Eratosthenes

43 results back to index


pages: 404 words: 131,034

Cosmos by Carl Sagan

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, Alfred Russel Wallace, Arthur Eddington, clockwork universe, dematerialisation, double helix, Drosophila, Edmond Halley, Eratosthenes, Ernest Rutherford, germ theory of disease, invention of movable type, invention of the telescope, Isaac Newton, Lao Tzu, Louis Pasteur, Magellanic Cloud, Mars Rover, Menlo Park, music of the spheres, pattern recognition, planetary scale, Search for Extraterrestrial Intelligence, spice trade, 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: 492 words: 149,259

Big Bang by Simon Singh

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, John von Neumann, Karl Jansky, 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, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, V2 rocket, 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.

 

pages: 532 words: 133,143

To Explain the World: The Discovery of Modern Science by Steven Weinberg

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, music of the spheres, On the Revolutions of the Heavenly Spheres, 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: 467 words: 114,570

Pathfinders: The Golden Age of Arabic Science by Jim Al-Khalili

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, Joseph Schumpeter, retrograde motion, 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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Ada Lovelace, Andrew Wiles, Arthur Eddington, Augustin-Louis Cauchy, computer age, Dava Sobel, Dmitri Mendeleev, Eratosthenes, Erdős number, four colour theorem, Georg Cantor, German hyperinflation, global village, Henri Poincaré, Isaac Newton, Jacquard loom, Jacquard loom, music of the spheres, New Journalism, Paul Erdős, Richard Feynman, Richard Feynman, 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.

 

pages: 310 words: 89,653

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, crowdsourcing, dark matter, Edmond Halley, Edward Charles Pickering, en.wikipedia.org, Eratosthenes, gravity well, Isaac Newton, Kuiper Belt, Mars Rover, planetary scale, Pluto: dwarf planet, polynesian navigation, Ronald Reagan, Saturday Night Live, Search for Extraterrestrial Intelligence, Stephen Hawking, V2 rocket

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.

 

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, Eratosthenes, Georg Cantor, P = NP

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: 184 words: 13,957

Haskell by Graham Hutton

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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: 184 words: 13,985

Programming in Haskell by Graham Hutton

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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: 304 words: 82,395

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

23andMe, Affordable Care Act / Obamacare, airport security, AltaVista, 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, Internet of things, invention of the printing press, Jeff Bezos, 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, performance metric, Peter Thiel, Post-materialism, 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, 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: 893 words: 199,542

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Andrew Wiles, conceptual framework, Douglas Hofstadter, Eratosthenes, Fermat's Last Theorem, Gödel, Escher, Bach, industrial robot, information retrieval, iterative process, 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: 566 words: 122,184

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Bill Gates: Altair 8800, Claude Shannon: information theory, computer age, Douglas Engelbart, Dynabook, Eratosthenes, Grace Hopper, invention of the telegraph, Isaac Newton, Jacquard loom, 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 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: 462 words: 172,671

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

continuous integration, database schema, domain-specific language, en.wikipedia.org, Eratosthenes, finite state, Ignaz Semmelweis: hand washing, iterative process, place-making, web application, WebSocket

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: 1,387 words: 202,295

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Andrew Wiles, conceptual framework, Douglas Hofstadter, Eratosthenes, Gödel, Escher, Bach, industrial robot, information retrieval, iterative process, 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: 551 words: 174,280

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, Gödel, Escher, Bach, illegal immigration, invention of movable type, Isaac Newton, Islamic Golden Age, Jacquard loom, Jacquard loom, John Conway, John von Neumann, Joseph-Marie Jacquard, Loebner Prize, Louis Pasteur, pattern recognition, Richard Feynman, Richard Feynman, Search for Extraterrestrial Intelligence, Stephen Hawking, supervolcano, technological singularity, The Coming Technological Singularity, the scientific method, Thomas Malthus, Thorstein Veblen, Turing test, Vernor Vinge, Whole Earth Review, William of Occam

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: 367 words: 99,765

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Asperger Syndrome, augmented reality, Bartolomé de las Casas, Berlin Wall, British Empire, clean water, David Brooks, 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.

 

pages: 315 words: 93,628

Is God a Mathematician? by Mario Livio

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, John von Neumann, music of the spheres, probability theory / Blaise Pascal / Pierre de Fermat, 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: 366 words: 100,602

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

centre right, colonial exploitation, Edmond Halley, Eratosthenes, Fellow of the Royal Society, Isaac Newton, 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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

3D printing, Admiral Zheng, Albert Einstein, Alfred Russel Wallace, Berlin Wall, Buckminster Fuller, butterfly effect, California gold rush, carbon-based life, 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, John von Neumann, Kickstarter, life extension, Mahatma Gandhi, Mars Rover, mutually assured destruction, Oculus Rift, operation paperclip, out of africa, Peter H. Diamandis: Planetary Resources, phenotype, purchasing power parity, RAND corporation, Ray Kurzweil, RFID, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, risk tolerance, 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, V2 rocket, 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: 385 words: 103,561

Pinpoint: How GPS Is Changing Our World by Greg Milner

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Ayatollah Khomeini, British Empire, data acquisition, Dava Sobel, 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, 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.

