The Rise and Fall of Alexandria (12 page)

 
 
It was into this inspired chaos that one of the most famous names from all antiquity was about to step, a man whose personal life is all but lost to us but whose name is still known in just about every school and college across the world. We have little idea when Euclid of Alexandria was born, or when he died (the most educated guesses suggest he was born around 325 BC and died sometime about 265 BC); Alexandria was where he chose to work, and his impact on mathematics catapulted the city into the scientific stratosphere. For at least 750 years after his death, if you wanted to be anything in mathematics, you simply had to study the subject in Alexandria. His book the
Elements
remained a standard text on geometry well into the twentieth century, even providing the basis of some of the calculations that NASA needed to put a man on the moon. Even now the knotty problems Euclid set his Alexandrian students remain the bane of schoolchildren and the delight of mathematicians. It is also now reckoned that his
Elements
is the most translated, most published, and most studied book in existence after the Bible. Since its reintroduction into Europe in AD 1482, having been lost in the West for nearly the whole medieval period, at least a thousand different editions of the work have been published.

Our only glimpse of this extraordinary man comes from the writings of Proclus, a Greek philosopher and head of the Athenian Academy, writing around AD 450, some seven hundred years after his subject’s death. Therefore, even this scrap cannot be relied on for its accuracy; but in its recollection of one personal story it may perhaps hold an echo of the man himself. “They say that Ptolemy once asked him if there was a shorter way to study geometry than the Elements, to which he replied that there was no royal road to geometry” (Proclus,
A Commentary on the First Book of Euclid’s “Elements”
).

Given the near-complete absence of information on Euclid’s life, Proclus had to do some detective work to discover even this. He tells us that parts of the
Elements
are based on the work of his predecessors Eudoxus and Theaetatus and that Euclid was younger than Plato’s circle, but older than Eratosthenes, while the mention of Euclid’s name by Archimedes, who Proclus knew was writing during the reign of Ptolemy II, helped him to narrow down the date. Even this is debatable, however, as some scholars believe the mention by Archimedes was inserted into his works after his death. Indeed, other scholars have gone on to doubt the very existence of the man at all, arguing that his name was a cover for a team of mathematicians working in Alexandria who took the name from the philosopher Euclid of Megara, who had lived a century earlier.

However, the only evidence for this assertion is that there is some stylistic variation in different sections of his book. Given that correct academic procedure in those days consisted of gathering up your predecessors’ findings and working on from there, this provides a perfectly adequate explanation for the stylistic variation in the
Elements
. So, regardless of whether he was one man or many, the simple fact is that from the earliest days of Alexandria there emerged one of the most important books of all time produced by one (or more) of the first great minds of the city and who, under the name “Euclid,” would go down in history as perhaps the greatest mathematician of all time.

What, then, was this great work about? The obvious answer to the question is of course geometry, but that is far from a summary. The thirteen books of the
Elements
open with a series of definitions and five propositions. Some seem deceptively simple: The first is merely that it’s possible to draw a straight line between any two points. To the points and lines are added circles, and then the existence of other geometrical objects is deduced from these. Proposition 4 states that all right angles are equal. This may seem obvious, but underlying this bland statement is the assumption that space is homogeneous—a figure is independent of its position in space. In short, Euclid was defining space—the whole canvas of the mathematical universe on which geometry could then be inscribed.

The famous fifth proposition is concerned with parallel lines and states that only one line can be drawn through a point parallel to a given line. It was only when this postulate was dropped in the nineteenth century that non-Euclidean geometry could emerge.

Books 1 through 6 of the
Elements
explore planar geometry—triangles, parallels, circles, and the like. Books 7 through 9 deal with number theory; book 10 deals with “irrational numbers”; and finally books 11 through 13 deal with three-dimensional geometry, the last being concerned with the five regular polyhedra (multisided 3-D figures). This book was used extensively by Johannes Kepler as he struggled to unravel the workings of the solar system in the seventeenth century AD.

Like so many of his contemporaries, Euclid didn’t stop at mathematics. Other surviving books include the
Elements of Music
and his
Optics,
which is the first extant work on perspective. The intriguing
Book of Fallacies
has sadly not survived, but Proclus describes it:

 
Euclid was, according to Proclus, a Platonist, and it was this philosophy, the philosophy that would come most to represent Alexandrian thought, that drove the “Father of Mathematics” to devote his entire life to the exploration of those forms and ideas which Plato saw as underlying the untidy jumble of the observed world. Plato had himself said that “the knowledge of which geometry aims is the knowledge of the eternal” (Plato,
Republic,
book 12, chapter 52).

For Euclid, mathematics was not simply an abstract idea but a method for seeking out the harmonies of shape which revealed the sublime, even divine, forms of creation. In his
Elements
Euclid began to set down a method by which Plato’s world could be explored and in doing so set Alexandria on a journey of discovery far beyond anything taken by the ships which came and went each day through the Great Harbor.

Years before, it is said, Plato had a motto written above the door to the Academy: “Let no one ignorant of mathematics enter here.” Now Euclid was showing the reason why.

Euclid’s work remained pivotal to the development of the European intellectual tradition for at least two thousand years, and one of the reasons for its longevity was that it was coherent and substantially accurate. For the story of Alexandria this is of critical importance. Here, in the reign of the first Ptolemaic pharaoh, his protolibrary and museum were invested with a completely trustworthy compilation of a major science which generations of succeeding scholars could call upon, not just for academic study but as a means of enhancing their own work. Then as now scholars returned again and again to the shelves holding Euclid’s works to compute, test, and verify their own research, in fields ranging from physics to geography and astronomy. The
Elements
is, even today, an anchor of mathematics, first dropped over two millennia ago into a sea of ignorance from the ship of Alexandria.

