In this expectancy of centennial change and renewal, how does the present day compare? Unlike all previous such periods, today we are getting an architecture which has been widely predicted for half a century or more, but relatively little built. In 2001, Nicholas Grimshaw's Eden Project in Cornwall, an eco-ark looking like a 1960s vision of a Moon city, is absolutely appropriate: this, people used to think, is what architecture will be like in 2001. It just took a while for affordable technology to catch up with the Buckminster Fuller theory. It is therefore not surprising that the strand of English architecture still known as high-tech is best represented in the Millennium projects: Lord Foster's Great Court at the British Museum with its toroidal latticework roof turns Sydney Smirke's Round Reading Room into a flying saucer, while his Great Glasshouse in Wales is the landed craft itself.

We also find the architecture of a post-industrial age, when power stations become art galleries, worked-out claypits become botanical gardens, redundant steelworks and warehouses and pumping stations become museums of one kind or another. At the Tate Modern they called it "Power into Art", as if this was a conscious reversal of Futurist thinking. The emblematic moment was not in London, however, but Gateshead. Once the honeycomb of silos had been gouged out of the interior of the former Baltic Flour Mill on the quayside facing Newcastle across theTyne, there was a moment when the space stood empty and unroofed, awaiting the insertion of the new galleries. At this moment, the space was colonised by the artist Anish Kapoor with his titanic stretched-fabric installation. Art had taken over from industry.

No less than the arrival of Anthony Gormley's Angel of the North on the site of former pit-head baths on the edge of town, this told you that Gateshead was deadly serious about cultural regeneration. Equally telling in its way is the project known as the Falkirk Wheel. Providing a vertical link between two restored canals to provide a navigable waterway from Edinburgh to Glasgow, it self-consciously assumes some of the language of Georgian and Victorian industrial structures - but utilises new technology in the cause of leisure. Tourism, therefore, is our post-industrial revolution. The gamble is that tourism will flow out from its traditional non-industrial bases to occupy the ground vacated by manufacturing, attracted by this or that new landmark. There have been some high-profile failures in this area so far: cultural regeneration is by no means a sure thing. But at the very least, as in the indoor-outdoor communal spaces provided by Glenn Howells' Market Place arts centre in Armagh, it provides hope, sometimes in extreme circumstances.

Leisure: this is what informs all our good and less good cultural environments. We do not see too many Millennium factories. There are no Millennium farms. There is precious little Millennium housing and the only Millennium office blocks are those with meaningless developers' names. In style terms, there is no issue: everything is "modern", even if that term spans a huge divide from classically-pure modernism to the chaotic forms of Daniel Libeskind. No, style is not the crux of the matter. Space is. Anything that is to with free time is granted its measure of free space. Especially, though not exclusively, if that space is in the context of a cultural or lightly educational institution.

In a post-industrial environment, the arts centre and the science centre are key. This is why the great public spaces of today - our 21st century agoras - are the courtyards and atria of the museums and galleries, opera houses and concert halls, the climate zones of the botanical glasshouses. Even our modern Colosseums, the latest sports stadia, now have the option of full enclosure. In the open air we discover the promenade spaces of the new pedestrian bridges, the car-free leisureways of boat and bicycle, an explosion of new and restored urban squares.

It is paradoxical that people in the UK in 2001 do not yet feel themselves to be the carefree flaneurs that all the new public promenade spaces, inside and out, imply. Despite our relative wealth, despite the absence of war, surveys reveal us to be anxious, overworked, selfish, generally stressed. We need to relax, calm down, do less hustling and bustling. In which case, it is perhaps feasible to suggest that the new architecture of free space is being created as a healing response to a dissatisfied society's demands. This is, of course, an ancient remedy. The Colosseum was built to keep a troublesome population happy with the status quo. It worked for quite a while.