B00B7H7M2E EBOK, page 2
At the time of Alexander’s and Aristotle’s deaths, within a year of one another, Athens was still the undisputed centre of the intellectual world. That pre-eminence was not to last. Alexander’s generals divided his empire, and Ptolemy’s portion was Egypt and Palestine. He made Alexandria, near the mouth of the Nile, his capital. This already prospering city began to grow in size and splendour, and Ptolemy and his successors, reputedly ruthless in their exploitation of the lands under their control, amassed a surplus of wealth, some of which they chose to spend on literature, the arts, mathematics and science. Scholars are divided as to which Ptolemy should get the credit (Ptolemy’s successors were also named Ptolemy), but either the first or the second of them, and perhaps it took both, decided to extend the royal patronage to found a library and museum. This was not an institution of the sort we call ‘museum’ today. As that name suggests, it was a temple to the muses, which meant both a religious shrine and a centre of learning.
Meanwhile the old, justly famous schools across the sea in Athens – schools founded by Plato, Aristotle, Epicureus and the Stoics – were no longer producing vibrant new ideas to quite the extent they had once done, though they were still the places a young man of Eratosthenes’s time would have wished to go for his education. Alexandria began to rival and eventually supplanted Athens as the focal point of the intellectual world, and the museum and library there became the premier research institution. The library grew large, containing by one ancient estimate nearly 500,000 rolls. Eratosthenes was its director or librarian at the end of the third century BC, with a salary provided from the royal coffers.
Most of us have heard that one of the devastating tragedies in the history of humankind was the burning of the contents of the library at Alexandria. The story (now thought to be apocryphal) is that all those rolls were burned to heat the public baths for six months in the seventh century AD. Today there is a campaign underway to raise funds to rebuild the structure, but that effort seems rather pitiful and beside the point, in view of what can never be retrieved – the assembled knowledge of our ancestors in antiquity, hard-won over many centuries. We sense that something dreadful happened to us with the loss of all those rolls, whether it occurred quickly and calamitously in the seventh century or, more likely, gradually through neglect and the many political, military and religious turns of fortune that affected the city of Alexandria prior to that. Perhaps its loss was the symbol and symptom of a greater tragedy: the increasing lack of any widespread perception that such intellectual achievement was valuable. By the seventh century, there was probably little left to burn. It took centuries for humanity in the Western world to reach again an intellectual level on a par with the civilization that had produced that lost collection. But when Eratosthenes was librarian (235–195 BC) that was all in the future. He knew the Alexandria library in its heyday.
Scholars in the Hellenic and Hellenistic worlds would have been mystified by our present-day concept of ‘science’ as a distinct category of knowledge and pursuit of knowledge. They had several different words for what we call ‘science’. Some modern words have evolved from these terms, but the modern words don’t have precisely the same meaning these had in ancient Athens and Alexandria. Some examples are: peri physeos historia (inquiry having to do with nature); philosophia (love of wisdom, philosophy); theoria (speculation); and episteme (knowledge). Hellenistic scholars thought of ‘physics’ as one of three branches of philosophy. The other branches were ‘logic’ and ‘ethics’.
The financial support of the Ptolemys and their efforts to outbid all competitors when it came to collecting the masterpieces of Greek literature and encouraging distinguished scholars to flock to Alexandria were motivated by desire for prestige – to add to the lustre and apparent power of the dynasty. They were also far from displeased when research could be applied to problems connected with weaponry. However, a key difference between the ancient way of thinking and ours is that although Hellenic and Hellenistic scholars didn’t ignore the possibility that their study might serve practical purposes, they were much more inclined to justify their work on the grounds that it contributed to wisdom, or improved one’s character, or led to a greater appreciation of the beauty of the universe and understanding of its creator. It seemed not to occur to these men and women that their efforts might hold the key to material progress. The work was its own reward, an end in itself, not a means to an end. The life of a scholar, the life of ‘contemplation’, was considered to be an exquisitely happy one. Doctors, whose efforts were intended to have more everyday practical value, were apt to differentiate themselves entirely from the ‘philosophers’.
