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Lewis Chessmen (made twelfth century). Walrus ivory and whales' teeth; found on the Isle of Lewis, Scotland

In 1972 the world was gripped by one of the great battles of the Cold War. It was fought in Iceland and it was a chess match - one between the American Bobby Fischer and the Russian Boris Spassky.

"I'm just going to go in there. I'm not going stay up nights worrying. It's going to be over pretty soon. This little thing between me and Spassky's a sort of a microcosm of the whole world political situation, you know, you always read about this. They suggest that the two world leaders should sort of fight it out hand-to-hand or something. This is that kind of thing now." (³ÉÈË¿ìÊÖ archive interview with Bobby Fischer)

At the time, Fischer declared "chess is war on a board", and at that moment in history it certainly seemed like it. But then it always has. If all games are to some degree a surrogate for violence and war, no game so closely compares to a set-piece battle as chess. Two opposing armies line up to march across the board, foot-soldier pawns in front, officers behind. Every chess-set shows a society at war. Whether that society is Indian, Middle Eastern or European, the way the pieces are named and shaped tells us a great deal about how that society functions. So, if we want to visualise European society around the year 1200, we could hardly do better than look at how they played chess. And no chess pieces offer richer insights than the 78 mixed pieces found on the Hebridean island of Lewis in 1831, and known ever since as the Lewis Chessmen.

Sixty-seven are in the British Museum. Eleven are owned by the National Museums of Scotland. Between them, these much-loved pieces take us into the heart of the medieval world.

"I was trying to define what chess is, and I asked Tony Miles, grandmaster. He said, 'It's not an art ... if I can find a way to win that's crude and blunt, I'll do it that way'. It's not an art, it's a fight ... it's a fight!" (Martin Amis)

"The Lewis Chessmen, they are so perfect, there are so many of them, a real family. They are so exquisitely made. They come from so far, far and cold away." (Miri Rubin)

This week, we're making an almost full turn of the globe around seven or eight hundred years ago, with porcelain in China, sculpture in Africa, and a throne from the Caribbean. We're also in Spain with a Jewish scientific instrument, but in this programme we're in Scandinavia and Scotland. Valuable objects are always markers of high status - but this week's objects show more than just wealth or power; the people who owned them were also showing off knowledge, taste and intellect.

For over five thousand years people have been playing board games, but chess is a relative newcomer - it seems to have been invented in India at some point after the year 500 AD. Over the next couple of hundred years, the game spread through the Middle East and on into Christian Europe, and in every place, the chess pieces were changed to reflect the society that played it. So in India, there are pieces named "war elephants", while in the Middle East, Islamic reservations about the human image ensured that all the pieces were virtually abstract. European pieces, by contrast, are often intensely human, and the Lewis Chessmen not only appear to show us particular kinds of characters, but strikingly reflect the structures of the great medieval power game as it was fought out across northern Europe, from Iceland and Ireland to Scandinavia and the Baltic.

They're much bigger than the figures that most of us play with today. The king, for instance, is about three inches (7.5 cm) high, and he comfortably fills a clenched fist. Most of them are carved out of walrus tusks, there are a few that are made out of whales' teeth, and some of the pieces would originally have been coloured red, rather than the black that we're used to today - but all of them are now a pale creamy brown.

Let's begin with the pawns. One of the puzzles of the Lewis Chessmen is that there are lots of major pieces and very few pawns. What we've got are pieces from a number of different incomplete sets - 78 pieces in all - but only 19 pawns among them. The pawns are the only pieces that aren't human; they're simply small ivory slabs that stand upright like gravestones. In medieval society, these are the peasants, brutally conscripted on to the battle-field. All societies tend to think of the people at the bottom of the heap as interchangeably identical, and the foot-soldiers here are shown with no individuality at all.

The main pieces, on the other hand, are full of personality. Elite guards, knights on horseback, commanding kings and meditative queens. Pride of place goes of course to the ultimate source of legitimate power - the king. Capture him, and all fighting stops. All the Lewis kings sit on ornate thrones, a sword across their knees. Guarding the kings are two kinds of specialist warriors. One is immediately familiar to us - he is the knight, fast-moving, versatile and mounted on horseback. From the very beginnings of chess in India, the mounted warrior is a constant - he's in every age and in every country and he's pretty well unchanged today. But these familiar knights are flanked by something much more sinister. At the edges of the board, where we now have castles, are the ultimate shock troops of the Scandinavian world. They stand menacingly, some of them working themselves into a frenzy of bloodlust by chewing the tops of their shields.

