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Inca gold llama (made between 1400 and 1550). Small statue from Peru

Some of you might just recognise the plaintive moan or humming sound of a llama. It's the sound that around five hundred years ago accompanied the building of an empire, the Empire of the Inca - bigger than Ottoman Turkey, bigger than Ming China, in fact, the largest in the world. Around 1500, the Inca Empire ran for over three thousand miles (5,000 km) down the Andes, and ruled over 12 million people from the Pacific Coast to the Amazonian jungle. In 1532 the Spanish would come, and everything would collapse. But until then, the Inca Empire flourished. It didn't have writing, but it was an efficient military society, an ordered, productive and wealthy civilisation centred on Cusco in Peru. Its economy was driven by manpower and, just as important, llama power. It's the biggest empire of the week - but it's represented by the smallest object - a llama that sits in my hand, a tiny, gold messenger from a mountain-topped world.

"I've seen llamas carrying packs in the Andes at elevations of up to 16,000 feet. The other domestic animal of the Andes, the guinea pig, weighs about two pounds, so you can't go very far with a guinea pig carrying your suitcase." (Jared Diamond)

This week's objects take us to empires all over the globe around five or six hundred years ago. As the Ming Dynasty was reordering China, and the Ottomans conquering eastern Europe, the Inca were constructing their vast empire, spreading from their heartland in southern Peru to a territory ten times the size by 1500. Although this empire was highly organised militarily, socially and politically, the Inca had no script, so we are - as so often in American history - heavily dependent on the accounts of the Spanish conquerors. But we know from these, and from the objects left behind, that the making of the Inca Empire is one of the most extraordinary achievements in the history of the world. Andean territory is forbiddingly mountainous. This was a vertical empire, that made terraced fields on mountain sides and roads that ran over the peaks. The Incas made the impassable passable, and the key to their success was the llama. But a state's dependency on animals was nothing new, as the scientist and writer Jared Diamond confirms:

"The availability and type of domestic animals has had a huge effect on human history and on human culture. For example in the old world, in Europe and Asia, the big domestic animals of Eurasia, the horse, cow, goat, sheep and pig, they provided meat and protein, some of them provided milk. Some of them were big enough to provide transport. The horses and the camels that could be ridden became war animals, and so they provided an enormous advantage for Eurasian people over peoples of other continents."

The zoological lottery that Jared Diamond describes - the pure chance of whether your local animals can be domesticated - enormously favoured Europe and Asia. Australia, by contrast, drew a very short straw. It's hard to domesticate an emu, and no-one ever rode into battle on a kangaroo. The Americas were almost as badly off, but they did have the llama. Llamas can't compete with the horse for speed, or the donkey for pack power. They also have an infuriating habit, when tired, of just stopping and refusing to move. But they are extraordinarily well adapted to high altitude; they cope well with the cold and can forage for their own food; they can provide wool, meat and manure; and although they can't carry people, a healthy llama can comfortably transport about 60 pounds (27 kg) of goods - which is just a bit more than the average baggage allowance on an airline. So they can be very useful indeed for carrying the kind of supplies required for military campaigns. And as they expanded down the great spine of the Andes, the Inca bred huge numbers of llamas as army pack animals. Not surprisingly, the Inca also made models of this hardy creature that was so fundamental to the lives of the people and to the running of the Empire.

Our little gold llama is so tiny that it can stand comfortably in the palm of my hand - it's only a bit over two inches (5 cm) high. It's hollow, made up of hammered-out thin leaves of gold, and so it's very light. It's an engagingly sprightly figure. It's got a straight neck, the ears are upright and alert, it's got large eyes and a mouth that's clearly smiling - making this an unusually cheerful-looking creature, for a species that normally seems to veer between amused condescension and a spitting sneer. If I put it down, it stands very pertly; this is a llama with attitude. Many little figures like this have been found, in gold and silver, all over Inca territory, and they were frequently buried as offerings on mountain peaks.

That territory was on three distinct levels. There was the flat coastal strip, there were mountainsides with the famous Andean terraced fields - which produced crops on very difficult terrain - and then there were the mountain plateaus with high grasslands, 12,000 feet (3,600m) above sea level. It was the llama that unified these three disparate Inca worlds, and held this vast empire together.

This was a world of different peoples, languages and gods, whose communities had often been at war with each other, and the full range of imperial techniques was deployed by the Inca to manage this swiftly-created state. Some local elites were ruthlessly eliminated. Others were co-opted, given private land, and excused taxation. Late-conquered territories, in northern Ecuador for example, were allowed to operate more or less as client states, instead of being fully incorporated into the Inca system. This cultural mosaic was welded together into one powerful empire by the Inca military machine, and that machine depended on thousands upon thousands of llamas, to provide portage and food. We know, for example, that after an early battle against the Spanish, the defeated Inca abandoned 15,000 llamas.