Related to this mindset that sees intellectual exercise as an end in itself is a perspective in which how to solve a problem is equally as interesting as actually solving it, often more so. This attitude arose partly out of necessity, for Greek and Hellenistic scholars were avidly interested in questions that they lacked the technology to answer definitively. Perhaps we can best acclimatize ourselves to the ancient way of thinking by recalling doing mathematics in school. Presented with the problem ‘If you ride your bicycle at an average of 30 miles per hour, and it takes you 10 minutes to get to school, how far is school?’ you do not immediately start quibbling that 30 miles per hour is not an accurate measurement of the speed you normally ride, that it actually takes you 12 minutes to get to school, and that this exercise isn’t going to end with anyone knowing how far your school really is. No. What everyone is interested in is your showing that you understand how to solve the problem. Move back a step and imagine that it was also up to you to invent the method for solving it – that no one, in fact, had ever even thought it possible to calculate the distance to your school, and that you couldn’t ride there to measure it directly – and you have put yourself a little in the shoes of Eratosthenes and other scholars of the Hellenic and Hellenistic world. It is an attitude which allows, indeed encourages, the formation of hypotheses, sometimes out of thin air, statements such as ‘We don’t know that this is true, but let’s assume for a moment that it is, and see where that gets us.’ Or even such a statement as ‘We know that this is not true, but let’s pretend for the moment that it is and ask “what then?” ’ To criticize the results of an exercise like that by saying the results are ‘wrong’ (i.e., do not accord with twentieth-century findings) is to miss the point.
Does this mindset in which the pursuit of knowledge was valued quite apart from any practical spin-off – where the method was often thought more important than the result, where hypotheses, even those based on false assumptions, were encouraged – provide a clue to Eratosthenes’s success? Perhaps. After all, the Hellenistic world had no practical need to know the circumference of the Earth. However, that attitude predated Eratosthenes by several centuries. What’s more, Eratosthenes’s results were remarkably accurate by twentieth-century standards. Did his success have something to do with the widening of mental horizons and the mixture of knowledge from many cultures that followed the campaigns of Alexander? It did, but, again, Eratosthenes was not the only inventive man to enjoy that legacy. And the notion that the Earth isn’t flat was nothing new either, nor was the idea of calculating its circumference. There had been estimates in Aristotle’s time. But it was Eratosthenes who did the measurement and got it right – or so close to right that his calculation impresses us to this day – using a line of thought that we can easily agree was correct.
Eratosthenes, ‘son of Aglaos’, was born not in Egypt or Greece but in the ancient city of Cyrene, west of Egypt on the northern coast of Africa. Citizens of Crete and Santorini had founded Cyrene some 350 years earlier and it had become one of the most cultured cities of the Hellenistic world, though still subordinate to the Egypt of the Ptolemys. Cyrene counted some distinguished figures among its citizenry. Besides Eratosthenes there was Aristippos, who founded the Cyrenaic school there. He was a pupil of Socrates. Aristippos’s daughter Arete followed him as head of the school. Her son Aristippos II succeeded her. He was nicknamed Metrodidactos, which translates as ‘mother-taught’.
The date given for Eratosthenes’s birth is the ‘ 126th Olympiad’, referring to the Olympic games that took place every four years. In modern dating, that puts it between 276 and 273 BC. He received most of his education in Athens at the feet of eminent scholars of the New Academy and the Lyceum. Plato and Aristotle had originally founded these schools (in Plato’s day the New Academy had been simply the Academy) and, though much had changed about them by the time Eratosthenes arrived, one still couldn’t do better by way of an education.
