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Mechanical galleon (made around 1585). Gilt automaton and clock; from South Germany

The magnificent ship is masted, rigged and ready to sail, the lookouts are standing in the crows' nests, high on the stern sits the Holy Roman Emperor of the German nation, and in front of him his grandest subjects parade one after another, turning and making obeisance. Deep in the hull of the ship an organ plays music. Then, the cannons fire in an explosion of noise and smoke, and the Imperial galleon moves majestically forward.

Well, that's how it was meant to be, but in fact all this is happening in miniature. In this programme I am with an elaborately crafted model of a sailing ship, made of gilded copper and iron, which stands about three feet (90 cm) high. It was designed not to sail the seas, but to trundle across a very grand table. It's a decoration, but it's also a clock, and a musical box - all in the shape of a masted galleon, of the kind that in the sixteenth century developed across Europe to expand trade and to make war. Its intricate inner workings actually did create noise, smoke and movement. Nowadays the ship is silent, calmly berthed in the British Museum. Yet it still looks magnificent. This gilded galleon is one of the great executive toys of the European Renaissance.

"I just think humankind is fascinated with things that move and turn under their own steam - that you can wind something up and it goes without you touching it. We just love it, always have done, always will." (Lisa Jardine)

This fantastical mechanical galleon sums up, I think, not just ship-building in Europe, but indeed Europe itself between 1450 and 1650. In the course of those two hundred years, thanks to tremendous advances in ship construction, Europe's view of the world and of its place in it was completely transformed. Those years of exploration and expansion are the theme of this week's programmes. The work-horse of this expansion was the galleon, a new kind of ship, specially designed for ocean-going and particularly well adapted to the winds of the Atlantic. In ships like this one, European adventurers set off across the high seas to encounter other societies in all five continents.

Our galleon crossed nothing more turbulent or more dangerous than a princely European dinner table, but it's a very fair likeness of those great ocean-going vessels. It's the kind of galleon that Henry VIII had in his 'Mary Rose', it's above all the kind of ship that Spain sent against England in the Great Armada. They were normally three-masted, round-hulled war vessels, designed to carry both troops and guns, and they were the key element in any sixteenth-century navy. Absurdly, they were also popular table decorations, always referred to by the French word for this kind of ship - a 'nef'.

We went to Portsmouth dockyard to meet the marine archaeologist Christopher Dobbs, who is in charge of the 'Mary Rose', to ask him to compare it with our gilded nef. Here he is:

"Well, we're standing here in the 'Mary Rose' Ship Hall, and we're looking out at the 'Mary Rose', over 35 meters long and 15 meters high. The 'Mary Rose' is a little bit different to the nef, it's a slightly earlier ship, but the 'Mary Rose' is a very, very important part of naval warfare, because it was one of the first to be built with purpose-built lidded gun ports close to the waterline. And these ships were so important, they were the powerful symbols of the time. This is the equivalent of the space shuttle. And I think that's why they would have been so proud to have a nef, which would trundle along the tables - you know, at a great dinner - because it wasn't only a fantastic mechanical object, but it actually also reflected the glory of the warships, which were perhaps the most advanced technological features of their time."

These great ships were indeed the largest and most complex machines in the Europe of their day. The miniature gilded galleon is also a wonderfully constructed object, a masterpiece of technological skill and high artistic decoration, of both mechanics and goldsmithery. Paradoxically, this little ship was created for a society hundreds of miles from any sea, and it's highly likely that Hans Schlottheim, the landlocked craftsman who made it, had never seen a sea-going vessel.

It was made at the end of the sixteenth century, in the rich banking city of Augsburg, in southern Germany, a Free City within the Holy Roman Empire, and so part of a great sprawling territory that ran from Poland in the east to the Belgian channel ports in the west, all of which owed allegiance to the Emperor Rudolph II.

And it is Rudolph that we see on the deck of our ship. Nailed to the mainmast is a great double-headed eagle, the heraldic emblem of the Holy Roman Empire. In front of Rudolph are the seven electors, those princes of church and state in the German-speaking world, who chose each new emperor and enriched themselves by bribes in the process. It's very likely that this ship was made for one of those electors, Augustus I of Saxony. We've recently discovered in Augustus's inventory a description that almost exactly matches the British Museum's galleon, and which we think must be it:

"A gilded ship, skilfully made, with a quarter and full hour striking clock, which is to be wound every 24 hours. Above with three masts, in the crows' nests of which the sailors revolve and strike the quarters and hours with hammers on the bells. Inside, the Holy Roman Emperor sits on the Imperial throne, and in front of him pass the seven electors with heralds, paying homage as they receive their fiefs. Furthermore ten trumpeters and a kettle-drummer alternately announce the banquet. Also a drummer and three guardsmen, and sixteen small cannons, eleven of which may be loaded and fired automatically."

