226 reason in, 199 religious superstitions opposed by, 2, 6, 10–11, 18–19, 36, 72, 74–75, 183, 184, 193–97, 199, 249, 299n Renaissance influenced by, 7–13 reputation of, 6–7, 8, 13, 51–52, 109, 185, 242–63 resurrection denied by, 171, 231–32 sexuality in, 103, 197–98, 201–2, 222, 247 soul in, 192–93, 196–97, 220, 231–32, 249, 251 space and time in, 186–89, 196–97, 237, 239, 244, 256 style of, 2–3, 7, 51 suffering in, 183, 195–98 swerve (clinamen) principle in, 7–13, 188–89, 297n syntax of, 182 title of, 46, 49, 181 translations of, 1–3, 184, 198, 201, 243–44, 247, 257–62, 267n, 297n–98n, 299n–300n, 305n universe as conceived in, 7–8, 73–74, 87, 186, 187, 189, 194, 220, 237, 238–39, 250–52, 306n void in, 187, 198–99 De rerum naturis (Maurus), 49 De runalibus (Serenus), 272n Descartes, René, 68, 239 desire, 197–98 detachment, 195–97 Deuteronomy, Book of, 285n dialogical disavowal, 222–23, 302n–3n Dialogue Concerning the Two Chief World Systems (Galileo), 255 dialogues, 69–72, 138–39, 147–49, 216–17, 222–26, 255, 302n–3n Diana, 99 Diderot, Denis, 262 Didymus of Alexandria, 81–82 Diogenes Laertius, 82, 278n diplomacy, 122–26, 155, 214 disciplina (whipping), 106 disillusion, 198–99 dispensations, 21, 136–37 divine will, 71, 74, 75, 102–3, 105, 187, 194–95, 220, 230–36, 249, 251, 285n divinity, 98–99, 183 documents, official, 56–57 Dominic, Saint, 108 Dominicans, 111, 168, 219, 240 Domitian, Emperor of Rome, 48, 275n Donatello, 211, 218 “Donation of Constantine,” 149–50, 224 Donne, John, 143 dowries, 301n drama, 77–78, 81, 94, 95, 104, 242–43 Dryden, John, 198, 201, 262, 267n, 297n–98n, 299n Duccio, 10 Dungal, 12 Duomo (Florence), 110, 113, 180, 217–18 Eastern Orthodox Church, 136 edicts, religious, 89–90 education, 24, 28, 59, 71, 91, 97, 104, 112–13, 121–22, 138–41, 151, 211, 214, 226 Egypt, 24–25, 42, 56–57, 61, 66, 84–94, 279n–80n Einstein, Albert, 262 elections, papal, 205–6, 293n Elijah, 90 Elsbeth of Oye, 108 emendations, textual, 226 empiricism, 73, 262–63 England, 163, 164, 205, 206–8, 227–40, 242–43, 257–62 English language, 184, 198, 201, 206, 257–62, 267n, 297n–98n, 299n, 305n Enlightenment, 262 Ennius, 273n Ephesus, 99 epic poetry, 48–49, 182, 243, 273n Epicurean, The (Erasmus), 227 Epicureanism, 1–5, 7, 58–59, 69–80, 82, 88–89, 97–109, 182–202, 219–41, 244–46, 249–63, 277n, 284n, 285n, 302n–3n Epicure Mammon, Sir, 77–78 Epicurus, 2, 62, 72–80, 101–2, 109, 222, 274n, 277n–78n Erasmus, 144, 227, 252 Eratosthenes, 59, 87 Ernst, Max, 1 eroticism, 197–98, 201–2 Essays (Montaigne), 243–49 Eton College, 248–49 Eucharist, 165, 252–53, 255–56 Euclid, 87 Eugenius IV, Pope, 211–12, 214, 290n Euripides, 81, 280n European Community, 205 Eve, 105 Evelyn, John, 257, 267n excommunication, 160, 166 executions, 104, 112, 158, 164, 172–73, 177–79, 213, 219, 228, 240–41, 255, 286n, 296n, 297n Expulsion of the Triumphant Beast, The (Bruno), 233–36 Facetiae (Poggio), 142–45, 146, 291n–92n Falstaff, Epicurus and, 102 families, 110, 112, 113–15, 127–29, 135, 137, 206, 210, 212–14 Fates, 195 Feast in the House of Levi, The (Veronese), 305n Ferreol, Saint, 38 Festus, Sextus Pompeius, 35 feudalism, 301n Ficino, Marsilio, 221, 224 Filelfo, Francesco, 143, 145 Fillastre, Guillaume, 295n fire, 41, 73, 83, 93, 191 Flaccus, Valerius, 272n, 300n flagellation, 28, 104, 106–9, 228, 285n–86n Flaubert, Gustave, 71 Florence, 10, 20–21, 22, 34, 49, 110, 113–34, 153, 162, 176, 179–80, 203, 210–18, 215–21, 226, 289n Florentine Republic, 122–26, 127, 215–17 Florentine Synod, 226 florins, 21, 211, 290n, 301n Florio, John, 243, 244 Foundling Hospital (Florence), 110 four elements, 73–74 Fra Angelico, 218 France, 11, 24, 38, 55, 122, 160, 163, 164, 176, 226, 233, 236, 249, 286n Franciscans, 111, 147–48 free will, 71, 74–75, 189 French language, 206, 243–44, 247, 257, 262 French Revolution, 11 Freud, Sigmund, 183 friars, 114, 143, 147–48, 163, 236, 240 Frontius, Julius, 152, 283n Fronto, Marcus Cornelius, 95 Frutti, Michaelle, 112 Fulda abbey, 44–50, 181 Galen, 87 Galileo Galilei, 8, 185, 239, 254–56, 306n Gamelion, 66 Ganymede, 140 Garcia Lopez (tailor), 236 Gassendi, Pierre, 257 Gaul, 106 Genesis, Book of, 3 geography, 87 geometry, 87 George of Trebizond, 21, 145–46, 215 Georgics (Virgil), 51–52, 273n Germany, 14–21, 29, 31, 33–34, 35, 36, 44–50, 159, 162, 164, 173–77, 181, 205, 206 Ghiberti, Lorenzo, 110, 218 Ghislieri, Michele, 227 Giotto, 113 Giunti, Filippo, 226 God, 10–11, 27, 37, 42, 89, 95, 97, 102–3, 105, 114, 166, 220, 233–36, 251, 253, 261, 285n gods and goddesses, 1–2, 5–6, 7, 10, 67–68, 71, 74, 88, 89, 98–99, 100, 101, 130, 139, 180, 183, 184, 193–94, 195, 197, 198, 199, 201–2, 226–27, 228, 231–36, 251, 260–61, 298n, 299n gold, 129, 280n Golden Age, 191 Gospels, 96, 97, 105 Gothic script, 115 Gothic Wars, 28, 49 Gottlieben Castle, 171 grain, 45, 66, 126, 279n–80n grammar, 12, 24, 25, 28–29, 31, 49, 97, 121 “Great Vanishing,” 86 Greek culture, 28, 59–60, 70, 72, 84, 87, 194–95 Greek language, 43, 88, 97, 119–20, 126, 217 Greek literature, 42, 58, 59, 60, 61, 62–63, 81, 84, 153, 182, 210, 228, 273n, 275n–76n see also specific works Greek philosophy, 72–80, 211, 252 Gregory I, Pope, 97, 103 Gregory XI, Pope, 293n Gregory XII, Antipope, 160, 180, 205 Guarino of Verona, 179 Guasconi, Biagio, 162 Guicciardini, Francesco, 127 guilds, 15, 16, 114 Gutenberg, Johann, 32, 219 Hamlet (Shakespeare), 3, 75, 233 handwriting, 37–38, 62, 112–13, 115–16, 121, 130, 135, 155–56, 179 happiness, 195–96, 198 Harriot, Thomas, 239 Harvey, William, 10 Hebrew language, 88, 95 Hebrews, 42, 283n Heidelberg, University of, 172 Heidenheim, 15 heliocentrism, 87, 306n Hell, 30, 288n Henry V, King of England, 206 Henry VIII, King of England, 228 Herculaneum, 54–59, 63–67, 68, 70–72, 77, 79, 81, 82 heresy, 13, 17, 155, 165, 166–68, 170–73, 177–79, 227, 233–41, 250–56 hermits, 35, 68, 107, 111 heroism, 104, 130 Hippolytus, 180 History of Florence (Poggio), 217 History of Rome (Livy), 23 Hobbes, Thomas, 10, 261 Holinshed Raphael, 228 holy orders, 120, 137–38, 147–48 Holy Roman Empire, 44, 120, 122, 155 Homer, 48–49, 62, 89, 182, 215 Hooke, Robert, 83–84 Hooker, Richard, 8 Horace, 84, 96 Houghton Library, 243 human existence, 190–92 humanities (studia humanitatis), 8–13, 23, 119–24, 134, 208, 214 Hume, David, 262 Hus, Jan, 166–68, 170, 171–72, 177, 253 Hutchinson, John, 257 Hutchinson, Lucy, 257–62, 267n, 305n hymn to Venus (Lucretius), 1–2, 10, 201–2, 228, 251, 260–61, 299n Hypatia of Alexandria, 91–93, 252, 282n hypocrisy, 37, 133, 138–39 Ignatius of Loyola, Saint, 108 Iliad (Homer), 3, 215 illness, 12, 75, 76–77, 104, 147, 195 illusion, 198–99 immortality, 6, 57, 75–76, 98, 99–100, 101, 150, 158, 159, 183, 192–95, 220, 223, 230–32, 244, 260 Incarnation, 98–99 inclinatio (swerve) principle, 7–13, 188–89, 297n Index of Prohibited Books, 227 India, 59, 87 indices, 39–40, 63, 227 individuality, 9–10, 16 indulgences, 158, 159, 161, 168 infallibility, 166 Inferno (Dante), 288n infinity, 186, 187, 189, 196–97, 237, 239, 244, 256 ink, 39, 40, 43, 82–86 Inquisition, 227, 236, 239–40, 254–56 Institutes (Quintillian), 177, 178–79, 296n intellectuals, 46–47, 51, 65–70, 87–88, 91–93, 122–26, 142–45, 227–33 “intelligent design,” 187–88, 220, 297n Iphegenia, 194 Ireland, 12, 38 Isaac, 194 Isambard, 236 Isidore of Seville, 12 Islam, 113, 282n–83n Italian language, 31, 206, 257, 262 italics, 115 Italy, 17, 21–22, 30, 31, 34, 43, 45, 60, 111, 122, 136, 160, 163, 174, 176, 205, 210–18, 233, 239–40, 249 see also specific towns and cities Janus, 99 Jefferson, Thomas, 262–63, 307n–8n Jerome, Saint, 53–54, 94–96, 109, 181, 283n Jerome of Prague, 168, 172–73, 177–79, 295n, 296n Jerusalem, 94 Jesuits, 250–51, 253–56 Jesus Christ, 9, 10, 19, 71, 98, 104–5, 107, 108, 139–40, 194, 236, 241, 252–53, 286n Jews, 3, 15, 39, 42, 67, 78, 87, 89, 91, 92, 98, 101, 136, 194, 227, 236, 283n Johann von Merlau, 45–46 John the Baptist, 90 John XXIII (Baldassare Cossa), Antipope, 152–78 abdication of, 160–61, 165–67, 170–80, 205 birthplace of, 158 as bishop of Rome, 137 as cardinal deacon of Bologna, 159–60 as cardinal of Florence, 179–80 corruption of, 136–41, 151–52, 165–66, 170–71, 181 at Council of Constance, 162–78, 180 criminal charges against, 170–71 curia of, 18, 19–21, 22, 31, 33, 36–37, 44, 45, 135–41, 144, 150–58, 161, 162–63, 165, 168–69, 170, 171, 180, 181 death of, 180 ecclesiastical career of, 158–60 election of, 154, 160, 161 entourage of, 137, 138, 161–62 in Florence, 162, 179–80 imprisonment of, 171, 179–80, 205 papacy of, 19–21, 22, 34, 44, 135–41, 150–78, 180, 205 papal name of, 171 Poggio’s relationship with, 157–58, 165–66, 170, 178, 180, 181, 205 poisoning accusation against, 159–60, 170–71 release of, 179–80 rival popes of, 160, 180, 205 in schism, 142–43, 155, 160, 161–78, 205 spiritual authority of, 136–37, 149–50, 164–65, 168–69 temporal authority of, 135–37, 157–58, 161–62 John XXIII (Angelo Roncalli), Pope, 171 Jonson, Ben, 77–78, 79, 243, 277n, 305n Jove, 75, 175, 233, 236 jubilee years, 159 Judaism, 39, 67, 101, 194, 236 Julian the Apostate, 101 Jung, Carl, 183 Jungkuntz, Richard, 285n Juno, 99 Jupiter, 88, 89, 100, 156 Jupiter Serapis, 88 Kaiserstuhl, 174 Kleve, Knut, 64 labor, manual, 25, 37 Lactantius, 102–3 Ladislas, King of Naples, 161–62 Lambin, Denys, 248–49, 256 landowners, 113–14, 228, 230 Lapo da Castiglionchio, 138–42, 144 Last Supper, 304n–5n Lateran palace, 156 Latin Festival, 69 Latin language, 2–3, 7, 12, 18, 19, 31–32, 42–52, 112–13, 119–22, 123–24, 130, 131–34, 135, 136, 138, 149, 155, 179, 180, 182, 202, 206, 210, 215, 217, 221–22, 225, 243, 247, 256 Latin literature, 42, 62–63, 81, 87, 117, 121–24, 182, 228, 273n, 275n, 289n see also specific works Laurentian Library, 115, 204, 290n laws, universal, 74–75 lawyers, 35, 137, 139 leap days, 87 legal systems, 17, 35, 38, 111–12, 125–26, 134, 137, 139, 158, 228, 232 legions, 59, 79 Leiden, University of, 204–5 Lent, 108 Leonardo da Vinci, 8, 9, 242 lettera antica, 121 letters patent, 137 Leucippus of Abdera, 73, 82 lexicography, 12, 35 liberty, 9–10, 16, 125, 239–40, 262–63 librarians, 29, 31–32, 39, 43, 50 libraries: monastic, 24–33, 37–38, 39, 43, 45–50, 65, 109, 117, 130–31, 152, 176–79, 204, 206–8, 209, 225, 271n–72n, 290n private, 54–60, 86, 94–96, 134 public, 54–63, 86–94, 91, 93, 130–31, 134, 275n–76n, 279n–83n, 290n Library of Pantainos, 276n Lippi, Filippo, 218 literacy, 17, 24–26, 93–94, 270n Livy, 23, 211 Lucca, 153 Luccarus, 112 Lucian of Samosta, 217 “Lucretiani,” 221 Lucretius (Titus Lucretius Carus: aesthetics of, 51 biography of, 52–54, 274n Cicero’s reference to, 51 classical references to, 23, 49–50, 51, 54 death of, 51, 53–54, 94, 109 as Epicurean, 1–2, 7, 52, 72–80, 104, 109, 222 family background of, 53 legacy of, 51–80, 109 madness ascribed to, 53–54, 94 name of, 49 Ovid’s reference to, 54 pacifism of, 52 as pagan, 53–54 readings by, 71–72 rediscovery of, 23–24, 43, 49–50 reputation of, 1–2, 7, 49–50, 51, 54, 71–72, 272n–73n in Rome, 71–72, 75 Saint Jerome’s account of, 53–54, 94, 109 skepticism of, 52, 72 suicide ascribed to, 53–54, 94, 109 Virgil influenced by, 51–52, 273n writings of, see De rerum natura (Lucretius) Lucullus, 155–56, 275n Ludwig von der Pfalz, 163 Luke, Saint, 105 Luna, Pedro de, 160, 205 Luther, Martin, 149, 172, 253 Macer, 23, 270n Machiavelli, Niccolò, 8, 144, 150, 185 Maestà (Duccio), 10 magic, 60–61, 73 Malpaghino, Giovanni, 121–22 Manilius, 48 manuscripts: annotation of, 23, 88, 221, 248–49, 256, 306n copies of, 17–18, 32–33, 35, 37–41, 47, 49, 50, 84–86, 88, 109, 112–16, 121, 130, 133–34, 135, 152, 154, 155–56, 173–77, 179, 206, 296n, 300n corruptions in, 41, 88 of De rerum natura, 11–13, 49–50, 88–89, 181, 182–85, 202, 203–5, 208–10, 218, 221–22, 225, 226, 231, 244, 256, 262, 272n, 300n destruction of, 7, 17–18, 23–24, 29, 41, 81–109, 130–31, 275n, 280n–83n editions of, 23, 87–88 fragments of, 54–59, 64–65, 70–72, 81 hunting for, 11–15, 22, 23–24, 29, 30, 31–36, 40, 42–43, 47–49, 53, 54, 62, 86, 88, 130, 131, 152–54, 176–81, 206–11, 212, 215, 218, 228, 300n illuminated, 17, 39, 40 market for, 28, 29–30, 84–86, 131 in monastic libraries, 24–33, 37–38, 39, 43, 45–50, 65, 109, 117, 130–31, 152, 176–79, 204, 206–8, 209, 225, 271n–72n, 290n on papyrus, 28, 40, 54–59, 62–65, 68, 69, 71, 77, 82–83, 88, 260, 280n, 283n on parchment, 17–18, 28, 38, 39–40, 42–43, 62, 82, 260, 283n printing of, 32, 38–39, 204, 219, 248–50, 256, 262, 279n in private libraries, 54–60, 86, 94–96, 134 production of, 28–29, 84–86 in public libraries, 54–63, 86–94, 91, 93, 130–31, 134, 275n–76n, 280n–83n, 290n references to, 23–24 scripts used for, 38, 84, 115–16, 121, 130 translation of, 88, 168, 210, 212, 215 see also specific books and manuscripts Manutius, Aldus, 32, 226 Marcellus, Nonius, 208 Marchetti, Alessandro, 257 Marco Datini, Francesco di, 114 Marcus Aurelius, Emperor of Rome, 71 Marolles, Michel de, 257 marriage, 127–29, 133, 136, 143, 212–13, 214, 215, 289n Mars, 2, 100, 226, 247, 281n Marsuppini, Carlo, 215 Martines, Lauro, 301n Martin V, Pope, 205–6, 211, 269n martyrs, 10, 107, 129 Marullo, Michele Tarchaniota, 226–27 Masaccio, 218 masks, ancestors, 62 master copies, 84–85 materialism, 9–10, 184–86, 190–91, 193, 198–201, 243, 244, 249, 259–63, 297n mathematics, 87, 91, 92, 239 Mazzei, Lapo, 111–12 Medici, Cosimo de,’ 216, 217, 290n Medici, Giovanni de,’ 213 Medici, Lorenzo de,’ 210, 213, 290n Medici family, 110, 210, 213, 215–16, 217, 290n, 301n medicine, 17, 60–61, 75, 87, 152 melancholy, 49, 133, 142–57, 216–17 Memmius, Gaius, 53, 273n–74n mendicant friars, 147–48 mental illness, 8, 19, 49, 133, 142–57, 216–17 mercenaries, 153, 293n–94n merchants, 15, 36, 219, 300n–301n Mercury, 233–36 messiahs, 67, 72–73, 98, 107, 184 Metrodorus, 277n Michelangelo, 9, 204 Michelozzi, Michelozzo di Bartolomeo, 110, 290n Micrographia (Hooke), 83–84 Middle Ages, 38, 52–53, 88–89, 106–8, 110–11, 116–17, 129, 132–33, 209–10, 251, 272n–73n Milan, 122, 153 Minerva, 99, 100 minims, 254 minuscules, 115 miracles, 142, 225 misogyny, 143, 212 missals, 17, 65 mistresses, 137, 141 Mithras, 90 moderation, 101–2 modernism, 6–7, 8, 13, 185, 242–63 Molière, 257 monasteries, 95, 106, 107–9, 111, 151, 168 see also libraries, monastic monks, 12, 21, 24–29, 31, 36–37, 90, 91, 131, 134, 147–48, 163, 180, 210, 211 Mons, 286n Montaigne, Michel Eyquem de, 9, 243–49, 256, 306n Monte Cassino, 152 Montepulciano, Bartolomeo Aragazzi da, 34–35, 44, 152–53, 162 morality, 11, 101–3, 124, 146–47, 178–79, 195–96 More, Thomas, 227–33, 236, 250, 251, 252, 263, 304n Morroni, Tomaso, 111 mortality rates, 191–92, 213 mortal sin, 16, 119 Mother of the Gods, 183 Mount Vesuvius, 54–59, 67, 94, 239 MS Rossi 884, 221 murder, 38, 148, 159–60, 170–71 Muses, 89 museums, 91, 93 music, 9, 70, 91, 93, 175, 219 mythology, 130, 193–96 Naples, 54–55, 60, 63, 64, 122, 153, 158, 161–62, 163, 233 natural world, 6, 10–11, 12, 70, 74–75, 188–90, 194, 248, 261–62, 298n Neptune, 99, 183, 226 Nero, Emperor of Rome, 48, 157, 275n New Testament, 24, 95–96, 97, 105 Newton, Isaac, 261 New World, 11–12, 136, 229–30 Niccoli, Niccolò, 126–34, 137–38, 222, 289n, 290n Nicholas V, Pope, 150, 214–15, 221, 226 nightmares, 95, 96 Nile River, 56, 174 Nolan philosophy, 233 “noonday demon,” 26 notaries, 84–85, 111–12, 122, 123, 135, 137 nuns, 106, 108 “Oblongus” manuscript, 204 obsessions, 4–5, 19, 116 “Of Cruelty” (Montaigne), 246 “Of Diversion” (Montaigne), 247 “Of Repentance” (Montaigne), 244–45 Old Testament, 43, 88, 95–96, 285n oligarchy, 110, 113–15, 135 Olivera, Alonso de, 249–50 Omar, Caliph, 282n–83n omnes cives studiosi (all learned citizens), 131 On Avarice (Poggio), 21, 133, 138, 147 On Nobility (Poggio), 147 On Pleasure (De voluptate) (Valla), 222–26, 303n “On some verses of Virgil” (Montaigne), 247 On the Excellence and Dignity of the Roman Court (Castiglionchio), 138–42, 144 On the Immense and the Numberless (Bruno), 239 On the Laws (De legibus) (Cicero), 155–56 On the Misery of Human Life (Poggio), 147 On the Nature of Things (De rerum natura) (Lucretius), see De rerum natura (Lucretius) On the Republic (Cicero), 43 On the Unhappiness of Princes (Poggio), 214 On the Vicissitudes of Fortune (De varietate fortunae) (Poggio), 147, 294n Opticks (Newton), 261 Orations (Cicero), 208 oratory, 31, 70, 93, 177–78 Order of St.


pages: 422 words: 119,123

To the Edges of the Earth: 1909, the Race for the Three Poles, and the Climax of the Age of Exploration by Edward J. Larson

back-to-the-land, British Empire, Charles Lindbergh, Eratosthenes, European colonialism, Fellow of the Royal Society, Livingstone, I presume, Scientific racism, the scientific method, trade route, yellow journalism

Only then, with the rising appeal of adventure travel and increasing economic and technological means for Europeans to reach ever more remote locations, did interest in the Arctic shift from the pragmatic goal of finding a Northwest Passage to a romantic one of attaining the North Pole. Not that the notion of a North Pole was anything new. At least since the third century before Christ, when Greek mapmaker Eratosthenes laid a grid of parallels and meridians on the Pythagorean concept of a spherical earth, educated Europeans had known that a geometric point, or “pole,” should mark the globe’s northernmost spot. Even Eratosthenes portrayed the Arctic as a frozen realm, however, and no one seemed interested in seeking its northern limit for over two millennia. Yet something in the pristine splendor and primeval struggle depicted in the tales brought back from the Northwest Passage expeditions captured the English imagination at the dawn of the Romantic era.

See also Great Ice Plateau; Polar Plateau Eckenstein, Oscar, 219–20 Ecuador, 88 Edward VII, xv, 80, 93, 120–22, 219, 263 Edward VII Land. See King Edward VII Land Edward VIII, 120 Egingwah, 205, 211–12 Elephant Island, 269 Elkins, Katherine, 1–3, 94, 219, 278 Ellesmere Island, 6–9, 36–43, 46, 99, 102, 106, 143, 148, 151, 259; exploration of, 113–14, 158 Encyclopedia Britannica, 221 Endurance (ship), 269 England, 120–22, 172, 209, 267, 276. See also Britain Eratosthenes, 4 Erebus (ship), 52 Erik (ship), 42, 146, 150–54, 156 Eskimo, as Peary’s term for Inuit, xx, 24, 29, 33, 104, 192 Etah, Greenland, 39–43, 117, 149–53, 156, 194, 259–60 Etukishuk, 151, 259–60 Evening Post (New York), 2 Exploration, Age of, xvi, 144 Explorer’s Club (New York), 103, 274–75 farthest north, 9–10, 15–17, 44, 74, 108–11, 157 farthest south, 48, 52, 59–61, 166, 178, 190 Fenoillet, Alexis, 15, 20 Ferrar, Hartley, 66–67 Fort Conger, 9–10, 35–38, 41, 99, 104, 149 Fort Portal, Uganda, 91 Foundation for the Promotion of the Art of Navigation, 213 Fram (ship), 11–12, 19, 30, 36, 38, 100, 273 France, 51, 56, 99, 278 Franke, Rudolph, 117, 151–54, 156 Frankenstein (book), xvii, 5, 77 Franklin, John, 4, 267 Franklin searches, 4, 6–7, 82 Franz Joseph Land, 12–21, 101 Frobisher, Martin, 4 frostbite, 14, 16, 104, 143, 198, 240, 245, 248, 266 Funafuti Islands, 67–69, 127 Furious Fifties, 51, 126–27 Gagarin, Yuri, 281 Gasherbrum massif, 231, 233 geography, study of, 53–56, 65, 88–89, 101–2 geology, science of, 50, 65–71, 223; Antarctic research in, 132, 137, 164–65, 184 George V, 121, 163 Gerlache, Adrian de, 55, 280 Germany, 55, 87, 99 Giordano, Felice, 83 glaciers, 62, 90–92, 137, 166, 179–83, 218–19, 224–48, 281 Glasgow, Scotland, 74, 95 Glenn, John, 281 Godwin-Austin, Henry, 219 Godwin-Austin Glacier, 219, 226–28, 230–32 Goodsell, John, 147, 151, 159, 161, 194–98, 258 Great Ice Barrier, 52, 58–59, 61, 129–30, 166.


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

Part of the power of stream processing is that it lets us ignore the order in which events actually happen in our programs. Unfortunately, this is precisely what we cannot afford to do in the presence of assignment, which forces us to be concerned with time and change. 188 Eratosthenes, a third-century B.C. Alexandrian Greek philosopher, is famous for giving the first accurate estimate of the circumference of the Earth, which he computed by observing shadows cast at noon on the day of the summer solstice. Eratosthenes’s sieve method, although ancient, has formed the basis for special-purpose hardware “sieves” that, until recently, were the most powerful tools in existence for locating large primes. Since the 70s, however, these methods have been superseded by outgrowths of the probabilistic techniques discussed in 1.2.6. 189 We have named these figures after Peter Henderson, who was the first person to show us diagrams of this sort as a way of thinking about stream processing.

x 7))) integers)) Then we can find integers not divisible by 7 simply by accessing elements of this stream: (stream-ref no-sevens 100) 117 In analogy with integers, we can define the infinite stream of Fibonacci numbers: (define (fibgen a b) (cons-stream a (fibgen b (+ a b)))) (define fibs (fibgen 0 1)) Fibs is a pair whose car is 0 and whose cdr is a promise to evaluate (fibgen 1 1). When we evaluate this delayed (fibgen 1 1), it will produce a pair whose car is 1 and whose cdr is a promise to evaluate (fibgen 1 2), and so on. For a look at a more exciting infinite stream, we can generalize the no-sevens example to construct the infinite stream of prime numbers, using a method known as the sieve of Eratosthenes.188 We start with the integers beginning with 2, which is the first prime. To get the rest of the primes, we start by filtering the multiples of 2 from the rest of the integers. This leaves a stream beginning with 3, which is the next prime. Now we filter the multiples of 3 from the rest of this stream. This leaves a stream beginning with 5, which is the next prime, and so on. In other words, we construct the primes by a sieving process, described as follows: To sieve a stream S, form a stream whose first element is the first element of S and the rest of which is obtained by filtering all multiples of the first element of S out of the rest of S and sieving the result.

