B00B7H7M2E EBOK (3 page)

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?

There is still one circumstance to be mentioned – a simple, trivial matter, yet Eratosthenes’s successful measurement of the circumference of the Earth would not have taken place without it. A happenstance, perhaps, that such a small gem of information reached the ears of this man who realized what it meant and what could be done with it. It is true that the fact that this snippet of news reached him
did
have something to do with the broadened mental horizons of the world, with improved communications from remote areas, with Eratosthenes’s own world centring on northern Africa, and with his habit of keeping his ears and eyes open and wanting to know everything and anything. He was indeed the right man in the right time and place. Perhaps there was no other so likely to run across this back-page news and recognize its worth:

In a well located at Syene (near modern Aswan), on the day
of
the summer solstice, a shaft of sunlight penetrated all the way to the bottom of the well.

To Eratosthenes there was nothing trivial about this information. It meant that the Sun was shining directly down at Syene, not at an angle, and he knew this showed that Syene was on the tropic. A stick set up at noon at Syene on the day of the summer solstice would not cast a shadow. A stick set up at Alexandria (which he thought was the same longitude as Syene)
would
. Accordingly, Eratosthenes set up a stick at Alexandria on the day of the summer solstice and measured the angle of its shadow when that shadow was at its shortest.

Figure 1.1
below shows the stick at Alexandria and its shadow, and what is meant by ‘the angle of the shadow’. The figure illustrates how that must also be the angle ‘subtended’ by the arc Syene–Alexandria at the centre of the Earth. To put that
a
bit more simply: if we draw a straight line from the point marked Alexandria (where the stick is casting a shadow) to the centre of the Earth, and a second straight line from the point marked Syene (where the stick casts no shadow) to the centre of the Earth, those lines will of course meet at the centre of the Earth. We want to know the angle between those two lines where they meet. Geometry tells us, as it told Eratosthenes, that the angle at the centre of the Earth and the angle of the shadow at Alexandria will be the same angle.