Lost Discoveries: The Ancient Roots of Modern Science--from the Baby

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LOST DISCOVERIES

The Ancient Roots of Modern Science—from the Babylonians to the Maya

DICK TERESI

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Library of Congress Cataloging-in-Publication Data

Teresi, Dick.

Lost discoveries: the ancient roots of modern science—from the Babylonians to the Maya / Dick Teresi.

p.  cm.

Includes bibliographical references and index.

1. Science, Ancient.  2. Science—History  I. Title.

Q124.95.T47 2002

509.3—dc21   2002075457

ISBN 978-0-6848-3718-5

eISBN-13: 978-1-439-12860-2

www.SimonandSchuster.com

Board 0f Advisers

Anthony Aveni

Alfred W. Crosby

Harold Goldwhite

George Gheverghese Joseph

Robert Kaplan

David Park

George Saliba

Sheila Seaman

Barbara C. Sproul

The above scientists, mathematicians, and scholars reviewed the manuscript for scientific, mathematical, and historical accuracy Some were chosen for a non-Western, others for a Western bias. While I deferred to these advisers on factual matters, they did not always agree with my interpretation of those facts. My point of view was greatly affected by the views expressed by my advisers, but ultimately it is my own. Where practical, I have stated differing views by the board in the endnotes.

Anthony Aveni is the Russell B. Colgate Professor of Astronomy and Anthropology at Colgate University. He is the author of Conversing with the Planets: How Science and Myth Invented the Cosmos and other works of archaeoastronomy.

Alfred W. Crosby is professor emeritus of history at the University of Texas. He is the author of Ecological Imperialism: The Biological Expansion of Europe, 900-1900, among other works.

Harold Goldwhite is professor of chemistry at California State University, Los Angeles, and is the coauthor, with Cathy Cobb, of Creations of Fire: Chemistry’s Lively History from Alchemy to the Atomic Age.

George Gheverghese Joseph is professor of mathematics at the University of Manchester (UK) and the author of The Crest of the Peacock: Non-European Roots of Mathematics.

Robert Kaplan has taught mathematics at a number of institutions, most recently Harvard University. He is the author of The Nothing That Is: A Natural History of Zero.

David Park is emeritus professor of physics at Williams College. He is the author of The Fire Within the Eye: A Historical Essay on the Nature and Meaning of Light.

George Saliba is professor of Arabic and Islamic science at the department of Middle East and Asian languages and cultures, Columbia University. He is the author of A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam, among other works.

Sheila J. Seaman is associate professor of geology at the University of Massachusetts at Amherst.

Barbara C. Sproul is director of the program in religion, Hunter College, City University of New York. She is the author of Primal Myths: Creation Myths Around the World and was one of the founders of the American section of Amnesty International, which won the Nobel Peace Prize in 1977.

Contents

1 A HISTORY OF SCIENCE: Rediscovered

2 MATHEMATICS: The Language or Science

3 ASTRONOMY: Sky Watchers and More

4 COSMOLOGY: That Old-Time Religion

5 PHYSICS: Particles, Voids, and Fields

6 GEOLOGY: Stories of Earth Itself

7 CHEMISTRY: Alchemy and Beyond

8 TECHNOLOGY: Machines as a Measure of Man

Notes

Selected Bibliography

Acknowledgments

Index

LOST DISCOVERIES

1

A HISTORY OF SCIENCE Rediscovered

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.¹ 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.² 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.³ 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.)⁴

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.

THE TEACHING OF multicultural science in the 1980s had hardly begun when it was met by a powerful backlash, much of it justified. I was part of the backlash, having accepted in the early 1990s an assignment to write an article about faulty multicultural science being taught in schools. While there was plenty to expose, the most egregious program was called the Portland African-American Baseline Essays, developed by the Multnomah County, Oregon, school board.