Knuth, Fundamental Algorithms (Volume 1 of The Art of Computer Programming) Jump to: A B C D E F G H I K L M N O P Q R S T U V W Z Index Entry Section A abstract models: 2.1.3 abstract syntax: 4.1.1 abstraction barriers: Chapter 2 abstraction barriers: 2.1.2 accumulator: 2.2.3 accumulator: 3.1.1 acquired: 3.4.2 action: 5.1.1 additive: 2.4.3 additively: Chapter 2 additively: 2.4 address: 5.3.1 address arithmetic: 5.3.1 agenda: 3.3.4 algebraic specification: 2.1.3 aliasing: 3.1.3 and-gate: 3.3.4 applicative-order: 4.2.1 applicative-order evaluation: 1.1.5 arbiter: 3.4.2 arguments: 1.1.1 assembler: 5.2.1 assertions: 4.4.1 assignment operator: 3.1 atomically: 3.4.2 automatic storage allocation: 5.3 average damping: 1.3.3 B B-trees: 2.3.3 backbone: 3.3.3 backquote: 5.5.2 backtracks: 4.3.1 balanced: 2.2.2 barrier synchronization: 3.4.2 base address: 5.3.1 Bertrand’s hypothesis: 3.5.2 bignum: 5.3.1 bindings: 3.2 binds: 1.1.8 binomial coefficients: 1.2.2 block structure: 1.1.8 bound variable: 1.1.8 box-and-pointer notation: 2.2 breakpoint: 5.2.4 broken heart: 5.3.2 bugs: Chapter 1 C cache-coherence: 3.4.1 call-by-name: 3.5.1 call-by-name: 4.2.2 call-by-name thunks: 3.5.1 call-by-need: 3.5.1 call-by-need: 4.2.2 call-by-need thunks: 3.5.1 capturing: 1.1.8 Carmichael numbers: 1.2.6 case analysis: 1.1.6 cell: 3.4.2 chronological backtracking: 4.3.1 Church numerals: 2.1.3 Church-Turing thesis: 4.1.5 clauses: 1.1.6 closed world assumption: 4.4.3 closure: Chapter 2 closure property: 2.2 code generator: 5.5.1 coerce: 2.5.2 coercion: 2.5.2 combinations: 1.1.1 comments: 2.2.3 compacting: 5.3.2 compilation: 5.5 compile-time environment: 5.5.6 composition: 1.3.4 compound data: Chapter 2 compound data object: Chapter 2 compound procedure: 1.1.4 computability: 4.1.5 computational process: Chapter 1 concurrently: 3.4 congruent modulo: 1.2.6 connectors: 3.3.5 consequent expression: 1.1.6 constraint networks: 3.3.5 constructors: 2.1 continuation procedures: 4.3.3 continued fraction: 1.3.3 control structure: 4.4.3 controller: 5.1 conventional interfaces: Chapter 2 conventional interfaces: 2.2.3 current time: 3.3.4 D data: Chapter 1 data: 2.1.3 data abstraction: Chapter 2 data abstraction: 2.1 data paths: 5.1 data-directed: 2.4 data-directed programming: Chapter 2 data-directed programming: 2.4.3 deadlock: 3.4.2 deadlock-recovery: 3.4.2 debug: Chapter 1 deep binding: 4.1.3 deferred operations: 1.2.1 delayed argument: 3.5.4 delayed evaluation: Chapter 3 delayed evaluation: 3.5 delayed object: 3.5.1 dense: 2.5.3 dependency-directed backtracking: 4.3.1 depth-first search: 4.3.1 deque: 3.3.2 derived expressions: 4.1.2 digital signals: 3.3.4 dispatching on type: 2.4.3 displacement number: 5.5.6 dotted-tail notation: 2.2.1 driver loop: 4.1.4 E empty list: 2.2.1 encapsulated: 3.1.1 enclosing environment: 3.2 entry points: 5.1.1 enumerator: 2.2.3 environment: 1.1.2 environment model: Chapter 3 environments: 3.2 Euclid’s Algorithm: 1.2.5 Euclidean ring: 2.5.3 evaluating: 1.1.1 evaluator: Chapter 4 event-driven simulation: 3.3.4 evlis tail recursion: 5.4.1 execution procedure: 4.1.7 explicit-control evaluator: 5.4 expression: 1.1.1 F failure continuation: 4.3.3 FIFO: 3.3.2 filter: 1.3.1 filter: 2.2.3 first-class: 1.3.4 fixed point: 1.3.3 fixed-length: 2.3.4 forcing: 4.2.2 forwarding address: 5.3.2 frame: 4.4.2 frame coordinate map: 2.2.4 frame number: 5.5.6 framed-stack: 5.4.1 frames: 3.2 free: 1.1.8 free list: 5.3.1 front: 3.3.2 full-adder: 3.3.4 function boxes: 3.3.4 functional programming: 3.1.3 functional programming languages: 3.5.5 G garbage: 5.3.2 garbage collection: 5.3 garbage collection: 5.3.2 garbage collector: 3.3.1 garbage-collected: 4.2.2 generic operations: Chapter 2 generic procedures: 2.3.4 generic procedures: 2.4 glitches: Chapter 1 global: 1.2 global: 3.2 global environment: 1.1.2 golden ratio: 1.2.2 grammar: 4.3.2 H half-adder: 3.3.4 half-interval method: 1.3.3 Halting Theorem: 4.1.5 headed list: 3.3.3 hiding principle: 3.1.1 hierarchical: 2.2 hierarchy of types: 2.5.2 higher-order procedures: 1.3 Horner’s rule: 2.2.3 I imperative programming: 3.1.3 indeterminates: 2.5.3 index: 5.3.1 indexing: 4.4.2 instantiated with: 4.4.1 instruction counting: 5.2.4 instruction execution procedure: 5.2.1 instruction sequence: 5.5.1 instruction tracing: 5.2.4 instructions: Chapter 5 instructions: 5.1.1 integerizing factor: 2.5.3 integers: 1.1 integrator: 3.5.3 interning: 5.3.1 interpreter: Chapter 1 interpreter: Chapter 4 invariant quantity: 1.2.4 inverter: 3.3.4 iterative improvement: 1.3.4 iterative process: 1.2.1 K k-term: 1.3.3 key: 2.3.3 L labels: 5.1.1 lazy evaluation: 4.2.1 lexical address: 5.5.6 lexical addressing: 4.1.3 lexical scoping: 1.1.8 linear iterative process: 1.2.1 linear recursive process: 1.2.1 linkage descriptor: 5.5.1 list: 2.2.1 list: 2.2.1 list: 2.2.1 list structure: 2.2.1 list-structured: 2.1.1 list-structured memory: 5.3 local evolution: 1.2 local state variables: 3.1 location: 5.3.1 logic-programming: Chapter 4 logical and: 3.3.4 logical deductions: 4.4.1 logical or: 3.3.4 M machine language: 5.5 macro: 4.1.2 map: 2.2.3 mark-sweep: 5.3.2 memoization: 1.2.2 Memoization: 3.3.3 memoize: 4.2.2 merge: 3.5.5 message passing: 2.1.3 message passing: 2.4.3 message-passing: 3.1.1 metacircular: 4.1 Metalinguistic abstraction: Chapter 4 Miller-Rabin test: 1.2.6 modular: Chapter 3 modulo: 1.2.6 modulo: 1.2.6 modus ponens: 4.4.3 moments in time: 3.4 Monte Carlo integration: 3.1.2 Monte Carlo simulation: 3.1.2 mutable data objects: 3.3 mutators: 3.3 mutex: 3.4.2 mutual exclusion: 3.4.2 N n-fold smoothed function: 1.3.4 native language: 5.5 needed: 5.5.1 networks: Chapter 4 Newton’s method: 1.3.4 nil: 2.2.1 non-computable: 4.1.5 non-strict: 4.2.1 nondeterministic: 3.4.1 nondeterministic choice point: 4.3.1 nondeterministic computing: Chapter 4 nondeterministic computing: 4.3 normal-order: 4.2.1 normal-order evaluation: 1.1.5 normal-order evaluation: Chapter 4 O obarray: 5.3.1 object program: 5.5 objects: Chapter 3 open-code: 5.5.5 operands: 1.1.1 operator: 1.1.1 operator: 4.1.6 or-gate: 3.3.4 order of growth: 1.2.3 ordinary: 2.5.1 output prompt: 4.1.4 P package: 2.4.3 painter: 2.2.4 pair: 2.1.1 pair: 2.1.1 parse: 4.3.2 Pascal’s triangle: 1.2.2 pattern: 4.4.1 pattern matcher: 4.4.2 pattern matching: 4.4.2 pattern variable: 4.4.1 pipelining: 3.4 pointer: 2.2 poly: 2.5.3 power series: 3.5.2 predicate: 1.1.6 predicate: 1.1.6 prefix: 2.3.4 prefix code: 2.3.4 prefix notation: 1.1.1 pretty-printing: 1.1.1 primitive constraints: 3.3.5 probabilistic algorithms: 1.2.6 procedural abstraction: 1.1.8 procedural epistemology: Preface 1e procedure: 1.2.1 procedure definitions: 1.1.4 procedures: Chapter 1 process: 1.2.1 program: Chapter 1 programming languages: Chapter 1 prompt: 4.1.4 pseudo-random: 3.1.2 pseudodivision: 2.5.3 pseudoremainder: 2.5.3 Q quasiquote: 5.5.2 queries: 4.4 query language: 4.4 queue: 3.3.2 quote: 2.3.1 R Ramanujan numbers: 3.5.3 rational functions: 2.5.3 RC circuit: 3.5.3 read-eval-print loop: 1.1.1 reader macro characters: 4.4.4.7 real numbers: 1.1 rear: 3.3.2 recursion equations: Chapter 1 Recursion theory: 4.1.5 recursive: 1.1.3 recursive: 1.1.8 recursive process: 1.2.1 red-black trees: 2.3.3 referentially transparent: 3.1.3 register machine: Chapter 5 register table: 5.2.1 registers: Chapter 5 released: 3.4.2 remainder of: 1.2.6 resolution principle: 4.4 ripple-carry adder: 3.3.4 robust: 2.2.4 RSA algorithm: 1.2.6 rules: 4.4 rules: 4.4.1 S satisfy: 4.4.1 scope: 1.1.8 selectors: 2.1 semaphore: 3.4.2 separator code: 2.3.4 sequence: 2.2.1 sequence accelerator: 3.5.3 sequences: 1.3.1 serializer: 3.4.2 serializers: 3.4.2 series RLC circuit: 3.5.4 shadow: 3.2 shared: 3.3.1 side-effect bugs: 3.1.3 sieve of Eratosthenes: 3.5.2 smoothing: 1.3.4 source language: 5.5 source program: 5.5 sparse: 2.5.3 special forms: 1.1.3 stack: 1.2.1 stack: 5.1.4 state variables: 1.2.1 state variables: 3.1 statements: 5.5.1 stop-and-copy: 5.3.2 stratified design: 2.2.4 stream processing: 1.1.5 streams: Chapter 3 streams: 3.5 streams: 3.5 strict: 4.2.1 subroutine: 5.1.3 substitution: 1.1.5 substitution model: 1.1.5 subtype: 2.5.2 success continuation: 4.3.3 summation of a series: 1.3.1 summer: 3.5.3 supertype: 2.5.2 symbolic expressions: Chapter 2 syntactic sugar: 1.1.3 syntax: 4.1 systematically search: 4.3.1 systems: Chapter 4 T tableau: 3.5.3 tabulation: 1.2.2 tabulation: 3.3.3 tagged architectures: 5.3.1 tail-recursive: 1.2.1 tail-recursive: 5.4.2 target: 5.5.1 thrashing: UTF thunk: 4.2.2 thunks: 4.2.2 time: 3.4 time segments: 3.3.4 tower: 2.5.2 tree accumulation: 1.1.3 tree recursion: 1.2.2 trees: 2.2.2 truth maintenance: 4.3.1 Turing machine: 4.1.5 type field: 5.3.1 type tag: 2.4.2 type tags: 2.4 type-inferencing: 3.5.4 typed pointers: 5.3.1 U unbound: 3.2 unification: 4.4 unification: 4.4.2 unification: 4.4.2 unification algorithm: 4.4 univariate polynomials: 2.5.3 universal machine: 4.1.5 upward-compatible extension: 4.2.2 V value: 1.1.2 value of a variable: 3.2 values: 2.3.1 variable: 1.1.2 variable-length: 2.3.4 vector: 5.3.1 W width: 2.1.4 wires: 3.3.4 wishful thinking: 2.1.1 Z zero crossings: 3.5.3 Jump to: A B C D E F G H I K L M N O P Q R S T U V W Z Next: Colophon, Prev: Figures, Up: Top [Contents] Prev: Term Index, Up: Top [Contents] Colophon On the cover page is Agostino Ramelli’s bookwheel mechanism from 1588.


pages: 283 words: 85,906

The Clock Mirage: Our Myth of Measured Time by Joseph Mazur

Albert Einstein, Alfred Russel Wallace, Arthur Eddington, computer age, Credit Default Swap, Danny Hillis, Drosophila, Eratosthenes, Henri Poincaré, Intergovernmental Panel on Climate Change (IPCC), invention of movable type, Isaac Newton, Jeff Bezos, job automation, Mark Zuckerberg, mass immigration, Pepto Bismol, self-driving car, Stephen Hawking, twin studies

Doubling the volume of a cube was at that time a rather profound proportion problem involving some tricky geometry. But Apollo might have had a weightier motive: to stir “the entire Greek nation to give up war and its miseries and cultivate the Muses, and by calming their passions through the practice of discussion and study of mathematics.”4 The original story was relayed to us by the Greek philosopher Theon of Smyrna from the third-century BC Platonic philosopher Eratosthenes, through his book The Platonist.5 It involves the ancients’ futile attempts at solving this problem, one that seemed simple: given the edge of a cube, construct the edge of a second cube whose volume is double that of the first. The doubling problem, however, must be solved with just the tools of straightedge and compass, because to prove its success the only accessible logical tool would have to have come from Euclid’s first principles.

Who, 121 Dumbelton, John, 81 Duration of time, sense of, 32–33, 139, 153, 156–57, 168–69, 221 Dutch clocks, 36 Dysrhythmia, 213–14 Earth: age of, 65–72 circumference of, 6–7 life on, 43 orbit around sun, 118–19, 124, 214, 224 rotation of, 33, 39, 51, 64, 180, 203, 218 world line, 123–24 Ecclesiastes, 39, 225 Eddington, Arthur, 93 Egypt, timekeeping in, 5–6, 7 Egyptian calendar, 40 Einstein, Albert: definition of time, 106–10, 147 and Poincaré, 105–6 relativity theory of, 70, 93, 94, 95, 97, 101, 110–11, 129 “Zur Elektrodynamik bewegter Körper,” 93–94, 106 Electromagnetic fields, as synchronizers, 214 End of life, proximity to, 157 Entropy, 131 Eratosthenes, The Platonist, 53 Euclid, 53, 79, 99 Exoplanets, 218–22 Eye: and depth perception, 205 Des-cartes’ analysis of, 177, 178–79, 180 Eyelid transparency, 181–82 Farey, John, Jr., 8 Fear, hormonal effect of, 210 Federal Aviation Administration, 207–8 Feng Tian, 219–20 Finger memory, 141–42, 170 Flow of time, 144, 145, 150, 151 Fossil record, 65, 66 Fourth dimension, 122, 123 Free time, and internal clock, 150 Frisch, Karl von, 186, 187 Fruit fly, 189, 191–94 Galaxy M87, 117 Galileo, 13, 25 De Motu, 79–80 observational method of, 79 time and motion measurement, 77–78, 79–81 Two New Sciences, 80–81, 85 Galison, Peter, Einstein’s Clocks, Poincaré’s Maps, 105–6 Gamow, George, 125 Genesis, 39 Geological processes, 65–67 God: as cause of time, 75, 76 and creation, 65, 70–71 Gott, J.


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

No Roman lost his life because he was absorbed in the contemplation of a mathematical diagram. Figure 11 Fortunately, while details of Archimedes’ life are scarce, many (but not all) of his incredible writings have survived. Archimedes had a habit of sending notes on his mathematical discoveries to a few mathematician friends or to people he respected. The exclusive list of correspondents included (among others) the astronomer Conon of Samos, the mathematician Eratosthenes of Cyrene, and the king’s son, Gelon. After Conon’s death, Archimedes sent a few notes to Conon’s student, Dositheus of Pelusium. Archimedes’ opus covers an astonishing range of mathematics and physics. Among his many achievements: He presented general methods for finding the areas of a variety of plane figures and the volumes of spaces bounded by all kinds of curved surfaces. These included the areas of the circle, segments of a parabola and of a spiral, and volumes of segments of cylinders, cones, and other figures generated by the revolution of parabolas, ellipses, and hyperbolas.

The Method When you read any book of Greek geometry, you cannot help but be impressed with the economy of style and the precision with which the theorems were stated and proved more than two millennia ago. What those books don’t normally do, however, is give you clear hints as to how those theorems were conceived in the first place. Archimedes’ exceptional document The Method partially fills in this intriguing gap—it reveals how Archimedes himself became convinced of the truth of certain theorems before he knew how to prove them. Here is part of what he wrote to the mathematician Eratosthenes of Cyrene (ca. 276–194 BC) in the introduction: Figure 13 I will send you the proofs of these theorems in this book. Since, as I said, I know that you are diligent, an excellent teacher of philosophy, and greatly interested in any mathematical investigations that may come your way, I thought it might be appropriate to write down and set forth for you in this same book a certain special method, by means of which you will be enabled to recognize certain mathematical questions with the aid of mechanics [emphasis added].


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

According to Toulmin, the Babylonian astronomers were masters of black-box predictions, far surpassing their Greek rivals in accuracy and consistency of celestial observations. Yet science favored the creative-speculative strategy of the Greek astronomers, which was wild with metaphorical imagery: circular tubes full of fire, small holes through which celestial fire was visible as stars, and hemispherical Earth riding on turtleback. It was this wild modeling strategy, not Babylonian extrapolation, that jolted Eratosthenes (276–194 BC) to perform one of the most creative experiments in the ancient world and calculate the circumference of the Earth. Such an experiment would never have occurred to a Babylonian data fitter. Model-blind approaches impose intrinsic limitations on the cognitive tasks that Strong AI can perform. My general conclusion is that human-level AI cannot emerge solely from model-blind learning machines; it requires the symbiotic collaboration of data and models.

., xxv, 41–53, 120, 191 AI as “helpless by themselves,” 46–48 AI as tool, not colleagues, 46–48, 51–53 background and overview of work of, 41–42 dependence on new tools and loss of ability to thrive without them, 44–46 gap between today’s AI and public’s imagination of AI, 49 humanoid embellishment of AI, 49–50 intelligent tools versus artificial conscious agents, need for, 51–52 operators of AI systems, responsibilities of, 50–51 on Turing Test, 46–47 on Weizenbaum, 48–50 on Wiener, 43–45 Descartes, René, 191, 223 Desk Set (film), 270 Deutsch, David, 113–24 on AGI risks, 121–22 background and overview of work of, 113–14 creating AGIs, 122–24 developing AI with goals under unknown constraints, 119–21 innovation in prehistoric humans, lack of, 116–19 knowledge imitation of ancestral humans, understanding inherent in, 115–16 reward/punishment of AI, 120–21 Differential Analyzer, 163, 179–80 digital fabrication, 167–69 digital signal encoding, 180 dimensionality, 165–66 distributed Thompson sampling, 198 DNA molecule, 58 “Dollie Clone Series” (Hershman Leeson), 261, 262 Doubt and Certainty in Science (Young), xviii Dragan, Anca, 134–42 adding people to AI problem definition, 137–38 background and overview of work of, 134–35 coordination problem, 137, 138–41 mathematical definition of AI, 136 value-alignment problem, 137–38, 141–42 The Dreams of Reason: The Computer and the Rise of the Science of Complexity (Pagels), xxiii Drexler, Eric, 98 Dyson, Freeman, xxv, xxvi Dyson, George, xviii–xix, 33–40 analog and digital computation, distinguished, 35–37 background and overview of work of, 33–34 control, emergence of, 38–39 electronics, fundamental transitions in, 35 hybrid analog/digital systems, 37–38 on three laws of AI, 39–40 “Economic Possibilities for Our Grandchildren” (Keynes), 187 “Einstein, Gertrude Stein, Wittgenstein and Frankenstein” (Brockman), xxii emergence, 68–69 Emissaries trilogy (Cheng), 216–17 Empty Space, The (Brook), 213 environmental risk, AI risk as, 97–98 Eratosthenes, 19 Evans, Richard, 217 Ex Machina (film), 242 expert systems, 271 extreme wealth, 202–3 fabrication, 167–69 factor analysis, 225 Feigenbaum, Edward, xxiv Feynman, Richard, xxi–xxii Fifth Generation, xxiii–xxiv The Fifth Generation: Artificial Intelligence and Japan’s Computer Challenge to the World (Feigenbaum and McCorduck), xxiv Fodor, Jerry, 102 Ford Foundation, 202 Foresight and Understanding (Toulmin), 18–19 free will of machines, and rights, 250–51 Frege, Gottlob, 275–76 Galison, Peter, 231–39 background and overview of work of, 231–32 clinical versus objective method of prediction, 233–35 scientific objectivity, 235–39 Gates, Bill, 202 generative adversarial networks, 226 generative design, 166–67 Gershenfeld, Neil, 160–69 background and overview of work of, 160–61 boom-bust cycles in evolution of AI, 162–63 declarative design, 166–67 digital fabrication, 167–69 dimensionality problem, overcoming, 165–66 exponentially increasing amounts of date, processing of, 164–65 knowledge in AI systems, 164 scaling, and development of AI, 163–66 Ghahramani, Zoubin, 190 Gibson, William, 253 Go, 10, 150, 184–85 goal alignment.


pages: 367 words: 99,765

Maphead: Charting the Wide, Weird World of Geography Wonks by Ken Jennings

Asperger Syndrome, augmented reality, Bartolomé de las Casas, Berlin Wall, Boris Johnson, British Empire, clean water, David Brooks, digital map, don't be evil, dumpster diving, Eratosthenes, game design, Google Earth, helicopter parent, hive mind, index card, John Harrison: Longitude, John Snow's cholera map, Mercator projection, Mercator projection distort size, especially Greenland and Africa, Mikhail Gorbachev, New Journalism, openstreetmap, place-making, Ronald Reagan, Saturday Night Live, Skype, Stewart Brand, Tacoma Narrows Bridge, traveling salesman, urban planning

The setting might be a Mecca alley or a prison cell, but either way, as Burton stares warily out at the viewer, he gives the impression that he’d rather be somewhere else entirely. There’s a funny disconnect between the rugged adventurers painted in oils here and the meek little men walking through the halls and poking through their maps. But then I reconsider: is the divide really all that wide? All the sweaty tropical valor of the Indian surveys was performed in the service of trigonometry, of all things—it’s hard to get nerdier than that. Eratosthenes, the mapmaker who was the first man to accurately measure the size of the Earth, was a librarian. The great mariners of the Age of Exploration, for all their naval derring-do, never would have left home if they hadn’t been map geeks as well: Columbus etched maps in his brother’s Lisbon print shop (“God had endowed me with ingenuity and manual skill in designing spheres, and inscribing upon them in the proper places cities, rivers, and mountains, isles, and ports,” he once wrote the king of Spain), and Vespucci was a map collector from his youth.

See Carroll, Lewis Downs, Roger, 139 Drummond, Bill, 242 Earth, seen from orbit, 25–26, 65–66, 214, 217, 220, 225 Echo & the Bunnymen, 242 Eco, Umberto, 212–13 Eddings, David, 115–16 Eden, Garden of, 85, 120 education, 10, 41, 45–55, 133–34, 146, 173 Eisenhower, Dwight, 168–69 Elden, Mary Lee, 124, 126, 131–32, 134, 137, 141, 146 Émile (Rousseau), 59 encyclopedias, collapse of sales, 234 epidemiology, 59 Eratosthenes, 90 Everest, Mount, 89, 119, 149, 156 EverQuest, 112 exploration destroyer of mystery, 85, 219, 242–43 fundamental nerdiness of, 90–91 in an overexplored world, 119–120, 149, 158–59, 199–200, 230, 238, 242–43 See also specific explorers Extra Miler Club, 11 fantasy literature, 113–21 Farrow, Mia, 193 Faulkner, William, 119 Ferdinandea, 161 Fischer, Joseph, 75 Five Graves to Egypt, 184 Fix, Bryan, 203 Flaming Lips, 227 Florida, as America’s phallus, 38 Four Corners Monument, 65 Frank, Ze, 240–42 Franken, Al, 38 Frémont, John C., 247 Friends, 36, 37 frillfin goby, 22 Frisch, Karl von, 25 Galileo, goofy hobbies of, 28 Gama, Vasco da, 92 Garriott, Richard, 196 Gaskin, Lilly, 122–24 geek culture, 112–19 gender, maps and, 139–41 Gentlemen Prefer Blondes, 36 geocaching, 186–211 appeal of, 189, 193–94, 195, 199, 202–3 author’s addiction to, 197, 201–3, 204–5, 207, 208–11 bizarrely avid practitioners of, 197–200, 202–4, 205–8 celebrity practitioners of, 193 extreme, 196 “First to Find” specialists, 203–5 invention of, 186–191 legal squabbles in, 190–91, 200–201 puzzles in, 196–97 ubiquity of caches, 191, 198–99 Geocaching.com, 189–91, 192, 193, 198, 201, 203, 209 geographic illiteracy, 32–55, 133–34, 146, 180, 233, 245 as American problem, 37–38, 42, 126, 151–52 dangers of, 50–52 historical, 36, 39 and parenting, 43–45 of political leaders, 36–38 geography academic, 45–49, 51–52, 55, 133–34 and journalists, 39–40 defined, 46–47, 78 ignorance of (see geographic illiteracy) geoslavery, 227–228 geotagging, 225, 227–28 Glenn, John, 25–26 global information systems (GIS), 47, 86, 227 Global Positioning System.


The Darkening Age: The Christian Destruction of the Classical World by Catherine Nixey

Eratosthenes, Index librorum prohibitorum, Socratic dialogue, the market place, trade route, wikimedia commons

‘In populous Egypt,’ one vinegary observer wrote, ‘many cloistered bookworms are fed, arguing endlessly in the chicken-coop of the Muses.’14 The brilliant mathematician and physicist Archimedes, who famously stepped in a bath, noticed its water move and announced ‘Eureka!’, had studied here.15 So too did Euclid, whose mathematical textbook remained the basis of maths education until the twentieth century. Eratosthenes, who worked out the circumference of the earth to an accuracy of 80 kilometres using little more than a stick and a camel, was also here, as too were the poet Callimachus; Aristarchus of Samos, who proposed the first heliocentric model of the solar system; the astronomer Hipparchus; Galen . . . The catalogue of Alexandria’s intellectuals is as remarkable as that of its books. Hypatia’s own father, Theon, had studied here.