Our little llama is made of gold, a key substance in Inca myth. Today, Inca objects in gold and silver are rare survivals - just tiny scraps of the dizzying opulence which was described by the Spanish when they arrived in the1520s. They wrote of palaces walled with sheets of gold, of gold and silver statues of humans and animals, and of miniature golden gardens inhabited by glittering birds, reptiles and insects. All of these would be either surrendered to or seized by the Spanish, and nearly all were melted down for bullion and then sent to Spain. So our little gold llama is a rare survivor.

Gold was the emblem of the great Inca sun-god, and represented his generative powers. Gold was described as "sweat of the sun" just as silver was the "tears of the moon". Gold was therefore related to masculine power, and above all to the power of the Inca himself, the emperor, the child of the sun.

As in all societies, planting and harvesting are accompanied by rituals and offerings to the gods, and with the Inca this often involved sacrifice of living beings, from guinea pigs to the children of the elite. And as the Peruvian Inca expert Gabriel Ramon explains, llamas were sacrificed by the thousand:

"As in any other big civilisation, I think that the Incas have [a] religious calendar. They have two calendars during the Incan period, I would say. One was [the] official Imperial calendar, and at the same time they have lots of small calendars from the provinces or territories that they conquered. But in the official calendar they tried to match the agricultural calendar with the main ceremonies. And it's in this official calendar that you have several ceremonies with the llama."

The greatest Inca religious rite was the Festival of the Sun. A Spanish chronicler has left us a full description:

"The first sacrifice of a young black llama was intended to observe the auguries and omens of the festival. They took the llama and placed it with its head facing the east. While still alive, its left side was opened and by inserting the hand they drew forth the heart, lungs and entrails. The whole must come out together from the throat downwards. They regarded it as a most happy omen if the lungs came out still quivering." (Hern�ndez Principe)

The same Spanish writer tells us that while real llamas were being slaughtered, the rulers of the provinces also brought to the Inca models of llamas made of gold and silver, tokens of the great animal wealth of the regions they ruled. Our llama may have been one of these tokens offered by a provincial ruler to the Inca.

Alternatively, and less comfortably, it may have been part of one of the other Inca religious rituals. Selected children were ritually exposed and left on the mountain peaks as living sacrifices to the mountain spirits, and little gold llamas like ours have been found beside their dead bodies.

The Inca Empire shaped not only the spiritual, but also the physical landscape of the Andes. Irrigation projects and canals changed the course of rivers and turned mountainsides into lush, terraced fields. Well-stocked storehouses and extensive highways showed their detailed concern with planning and provisioning.

The wealth of this Inca Empire depended on the vast herds of llamas, but also on the Incas' ability to force their conquered subjects to work for them. But the subjects were by no means as docile as the llamas, and many Andeans - dispossessed and exploited - bitterly resented the Inca as alien aggressors:

"Inca tyranny is at our gate . . . If we yield to the Inca, we shall be obliged to give up our former freedom, our best land, our most beautiful women and girls, our customs, our laws . . . We shall become for all time this tyrant's vassals and servitors." (Garcilasco de la Vega)

The Inca hold on many of its provinces was fragile. Continuous rebellions tell of potential weakness, which turned out to be crucial when the Spanish arrived on the northern shore of Peru in 1532. Some of the local elites immediately seized the opportunity to ally with the incomers and to throw off the Inca yoke. They joined the Spanish forces to bring down the Inca.

As well as being joined by a growing number of rebels, the Spanish had swords, armour and guns, none of which the Inca had - and crucially they also had horses. The Inca had never before seen men on the backs of animals, nor had they seen the speed and agility with which this combination of man and beast could move. The Inca llamas must suddenly have looked hopelessly delicate and slow. It was all over fairly quickly. A mere couple of hundred Spaniards massacred the Inca army, captured their emperor, installed a puppet ruler and seized and melted down their gold treasures. Our little llama is a rare survivor. The Spanish had come to Peru, lured by tales of enormous quantities of gold. But ironically, they discovered instead the richest silver mines in the world and they began to mint the coins that would power the world's first global currency. The Inca measured the wealth of their empire in llamas. The Spanish would measure theirs in silver pieces of eight.

In the next programme we're with another empire . . . we're in central Asia, with an astronomer prince and a jade cup.