The scientific portion of the curriculum was a disaster. It cited evidence of the use of gliders in ancient Egypt from 2500 B.C. to 1500 B.C., adding that the Egyptians used their early planes for travel, expeditions, and recreation. The Portland essays speculated that these gliders were made from papyrus and glue. The evidence cited for this ancient Egyptian air force was the discovery in 1898 of a birdlike object made of sycamore wood. It sat in a box of other birdlike objects in the Cairo Museums basement until 1969, when an archaeologist and his flight-engineer brother concluded that the object was a model glider with a distinctive resemblance to an American Hercules transport aircraft because of its reverse dihedral wing. The Portland essays insisted that this fourteen-centimeter-long object was a scale model of full-sized gliders that once filled the skies over the Great Pyramids, which, one can therefore assume, served as platforms for ancient air-traffic controllers.⁵

The Portland essays also claimed that the ancient Egyptians and Mesopotamians knew how to make batteries. Clay pots found in 1962 in Baghdad contained five-inch-long cylindrical sheet-copper cores with a lead-tin alloy at the bottom. Inside the copper tube was an iron or bronze rod thought to have been surrounded by a solution of sulfate, vinegar, acetic acid, or citric acid. A General Electric laboratory demonstrated that ten such batteries connected in series could produce up to two volts. Were these really batteries? It’s possible, though the Portland essays do not explain how it was known that acid was used in the pots. Nor do we know to what use the batteries were put.

The Portland essays also touted the Egyptians as masters of psi: precognition, psychokinesis, and remote viewing. The essays make a distinction between magic, which they disregard, and psi, or psychoenergetics, which they describe as being science. We will not take time here to discuss the Egyptians’ alleged accomplishments in psychoenergetics.⁶ One can only wonder why this ancient civilization, with airplanes and telekinesis at its disposal, bothered with swords and spears to fight its battles.

Some multiculturists claimed that eleventh-century Chinese warriors were armed with machine guns, and that the Incas frolicked above the Nasca plains in hot-air balloons. Certain Afrocentric scholars have made some dubious claims: that the Greek mathematician Euclid was black, for example, and that the Olmec heads, huge sculpted heads with Negroid features found in Mexico, are proof that Nubians visited the Americas.

In its issue of April 18, 1999, the New York Times Magazine chose the best inventions, stories, and ideas of the previous one thousand years. Richard Powers wrote that the most important scientific event of the last millennium occurred at its very beginning, around A.D. 1000, when the Arab scientist Alhazen solved a centuries-old problem: how does vision work? Alhazen, who was born as Abu Ali al-Hasan ibn al-Haytham in Basra, in what is now Iraq, dispatched the ray theory, which had been around since ancient Greece. This theory, espoused by Euclid, Ptolemy, and others, held that the eye sent out a ray to the object in order to see it. The ray theory seems ridiculous today because we know the speed of light and how far away the stars are. If our eyes had to send out rays, we’d be waiting years before we could see even the nearest stars.

In 1000, the ray theory seemed reasonable. Alhazen conducted a simple experiment: he and others looked into the sun; it hurt. Clearly, if there were rays, they were coming into the eye, not going out of it. He developed a comprehensive theory of vision that dominated optics in Europe until 1610, when Kepler improved upon it. Alhazen may not have been smarter than Euclid and Ptolemy, but he worked quite differently. The latter two followed a classic Greek method of announcing a set of axioms, then reasoning from them. Alhazen began with his observations of and experiments with light, then reasoned toward a theory.⁷ Ptolemy and Euclid also collected measurements and made observations, but the Greek ideal made the data subservient to the precept. Powers was reaching, perhaps, when he stated that Alhazen’s challenge of the old optical theory has led to the certainties of electron microscopy, retinal surgery, and robotic vision, but he was correct in stating that the vesting of authority in experiment and the skeptical rejection of concept in favor of evidence began not in Europe but in the Islamic world.⁸

For some, the failure to acknowledge the successes of non-Western cultures derives not just from ignorance but from a conspiracy. Martin Bernal, a professor of government studies at Cornell University, is the author of Black Athena, a series of books that challenges our Greek-rooted view of history. Bernal believes that the roots of Greek civilization are to be found in Egypt and, to a lesser extent, in the Levant—the Near East of the Phoenicians and the Canaanites. Using linguistic analysis, he determined that 20 to 25 percent of the Greek vocabulary derived from the Egyptian. The roots of European civilization are Afro-Asiatic. The Greeks knew this and wrote about it, telling of Egyptian colonies in Greece during the Bronze and even the Iron Ages. The great Greek wise men, including Pythagoras, Democritus, and even Plato, traveled to Egypt and brought back Egyptian ideas and knowledge. (We have Democritus’s own writings to acknowledge that his math skills were honed in the shadow of the pyramids.) The Greeks acknowledged their debt to Egypt. This ancient model held that the Greek culture had arisen as the result of colonization, in around 1500 B.C., by Egyptians and Phoenicians, and that the Greeks continued to borrow heavily from Near Eastern cultures. It was the conventional wisdom among Greeks in the classical and Hellenistic ages. This ancient model, writes Bernal, was also embraced by Europeans from the Renaissance through the nineteenth century. The Europeans, says Bernal, were enamored of Egypt.

