Beginning Of The Modern World
The most important scientific achievement in Western history is commonly ascribed to Nicolaus Copernicus, who on his deathbed published Concerning the Revolutions of the Heavenly Spheres. Science historian Thomas Kuhn called the Polish-born astronomer's accomplishment the "Copernican Revolution." It represented a final break with the Middle Ages, a movement from religion to science, from dogma to enlightened secularism. What had Copernicus done to become the most important scientist of all time?
In school we learned that in the sixteenth century, Copernicus reformed the solar system, placing the sun, rather than the earth, at its center, correcting the work of the second-century Greek astronomer Ptolemy. By constructing his heliocentric system, Copernicus put up a fire wall between the West and East, between a scientific culture and those of magic and superstition.
Copernicus did more than switch the center of the solar system from the earth to the sun. The switch itself is important, but mathematically trivial. Other cultures had suggested it. Two hundred years before Pythagoras, philosophers in northern India had understood that gravitation held the solar system together, and that therefore the sun, the most massive object, had to be at its center. The ancient Greek astronomer Aristarchus of Samos had put forth a heliocentric system in the third century B.C. The Maya had posited a heliocentric solar system by A.D. 1000. Copernicus's task was greater. He had to repair the flawed mathematics of the Ptolemaic system.
Ptolemy had problems far beyond the fact that he chose the wrong body as the pivot point. On that, he was adhering to Aristotelian beliefs. A workable theory of universal gravitation had yet to be discovered. Thus hampered, Ptolemy attempted to explain mathematically what he saw from his vantage in Alexandria: various heavenly bodies moving around the earth. This presented problems.
Mars, for instance, while traveling across our sky, has the habit, like other planets, of sometimes reversing its direction. What's happening is simple: the earth outspeeds Mars as both planets orbit the sun, like one automobile passing another. How does one explain this in a geocentric universe? Ptolemy came up with the concept of epicycles, circles on top of circles. Visualize a Ferris wheel revolving around a hub. The passenger-carrying cars are also free to rotate around axles connected to the outer perimeter of the wheel. Imagine the cars constantly rotating 360 degrees as the Ferris wheel also revolves. Viewed from the hub, a point on the car would appear to move backward on occasion while also moving forward with the motion of the wheel.
Ptolemy set the upper planets in a series of spheres, the most important of which was the "deferent" sphere, which carried the epicycle. This sphere was not concentric with the center of the earth. It moved at a uniform speed, but that speed was not measured around its own center, nor around the center of the earth, but around a point that Ptolemy called the "center of the equalizer of motion," later to be called the `equant." This point was the same distance from the center of the deferent as the distance of the deferent's center from the earth, but in the opposite direction. The result was a sphere that moved uniformly around an axis that passed not through its own center but, rather, through the equant.
The theory is confusing. No number of readings or constructions will help, because Ptolemy's scheme is physically impossible. The flaw is called the equant problem, and it apparently eluded the Greeks. The equant problem didn't fool the Arabs, and during the late Middle Ages Islamic astronomers created a number of theorems that corrected Ptolemy's flaws.
Copernicus confronted the same equant problem. The birth of Isaac Newton was a century away, so Copernicus, like Ptolemy and the Arabs before him, had no gravitation to help him make sense of the situation. Thus, he did not immediately switch the solar system from geocentricity to heliocentricity. Instead, he first improved the Ptolemaic system, putting the view of the heavens from earth on a more solid mathematical basis. Only then did Copernicus transport the entire system from its earth-centered base to the sun. This was a simple operation, requiring Copernicus only to reverse the direction of the last vector connecting the earth to the sun. The rest of the math remained the same.
It was assumed that Copernicus was able to put together this new planetary system using available math, that the Copernican Revolution depended on a creative new application of classical Greek works such as Euclid's Elements and Ptolemy's Almagest. This belief began breaking down in the late 1950s when several scholars, including Otto Neugebauer, of Brown University; Edward Kennedy, of the American University of Beirut; Noel Swerdlow, of the University of Chicago; and George Saliba, of Columbia University, reexamined Copernicus's mathematics.
They found that to revolutionize astronomy Copernicus needed two theorems not developed by the ancient Greeks. Neugebauer pondered this problem: did Copernicus construct these theorems himself or did he borrow them from some non-Greek culture? Meanwhile, Kennedy, working in Beirut, discovered astronomical papers written in Arabic and dated before A.D. 1350. The documents contained unfamiliar geometry. While visiting the United States, he showed them to Neugebauer.
