B00B7H7M2E EBOK (2 page)

The story of our wanting to know ‘how far’ – to make ridiculously out-of-reach measurements – must surely have begun before the beginning of recorded history. The known story of our success began some 2,200 years ago in north Africa near the mouth of the Nile with the measurement of the circumference of our own planet, long before anyone was able to circumnavigate it. The Hellenistic librarian Eratosthenes didn’t need to know the circumference of the Earth. Nevertheless, he set about measuring it and he did it in a remarkably simple way. We now call Eratosthenes the father of the science of Earth measurement, ‘geodesy’. The word has the sound of ‘odyssey’ in it.

We learn from Eratosthenes what I learned from my father . . . and we shall see it demonstrated repeatedly in this book: what can’t be measured directly – what it is unthinkable that we should ever measure directly –
can
be measured in roundabout, inventive ways. In the first decade of the twenty-first century we determined the distance to the borders of the observable universe, far beyond any pinprick of light we see with the naked eye in the night sky, and measured time back to the origin of the universe. The numbers are indeed too enormous to make sense to our little minds. Nevertheless our little minds have figured them out, one resourceful step at a time, each step building upon the last. It has been a history of astounding improvement
in
our technology, particularly in the twentieth century, but more than that, a history of raw ingenuity. It still is. Frontier inventiveness is not out of date.

With the benefit of hindsight we may be tempted to exclaim, ‘Of course! Why . . .
I
could have thought of that! The windmill has a shadow. Of course!’ for many of the methods we’ve devised to measure distances to out-of-reach places are simple enough for nearly everyone to understand – only a little more complicated than measuring my grandfather’s windmill. But to figure these things out for the first time . . . how impossibly clever!

Kitty Ferguson,

November 2012

CHAPTER 1

A Sphere with a View

Third Century
BC

The great mind, like the small, experiments with different alternatives, works out their consequences for some distance, and thereupon guesses (much like a chess player) that one move will generate richer possibilities than the rest . . . It still remains to ask how the great mind comes to guess better than another, and to make leaps that turn out to lead further and deeper than yours or mine. We do not know.

Jacob Bronowski

ASK WHO ERATOSTHENES
of Cyrene was, and unless you are talking to someone who specializes in the minutiae of Hellenistic culture, you are unlikely to hear that he was a man who attempted to fix the dates of the major literary and political events from the conquest of Troy until his own time in the third century
BC
, that he composed a treatise about theatres and theatrical apparatus and the works of the best-known comic poets of the ‘old comedy’; that he suggested a way of solving a problem that had tantalized mathematicians for two centuries – ‘duplicating a cube’; that he let his voice be heard on the subject of moral philosophy and felt it essential to criticize those who were ‘popularizing’ philosophy, accusing them of ‘dressing it up
in
the gaudy apparel of loose women’. It is true for Eratosthenes, as it is for many celebrated figures, that the strokes of genius for which he is revered were only a minuscule part of a lifetime of achievement, and not necessarily the part he judged most important.

Nothing on the list above won Eratosthenes his place in the history books. Two additional accomplishments did: the invention of ‘the sieve of Eratosthenes’ – a method for sifting through all the numbers to find which are prime numbers; and his remarkably accurate measurement of the circumference of the Earth.

Dismiss any thought that before Columbus no one knew the Earth was round. Admittedly, the shape of the Earth probably wasn’t of much daily practical interest to most people in the ancient world. However, long before even Eratosthenes, those few who were wondering about it at all were not seriously suggesting that the Earth was flat or, indeed, any shape but spherical. The Pythagoreans, a school of thinkers with particular genius for mathematics and music, had decided as early as the sixth and fifth centuries
BC
that the Earth is a sphere. Plato, still a century before Eratosthenes, pictured a cosmos made up of spheres within spheres, nested one within another, with a spherical Earth at the centre. Aristotle, only a little later than Plato, vigorously subscribed to the idea of a spherical Earth, and his defence proved convincing not only to the ancient world but also to the Middle Ages. The idea that scholars of the Middle Ages believed the world was flat is, in fact, a myth created in modern times.

Aristotle used a number of arguments. During an eclipse of the Moon, the shadow cast by the Earth on the Moon is always curved. When we on the Earth move from north to south or vice versa we notice what appears to be a change in the position of the stars in relation to ourselves. In Aristotle’s words:

There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves
northward
or southward. Indeed there are some stars seen in Egypt and in the neighborhood of Cyprus which are not seen in the northerly regions; and stars which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the Earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be so quickly apparent.

Aristotle speculated that the oceans of the extreme west and the extreme east of the known world might be ‘one’, and he reported with some sympathy the arguments of those who had noticed that elephants appeared in regions to the extreme east and the extreme west, and who thought therefore that those regions might be ‘continuous’.

These reasons for belief in a spherical Earth came from observation, but Aristotle also argued on the basis of his philosophy. In that philosophy, five elements, earth, air, water, fire and aether, each have a natural place in the universe. The natural place for the element earth is at the centre of the universe, and for that reason earth (the element) has a natural tendency to move towards that centre, where it must inevitably arrange itself in a symmetrical fashion around the centre point, forming the sphere we call
the
Earth. Aristotle reported that mathematicians had estimated the Earth’s circumference to be 400,000 stades; that is, about 39,000 miles or 63,000 kilometres (more than half again as large as the modern measurement). No record survives of the method they used to arrive at that number.

When Aristotle died in 322
BC
at the age of 62, the military campaigns of his most highly achieving pupil, Alexander the Great, had just ended with the death of Alexander. Though there is a tendency to speak of ‘the Greeks’ and toss names like Eratosthenes into that file, the civilization and the culture we are dealing with after Alexander was much larger both in
territory
and concept than what is implied in the word ‘Greek’. Alexander’s campaigns had carried Greek knowledge, language and culture throughout Asia Minor and Mesopotamia as far east as present-day Afghanistan and Pakistan, all the way to the Indus River, as well as to Palestine and Egypt. Vastly widened intellectual horizons were part of his extraordinary legacy. The culture of Greece and its colonies and the cultures of the conquered peoples began to mix and marvellously enrich one another. This was the dawn of the Hellen
istic
era, as opposed to the Hellenic era. That is, Greek
ish
, as opposed to Greek.

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.