For several centuries, Europe believed that Egypt was the cradle of civilization. This began to change in the eighteenth century when Christian apologists worried about Egyptian pantheism, and ideas of racial purity began taking hold among Locke, Hume, and other English thinkers. This led to the Aryan model in the first half of the nine-teenth century. This view denied the existence of Egyptian settlements. Later, as anti-Semitism grew during the late nineteenth century, proponents of the Aryan model also denied Phoenician cultural influences.

The Aryan model was refined throughout the years to establish ancient Greece as distinctly European. Accordingly, there had been an invasion from the north—unreported in ancient tradition—that had overwhelmed the local Aegean or pre-Hellenic culture. Thus, Greek civilization was now seen as the result of the mixture of the Indo-European-speaking Hellenes and their indigenous subjects. It is this Aryan model that most of us were taught during the twentieth century. Bernal advocates a return to a modified ancient model, which is supported by the historian Herodotus and other ancient Greeks.

IN ITS JANUARY 14, 2000, issue, on the occasion of the beginning of the third millennium, Science magazine, in conjunction with the American Association for the Advancement of Science (AAAS), published a time line, called Pathways of Discovery, that detailed ninety-six of the most important scientific achievements in recorded history. The Science time line included some sophisticated choices that many educators would have missed: William Ferrel’s 1856 work on ocean winds and currents, the 1838-39 cell theory of Matthias Schleiden and Theodor Schwann, and William Gilbert’s 1600 theory that the earth behaves like a huge magnet.

Of those ninety-six achievements, only two were attributed to non-white, non-Western scientists: the invention of zero in India in the early centuries of the common era and the astronomical observations of Maya and Hindus in A.D. 1000. Even these two accomplishments were muted by the editors of Science. The Indians were given credit only for creating the symbol for zero, rather than the concept itself. The Mayan and Hindu skywatchers (the word astronomer was not used) made their observations, according to the journal, for agricultural and religious purposes only.

Most interesting is the first entry in the time line: Prior to 600 B.C., Prescientific Era. Science proclaimed that during this time, before the sixth-century B.C. pre-Socratic philosophers, Phenomena [were] explained within contexts of magic, religion, and experience. Science thus ignored more than two millennia of history, during which time the Babylonians invented the abacus and algebra, the Sumerians recorded the phases of Venus, the Indians proposed an atomic theory, the Chinese invented quantitative chemical analysis, and the Egyptians built pyramids. In addition, Science gave Johannes Gutenberg credit for the printing press in 1454, though it was invented at least two centuries earlier by the Chinese and Koreans. An essential precursor to the printing press is paper, which was invented in China and did not reach Europe until the 1300s.⁹ Science cited Francis Bacon’s work as one of its ninety-six achievements, yet ignored his opinion that inventions from China created the modern world.

Pre-Columbian achievements in the New World have long eluded traditionalists. The Maya invented zero about the same time as the Indians, and practiced a math and astronomy far beyond that of medieval Europe. Native Americans built pyramids and other structures in the American Midwest larger than anything then in Europe.

MANY TRADITIONAL Western historians believe that little original science was conducted after the collapse of the Greek civilization; that the Arabs copied the work of Euclid, Ptolemy, Apollonius, et al.; and that eventually Europe recouped its scientific heritage from the Islamic world. During the Middle Ages, Arab scholars sought out Greek manuscripts and set up centers of learning and translation at Jund-i-Shapur in Persia and Baghdad in Iraq. Western historians don’t often like to admit that these same scholars also sought manuscripts from China and India, and created their own science.

