What does it do to your perception of a religious text when you discover that it comes from an older society, with a very different set of beliefs? I asked the UK’s Chief Rabbi, Sir Jonathan Sacks:
Clearly there is a core event behind both narratives, which was a great flood, part of the folk memory of all the peoples of that area. What the ancient texts that tell flood stories do is talk essentially of the great forces of nature being controlled by deities who don’t like human beings very much, and for whom ‘might makes right’. Now the Bible comes along and retells the story, but does so in a unique way – God brings the flood because the world was filled with violence, and the result is that the story becomes moralized, and that is part of the Bible’s programme. This is a radical leap from polytheism to monotheism – to a world in which people worshipped power, to the Bible’s insistence that power must be just and sometimes compassionate, and from a world in which there are many forces, many gods, fighting with one another, to this world in which the whole universe is the result of a single rational creative will. So the more we understand what the Bible is arguing against, the deeper we understand the Bible.
But the Flood Tablet was important not just for the history of religion; it is also a key document in the history of literature. Smith’s tablet comes from the seventh century BC, but we now know that other versions of the Flood story had originally been written down a thousand years before that. It was only later that the Flood story was woven by storytellers into the famous Epic of Gilgamesh, the first great epic poem of world literature. Gilgamesh is a hero who sets off on a grand quest for immortality and self-knowledge. He confronts demons and monsters, he survives all kinds of perils, and, eventually, like all subsequent epic heroes, he has to confront the greatest challenge of them all: his own nature and his own mortality. Smith’s tablet is just the eleventh chapter of the story. The Epic of Gilgamesh has all the elements of a cracking good tale, but it’s also a turning-point in the story of writing.
Writing in the Middle East had begun as little more than bean-counting – created essentially for bureaucrats to keep records. It had been used above all for the practical tasks of the state. Stories, on the other hand, were usually told or sung, and they were learnt by heart. But gradually, around 4,000 years ago, stories like that of Gilgamesh began to be written down. Insights into the hero’s hopes and fears could now be shaped, refined and fixed – an author could be sure that his particular vision of the narrative and his personal understanding of the tale would be transmitted directly, and not constantly reshaped by other storytellers. Writing moves authorship from the community to the individual. Hardly less important, a written text can be translated, and so one particular form of a story could now pass easily into many languages. Literature written down like this can become world literature. David Damrosch puts it in perspective:
Gilgamesh is now very commonly assigned as a very first work in literature courses, and it shows a kind of early globalization. It’s the first work of world literature that circulates widely around the ancient world. The great thing about looking at Gilgamesh today is that we see that, if we go back far enough, there’s no clash of civilizations between the Middle East and the West. We find in Gilgamesh the origins of a common culture – its offshoots go off into Homer, the 1001 Nights, and the Bible – so it is really a sort of common thread in our global culture.
The fine, small cuneiform writing of the Flood Tablet was pressed into damp clay
With the Epic of Gilgamesh, represented here by Smith’s Flood Tablet, writing moved from being a means of recording facts to a means of investigating ideas. It changed its nature. And it has changed ‘our’ nature: for literature like Gilgamesh allows us not just to explore our own thoughts but to inhabit the thought worlds of others. That, of course, is also the point of the British Museum, and indeed of the objects that make up this thread of human history that I’m attempting to trace: they offer us the chance of other existences.
Part of the Rhind Mathematical Papyrus showing how to calculate the area of a triangle
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Rhind Mathematical Papyrus
Papyrus found at Thebes (near Luxor), Egypt
AROUND 1550 BC
In seven houses there are seven cats. Each cat catches seven mice. If each mouse were to eat seven ears of corn and each ear of corn, if sown, were to produce seven gallons of grain, how many things are mentioned in total?
This is just one of dozens of similar problems, all equally complicated, all carefully written out – with the answers and showing the working in best schoolbook manner – that are recorded in the Rhind Mathematical Papyrus. This object is the most famous mathematical papyrus to have survived from ancient Egypt, and the major source for our understanding of how the Egyptians thought about numbers.
The Rhind Papyrus gives us no sense of maths as an abstract discipline through which the world can be conceived and contemplated anew. But it does let us glimpse – and share – the daily headaches of an Egyptian administrator. Like all civil servants, he seems to be looking anxiously over his shoulder at the National Audit Office, eager to ensure that he is getting value for money. So there are calculations about how many gallons of beer, or how many loaves of bread, you should be able to get from a given amount of grain, and how to calculate whether the beer or the bread that you’re paying for has been adulterated.
The papyrus contains eighty-four mathematical problems. Red ink indicates the name of or answer to a problem
The whole Rhind Papyrus contains eighty-four different problems – calculations that would have been used in different scenarios to solve the practical difficulties of administrative life, for instance how to calculate the slope of a pyramid, or the amount of food necessary for different kinds of domesticated birds. It’s mostly written in black, but red is used for each problem’s title and solution. And, interestingly, it is written not in hieroglyphs but in a particular kind of scribbly administrative shorthand that’s much quicker, much simpler, to write.
