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Olmec stone mask (made around 2,500 years ago) found in Mexico

I'm holding a face in my hand, and it's very definitely a face, and not a head. It's made in polished green stone, and it's hollowed out at the back - so in fact it's a miniature mask. The dark stone is flecked with white, snake-like streaks, which gives it its name, 'serpentine' - and when you look more closely, you can see the face has been pierced, and has been ritually scarred. The people of this mask are the Olmec, who ruled in what's now Mexico for around a thousand years, from 1400 to 400 BC. They've been called the mother culture - the 'cultura madre' - of Central America, and it was this Olmec mother culture that produced this unsettling face.

So far this week the objects in this world history have taken me along the royal roads of the Persian Empire, into mythical battles in Athens and to some heavy drinking in northern Europe. Each object has shown how the people who made it defined themselves and the world around them about two and a half thousand years ago. In Europe and Asia it's striking that that self-definition was usually in distinction to others - partly by imitation, but usually in opposition. Today I'm on the continent of the Americas - to be precise, in the lowland rainforests of south-east Mexico, and my object, this Olmec face-mask, shows me a culture looking only at itself.

"To go as far back as the Olmecs is to go as far back as the Egyptians, because the culture of Egypt of the pharaohs and the Olmec culture of Mexico are contemporary. So it's a part of our continuity, the great continuity of Mexican culture." (Carlos Fuentes)

Most of us don't learn a lot about Central American civilisations at school; we're all taught about the Parthenon, and we've all heard of Confucius as a great Chinese thinker, but we don't know a lot about the great civilisations occurring at the same time in Central America. Yet the Olmecs were a highly sophisticated people, who built the first cities in Central America, mapped the heavens, developed the first writing and probably evolved the first calendar there. They even invented one of the world's earliest ball games - which the Spanish would encounter about three thousand years later. It was played using rubber balls - rubber being readily available from the local tropical gum trees - and although we don't know what the Olmecs called themselves, it's documented that the Aztecs called them Olmen, meaning 'the rubber country'.

It's only relatively recently that Olmec civilisation was uncovered from the jungles of Mexico; it was after the First World War that their sites, their architecture and above all their sculptures were found and investigated. Finding out when the Olmecs lived took even longer. In the 1950s radiocarbon dating came in, and that allowed archaeologists to date the buildings and therefore the people that lived in them. The results showed that this great civilisation flourished about three thousand years ago. The discovery of this ancient and long-standing culture has had a profound effect on the cultural identity of Mexicans today. We asked the celebrated Mexican writer Carlos Fuentes what it means to him:

"It means that I have a continuity of culture that is quite astonishing. Many Latin Americans who are merely migrants from European countries, or do not have a strong Indian culture behind them, don't have the extraordinary strength of the culture of Mexico, which begins a very long time ago - as proven by the Olmeca culture, which begins in the twelfth or thirteenth century before Christ.

"We consider ourselves heirs to all these cultures. They are a part of our make-up, a part of our race. We are basically a Mestizo country, Indian and European. The Indian culture has infiltrated into our literature, into our painting, into our habits, into our folklore. It is everywhere. It is a part of our heritage, as much as the Spanish culture, which for us is not only Iberian but also Jewish and Moorish. So Mexico is a compound of many, many civilisations and part of them of course are the great Indian civilisations of the past."

So who were the Olmecs? Whose face does this mask show, and how was it worn? Olmec masks have been intriguing historians for a long time. Scrutinising their features, many scholars believed that they were looking at Africans, Chinese or even Mediterraneans, who'd come to colonise the New World. I suppose if you look at our mask, wanting to see an African or a Chinese face, you can just about persuade yourself that you can, but the features, in fact, are totally characteristic of Central American people. This face is one that can still be seen in the descendants of the Olmecs still living in Mexico today. I find this desire to discover European or Asian elements in ancient American societies fascinating. I think it's because the similarities between the cultures of the old and the new worlds are so strong - both produced pyramids and mummification, temples and priestly rituals, social structures and buildings that function in similar ways - that scholars found it hard to believe that these American cultures could have evolved like this in isolation. But they did.