M. ref1 Decian persecution (AD 250 to AD 251) ref1, ref2 Decius, Emperor ref1 Edict ref1 Delphi ref1 Demeas ref1 Demeter ref1 Democritus ref1, ref2 demons ref1 connected with the old religions ref1, ref2 countering diabolic whispers ref1 descriptions of ref1 explanations ref1 hideous army of ref1 methods of attack ref1 motivations ref1 plots against mankind ref1 power of ref1 prophecies of ref1 and religious contamination ref1 Serapis considered a demon ref1 wicked thoughts and temptations ref1 Dendera ref1 desert monks asceticism of ref1 and battles with demons and Satan’s minions ref1 beset by visions and temptations ref1 clothing ref1 considered mad and repellent ref1 description of ref1, ref2 diet and starvation ref1 grim tales concerning ref1 as poor and illiterate ref1 reasons for peculiar practices ref1 slaves advised to become ref1 and thoughts of death ref1 as vicious and thuggish ref1 see also monks Devil ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, ref10, ref11, ref12, ref13 Diocletian, Emperor ref1 Diogenes ref1 Dionysus ref1 Domitian, Emperor ref1 Domitius ref1 Drake, H. A. ref1n Eco, Umberto ref1 The Name of the Rose ref1 Edict of Milan (313) ref1, ref2 Einstein, Albert ref1 Elgin, Lord ref1 empiricism ref1 and note Engels, Friedrich ref1 Ephesus ref1, ref2, ref3, ref4 Eratosthenes ref1 erotica at Pompeii ref1 and bathhouses ref1 Christian moralizing on food, sex and women ref1, ref2 classical statues ref1 and homosexuality ref1 in literature ref1, ref2, ref3, ref4, ref5, ref6 and sex within marriage ref1 sexual practice in the Roman world ref1 Euclid ref1 Eulalia ref1, ref2 Eunapius ref1, ref2 Euripides ref1 Eusebius ref1, ref2, ref3 Firmicus Maternus ref1 Flora ref1 food and drink ref1, ref2 Frend, W.


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

Charts vary enormously in scope: the large-scale ones of harbors might cover an area of only a few square miles, while others cover entire oceans. The smaller-scale ones are framed by a scale of degrees and minutes of latitude (north–south) and longitude (east–west), and the surface is carved up by lines marking the principal parallels and meridians—an abstract system of coordinates first conceived by Eratosthenes (c. 276–194 BCE) and then refined by Hipparchus (c.190–120 BCE). Compass “roses” help the navigator to lay off courses from one point to another and show the local magnetic variation—the difference between true north and magnetic north. From my father I learned something about surveying and the use of trigonometry—the mathematical technique for deducing the size of the unknown angles and sides of a triangle from measurements of those that are known.

., 308n18 dolphins, 22, 137, 193, 218, 267, 275 Donkin Cove, 203 double-reflection principle, 30, 31 Drake, Francis, 194 Du Vivier, Alexa and arrival in England, 269 and departure from Halifax, 13 and food on board Saecwen, 193 and music on board Saecwen, 193, 219 and North Atlantic weather, 111–13 and preparations for Atlantic crossing, 8, 10 and routine at sea, 17, 22, 48, 239 and sail repairs, 137 and watch schedule, 48, 85, 218 dung beetles, 23 Dunn, Richard, 108n Dutch East Indies, 43, 51 Dutch States General, 64–65 dysentery, 43, 52, 103, 175 early humans, 23–24, 284–85 Earnshaw, Thomas, 68 East India Company, 76, 82, 88, 168 East Indies, 120 Easter Island, 90, 126 echo sounders, 5, 46 eclipses, 169 electronic chart display and information systems (ECDIS), 282 electronic navigation aids, 265, 286 Elephant Island, 247, 249, 251, 256, 261 Emergency Position-Indicating Radio Beacon (EPIRB), 302n3 emperor penguins, 245–46 Endeavour, 88–89, 96–97, 98–101, 103, 107, 167, 264 Endurance, 241–50 England, 2–3 English Channel, 5, 32–33, 50, 51, 166–67 Entrecasteaux, Joseph-Antoine Bruny d’, xvi–xvii, 133–34 ephemeris tables, 60, 63, 219 equal altitude circles, 220–23, 222, 280, 311n6 Eratosthenes, 4 Escures, Charles d’, 127–28 Euler, Leonhard, 73 Europa, 138 European Union, 280 evolution, 212, 217 Falkland Islands, 114–15, 210 Falmouth, Maine, 8 Fame, 138 Far East, 168 Fidget, 6 Fiji, 40, 134 Fitz Hugh Sound, 152 FitzRoy, Robert on “Breaker Bay,” 206–7, 232 on natural navigation methods, 262 navigational skills, 219 and timekeeping challenges, 225–26 and voyage of the Beagle, 200–210, 210–17 and weather prediction, 170, 206 Flinders, Matthew and Bligh, 157–59, 162 captivity, 182–85 chart-making skills, 185–88 explorations with Bass, 159–63, 170–71 financial difficulties, 188–89 and meteorology, 215 personal papers, 189n and Phillip King, 195 and place-names, 189–90 shipwreck, 177–82 survey of Australian coast, 163–76 and Trim (cat), 190–92, 277 and weather prediction, 206 Flinders, Samuel, 167, 174, 187 Flinders bars, 170 Flinders-Petrie, William, 189, 189n Forster, Johann, 91, 93, 106 fothering, 97 France, 85 Francis, 181 Franklin, John, 167–68 French Frigate Shoal, 129 French Revolution, 133, 142, 183 Frisius, Gemma, 59 fur trade, 139 Fury Island, 231 Galapagos Islands, 211 Galiano, Dionisio Alcalá, 147, 147n Galileo Galilei, 59, 64–65 Gamboa, Pedro Sarmiento de, 196–97n Ganges, 200 geography, 60–61 geometry, 69 George III, 68, 155 George’s Island, 229 George’s River, 160 Gilbert, Humphrey, 14 Gillray, James, 155 Gladwin, Thomas, 263 glass fiber-reinforced plastic (GRP), 46 Global Navigation Satellite Systems (GNSS), 299n11 Global Positioning System (GPS), xix–xx, 265, 279–83, 313n27 global warming, 87n GLONASS (Russian satellite navigation system), 280 Glorious First of June (1794), 159 Gloucester, Massachusetts, 8 Godfrey, Thomas, 32 Godin, Louis, 60–61 Gooch, William, 146, 152 Grand Banks, 14, 22, 22n Grand Manan Island, 9, 227 Grand Tour, 142 gravitational field of earth, 303n6 Great Barrier Reef and Bligh’s explorations, 39, 41, 43–44 and Cook’s explorations, 96–97, 98–102, 104 and Flinders’s explorations, 173 Great Britain, xvii Great Circle route, 33 Greek culture, 58, 303n1 Green, Charles, 102–3, 103–4 Greenwich Hour Angle (GHA), 69 Greenwich meridian, 15, 59, 80 Greenwich Time chronometers synchronized with, 70, 104, 144, 251 and “clearing the distance,” 77 and determining longitude, 59–60, 64, 69, 70, 186–87, 220 Grenville, William, 1st Baron, 155 growlers, 11 Guadalcanal, xv Guadeloupe, 65 Gulf of Carpentaria, 120, 173–74 Gulf of Peñas, 198 Gulf Stream, 18 Gulliver’s Travels (Swift), 168–69n H4 watch, 66–67, 78–80, 102, 104 Hadley, John, 31–32, 74 Hadley’s quadrant, 31, 31–32, 82, 89, 114, 299n8 Hakluyt, Richard, 14 Halifax, Nova Scotia, 10, 11, 229 Harbor of Mercy, 196–98 Harrison, John, 66–68, 68n, 72, 77–80, 82 Harrison, William, 67–68, 78 Hawaiian Islands, 90, 94, 140, 143–44, 152, 154 heaving to, 171, 214–15, 241, 256–57 Heelstone (at Stonehenge), 24 heliocentric view of the universe, 17 Hermite Island, 208 Heywood, Peter (“Pip”), 44 Hicks, Lieutenant (Cook expedition), 100 Hilleret, Paul-Gustave-Eugène, 222 Hipparchus, 4 Hiva Oa, 236n Hobart, Tasmania, 135, 162–63 Hogarth, William, 66 Hōkūle’a (double canoe), 263 Holland, Samuel, 10 Homer, 16–17 homing pigeons, 23 honeybees, 23 Hood, 36, 45, 301n1 Hook, Robert, 300n12 Hope, 180 horizontal sextant angles, 147, 239 Horror Rock, 257n hourglasses, xv Houtman, Frederick de, 51 Howard, Trevor, 1, 37 hurricanes, xv Huygens, Christiaan, 59 hydrography, xvii, 61, 85, 108, 166, 185–88.


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

In other regions, surely there must be other Earths, other men, other beasts of burden.”17 Greek philosophy sought to replace fear and superstition with rational thought. Humans had long had the capacity for abstraction, but in the hands of the Greeks it was augmented with mathematics and formal rules of logic. Aristarchus used geometry and an understanding of eclipses and lunar phases to deduce that the Sun must be larger than the Earth, and this led him to propose a heliocentric model nearly two thousand years before Copernicus. Eratosthenes combined his knowledge that the Earth was round—from the shape of its shadow in a lunar eclipse—with the way the Sun casts shadows at different places on the Earth’s surface, to estimate the size of the Earth. This philosopher, who had never traveled more than a hundred miles in his life, could understand what was unknown to the early humans who had made epic migrations across the planet. The philosophers of ancient Greece extended mental models into entirely new regimes.

., 36–39, 73, 79 electric cars, 96 electric solar sails, 186 electromagnetic waves, 186 e-mail, 78 embryo transport, 251 Enceladus, 177, 182, 227 potential habitability of, 125, 278 Encyclopædia Britannica, 95, 283 Endangered Species Act (1973), 201 energy: aliens’ use of, 190 civilizations characterized by use of, 252–57, 254, 258 dark, 256 declining growth in world consumption of, 257 Einstein’s equation for, 220 production and efficiency of, 219–24, 220 as requirement for life, 123–24 in rocket equation, 110 Engines of Creation (Drexler), 226 environmental disasters, 245 environmental protection: as applied to space, 147 movement for, 45, 235, 263, 270 Epicureans, 18 Epsilon Eridani, 187 Eratosthenes, 19 ethane, 52, 125 Ethernet, 213 eukaryotes, 172 Euripides, 18 Europa, 52, 97–98 potential habitability of, 125, 125, 161, 278 Europa Clipper mission, 98 Europe: economic depression in, 28 population dispersion into, 7–8, 11, 15 roots of technological development in, 23–24 European Southern Observatory, 133 European Space Agency, 159, 178–79 European Union, bureaucracy of, 106 Eustace, Alan, 120, 272 Evenki people, 119–20 Everest, Mount, 120 evolution: genetic variation in, 6, 203, 265 geological, 172 of human beings, 16–17 off-Earth, 203–4 evolutionary divergence, 201–4 exoplanets: Earth-like, 129–33, 215–18 extreme, 131–32 formation of, 215, 216 incidence and detection of, 126–33, 128, 233 exploration: as basic urge of human nature, 7–12, 109, 218, 261–63 imagination and, 262–63 explorer gene, 86 Explorer I, 38 explosives, early Chinese, 21–23 extinction, 201–2 extraterrestrials, see aliens, extraterrestrial extra-vehicular activities, 179 extremophiles, 122–23 eyeborg, 205–6 Falcon Heavy rocket, 114 Falcon rockets, 96, 97, 101, 184 Federal Aviation Administration (FAA), 82, 93, 105–7, 154 Fédération Aéronautique Internationale, 272 Felix and Félicette (cats), 48–49 Fermi, Enrico, 239–41 Fermilab, 254 “Fermi question,” 240–41, 243 Feynman, Richard, 179–80, 230, 270, 280 F4 Phantom jet fighter, 82 51 Peg (star), 126, 133 55 Cancri (star), 131 F-117 Nighthawk, 69 fine-tuning, 256, 294 fire arrows, 23, 68 fireworks, 21–24, 31 flagella, 180 flight: first human, 68 first powered, 69 principles of, 67–73 stability in, 82–83 “Fly Me to the Moon,” 45 food: energy produced by, 219, 220 in sealed ecosystem, 194–95 for space travel, 115–16, 159, 170 Forward, Robert, 223 Foundation series (Asimov), 94 founder effect, 202–3 Fountains of Paradise, The (Clarke), 149 France, 48, 68, 90 Frankenstein monster, 206, 259 Fresnel lens, 223 From Earth to the Moon (Verne), 183 fuel-to-payload ratio, see rocket equation Fukuyama, Francis, 207 Fuller, Buckminster, 151, 192 fullerenes, 151 Futron corporation, 155 Future of Humanity Institute, 245 “futurology,” 248–52, 249 Fyodorov, Nikolai, 26, 27 Gagarin, Yuri, 40–41, 41, 66, 269 Gaia hypothesis, 286 galaxies: incidence and detection of, 235 number of, 255 see also Milky Way galaxy Galileo, 49–50, 183, 270 Gandhi, Mahatma, 147 Garn, Jake, 114 Garn scale, 114 Garriott, Richard, 92 gas-giant planets, 125, 126–29 Gauss, Karl Friedrich, 238 Gazenko, Oleg, 47 Gemini program, 42 Genesis, Book of, 148–49 genetic anthropology, 6 genetic code, 5–7, 123 genetic diversity, 201–3 genetic drift, 203 genetic engineering, 245, 249 genetic markers, 6–7 genetics, human, 6–7, 9–12, 120, 201–4 Genographic Project, 7, 265 genome sequencing, 93, 202, 292 genotype, 6 “adventure,” 11–12, 98 geocentrism, 17, 19–20, 49 geodesic domes, 192 geological evolution, 172 George III, king of England, 147 German Aerospace Center, 178 Germany, Germans, 202, 238 rocket development by, 28, 30–34, 141 in World War II, 30–35 g-forces, 46–49, 48, 89, 111, 114 GJ 504b (exoplanet), 131 GJ 1214b (exoplanet), 132 glaciation, 172 Glenn Research Center, 219 global communications industry, 153–54 Global Positioning System (GPS), 144, 153–54 God, human beings in special relationship with, 20 Goddard, Robert, 28–32, 29, 36, 76, 78, 81–82, 94, 268 Goddard Space Flight Center, 178 gods, 20 divine intervention of, 18 Golden Fleece awards, 238 Goldilocks zone, 122, 126, 131 Gonzalez, Antonin, 215 Goodall, Jane, 14 Google, 80, 92, 185, 272, 275 Lunar X Prize, 161 Gopnik, Alison, 10, 13 Grasshopper, 101 gravity: centrifugal force in, 26, 114, 150 in flight, 68 of Mars, 181, 203 Newton’s theory of, 25, 267 and orbits, 25, 114–15, 127, 128, 149–50, 267 in rocket equation, 110 of Sun, 183 waves, 255 see also g-forces; zero gravity Gravity, 176 gravity, Earth’s: first object to leave, 40, 51 human beings who left, 45 as obstacle for space travel, 21, 105, 148 as perfect for human beings, 118 simulation of, 168–69 Great Art of Artillery, The (Siemienowicz), 267 Great Britain, 86, 106, 206, 227 “Great Filter,” 244–47 Great Leap Forward, 15–16 “Great Silence, The,” of SETI, 236–39, 240–41, 243–44 Greece, ancient, 17–19, 163 greenhouse effect, 171, 173 greenhouse gasses, 132, 278 Griffin, Michael, 57, 147, 285–86 grinders (biohackers), 207 Grissom, Gus, 43 guanine, 6 Guggenheim, Daniel, 81, 268 Guggenheim, Harry, 81 Guggenheim Foundation, 30, 81–82, 268 gunpowder, 21–24, 267 Guth, Alan, 257 habitable zone, 122, 124–26, 130–31, 132, 188, 241, 246, 277–78, 286, 291 defined, 124 Hadfield, Chris, 142 hair, Aboriginal, 8 “Halfway to Pluto” (Pettit), 273 Hanson, Robin, 247 haptic technology, 178 Harbisson, Neil, 205, 288 Harvard Medical School, 90 Hawking, Stephen, 88, 93, 198, 259 HD 10180 (star), 127 Heinlein, Robert, 177 Heisenberg compensator, 229 Heisenberg’s uncertainty principle, 229–30 heliocentrism, 19 helium, 68 helium 3, 161–62 Herschel, William, 163 Higgs particle, 256 High Frontier, 146–47 Hilton, Paris, 88, 101–2 Hilton hotels, 145 Hinduism, 20 Hiroshima, 222 Hitler, Adolf, 32, 34 Hope, Dennis M., 145, 147 Horowitz, Paul, 237–38 hot Jupiters, 127–28, 130 Hubble Space Telescope, 56–57, 65, 218, 225 Huffington, Arianna, 92 human beings: as adaptable to challenging environments, 118–22 as alien simulations, 260–61, 260 creative spirit of, 73, 248 early global migration of, 5–12, 9, 11, 15, 19, 118, 120, 186, 202, 218, 262, 265 Earth as perfectly suited for, 118–22, 121 exploration intrinsic to nature of, 7–12, 109, 218, 261–63 first appearance of, 5, 15, 172, 234 impact of evolutionary divergence on, 201–4 as isolated species, 241–42 as lone intelligent life, 241, 243 merger of machines and, see cyborgs minimal viable population in, 201–2, 251 off-Earth, 203–4, 215, 250–52 requirements of habitability for, 122, 124–26, 129, 130–31 sense of self of, 232, 261 space as inhospitable to, 53–54, 114–17, 121, 123 space exploration by robots vs., 53–57, 66, 98, 133, 161, 177–79, 179, 208, 224–28 space travel as profound and sublime experience for, 45, 53, 117, 122 speculation on future of, 93, 94, 204, 207–8, 215, 244–47, 248–63, 249 surpassed by technology, 258–59 threats to survival of, 94, 207–8, 244–47, 250, 259–62, 286, 293 timeline for past and future of, 248–50, 249 transforming moment for, 258–59 Huntsville, Ala., US Space and Rocket Center in, 48 Huygens, Christiaan, 163 Huygens probe, 53 hybrid cars, 96 hydrogen, 110, 156, 159, 161, 187, 219, 222 hydrogen bomb, 36 hydrosphere, 173 hyperloop aviation concept, 95 hypothermia, 251 hypothetical scenarios, 15–16 IBM, 213 Icarus Interstellar, 224 ice: on Europa, 125 on Mars, 163–65, 227 on Moon, 159–60 ice ages, 7–8 ice-penetrating robot, 98 IKAROS spacecraft, 184 imagination, 10, 14, 20 exploration and, 261–63 immortality, 259 implants, 206–7 inbreeding, 201–3 India, 159, 161 inflatable modules, 101–2 inflation theory, 255–57, 255 information, processing and storage of, 257–60 infrared telescopes, 190 Inspiration Mars, 170–71 Institute for Advanced Concepts, 280 insurance, for space travel, 106–7 International Academy of Astronautics, 152 International Geophysical Year (1957–1958), 37 International Institute of Air and Space Law, 199 International MicroSpace, 90 International Scientific Lunar Observatory, 157 International Space Station, 55, 64–65, 64, 71, 75, 91, 96, 100, 102, 142, 143, 144, 151, 153, 154, 159, 178–79, 179, 185, 272, 275 living conditions on, 116–17 as staging point, 148 supply runs to, 100–101, 104 International Space University, 90 International Traffic in Arms Regulation (ITAR), 105–6, 144 Internet: Congressional legislation on, 78, 144 development of, 76–77, 77, 94, 95, 271 erroneous predictions about, 213–14 limitations of, 66–67 robotics and, 206 space travel compared to, 76–80, 77, 80 Internet Service Providers (ISPs), 78 interstellar travel, 215–18 energy technology for, 219–24 four approaches to, 251–52 scale model for, 219 Intrepid rovers, 165 Inuit people, 120 Io, 53, 177 property rights on, 145 “iron curtain,” 35 Iron Man, 95 isolation, psychological impact of, 169–70 Jacob’s Ladder, 149 Jade Rabbit (“Yutu”), 139, 143, 161 Japan, 161, 273 Japan Aerospace Exploration Agency (JAXA), 184 Jefferson, Thomas, 224 Jemison, Mae, 224 jet engines, 69–70 Jet Propulsion Laboratory, 141 Johnson, Lyndon, 38, 42, 45, 158, 269 Johnson Space Center, 76, 104, 179, 206, 229, 269 see also Mission Control Jones, Stephanie Tubbs, 74 Joules per kilogram (MJ/kg), 219–20, 222 Journalist in Space program, 74 “junk” DNA, 10, 266 Juno probe, 228 Jupiter, 126, 127, 177, 217, 270 distance from Earth to, 50 moons of, 97, 125, 125 probes to, 51–52, 228 as uninhabitable, 125 Justin (robot), 178 Kaku, Michio, 253 Karash, Yuri, 65 Kardashev, Nikolai, 253 Kardashev scale, 253, 254, 258 Kármán line, 70, 70, 101 Kennedy, John F., 41–43, 45 Kepler, Johannes, 183 Kepler’s law, 127 Kepler spacecraft and telescope, 128, 128, 129–31, 218, 278 Khrushchev, Nikita, 42, 47 Kickstarter, 184 Killian, James, 38 Kline, Nathan, 205 Knight, Pete, 71 Komarov, Vladimir, 43, 108 Korean War, 141 Korolev, Sergei, 35, 37 Kraft, Norbert, 200 Krikalev, Sergei, 115 Kunza language, 119 Kurzweil, Ray, 94, 207, 259 Laika (dog), 47, 65, 269 Laliberté, Guy, 75 landings, challenges of, 51, 84–85, 170 Lang, Fritz, 28, 268 language: of cryptography, 291 emergence of, 15, 16 of Orcas, 190 in reasoning, 13 Lansdorp, Bas, 170–71, 198–99, 282 lasers, 223, 224, 225–26, 239 pulsed, 190, 243 last common ancestor, 6, 123, 265 Late Heavy Bombardment, 172 latency, 178 lava tubes, 160 legislation, on space, 39, 78, 90, 144, 145–47, 198–200 Le Guin, Ursula K., 236–37 Leonov, Alexey, 55 L’Garde Inc., 284 Licancabur volcano, 119 Licklider, Joseph Carl Robnett “Lick,” 76–78 life: appearance and evolution on Earth of, 172 artificial, 258 detection of, 216–18 extension of, 26, 207–8, 250–51, 259 extraterrestrial, see aliens, extraterrestrial intelligent, 190, 235, 241, 243, 258 requirements of habitability for, 122–26, 125, 129, 131–33, 241, 256–57 lifetime factor (L), 234–335 lift, in flight, 68–70, 83 lift-to-drag ratio, 83 light: from binary stars, 126 as biomarker, 217 Doppler shift of, 127 momentum and energy from, 183 speed of, 178, 228–29, 250, 251 waves, 66 Lindbergh, Charles, 30, 81–82, 90–91, 268 “living off the land,” 166, 200 logic, 14, 18 Long March, 141 Long March rockets, 113, 142, 143 Long Now Foundation, 293 Los Alamos, N.


pages: 424 words: 108,768

Origins: How Earth's History Shaped Human History by Lewis Dartnell

agricultural Revolution, back-to-the-land, bioinformatics, clean water, Columbian Exchange, decarbonisation, discovery of the americas, Donald Trump, Eratosthenes, financial innovation, Google Earth, Khyber Pass, Malacca Straits, megacity, meta analysis, meta-analysis, oil shale / tar sands, out of africa, Pax Mongolica, peak oil, phenotype, Rosa Parks, Silicon Valley, South China Sea, spice trade, supervolcano, trade route, transatlantic slave trade

A NEW WORLD While the Portuguese had been finding a route around the southern tip of Africa, a Genoese navigator was trying to raise support for a voyage sailing in the opposite direction: he believed he could reach the orient by sailing west. He finally found patronage from Queen Isabella of Castile, who in 1469 had married King Ferdinand II of Aragon to unify their realms and form Spain. He was known to his sponsors as Cristóbal Colón. In English, we call him Christopher Columbus. Contrary to a commonly held view today, no educated person in medieval times believed the Earth to be flat. In the third century BC Eratosthenes, a Greek geographer, astronomer and mathematician working at the Library of Alexandria, understood that the world is a sphere and calculated its circumference to be 250,000 stadia, or around 44,000 kilometres–remarkably close to its real value. Indeed, the techniques of celestial navigation used by sailors to plot their latitude by the stars is predicated on the very principle that the Earth is round.