Scholarship moved to Cairo and then to Córdoba and Toledo in Spain as the Muslim empire expanded into Europe. When the Christians recaptured Toledo in the twelfth century, European scholars descended upon the documents.¹⁰ They were interested in all Arabic documents— translations of Greek works but also original Arabic writings and Arabic translations of other cultures’ manuscripts. Much of the scientific knowledge of the ancient world—Greece as well as Babylonia, Egypt, India, and China—was funneled to the West through Spain. George Saliba has found that there was an intense traffic in Arabic manuscripts between Damascus and Padua during the early 1500s, and more and more scientific documents, written in Arabic, are being rediscovered in European libraries. Saliba has documented that many European scholars in the Renaissance were literate in Arabic. They read the Islamic papers and shared the information with their less literate colleagues.¹¹

One example is Copernicus, who studied at Padua. Saliba points out that if Copernicus did borrow from Islamic astronomers—and the jury is still out—he had good reason not to acknowledge his intellectual debt. It would have been impolitic, says Saliba, to mention Islamic science when the Ottoman Empire was at the door of Europe. Another European scholar who studied at Padua was William Harvey, who established the geometry of the human circulatory system in 1629, another landmark in science according to the AAAS’s Science time line. A 1241 Arab document, notes Saliba, lays out the same geometry, including the crucial assertion that the blood must first travel through the lungs before passing through the heart, contrary to the opinion of the ancient Greek physician Galen and past medical scholarship.¹²

Historian Glen Bowersock of the Institute for Advanced Study writes that the classical antecedents of western civilization have long served to justify the study of ancient Greece and Rome, but he admits that the porousness of Greek culture and the parallels to its achievements in other cultures have never been a secret…. The Greeks did not emerge, like Athena from the head of Zeus, fully equipped with their arsenal of culture…. An expression like ‘the Greek miracle’ was a catchy phrase for great drama, heroic statues and the Parthenon, but all this had its historical context. For the Greeks themselves, the context was Phoenicia and Egypt.¹³

The AAAS and Science magazine, in their Pathways of Discovery time line, acknowledge that from the ninth to the fifteenth centuries, "The flow of science and technology is mostly into Europe from Islam and China" (italics theirs). Yet Science reports that the contributions of Islam and China are among those events that represent the countless twists, turns, ironies, contradictions, tragedies, and other unkempt historical details that have synthesized into the far more complex and multitextured reality of the scientific adventure. Other such events they list are Isaac Newton’s practice of alchemy, the false discovery of N-rays, and the failure of geologists to accept the theory of continental drift.

This shall be a book of unkempt historical details—a tale of the non-Western roots of science. I began to write with the purpose of showing that the pursuit of evidence of nonwhite science is a fruitless endeavor. I felt that it was only responsible, however, to attempt to find what meager legitimate non-European science might exist. Six years later, I was still finding examples of ancient and medieval non-Western science that equaled and often surpassed ancient Greek learning.

My embarrassment at having undertaken an assignment with the assumption that non-Europeans contributed little to science has been overtaken by the pleasure of discovering mountains of unappreciated human industry, four thousand years of scientific discoveries by peoples I had been taught to disregard.

There is no good definition of science. The AAAS, for example, does not have one. After many trials, the American Physical Society (for physicists) finally decided upon a definition. The APS found that if the definition was too broad, pseudosciences like astrology could sneak in; too tight, and things such as string theory, evolutionary biology, and even astronomy could be excluded.

For the purposes of this book, science is a logical and systematic study of nature and the physical world. It usually involves both experiment and theory. Those theories normally arise from or are verified by experiment. That’s a bit squishy, but most definitions of science are. I put usually in italics because if we absolutely require experiment, we might have to exclude astronomy, the oldest science, since one cannot re-create new stars or galaxies in the laboratory or reenact the formation of the solar system. Yet the observations in astronomy are often as good as experiment. Halley’s comet returns with stunning regularity; the sun comes up each morning.

The philosopher Karl Popper introduced the requisite of falsification. Science is falsifiable; religion is not. A scientific theory or law can never be proved absolutely, but it should be able to be falsified. For example, Newton said that force equals mass times acceleration (F = ma). We cannot prove that every object in every galaxy obeys this law or that all objects will always obey this law. We can prove it wrong, however, in an experiment. (And some of Newton’s concepts have been proved wrong, by Albert Einstein and by quantum physicists.) So scientists must come up only with theories that can be falsified, as Popper put it. They must be testable. There is no such requirement for religion.