The papyrus owes its name to an Aberdeen lawyer, Alexander Rhind, who took to wintering in Egypt in the 1850s because the dry heat helped his tuberculosis. There, in Luxor, he bought this papyrus, which turned out to be the largest ancient mathematical text we know, not just from Egypt but from anywhere in the ancient world.
Because it is extremely sensitive to humidity and to light, we keep it in the Papyrus Room of the British Museum. It’s pretty dry and stuffy there, and above all it’s dark, all of which suits the papyrus, which rots in the damp and fades in bright light. It’s the nearest we can get in Bloomsbury to conditions in an ancient Egyptian tomb, where the papyrus presumably spent most of its existence. The whole papyrus would originally have been about 5 metres (17 feet) long and would normally have been rolled up in a scroll. Today it’s in three pieces. The two largest ones are in the British Museum, framed under glass to protect them (the third is in the Brooklyn Museum, New York). The papyrus is about 30 centimetres (roughly a foot) high, and if you look closely you can see the fibres of the papyrus plant.
Making papyrus is laborious but quite straightforward. The plant itself – a kind of reed which can grow to about 4.5 metres (15 feet) high – was plentiful in the Nile Delta. The pith of the plant is sliced into strips, which are soaked and pressed together to form sheets, and the sheets are then dried and rubbed smooth with a stone. Conveniently, the organic fibres of papyrus mesh together without the need for glue. The result is a wonderful surface for writing on – papyrus went on being used across the Mediterranean until about a thousand years ago, and indeed gave most European languages their very word for paper.
But papyrus was expensive – a 5-metre roll like the Rhind Papyrus would have cost two copper deben, about the same as a small goat. So this is an object for the well off.
Why would you spend so much money on a book of mathematical puzzles? I think because to own this scroll would have been a good career move. If you wanted to play any serious part in the Eg
yptian state, you had to be numerate. A society as complex as theirs needed people who could supervise building works, organize payments, manage food supplies, plan troop movements, compute the flood levels of the Nile – and much more. To be a scribe, a member of the civil service of the pharaohs, you had to demonstrate your mathematical competence. As one contemporary writer put it:
So that you may open treasuries and granaries, so that you may take delivery from one corn-bearing ship at the entrance to the granary, so that on feast days you may measure out the gods’ offerings.
The Rhind Papyrus teaches you all you need to know for a dazzling administrative career. It is effectively a crammer for the Egyptian civil service exams around 1550 BC. Like self-help publications today that promise instant success, it has a wonderful title, written boldly in red on the front page:
The correct method of reckoning, for grasping the meaning of things, and knowing everything – obscurities and all secrets.
In other words: ‘All the maths you need to know. Buy me, and you buy success.’
The numeracy of the Egyptians, honed by works like the Rhind Papyrus, was widely admired across the ancient world. Plato, for example, urged the Greeks to copy the Egyptians, for whom
The teachers, by applying the rules and practices of arithmetic to play, prepare their pupils for the tasks of marshalling and leading armies and organizing military expeditions and all together form them into persons more useful to themselves and to others and a great deal wider awake.
But if everybody agreed that training like this produced a formidable state machine, the question of what mathematics the Greeks actually did learn from the Egyptians remains a matter of debate. The problem is that we have only a very few surviving Egyptian mathematical documents – many others must have perished. So, although we have to assume that there was a flourishing higher mathematics, we just do not have the evidence for it. Professor Clive Rix, of the University of Leicester, emphasizes the significance of the Rhind Papyrus:
The traditional view has always been that the Greeks learnt their geometry from the Egyptians. Greek writers such as Herodotus, Plato and Aristotle all refer to the outstanding skills of the Egyptians in geometry.
If we didn’t have the Rhind Mathematical Papyrus, we’d actually know very little indeed about how the Egyptians did mathematics. The algebra is entirely what we would call linear algebra, straight-line equations. There are some of what we call arithmetical progressions, which are a little bit more sophisticated. The geometry’s a very basic kind as well. Ahmose [the original copyist of the papyrus] tells us how to calculate the area of a circle, and how to calculate the area of a triangle. There is nothing in this papyrus that would trouble your average GCSE student, and most is rather less advanced than that.
But this is, of course, what you’d expect, because the person using the Rhind Mathematical Papyrus is not training to be a mathematician. He just needs to know enough to handle tricky practical problems – like how to divide up rations among workmen. If, for instance, you have 10 gallons of animal fat to get you through the year, how much can you consume every day? Dividing 10 by 365 was as tricky then as it is now, but it was essential if you were going to keep a workforce properly supplied and energized. Eleanor Robson, a specialist in ancient mathematics from Cambridge University, explains:
Everyone who was writing mathematics was doing it because they were learning how to be a literate, numerate manager, a bureaucrat, a scribe – and they were learning both the technical skills and how to manage numbers and weights and measures, in order to help palaces and temples manage their large economies. There must have been a whole lot of discussion of mathematics and how to solve the problems of managing huge building projects like the pyramids and the temples, and managing the huge workforces that went with it, and feeding them all.