Index Abbasids 212 Aberdeen: granite 148, 151 Abu Dhabi: Sheikh Zayed Mosque 136 Abu Simbel, Egypt: Great Temple of Rameses II 132 Achaemenid Empire 202 Acheulean tools 17, 22 acid rain 142, 280 Aden 107 Aden, Gulf of 11 adobe bricks 131, 155 Aegean/Aegean Sea 99, 100, 117, 162 Aegospotami, Battle of (405 BC) 118 Afar region/triangle 11, 18 Afghanistan 183, 190, 194 Africa 11, 15, 21, 56, 98, 104, 105, 106, 139, 160, 218n, 219, 220, 267, 285 animals 88, 89 hominin migration from 22, 23, 45–6, 47, 52, 63 plants 67, 87 see East, North, South and West Africa African-Americans 125–6 Agassiz, Lake 60, 61–2 agriculture/farming 25, 26, 28, 52, 59, 61, 62, 63–5, 70–71, 87–8, 90, 130, 203, 205, 255, 256–7, 258, 280, 281, 285 and climate change 280 and oil 274 and population growth 70 tools and ploughs 76, 77, 165–6, 215n, 255, 268, 285, 286 see also cereal crops; fruit; legumes aircraft engines 175, 176 Akkadians 131 Akrotiri, Thera 163 Akshardham, Delhi 136 Alabama 125, 126 cotton plantations 125, 253–4 Alans 207 Alaska 48–9, 52, 195 Alborán microcontinent 218n Alborz Mountains 29–30 Alcáçovas, Treaty of (1479) 229, 230 Alexander the Great 101, 117n, 202 Alexandria 101, 187 Library 227 algae 138, 171, 261 Algeria 100 alpacas 76, 88, 89 Alps, the 32, 56, 58, 116, 135, 140, 154, 159, 163, 285 Altai Mountains 47, 196, 202 aluminium 174–5, 177, 182 aluminium silicates 266 Amazon 7, 63, 189 rainforest 223n, 275, 285 America(s) 55, 194n animals 88–9 discovery of 231, 237 human migration into 48–52 see also North America; South America; United States American Civil War 124, 126, 254 American War of Revolution (1775–83) 122 ammonites 138 Amnissos, Crete 162 amphibians 79, 262 Amsterdam: banking 97 Anatolia 131, 157, 165, 204, 205 Andes Mountains 32, 54, 66, 67, 74 angiosperms 40, 78, 79–82, 90, 141n Angkor Wat, Cambodia 129 animals, wild 13, 33–4, 49, 72, 83, 88–9, 66n domestication of 52, 59, 74–8, 88–90, 199 megafauna 53n see also mammals Antarctica 39, 40, 42, 43, 44, 53, 86, 104, 267, 277 antelopes 12, 83 ‘Anthropocene’ Age 3 antimony 175 APP mammals 82, 84, 85, 86 Appalachian Mountains 55, 124, 125, 267, 270 Aqaba, Gulf of 110n Arabia/Arabian Peninsula 11, 27, 28, 47, 53, 75, 104, 107, 108–9, 110, 115, 188, 191 camels 89 deserts 29, 190, 192, 215, 285 stone tools 52n Aragon, Spain 218 Aral Sea 105, 196 architecture 129–30, 131 American 134–5, 136 and n ancient Egyptian 132–3 British 134, 151–3, 154–5 Minoan 161, 162 Roman 136n, 162n Arctic, the 36, 38, 39, 40, 43, 64, 85 Arctic Ocean 60 Ardipithecus ramidus 13–15, 18 Argentina: pampas 196 artiodactyls 82–3, 84, 86, 144 Asia, South East 10, 75, 91, 119, 239 islands 111–15, 112–13 asphalt 273, 274 Assyrian Empire 27, 131, 202 asteroids 94, 143n, 168, 178n, 179 astronomy 194, 252n Athens 116, 117–18 Atlantic Ocean 43, 61, 62, 95, 96, 99, 104, 106, 122, 139, 218, 219–20, 222, 226, 227, 229–30, 231, 237, 238, 267 and Mediterranean 105, 106, 118 Atlantic Trade Triangle 246, 249, 250–51, 252–4 Atlas Mountains 105, 163, 267 Attila the Hun 207 aurochs 74 Australia 10, 42, 48, 52n, 54, 121, 252 and n, 267, 285 domesticable animals 88 rare earth metals 181 grasses 87 Australopithecus 14–15, 16 A. afarensis 14, 18 Avars 203 avocados 66n Awash river valley 13, 14, 18 Azores, the 218, 219, 220, 221, 222, 229, 230, 231 Aztec culture 28 Bab-el-Mandeb strait 47, 107, 108, 110, 119, 121 Babylon 71, 273 Babylonians 131 Bacan Islands 114 Baghdad 110, 190, 212 Bahamas, the 230 Bahrain 120 Baikonur Cosmodrome, Kazakhstan 197n Balaclava, Battle of (1854) 129 Banda Islands 111, 112–13, 114, 115 Banded Iron Formations (BIFs) 169–70, 173, 177, 179 Bank of England, London 134 banks and banking 97, 134 Barbarossa, Operation 215 Barbegal, France: waterwheels 257 barley 61, 65, 67, 117 basalt eruptions/flood basalt 141, 142, 143, 144, 145 basalt(ic) rocks 11, 141, 143, 145, 146, 160 Batavia (Jakarta), Indonesia 252 batteries, rechargeable 176, 180 bay (herb) 115n beans 66, 81 Beatles, the: ‘Lucy in the Sky with Diamonds’ 14n Bedouins 129 belemnites 138 Belgium 96, 269, 284 Belize 28 Bering land bridge/Strait 48, 49, 51, 52, 54, 89, 191 Bessemer Process 166–7 BIFs see Banded Iron Formations Big Bang 167 Biological Old Regime 258 bipedalism 14–15, 16 birds 33, 80, 219n, 263 bison 49, 214n bitumen 273 ‘Black Death’ (accumulation of shale) 279 Black Death (plague) 211–12 Black Sea 105, 106, 117, 118, 120, 185, 190, 196, 207, 278n ‘black smokers’ 159, 160, 163 blast furnaces 165, 211, 257, 259 Bojador, Cape 223–4, 225 bone china 149 Borneo 112 Bosphorus 196, 117, 118, 120 Boston, Massachusetts 56 Brahmaputra River 91 brassicas 81, 82 Brazil 181, 244n, 247n coffee plantations 252, 253, 254 Brazil Current 238, 239, 253 bricks 131, 139, 149, 152, 174, 255 adobe 131, 155 firebricks 131–2 Britain/England 56–9, 97 architecture 134, 152–3, 154–5 ceramics 149–50 coalfields/mines 259–60, 266, 269, 270–72, 271 corsairs 249 electricity 271n exploration 229, 231 geology 150–53, 151 Labour Party 270, 271, 271–2 maritime trade 107n, 245 railways 260 Roman coal mines 259 Royal Navy 58, 118, 119 steam engines 259–60 see also Industrial Revolution; London British Museum, London 134, 148 bromine 175 bronze/bronze artefacts 1578, 161, 165, 174 Bronze Age 99, 137, 156, 158, 160–61, 164, 174, 200n Brouwer, Captain Henrik 250–51 Brouwer Route 119n, 246, 250, 250–52 bubonic plague 211–12 Buckingham Palace, London 134 Buffalo, New York 55 Bukhara, Uzbekistan 190, 212 Bulgars 203, 204 Burgundians 207 Burma 92 Bush, President George W. 124 Bushveld Complex, South Africa 179–80 butane 276 Byblos 101n Byzantine Empire 205, 213 Cabot, John 231 cacti 80 calcium carbonate 41, 129, 133, 139, 140 Calicut, India 240 California 52n, 248 Cambodia 92 Cambrian Period 152, 153 camels 19, 49, 75, 76, 77, 83, 88, 89, 107, 187, 191–2, 193, 197 Bactrian camels 89, 191 dromedaries 89, 191 Canada 49, 60, 63, 89, 163, 179, 195, 267, 277 fur trade 195 canals 71, 74, 150 and n, 152, 187 Canary Current 237 Canary Islands 218–19, 220, 222, 223, 225, 227, 228, 229, 230 Cape Cod, Massachusetts 56 Cape of Good Hope 121, 225–6, 231, 250 Cape Town 252 Cape Verde Islands 218, 219, 220, 229, 239, 253n capitalism 96–7, 154, 270 caravans, merchant 81, 107, 110, 187, 188, 192–3, 194, 201, 211, 218 caravels 246 carbon 1, 85n, 157, 165, 166, 167, 175, 261, 263, 273, 275–6, 278, 279, 280, 281 carbon dioxide 10, 38, 40, 42, 44, 65, 84, 85 and n, 139, 142, 143, 144–5, 170, 171, 172, 261, 265, 275, 279–80, 281 and n, 287 Carboniferous Period 6, 78–9, 134, 151, 261–8 Caribbean, the 28, 52, 61, 230, 231, 237 sugar plantations 252, 253, 254 Carnegie, Andrew 270 Carolinas, the 124, 125 cotton plantations 253–4 Carpathian Mountains 163, 185, 196, 204 Carrara marble 135 cars/automobiles 174, 273 Carthage 100–1, 105n, 208 cartwheel hubs 130 Caspian Sea 105, 120, 196, 201, 207 cassava 131 Castile, Spain 217, 218 catalysts, chemical 178, 180 catalytic converters 178 cathedrals 127, 129, 134 Catholicism 185n cattle/cows 67, 74, 75, 76, 77, 82n, 83, 84n, 86–7, 88, 172n, 198, 198, 201 Caucasus 185, 196, 204, 207, 209, 215 cedars/cedarwood 73, 70, 101n, 131 cellulose 263, 264 cement 139, 140–41 ‘pozzolanic’ 162n Cenozoic cooling 9–10, 39–40, 81 Cenozoic era 42, 44, 90, 141n Central Steppe see Kazakh Steppe ceramics/pottery 131–2, 255 porcelain 112, 115, 149–50 cereal crops 65, 67–9, 70, 78, 80, 86–7, 90, 125, 287; see also grain(s) Cerne Abbas Giant, Dorset 137 Cerro Rico see Potosí Ceuta, Morocco 217–18 Ceylon see Sri Lanka chalk 132, 136–8, 139–40, 152 Channel Tunnel 137 charcoal 157, 161, 164, 166, 173n, 255, 269 chariots, war 76, 116n, 200n chert 17n, 156, 170 Chicago 55, 56, 135 chickens 74 Chile 54 chimpanzees 7, 14, 16, 46 China 28n, 182, 183–5, 186, 187, 190, 195, 206, 213, 214 agriculture 63, 65–6, 67, 77, 184 blast furnaces 165, 257 bronze 157 bubonic plague 211 canals 187 coal 258–9, 264 collar harnesses 77 compasses 169 exports 112, 115, 249 first humans 48, 52n, 53 ginkgo 79 Great Wall 203–4, 208 Homo erectus 23, 47 Mongols (Yuan dynasty) 209, 210, 212, 214 and oil 121 population 92, 186, 211, 284 porcelain 112, 115, 149 rare earth metals 177, 181 salt production 273 silk 112, 115, 187–8, 193n and South American silver 249 and steppe nomads 202–3 tea 112 and Tibet 91–3 waterwheels 165, 257 and Xiongnu 202, 206 china, bone 149 see also porcelain chokepoints, naval 98, 115, 118–19, 121, 217n, 273 Christianity 185n, 217 cinnamon 113, 114, 193, 241 civilisations, early 25–30, 26–7, 70–74, 90, 98–9, 132 Clarke, Arthur C. 94 clathrate ice 85–6 clay 130, 131–2, 152, 266 soils 154–5, 166 Cleopatra VII, of Egypt 101, 147 ‘Cleopatra’s Needles’ 147 Cleveland, Ohio 55 climate changes 2–3, 9–10, 11–12, 18–19, 21–5, 61, 63, 64, 70–71, 72, 84–5, 86, 143–4, 279–81; see also ice ages Clinton, Hillary 122 cloves 114, 115n, 241, 247 clubmosses 262 clunch 152 coal 78, 149, 258–60, 279 formation of 261–8, 267, 274, 280 politics of 269, 270, 270–72, 271 cobalt 159, 175 coccolithophores 138, 139, 140, 144 coccoliths 274, 275 cockroaches 262 cocoa 66n coconuts 81 Cocos Plate 28 cod 95, 97 coffee plantations, Brazilian 252, 253 coins 168n, 182 Coleridge, Samuel Taylor Kublai Khan 210 The Rime of the Ancient Mariner 97n, 234 Cologne Cathedral 127 Colombia: platinum 178n Colosseum, Rome 133 Columbian Exchange 113n Columbus, Christopher 52, 227–31, 236, 239, 241 comets 94, 143n, 178n compasses, navigation 118n, 169 concrete 56, 139, 140–41, 272 reinforced 130n, 167 Congo 7, 11 conifers 79, 130, 141, 195 Constantinople (Istanbul) 185n, 193n, 205, 207, 211, 213 cooking food 15, 17, 69, 131, 132 cooling, global see Cenozoic cooling; ice ages copper/copper ore 157, 158, 159, 160–62, 163–4, 174, 175, 179, 182, 201n smelting 131, 156, 157, 161 coppicing 256 coral/coral reefs 193, 252n, 280 Cordilleran ice sheet 49 coriander 115n Corinth 117 Coriolis effect 233, 235, 237 Cornwall Eden Project 150n granite 267n kaolin 149, 150n tin mines 158, 267n Corsica 208 Cotswolds, the 152 cotton 82, 112, 125, 126, 193, 252, 253–4, 255, 259, 263, 269 courgettes 66n cows see cattle Cretaceous Period 40, 42, 80, 123, 124, 137, 138, 139, 141n, 143n, 144, 145, 152, 178n, 274, 276–9, 278 Crete 99, 161–3 Crimean Peninsula 129 crocodiles 72, 85 crops 255 domestication of 52, 63–4, 65–9, 68–9 rotation 255 see also cereal crops; grain(s) Cuba 230 Cumans 203 Cumberland: coalfields 272 cumin 115n current sailing see sailing and navigation cyanobacteria 171, 173 Cyclades, the 99 Cyprus 99, 160 copper mining 158, 160–62, 163 Troodos Mountains 160, 163 Da Gama, Vasco 239–41, 244 Danube River/Valley 185 and n, 196, 204, 206, 207, 208 Dardanelles, the 117, 118, 120 ‘Dark Ages’ 219 Dartmoor 147, 151 dates (fruit) 81 Dead Sea 106, 110n Deccan Traps 143n deer 83 Delhi: Akshardham 136 Denisovan hominins 16, 23, 47, 50–51, 51, 53 deserts 1, 12, 29, 61, 72, 73, 80, 81, 89, 100, 107, 148n, 184, 189, 190–92, 195, 215–16, 232, 285 see also specific deserts Detroit, Michigan 55 Dias, Bartolomeu 225–7, 229, 239 diatoms 140, 171, 274 dinoflagellates 85, 274 dinosaurs 40, 80, 82, 141, 143n Diomede Islands 48 Djibouti 11, 18 DNA, hominins’ 45–7 Dogger Bank/Doggerland 95, 96, 97 dogs 74 doldrums, the 224, 234–5, 239 donkeys 76, 83, 88, 89, 192 Dover, Strait of 57, 59 dragonflies, giant 262–3, 265 Drake, Sir Francis 55, 249 Dublin: Leinster House 136n Durham: coalfields 272 Dutch East India Company 250 dysprosium 175 Dzungaria, China 197, 214 Dzungarian Gate, China–Kazakhstan border 189, 196–7, 203, 204 Eanes, Gil 223–4 Earth 282–3, 284, 286–7 circumference 227, 228 creation 94, 168 first circumnavigation 232, 248 magnetic field 169 orbit round the Sun 19, 21, 22, 24, 35, 36–9, 37 tilt 19, 35, 36–9, 37, 38, 44–5; see also Milankovitch cycles see also climate changes; tectonic plates earthenware pots 131, 149 earthquakes 8, 25, 28, 29, 30 East Africa 7–8, 10, 11, 12, 15, 16 climate 12, 18–25, 44 tectonic processes 10–13, 18–21, 24, 25, 30, 189 East African Rift 2n, 10–13, 17n, 18, 20, 20–25, 44, 108, 189, 287 East China Sea 114, 187 East India Company 222n East Indies 111 Eastern Desert 107, 133 Eastern Orthodox Church 185n Eastern Steppe 197 eccentricity cycle 19, 21, 22, 36, 37, 39 Ecuador: platinum 178n Edinburgh 151 Egypt/ancient Egypt 26, 28n, 64, 72–3, 100, 101, 107, 110, 119, 157, 184 buildings 132–3 pharaohs 72, 101, 127, 129, 147 pyramids 127–8, 129, 133, 138 sculpture 133, 147–8 electricity 156, 174, 271n, 272, 281, 282–3, 284, 286 electronic devices 157, 168, 175, 176, 178, 180, 181–2 elephants 33, 72, 256n Elgon, Mount 12 elm 130 Empire State Building, New York 134 Energy Return on Investment (EROI) index 274 English Channel 56, 57, 58–9, 134, 137 Eocene Epoch 129 equator, the 189, 232, 233, 234, 235, 238 equids 88–9, 197–8 Eratosthenes 227 Eridu 71 Eritrea 11 EROI index see Energy Return on Investment Erzgebirge Mountains: tin mines 158 ethane 276 Ethiopia 10, 11, 13, 14, 18, 28n, 72 Etna, Mount 117 Etruscans 27, 28 Euphrates, River 27, 65, 90, 107 Eurasia 9, 26, 27, 28, 39, 42, 47, 56, 77, 106, 143, 183, 194 climate 2, 48, 196–7 fauna and flora 49, 53n, 79, 87–90 warfare 76 Exeter Cathedral 134 Exploration, Age of 96, 216, 217, 246 extinctions, mass 40, 82, 85, 141, 142–3 and n, 144, 145, 178n factories (coastal forts) 253 farming see agriculture feldspar 148 Ferdinand II, of Aragon 227 ferns 78, 79, 262 Ferrel cells 235–6, 248 Fertile Crescent 63, 65, 66, 67, 158, 269 fertilisers, artificial 120, 178–9 feudalism 212 Finland 195, 286 fir trees 79, 130, 141 fire 15, 17, 69, 131–2, 173–4 firebricks 131–2 fish/fishing 95–6, 97, 275, 280 flax 82 flint 17n, 137, 139–40, 156, 164 Florida 237 flour 63, 68–9, 257 flowers see plants and flowers foraminifera/forams 85, 128–9, 133, 138, 139, 140, 144, 275 forests see rainforests; trees/forests fossils 13–14, 18, 40, 52n, 137–8, 141, 150n, 160 France 56, 57, 58, 185, 207, 208, 267, 269, 284 corsairs 249 fur trappers 195 maritime trade 245 waterwheels 257 wine regions 137 frankincense 192, 193 Franks 207, 208 frogs 85 fruit/fruit trees 78, 81 fungi 263, 264 fur trade 195 Galilee, Lake 110n gallium 176, 180 Ganges Basin 268 Ganges River 26, 66, 267 Gansu Corridor 184–5, 188, 203, 204 gas, natural 274, 276, 279, 280 Gaul 185, 207 Gazelles 61, 72, 275 genetic diversity 45–7 Genghis Khan 205, 209 Genoa/Genoese 99, 211, 212, 217, 227, 229 geological map, first 150 and n Germanic tribes 185n, 206–7, 208, 269 Germany 58, 59, 127, 185n, 208, 273, 284 Giant’s Causeway, Northern Ireland 143 Gibraltar 217n Strait of 99, 101, 106, 118, 158, 217 and n, 220 ginger 112–13, 114, 241 ginkgo 79 giraffes 83 Giza, Egypt: pyramids 127–8, 129, 133, 138 glaciation/glaciers 31, 32, 40, 54–7, 58, 60, 91, 146, 171–2, 184, 264–5 glass/glass-making/glassware 115, 132, 140, 193, 255 glazing pottery 131 globalisation 246 global warming 31, 38, 86, 281n; see also climate changes; greenhouse gases gneiss 133 Goa, India 245 goats 67, 74, 75, 77, 83, 88, 117 Gobi Desert 184, 185, 189, 191, 197 GOE see Great Oxidation Event gold 159, 168 and n, 174, 175, 178, 182, 192, 193, 218 Gona, Ethiopia 18 Gondwana 139, 264, 265, 267 gourds 66n grain(s) 63, 65, 65, 67–8, 73, 74, 116–18, 120, 166, 200, 205, 208, 257; see also cereal crops Grampian Mountains 148 Granada, Spain 218 and n granite 127–8, 132, 133, 145–8, 158, 267n grasses 67, 77, 80–81, 87–8, 90 grasslands 15, 77; see also savannah; steppes Great Hungarian Plain 196, 205 Great Indian Desert 29 Great Oxidation Event (GOE) 171–2, 173, 280n Great Pyramid, Giza 127–8, 129, 138 Great Sandy Desert, Australia 190 Great Wall of China 203–4, 208 Greece/ancient Greeks 27, 28, 73, 99, 100, 107, 110–11, 115–18, 135 armies 116n, 118 city-states 73, 116–17 Huns 207 greenhouse effect 10, 40, 42, 84–5, 142, 171 greenhouse gases 38, 40, 42, 44, 279–80 see also carbon dioxide; methane Greenland 32, 40, 96, 143 Grenville Mountains 153 Guatemala 28 guilds, medieval 212 Guinea, Gulf of 224, 239, 253 guinea fowl 74 guinea pigs: and scurvy 241n Gulf Stream 43, 61, 237, 238, 286 Gunflint Iron Formation 170n gunpowder 194, 200n, 211, 213 gymnosperms 79, 141 gyres, ocean 237, 238n, 247 Hadley cells 232–3, 235–6, 285 haematite 170 Haifa, Israel 101 Han dynasty (China) 93, 183, 184, 186, 187 and n, 190–91, 203–4 Harappan civilization 26–7, 64 Hawaii 107n, 222n helium 167, 180n Hellespont, the 117, 118, 120 hemp 82 Henry VII, of England 231 Herat, Afghanistan 190, 194 herbicides 120, 274 herbs 115n Herculaneum 162 Herodotus 73 hickory 130 hides/leather 75, 77, 88, 140, 193, 255 structures 130 Himalayas, the 9, 10, 11, 26, 32, 42, 48, 159, 184, 191, 195, 203, 242, 243, 268, 285 Hindu Kush 190, 203 hippopotamuses 33, 83n Hispaniola 230 Hitler, Adolf 215 Holland see Netherlands Holocene Epoch 32, 40, 42, 64–5 Homer: Iliad 200n hominins 7–8, 12–16, 22, 23, 30, 44, 53 bipedalism 14–15, 16 brains and intelligence 15, 16, 17, 19–20, 22, 24, 25 DNA 45–7 as hunters 15, 17 migration from Africa 22, 23, 45–6, 47, 52, 63 and see below Homo erectus 15–18, 22, 23, 47 Homo habilis 15, 16 Homo heidelbergensis 16 Homo neanderthalensis see Neanderthals Homo sapiens/humans 7, 8, 16, 22, 23, 25, 47, 49–54, 84 Hormuz, Strait of 107, 119, 120–21 ‘horse latitudes’ 235 horses 49, 75, 76, 77, 83, 86–7, 88, 89–90, 192, 197–200, 201–2, 205, 213, 214 Hudson Bay, Canada 49 Humboldt Current 247, 249 Hungary 185n, 202, 209 Huns 203, 204, 205, 206, 207, 208 hunter-gatherers 15, 61, 62, 63, 70, 74, 75, 80, 197 hydrogen 167, 175 hydrogen chloride 142 hydrogen sulphide 280 Iberian Peninsula 104, 105, 185, 208, 217 see also Portugal; Spain ice ages 19, 23, 24, 31–5, 34–5, 38–9, 44–5, 48–52, 53-60, 61, 64, 95, 172, 265 Little Ice Age 195n, 211 ichthyosaurs 133 igneous rocks 132, 179 incense 115, 192 India 9, 26, 27, 28n, 42, 48, 91, 92, 104, 110–11, 114, 188, 191, 202, 203, 213, 228, 244, 245, 267, 285 cotton 112, 193, 259, 269 eruption of Deccan Traps 143n exports 193 Mogul Empire 210n, 249 monsoons/monsoon winds 1, 10, 110, 242–4 population 284 rare earth metals 177 spices 112–13, 115, 218 Indian Ocean 10, 11, 29, 107, 108, 110, 111, 119, 187, 191, 226, 227, 229, 237, 238, 239–40, 243, 244, 245, 248, 252 Indiana limestone 134–5 indigo 193 indium 175, 176, 180, 181, 182 Indonesia 47, 48, 54, 121, 285 volcanic activity 111 Indonesian Seaway 10, 11 Indus River/Valley 26, 91, 107, 190, 268 civilisations 26–7, 66, 73, 90, 157 Industrial Revolution 5, 31, 78, 97, 125, 130n, 150, 152, 167, 254, 259–60, 266, 268, 269, 279, 286 insects 80, 262–3, 265 internal combustion engine 78, 273 Intertropical Convergence Zone (ITCZ) 234–5, 243 Iran 29–30, 48, 110, 120, 121, 190; see also Persia Iraq 48, 71, 120 iridium 177–8 iron 1, 92, 130n, 163, 164–5, 167, 168–9, 170, 174, 177, 178, 280n and Banded Iron Formations 169–70, 173, 177 cast 165 production 164–5, 183, 257, 259, 260, 266, 269, 270 tools and weapons 128, 165–6, 173, 174, 285 wrought 164–5, 166 see also steel Iron Age 156, 165, 167, 174 irrigation 65, 71, 73, 90, 92, 116, 200 Isabella, of Castile 226n, 227, 229, 230 Isfahan, Iran 190 Islam/Islamic culture/Muslims 110, 205, 212, 213, 217–18 and diet 83n Israel 52n, 101n, 163, 285 Istanbul see Constantinople Italy 105n, 133, 207, 208, 285 see also Rome ITCZ see Intertropical Convergence Zone jade 183 Jakarta, Indonesia 252 Janissaries 205 Japan/Japanese 121, 122n, 222n, 228, 245, 248 exports 112 landfill mining 182 Java 111, 114, 119n, 251, 252 Jefferson, President Thomas 136n, 147 Joao II, of Portugal 226, 229 Jordan valley 110n Judaism: and diet 83n Jupiter 36, 180n Jurassic Coast, England 137–8 Jurassic Period 133, 134, 274, 279 Kalahari Desert 190 Kalmuks 203 kaolin 148–9, 150n Karakorum, Mongolia 209, 211 Kazakh Steppe 196, 197n, 201 Kellingley, Yorkshire: coalmine 271 Kenya 10, 239 Kenya, Mount 12 kerosene 273 Khitans 202 Khufu, Pharaoh 127 Khwarezmids 212 Khyber Pass 190, 203, 204 Kilimajaro, Mount 12 Kirghiz, the 202 Kish 71 Knossos palace, Crete 161 Korea/South Korea 121, 184 Krakatoa, eruption of (1883) 111 Kublai Khan 210 Kunlun Mountains, China 191 Kuwait 120 Laetoli, Tanzania 14 lakes 20, 20, 21, 57, 72 ‘amplifier’ 20, 21, 22, 24, 44 meltwater 60 Lancashire: coalfields 272 landfill mining 182 ‘lanthanide’ elements 176 lanthanum 176–7 lapis lazuli 183 larches 79 Laurasia 139, 267 Laurentia 153 Laurentide ice sheet 49, 55–6 lava, volcanic 12–13, 24, 132, 141–2, 143, 144 lead 131, 159, 163, 168, 174 leather see hides Lebanon 101n, 131, 163, 285 Le Clerc, ‘Peg Leg’ 249 legumes 81 Lesser Antilles 230 Levant, the 23, 60, 61, 65, 73, 74 Lewis (Meriwether) and Clark (William) 55 Libya 100, 277 lignin 264 limestone 85n, 132, 144, 153, 257, 266 hot-spring 133 Indiana 134–5 nummulitic 127, 128–9, 132–3 oolitic 133–4 Tethyean 135–6 travertine 133 linen 193, 255, 263 lions 33–4 lithium 167, 180, 182 llamas 74, 76, 88, 89 loess soils 56, 65, 184 and n Lombards 207 London 135, 137, 152, 154–5, 272 Bank of England 134 British Museum 134, 148 Buckingham Palace 134 Cleopatra’s Needle 147 Great Fire (1666) 134 Marble Arch 135 One Canada Square 154–5 St Paul’s Cathedral 134 The Shard 154–5 Tower of London 134 Underground/Tube 155 Los Angeles 248 Getty Center 133 Lucy (hominin) 14, 18 lycopsids 262 Macau, China 245 mace 114, 115n Mackenzie River 60 Madeira 218, 220, 222, 229, 253n Magellan, Ferdinand 54, 247–8 Magellan Strait 54–5 magma 11, 20, 28, 111, 132, 142, 143, 145, 146, 148n, 158, 1 59, 179 Magna Carta 58 magnetic field, Earth’s 169 magnetite 170 magnets 175, 176, 180n Magyars 203, 204 Maison Carrée, Nîmes, France 136n maize 66, 67 Makian Island 114 Malabar Coast, India 114, 240 Malacca, Malaysia 114–15, 245 Strait of 114, 115, 119, 121, 249 Malay Peninsula 114–15, 245 Mali 10, 193 Malindi, Kenya 239 Mallorca 221 mammals 5, 7, 12, 40, 53n, 61, 75, 86–7, 88, 90, 141n, 144 APP 82–4 mammoths 31, 49, 66n Manchuria 197, 202 Mani Peninsula, Greece 135 Manila Cathedral 136 Manila Galleon Route 246, 248–9, 250, 250–51 Mao Zedong 91 map-making 194 marble 132, 135–6 Marble Arch, London 135 marine snow 275 marjoram 115n Marmara, Sea of 117 mastodons 66n mathematics 194 Mayan civilisation 28, 64 meat 17, 75, 77, 83n, 84, 90, 198, 199, 255 medicines 82, 114, 175, 178, 194 Mediterranean region/Sea 28, 98–106, 112, 116, 118, 135, 158, 160, 163, 185, 187, 246 Megara, Greece 117 Mekong River 91 Melanesia 47 Merv, Turkmenistan 190, 212 Mesoamerica 28, 63, 66, 67, 129 Mesopotamia 26, 27, 28, 65, 67, 70–71, 71, 72, 200, 202 bronze 157–8 civilisations 130–31, 132 Mesozoic Era 42, 141 metals/metalworking 74, 130 and n, 131, 156–7, 255 casting 157 smelting 131, 132, 156 see also specific metals metamorphic rocks 132 methane 40–41, 84, 85n, 171–2, 172n, 276, 280n methane clathrate 85–6 Mexican War of Independence (1810–21) 248 Mexico 28, 66, 74, 248 Gulf of 279 Michelangelo Buonnaroti: David 135 microchips 17n, 148n, 175–6 Mid-Atlantic Ridge 9, 160, 221 Middle East 47, 65, 81, 104, 119, 120, 197, 202, 209, 211, 215n` Middle Passage 253n Milankovitch cycles 19, 37, 37–9, 44, 60, 70, 281n Military Revolution 213 milk 75–6, 88, 90, 199, 255 millet 65, 57, 184 millstones 63, 68 Ming dynasty (China) 204, 212 Minoan civilisation 27–8, 99, 161–3 Linear A script 163n Mississippi River 55, 123, 124, 125 Missouri River 55 mitochondria 45 Mitochondrial Eve 45–6 mobile phones see smartphones Mogadishu, Somalia 240 Mogul Empire 210n, 249 Mojave Desert 191 Moluccas, the 112–13, 113, 114, 115, 247 and n Mongol Empire 202, 203, 204, 205, 206, 209–13, 214 Mongolia 47, 197, 209 monsoons 72, 114, 189–90, 192, 238–9, 285 winds 110, 192, 240–44, 243, 251 moraines 54, 55–6, 95 Morocco 217–18, 223, 267 mortar 132, 139, 140–41 Moscow 195 Moti Island 114 mountain ranges 8, 9, 26, 28, 91, 98, 99, 104–5, 139, 144, 146–7, 159–60, 267–8, 285; see also volcanoes and specific ranges Mousterian tools 17, 22 Mozambique 11, 239 mules 76, 77 Mumbai, India 107n Muslims see Islam Mycenaeans 163 myrrh 192 Nagasaki, Japan 245 Napoleon Bonaparte 58, 59, 222n Native Americans 47 Natufians 61, 62 Neanderthals 16, 17, 23–4, 47, 50–51, 51, 53, 164 Neoclassicism: in architecture 136n Neolithic era 63–5, 158, 198 Nepal 92 Netherlands 58, 96–7, 114n, 119 and n, 284 corsairs 249 and Japan 122n maritime trade 245, 250–52 windmills 257 Newfoundland 96, 231 New Guinea 10, 48, 63 agriculture 66, 67 New York 55, 56, 114n, 153–4 Chrysler Building 153 Cleopatra’s Needle 147 Empire State Building 134, 153 Rockefeller Center 153 skyscrapers 154, 155 United Nations building 134, 145 Yankee Stadium 134 New Zealand 32, 237 nickel 167, 168, 175, 179 Nile, River/Nile Valley 23, 65, 72–3, 90, 100, 101, 106, 127, 132, 133, 184, 185, 187, 285 Delta 102, 107 Nineveh 71 Nippur 71 nitrogen 170, 178–9 noble metals see platinum group metals nomadic tribes 200, 201–3, 204–5, 206, 286 see also pastoral nomads Noranda (mine), Canada 163 Norfolk: cottages 152 Norilsk, Russia: mines 179 Norse fishermen and seafarers 95, 96 North Africa 89, 110, 128, 129, 138, 206, 208, 211, 215 agriculture 63, 65 camel caravans 192–3 climate 72, 101 coastline 99, 100–2, 105, 185, 217n North America 32, 33, 39, 43, 44, 48, 49, 51, 60, 63, 64, 103–4, 139, 143 animals 53n, 197, 214n grasses 87 prairies 79, 196, 214n, 284 see also Canada; United States North Atlantic Garbage Patch 238n North Atlantic Gyre 238n North Atlantic Igneous Province 143 North Downs 137 North Pole 37, 38, 39, 40, 43, 44, 224 North Sea 57, 95, 96, 279, 286 Northumberland: coalfields 272 Norway 54, 286 nuclear fission/fusion 167–8, 169, 182n, 281 Nummulites/nummulitic limestone 128–9, 132–3 nutmeg 114, 114n, 115n, 241, 247 oats 67 Obama, President Barack 124 obsidian 17n, 140, 156 Oceania 47 oceans 5, 10, 41, 43, 85, 86, 94–5, 97–8 acidic 280 anoxic 142, 173, 278, 278–9 Banded Iron Formations 170, 171, 179 black smokers (hydrothermal vents) 159, 160 chokepoints 98, 115, 118–19, 121, 217n, 273 crust 8–9, 94, 104, 139, 142, 145–6, 159, 160, 163, 221 currents and current sailing 5, 41, 219–20, 222, 223–4, 226, 227, 230–31, 232, 244n, 246 doldrums 224, 234–5, 239 falling/lower levels 32, 34, 44, 45, 48, 49, 50, 53–4, 56–7, 89, 95, 125, 138–9 gyres 237, 238n, 247 and iron 173 and plankton 85, 144–5, 274–6 rising/higher levels 31, 33, 38, 40, 52, 54, 57, 60, 96, 97, 124–5, 129, 138, 221, 268, 277, 280 salt content 105–6 thermohaline circulation 61–2, 278 see also specific oceans and seas ochre 164 Ogodei Khan 209 Ohio River 55 oil 120–21, 262–3, 273–9, 280, 286, 287 ‘oil window’ 276 Oldowan tools 16–17, 18, 22 olive oil 257 Oman 131 onagers 89 One Thousand and One Nights 110 ooliths 133–4 oolitic limestone 134 ophiolites 160, 163, 201n opium 115 oregano 115n Organic Energy Economy 258 orogeny 267n Orpheus and Eurydice 135 osmium 177 ostriches 72 Ostrogoths 207, 208 Ottoman Turks 205, 213 oxen 75, 77, 200 Oxford University 134 oxygen 167, 170–74, 175, 265, 275, 278, 280 ozone layer 142 172 and n Pacific Ocean 10, 43, 111, 122, 191, 222n, 237, 247, 248 Pacific Trash Vortex 238n Pakistan 92, 284 Palaeocene–Eocene Thermal Maximum (PETM) 40, 84–6, 129, 143, 145, 279–80, 287 Palaeogene Period 42, 178n Palaeozoic Era 42, 141 Palestine 185 Palin, Sarah 48n palladium 175, 177, 179, 182n Pamir Mountains 189, 191 Panama Canal 55, 120 Panama Isthmus 43, 44, 49, 88, 89, 249 Pangea 87, 103, 104, 138, 139, 141, 143, 144, 201n, 262, 267, 267, 268, 276 Panthalassa 103n Pantheon, Rome 135, 162n paper/paper-making 79, 194, 263 Paris Arc de Triomphe du Carrousel 200n Cleopatra’s Needle 147 Parks, Rosa 126 pastoral nomads 77, 200, 201, 203, 213, 214, 286 horse-riding 201–2, 208, 213–14, 215 Patagonian Desert 190 Patagonian Ice Sheet 54 Patzinaks 203 ‘Pax Mongolica’ 210–11 Pearl Harbor 222n peat 261–2, 263, 265, 266, 268 Peloponnesian War (431–405 BC) 117–18, 120 Pentagon, Virginia 134 pepper/peppercorns 112–13, 114, 115n, 193, 241 peppers 81, 113n perissodactyls 82–3, 84, 86, 144 permafrost 33, 86, 91 Permian Period 42, 103, 138, 141, 142, 143, 179, 264 Persia 27, 117n, 187, 188–9, 202, 207 exports 131, 193 kerosene 273 mythology 200n Wall 207–8 windmills 257 Persian Gulf 70, 104, 107, 108, 110, 119 oil 120, 121, 279, 286 Peru 67, 278n, 286 pesticides 120, 274 PETM see Palaeocene–Eocene Thermal Maximum petroleum 178, 273 PGMs see platinum group metals pharaohs 72, 101, 127, 129, 147 pharmaceuticals 120, 178, 274 Pharos, island of 101 Philippines, the 248, 249 philosophies, spread of 194 Phoenicia/Phoenicians 99, 100, 101n, 107, 158, 163, 219, 237 photosynthesis 142, 171, 258, 261, 265, 274–5 phytoplankton 274–5 pig iron 165, 166, 177 pigs 74, 83, 88 pine trees 79, 130, 161 Pittsburgh, Pennsylvania 270 plague 211–12 plankton 85, 138, 140, 144, 145, 274–6, 278, 287 plants and flowers 78 angiosperms domestication of 52, 59, 62, 64, 65–7, 68, 81, 87, 214n gymnosperms see also cereal crops; crops; photosynthesis plastics 120, 150n, 175, 178, 238n, 274 plate tectonics see tectonics platinum 177, 178–9, 182 platinum group metals (PGMs) 168, 176, 177–8, 179–80, 182n pliosaurs 133 ploughs 76, 77, 165–6, 215n, 255, 268, 285, 286 Polar cells 235 Polaris 37, 224 Polo, Marco 258–9 Pompeii 162 Pontic–Caspian Steppe 196, 214 population growth 2, 22–3, 70, 72, 87, 117, 166, 255, 256, 257 porcelain 112, 115, 149–50, 249 Portland stone 134 ports 98, 100, 101, 105n, 115, 119, 194, 212 Portugal/Portuguese 193, 217–18, 219–20, 222, 229, 245, 247n sailors 119, 193, 223–7, 231, 234, 239–41, 244–5, 247–8 slavery/slave trade 218, 222, 253n Portuguese Route 249–50, 250–51 potatoes 66, 81, 82, 131 Potosí silver mines, Bolivia 248–9 pottery see ceramics precession 19, 21, 23, 36–7, 37, 44 primates 82, 84, 86, 144 printing 194 Pripet Marshes 204 promethium 176 propane 276 Protestantism 185n Ptolemy (geographer) 111, 226 pumpkins 66n pyramids 127–8, 129, 133, 138 Pyrenees Mountains 267 Qatar 120 Qin dynasty (China) 184, 203 Qing dynasty (China) 91, 195, 214 quartz 148 and n quartzite 17n Quaternary Period 31, 32, 34–5, 40, 42 quicklime 139 radiolarians 140, 275 railways 55, 56, 100, 150n, 152, 167, 260 rain-shadow effect 11, 190, 195, 214n rainfall 10, 11, 21, 64, 142, 189, 280 rainforests 7, 80, 190, 223n, 232, 275, 285 rare earth metals (REMs) 168, 176–7, 180, 181–2 Ravenscroft, George 140 Reconquista, the 217, 219 Red Sea 11, 104, 107, 108–10, 121, 133, 187, 192, 193 redwoods 79 Reformation, Protestant 185n religions 194 see also Christianity; Islam; Judaism REMs see rare earth metals reptiles 79, 82, 133 Rhine, River 57, 185, 206, 207, 208 rhinoceroses 33, 83 rhodium 177, 182n rice 65–6, 67, 69, 91 Rio Tinto mine, Spain 163 rivers 2, 41, 61, 70, 72, 90, 91–3, 92, 116, 144 see also specific rivers roads 2, 56, 74, 93, 100, 187, 273, 274 Roaring Forties 43, 237, 250, 251, 252 and n rock types 132; see also basalt(ic) rocks; shale rocks Rocky Mountains 55 Rodinia 153 Roman Empire/Romans 27, 28, 73, 99, 100–1, 110–11, 162, 183, 185–7, 190–91, 206–8, 210–11, 218 architecture 136n, 162n coalmines 259 metalworking 259 population 186 underfloor heating systems 259 waterwheel 257 Rome 185, 207, 208 Colosseum 133 Pantheon 135, 162n Trajan’s Column 135 root plants 81–2 rosemary 115n Rove Formation 170n Rub’ al-Khali Desert 191 rubber, synthetic 178 rubies 241 ruminants 83; see also cattle/cows Run, island of 114n Rushmore, Mount 147 Russia/Soviet Union 48–9, 195, 197n, 209, 213, 214 Hitler’s invasion 215 trade 120 wheatfields 214, 215n see also Siberia ruthenium 177, 182n Rwanda 28n rye 61, 52, 67 sabre-toothed tigers 31, 49 saffron 115n Sahara Desert 66, 72, 89, 189, 192–3, 217–18, 220, 223n Sahel, the 63, 66, 74 Sahul 48 sailing and navigation 118n, 169 current sailing (volta do mar) 219–20, 223–4, 226, 227, 230–31, 232, 244n in doldrums 224, 234–5, 239 see also oceans; ships; trade routes, maritime St Christopher, Gulf of 226 Saint Helena 221n St Lawrence River 55 St Paul’s Cathedral, London 134 Salisbury Plain 137 salt 105, 193, 273 Salween River 91 Samarkand, Uzbekistan 190, 194, 212 Sanchi Stupa, India 129 sand 148n sandstone 132, 151–2, 276 Nubian 132, 133 Santa Marta, Gulf of 225 Santa Vitória, Brazil 225 Santorini (Thera) 162–3 Sao Tomé 225 Sardinia 99, 208 Sargasso Sea 238n Saturn 181n Saudi Arabia 120–21 savannah 7–8, 12, 14, 24, 66, 189 Scandinavia 32, 57, 58, 95, 195 scandium 176 schist 153, 154 Scotland 54, 57, 58, 148, 150 screens, TV and smartphone 176, 181 scurvy 240 and n, 241 Scythians 202 seas see oceans seaweed 171, 238n sedimentary rocks 132 Sefidabeh, Iran 29 Serengeti Desert 33 Shah Jahan 249 shale rock 125, 170, 266, 276, 279 sheep 74, 75, 76, 77, 83, 86–7, 88, 117, 198, 199, 201, 209 ships/shipping 78, 95, 96, 98, 101n, 107–8, 117–21, 167, 193, 219, 228, 246 galleons 237, 246, 248–9 galleys 219 hammocks 230n masts 130 scurvy 240 and n, 241 slave ships 253–4 steamships 107n, 122n, 260 warships 119, 122n see also sailing and navigation Siberia 32, 47, 48, 52, 142, 185, 195, 201n, 267, 279, 286 Siberian Traps 141–2, 143, 179 Sicily 105n, 208 siderophile metals 168, 178 Sierra Nevada Mountains 218n silica/silicon/silicon dioxide 17n, 140, 146, 148n, 167, 168, 175, 178n silk 112, 115, 187 and n, 193n, 249, 255 Silk Road 110, 182, 186, 187–91, 193–4, 197, 203–4, 211, 215, 285 silver 159, 163, 168, 174, 175, 177, 182, 193, 248–9 Sinai/Sinai Peninsula 23, 47, 131 Sinai Desert 110, 192 sisal 82 skyscrapers 153, 154, 155, 167 slate 132, 152–3 slavery/slave trade 116n, 125–6, 205, 218, 222, 253–4, 269 sloths, ground 49 smartphones 168, 175, 176, 181–2 Smith, William 150n Snowball Earth 172 solar energy 67, 171, 255, 257–8, 281 solar wind 169 Somatic Energy Regime 258 Sonoran Desert 191 sorghum 66, 67 South Africa 11 Cape of Good Hope 121, 225–6, 231, 250 platinum group metals 179–80 rare earth metals 177 veld 196 South America 42, 43, 48, 49–50, 54, 89, 104, 139, 237, 267 slave trade 254 South China Sea 115 South Downs 137 Southern Cross 225 South Pole 42, 43, 44, 103, 265 Soviet Union see Russia soya beans 65 Spain/the Spanish 58, 59, 90, 118, 218 and n, 226n, 227, 229, 231, 247n, 267 explorers and navigators 119, 218n, 219, 231, 237, 245, 247, 248–9 galleons 246, 249 mines 163 Reconquista 217, 218 saffron 115n Visigoths 208 Sparta 117–18 Spice Islands 96, 240, 245, 247, 251 spice trade 112–15, 193, 211, 218, 241, 245, 249, 252 spiders 262 spore-forming plants 78–9 spruce trees 79 squash plants 66, 81, 214n Sri Lanka (Ceylon) 113, 221, 245n Staffordshire: coalfields 272 star fossils 138 stars 37, 118n, 148n, 167–8, 169, 224, 227, 240, 252n, 281 steam engines 78, 97, 149, 233, 254, 259–60, 273 steam-powered machinery 148 steamships 107n, 122n, 260 steel 130n, 166–7, 174, 255, 272 step pyramids, Mesoamerican 128 steppes 33, 61, 62, 77, 79, 89, 196–203, 198–9, 204, 208 nomads 200, 204–5, 206, 208, 213–14 stirrups 194 stock market, first 97 Stoke-on-Trent: potteries 149 Stonehenge, England 137 Strabo 111, 228 ‘subtropical highs’ 232, 233 Sudbury Basin, Canada 179 Suez, Gulf of 110n Suez Canal 107n, 120, 121 Suffolk: cottages 152 sugar plantations 222, 252, 253 Sugarloaf Mountain, Rio de Janeiro 147 sulphides 157, 159, 280 sulphur 1, 167, 259 sulphur dioxide 142 Sumatra 111, 112, 114, 115, 119n, 252 Sumerians 71, 131 Sun, the/sunlight 36, 41, 43, 44, 171, 232, 258, 281 Earth’s orbit round 19, 21, 22, 24, 35, 36–9, 37 proto- 9, 168 solar wind 169 ultraviolet radiation 142, 170, 172 and n see also solar energy Sunda Strait 119n, 252 Sundaland 48 sunflowers 214n supernovae 167 swamp forests 262–3, 265–6, 268, 274 Sweden 286 Syria 163, 285 Tabriz, Iran 30 taiga 79, 195, 196 Taj Mahal, Agra, India 249 Taklamakan Desert 185, 189–90, 191 Tambora, eruption of (1815) 111, 141n tantalum 175 Tanzania 10, 11, 14 tapirs 83 Tarim Basin, China 185, 189, 204 taro 66 Tasmania 48, 97 Taurus Mountains 74, 163 Teays River 55 tectonic plates 8–10, 11, 12–13, 18, 24, 25, 41, 43, 56, 88, 98–9, 102–3, 106, 111, 135, 145–6, 148n, 159, 160, 161–2, 190–91, 218n, 262, 266, 268 and convergent plate boundary 9 and early civilisations 25–30, 70 Tehran, Iran 29–30 Ternate Island 114 Tethyean limestone 135 Tethys Ocean/Sea 102–3, 103, 104, 104–5, 105, 129, 135, 136, 138, 160, 163, 218n, 267, 274, 276–7, 279, 285 textiles 259, 269; see also cotton; wool Thames, River/Thames Valley 57, 154 Thar Desert 191 thatch-roofed buildings 152 Thebes, Egypt: Luxor Temple 132 Thera (Santorini) 162–3 thermohaline circulation 61–2, 278 Thirty Years War (1618–48) 58 thrust faults 28–30 thyme 115n Tian Shan Mountains 191, 196 Tibet/Tibetan Plateau 10, 28n, 91–3, 92, 184, 185, 191, 242, 243, 285 Ticino, River 140 Tidore Island 114 Tigris, River 27, 65, 90, 107 timber 73, 79, 130, 255–6 timber-framed houses 152 Timbuktu, Mali 193 tin 158, 164, 175, 267n tipis 130 Tivoli, Italy: mineral springs 133 Toba, eruption of 111 tobacco 252, 254 toilets, Minoan 161 tomatoes 66, 81 tools 15, 16–17, 22, 24, 137, 140, 156 Acheulean 17, 22 agricultural 76, 165–6, see also ploughs bronze 157–8, 161, 164, 165 iron 165 Oldowan 16–17, 18, 22 steel 166–7 Tordesillas line 247n Toscanelli, Paolo dal Pozzo 228 Towers of Paine, Chile 147 trade routes 29, 30, 58, 76, 89, 110, 158, 185, 194, 203, 215 maritime 106–11, 108–9, 110, 112, 114–15, 118, 119–21, 194, 216, 218, 232, 247–54 see also Silk Road trade winds 73, 219, 220, 230, 233–4, 235, 237, 238, 243–4, 246, 247, 253 Trafalgar, Battle of (1805) 58, 118 travertine 133 trees/forests 12, 15, 33, 40, 44, 61, 78, 79, 80, 81, 85, 161, 189, 255, 258, 263–4 and coal formation 261–5 coppicing 256, 258, 259 swamp 262–3, 265, 266 see also rainforests; timber Triassic Period 141, 143 Troodos Mountains, Cyprus 160, 163 Trump, President Donald 122, 124 tsunamis 25, 163 tundra 31, 33, 53, 79, 195 tungsten 168 Tunisia 100, 105 Turkey 65, 70, 88 see also Ottoman Turks turkeys 74 Turkmenistan 190, 212 Uffington White Horse, Oxfordshire 137 Uighurs 202 Ukraine 120, 202 Umayyad Caliphate 217 ungulates 12, 82–4, 86–7, 90, 196, 200, 287 see also camels; cattle; hippopotamuses; horses; pigs; rhinoceroses; zebras etc United Arab Emirates 120 United Nations building, New York 134, 145 United States 55–6, 121, 122, 124–5, 262, 267 architecture 134–5, 136 ‘Black Belt’ 125–6 coal industry 279–70 cotton plantations 125, 252, 253–4 elections (2008, 2012, 2016) 122, 123, 124 forests 195 and Hawaii 107n, 222n Indiana limestone 134–5 and Japan 122n, 222n population 284 rare earth metals 181 slavery 125–6, 253–4 see also Alaska; North America Ur 71 Ural Mountains 163, 196, 200–1 and n, 267 uranium 168, 181n, 182n Uruk 71 Uzbekistan 190, 194, 212 Vandals 207, 208 Variscan Orogeny 267 Vega 37 vegetables 66 and n, 69, 78, 81–2, 131 Venezuela 231, 279 Venice 99, 115, 140, 211, 212, 217, 229 Vienna 209 Vietnam 92 Virginia Pentagon 134 State Capitol 136n tobacco plantations 254 University Library 136n Visigoths 207, 208 volcanoes/volcanic activity 8, 9, 12–13, 24, 25, 28, 43, 85–6, 98, 107, 111, 133, 141–2, 162 and n, 172, 173, 221n, 222, 277 Krakatoa 111 Mount Elgon 12 Mount Etna 117 Mount Kenya 12 Mount Kilimanjaro 12 Popocatepetl 28 Potosí (Cerro Rico) 177, 248n Tambora 111, 141n Thera 162–3 Vesuvius 162 wagons 76, 77, 200 Wales coal 266, 272 slate 152–3 warfare 57–8, 76, 98, 101, 116n, 117–18, 119, 122, 124, 126, 184, 200n, 217, 222n, 229, 245, 247n, 248, 254 nomadic tribes 201–3, 204–6, 213 see also gunpowder; weapons Washington, DC Capitol Building 136n Hoover Building 136n National Cathedral 134 Peace Monument 136 Treasury Building 136n White House 136n water buffalo 77 Waterloo, Battle of (1815) 222n waterwheels 68, 130, 165, 257, 259 wattle and daub 152 Weald–Artois anticline 56, 154 weapons 17, 137, 140, 156, 200n bronze 116n, 157–8, 164, 165 iron 165, 166 steel 166, 174 West Africa 66, 75, 242 coastline 193, 218, 223, 224, 253 Western Ghats, India 114 Western Steppe 196, 201 whales 83n, 95, 275 wheat 61, 65, 67, 87–8, 117, 184, 214, 215n, 286 White Cliffs of Dover 57, 137, 138, 145 White House, the 136n Wight, Isle of 137, 221 wigwams 130 wildebeest 33 windmills 68, 96, 130, 257 winds 5, 32, 56, 61, 99, 197, 216, 220, 223n, 232–3 and Coriolis effect 233, 235, 237 easterly trade winds 73, 219, 220, 230, 233–4, 235, 237, 238, 243–4, 246, 247, 253 monsoon 110, 192, 240–44, 243, 251 polar easterly 235, 238 solar 169 southwesterly/westerly 220, 226, 230, 236, 237, 238, 239, 244 wool 76, 77, 88, 90, 115, 201, 255, 259 Wren, Sir Christopher: St Paul’s Cathedral 134 writing/script Minoan 163n Phoenician 101n Sumerian 131 Xiongnu, the 202, 206; see also Huns Y-chromosome Adam 46 yams 66, 82 Yangtze River 28n, 65–6, 91, 184, 187 Yankee Stadium, New York 134 Yellow River/Valley 28n, 63, 65, 73, 90, 91, 184, 187 yew trees 79 Yorkshire 134, 152, 271, 272 Yosemite National Park, USA 147 Younger Dryas Event 61, 62, 64 yttrium 175, 176 Yuan dynasty (China) 91, 210, 212 yurts 130 Zagros Mountains 27, 71, 74, 104, 110 zebras 12, 83, 89 ziggurats 131 zinc 159, 163, 174 zooplankton 275


