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North American buckskin map (made around 1775), from mid-western USA

The first world war began in 1756. For the next seven years Britain and France were to fight each other on land and sea in Europe and Africa, India and America. It was the first truly global conflict, and it was particularly hard fought in America. A satirical account of the time explained why the two countries were fighting over the chill wilderness of North America.

"They are at present engaged in a very destructive war. They have already spilled much blood, and all on account of each side desiring to want greater quantities of fur than the other. The pretext of the war is about some land a thousand leagues off. A country cold, desolate and hideous. A country of a people who were in possession from time immemorial."

The "hideous land" actually refers to Canada, and the author, the poet and novelist Oliver Goldsmith, goes on to argue that Britain and France are despoiling the legitimate inhabitants of the countries they explore and exploit.

From Canada, the war drifted south, and today's object is a map which shows part of the area that the British moved into, as they captured the long line of French forts that ran from the Great Lakes to the Mississippi, as far south as St Louis. The map was made around 1774, probably by a Native American - one of the people who had, in Goldsmith's words, been "in possession from time immemorial".

"If you give up land, and you move away from your homeland, you are moving away from God for practical purposes. So that's why the Indian Removal, or the removal of people off land is very, very traumatic." (David Edmunds)

"It's a particularly rich map. With a lot of research I could relate it with a high degree of certainty to when, exactly when, and exactly why it was made." (Malcolm Lewis)

This week I'm looking at Europe's engagement with the rest of the world in the eighteenth century, the intellectual curiosity that led to the gathering of vital knowledge about oceans and continents. But dispassionate learning often came accompanied by commerce and conquest. The buckskin map, and our story in this programme, come from the years between the British defeat of the French in North America in 1763, and the outbreak of the American War of Independence in 1776. The war had left the British government in charge of a new stretch of territory to the west of the existing British colonies, from the Great Lakes down to the Mississippi. In charge, but not necessarily in control. If the French had gone, the British colonial governors now had their own countrymen to contend with. British settlers were eager to move west, violating agreements already struck with Native American leaders, and they were negotiating illegal land deals with local tribes - a recipe for future conflict.

This map was made for one of these problematic land deals. It shows us an encounter not just between two different worlds, but between two different ways of imagining the world. The frontiers between the lands represented, but also the frontiers between two cultures - cultures which had quite different conceptual, spiritual and social ways of being. Mapping for Europeans was a central technique of control. Partly intellectual control - the pursuit of accurate knowledge of the world - but also of course political and military control. For a Native American, mapping - as we shall find out - was about something quite else.

The map is drawn on the hide of a deer, and it is roughly three feet (90 cm) by four feet (120 cm). Disturbingly, the deer itself still seems to be very present, because you can see exactly how it died. In the hide there are holes from a musket ball, that passed through the animal's right shoulder, through its heart, and out through its rear left side. This deer was killed by a top-class shot, somebody who knew how to hunt.

Looking at the buckskin map with a modern map in my hand, I can see exactly where we are. We're surveying the vast drainage basin formed by the confluence of the Ohio and the Mississippi. We are just below Lake Michigan, and the area of the map is effectively four modern states - pretty well all of Illinois and Indiana, and large parts of Ohio and Missouri.

It's this area that after 1763 British settler companies wanted to exploit, and the map is the record of one of many conversations between these intrusive settlers and Native Americans. Near the centre of the map is the phrase "Piankashwa sold" - indicating a land transaction that has already been agreed.

The Piankashaw, as they're usually known today, were a tribe of Native Americans living in an area that includes modern Indiana and Ohio. The map was probably made for the Wabash Land Company, which had been set up by British settlers to buy land along the River Wabash from the Piankashaw Indians around 1775. Malcolm Lewis, expert on maps and North American native cultures, explains:

"It was almost certainly used in the process of negotiating with the Piankashaw Indians to try and buy land. I'm not sure that the actual example which we have is the original. It was done at the same time, or very soon afterwards, but it's very delicately done. Original Indian maps were usually rather cruder. So my guess is it was a contemporary copy - probably made by a white person - of an original which had been made by the Indians - and almost certainly the Piankashaw Indians who were the ones who were being negotiated with - with a view to purchase."