By the middle of the century Eratosthenes had written a few philosophical and literary works and some of these had come to the attention of Ptolemy III Euergetes. The ‘brain-drain’ from Athens being in the general direction of Alexandria, Eratosthenes in about 244 BC agreed to move there and become a fellow of the museum and tutor to the prince, Philopator. (It isn’t to Eratosthenes’s credit that his pupil, though a patron of arts and learning, gained a reputation for dissipation and crimes equal to Nero’s and Caligula’s later in Rome.)
In the course of time Eratosthenes became a senior (alpha) fellow of the museum and upon the death of the chief librarian took over that post – an absolutely unparalleled vantage point from which to keep up with everything that was going on in the intellectual world.
Eratosthenes’s colleagues gave him two nicknames: pentathlos and beta. The word pentathlos came from athletics. It was a name for those who entered the ‘pentathlon’, which required five skills: jumping, discus throwing, running, wrestling and either boxing or javelin throwing. Eratosthenes was no athlete. The nickname for him implied a jack-of-all-trades. Beta means ‘B’ or number two, or second. Put those together and you get ‘jack-of-all-trades and master of none’. Whether these names were fondly or snidely given isn’t clear. Probably snidely. It seems a bit odd that in an era following so closely on the heels of Plato and Aristotle, who had their fingers in just about every intellectual pie around, a man should be mocked for being a jack-of-all-trades. Perhaps in the three-quarters of a century between Aristotle’s death and Eratosthenes’s arrival at Alexandria, scholarship had become more specialized and specialists had begun to sneer at those who were not specialists. Eratosthenes was evidently old-fashioned to be such a polymath, but he had been educated that way . . . and how could a man focus very narrowly when he was head of the library, the repository of knowledge and ideas on every subject, holding a job which made him responsible for helping the Ptolemys add to that collection. Eratosthenes was bombarded daily by new thoughts and discoveries. Modern scholars compare the breadth of his knowledge to that of Aristotle and Leonardo da Vinci. Whatever criticism Eratosthenes endured, his eclecticism served him well. ‘Beta’ is remembered while some who dubbed him that have long since been forgotten.
Unfortunately, none of Eratosthenes’s many works have survived except in fragments. It’s not even certain that all the fragments attributed to him are genuine. Most information about him comes through reports and references of others. However, there is enough to tell that Eratosthenes’s measurement of the Earth, and also his motive for attempting it, were rooted in his eclectic and far-ranging knowledge and interests. Eratosthenes was a man of the world, in the real sense of those words. He refused to categorize people as Greeks opposed to Barbarians, adopting a more cosmopolitan attitude which differed from the mindset of Greece in earlier centuries but was not uncommon in Hellenistic times. Perhaps it isn’t inaccurate to use a modern term and call this a global point of view. Eratosthenes not only thought that way, but he followed through by collecting information about the people, products and geography of far-flung areas. He wrote about the history of geographical measurement, recalling old ideas going back to Homer about the size, shape and geographical lay-out of the Earth. In fact, he did nothing less than pull together virtually all the geographical knowledge that had been accumulating up until his own time.
Over the centuries, this material had taken a variety of forms. It came from traders, explorers, travellers – as well as mathematicians and philosophers – and it ranged from fantastic tales to more straightforward reporting, from speculation to measurements and estimates resting on what were probably recognized as shaky assumptions. Among the more reliable sources were eye-witness accounts of Alexander the Great’s expeditions and the measurements and records of distances covered on those marches. There were itineraries of coastal voyages and maps and charts connected with them. There was a treatise on harbours by Timosthenes, the admiral of the Ptolemaic fleet, who also studied the winds. There was a book entitled On the Ocean by the merchant sea-captain Pytheas, who in about 320 BC sailed north along the coast of Spain and France and reached Cornwall, then continued all the way up to the Orkneys and the Shetlands to latitudes near those of the midnight sun. Pytheas took bearings throughout his voyage and recorded them in his book, which also has descriptive passages:
The barbarians showed us where the Sun keeps watch at night, for around these parts the night is exceedingly short, sometimes two and sometimes three hours, so that only a short interval passes after the Sun sets before it rises once more.
