Founded in 1683, the Ashmolean Museum in Oxford is not just the oldest museum in Britain; it can also boast the most identity crises. Time and again it has stood on the brink of dissolution or obsolescence, only for a new version to rise, like the proverbial phoenix, out of the ashes of the old. The latest and already much-feted makeover, which has cost £61m, was not prompted by any major crisis, but is as radical as any of its precursors. A sleek five-storey structure with 39 new galleries designed by the architect Rick Mather has been slotted with surgical precision behind Charles Cockerell's neoclassical temple of the arts, built in 1845 as a showcase for European sculpture and painting. It gives the museum a new heart and lungs.

There is no doubting the efficiency and accessibility of Mather's building. Display space has doubled and far more of the rich and varied permanent collection is on view. Just as striking is the catch-all concept that informs the new galleries and displays: "Crossing Cultures Crossing Time". It is no accident that this slogan is unpunctuated, for this part of the museum is meant to be a free-flowing, postmodern temple to globalisation and trade. Yet reminders of old Ashmoleans loom large - the "cabinet of curiosities", the "palace of art" - making it perhaps the best place in the world to meditate on how the meaning of the word "museum" has changed down the centuries.

The Greek term "museion" was first applied to temples dedicated to the muses, the nine goddesses who inspired practitioners of the various arts and sciences. These temples played host to literary societies rather than having permanent collections, though some devotees may have left copies of their latest poem or pot. It was Aristotle who first used the term "museum" in relation to a collection of objects. In contrast to his teacher Plato, who was obsessed with ideal forms, Aristotle based his philosophy on the observation and classification of material reality, and his teaching institution, the Lyceum, had a study collection of specimens called a museum. This inspired the first great museum, founded in around 290BC by Ptolemy, King of Egypt, in the new city of Alexandria. The legendary institution, with its great library, was dedicated to the preservation of all kinds of texts and objects, both man-made and natural, and accommodated a large team of scholars. Texts, however, were more valued than images or objects. It was accidentally burnt down by Julius Caesar in 48BC.

The ancient idea of the museum was revived, on a smaller scale, in the Renaissance "cabinet of curiosities", and it is with just such a collection that the Ashmolean was founded. The works of nature and man were displayed together, some in specially made cabinets, but the emphasis was at least as much on finding exceptional marvels as in compiling complete series of "mundane" specimens. Entertainment as much as education was the order of the day. So for every systematic collection of Roman coins, local rocks, herbs, tools and machines, there might be a stuffed crocodile and other creatures suspended from the ceiling, unicorn horns and giant bones, and ethnographic exotica brought back by travellers, traders, pirates and proto-imperialists from many corners of the world.

As taxidermy was in its infancy, specimens that would survive were preferred, such as toucans' beaks, the snouts of swordfish and hard-bodied creatures including tortoises, iguanas and crocodiles. The all-powerful Habsburg dynasty, famously ugly through inbreeding, had a penchant for pictures of dwarfs and giants. Peter the Great pickled just about anything, the more freakish the better. They were regarded as the "jokes" of nature. Damien Hirst, with his pickled animals and shelves of pills and shells, would have been even more in demand then than now. Ditto Salvador Dalí.

Stones believed to have health-giving properties, such as coral and bezoars (found in the intestines of cows and other grazing animals), as well as ostrich eggs and nautilus shells, were given elaborate settings, like religious relics. Topographical landscape sculptures were also made: a Bohemian Calvary survives in which the hill is made from lumps of local stone (proustite, argentite, malachite, quartz and fluorite), surmounted by a gold crucifixion scene. Half way up the hill is the mouth of a mineshaft and a miner at work. Mining and metallurgy are evidently God's work, because without them gold crucifixes cannot be made, and because God was the first "artifex" or "maker".

The origins of the Ashmolean collection lie in one of the first great cabinets of curiosities to be formed in England - that of the plantsman and garden designer John Tradescant the elder, who worked for leading aristocrats and King Charles I. Tradescant collected natural and man-made rarities on his travels - "the Bigest that Can be Gotten" - and acquired them from returning travellers. They were exhibited in his house in Lambeth, and could be seen by anyone for sixpence - the price of a pound of butter. The house was popularly known as the Ark, though there was far more than just animal specimens. A visitor on leave from the East India Company spent a whole day "in peruseing, and that superficially, such as hee had gathered together . . . so that I am almost perswaded a Man might in one daye behold and collecte into one place more Curiosities than hee should see if hee spent all his life in Travell". Star exhibits included Henry VIII's cap, stirrups and hawking glove; the "robe of the King of Virginia"; the "masking suit" worn by Queen Henrietta Maria's favourite dwarf; a phoenix wing and a stuffed dodo (some of these are on display in the basement of the Mather building).

The collection was inherited and expanded by Tradescant's gardener son, and he in turn left it to Elias Ashmole (1617-92), who had financed and co-authored a systematic catalogue of the collection in 1656, the first of its kind. Ashmole was a royalist who married into money. He was a true "renaissance man": an expert administrator and lawyer; collector of coins, books and manuscripts; historian of the Order of the Garter; founder member of the Royal Society. He was also an alchemist and astrologer, making predictions for King Charles II. Samuel Pepys described him as "a very ingenious man" of high spirits who enjoyed a singalong.

Thanks to close Oxford connections, Ashmole left his collections to the university, once it agreed to build a home for it in Broad Street. It was a symbol of the empirical new science propounded earlier in the century by Francis Bacon: a museum display was on the top floor, a school of natural history at ground level and a chemistry laboratory in the basement. In charge was Robert Plot, Oxford's first professor of chemistry. Because of its emphasis on "the inspection of particulars", traditionalists dismissed it as a "Knick-Knackatory".