All this said, there remain problems with such a definition. Astrology, for instance, is falsifiable. If your astrologer says you will meet a handsome stranger on Tuesday, you can test this. On the other hand, superstring theory, posited by some physicists as the theory of everything, would require a particle accelerator ten light-years in diameter to falsify it. Most of evolutionary biology cannot be verified experimentally either. One cannot reenact the evolution of a new species or re-create the dinosaurs beginning with a one-celled animal. If we follow the falsification rule too closely, we have to include astrology and exclude evolutionary biology, string theory, and maybe even astronomy.

So let’s not take falsification too seriously. Otherwise we might have to exclude all science practiced by the ancient Greeks. The Greeks not only avoided experiments, they abhored them, trusting reason over empirical evidence.

We will confine ourselves to the hardest sciences here: physics, astronomy, cosmology, geology, chemistry, and technology. We shall include math also, as it is indispensable to science and inextricably entwined with it. We will leave the softer disciplines—anthropology, agronomy, psychology, medicine, and the like—for another time.

One thing we won’t consider is the pragmatism of the science or the motivation of the scientist. These have often been used to discredit non-Western science: yes, it’s good work, but it wasn’t pure; or, conversely, it wasn’t practical. As for motivation, many scientific discoveries were driven by religion: Arab mathematicians improved algebra, in part, to help facilitate Islamic inheritance laws, and Vedic Indians solved square roots to build sacrificial altars of the proper size. This was science in the service of religion, but science nonetheless.

Stigler’s law of eponymy, formulated by statistician Stephen Stigler, states that no scientific discovery is named after its original discoverer. Journalist Jim Holt points out that Stigler’s law itself is self-confirming, given that Stigler admits that it was discovered by someone else: Robert K. Merton, a sociologist of science.¹⁴

The most famous Stiglerism is the Pythagorean theorem, which holds that the sum of the squares of the perpendicular sides of a right triangle equals the square of the hypotenuse. Or, in math parlance, a2 + b2 = c2 where a and b are the sides and c is the hypotenuse. Jacob Bronowski writes:

To this day, the theorem of Pythagoras remains the most important single theorem in the whole of mathematics. That seems a bold and extraordinary thing to say, yet it is not extravagant; because what Pythagoras established is a fundamental characterisation of the space in which we move, and it is the first time that it is translated into numbers. And the exact fit of the numbers describes the exact laws that bind the universe. In fact, the numbers that compose right-angled triangles have been proposed as messages which we might send out to planets in other star systems as a test for the existence of rational life there.

The only problem is that Pythagoras is not the first mathematician to come up with the theorem. By Bronowski’s own admission, the Indians, Egyptians, and Babylonians used Pythagorean triplets in order to determine right angles when constructing buildings. A Pythagorean triplet is a set of three numbers that describes the sides of a right triangle. The most common triplet is 3: 4: 5 (32 + 42 = 52, or 9 + 16 = 25. Others you probably learned in high school include 5: 12: 13, 12 : 16: 20, and 8: 15: 17. Pythagoras invented his theorem around 550 B.C. The Babylonians, Bronowski concedes, had cataloged perhaps hundreds of triplets by 2000 B.C., long before Pythagoras. One of the triplets the Babylonians found is the enormous 3,367 : 3,456 : 4,825.

Nevertheless, Bronowski dismisses Babylonian triplets (as well as Egyptian and Indian triplets) as being merely empirical. That is, he believes that they somehow arrived at triplets (or triples) such as 3,367 : 3,456 : 4,825 by trial and error. Yet there is considerable evidence that the Babylonians used various algebraic techniques derived from a2 + b2 = c2 to generate Pythagorean triplets. There’s no way even God could come up with all Pythagorean triples by trial and error, says mathematician Robert Kaplan.

What Pythagoras arguably did that impressed Bronowski and others—and justifiably so—was to construct a geometric proof of the theorem. The concept of the proof as more important than the theorem itself was promulgated two centuries later by Euclid. Thus, non-Western mathematics has been viewed as second-rate because it is empirically based rather than proof based. Both methods are useful. The Euclidian geometry most of us learned is axiomatic. It begins with an axiom, a law assumed to be true, and deduces theorems by reasoning downward. It is deductive and assumptive. Centuries later, Alhazen in the East and, notably, Galileo in the West helped popularize an inductive, empirical method for science, much as the Babylonians, Egyptians, and Indians had used. One begins not with assumptions but with data and measurements, and then reasons upward to overarching truths.¹⁵ Most of what we call science today is empirical. When Isaac Newton collected data on the passage of comets, on the moons of Jupiter and Saturn, and on the tides in the estuary of the Thames River to construct his great syntheses in Principia, he was being empirical and inductive.