I've got one in my hands now, and they are pretty terrifying - these are the fighters called "berserkers". It's an Icelandic word for a soldier wearing a shirt made of bear skin and the word "berserk" even today is synonymous with wild, destructive violence. More than any other piece on this board, the berserkers take us to the terrifying world of Norse warfare.

The Lewis Chessmen were discovered in what is now modern Scotland, and recently some politicians have advanced the case that some or all of the Chessmen should be returned back to the Isle of Lewis. That's a comparatively modern controversy though.

Around 1200, the Isle of Lewis, on the north-west edge of what's now Scotland, was at the heart of the Norse world. It was part of the kingdom of Norway. The language was Norwegian, and its archbishop had his cathedral in Trondheim, 250 miles north of Oslo. Trondheim was one of the great centres for carving walrus ivory, and the style of the Lewis Chessmen is very close to pieces made there. We know that similar chess pieces have also been found in Ireland, and Lewis was a staging post on the thriving sea route between Trondheim and Dublin. Here's medieval historian Miri Rubin:

"I personally believe that they come from Norway, and I personally believe they probably came from somewhere around Trondheim, it looks like so much that's produced there. But the thing is, if we think of Great Britain not as - as it is now - very much connected to the central and southern European sphere, but if we think of the North Sea as a sort of "connector" of regions, there is that whole North Sea region ... that's where the Vikings came from, that's where the predecessors of the Normans who ultimately conquered England came from. So if we think of that as a sort of commonwealth, a northern commonwealth, that traded in those ... and that became rich because it had these ... amazing raw materials of wood, and amber, and fur, and metals, then we can imagine better how something produced in Norway can end up on the west end of Scotland."

The Lewis chess pieces were discovered in 1831, at Uig Bay on Lewis, in a small stone chamber concealed in a sandbank. By far the most likely explanation for their being there, is that they were hidden for safety by a merchant, who may have been intending to sell them on Lewis itself. A thirteenth-century poem, for example, names a powerful figure, Angus Mor of Islay, as King of Lewis, and has him inheriting his father's set of ivory chess pieces:

"To you he left his position, yours his breastplate ... each treasure ... his slender swords, his brown ivory chessmen."

By playing chess, a ruler like Angus Mor indicated that although his local power base was on the extreme outer edge of the continent, he was nonetheless part of an elite high culture that embraced all the courts of Europe. And the figure on the board that more than any other represents those European courts is, of course, the queen.

Unlike Islamic society, where the rulers' wives would generally have remained hidden from public view, the European queen enjoyed a public role and the high status of adviser to the king. So, on the Islamic chess board the king is accompanied by his male adviser, the vizier, while the European king sits beside his queen. In the Lewis chess pieces, the queens all sit staring into the distance, holding their chin in their right hand - suggesting to their contemporaries intense thought and wise counsel, but to us looking comically glum.

And perhaps these queens had something to be glum about. In medieval chess, the queen doesn't actually have much power, she can move only one diagonal space at a time. Her modern sister, on the other hand, is the most powerful person on the board. In the world of chess, feminism came early.

But apart from the queen, surprisingly little has actually changed in chess since medieval times, least of all the formidable mathematics of the possible moves. And this sedentary, cerebral game has always aroused passionate emotion. The writer Martin Amis has long been fascinated by both aspects:

"The maths of chess is very interesting in that after four moves, each of the possibilities are already in the billions. It is the supreme board game. All I can say of my achievements on the board is I'm not a complete mug, but very occasionally you do glimpse a combination, that a great player would be seeing all the time. And suddenly the board looks tremendously rich, it seems to bristle with possibilities. And combative will is what you see in all the great players. They've all got the killer instinct."

And sometimes, it is literally the killer instinct. In 1279 an English court record tells us that when David de Bristoll was playing chess against Juliana le Cordwaner, they quarrelled so violently that he struck her in the thigh with a sword, and she died immediately. An early example of chess rage!

There's one piece I haven't looked at yet, but it's perhaps it's the most fascinating figure of all the Lewis Chessmen, and it's one that gives us a crucial insight into the society that made it. It's the bishop, who in medieval Europe was one of the great powers of the state, controlling not only spiritual life, but commanding land and men. The bishops of the Lewis Chessmen are the oldest ones still in existence, and they're powerful reminders that across Europe, the Church was a key participant in the great military campaigns - and this was a Europe hungry for a fight! We all know about the Crusades to the Holy Land and the role that the Church played in them, but at the same time there was also a northern crusade -led by the Teutonic knights - that conquered and Christianised eastern Europe. And in the south, Castile and central Spain were being reclaimed for Christendom from their Islamic rulers.

It's from that Spain, newly Christian but with Muslim and Jewish citizens, that the next programme's object comes. It's the versatile, multi-functional, smart phone of its time ... it's an astrolabe.