Neugebauer recognized the documents' significance immediately. They contained geometry identical to Copernicus's model for lunar motion. Kennedy's text was written by the Damascene astronomer Ibn al-Shatir, who died in 1375. His work contained, among other things, a theorem employed by Copernicus that was originally devised by another Islamic astronomer, Nasir al-Din al-Tusi, who lived some three hundred years before Copernicus.
The Tusi couple, as the theorem is now called, solves a centuries-old problem that plagued Ptolemy and the other ancient Greek astronomers: how circular motion can generate linear motion. Picture a large sphere with a sphere half its size inside it, the smaller sphere contacting the larger at just one point. If the large sphere rotates and the small sphere revolves in the opposite direction at twice that speed, the Tusi couple dictates that the original point of tangency will oscillate back and forth along the diameter of the larger sphere. By setting the celestial spheres properly, this theorem explained how the epicycle could move uniformly around the equant of the deferent, and still oscillate back and forth toward the center of the deferent. All this could now be done by positing spheres moving uniformly around axes that passed through their centers, thus avoiding the pitfalls of Ptolemy's configurations. A rough analogy is a steam-engine piston, which moves back and forth as the wheel is turning.
A second theorem found in the Copernican system is the Urdi lemma, after the scientist Mu'ayyad al-Din al-'Urdi, who proposed it sometime before 1250. It simply states that if two lines of equal length emerge from a straight line at the same angles, either internally or externally, and are connected up top with another straight line, the two horizontal lines will be parallel. When the equal angles are external, all four lines form a parallelogram. Copernicus did not include a proof of the Urdi lemma in his work, most likely because the proof had already been published by Mu'ayyad al-Din al-'Urdi. Columbia's George Saliba speculates that Copernicus didn't credit him because Muslims were not popular in sixteenth-century Europe.
Both the Urdi lemma and the Tusi couple are, in the words of Saliba, "organically embedded within [Copernican] astronomy, so much so that it would be inconceivable to extract them and still leave the mathematical edifice of Copernican astronomy intact."
Saliba emphasizes that plagiarism is not the issue here. Those who have been involved in a plagiarism case are probably familiar with the standard defense: independent execution.' This is an especially powerful defense in the sciences, in which there are "right" and "wrong" solutions. If Copernicus's theorem looks like al-Tusi's, perhaps that's because it's the one correct answer to the problem.
Map publishers sometimes insert fictitious islands or other features into their maps to trap plagiarists. Did Copernicus borrow al-Tusi's theorem without credit? There's no smoking gun, but it is suspicious that Copernicus's math contains arbitrary details that are identical to al-Tusi's. Any geometric theorem has the various points labeled with letters or numbers, at the discretion of the originator. The order and choice of symbols is arbitrary. The German science historian Willy Hartner noted that the geometric points used by Copernicus were identical to al-Tusi's original notation. That is, the point labeled with the symbol for alif by al-Tusi was marked A by Copernicus. The Arabic ba was marked B, and so on, each Copernican label the phonetic equivalent of the Arabic. Not just some of the labels were the same - almost all were identical.
There was one exception. The point designating the center of the smaller circle was marked as f by Copernicus. It was a z in Tusi's diagram. In Arabic script, however, a z in that hand could be easily mistaken for an f.
Johannes Kepler, who stretched Copernicus's circular planetary orbits into ellipses later in the century, wondered why Copernicus had not included a proof for his second "new" theorem, which was in fact the Urdi lemma. The obvious answer has eluded most historians because it is too damaging to our Western pride to accept: the new math in the Copernican Revolution arose first in Islamic, not European minds. From a scientific point of view, it's not important whether Copernicus was a plagiarist. The evidence is circumstantial, and certainly he could have invented the theorems on his own. There is no doubt, however, that two Arab astronomers beat him to the punch.
Western science is our finest accomplishment. Does any other culture, past or present, boast a scientific edifice equal to that built by Galileo, Newton, Leibniz, Lavoisier, Dalton, Faraday, Planck, Rutherford, Einstein, Heisenberg, Pauli, Watson, and Crick? Is there anything in the non-Western past to compare to present-day molecular biology, particle physics, chemistry, geology, or technology? There's little debate. The only question is where this science came from. Who contributed to it? The consensus is that science is almost entirely Western in origin. By Western we mean ancient and Hellenistic Greece, and Europe from the Renaissance to the present. Greece is traditionally considered European, as opposed to being part of Mediterranean culture, which would include its neighbors in Africa. For the purposes of this book, Western means Europe, Greece, and post-Columbian North America. Non- Western means, generally, everywhere else, including the Americas of the Amerindians before Columbus. Non-Western thus takes in considerable area, and the prevailing opinion is that modern science owes little to the peoples of these lands.