The words on the map - "Piankashwa sold" - suggest that this is a record of a deal that's already done and dusted. But in fact this deal was never ratified by the British colonial authorities, because it was illegal, in breach of the official treaties. In any case it is unclear what it could have meant to the Piankashaw Indians themselves. The Wabash Company used interpreters, but plenty was lost in translation.

"The said witnesses, in their quality as interpreters, have done for the best in their souls and consciences, according to the best of their understanding and knowledge, and have faithfully and plainly explained to the said chiefs . . . to which they have set their ordinary marks, with their own hands."

The report tells us that everything had been "faithfully and plainly explained" to the chiefs, but the Piankashaw had never encountered the concept of European-style land purchase. Settler ideas of land ownership were alien to Native Americans, who thought essentially in terms of residence and use.

What the map shows above all, is rivers. In the centre, running down the spine of the deer, as it were, is the Wabash River - hence the Wabash Land Company - and other rivers come in as straight, angled lines, placed like vertebrae - except for the Mississippi, which runs down the left, and curves around the bottom all the way to the right. The map shows the rivers and the settlements, not the land over which the people roamed and hunted. This is a map about communities, not about geography: it's about habits of use, not patterns of ownership. So, rather like the map of the London Underground, it doesn't show accurately the physical distances on the ground, but rather their relative positions. Native Americans, like everybody else, mapped what mattered to them. Tellingly, although the map shows all the rivers, it shows almost exclusively the settlements of the Indians. Virtually none of the European settlements is here. St Louis, for example, which was already a great centre of trade and communications, is just not shown. European maps of the same area do effectively the same but in reverse, showing the European settlements but not the Indian ones, plotting the space, but not the use. Each people reads the same physical landscape in a quite different way. You could hardly have a better demonstration of a central Enlightenment problem - the difficulty of any one society in trying to understand another.

If the Indians didn't understand the notion of exclusive land ownership, the Europeans could not grasp the Indians' intense spiritual relationship to their land, the notion that the "loss of earth was in some measure the loss of heaven". Here's David Edmunds, Professor of American History at the University of Texas:

"Well, I think the Native American relationship with the land is very, very important. You have to understand that land for tribal people is not a commodity. It was never a commodity, it was a place where you lived, it was a place that you shared, it was a place that you utilised - but it was not something that you particularly owned. One could not anymore own the land, than one could own the air above the land, or the rain that fell on it, or the animals that lived on it.

"Land is so important, and place is so important, to tribal people, that history for tribal people is more a function of place than it is of time. That people are associated with a particular region, the region is the centre of their world. And consequently, that land then is so intricately bound into the very soul of most tribal people, that it's not something that you trade back and forth. And when they will be forced to trade lands, in the early part of the nineteenth century, and give up land, in order to survive, it's a very traumatic experience for them. And I think another thing to remember is that most of the religious beliefs of tribal people are site-specific. And by that I mean that their ideas of cosmology, the powers in their universe, are also tied to the particular area in which they live."

The settlers failed to push through this particular land deal, which was struck down by the British colonial governors. A few years later this tension - between settlers wanting land, and the British Crown eager to maintain good relations with the Native American chiefs - would be one of the elements that triggered the War of Independence. But independence did not make the problem go away. US state governors later faced exactly the same dilemma as their British predecessors, and they, too, had to strike down more attempts at land sales between the Wabash Company and the Piankashaw that breached existing treaties. This map, and the abortive negotiations around it, remain as evidence of three quite different ways of thinking about the world. Those of Native Americans with their deep and spiritual connection to the land, the settlers who wanted to appropriate and exploit it, and the authorities in London and later in Washington, who tried to mediate a solution but were powerless to enforce it.

In the next programme, more mapping, and further consequences of European encounters in the eighteenth century. We shall be with Captain Cook, as he charts the coastline of eastern Australia. And the object is not a map, but a wooden bark shield . . . and it, too, represents a fateful encounter between one world and another.