There was more. As it moved across the table, the little galleon played music. And from the surviving workings we can reconstruct it pretty well.

What would those south German dinner guests have thought watching this amusing and amazing object in action? They would, of course, have admired the clockwork brilliance of this playful automaton, but they must also have been fully aware that this was a metaphor in motion, a symbol of the ship of state. That idea of the state as a ship, and its ruler as the helmsman or captain, is a very old one in European culture. It's frequently used by Cicero, and indeed our word 'governor' comes from the Latin for 'helmsman' - 'gubernator'. Even more enticingly for this programme, the root of 'gubernator' is the Greek 'kubernetes', which is the origin of our word cybernetics and so the notions of ruling, steering and robotics are all present together in our language and in this one galleon.

The state that this model ship symbolised was like no other. The Holy Roman Empire was a unique phenomenon in Europe. Covering the area of modern Germany and a great deal beyond, it was a mechanism every bit as complex as our model ship. It was not a state in the modern sense of the word, but an intricate meshing of church lands, huge princely holdings and small, rich city states. It was an old European dream that so many diverse elements could co-exist in peace, all held together by loyalty to the person of the Emperor - a dream that had proved astonishingly adaptable.

By the time of our gilded galleon, the ancient metaphor of the ship of state ruled by its helmsman, was acquiring a new layer of meaning. Ships had become the focus of an intense interest in mechanics and technology, which was absorbing, indeed obsessing, rulers right across Europe. Historian Lisa Jardine explains:

"The rich, the wealthy of all kinds, the aristocracy, everybody wants to own a bit of technology - something with cogs and wheels and winding bits. A clock - a very ornamental clock - or a very ornamental position-finding instrument. Jewelled, gilded, they survive and you can see them in our museums. It was fashionable to own scientific instruments because they were the means of expansion, discovery. Clockwork is fundamentally European and it develops in the early sixteenth century, at least on a small scale. It's all hand-worked, it's not mass-produced at all, it's minute craftsmanship and it's mostly done by gold and silversmiths. It immediately fascinates everyone that you can wind something up and it goes without you touching it. Clockwork is magic in the sixteenth century."

Magic it may have been, but clockwork was also big business in sixteenth-century Germany. In our ship, the greatest technical skill is not the modelling or the gilding of the galleon itself, but the precision engineering of the clock and the automated moving parts. Contemporary observers repeatedly stressed the precision, the orderliness, the grace of mechanisms like this one, which embodied the ideal of the early modern European state - as it ought to have been and so rarely was - with everything working together harmoniously under the control of one guiding idea and one beneficent sovereign. And its appeal went far beyond Europe. Automata like our galleon were presented as gifts to the Emperor of China and to the Ottoman Sultan, and were greatly prized. After all, what ruler, from Dresden to Kyoto, would not gaze in delight as figures moved to his command in strict and unswerving order? So unlike the messiness of ruling in the real world.

Even in the sixteenth century, automata like this are far more than just boys' toys for the rich. They're central to the experimental sciences, mechanics, engineering and the search for perpetual motion, that growing desire to control the world by taking possession of its secrets. Even more fundamental, they speak of that urge to imitate life by mechanical means - which would ultimately be the basis of modern automation and cybernetics. I think you can say that it's around 1600 - so more-or-less when this ship was made - that our understanding of the whole world as a mechanism really begins to crystallise, seeing the cosmos as a kind of machine, complex and difficult to understand, but ultimately manageable and controllable.

The state that this galleon symbolises, the Holy Roman Empire, handicapped by its cumbersome structures of government and weakened by religious division, was heading into very stormy seas. Hemmed in to the east by the Turks, it was about to be overshadowed by the Atlantic-facing states of western Europe - Portugal and Spain, France, England, the Netherlands. These states, backed by the new ocean-going technologies represented by this galleon, were embarking on a dialogue with the rest of the world which would make them rich as never before, and which would ultimately overturn the balance of power in Europe.

Sailing in ships like this gilded galleon, they would encounter kingdoms and empires around the world whose sophistication dazzled them, with whom they would trade, whom they would often misunderstand, and some of whom they would destroy. These ocean-going expeditions have, in large measure, shaped the world we live in today.

In the next programme we'll be looking at the first part of the world that these new ships allowed the Europeans to visit. We'll be in Nigeria, more precisely in Benin with the famous bronzes.