pages: 385 words: 103,561

Pinpoint: How GPS Is Changing Our World by Greg Milner

Ayatollah Khomeini, British Empire, creative destruction, data acquisition, Dava Sobel, different worldview, digital map, Edmond Halley, Eratosthenes, experimental subject, Flash crash, friendly fire, Hedy Lamarr / George Antheil, Internet of things, Isaac Newton, John Harrison: Longitude, Kevin Kelly, land tenure, lone genius, low earth orbit, Mars Rover, Mercator projection, place-making, polynesian navigation, precision agriculture, race to the bottom, Silicon Valley, Silicon Valley startup, skunkworks, smart grid, the map is not the territory

GPS had to have a model of the world within itself, to access when making its computations. Knowledge of where the Man fell to Earth—and, presumably, every other GPS location—was somehow a function of WGS 84. So now I needed to understand this common language, this mediating grid. The modern science of geodesy—refining our ability to measure the size of the earth and its gravity field—extends back more than 2,000 years. The Greek astronomer Eratosthenes used observation of the sun and the measured distance between Alexandria and the Egyptian town of Syene (now Aswan) to compute the planet’s circumference. His conclusion—25,000 miles—is only about 100 miles off from the figure we use today. The related practice of land surveying—attempts to get an accurate sense of spatial relations on the planet—is even older, traceable to ancient Egypt. The first land survey to use modern methods—essentially, the first organized attempt to define “here” and “there” over large swaths of land—was undertaken by the French astronomer Jean Picard in 1669, and continued by the Italian astronomer and mathematician Giovanni Cassini after Picard’s death.

., 29–30 electrical engineering, 48 electrical transmission, 158–61, 163–64 costs of, 241 disruption of, 158–59, 160 energy sources for, 160, 241 monitoring of, 159–61 electronic distance measurement (EDM), 251, 253 electronic monitoring systems, 175–77, 194–200 Electronic Route Guidance System (ERGS), 121 electronics, 85, 127 Elgin Air Force Base, 70 Elizabeth, N.J., 249 Elko County, Idaho, 136 ellipsoids, 247–49 Ellis, Roland, 63 eLoran, 166 El Segundo Air Force Base, 53 Endeavour, HMS, 7, 8–10 Enge, Per, 142, 171 England, xiv, 25–27, 104, 153 Hertfordshire County in, 197 Yorkshire County in, 113 English Channel, 166–67, 246 Enlightenment, 26 Eratosthenes, 245 Eschenbach, Ralph, 78–81, 83, 85, 87, 93 espionage, 55 Esri software company, 239 etak, 18–22, 118, 240, 262, 263, 265–66 definitions of, 18–19 Etak company, 122–23 Eurasia, 3 European Convention on Human Rights, 187 European Court of Human Rights, 187–88 European Datum 1952, 250 European Geostationary Navigation Overlay Service (EGNOS), 142 European Parliament, 104 European Space Agency, xvii European Union (EU), xvii, 144 Everest, Mount, 90 Eyjafjallajökull volcano, 230 F-4 aircraft, 59–60 Facebook, 194 Falcon Air Force Base, 62–63 Fallen Man photograph, 235–39, 235, 241–42, 248 GPS coordinates linked to, 238 location depicted in, 236, 245, 256 people and shops in, 236–38 time stamp on, 238 fascism, 177 Federal Aviation Administration (FAA), 140–41, 142, 151, 171 safety requirements of, 141 Federal Bureau of Investigation (FBI), 170, 178 Federal Communications Commission (FCC), 200, 201 Federal Express, 143 Federal Highway Administration, U.S., Electronic Route Guidance System (ERGS) of, 121 fertilizer, 102, 103 Fiji, 4, 10 financial services industry, 161–64 Finney, Ben, 264–65 fixed-wing gunships, 50–51 fleet management industry, 183–84, 201, 282 Florida, 30, 31, 70, 90, 195–96 Fontainebleau, 246 Forbes, 127 Forlander, Abraham, 12 Fort Carson, xiii Fort Collins, Colo., 74, 75, 101 Fort Davis, Tex., 214 Fort Walton Beach, Fla., 70–71 fossils, 205 France, 158, 252, 263 Frankenstein, Julia, 130, 132 Freiburg, University of, Center for Cognitive Science at, 130 Freundschuh, Scott, 125 Fukushima Daiichi nuclear power plant, 222, 225 Fulton, Steve, 139, 279 Gable, Ralph, see Schwitzgebel, Ralph Gable, Robert, see Schwitzgebel, Robert Galileo Galilei, 29 Galileo system, xvii–xviii, 144 Gambale, Nunzio, 164–66 Garmin C550 receivers, 126 Garmin GPS Systems, 100, 126–27, 242 consumer electronics segment of, 127 Gastineau Channel, 138 Gatty, Harry, 17 General Accounting Office, 60 General Electric, 44 General Motors, 120 geochronology technologies, 207 geodesy, 245–48, 250–55, 286 geographic information systems (GIS), 239–42 GPS linked to, 239–40, 245 perception of the world shaped by, 241–42 geography, 3–4, 19, 118, 125 geoids, 247, 256 Geological Survey, U.S.


pages: 481 words: 121,300

Why geography matters: three challenges facing America : climate change, the rise of China, and global terrorism by Harm J. De Blij

agricultural Revolution, airport security, Anton Chekhov, Ayatollah Khomeini, Berlin Wall, British Empire, colonial exploitation, complexity theory, computer age, crony capitalism, demographic transition, Deng Xiaoping, Eratosthenes, European colonialism, F. W. de Klerk, failed state, Fall of the Berlin Wall, Francis Fukuyama: the end of history, global village, illegal immigration, Internet Archive, John Snow's cholera map, Khyber Pass, manufacturing employment, megacity, Mercator projection, MITM: man-in-the-middle, Nelson Mandela, out of africa, RAND corporation, risk tolerance, Ronald Reagan, South China Sea, special economic zone, Thomas Malthus, trade route, transatlantic slave trade, UNCLOS, UNCLOS

Actually, the public's perception may not be so accurate, but people think they know what historians, geologists, and biologists do. We geographers are used to it. Sit down next to someone in an airplane or in a waiting room somewhere, get involved in a conversation, and that someone is bound to ask: Geography? You're a geographer? What is geography, anyway? In truth, we geographers don't have a single, snappy answer. A couple of millennia ago, geography essentially was about discovery. A Greek philosopher named Eratosthenes moved geographic knowledge forward by leaps and bounds; by measuring Sun angles, he not only concluded that the Earth was round but came amazingly close to the correct figure for its circumference. Several centuries later, geography was propelled by exploration and cartography, a period that came to a close, more or less, with the adventures and monumental writings of Alexander von Humboldt, the German naturalist-geographer.