By the beginning of the 18th century the museum (like the university) was in decline, due to absentee and apathetic curators. "Nothing can equal the negligence with which the Ashmolean Museum was kept," wrote one visitor. The displays became increasingly shambolic and filthy, with curators letting paying visitors tramp unsupervised through the dilapidated museum, manhandling and stealing exhibits. Many zoological specimens had to be chucked out. Tradescant's famous dodo rotted away, and only the head and one foot survive.

In the 19th century there were moves to transfer the remaining collections to Oxford's Bodleian Library, which had substantial collections of its own. The trend towards specialisation in museums also endangered the Ashmolean. It teetered on the brink of closure when the natural history and ethnographic collections were sent to dedicated museums in 1860 and 1886 respectively. But the museum didn't go the way of its dodo. Elias Ashmole had prospered because of a marriage of convenience; his museum survived because of its own marriage of convenience to the University Galleries in around 1900. Renamed the Ashmolean Museum of Art and Archaeology, it would be a showcase for national cultures and schools of art, and a repository of beautiful as well as useful and historical things.

The University Galleries had been founded in 1839 to house the university's widely scattered collections of antique sculpture, paintings and drawings. There must have been an element of competition with Cambridge University, for the architect of the galleries, Charles Cockerell, had just finished the Fitzwilliam Museum. Antique sculptures (mostly casts) were displayed on the ground floor, with portraits of Oxford worthies and copies of Raphael's tapestry cartoons on the first floor. Gradually, as bequests arrived, authentic old masters supplanted the undistinguished opening display. This basic format survives today, with antique sculpture on the ground floor and, above, Italian old masters from Giotto and Uccello to Titian and Bronzino. The acquisition in 1841 of a huge collection of drawings by Raphael and Michelangelo for £7,000 hugely strengthened this strand of the collections.

If the cabinet of curiosities marks the first phase of museums, this two-storey display of "works of art" marks the second. It served a practical purpose, placing heavy sculptures at ground level, but the overall arrangement was also freighted with meaning. It underscored the idea that antique sculpture was the bedrock for the best of modern European art, especially that of Raphael and his followers. More subtly, it suggested that modern painting, with its predominantly Christian themes, rose "higher" than pagan sculpture, even if the building that housed them was neoclassical.

During the course of the 19th century, however, museums stopped simply trying to show the peaks of European painting and sought to trace the stylistic development of national schools right back to the "primitive" middle ages. The University Galleries got off to a head start when in 1850 they were given 40 Italian paintings from before the time of Raphael. The most famous of these is Paolo Uccello's perspectival fairytale, Hunt in the Forest (c 1470). These pictures showed, as it were, the origin of the Italian "species" of art that reached its fullest development in Raphael.

James Hall
The Guardian

"Crossing Cultures Crossing Time" is the brainchild of the Ashmolean's director, Dr Christopher Brown, an expert in Dutch and Flemish painting. He was previously chief curator at the National Gallery in London, and while there, rehung the collections so that the Italian schools were no longer displayed as a self-contained unit, but were interspersed with other European art to suggest greater cross-fertilisation. It's a kind of "Euro-hang" that would have been impossible before Britain had joined the European Community. The new Mather galleries, dedicated to ancient and non-western art, want to erode national schools and identity even more radically, and on an intercontinental scale. This goal is spectacularly expressed by the central feature of the new building - a full-height, light-filled atrium which is lined by staircases, traversed by walkways, and punctuated by large and small openings into galleries. Despite the clean minimalist interiors, there are no ivory towers or chapel-like spaces here. Every gallery is a room with an overview.

The justification for all this is supremely macrocosmic: international trade. Giant maps chart the trade routes to and from western Europe, and we are led to believe that trade was and is a major and largely benign driver of cultural change. "Trade generally eased relations between peoples of different faiths and origins"; "By AD400 a network of land and sea trade and communications routes crisscrossed and connected the whole region" (they actually mean the whole world). "Hybrid" artworks, such as Gandhara sculpture, in which Buddhist gods are given ancient Greek bodies and dressed in togas, are seen as exemplary. It's Raphael's Parnassus redrawn by Adam Smith.

A problem with these assertions is that many great traditions or "schools" in art are self-perpetuating, and actively hostile to "trading" ideas with outsiders. Members of guilds were expected to preserve trade secrets. This is what made them distinctive. Look at Michelangelo, slagging off Flemish art (too sentimental, too detailed), Venetian art (Titian couldn't draw), and burning his drawings so no one could steal his ideas (the Ashmolean has a superb group of Michelangelo drawings). Look at the Chinese, keeping the "secret" of porcelain production for centuries, and exporting inferior-quality blue and white china to Europe. Look at Egyptian art (the Ashmolean has a fine collection), scarcely changing for thousands of years. One thinks of Marinetti's remark about museums being places "where one lies forever beside hated or unknown beings".

Here, non-western art and artefacts fully exist only once they are being traded with Europe. To take one example: we are told that Chinese porcelain was first imported in the 1500s and that its "high status and value led the Dutch and English trade companies to capture this lucrative trade". Peerless pottery had been produced in China for thousands of years, with rival kilns clustered around the eastern edge of the country. Yet the ways in which these potters operated in their studios and in their region - the "microcosmic" view - seems to be marginalised. "Doing" Chinese ceramics on the basis of pots traded with western Europe is the equivalent of writing an introduction to Shakespeare concerned solely with the reception and performance of his plays in China.

This makeover should nonetheless be considered a great achievement. Its novel approach certainly does add to the overall interest. The more traditional displays in the old building complement as well as critique those in the new, and vice versa. The clash of museum cultures gets you thinking as well as looking. Intellectual sparks from the new Ashmolean will, unlike the dodo, fly far and wide.