Eratosthenes respected Pytheas’s information, though it must have seemed almost as fantastic as Homer’s, while many other scholars were contemptuous and disbelieving. Living as Eratosthenes did in Hellenistic Egypt, he may also have known of centuries-old and astoundingly accurate Egyptian geographical calculations.
Eratosthenes’s expertise on longitude and latitude surpassed any other of his day or earlier. His predecessors had divided the map into zones. He took that work several steps further by improving on a map devised about 25 years before his birth by a man named Dicaearchus of Messene. Dicaearchus had divided the known world by using two lines or bands that intersected one another – one running east—west, the other north—south. On Eratosthenes’s revised map the two lines crossed at Rhodes, a little to the east of where Dicaearchus’s lines had met. The horizontal line passed near Gibraltar (then known as the Pillars of Hercules), ran the length of the Mediterranean and then followed the Taurus chain of mountains in southern Turkey (Toros Daglari on modern maps). That line is remarkably near to following what we call the 37th parallel – an impressive achievement for men without the benefit of the mathematical and astronomical knowledge that would go into later mapmaking. It was not yet possible to figure out latitudes with very great precision, and it was virtually impossible to determine longitude (which would prove to be a problem in Eratosthenes’s measurement of the Earth). On Eratosthenes’s map the vertical line followed the Nile, which doesn’t line up so perfectly with Rhodes on modern maps. He added six further lines drawn vertically at intervals between the western and eastern boundaries of the inhabited world, and six more horizontal lines drawn at intervals between its northern and southern boundaries, and he established and measured geographic zones, dividing the world horizontally between the tropical region, the temperate region and the polar circles.
Eratosthenes was also well-acquainted with state-of-the-art geometry, both from Euclid’s profound summing-up about 25 years before Eratosthenes’s birth and from his association with Archimedes, one of the towering creative geniuses that Greek and Hellenistic civilization produced and also one of history’s greatest eccentrics. Most schoolchildren have heard the tale of Archimedes solving a mathematical problem in his bath, leaping from the water, and running naked through the streets shouting ‘Eureka!’ This avid mathematician eventually lost his life when Roman troops sacked Syracuse. Archimedes, so the story goes, was drawing a mathematical figure in the sand when a Roman soldier (who had missed hearing an order from his superiors to respect the person of this famous old man) asked him to pack up and move along. Archimedes unwisely told the soldier not to interrupt his thought process.
The Hellenistic world revered Archimedes as an inventor (though he himself dismissed such practical achievements as unworthy of notice) and a useful man to have around in a war. Legend has it that he destroyed an entire Roman fleet by using burning mirrors. The Middle Ages thought of him as an engineer and a wizard and credited him with the invention of the Staff of Archimedes. This device was a stick with a small flat disc that could be run up and down it. An observer held the stick up to the Sun and moved the disc along it until it appeared to cover the Sun, then noted on a scale the distance from disc to eye, thus deriving the Sun’s apparent diameter.
Modern history and mathematics books recall Archimedes as a brilliant mathematician and geometer who contributed significantly to the understanding of circles and spheres. Archimedes was in the habit of sharing his discoveries and his methods with Eratosthenes and even dedicated his greatest work, Method, to him. Eratosthenes must have welcomed, another scholar who was almost as eclectic as he was himself.
Eratosthenes’s thoughts stretched to the horizon in all directions. Perhaps it follows that he would have longed to know not only what was beyond those horizons but how far ‘beyond’ was? Mapping and systematizing things geographically was his bent. Would he not have been unusually curious about how large the total map was? How remarkable if it really should turn out to be, as Aristotle speculated, ‘a sphere of no great size’! Eratosthenes’s thoughts often took a historical turn, and he was aware of previous attempts to measure the Earth or estimate that measurement. Would he not have wanted to try his own hand at it, using Euclid’s and Archimedes’s newer understanding of geometry?