See also specific regions and countries and geography, 10, 15 and Islam, 164 and NAFTA, 3 and population, 95-96 and terrorism, 175 Economist, 52, 95, 257 Ecuador, 120, 180 education graduate education of geographers, 6, 46 on Islam, 164 and population, 96 status of geography, X, 12, 13, 14-19 Eemian interglacial, 69, 72-73, 82, 83, 90 Egypt ancient civilization of, 128, 134,258-59 Islam in, 162, 185 terrorism, 156, 159, 161, 176 Ehriich, Paul, 93 empires, 77, 135, 138-44 The End of History (Fukuyama), 57 The End of Science (Horgan), 57 energy crises, 21,51, 132, 277-78. See also natural gas; oil England, 202. See also United Kingdom English Channel, 74 Enlai, Zhou, 125 Environmental Conservation, 15 environmental determinism, 11, 87-90 environmental issues, 6, 15, 100-101, 102, 115. See also global warming Eocene era, 55, 59, 63, 64, 64, 66 epidemiology, 6, 42-44, 43 equal-area projections in maps, 33 Equatorial Guinea, 185 Eratosthenes, 5 Eritrea, 118, 176, 184, 185 Estonia borders and boundaries, 169, 231 and European Union, 217, 218, 225, 227 language, 198, 199, 201 and NATO, 229 and Russia, 231, 234, 236 Ethiopia (formerly Abyssinia) borders and boundaries, 118, 259 colonialism, 111-12, 184 Ogaden, 184, 186, 260 population, 103 religion, 182, 184, 185, 260 wars, 266 ethnic groups and ethnic conflict. See also specific groups, such as Pushtuns and Kurds in Afghanistan, 157-58, 158 in Africa, 184, 261-62, 263, 264, 264, 265, 269 in China, 144 in Eastern Europe, 110, 207, 227-28, 229 in Iraq, 193 in Russia, 144, 146, 234, 242, 244-45, 246-47, 250, 253, 254 in Turkey, 228 United States on, 276 eukaryotes, 60 Eurasia.


pages: 482 words: 125,429

The Book: A Cover-To-Cover Exploration of the Most Powerful Object of Our Time by Keith Houston

clean water, Commentariolus, dumpster diving, Eratosthenes, financial innovation, invention of movable type, Islamic Golden Age, Kickstarter, knowledge economy, means of production, Murano, Venice glass, paper trading, Ponzi scheme, wikimedia commons

Collectively, Calliope, Clio, Euterpe, Terpsichore, Erato, Melpomene, Thalia, Polyhymnia, and Urania were the source of all divine inspiration, believed by poets, actors, astronomers, and philosophers to be the wellspring of their creativity and talents.39 Fittingly, the Mouseion, as their temple was known (we call its successors “museums”), was dedicated to the study of the natural world and the heavens above it.40 The Ptolemies attracted scholars with tax breaks and free accommodation, and encouraged them to spend their days in discussion, contemplation, reading, and writing.41 Euclid wrote Elements, his groundbreaking book on mathematics, at the Mouseion; it was there that an astronomer named Aristarchus surmised that the Earth orbited the sun and not the other way around, while his colleague Eratosthenes calculated the diameter of the Earth to a scarcely believable accuracy of fifty miles. And it was here that Archimedes, a Sicilian engineer who had grown up by the sea and who must have felt at home in the mighty port of Alexandria, was inspired to invent a screw-shaped pump later given his name.42 The Mouseion’s crown jewel was the fabled Library of Alexandria, reputed to contain some 700,000 scrolls.43 And just as a visit to any modern library reveals shelf after shelf of nigh-identical books, each one a variation on the same basic design, a visiting scholar at Alexandria would have been greeted by endless rows and cubbyholes of scrolls all produced according to a common standard.

Cuthbert Gospel, 295–96 tooled designs on, 303–4 Cowper, Edward, 134 Crates of Mallus, 23, 272–73 Crocodilopolis, Egypt, 241 crocuses, 172 Cromwell, Oliver, 323–24 Crusades, book burning in, 56, 58 cuneiform script, 9, 79–80, 81, 82, 93–94, 242 Cusanus (Nicholas of Kues), 107–9 Cuthbert, Saint, 284–85 dabbers (ink balls), 120, 122, 193 Daguerre, Louis-Jacques-Mandé, 227, 229 daguerreotypes, 227–28 Damascus, 54 Dandolo, Andrea, 175 Dante Alighieri, 208–9 Dark Ages, 164 Dattari, Maria, 279 Davenport, Cyril, 266, 268 Dazangjing (Great Treasury of Sutras), 181 deacidification, of books, 71–72 Dead Sea Scrolls, 26 De casibus virorum illustrium (On the Fates of Famous Men), 203, 205 deckle edges, 314 deckles, 314 in papermaking, 45–46 dedication, ix De dissectione partium corporis humani libri tres (On dissection of the human body; Estienne), 195 De diversis artibus (The Various Arts; Theophilus), 28–29 De integritatis et corruptionis virginum notis (Thoughts on the integrity and corruption of virgins), 305–6, 307 Demaratus, 96, 258–59 demotic scripts, Egyptian, 90–91, 244 Den, pharaoh, 244 Deng, dowager empress of China, 47 Densmore, James, 140 dermis, 24 Des destinées de l’âme (The destinies of the soul; Houssaye), 305–6 Destruction of Pharaoh’s Host in the Red Sea (Titian), 198 Deuteronomy, Book of, 26 devotional images (Andachtsbilder), 192–93 as pilgrims’ souvenirs, 192–93 woodblock printing of, 193 Diamond Sutra, oldest printed edition of, 183–84, 184 dichromated gelatin, 230, 231, 233 Didot, Saint-Léger, 64–65 Diether von Isenburg, archbishop of Mainz, 127 diethyl zinc (DEZ), 72 difthérai, 274 diminuendo, 162 dingbat, vii Diodorus of Sicily, 89 diptych (writing tablet), 257, 258, 274 Disquisition on the Composing Stick (Speckter), 121 Divine Comedy (Dante), 208–9 Djedkare Isesi, pharaoh, 248 Dōkyō, 182 Domesday Book, 233, 235 Dominican Order, 193 Donatus, Aelius, 106–7 Doresse, Jean, 277, 289 Dou, empress of China, 40–41, 47–48 double-cord binding, 296–98, 297, 330–31 drop cap, 3 Dunhuang, China, 37, 179, 183–85, 266, 267 Dünne, Hans, 114–15, 116 duodecimo (book size), 321, 323, 326 Dürer, Albrecht, 198, 203, 209, 212–13 woodcuts of, 195, 196, 197 Durham, England, 284–85 Durham Cathedral, 285 dust jackets, 304 duxustus parchment, 27 Eadfrith, 287 East Asia, papermaking in, 50, 53 e-books, xv–xvi publisher deletions of, xvi Edelstein, Der (The Precious Stone; Boner), 199, 201 Edinburgh, Scotland, 214, 304–5 Edinburgh, University of, 304 Egypt: Copts in, 294 linen-based paper in, 37 Egypt, ancient, 3–4, 6–10, 82–84, 89, 241–49, 270–71 Alexander’s conquest of, 88, 249 Books of the Dead in, 20, 157–58, 159, 245 inks in, 84–85, 242 papyrus scrolls in, 243–45, 247–56 scribes in, 85, 87–88, 87, 246, 250–51 taxation in, 249 writing on leather in, 20 Egypt, Ptolemaic, 19–22, 22, 88, 159, 249–52, 276 Antiochus’s invasion of, 22–23 Roman conquest of, 88 Egypt, Roman, codices in, 261–65, 270 Egyptology, 3 Eid, Albert, 289–90 Eid Codex (Jung Codex; Codex I), 289–91 El-Bahnasa, Egypt, 261–63 electronic books, see e-books electronic documents, as analogous to papyrus scrolls, 254 Elements (Euclid), 250 Elephantine Island, 270–71 enchiridion (handbook), 317 Encyclopedia Britannica, 90 endbands, 300–301, 331 endpapers, 300, 308, 331 England, 63 see also Great Britain; United Kingdom English Civil War, 323 engravings, 203–5, 206, 207–10, 207, 215–16, 220, 234 Epigrams (Martial), 274–76 epilogues, 329 Erasmus, 195 Eratosthenes, 250 Erotemata (Questions), 316, 317 Estienne, Charles, 195 etching: on armor, 210–11 copperplate printing and, 211–13, 216, 230 on iron plates, 211 Ethiopians, 293 Etruscans, alphabet of, 92 Euclid, 250 Eumenes II, king of Pergamon, 19–20, 21, 23 Euphrates River, 79 Euripides, 15 Europe: illuminated manuscripts in, 165–66 papermaking in, 56, 57, 58–63 spread of Christianity in, 164–65 woodblock printing in, 190–201 extract, 13 Eyck, Jan van, 121 Facen, Jacopo, 190–91 Fangshan, China, 181 feiqian (flying money), 187 Fellowship of the Ring, The (Tolkien), 298 Feltre, Italy, 190–91 Fenerty, Charles, 36 Feng Dao, 185 ferrous sulfate (copperas), 97, 100–101 Fifty Shades of Grey (James), 220 Filippo de Strata, 128–29 Finiguerra, Maso, 204, 206 First Folio (Shakespeare), 233 flying money (feiqian), 187 folio (book size), 313, 314, 314, 317–18, 325–26, 330 folio (page number), 10, 11 folios, 290, 291, 316 gatherings of, 311–12 fonts, monospaced, 142 foolscap (paper size), 324 foot margin, 6 footnotes, xv, 320 formes, 121, 122, 227, 230 four-color art, 307 Fourdrinier, Henry and Sealy, 65 Fourdrinier papermaking machine, 64–66, 67, 73, 76, 133, 135, 308, 314, 327, 329 Francesco Griffo, 317, 320 Frances Loeb Library, 280, 297 Frankfurt Book Fair, 123 Franks, 156, 165 Frederick II, Holy Roman emperor, 56 freesheet paper, 74, 75 French Revolution, 64 French Royal Academy, 68 Frey, Don, 256 Frisia, 298 frisket, 120 Fritsch, Ahasverus, 71 frontmatter head, xi, xv Fujiwara, Japan, 181 full-page art, 57 Fust, Johann, 106, 109, 126–27 Fust & Schöffer, 127, 329 Gaels, 161 galley, 121 Gamble, John, 65 Gardiner, Alan H., 92–93 Gardiner, Maine, 66, 68 Gaul, 156 Genoa, 175, 189 Gentleman’s Magazine, 70 Germanic tribes, 156, 164–65 Germany, 36, 63, 105, 107, 132, 139, 199, 206, 210–11, 225, 318, 325 see also Mainz, Germany gesso, 171 gewil parchment, 27 Gleissner, Franz, 221–22, 224 Gnostics, 279 goatskin, 20, 28, 30, 279, 295, 304 goldbeater’s skin, 171 Golden Ratio, 324 gold leaf, 169, 171 on covers, 304 Gorgo, queen of Sparta, 259 Gorstein, Irina, 280, 297 Gothic textura (blackletter) script, 99, 107, 123, 318 Goths, 156 Graf Zeppelin, 171 graphite pencils, 259 Great Britain, 156 illuminated manuscripts in, 161 parliament of, 323–24 Viking invasions of, 164, 284 see also England; United Kingdom Great Harris Papyrus, 249 Greece, ancient, 159 alphabet of, 92 papyrus in, 9–10, 94 papyrus scrolls in, 10, 244, 250–56 pen-and-ink writing in, 94–96 Greek, typefaces for, 316–17 Greeneville, Conn., 67 Gregory I, Pope, 166 Grenfell, Bernard P., 261–65, 276 grimoires, 34 guilds, medieval, 103 gum arabic, 30, 85, 94, 95, 100 oleophobic quality of, 223, 224 gunpowder, Chinese invention of, 177 Gutenberg, Johannes, 62, 101, 102–3, 169, 177, 199, 225, 301, 316 Ars grammatica of, 107, 199, 201 background of, 105 Bible of, 109, 114–23, 124–25, 145, 199, 229, 314, 316–17, 318, 324 holy mirror business of, 104–5 ink and, 121–22 movable type and, 106, 109, 114–23, 128 papal indulgences printed by, 108–9 presses of, 122–23 in Strasbourg, 103–6 gutter, 6 Haas, Wilhelm, 129 Hahl, August, 139–40 half title, iii halftone printing, 230, 231, 330 movable type and, 230, 233 Hancock, William, 308–9, 310 Han period, 39, 180 Hapi, 8 Hare, William, 304 Harun al-Rashid, 54 Havell, Robert, Jr., 216, 217, 218 He, emperor of China (Liu Zhao), 40–41 headbands, 300–301 head margin, 6 Hebrew language, 93 hei laohu (black tigers), 180 Hellespont, 6–7 Helmasperger, Ulrich, 126 Helmasperger Notarial Instrument, 126 Hemaka, 244–45 hemp, in papermaking, 37, 41, 42, 55 Hendriks, Ignace H.


The Art of Computer Programming by Donald Ervin Knuth

Brownian motion, complexity theory, correlation coefficient, Donald Knuth, Eratosthenes, G4S, Georg Cantor, information retrieval, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, Menlo Park, NP-complete, P = NP, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, sorting algorithm, Turing machine, Y2K

[MSP] In the notation of exercise 3.1-7 and Section 1.2.11.3, prove that the average value of the least n such that Xn = X^(n)_i lies between 1.5Q(m) — 0.5 and 1.625Q(m) -0.5. 5. [21] Use Fermat's method (Algorithm D) to find the factors of 11111 by hand, when the moduli are 3, 5, 7, 8, and 11. 6. [M24] Up is an odd prime and if N is not a multiple of p, prove that the number of integers x such that 0 < x < p and x2 — N = y2 (modulo p) has a solution y is equal to (p±l)/2. 7. [25] Discuss the problems of programming the sieve of Algorithm D on a binary computer when the table entries for modulus rrii do not exactly fill an integral number of memory words. > 8. [23] (The sieve of Eratosthenes, 3rd century B.C.) The following procedure evi- evidently discovers all odd prime numbers less than a given integer N, since it removes all the nonprime numbers: Start with all the odd numbers between 1 and N; then successively strike out the multiples pi, Pk(pk + 2), Pk{Pk + 4), . . . , of the fcth prime Pki for k = 2, 3, 4, ..., until reaching a prime Pk with pi > N. Show how to adapt the procedure just described into an algorithm that is directly suited to efficient computer calculation, using no multiplication. 9.

(As a consequence of (b), we can completely factor a given number n by doing only O(lognJ arithmetic operations on arbitrarily large integers: Given a partial factor- factorization n = ni...nr, each nonprime rii can be replaced by f(rii) • (ni/f(rii)) in Y2 O(log rii) = O(log n) steps, and this refinement can be repeated until all rii are prime.) > 41. [M2S] (Lagarias, Miller, and Odlyzko.) The purpose of this exercise is to show that the number of primes less than N3 can be calculated by looking only at the primes less than iV2, and thus to evaluate ir(N3) in O(N2+€) steps. Say that an "m-survivor" is a positive integer whose prime factors all exceed m; thus, an m-survivor remains in the sieve of Eratosthenes (exercise 8) after all multiples of primes < m have been sieved out. Let f(x, m) be the number of m-survivors that are < x, and let fk(x,m) be the number of such survivors that have exactly k prime factors (counting multiplicity). a) Prove that 7r(iV3) = ir(N) + f{N3, N) - 1 - /2(iV3, N). b) Explain how to compute f2{N3, N) from the values of ir(x) for x < N2. Use your method to evaluate /A000,10) by hand. c) Same question as (b), but evaluate f(N3,N) instead of f2(N3,N).

If k < M, then set X[k] 4-0, k 4- k + p, and repeat this step. 54. Set j 4- j + 1, p 4- p + 2, q 4- q + 2p - 2. If j < M, return to S2. | A major part of this calculation could be made noticeably faster if q (instead of j) were tested against M in step S4, and if a new loop were appended that outputs 2j + 1 for all remaining X[j] that equal 1, suppressing the manipulation of p and q. 4.5.4 ANSWERS TO EXERCISES 659 Notes: The original sieve of Eratosthenes was described in Book 1, Chapter 13 of Nicomachus's Introduction to Arithmetic. It is well known that 5Zpprime[p < N]/p = lnlnJV + M + O((logiV)-10000), where M = 7 + Efe>2 A*(fc) lnC(fc)/fc is Mertens's constant 0.26149 72128 47642 78375 54268 38608 69585 90516-; see F. Mertens, Crelle 76 A874), 46-62; Greene and Knuth, Mathematics for the Analysis of Algorithms (Boston: Birkhauser, 1981), §4.2.3.


pages: 158 words: 49,168

Infinite Ascent: A Short History of Mathematics by David Berlinski

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Douglas Hofstadter, Eratosthenes, four colour theorem, Georg Cantor, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, Murray Gell-Mann, Stephen Hawking, Turing machine, William of Occam

Like Pythagoras, Euclid is largely a man of mystery, with even the dates of his birth and the city of his origin unknown. It is the Greek philosopher and mathematician Proclus who has provided the most extended commentary on Euclid’s life. It amounts to only a single paragraph. “The man lived,” Proclus writes, “in the time of the first Ptolemy.” Euclid was thus younger, Proclus adds, than Plato’s students and older than Eratosthenes and Archimedes. Ptolemy I, the ruler of Egypt and so a midget among these mighties, makes a brief ignominious appearance in the account that Proclus offers, asking “if in geometry there was any shorter way than the Elements.” “There is no royal road to geometry,” Euclid informed the pharaoh brusquely. Very conscious of the importance of his subject, Euclid maintained a sideline in caustic commentaries.


pages: 194 words: 49,310

Clock of the Long Now by Stewart Brand

Albert Einstein, Brewster Kahle, Buckminster Fuller, Colonization of Mars, complexity theory, Danny Hillis, Eratosthenes, Extropian, fault tolerance, George Santayana, Internet Archive, Jaron Lanier, Kevin Kelly, knowledge economy, life extension, longitudinal study, low earth orbit, Metcalfe’s law, Mitch Kapor, nuclear winter, pensions crisis, phenotype, Ray Kurzweil, Robert Metcalfe, Stephen Hawking, Stewart Brand, technological singularity, Ted Kaczynski, Thomas Malthus, Vernor Vinge, Whole Earth Catalog

The famous library and museum at its peak may have held six hundred thousand scrolls—the equivalent of one hundred twenty thousand modern books. Alexandria’s library was an intensely productive community of writers, translators, editors, historians, mathematicians, astronomers, geographers, and physicians. Its librarians included Apollonius of Rhodes (poet of The Argonauts), Callimachus (the father of bibliography), Eratosthenes (who estimated the diameter of the Earth), Aristarchus of Samos (a Sun-centered Copernican eighteen centuries before Copernicus), and Hipparchus (discoverer of the precession of the equinoxes). By dint of exhaustive collection and close scholarship, canonical editions of classics such as Homer, Plato, and the Athenian playwrights were created and distributed. Later, the Hebrew Bible was translated into Greek in Alexandria.


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

.* To gauge latitudes north or south of the equator, Ptolemy counts the stars—those that rise and set over a given region at different times over the course of the year, those that neither rise nor set but always appear as darkness falls, and those that never come into view, though they be well known elsewhere. On the Island of Thulē (Shetland Islands), for example, far up at 63 degrees north, where the longest day lasts a full twenty hours, no one sees the mid-summer return of the Dog Star that marks the flooding of the Nile in Egypt. Ptolemy assumes the world to measure 18,000 miles around. His predecessor Eratosthenes had figured the earth’s circumference at a more generous 25,000 miles in 240 B.C., by comparing shadow lengths in two cities along the Nile on the day of the summer solstice, but Ptolemy favors the more recent work of Poseidonius, about 100 B.C., who observed the stars to shrink the globe. Ptolemy’s Geographia offers instructions for creating globes as well as flat map projections. However, the “known world,” as Ptolemy calls it—or “the inhabited world” or “the world of our time”—occupies only half a hemisphere.


pages: 852 words: 157,181

The Origins of the British by Stephen Oppenheimer

active measures, agricultural Revolution, British Empire, Eratosthenes, gravity well, mass immigration, out of africa, phenotype, the scientific method, trade route

Second, but equally important for untangling the Celtic mystery, both Greek authors feel the need to explain how the local term ‘Celt’ came to be conflated by Roman writers such as Julius Caesar with the much larger regional labels of ‘Gaul’ and ‘Gauls’. And others Apart from anything else, this southern homeland would go a long way to explaining anachronistic mentions of Celtici in the south-west of Spain and Celtiberi to the east of Madrid as early as the sixth century BC.40 This information comes from authors such as Herodotus, Eratosthenes (third century BC)41 and Ephorus (405–330 BC), who is cited by Strabo: ‘Ephorus, in his account, makes Celtica so excessive in its size that he assigns to the regions of Celtic most of the regions, as far as Gades [Cadiz], of what we now call Iberia’ (see also below).42 Diodorus Siculus, probably citing Poseidonius, states that the ‘Celtiberes are a fusion of two peoples and the combination of Celts and Iberes only took place after long and bloody wars’.43 The Romantic mythologist Parthenius of Apamea (first century BC) gave a telling and charming version of the popular legend of the origins of the Celts in his Erotica pathemata,44 which preserves the Spanish connection and even hints at Ireland.

15, 320, 330 communal settlements 159 Continental celtic insular celtic link 90, 105 insular celtic split 98 languages 97 copper-mining 100, 103, 269–70 Corded Ware/Battle Axe Culture 260, 263–4 Cornish 70–1 Cornovii (England/Scotland) 79, 81 Cornwall 2–3, 41, 67, 70, 80, 81, 109, 144, 308 court tombs (or cairns) 252 craniometry 51 Crawford, Sally 400 Creswellian culture 120, 121, 143, 148 Cronan, Dennis 350 Cruithni tribe 87 culture Atlantic coast 160–1 English autonomy 15, 175 invasion vs cultural links 449, 468 and language 281 non-agricultural 182 North Sea–Creswellian links 148 two-source flow 114, 204–5, 269, 297, 301, 308–9, 481 Cumbria 67 Cumbric 71, 72–3 Cunliffe, Barry 2–4, 6, 35, 41, 46, 102–3, 109–10, 109–10, 161, 199, 210–11, 255, 260, 262, 268–70, 331, 445–6, 447, 459–60, 473 Damnonii 75, 78 Danelaw 448, 449 Danish Mesolithic 157 Danube, river Herodotus’ error 24, 31–4, 54 as LBK route 200–1 as Neolithic route 6, 210–11, 226, 227 spread of farming 16 Dark Ages Anglo-Saxon ‘invasion’ 10–11, 147, 214–15, 233, 305–6 English cultural change 403 Frisian ‘invasion’ 15, 172, 195, 225 Irish Gaelic spread 86 Viking founding clusters 450–5 Deceangli tribe 69 Denmark gene matches in Britain 195, 450–1, 455 individual graves 260–1 landbridge 181, 182 Viking raids from 444–5, 448 Diamond, Jared 283, 401 diet hunters vs farmers 206–7 seafood 157, 158 wild animals 123, 154–5, 158–9 diffusionism 56 Dillon, Myles 23 Diodorus Siculus 43, 44, 65 dolmens 252, 253 Domesday Book 413, 463, 464 Dumnonii 78, 80 Dyen, Isidore 95–6, 97, 251, 292, 293, 347 Early Bronze Age 270–1 Early Neolithic 228, 253 East Anglia Continental land bridge 192 Danish army in 448 Low Countries link 425–6 Norwegian–Swedish links 392, 396 East Germanic languages 340–1 eastern Britain Bronze Age gene inflow 308–9 Mesolithic colonization 175–7, 192, 194 Neolithic input 198, 308–9 Rhine connection 276 Scandinavian links 403–4, 481 Eastern Europe Celtic ‘evidence’ 64 Ice Age refuges 189 language vs gene flow 293, 296–7 LGM activity 117 E3b male group (Y) 235–9, 270 England 364–7 Anglo-Saxons in 14, 214–15 celtic language in 10–11, 66, 80, 105 Danish Viking raids 448 Germanic continuity 404 Iberian influence 308, 437 Low Countries closeness 425–6 recent immigration 486–7 Scandinavian roots 391 separateness of 15, 16, 175 tribes of 73–9 see also southern England English Channel 115, 142, 145 English (language) ancient roots theory 353–5 Norman invasion effect 463 Norse influence 481–2 pre-Dark Ages roots 482 preponderance of Germanic words in 11 separate branch of Germanic languages 481 English (people) English–Welsh divide 4, 69, 301, 405–7, 413–16 during Roman invasion 12–15 self-perception 482–3 Ephorus 44 Epi-Gravettian culture 125 Érainn (Iverni; Firbolgs) tribe 86, 87, 100 Eratosthenes 44 ‘ethnic group’ 383–4 ‘ethnicity’ 383–4 Eurasia 198 Europe Celtic invasions of 46, 58, 61 Indo-European expansion 99 Neolithic spread 210–11 post-LGM recolonization 118, 128–37 see also Eastern Europe; north-west Europe; Northern Europe; Western Europe European Neolithic celtic language origins 6 entry routes 198, 200, 204, 212–18, 217 forest clearance 209 intrusion rates 244–5 Evans, David Ellis 315, 320, 324 farming advantages of 205–7 ploughs 255 spread of 16, 104, 111, 199, 285 Finland 185 Firbolgs see Érainn fishing 158, 179 FMH (Frisian Modal haplotype) 172, 224 foederati 357, 364 forests clearance 207–9 forest-dwellers 207–9 Forster, Peter 98–9, 104, 110, 215, 216, 251, 299–300, 350–5, 442, 473, 476 forts 359–62 Fosna-Hensbacka culture 178 founder effect 121, 124 France 6, 34, 41 frequency maps 407–10 Frisia as Anglo-Saxon source 422 British invasion theory 15, 172, 195, 225, 428 English similarities 15, 146, 149, 194, 225, 374, 411–12, 431 Frisian language 345, 346, 348 Frisian Modal haplotype (FMH) 172, 224 Frisians British invasion theory 378 presence in Britain 379–80 funnel-necked-beakers 253, 262 Gaelic (Goidelic) Goidelic/Brythonic split 97, 99, 110 as Q-celtic 88 Spanish-Celtic theory 86 vs Brythonic 87, 96 see also Irish Gaelic; Scottish Gaelic ‘Gaelic Modal Haplotype’ 222 Galatia 64–5 Gallaeci tribe 64, 76 gallery graves 253, 255 Gallic War 330, 331 Garonne river 105 Gaul 12, 48–9, 51, 58, 61, 78, 313 Gaulish evidence for 59 insular celtic link 98 insular celtic split 98 lacks own script 61 as related to Brythonic 87, 88 Welsh link 87, 89, 98 Gaulish/Lepontic languages 88 Gauls 43 gene group frequency 423–5, 428 gene pool British 132 founder effect 112–13, 124 LUP contribution?


