I was lucky enough to cover two huge, international cultural festivals this week.

Scotland loomed large in both. One, in Venice, is one of the most prestigious, the Biennale of visual art, which saw 88 national shows and more than 40 other "collateral" exhibitions open. The other, on Thursday, was the launch of the world's biggest cultural festival, the 2013 Edinburgh Festival Fringe. Both events have similarities: they are large, vibrant and mercurial, a little unwieldy, and can seem intimidatingly complex at first glance.

The 392 pages of the new Fringe programme can prop open a dodgy door. In Venice, the main Giardini gardens are rich and extensive enough, but add the massive Arsenale area plus dozens of shows hidden in the maze of the canal city itself, and the event in its entirety seems uncoverable.

But what both events showed, from the perspective of Scotland, is that this nation is, should we forget or downplay it, a major player at the top table of world culture. There is hardly anything like the Fringe (especially in scale) anywhere on the globe, and in Venice, Scotland's own exhibition, separate from the UK Pavilion, now has 10 excellent years behind it. In Venice, people I met said it over and again: Scotland is brilliant at putting on shows, writing, making music and dance, nurturing and being a home to artists born in the land or elsewhere, and making art itself. In the past 20 years, visual art has become one of the nation's global success stories. This is not just myopic hyperbole: the Scottish visual art scene is respected and recognised worldwide.

It made sense that Fiona Hyslop, the culture secretary, visited the Biennale this year, not only to celebrate the decade of the Scotland + Venice project, but also because Scotland's presence there, and at the alternating Biennale of Architecture, could change radically in the years to come, depending on the outcome of the independence referendum. If the vote is a Yes, Scotland will have a case for its own National Pavilion at what one figure called the Art Olympics. And the UK Pavilion, a neoclassical pile at the top of the Giardini, would become - what exactly? The England Pavilion? (Wales has its own already.) The existence of one of the UK's key cultural bodies, the British Council, would also have to be questioned. The council supports both the UK Pavilion and the Scottish show. It does huge amounts of cultural work throughout the world, and has done much to support Scottish artists and companies. If Scotland leaves the Union, its role and name may have to change.

Ms Hyslop, when I asked her, said she was not in the city to talk about (or pave the way for) a separate national show, but instead to honour the work done and the artists representing Scotland: Duncan Campbell, Corin Sworn and Hayley Tompkins. Earlier this year, the chairman of the Biennale joked that for a show to be deemed national, he has a book of countries and if you are in it, that is fine by him. Is Scotland in it?

Interestingly, next week will see Ms Hyslop's biggest speech on the matter of culture to date, at the Talbot Rice Gallery in Edinburgh.