 
 
Mathematics was not the only early love of Alexandrians, however. Another great area of exploration in these early days of the museum was medicine.

It was Alexandria’s geographical and cultural position that would make it so pivotal in the development of medicine. Here in Egypt, Greek scholars could draw upon a complex body of Egyptian traditions and practices regarding the preservation of the human body after death by mummification. Whereas in the classical world Greece, Rome, and the states of the Near East maintained strong taboos on the study of the dead, for thousands of years the Egyptians had done their best to preserve corpses through mummification, which, of course, required an intimate knowledge of the inner workings of the human body and a high level of skill in dissection.

Mummification entailed the removal of the brain and all the soft organs of the body cavity except the heart (which was considered the center of intelligence and feeling) and was standard practice at the time of the Macedonian conquest. Now in Alexandria two young scientists, Herophilus of Chalcedon and Erasistratus of Ceos, seized upon this breach of normal mortuary taboo and began to explore the human body in minute detail, thus founding the great Alexandrian tradition of anatomy and physiology.

Though human dissection was still anathema to Greeks, here in Alexandria such things were hugely more open. Not only were the two physicians allowed to carry out their work (some say they were master and pupil, others that they headed rival schools), they were actively encouraged and even given live condemned prisoners to vivisect. The scene must have been disturbing and bloody, but it was taking them into another world, one that was secret and unknown. Guided by the mortuary technicians with their centuries of experience in mummifying the dead, these Greeks were now opening up the world of the living body, seeing for the first time into the machine that housed the soul, discovering by experiment its form and function.

Their progress was amazing. Casting aside the magical and mystical beliefs and superstitions of their predecessors, Herophilus first described the linked functions of the brain, spinal cord, and nervous system, rightly relocating the center of thought from the heart to the brain. He went on to distinguish correctly between motor and sensory neurons and to establish the link between the eye and the brain in the optic nerve. As well as making detailed observations of the physiology of the eye, he explored and described all the internal organs—heart, liver, pancreas, intestines, and reproductive organs. He was also the first to distinguish between veins and arteries, to show that blood rather than air flowed through these vessels, and to examine the valves of the heart in detail. This in turn led him to link the heart to the pulse and to use the latter diagnostically. Through his extensive (and public) dissections he established the heart as not the center of feeling but the center of the circulatory system, thereby anticipating William Harvey’s “discovery” of the circulation of the blood by nineteen hundred years.

Erasistratus refined Herophilus’s work, making minute observations of the bicuspid and tricuspid valves of the heart and establishing their one-way flow system. He then went on to consider the digestive, respiratory, and vascular systems and made a bold attempt to show how substances vital to our functioning were channeled around the body.

Perhaps more basic and important than the specific details of their work (all of Herophilus’s work is lost, but he is quoted at length by followers of his school) was that they were the first to establish a new concept of the causes of disease and illness. At a time when it was commonly held that sickness and ill fortune descended on mortals from the gods, as divine punishment, these Alexandrians insisted that illnesses had natural causes and should therefore be addressed by secular, scientific means. For them good health was the key to human happiness, and understanding the operation of the human machine was the key to achieving this.

Their methods are summed up by Celsus, a Roman physician and poet of the first century AD:

 
Already the scope of the museum and library of Alexandria were extending far beyond Demetrius’s exhortation to gather the materials for Ptolemy’s own book, but by now the desire to know more—to try to know everything—seems to have gripped them both. How these two men worked together in these early days, and what persuaded Ptolemy to extend the scope of his project from simply collecting personal research materials to making his city the center of the academic world, is something of a mystery. But there is one clue.

For once we appear, at least at first glance, to have remarkably detailed information on this dramatic and decisive period in the formation of the city and its schools, though as we shall see, not all is as it seems. To appreciate the context of the work we need to backtrack a little into Jewish history.

Persian rule in Egypt before the arrival of Alexander had been profoundly unpopular, but not every aspect of it had disappeared entirely under the rule of the Ptolemies. The Persians had relied heavily, and successfully, on large numbers of Jewish administrators to run Egypt on their behalf. Ptolemy I had continued this program during his early wars, bringing as many as one hundred thousand Jewish prisoners from Israel to Egypt (and Alexandria in particular). Many of these he treated very well, and they became an important element in his army and in the administration. Living and working in a Greek-speaking world (indeed, many may have come from the Greek-speaking world), some of these Jews had become very Hellenized, although no pressure seems to have been put upon them to change their religious customs and practices. Contact with the Jewish population only increased Ptolemy’s interest in further expanding his book collection, as Demetrius was encouraging him to look beyond the confines of Greek literature to the other great books of Egypt and the Near East, and large sums of money had been set aside for their acquisition. The problem of course was that most of these texts were not in Greek, but Syriac, Persian, Egyptian, and Hebrew, and this didn’t suit either the Greek masters of Alexandria or the increasingly Hellenized immigrants whose native tongue was slipping away, leaving them unable to read the literature and holy books of their native land. How Ptolemy I, Demetrius, and the immigrant population of Alexandria went about solving this problem survives in a document that claims to be by a Jewish scholar named Aristeas living during the reign of Ptolemy’s son. There is no trace of the supposed original of this account, but it is apparently faithfully reproduced in full by the early Greek church historian Eusebius of Caesarea (c. AD 260-339) in his
Praeparatio Evangelica
(Preparation for the Gospel), dating to approximately AD 314-318.