;Only once before in our history was there the promise of a brilliant scientific civilization. Beneficiary of the Ionian Awakening, it had its citadel at the Library of Alexandria, where 2,000 years ago the best minds of antiquity established the foundations for the systematic study of mathematics, physics, biology, astronomy, literature, geography and medicine. We build on those foundations still. The Library was constructed and supported by the Ptolemys, the Greek kings who inherited the Egyptian portion of the empire of Alexander the Great. From the time of its creation in the third century B.C. until its destruction seven centuries later, it was the brain and heart of the ancient world.

The last scientist who worked in the Library was a mathematician, astronomer, physicist and the head of the Neoplatonic school of philosophy -- an extraordinary range of accomplishments for any individual in any age. Her name was Hypatia. She was born in Alexandria in 370. At a time when women had few options and were treated as property, Hypatia moved freely and unselfconsciously through traditional male domains. By all accounts she was a great beauty. She had many suitors but rejected all offers of marriage. The Alexandria of Hypatia's time -- by then long under Roman rule -- was a city under grave strain. Slavery had sapped classical civilization of its vitality. The growing Christian Church was consolidating its power and attempting to eradicate pagan influence and culture. Hypatia stood at the epicenter of these mighty social forces. Cyril, the Archbishop of Alexandria, despised her because of her close friendship with the Roman governor, and because she was a symbol of learning and science, which were largely identified by the early Church with paganism In great personal danger, she continued to teach and publish, until, in the year 415, on her way to work she was set upon by a fanatical mob of Cyril's parishioners. They dragged her from her chariot, tore off her clothes, and armed with abalone shells, flayed her flesh from her bones. Her remains were burned, her works obliterated, her name forgotten. Cyril was made a saint.

The glory of the Alexandrian Library is a dim memory. Its last remnants were destroyed soon after Hypatia's death. It was as if the entire civilization had undergone some self-inflicted brain surgery, and most of its memories, discoveries, ideas and passions were extinguished irrevocably. The loss was incalculable. In some cases, we know only the tantalizing titles of the works that were destroyed. In most cases, we know neither the titles nor the authors. We do know that of the 123 plays of Sophocles in the Library, only seven survived. One of those seven is Oedipus Rex. Similar numbers apply to the works of Aeschylus and Euripides. It is a little as if the only surviving works of a man named William Shakespeare were Coriolanus and A Winter's Tale, but we had heard that he had written certain other plays, unknown to us but apparently prized in his time, works entitled Hamlet, Macbeth, Julius Caesar, King Lear, Romeo and Juliet.

Carl Sagan recounts the destruction of science and enlightenment in ancient Alexandria at the hands of religious zealotry.

According to legend, the first mathematical formulation of what we might today call a law of nature dates back to an Ionian named Pythagoras (ca. 580 BC-ca. 490 bc), famous for the theorem named after him: that the square of the hypotenuse (longest side) of a right triangle equals the sum of the squares of the other two sides. Pythagoras is said to have discovered the numerical relationship between the length of the strings used in musical instruments and the harmonic combinations of the sounds. In today's language we would describe that relationship by saying that the frequency—the number of vibrations per second—of a string vibrating under fixed tension is inversely proportional to the length of the string. From the practical point of view, this explains why bass guitars must have longer strings than ordinary guitars. Pythagoras probably did not it really discover this—he also did not discover the theorem that bears his name—but there is evidence that some relation between string length and pitch was known in his day If so, one could call that simple mathematical formula the first instance of what we now know as theoretical physics.

Apart from the Pythagorean law of strings, the only physical laws known correctly to the ancients were three laws detailed by Archimedes (ca. 287 BC-ca. 212 bc), by far the most eminent physicist of antiquity. In today's terminology, the law of the lever explains that small forces can lift large weights because the lever amplifies a force according to the ratio of the distances from the lever's fulcrum. The law of buoyancy states that any object immersed in a fluid will experience an upward force equal to the weight of the displaced fluid. And the law of reflection asserts that the angle between a beam of light and a mirror is equal to the angle between the mirror and the reflected beam. But Archimedes did not call them laws, nor did he explain them with reference to observation and measurement. Instead he treated them as if they were purely mathematical theorems, in an axiomatic system much like the one Euclid created for geometry.

As the Ionian influence spread, there appeared others who saw that the universe possesses an internal order, one that could be understood through observation and reason. Anaximander (ca. 6io BC-ca. 546 bc), a friend and possibly a student of Thales, argued that since human infants are helpless at birth, if the first human had somehow appeared on earth as an infant, it would not have survived. In what may have been humanity's first inkling of evolution, people, Anaximander reasoned, must therefore have evolved from other animals whose young are hardier. In Sicily, Empedocles (ca. 490 BC-ca. 430 bc) observed the use of an instrument called a clepsydra. Sometimes used as a ladle, it consisted of a sphere with an open neck and small holes in its bottom. When immersed in water it would fill, and if the open neck was then covered, the clepsydra could be lifted out without the water in it falling through the holes. Empedocles noticed that if you cover the neck before you immerse it, a clepsydra does not fill. He reasoned that something invisible must be preventing the water from entering the sphere through the holes—he had discovered the material substance we call air.

Around the same time Democritus (ca 460 BC-ca. 370 bc). from an Ionian colony in northern Greece, pondered what happened when you break or cut an object into pieces. He argued that you ought not to be able to continue the process indefinitely. Instead he postulated that everything, including all living beings. is made of fundamental particles that cannot be cut or broken into parts. He named these ultimate particles atoms, from the Greek adjective meaning "uncuttable." Democritus believed that every material phenomenon is a product of the collision of atoms. In his view, dubbed atomism, all atoms move around in space, and, unless disturbed, move forward indefinitely. Today that idea is called the law of inertia.

The revolutionary idea that we are but ordinary inhabitants of the universe, not special beings distinguished by existing at its center, was first championed by Aristarchus (ca. 310 BC-ca. 230 BC), one of the last of the Ionian scientists. Only one of his calculations survives, a complex geometric analysis of careful observations he made of the size of the earth's shadow on the moon during a lunar eclipse. He concluded from his data that the sun must be much larger than the earth. Perhaps inspired by the idea that tiny objects ought to orbit mammoth ones and not the other way around, he became the first person to argue that the earth is not the center of our planetary system, but rather that it and the other planets orbit the much larger sun. It is a small step from the realization that the earth is just another planet to the idea that our sun is nothing special either. Aristarchus suspected that this was the case and believed that the stars we see in the night sky are actually nothing more than distant suns.

The Ionians were but one of many schools of ancient Greek philosophy, each with different and often contradictory traditions. Unfortunately, the Ionians' view of nature—that it can be explained through general laws and reduced to a simple set of principles—exerted a powerful influence for only a few centuries. One reason is that Ionian theories often seemed to have no place for the notion of free will or purpose, or the concept that gods intervene in the workings of the world. These were startling omissions as profoundly unsettling to many Greek thinkers as they are to many people today. The philosopher Epicurus (341 BC-270 bc), for example, opposed atomism on the grounds that it is "better to follow the myths about the gods than to become a 'slave' to the destiny of natural philosophers." Aristotle too rejected the concept of atoms because he could not accept that human beings were composed of soulless, inanimate objects. The Ionian idea that the universe is not human-centered was a milestone in our understanding of the cosmos, but it was an idea that would b dropped and not picked up again, or commonly accepted, until Galileo, almost twenty centuries later.

Stephen Hawking provides a fascinating summary of what the ancient Ionians knew about the natural world.