How that more sophisticated discussion of mathematics was conducted, or transmitted, we can only guess. The evidence that has come down to us is maddeningly fragmentary, because papyrus is so fragile that it tends to crumble, it rots in damp conditions, and it burns so easily. We don’t even know where the Rhind Papyrus came from, but we presume that it must have been a tomb. There are some examples of private libraries being buried with their owners – presumably to establish their educational and administrative credentials in the afterlife.
This loss of evidence makes it very hard to form a view of how Egypt stood in comparison with its neighbours and to understand exactly how representative Egyptian mathematics is around 1550 BC. Eleanor Robson tells us:
The only evidence from the same time we’ve got to compare it with is from Babylonia, in southern Iraq, because they were the only two civilizations at that point that actually used writing. I’m sure that lots of other cultures were counting and managing with numbers, but they all did it – as far as we know – without ever writing things down. The Babylonians we know a lot more about, because they wrote on clay tablets and, unlike papyrus, clay survives very well in the ground over thousands of years. So for Egyptian mathematics we have perhaps six, maximum ten, pieces of writing about mathematics, and the biggest of course is the Rhind Papyrus.
For me, the most remarkable thing about this papyrus is how close it lets us get to the quirky details of daily life under the pharaohs, not least the culinary aspects. From it we learn that if you force-feed a goose it needs five times as much grain as a free-range goose will eat. So did the Egyptians eat foie gras? Ancient Egypt also seems to have had battery-farming, because we’re told that geese kept in a coop – presumably unable to move – will need only a quarter of the food consumed by their free-range counterparts, and so would be much cheaper to fatten for market.
‘In seven houses there are seven cats …’
In between the beer and the bread, and the hypothetical foie gras, you can see the logistical infrastructure of an enduring and powerful state, able to mobilize vast human and economic resources for public works and military campaigns. The Egypt of the pharaohs was, to its contemporaries, a land of superlatives – astonishing visitors from all over the Middle East by the colossal scale of its buildings and sculptures, as it still does us today. Like all successful states, then as now, it needed people who could do the maths.
And if you’re still puzzling over the cats, and the mice, and the ears of grain in the puzzle that I began with, the answer is … 19,607.
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Minoan Bull-leaper
Bronze statue of bull and acrobat, found in Crete, Greece
1700–1450 BC
A small bronze sculpture of a bull with a figure leaping over it is now one of the highlights of the British Museum’s Minoan collection. It comes from the Mediterranean island of Crete, where it was made around 3,700 years ago.
The bull and the leaper are both made of bronze, and together they’re about 5 centimetres (2 inches) long and between 10 and 13 centimetres (4 or 5 inches) high. The bull is in full gallop – legs outstretched and head raised – and the figure is leaping over it in a great arching somersault. It’s probably a young man. He’s seized the bull’s horns and thrown his body right over, so that we see him at the point where his body has completely flipped. The two arching figures echo each other – the outward curve of the boy’s body being answered by the inward curve of the bull’s spine. It’s a most dynamic and beautiful piece of sculpture, and it carries us at once into the reality – and, no less important, the myth – of the history of Crete.
The image is a literal representation of something that to most people today is just a metaphor – ‘taking the bull by the horns’ is what we’re all meant to do when confronted with the big moral problems of life. But archaeology suggests that about 4,000 years ago a whole civilization seems to have been collectively fascinated by both the idea and the act of confronting the bull. Just why they were is one of the many mysteries of a society at the crossroads of Africa, Asia and Europe that played a key role in shaping what we now call the Middle East. It was a society that Homer desc
ribed in lyric terms:
Out in the middle of the wine-dark sea, there is a land called Crete, a rich and lovely land washed by the sea on every side; and in it are many peoples and ninety cities. There, one language mingles with another … Among the cities is Knossos, a great city; and there Minos was nine years king, the boon companion of mighty Zeus.
In Greek myth, Minos, ruler of Crete, had a complex relationship with bulls. He was the son of the beautiful Europa by Zeus, king of the gods, but in order to father him and abduct Europa, Zeus had turned himself into a bull. Minos’s wife in turn had conceived an unnatural passion for a very beautiful bull, and the fruit of that obsession was the Minotaur, half-man, half-bull. Minos was so ashamed of his monstrous stepson that he had him imprisoned in an underground labyrinth, and there the Minotaur devoured a regular supply of maidens and youths sent every year by Athens – until, that is, the Greek hero Theseus succeeded in killing him. The story of Theseus and the Minotaur, of man first burying then confronting and slaying his monstrous demons, has been told and retold for centuries, by Ovid, Plutarch, Virgil and others. It’s part of the high canon of Greek myth, of Freudian psychology and of European art.
A History of the World in 100 Objects Page 11