At only five inches (12.5 cm) high, the mask is obviously far too small to have been worn over anybody's face, and it's much more likely that you'd have worn this round your neck or in a headdress, possibly for some kind of ceremony. Small holes have been bored at the edges and at the top of the mask, so that you could easily fasten it with a bit of twine or thread. On either cheek you can see what, to my European eyes, look like two candles standing on a holder. To the eyes of the great Olmec specialist, Karl Taube, they're more likely to be the cardinal points of the compass, and they suggest that this person may have been a king:

"For the Olmec we have these great colossal heads, we have thrones, portraits of kings and very often, important here too, is the concept of centrality. And so, on this finely carved serpentine mask, we see four elements on the cheek which are probably the four directions. And so for the Olmec, of major concern were the world directions and world centre, with the king being the pivotal world axis in the world centre."

Here we are again: every culture this week - and indeed most cultures in this history - see themselves quite naturally as the centre of the world.

As well as honouring a wide range of gods the OImecs also revered their ancestors - so it's possible that this mask with its particular features and markings might well represent a historic king or a legendary ancestor. Karl Taube again:

Contributor: Karl Taube There's also in a number of jades a person's face, we call him the 'Lord of the double scroll', and it looks like he has tattooing quite similar to this piece also in the British Museum. That's probably tattooing on his face (that light incision) and so we see a number of jades, this Lord of the double scroll, suggesting this was an individual that had this facial marking. And so portraiture was obviously important here, denoting the king as an individual and historic figure.

Whoever he was, the man of the serpentine mask must have cut quite a dash when he appeared in public. The ears are pierced in several places, presumably for gold earrings. But at the corners of his mouth are what look like enormous dimples. They must in fact represent circular holes. We're used now to face-piercings and studs, but this man must have been wearing plugs. We know that piercings and plugs are common throughout the history of Central America. Alterations like these, in the name of Olmec beauty, would have transformed the face - and today it's only in masks like this that we can have any idea of what the Olmecs would have looked like, for the skeletons have completely dissolved in the acid soil of the rainforest. But the Olmec sense of personal beautification could go far beyond cosmetics or jewellery. Here's Karl Taube again:

"They would modify their heads - it's often called cranial deformation, but I think that's a loaded word. For them it was a mark of beauty. For newborns, they would bind their heads, and so they would become elongated - some people call it avocado head. But really what they're evoking is their head as an ear of corn. And so the Olmec really were truly the people of maize."

Sadly there are only a few Olmec inscriptions - or glyphs - now surviving, and decipherment of their writing is tentative at best. There just isn't enough continuous writing to let us be certain of what the symbols mean. But there are lots of objects bearing symbols, marks and glyphs, such as pottery and sculptures, and they show us that writing was originally widespread across the Olmec heartland.

Even if we can't yet read their writing, we can learn a lot about the Olmecs from the buildings and the cities that have recently been uncovered. Major cities such as La Venta, near the Gulf of Mexico, had impressive step-pyramids with temple monuments for the worship of the gods and the burials of the kings. These would have formed the centre of the city. The pyramid itself was often topped by a temple, just as at the same time the Parthenon was built overlooking Athens.

But whereas the Parthenon stood on the naturally formed rock of the Acropolis, the Olmecs built artificial mountains - platforms is far too mild a word - on which to put their temples to overlook the city. The layout of the city, and its placing in an ordered landscape, typified not just Olmec, but most later Central American urban centres - like the Mayas and the Aztecs. All were a variation of the Olmec model of a temple overlooking an open square, flanked by smaller temples and palaces.

By 400 BC La Venta, along with all the other Olmec centres, was abandoned. It's a pattern that occurs with disconcerting frequency in Central America - great population centres are suddenly, mysteriously, abandoned. In the case of the Olmecs, it could have been the overpopulation of this fragile tropical river valley, or a shift in the earth's tectonic plates making rivers change their course, the eruption of one of the local volcanoes, or a temporary climate change caused by the shifting patterns of the El Ni�o ocean current - all of them are possibilities.

I've just climbed about three hundred steps up a great pyramid in central Mexico. We're around 240 feet (73m) high, and it's blazing hot. Below me are the ruins of the ancient city of Teotihuacan, a city founded several centuries after the mysterious collapse of the Olmec heartland. But what Teotihuacan demonstrates is the continuing power of the Olmec culture. In the ruins you can see the monumental avenues, pyramids and public buildings of a city that in its day was the same size as ancient Rome. But it's a city that owes a great deal of its shape to the models given them by the Olmecs. The culture of the Olmecs casts a very long shadow, establishing models and patterns that were going to be followed by other cultures for centuries to come.

My object in the next programme also embodies a cultural model that lasted for thousands of years. And it is also one that is quite separate from developments in Europe. It's a bell, made in China.