The short form of the hypothesis is this: science was born in ancient Greece around 600 B.C. and flourished for a few hundred years, until about 146 B. c., when the Greeks gave way to the Romans. At this time science stopped dead in its tracks, and it remained dormant until resurrected during the Renaissance in Europe around 1500. This is what's known as the "Greek miracle." The hypothesis assumes that the people who occupied India, Egypt, Mesopotamia, sub-Saharan Africa, China, the Americas, and elsewhere prior to 600 B.C. conducted no science. They discovered fire, then called it quits, waiting for Thales of Miletus, Pythagoras, Democritus, and Aristotle to invent science in the Aegean.
As amazing as the Greek miracle is the notion that for over fifteen hundred years, from the end of the Greek period to the time of Copernicus, no science was conducted. The same people who stood idly by while the Greeks invented science supposedly demonstrated no interest or skill in continuing the work of Archimedes, Euclid, or Apollonius.
The hypothesis that science sprang ab ovo on Greek soil, then disappeared until the Renaissance seems ridiculous when written out succinctly. It's a relatively new theory, first fashioned in Germany about 150 years ago, and has become subtly embedded in our educational consciousness. The only concession made to non-European cultures is to Islam. The story goes that the Arabs kept Greek culture, and its science, alive through the Middle Ages. They acted as scribes, translators, and caretakers, with, apparently, no thought of creating their own science.
In fact, Islamic scholars admired and preserved Greek math and science, and served as the conduit for the science of many non-Western cultures, in addition to constructing their own impressive edifice. Western science is what it is because it successfully built upon the best ideas, data, and even equipment from other cultures. The Babylonians, for example, developed the Pythagorean theorem (the sum of the squares of the two perpendicular sides of a right triangle is equal to the square of the hypotenuse) at least fifteen hundred years before Pythagoras was born. The Chinese mathematician Liu Hui calculated a value for pi (3.1416) in 200 A.D. that remained the most accurate estimation for a thousand years. Our numerals 0 through 9 were invented in ancient India, the Gwalior numerals of A.D. 500 being almost indistinguishable from modern Western numerals. Algebra is an Arab word, meaning "compulsion," as in compelling the unknown x to assume a numerical value. (One traditional translation, that algebra means "bone setting," is colorful but incorrect.)
The Chinese were observing, reporting, and dating eclipses between 1400 and 1200 B.C. The Venus Tablets of Ammizaduga record the positions of Venus in 1800 B.C. during the reign of the Babylonian king. Al-Mamum, an Arabian caliph, built an observatory so his astronomers could double-check most of the Greek astronomical parameters, thus giving us more accurate values for precession, inclination of the ecliptic, and the like. In 829 his quadrants and sextants were larger than those built by Tycho Brahe in Europe more than seven centuries later.
Twenty-four centuries before Isaac Newton, the Hindu Rig-Veda asserted that gravitation held the universe together, though the Hindu hypothesis was far less rigorous than Newton's. The Sanskrit-speaking Aryans subscribed to the idea of a spherical earth in an era when the Greeks believed in a flat one. The Indians of the fifth century A.D. somehow calculated the age of the earth as 4.3 billion years; scientists in nineteenth-century England were convinced it was 100 million years. (The modern estimate is 4.6 billion years.) Chinese scholars in the fourth century A.D. - like Arabs in the thirteenth century and the Papuans of New Guinea later on - routinely used fossils to study the history of the planet; yet at Oxford University in the seventeenth century some faculty members continued to teach that fossils were "false clues sown by the devil" to deceive man. Quantitative chemical analyses set down in the K'ao kung chi, an eleventh-century B.C. Chinese text, are never more than 5 percent off when compared to modern figures.
Mohist (Chinese) physicists in the third century B.C. stated, "The cessation of motion is due to the opposing force. . . . If there is no opposing force . . . the motion will never stop. This is as true as that an ox is not a horse." It would be two thousand years before Newton would set down his first law of motion in more prosaic terms. The Shu-Ching (circa 2200 B.C.) stated that matter was composed of distinct separate elements seventeen centuries before Empedocles made the same observation, and hypothesized that sunbeams were made of particles long before Albert Einstein and Max Planck posited the ideas of photons and quanta. Big bang? The creation myths of Egypt, India, Mesopotamia, China, and Central America all begin with a "great cosmic copulation" - not quite the same as a big bang, but more poetic.
As for practical matters, Francis Bacon said that three inventions - gunpowder, the magnetic compass, and paper and printing - marked the beginning of the modern world. All three inventions came from China. The Incas of the Andes were the first to vulcanize rubber, and they discovered that quinine was an antidote for the malaria that spread among them. The Chinese made antibiotics from soybean curd twenty-five hundred years ago.
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