 

The Art of Computer Programming by Donald Ervin Knuth

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Brownian motion, complexity theory, correlation coefficient, Eratosthenes, 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: 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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, 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: 852 words: 157,181

The Origins of the British by Stephen Oppenheimer

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

agricultural Revolution, British Empire, Eratosthenes, gravity well, 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?

 

pages: 482 words: 125,429

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

clean water, Commentariolus, dumpster diving, Eratosthenes, financial innovation, invention of movable type, Islamic Golden Age, 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.

 

pages: 565 words: 164,405

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, ice-free Arctic, imperial preference, income inequality, intermodal, James Hargreaves, John Harrison: Longitude, Khyber Pass, low skilled workers, non-tariff barriers, 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, transatlantic slave trade, transcontinental railway, upwardly mobile, working poor

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.

 

pages: 577 words: 149,554

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, 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: 158 words: 49,168

Infinite Ascent: A Short History of Mathematics by David Berlinski

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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: 190 words: 52,570

The Planets by Dava Sobel

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, Colonization of Mars, Dava Sobel, Edmond Halley, Eratosthenes, friendly fire, Isaac Newton, Kuiper Belt, music of the spheres

.* 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: 194 words: 49,310

Clock of the Long Now by Stewart Brand

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, Brewster Kahle, Buckminster Fuller, Colonization of Mars, complexity theory, Danny Hillis, Eratosthenes, Extropian, fault tolerance, Internet Archive, Jaron Lanier, Kevin Kelly, knowledge economy, life extension, nuclear winter, pensions crisis, phenotype, Ray Kurzweil, 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: 231 words: 72,656

A History of the World in 6 Glasses by Tom Standage

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, 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.

 

pages: 282 words: 82,107

An Edible History of Humanity by Tom Standage

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, 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.

 

pages: 685 words: 203,949

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

airport security, Albert Einstein, Amazon Mechanical Turk, Anton Chekhov, 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, meta analysis, meta-analysis, more computing power than Apollo, Network effects, new economy, Nicholas Carr, optical character recognition, pattern recognition, phenotype, placebo effect, pre–internet, profit motive, randomized controlled trial, Skype, Snapchat, statistical model, Steve Jobs, supply-chain management, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Turing test, ultimatum 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: 661 words: 169,298

Coming of Age in the Milky Way by Timothy Ferris

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, Albert Michelson, Alfred Russel Wallace, anthropic principle, Arthur Eddington, Atahualpa, Cepheid variable, Chance favours the prepared mind, 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, 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, Richard Feynman, Search for Extraterrestrial Intelligence, Searching for Interstellar Communications, Solar eclipse in 1919, Stephen Hawking, 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: 335 words: 107,779

Some Remarks by Neal Stephenson

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, 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, 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: 1,402 words: 369,528

A History of Western Philosophy by Aaron Finkel

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

British Empire, Eratosthenes, Georg Cantor, invention of agriculture, Mahatma Gandhi, Plutocrats, plutocrats, 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: 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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Berlin Wall, Eratosthenes, full employment, Isaac Newton, Ronald Reagan, Silicon Valley, V2 rocket, 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.

 

pages: 420 words: 143,881

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

epigenetics, Eratosthenes, Fellow of the Royal Society, 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: 903 words: 235,753

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, 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, Edward Snowden, Elon Musk, en.wikipedia.org, Eratosthenes, 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, intermodal, Internet of things, invisible hand, Jacob Appelbaum, Jaron Lanier, Jony Ive, Julian Assange, Khan Academy, linked data, Mark Zuckerberg, market fundamentalism, Marshall McLuhan, Masdar, McMansion, means of production, megacity, megastructure, Menlo Park, Minecraft, Monroe Doctrine, Network effects, new economy, offshore financial centre, oil shale / tar sands, packet switching, PageRank, pattern recognition, peak oil, performance metric, personalized medicine, Peter Thiel, phenotype, place-making, planetary scale, RAND corporation, recommendation engine, reserve currency, RFID, 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, universal basic income, urban planning, Vernor Vinge, Washington Consensus, web application, 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.”

 

pages: 855 words: 178,507

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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, 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, Jacquard loom, Jaron Lanier, jimmy wales, John von Neumann, Joseph-Marie Jacquard, Louis Daguerre, Marshall McLuhan, Menlo Park, microbiome, Milgram experiment, Network effects, New Journalism, Norbert Wiener, On the Economy of Machinery and Manufactures, PageRank, pattern recognition, phenotype, pre–internet, Ralph Waldo Emerson, RAND corporation, reversible computing, Richard Feynman, Richard Feynman, 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: 1,051 words: 334,334

Gravity's Rainbow by Thomas Pynchon

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

centre right, Eratosthenes, experimental subject, invisible hand, Isaac Newton, 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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

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.