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The Problem of Political Authority: An Examination of the Right to Coerce and the Duty to Obey by Michael Huemer

Cass Sunstein, Chelsea Manning, cognitive dissonance, cuban missile crisis, Daniel Kahneman / Amos Tversky, en.wikipedia.org, Eratosthenes, experimental subject, framing effect, Gini coefficient, illegal immigration, impulse control, Isaac Newton, Julian Assange, laissez-faire capitalism, Machinery of Freedom by David Friedman, Milgram experiment, moral hazard, Phillip Zimbardo, profit maximization, profit motive, Ralph Nader, RAND corporation, rent-seeking, Ronald Coase, Stanford prison experiment, The Wealth of Nations by Adam Smith, unbiased observer, uranium enrichment, WikiLeaks

Hume uses this premise to reject the social contract theory, which in his time held little sway with the public. His strong thesis of moral infallibility may be explained by his antirealist metaethics (1992, Section III.i.1–2). 6 Lindberg 1992, 58; Russell 1991. In the fourth century BC, Aristotle discussed the arguments establishing the earth’s sphericity (De Caelo, 297a9–297b20), and in the third century BC, Eratosthenes provided a reasonably accurate estimate of the earth’s circumference. 7 See Stove (1995, 58–62) on ‘The Columbus Argument’ for further discussion. 8 See McLean and Hewitt’s introduction to Condorcet 1994 (35–6). Condorcet notes that when we assume individuals are 80 percent reliable and the majority outnumbers the minority by as few as nine persons, the probability of the majority being correct exceeds 99.999 percent.

Filburn, 224 court packing, 225 courtrooms, 118, 119–20 courts costs of using, 282 delays, 282 privatization of, 325–6 and wrongful convictions, 270, 276, 278–80 see also arbitration Cowen, Tyler, 258–9 credit reporting, 270–1 crime attitudes of victims toward, 275 exonerations, 278–80 government protection from, 81–2 uncompensable, 273–4 criminal justice system, prospects for reform, 284–6 criminal record reporting, 270–1, 273–4 criminals character of, 277 protected by government, 240 unprofitability of protecting, 239 Cthulhu, 92 culture, 115 death penalty, 324 defense, societal, 82, 144 see also military; war deliberative democracy defined, 60–1 as fantasy, 61–4 irrelevance of, 64–5 Delli Carpini, Michael, 211 DeLue, Steven, 101n2 democracy advantages of, 79, 185, 228–9 and legitimacy, 77–9 problems of, 208–13, 219–21 not supported by obedience, 70–1 spread of, 321–2, 330 democratic law, 65 democratic peace, 303–5 deterrence, 306–10 developing world, as target for social programs, 152–4 diffidence, 198, 201 diminishing marginal utility, 150 disagreement, sources of, 49–50 diseconomies of scale, 255–6 disobedience and acceptance of punishment, 164–6 justified, 163–4 as threat to social order, 83–4, 91, 173–4 dissenters, 91–3 distance, emotional, 122–3 distributive justice, see social welfare programs doing/allowing distinction, 142–3 drug laws, 89, 139–40, 172, 173–4, 330 effect on organized crime, 248 Duane, James, 168n36 Dugard, Jaycee Lee, 124 duty to do good, 83–4 Dworkin, Ronald, 37n2 economies of scale, 254–5 Edmundson, William, 9n6, 128n48 egalitarianism, 148–9, 192–3, 244 egoism, ethical, 176 egoism, psychological, see selfishness Egypt, 293–4 elections influences on, 218, 242–3 probability of tie, 210 see also democracy; voting Ellsberg, Daniel, 216 emigration, 252 eminent domain, 29 emotional distance, 122–3 equal advancement of interests, 67–70 equality and argument for authority, 65–7 incompatible with coercion, 75–7 interpretation of, 71–3 of judgment, 74–5 of power, 202 Eratosthenes, 103n6 Estonia, 293, 330 ethics, 14–15 knowledge of, 170–1, 172–3 necessary conditions for reliability, 55–7 principles independent of government, 84 procedural versus substantive constraints, 54–5 progress in, 332 sufficient conditions for reliability, 52–5 examples Abel, 200–1, 205, 206 Alastair, 55 Amnesty International, 78–9 Archer Midland, 142 bar tab, 59, 64–5, 75–7 board meeting, 22, 25–6, 26–7 cabin in the woods, 160 car sale, 51 car theft, 94, 95 charitable tax-evader, 93 Charity Case, 69–70 charity mugging, 154–9 child-beating chauffeur, 161–2 child retrieving cat, 187–9 cigarette prohibition, 139–40 class lottery, 23 cold child, 152 diamond, 51 disrespecting colleagues, 78 dog hit by car, 183–4 drowning child, 83, 84–5, 149, 154–9 gardener, 175–6 Gumby and Pokey, 98–9 examples – continued homophobic gang, 166, 169 incompetent bystander, 149–50 landmines on lawn, 316 lifeboat, 87–8, 90–1, 92, 94–5, 97, 98 Lindsey Lohan, 217 lost keys, 54 man on ship, 28 mom against drunk driving, 184 overworked philanthropist, 157 painter, 42 party, 26 private party hostile to foreign government, 301 private security failure, 219 prostitution, 138–9 protection cartel, 259 reasonable employment offer, 44, 51 restaurant, 22–3, 26, 27 Sally’s widgets, 257–8, 268 Sam’s gang, 163–4 self-flagellation, 90–1 shipwreck, 44–5 Sneaku ad agency, 93–4 soldier/unjust war, 171 starving Marvin, 142–3 stealing from company, 170 suicide, 140 Superior/Inferior election, 217–9 Tannahelp/Murbard, 250–2 Target return, 269 Tax Case, 69–70 traffic violation, 9 unconscious patient, 37–8 vigilante, 3–4, 7–8, 144 exonerations, 278–80 extortion, 249–53 extremism, 337 fairness, 51–2 and argument for authority, 171 and argument for political obligation, 86–93 conditions for obligation based on, 87–8 farm bill, 212–13, 214–15 fixed costs, 255 food crisis, 213 force, see coercion foreign policy, 209, 312–13 foreigners, 209, 237 Freud, Anna, 126n45 Friedman, David, 192n16, 200n6, 250n25, 251n26 Friedman, Milton, 191n14 Gandhi, Mohandas K., 292 Gaus, Gerald, 42n12 gay marriage, 96, 208 generality, 12 genocide, 207 gerrymandering, 72–3 Gini coefficient, 193n18 gladiators, 323 glory, 198 Goodin, Robert, 154n22 Gorbachev, Mikhail, 293 government benefits of, 18, 81–3 differentiated from anarchy, 232–3 functions of, 4, 20, 45, 197 has incentives to fail, 220, 285 lack of competition, 262 private, 261n44 as threat to human species, 318–19 government leaders, motives, 237 Grenada, 308–9 Gross, Samuel, 278–9 Grossman, Dave, 235 guerilla warfare, 289–91 gulags, 132 Habermas, Jürgen, 61, 64 Hamas, 314 Hamilton, Alexander, 221n39 Harsanyi, John, 46n15, 51n28, 56n35 Hearst, Patricia, 123–4 Hitler, Adolf, 108–10, 297, 300–1 Hobbes, Thomas, 20n1, 198–200 Hoffman, Elizabeth, 190n9 homeowners associations, 261–2 Hong Kong, 330 Honoré, Tony, 101n1 horses, 277 Huckabee, Mike, 216 Huemer, Michael, 50n26 human nature, 187–94, 241, 242 humanity, history of, 321–2 Hume, David, 21–2, 28, 102n3, 102n5 hypothetical consent, 36 conditions for validity of, 37–9 invalidity of, 38–9, 43–5, 51–7, 64 and reasonableness, 39–40 unattainability of, 40–3, 48–50, 64 hypothetical examples, see examples idealization, 191–2 ideas, as agents of social change, 331–4 identification with the aggressor, 126, 128 identification with government, 128n47 ideology, 191–2 ignorance, 189 illusions, 135–6 immigration, 96, 142–3, 209 imprisonment, 283–4 Indian independence movement, 292 indigenous people, 91 individualism, 83 insurance for arsonists, 239 intergovernmental disputes, 299–302 interstate commerce, 223, 224–5 investment, affected by wealth distribution, 151 Iran, 317 Iran-Iraq War, 297, 298, 300, 302 Iraq-U.S.


pages: 1,002 words: 276,865

The Great Sea: A Human History of the Mediterranean by David Abulafia

agricultural Revolution, British Empire, colonial rule, David Attenborough, Eratosthenes, ghettoisation, joint-stock company, long peace, mass immigration, out of africa, spice trade, trade route, wikimedia commons, Yom Kippur War

And, despite the warnings from Ugarit, Cyprus suffered terribly; its towns were demolished – this was followed by the arrival of Greek refugees or invaders, bringing their archaic linear script and an early form of Greek. On Crete, part of the population moved inland to inaccessible points high above the island, at Karphi and Vrokastro. And then, around the date assigned by the classical author Eratosthenes to the fall of Troy (1184), Troy was destroyed again, and this time the city went up in flames; the skeleton of one unfortunate Trojan who was trying to flee has been found beneath the debris of Troy VIIa.15 Thus, if the Greeks did destroy Troy at this stage, their victory occurred when their own towns had also passed the peak of their prosperity. Rather than a clash between Mycenae rich in gold and the wealthy horse-tamers of Troy, the fall of Troy VIIa was a battle between declining powers.

The Septuagint was one of the great contributions of Alexandria to the cultural history of the Mediterranean, adopted by the Christians of Constantinople as the text of the Old Testament; indeed, Byzantine Christianity preserved much more of Alexandrian Jewish culture than the Jews themselves, including the voluminous works of Philo. It would be easy to produce a catalogue of the remarkable Greek scholars who studied in Ptolemaic Alexandria. Some of the most influential are also the murkiest: was Euclid a man or a committee of mathematicians? In the third century, Eratosthenes, who worked out with remarkable precision the diameter of the earth, served as librarian of Alexandria; another innovative scientist was Aristarchos, who deduced that the earth revolves around the sun, though he was not taken seriously, and his influence waned further in the Roman period when another Alexandrian, Claudius Ptolemy, published his own very influential description of the earth in which it remained at the centre of the universe.

In the third century, Eratosthenes, who worked out with remarkable precision the diameter of the earth, served as librarian of Alexandria; another innovative scientist was Aristarchos, who deduced that the earth revolves around the sun, though he was not taken seriously, and his influence waned further in the Roman period when another Alexandrian, Claudius Ptolemy, published his own very influential description of the earth in which it remained at the centre of the universe. There was a vibrant medical tradition in Alexandria; understanding of the human body was enhanced by the practice not just of autopsy but of dissecting condemned prisoners while still alive. Archimedes probably spent only a relatively short part of his long life (287–212 BC) in Egypt, but he maintained contact with Alexandrian mathematicians such as Eratosthenes.37 His career serves as a reminder of the fascination of the Ptolemaic court with ingenious machines. One of these has been recovered from the Mediterranean seabed off the island of Antikythera, and appears to be a mechanical model of the universe.38 Alexandrian science was of more than local interest. The discoveries and inventions of many of these figures were of lasting importance, and provide further proof of the great vitality of Hellenistic culture, of which Alexandria established itself as the capital.


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

By the time of Archimedes’ death the world center of intellectual life already had shifted from Athens to Alexandria, the city Alexander the Great had established a century earlier with the charter—inspired, I suppose, by his boyhood tutor Aristotle—that it be a capital of learning modeled on the Greek ideal. Here Ptolemy I, the Macedonian general and biographer of Alexander, established with the wealth of empire a vast library and a museum where scientists and scholars could carry on their studies, their salaries paid by the state. It was in Alexandria that Euclid composed his Elements of geometry, that Ptolemy constructed his eccentric universe, and that Eratosthenes measured the circumference of the earth and the distance of the sun to within a few percent of the correct values. Archimedes himself had studied at Alexandria, and had often ordered books from the library there to be sent to Syracuse. But the tree of science grew poorly in Alexandrian soil, and within a century or two had hardened into the dead wood of pedantry. Scholars continued to study and annotate the great books of the past, and roomfuls of copiers laboriously duplicated them, and historians owe a great debt to the anonymous clerks of the library of Alexandria, but they were the pallbearers of science and not its torchbearers.

Symmetry Principles in Particle Physics. London: Oxford University Press, 1972. Epictetus. Discourses, trans. George Long. Chicago: University of Chicago Press, 1952. —————. Discourses, trans. W.A. Oldfather. Cambridge, Mass.: Harvard University Press, 1979. Epstein, Lewis Carroll. Relativity Visualized. San Francisco: Insight, 1985. Amply illustrated, right-forebrain explication of the special and general theories. Eratosthenes. Measurement of the Earth, trans. Ivor Thomas. Cambridge, Mass.: Harvard University Press, 1980. Euclid. The Elements, trans. Isaac Barrow. London: Redmayne, 1705. —————. The Elements, ed. and trans. Thomas L. Heath. 3 vols. New York: Dover, 1956. Eve, A.S. Rutherford. London: Cambridge University Press, 1939. Fakhry, Ahmed. The Pyramids. Chicago: University of Chicago Press, 1974.


pages: 565 words: 164,405

A Splendid Exchange: How Trade Shaped the World by William J. Bernstein

Admiral Zheng, asset allocation, bank run, Benoit Mandelbrot, British Empire, call centre, clean water, Columbian Exchange, Corn Laws, David Ricardo: comparative advantage, deindustrialization, Doha Development Round, domestication of the camel, double entry bookkeeping, Eratosthenes, financial innovation, Gini coefficient, God and Mammon, ice-free Arctic, imperial preference, income inequality, intermodal, James Hargreaves, John Harrison: Longitude, Khyber Pass, low skilled workers, non-tariff barriers, Paul Samuelson, placebo effect, Port of Oakland, refrigerator car, Silicon Valley, South China Sea, South Sea Bubble, spice trade, spinning jenny, Steven Pinker, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, trade liberalization, trade route, transatlantic slave trade, transcontinental railway, upwardly mobile, working poor, zero-sum game

As with any gigantic historical figure of whom we have a less than complete documentary record, Columbus acquired more than his share of apocrypha and tall tales, particularly the famous stories of Queen Isabella pawning her jewels to finance his first voyage and of "Columbus and the egg."" But none of the Columbus tales was to prove more hardy, well-known, or iconic than his pioneering the idea that the earth was round. More importantly, this myth also cuts to the heart of why he had such a difficult time selling his scheme to Europe's rulers. By the medieval era, no educated person thought the world flat. As early as 205 BC, Eratosthenes, a Greek living in Alexandria, deduced that the earth was a sphere, and even calculated its size with an accuracy that would not be surpassed for nearly another two thousand years. Nor was Columbus the first to propose reaching the Indies by sailing west. The transatlantic route to India had been suggested as far back as the first century after Christ by the Roman geographer Strabo, and perhaps even by Aristotle before him.

., The Age of the Galley (Edison, NJ: Chartwell, 2000), 21-22. 28. 1 Kings 9:26-28, King James Version. 29. The identification of "Ophir" as India is a matter of some dispute; historians have also suggested Yemen, Sudan, and Ethiopia as possibilities. See Maria Eugenia Aubert, The Phoenicians and the West, 2nd ed. (Cambridge: Cambridge University Press. 2001), 44-45. 30. Harden, 157-179. 31. Herodotus, 255. 32. Not until 205 BC-well over two centuries after Histories was writtenwould Eratosthenes correctly calculate the circumference of the earth from the difference between the angles of the sun at Alexandria and Syene, putting the equator well south of even Alexandria. 33. Hourani and Carswell, 8-19. 34. Ibid., 19. 35. Carol A. Redmount, "The Wadi Tumilat and the 'Canal of the Pharaohs,"' Journal of Near Eastern Studies, 54:2 (April 1995): 127-135; and Joseph Rabino, "The Statistical Story of the Suez Canal," Journal of the Royal Statistical Society, 50:3 (September 1887): 496-498. 36.


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A History of the World in 6 Glasses by Tom Standage

Berlin Wall, British Empire, Colonization of Mars, Copley Medal, Edmond Halley, Edward Lloyd's coffeehouse, Eratosthenes, European colonialism, interchangeable parts, invention of agriculture, Isaac Newton, joint-stock company, Kickstarter, laissez-faire capitalism, Lao Tzu, multiplanetary species, out of africa, South Sea Bubble, spice trade, spinning jenny, The Wealth of Nations by Adam Smith, trade route, transatlantic slave trade

The symposion, with its rules for preventing a dangerous mixture from getting out of hand, thus became a lens through which Plato and other philosophers viewed Greek society. The Philosophy of Drinking Philosophy is the pursuit of wisdom; and where better to discover the truth than at a symposion, where wine does away with inhibitions to expose truths, both pleasant and unpleasant? "Wine reveals what is hidden," declared Eratosthenes, a Greek philosopher who lived in the third century BCE. That the symposion was thought to be a suitable venue for getting at the truth is emphasized by its repeated use as a literary form, in which several characters debate a particular topic while drinking wine. The most famous example is Plato's Symposium, in which the participants, including Plato's depiction of his men tor, Socrates, discuss the subject of love.


The Life and Death of Ancient Cities: A Natural History by Greg Woolf

agricultural Revolution, capital controls, Columbian Exchange, demographic transition, endogenous growth, Eratosthenes, European colonialism, global village, invention of agriculture, invention of writing, joint-stock company, mass immigration, megacity, New Urbanism, out of africa, Scramble for Africa, social intelligence, social web, trade route, urban planning, urban sprawl

He postulated that there was always a cyclical struggle between urban civilizations and the tribal populations that surrounded them. Each time an urban civilization fell to the barbarians, the conquerors themselves began to grow soft and less warlike, to enjoy the comforts and luxuries of the city, until they in turn were overtaken by new invasions of barbarians. That opposition had classical precedents. The Greek geographer Eratosthenes had proposed classifying peoples into those who lived by law and in cities and those who did not (the barbarians), and the historian Herodotus had had one Greek character tell a Persian Emperor that “soft lands breed soft people.” Thucydides, pondering the early days of Greece, suggested that once upon a time everyone lived as barbarians did in his day. These writers shared an underlying assumption that urbanization was a sign of civilizational progress.

Their men were soft, their women ferocious, and so on. Greeks who had sided with the Persians were accused of “Medizing”—that is, siding with the barbarian Medes against fellow Greeks in the Persian Wars. By the fourth century Aristotle was producing rationalizations of the common view that barbarians were “natural” slaves and Greeks their “natural” masters. That prejudice was never completely accepted. The third-century b.c.e. polymath Eratosthenes pointed out that many other people, including the Phoenician Carthaginians, had political institutions, laws, and other things generally associated with civilized peoples rather than barbarians. Yet a strong sense that Greeks were a people apart persisted. The fact that so many barbarian peoples now made art that depicted Greek myths (as the Etruscans did), claimed Greek origins (as many Asian peoples would), and even adopted Greek as a language for public affairs (as the Lycians did) must have helped bolster that view.


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

CXXVII. 1883). 3This is not, strictly speaking, an assumption; it is a proposition proved later by means of the result of an experiment about to be described. 4 The proposition here assumed is of course equivalent to the trigonometrical formula which states that, if α, β are the circular measures of two angles, each less than a right angle, of which α is the greater, then THE METHOD OF ARCHIMEDES TREATING OF MECHANICAL PROBLEMS—TO ERATOSTHENES “Archimedes to Eratosthenes greeting. I sent you on a former occasion some of the theorems discovered by me, merely writing out the enunciations and inviting you to discover the proofs, which at the moment I did not give. The enunciations of the theorems which I sent were as follows. 1. If in a right prism with a parallelogrammic base a cylinder be inscribed which has its bases in the opposite parallelograms,[1] and its sides [i.e. four generators] on the remaining planes (faces) of the prism, and if through the centre of the circle which is the base of the cylinder and (through) one side of the square in the plane opposite to it a plane be drawn, the plane so drawn will cut off from the cylinder a segment which is bounded by two planes and the surface of the cylinder, one of the two planes being the plane which has been drawn and the other the plane in which the base of the cylinder is, and the surface being that which is between the said planes; and the segment cut off from the cylinder is one sixth part of the whole prism. 2.

A palimpsest is an ancient document that has had its original contents washed off so that new contents could be written on it. Upon reading the few lines of the manuscript published by Kerameus, the Danish classics scholar Johan Ludvig Heiberg recognized characteristic Archimedean traits. He suspected that the underlying manuscript must be a work of Archimedes. Heiberg must have been amazed when he examined the palimpsest firsthand. Kerameus had found the long lost treatise, The Method, which begins, “Archimedes to Eratosthenes greeting.” The presence of other Archimedean works in the palimpsest only confirmed its authorship. The Kerameus–Heiberg palimpsest was originally written in the tenth century. In the thirteenth century, a monk had washed away the original ink so that he could write a book of devotional prayers. The monk must have had no idea of what he had washed away. Nor could he have imagined the palimpsest’s future value.

-S, 18–20 Apollodorus the “calculator,” 10 Apollonius, 297, 318 appellative signs, 861 Applications of the Calculus of Probabilities (Laplace) The Application of the Calculus of Probabilities to Natural Philosophy, 454–472 Application of the Calculus of Probabilities to the Moral Sciences, 472–473 Concerning Illusions in the Estimation of Probabilities, 498–506 Concerning Tables of Mortality, and of Mean Durations of Life, of Marriages, and of Associations, 488–493 Concerning the Benefits of Institutions Which Depend upon the Probability of Events, 493–498 Concerning the Laws of Probability which Result from the Indefinite Multiplication of Events, 447–454 Concerning the Probabilities of Testimonies, 473–481 Concerning the Probability of the Judgments of Tribunals, 484–488 Concerning the Selections and the Decisions of Assemblies, 481–484 Concerning the Unknown Inequalities Which May Exist among Chances Which are Supposed to be Equal, 445–447 Concerning the Various Means of Approaching Certainty, 507–511 Games of Chance, 444–445 Historical Notice Concerning the Calculus of Probabilities, 511–517 approximation, 449–450 approximation formula, 1049–1050 arbitrary mark of signs, 860 arc, ultimate ratio of, 376–377 Archimedes, 106, 371, 1225 biography, 119–125 Measurement of the Circle, 121, 194–199 The Method of Archimedes Treating of Mechanical Problems - to Eratosthenes, 123–125, 209–239 The Sand Reckoner, 200–208 On the Sphere and Cylinder - Book I, 123, 126–167 On the Sphere and Cylinder - Book II, 168–194 area bound by curves and solids, 121 circle, 121–122, 194–195 of domain, 1224 figures with homologous sides, 376 Integral Length and Area (Lebesque), 1212–1215 right-angled triangles, equal, 268–269 set, 1223–1225 Aristarchus of Samos, 200–201 Aristotle, 10, 47, 61, 106 and Boole, 839, 840, 842–843 logic, 42, 43, 848–849 reasoning, 844 arithmatical relation, 1279 arithmetic geometry’s roots in, 5 incompleteness, 1257 limitations of, 3 rational right-angled triangles, 14–18 Arithmetic Disquisitions (Gauss) Congruences of the Second Degree, 625–661 Residues of Powers, 599–625 Ascoli, 1029 assemblies, 481–484 associates, 617 associations, 488–493 assurance, 857–858 Athenaeus, 10 auditors, 421–422 augend, 1176 automatic machines, 1295 axioms, 1267 axis complementary segment of sphere, 227 conic section, 321 axis ray, 766–767 Ayscough, Hannah, 365–366 B Bachet, Claude, 392 Bacon, 508–509 Baltzer, Richard, 749 barometer, periodic oscillations in, 465–466 Barrow, Isaac, 62, 367 Bartels, Martin, 698 base-element, 1104 Basel Problem, 386–387 base-number, 1105 Basic Geometry (Elements), 7–24 Bayes, 514 Beeckman, Isaac, 287 Beltrami, Eugenio, 703 benefit relative versus absolute value, 429 series of probable events, 428–429 Bentley, Reverend Richard, 411 Bernoulli, Daniel, 503, 504, 525–526, 994–995 Bernoulli, Jacob, 386 Bernoulli, Jacques, 448, 512 Bernoulli, Johann I, 383–385, 667 Bhaskara, 13 bias, 416 Billingsly, Henricus, 705 binomial, property of, 431–432 binomial differentials, 443 biography, 697–703 biquadratic equation, 358 birth rate, 500 birth rate, ratio to population, 448, 450–453 Bolyai, Farkas Wolfgang, 708, 743–746, 747–748, 753, 754, 792 Bolyai, János, 753 appendix, 708–709 biography, 743–749, 755–761 The Science of Absolute Space, 762–785 Explanation of Signs, 761–762 Light from Non-Euclidean Spaces on the Teaching of Elementary Geometry, 790–795 Remarks on the Preceding Treatise, by Bolyai Farkas, 785–788 Some Points in John Bolyai’s Appendix Compared with Lobachevski, by Wolfgang Bolyai, 788–790 Translator’s Introduction, 750–761 Bolzano, B., 1077 Boole, George biography, 835–841 on Certain Methods of Abbreviation, 936–951 The Claims of Science, especially as founded in it Relations to Human Nature, 838–839 of the Conditions of a Perfect Method, 951–958 Derivation of the Laws of the Symbols of Logic from the Laws of the Operations of the Human Mind, 870–878 Of the Division of Propositions into the Two Classes of “Primary” and “Secondary;” of the Characteristic Properties of Those Classes, and of the Laws of the Expression of Primary Propositions, 879–888 on Elimination, 913–924 Of the Fundamental Principles of Symbolic Reasoning, and of the Expansion or Development of Expressions Involving Logical Symbols, 889–899 Of the General Interpretation of Logical Equations, and the Resulting Analysis of Propositions.. . .


pages: 685 words: 203,949

The Organized Mind: Thinking Straight in the Age of Information Overload by Daniel J. Levitin

airport security, Albert Einstein, Amazon Mechanical Turk, Anton Chekhov, Bayesian statistics, big-box store, business process, call centre, Claude Shannon: information theory, cloud computing, cognitive bias, complexity theory, computer vision, conceptual framework, correlation does not imply causation, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, delayed gratification, Donald Trump, en.wikipedia.org, epigenetics, Eratosthenes, Exxon Valdez, framing effect, friendly fire, fundamental attribution error, Golden Gate Park, Google Glasses, haute cuisine, impulse control, index card, indoor plumbing, information retrieval, invention of writing, iterative process, jimmy wales, job satisfaction, Kickstarter, life extension, longitudinal study, meta analysis, meta-analysis, more computing power than Apollo, Network effects, new economy, Nicholas Carr, optical character recognition, Pareto efficiency, pattern recognition, phenotype, placebo effect, pre–internet, profit motive, randomized controlled trial, Rubik’s Cube, shared worldview, Skype, Snapchat, social intelligence, statistical model, Steve Jobs, supply-chain management, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, Turing test, ultimatum game, zero-sum game

After nightfall, time was kept by a number of means, including tracking the motion of the stars, the burning of candles, or the amount of water that flowed through a small hole from one vessel to another. The Babylonians also used fixed duration with twenty-four hours in a day, as did Hipparchus, the ancient Greek mathematician and astronomer. The division of the hour into sixty minutes, and the minutes into sixty seconds is also arbitrary, deriving from the Greek mathematician Eratosthenes, who divided the circle into sixty parts for an early cartographic system representing latitudes. For most of human history, we did not have clocks or indeed any way of accurately reckoning time. Meetings and ritual get-togethers would be arranged by referencing obvious natural events, such as “Please drop by our camp when the moon is full” or “I’ll meet you at sunset.” Greater precision than that wasn’t possible, but it wasn’t needed, either.