Math is slightly different, but many mathematicians see a need to include both proof based and empirically based work. A case in point in the present century is the great Indian mathematician Srinivasa Ramanujan, whose notebooks contain the germs of superstring theory and whose work has been used to evaluate pi to millions of digits past the decimal point. According to his wife, Ramanujan did his calculations on a handheld slate, then transferred the final results to his notebooks, erasing the slate; thus, we have few clues as to how he arrived at these equations, yet no one doubts that they are true.¹⁶

According to one historical account, Pythagoras brought back his eponymous theorem from his travels to the East and founded the tradition of proof because his less numerate countrymen refused to accept the theorem. Consider, too, the naming of Fermat’s last theorem, the work of the Frenchman Pierre de Fermat in the seventeenth century. The last theorem is a remote derivation from the Pythagorean theorem, but Fermat neglected to leave us a proof—at least not one we could find. Yet for more than three hundred years, Fermat’s last theorem has worked. A few years ago, Andrew Wile, of Princeton University, finally devised a proof. Still, we have yet to hear an outcry to change the name of Fermat’s last theorem to Wile’s first theorem. (It is an in-joke among mathematicians that the correct name is Fermat’s last conjecture, a conjecture being an unproved theorem.)

In 1915, about the time, according to Otto Neugebauer, that the Germans were rewriting their encyclopedias to edit out the Phoenicians from Greek history, the English science historian G. R. Kaye admonished western investigators in the history of knowledge to look for traces of Greek influence because the achievements of the Greeks form the most wonderful chapters in the history of civilisation. ¹⁷ Our pop science historians—Bronowski, Daniel Boorstin, Carl Sagan, et al.—have certainly been faithful to that directive. Western historians have also criticized past non-Western scientists, such as the Maya and Egyptians, for their strange religious beliefs, implying that acute religiosity disqualifies the work of a scientist. Then again, when Pythagoras finally proved his theorem, he offered a hundred oxen to the Muses in thanks.¹⁸

Science is science. It can be practical or impractical. The Danish physicist Niels Bohr owned a cabin retreat, to which he invited his scientist friends for long intense discussions about the meaning of quantum physics. Over the door of the cabin was hung a horseshoe on a nail. His guests often viewed this with a roll of the eyes. Finally, one screwed up the courage to say, Come on now, Niels. You don’t believe in this nonsense, do you?

According to legend, Bohr replied, That’s the beauty of it. It works whether I believe in it or not. For our purposes, science embraces those facts about the physical world that work … whether we believe in them or not.

2

MATHEMATICS The Language of Science

THE Mark’s Meadow School is a public elementary school in Amherst, Massachusetts, in the western region of the state. Located across North Pleasant Street from the University of Massachusetts (UMass), it has served as a laboratory for the university’s school of education. Education majors can sit in a darkened, elevated corridor and secretly observe the students through two-way mirrors in the ceiling while eavesdropping through the use of a hidden sound system. In the future, they may want to listen more carefully during math lessons.

Recently I took a group of Mark’s Meadow fourth graders to the local mall, where we stopped to eat at a Taco Bell. The kids read the menu and started laughing. The joke was this: there were three sizes of drinks—small, medium, and large; twelve ounces, sixteen ounces, and twenty ounces—and three prices, $1.19, $1.49, and $1.79. The kids were laughing at the sign beneath the prices: UNLIMITED REFILLS!

Then a group of college students wearing UMass sweatshirts joined the line. They studied the sign. Hey, let’s get the large drinks, said one.

Yeah, said another. Then we’ll really clean up on the unlimited refills.

What the fourth graders understood that the college kids did not is the concept known as infinite sets. In the above case, one infinite set is equal to another. Take a ruler and cut it into infinitesimally small segmerits from the 1-inch line to the 2-inch line. There would be an infinite number of slices. Do the same with the ruler from the 2-inch line to the