THERE'S no doubt which is the best stage in Edinburgh during its annual, month-long Olympian orgy of culture and capers.

Obviously, it is the city itself which, with its compact size, dramatic setting and unpredictable weather, is the perfect backdrop for what is surely the greatest show on the planet.

This was one of the reasons it was chosen by Rudolf Bing, its first director and principal conductor. In the immediate aftermath of the second world war, Bing, an Austrian-born, opera impresario, had visited several English cities in his quest to realise his vision of a city which could play host to a festival whose raison d'etre would be to heal the septic wounds caused by the Nazis.

None quite fitted the bill. Edinburgh, however, that "mad god's dream", as Hugh MacDiarmid described it, was different.

Walking along Princes Street one evening Bing looked up to the castle and was smitten. Instantly, he knew that he had found what he'd been looking for. Here, served on a plate, was romance, drama, history, poetry, myth and something he couldn't quite put his finger on, something in the air, something he could feel but couldn't name. You might sum it up as potential.

Bing's first festival in 1947 provided the cultural equivalent of a visit to Paris for gourmands starved of anything to stimulate the taste buds. There was the Vienna Philharmonic Orchestra under the baton of Bruno Walter, with the incomparable Kathleen Ferrier as the soloist in Mahler's Das Lied von der Erde. The Louis Jouvet company from France performed Moliere and there were productions from Glyndebourne, from whence Bing came, of Le Nozze di Figaro and Macbeth. For performers and audience alike it was a revelation, offering much-needed hope after such a long period of despair.

Sixty-five years on, the Festival remains true to its origins. It has, however, grown not so much like Topsy but like leylandii. Every year, it appears, it gets bigger and broader, expanding its reach and finding new audiences when it seemed it had exhausted all possibilities.

This year, for instance, there have been more visitors from the Far East, from India, China and Japan, than ever before, wandering goggle-eyed around this once sooty and smelly city as if they'd just landed on Mars.

What appealed to Bing is that this is a city in which the best way still to get around is on foot. Early one morning I started my tour in St Andrew Square where there is a tented village. Immediately I was approached by a young woman with hair the colour of candy floss who thrust a leaflet in my face and asked, "Ever thought what Nick Clegg and Macbeth have in common?" I confessed that I hadn't and moved swiftly on.

At the west end of the boulevard lies Charlotte Square, home normally to anonymous financiers but during August, it is given over to the Book Festival. On any given day you can bump into the gamut of the literary world. Crossing the square, I saw an eminent American author whose orienteering skills had momentarily deserted her and volunteered to steer her towards her hotel.

"Is Edinburgh always like this?" she asked, knowing of course that it is not, that in a week or so it will go back to being itself, like someone who's been pole-axed for a spell with flu.

At the Mound, next to the National Gallery, whose Doric columns are covered in giant posters advertising exhibitions featuring Van Gogh and Kandinsky and Picasso, crowds gathered in the late morning sunshine to listen to buskers and watch whoever turns up. One man drew an audience of hundreds, though his act seemed simply to consist of twisting balloons into the shape of poodles. Less popular is a Chinese man, dressed like a Ming Dynasty emperor, who is plucking his giant guitar with what looks like a wallpaper scraper.

Such wanton eccentricity, such boundless bonhomie, is a large part of the Festival's charm and allure. You can, of course, if you so desire, immerse yourself in art both high and low. One minute you may be listening to a comedian in turquoise kung-fu pants telling you he is "UK spokesperson for the Pseudo Sciences", the next being moved to tears by Bill Paterson playing the husband of a wife who wants to end her life because she has cancer.

From the Mound you walk down the Royal Mile to the Tron, serenaded by the likes of Simply the Jest from Exeter advertising their show Middle Class Tripe. In the Grassmarket, there's a man singing country and western songs to no one. Is he a bona fide performer or just rendered lyrical with Buckfast? It's hard to tell. In Middle Meadow Walk there's a man on a tightrope playing a fiddle who doffs his bowler hat to passers-by without falling off. How?

It is a question constantly asked of the Festival itself. How does it come about year after year-after-year? History shows that it has had its ups and downs, its controversies and stale periods, its Jeremiahs and party poopers, its councillors for whom the sight of a bare breast or a penis tied in knots is the cue to start their mouths foaming. Perennially, there are questions over whether Edinburghers appreciate what they themselves have created.

Meanwhile, Festival organisers bleat periodically about a lack of funding, raising the spectre that Edinburgh will be supplanted if it does not continue to invest in what is undoubtedly the world's greatest and biggest event of its kind. It was not so long ago, for example, that Manchester was mooted as a rival, as if throwing money at place can instantly create such a phenomenon.

Now of pensionable age, the Festival and its ever-multiplying offsping ought to be showing signs of wear and tear. But it isn't. It seems to get bigger and better and more popular, inventive and successful.