., 291 Dupin, Amantine (George Sand), 283 dysexecutive syndrome, 166–67 Ebbinghaus illusion, 21, 22 Eberts, Jake, 195, 337 echinacea, 253–55 The Economist, 251 Edison, Thomas, 201, 292 Einstein, Albert, 375, 380 Eisenhower, Dwight D., 371 e-mail, 98–102, 214, 303–4, 306–7 empathy, 119, 158, 368–69 Empire State Building weight question, 356–57, 360–64 engagement in tasks, 205–6 epidemiological studies, 350 Epley, Nicholas, 135, 151 Erasmus, 14–15 Eratosthenes, 163 Ernst, Edzard, 253 estimation, 352–55, 355–64, 449n224. See also statistics ethics, 280–83 evolution and attention, 41 and the attentional system, 7–8, 16 and brain architecture, xix and categorization, 64 and expansion of physical possessions, 78 and kinship models, 26 and preference for order, 31–32 and probability, 222 and social relations, 120, 125–26 executive assistants, 124–25, 196, 210, 213–14, 299–301 executive attention system, 196–97, 368–69.


pages: 282 words: 82,107

An Edible History of Humanity by Tom Standage

agricultural Revolution, amateurs talk tactics, professionals talk logistics, Bartolomé de las Casas, British Empire, carbon footprint, Columbian Exchange, Corn Laws, demographic transition, Deng Xiaoping, Eratosthenes, financial innovation, food miles, Haber-Bosch Process, invisible hand, James Watt: steam engine, Kickstarter, Louis Pasteur, Mikhail Gorbachev, special economic zone, spice trade, The Wealth of Nations by Adam Smith, Thomas Malthus, trade route, transatlantic slave trade, women in the workforce

The interdependence between geography and trade was pointed out by Ptolemy himself, who noted that it was only due to commerce that the location of the Stone Tower, a key trading post on the Silk Road to China, was known. He was well aware that the Earth was spherical, something that had been demonstrated by Greek philosophers hundreds of years earlier, and he agonized about how best to represent it on a flat surface. But Ptolemy’s estimate of the circumference of the Earth was wrong. Although Eratosthenes, a Greek mathematician, had calculated the circumference of the Earth four hundred years earlier and arrived at almost exactly the right answer, Ptolemy’s figure was one-sixth smaller—so he thought the Eurasian landmass extended farther around the world than it actually did. This overestimate of the extent to which Asia extended to the east was one of the factors that later emboldened Christopher Columbus to sail west to find it.


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

In spite of Euclid being a “best-selling” author (only the Bible sold more books than Elements until the twentieth century), his life is so veiled in obscurity that even his birthplace in unknown. Given the contents of the Elements, it is very likely that Euclid studied mathematics in Athens with some of Plato's students. Indeed, Proclus writes about Euclid: “This man lived in the time of the first Ptolemy … he is then younger than the pupils of Plato, but older than Eratosthenes and Archimedes.” The Elements, a thirteen-volume work on geometry and number theory, is so colossal in its scope that we sometimes tend to forget that Euclid was the author of almost a dozen other books, covering topics from music through mechanics to optics. Only four of these other treatises survived to the present day: Division of Figures, Optics, Phaenomena, and Data. Optics contains some of the earliest studies of perspective.


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

Without a doubt, its influence ebbs and flows, but over the long haul, it heads upward. It is hard to overstate just how intertwined civilization and progress are. You can tell the story of scientific and material progress by looking across time and noting places where civilization flourished. Consider Classical Greece, almost 2,500 years ago. Civilization blossomed, democracy was born. Philosophy advanced and the rule of law was enforced. And what a time of progress it was. Eratosthenes calculated the circumference of the earth. Hippocrates made medicine a science. Theophrastus classified and named plants. Eupalinus built a magnificent aqueduct, Archimedes made his famous screw to raise water, and Anaximander postulated that life on earth began in the oceans. The list goes on and on. Three centuries later, civilization exploded in China. The Han dynasty unified China under an efficient bureaucracy and saw great advances in art and culture.


pages: 1,402 words: 369,528

A History of Western Philosophy by Aaron Finkel

British Empire, Eratosthenes, Georg Cantor, George Santayana, invention of agriculture, liberation theology, Mahatma Gandhi, plutocrats, Plutocrats, source of truth, Thales and the olive presses, Thales of Miletus, the market place, William of Occam

Copernicus came to know something, though not much, of the almost forgotten hypothesis of Aristarchus, and was encouraged by finding ancient authority for his innovation. Otherwise, the effect of this hypothesis on subsequent astronomy was practically nil. Ancient astronomers, in estimating the sizes of the earth, moon, and sun, and the distances of the moon and sun, used methods which were theoretically valid, but they were hampered by the lack of instruments of precision. Many of their results, in view of this lack, were surprisingly good. Eratosthenes estimated the earth’s diameter at 7850 miles, which is only about fifty miles short of the truth. Ptolemy estimated the mean distance of the moon at 29Æ times the earth’s diameter; the correct figure is about 30.2. None of them got anywhere near the size and distance of the sun, which all underestimated. Their estimates, in terms of the earth’s diameter, were: Aristarchus, 180; Hipparchus, 1245; Posidonius, 6545.

The Ptolemies were patrons of learning, and attracted to their capital many of the best men of the age. Mathematics became, and remained until the fall of Rome, mainly Alexandrian. Archimedes, it is true, was a Sicilian, and belonged to the one part of the world where the Greek City States (until the moment of his death in 212 B.C.) retained their independence; but he too had studied in Alexandria. Eratosthenes was chief librarian of the famous library of Alexandria. The mathematicians and men of science connected, more or less closely, with Alexandria in the third century before Christ were as able as any of the Greeks of the previous centuries, and did work of equal importance. But they were not, like their predecessors, men who took all learning for their province, and propounded universal philosophies; they were specialists in the modern sense.

.), 326 Epirus, 261, 343 episcopate, 395, 396–397, See also bishops epistemology, 702, 713, 716, 760, See also theory of knowledge equality, 139, 140 of man, in ancient philosophy, 114, 174, 189, 191, 270 of man, in modern philosophy, 183, 550, 597, 695, 726–727, 729, 765, 775, 776 of women, in, 723 Erasmus, Desiderius (Gerhard Gerhards), Dutch scholar (1466?–1536), 512–517, 518, 523 quoted, 514, 515, 517 Erasmus (Huizinga), 513* Erastianism, 363 Erastus. See Lüber Eratosthenes, Greek astronomer (fl. 3rd cent. B.C.), 216, 223 Erigena, Johannes Scotus. See John the Scot Erinys, 44 Eros, 19 error(s), 822 in Aristotle, 161, 197–199, 201–202 in Platonic theory of ideas, 126 eschatology, 363, 364 Essais philosophiques (Descartes), 561 Essay Concerning Human Understanding (Locke), 604–617; “Of Enthusiasm,” 607 “Of Reason,” 607–608 “Of Degrees of Assent,” 608–609; “Of General Terms,” 610 “Of the Names of Substances,” 610–611 Essay on Man (Pope), 371 Essay on Miracles (Hume), 660 Essays on Government (Locke), 633 essence, 126, 144, 146, 293, 294, 405, 467, 468, 586, 610–611 and Aquinas, 455, 457, 467 and Aristotle, 164–165, 166, 167, 170, 200–201 essences, 136, 139, 140, 141 Essenes, 315* Essex (Robert Devereux), 2nd Earl of, (1567–1601), 541 Este, Italian princely family (fl. 996–1803), 582 Esthonia, 634 eternity, 37, 46, 144–145, 292, 758, 820 ethic(s), 79, 116, 117–118, 306, 378–380, 729, 778–779, 834 and Aquinas, 458–460 aristocratic, 768 and Aristotle, 132, 171–184, 205 and Bentham, 777 Christian, 92, 205, 297 contemplative ideal in, 34 and differences between Continental and British philosophy, 644–647 and Epicurus, 245 and good of community, 711 Greek, 33–34, 42, 63, 72, 92, 297 and Hegel, 735, 736, 743, 827 in Hellenistic world, 228 and Helvetios, 722 and James, 814–815 Jewish, 319, 320, 321 and Kant, 268, 710–712 and Locke, 613–617, 627 and (Marx, 788 and More, 521 and Nietzsche, 42, 760, 762–763, 764, 769, 770 “noble,” 644–645 and Plato, 106, 132, 358 in Roman world, 476 romantic, 682 and Rousseau, 687 and Schopenhauer, 756–757, 760 and Socrates, 73, 91, 106 and Spinoza, 569, 570–577, 578 and Stoicism, 252, 258, 266–269 and utilitarians, 704, 779 Ethics (Aristotle).


pages: 335 words: 107,779

Some Remarks by Neal Stephenson

airport security, augmented reality, barriers to entry, British Empire, cable laying ship, call centre, cellular automata, edge city, Eratosthenes, Fellow of the Royal Society, Hacker Ethic, impulse control, Iridium satellite, Isaac Newton, Jaron Lanier, John von Neumann, Just-in-time delivery, Kevin Kelly, music of the spheres, Norbert Wiener, offshore financial centre, oil shock, packet switching, pirate software, Richard Feynman, Saturday Night Live, shareholder value, Silicon Valley, Skype, slashdot, social web, Socratic dialogue, South China Sea, special economic zone, Stephen Hawking, the scientific method, trade route, Turing machine, undersea cable, uranium enrichment, Vernor Vinge, X Prize

The first one dates back to the city’s early Ptolemaic rulers, who were Macedonians, not Egyptians. It was modeled after the Lyceum of Aristotle, who, between other gigs, tutored Alexander the Great. Back in the days when people moved to information, instead of vice versa, this library attracted most of the most famous smart people in the world: the ultimate hacker, Archimedes; the father of geometry, Euclid; Eratosthenes, who was the first person to calculate the circumference of the earth, by looking at the way the sun shone down wells at Alexandria and Aswan. He also ran the library for a while and took the job seriously enough that when he started to go blind in his old age, he starved himself to death. In any event, this library was burned out by the Romans when they were adding Egypt to their empire. Or maybe it wasn’t.


pages: 931 words: 79,142

Concepts, Techniques, and Models of Computer Programming by Peter Van-Roy, Seif Haridi

computer age, Debian, discrete time, Donald Knuth, Eratosthenes, fault tolerance, G4S, general-purpose programming language, George Santayana, John von Neumann, Lao Tzu, Menlo Park, natural language processing, NP-complete, Paul Graham, premature optimization, sorting algorithm, Therac-25, Turing complete, Turing machine, type inference

For example, we can pass only those elements that are odd integers: local Xs Ys S in thread Xs={Generate 0 150000} end thread Ys={Filter Xs IsOdd} end thread S={Sum Ys 0} end {Browse S} end where IsOdd is a one-argument boolean function that is true only for odd integers: fun {IsOdd X} X mod 2 \= 0 end Figure 4.10 shows this pattern. This figure introduces another bit of graphic notation, the dotted arrow, which denotes a single value (a non-stream argument to the function). 260 Declarative Concurrency Sieve X Xs X | Zs Xr Zs Filter Ys Sieve Figure 4.11: A prime-number sieve with streams. Sieve of Eratosthenes As a bigger example, let us define a pipeline that implements the prime-number sieve of Eratosthenes. The output of the sieve is a stream containing only prime numbers. This program is called a “sieve” since it works by successively filtering out nonprimes from streams, until only primes remain. The filters are created dynamically when they are first needed. The producer generates a stream of consecutive integers starting from 2. The sieve peels off an element and creates a filter to remove multiples of that element.


pages: 420 words: 143,881

The Blind Watchmaker; Why the Evidence of Evolution Reveals a Universe Without Design by Richard Dawkins

epigenetics, Eratosthenes, Fellow of the Royal Society, lateral thinking, Menlo Park, pattern recognition, phenotype, random walk, silicon-based life, Steven Pinker

In essence, it amounts simply to the idea that non-random reproduction, where there is hereditary variation, has consequences that are far-reaching if there is time for them to be cumulative. But we have good grounds for believing that this simplicity is deceptive. Never forget that, simple as the theory may seem, nobody thought of it until Darwin and Wallace in the mid nineteenth century, nearly 200 years after Newton’s Principia, and more than 2,000 years after Eratosthenes measured the Earth. How could such a simple idea go so long undiscovered by thinkers of the calibre of Newton, Galileo, Descartes, Leibnitz, Hume and Aristotle? Why did it have to wait for two Victorian naturalists? What was wrong with philosophers and mathematicians that they overlooked it? And how can such a powerful idea go still largely unabsorbed into popular consciousness? It is almost as if the human brain were specifically designed to misunderstand Darwinism, and to find it hard to believe.


pages: 453 words: 142,717

The Last Man on the Moon: Astronaut Eugene Cernan and America's Race in Space by Eugene Cernan, Donald A. Davis

Berlin Wall, Charles Lindbergh, Eratosthenes, full employment, Isaac Newton, orbital mechanics / astrodynamics, Ronald Reagan, Silicon Valley, white flight

Jack and I went back into the lander, ran the final checks, and pronounced Challenger ready to rip. Ron had not found his scissors, but Jack had found his tongue. Now that we were in orbit, he went on a verbal rampage, words spilling out in a Niagara of information. Earthly clouds and low-pressure fronts were long forgotten. He was pointed the other way now, at the Moon, and was talking rapidly in short stories of science, describing Eratosthenes, dark albedo areas within the ejecta of Copernicus, central peaks like Rein-hold and Lansberg, the nonlinear characteristics of ray patterns, the Marius Hills, Oceanus Procellarum, and the irregular swirls in Mare Marginis. Not mere sentences, but whole long paragraphs in a single breath, driving the poor transcribers back in Houston nuts, and we hadn’t done a damn thing yet except reach lunar orbit.


Crypto: How the Code Rebels Beat the Government Saving Privacy in the Digital Age by Steven Levy

Albert Einstein, Claude Shannon: information theory, cognitive dissonance, computer age, Donald Knuth, Eratosthenes, Extropian, invention of the telegraph, John Markoff, Kevin Kelly, knapsack problem, Marc Andreessen, Mitch Kapor, MITM: man-in-the-middle, Network effects, new economy, NP-complete, Ronald Reagan, Saturday Night Live, Silicon Valley, Simon Singh, Stephen Hawking, Steven Levy, Watson beat the top human players on Jeopardy!, web of trust, Whole Earth Catalog, zero-sum game, Zimmermann PGP, éminence grise

A prime number, of course, is one that cannot be arrived at by multiplying two numbers together (the lone exception being the prime itself and the number one). If you multiply two large primes together, then, you get a much larger number that isn’t a prime. To factor that number, you have to somehow reverse the process, identifying the two original seeds that produced it. This had been understood as a hard problem ever since a few years before Christ’s birth, when Eratosthenes of Alexandria devised a mathematical process called a “sieve” to try to perform this task. At that time, people considered factoring to be virtually the same problem as trying to figure out whether a number was a prime or not. Twelve hundred or so years later, Fibonacci improved the method somewhat, but by no means did he offer a way to reasonably break down a large product into its two parent primes.


The Art of Computer Programming: Sorting and Searching by Donald Ervin Knuth

card file, Claude Shannon: information theory, complexity theory, correlation coefficient, Donald Knuth, double entry bookkeeping, Eratosthenes, Fermat's Last Theorem, G4S, information retrieval, iterative process, John von Neumann, linked data, locality of reference, Menlo Park, Norbert Wiener, NP-complete, p-value, Paul Erdős, RAND corporation, refrigerator car, sorting algorithm, Vilfredo Pareto, Yogi Berra, Zipf's Law

Set n «— n + d, d <- 6 — d, and return to (b). Thus the computation begins as follows: Queue contents Primes found B5, 10, 30) 5, 7, 11, 13, 17, 19, 23 C5, 20, 30)D9, 28, 42) 29, 31 D9, 28, 42)E5, 10, 30) 37, 41, 43, 47 E5, 10, 30)G7, 14, 42)A21, 22, 66) 53 If the queue is maintained as a heap, we can find all primes < N in O(Nlog N) steps; the length of the heap is at most the number of primes < y/~N. The sieve of Eratosthenes, as implemented in exercise 4.5.4-8, is a O(iV log log N) method requiring considerably more random access storage. More efficient implementations are discussed in Section 7.1. 16. Step 1. Set K <— key to be inserted; j <— n + 1. Step 2. Set i «- [j/2\. Step 3. If i = 0 or Ki > K, set K3• «— K and terminate the algorithm. Step 4. Set Kj ¦<— Ki, j 4— i, and return to step 2. [T. Porter and I.

Entropy, 442-446, 454, 457-458. Enumeration of binary trees, 60—61, 295. balanced, 467, 479. leftist, 157. Enumeration of permutations, 12, 22—24. Enumeration of trees, 287. Enumeration sorting, 75-80. Eppinger, Jeffrey Lee, 434, 435. Equal keys, 194-195, 341, 391, 395, 431, 635. approximately, 9, 394—395. in heapsort, 655. in quicksort, 136, 635-636. in radix exchange, 127-128, 137. Equality of sets, 207. Eratosthenes of Cyrene ('Epaxoa9svr}<; 6 Kupr}valo<;), 642. Erdelyi, Arthur, 131. Erdos, Pal (= Paul), 66, 155, 658. Erdwinn, Joel Dyne, 2. Erkio, Hannu Heikki Antero, 623. Error-correcting codes, 581. Ershov, Andrei Petrovich (EpuioB, AHApeii IleTpoBHH), 547. Espelid, Terje Oskar, 259. Estivill-Castro, Vladimir, 389. Euler, Leonhard (Bijiep, JleoHapA), 8—9, 19-21, 35, 38-39, 395, 594, 726. numbers (secant numbers), 35, 610-611. summation formula, 64, 129, 626, 702.


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 library, amassing hundreds of thousands of papyrus rolls, maintained the greatest collection of knowledge on earth, then and for centuries to come. Beginning in the third century BCE, it served the Ptolemies’ ambition to buy, steal, or copy all the writings of the known world. The library enabled Alexandria to surpass Athens as an intellectual center. Its racks and cloisters held the dramas of Sophocles, Aeschylus, and Euripides; the mathematics of Euclid, Archimedes, and Eratosthenes; poetry, medical texts, star charts, mystic writings—“such a blaze of knowledge and discovery,” H. G. Wells declared, “as the world was not to see again until the sixteenth century.… It is the true beginning of Modern History.”♦ The lighthouse loomed large, but the library was the real wonder. And then it burned. Exactly when and how that happened, no one can ever know. Probably more than once.


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

Others visited the British Isles or ventured out into the mid-Atlantic, perhaps (though probably not) even as far the Azores and the Sargasso Sea, which begins about 3,000 kilometers east of the Straits of Gibraltar, halfway to the American East Coast.25 Greeks, hailing from city-states in the Aegean, followed suit. From their base in Marseille they established trade connections with Britain to obtain metal. By the fourth century BCE, Greek sailors had mapped routes to the Shetlands and into the Baltic. Pytheas sailed in the waters surrounding Britain and Ireland and advanced northward to (probably) the Faroes and finally “Thule,” just possibly Iceland. Famous Greek scholars such as Aristotle and Eratosthenes raised—though did not endorse—the possibility of crossing the Atlantic in order to reach India.26 A similar degree of engagement can be observed in other parts of the Old World. Around the beginning of the Common Era, Madagascar was settled by people from Indonesia, more than 6,000 kilometers away. By then, Polynesian explorations of the Pacific out of Tonga and Samoa were already well under way.


pages: 903 words: 235,753

The Stack: On Software and Sovereignty by Benjamin H. Bratton

1960s counterculture, 3D printing, 4chan, Ada Lovelace, additive manufacturing, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic trading, Amazon Mechanical Turk, Amazon Web Services, augmented reality, autonomous vehicles, basic income, Benevolent Dictator For Life (BDFL), Berlin Wall, bioinformatics, bitcoin, blockchain, Buckminster Fuller, Burning Man, call centre, carbon footprint, carbon-based life, Cass Sunstein, Celebration, Florida, charter city, clean water, cloud computing, connected car, corporate governance, crowdsourcing, cryptocurrency, dark matter, David Graeber, deglobalization, dematerialisation, disintermediation, distributed generation, don't be evil, Douglas Engelbart, Douglas Engelbart, Edward Snowden, Elon Musk, en.wikipedia.org, Eratosthenes, Ethereum, ethereum blockchain, facts on the ground, Flash crash, Frank Gehry, Frederick Winslow Taylor, future of work, Georg Cantor, gig economy, global supply chain, Google Earth, Google Glasses, Guggenheim Bilbao, High speed trading, Hyperloop, illegal immigration, industrial robot, information retrieval, Intergovernmental Panel on Climate Change (IPCC), intermodal, Internet of things, invisible hand, Jacob Appelbaum, Jaron Lanier, Joan Didion, John Markoff, Joi Ito, Jony Ive, Julian Assange, Khan Academy, liberal capitalism, lifelogging, linked data, Mark Zuckerberg, market fundamentalism, Marshall McLuhan, Masdar, McMansion, means of production, megacity, megastructure, Menlo Park, Minecraft, MITM: man-in-the-middle, Monroe Doctrine, Network effects, new economy, offshore financial centre, oil shale / tar sands, packet switching, PageRank, pattern recognition, peak oil, peer-to-peer, performance metric, personalized medicine, Peter Eisenman, Peter Thiel, phenotype, Philip Mirowski, Pierre-Simon Laplace, place-making, planetary scale, RAND corporation, recommendation engine, reserve currency, RFID, Robert Bork, Sand Hill Road, self-driving car, semantic web, sharing economy, Silicon Valley, Silicon Valley ideology, Slavoj Žižek, smart cities, smart grid, smart meter, social graph, software studies, South China Sea, sovereign wealth fund, special economic zone, spectrum auction, Startup school, statistical arbitrage, Steve Jobs, Steven Levy, Stewart Brand, Stuxnet, Superbowl ad, supply-chain management, supply-chain management software, TaskRabbit, the built environment, The Chicago School, the scientific method, Torches of Freedom, transaction costs, Turing complete, Turing machine, Turing test, undersea cable, universal basic income, urban planning, Vernor Vinge, Washington Consensus, web application, Westphalian system, WikiLeaks, working poor, Y Combinator

Paul Virilio in Raymond Depardon and Paul Virilio, Native Land, Stop Eject (Paris: Fondation Cartier pour l’art contemporain, 2008). 32.  Gopal Balakrishnan, Antagonistics: Capitalism and Power in the Age of War (London: Verso, 2009). 33.  Its terminological origins are not obscure. Geo from the Greek γαια (“Earth”) refers to our planet, and specifically to the land, the ground, the land as ground, and when paired with “to describe,” as geography, γεωγραϕία (as for Eratosthenes, who first calculated the circumference of the Earth around 240 B.C.E.) to literally measure and give exact scale to the ground, and to spaces themselves, one smaller and larger than another. So for our virtual political geography, where the Earth is rerotated again from another center of a space in which it was located, there is an implicit correspondence between geography and cosmology, the scientific conception of the universe as well then to cosmograph, the “writing-describing of the universe” and to cosmogram, the “writing-image of the universe.”


Egypt Travel Guide by Lonely Planet

call centre, carbon footprint, Eratosthenes, friendly fire, G4S, haute cuisine, Khartoum Gordon, late fees, low cost airline, low cost carrier, spice trade, sustainable-tourism, Thales and the olive presses, trade route, urban planning, urban sprawl

The city developed into a major port and became an important halt on the trade routes between Europe and Asia. Its economic wealth was equally matched by its intellectual standing. Its famed library (Click here) stimulated some of the great advances of the age: this was where Herophilus discovered that the head, not the heart, is the seat of thought; Euclid developed geometry; Aristarchus discovered that the earth revolves around the sun; and Eratosthenes calculated the earth’s circumference. A grand tower, the Pharos (Click here), one of the Seven Wonders of the Ancient World, was built on an island just offshore and served as both a beacon to guide ships entering the booming harbour and an ostentatious symbol of the city’s greatness. During the reign of its most famous regent, Cleopatra, Alexandria rivalled Rome in everything but military power – a situation that Rome found intolerable and was eventually forced to act upon.


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

All these researches prepared the way for Euclides of Alexandria (fl. c.300), whose Elements is said to have reigned supreme for longer than any book save the Bible. Euclid was the great mathematical systematizer, who set out to provide lasting proofs for all existing knowledge. When asked by the ruler of Egypt whether geometry could not be made more simple, he replied that there was ‘no royal road’. The next generation was dominated by Archimedes and by Eratosthenes of Cyrene (276–196), who, in calculating the earth’s diameter at 252,000 stades or 7,850 miles, erred by less than 1 per cent. Lastly there was Apollonius of Perge (fl. c.220 BC), who wrote a vast eight-volume study of Conies and found an approximation for pi that was even closer than that of Archimedes. [ARCHIMEDES] Greek moral philosophy, divided in the later centuries into several rival schools, greatly modified the teachings of traditional religion.

In the long watches on the Syracusan walls, it was entirely possible that some of Archimedes’ men, if not Archimedes himself, could have realistically mused: Roma delenda est—that is, until the plague struck and Moeriscus opened the gate. The Syracusans’ knowledge of the world would have been largely confined to the Great Sea, and to the countries of the East. The science of geography had made great advances in classical Greece, although the frontiers of the world directly known to the ancients had not radically changed. A contemporary of Archimedes, Eratosthenes of Cyrene (276–196), librarian at Alexandria, had concluded that the world was a sphere; and his work was known to Ptolemy and Strabo. But, apart from the Phoenician route to the Tin Islands, little progress was made in practical exploration. No known contact was ever made with West Africa, with the Americas, or with the more distant parts of northern Europe. The rigid division between the ‘civilized’ world of the Mediterranean shoreline and the ‘barbarian’ wilderness beyond was not overcome.


pages: 1,051 words: 334,334

Gravity's Rainbow by Thomas Pynchon

centre right, Eratosthenes, experimental subject, invisible hand, Isaac Newton, ought to be enough for anybody, plutocrats, Plutocrats, random walk

"Perhaps someday to the Moon." "The Moon ..." as if he were going to tell her a story. When none followed she made up her own. The engineer in the next cubicle had a map of the Moon tacked to his fiberboard wall, and she spent hours studying it, deciding where she wanted to live. Passing over the bright rays of Kepler, the rugged solitude of the Southern Highlands, the spectacular views at Copernicus and Eratosthenes, she chose a small pretty crater in the Sea of Tranquillity called Maskelyne B. They would build a house right on the rim, Mutti and she and Pokier, gold mountains out one window and the wide sea out the other. And Earth green and blue in the sky.... Should he have told her what the "seas" of the Moon really were? Told her there was nothing to breathe? His ignorance frightened him, his ineptitude as a father. . . .


pages: 1,178 words: 388,227

Quicksilver by Neal Stephenson

Danny Hillis, dark matter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Isaac Newton, joint-stock company, out of africa, Peace of Westphalia, retrograde motion, short selling, the scientific method, trade route, urban planning

The result of his lucubrations was classically French in that it did not square with reality but it was very beautiful, and logically coherent. Since then our friends Huygens and Wren have expended more toil towards the same end. But I need hardly tell you that it is Newton, far beyond all others, who has vastly expanded the realm of truths that are geometrickal in nature. I truly believe that if Euclid and Eratosthenes could be brought back to life they would prostrate themselves at his feet and (pagans that they were) worship him as a god. For their geometry treated mostly simple abstract shapes, lines in the sand, while Newton’s lays down the laws that govern the very planets. I have read the copy of Principia Mathematica that you so kindly sent me, and I know better than to imagine I will find any faults in the author’s proofs, or extend his work into any realm he has not already conquered.