We are already aware that the Millennium Dome will be capacious. Every schoolboy knows (provided he can actually read) that you could fit Nelson's Column under the Teflon canopy and surround it with four Albert Halls. But an equally pertinent question would be: "Is it big enough to contain Peter Mandelson's ambitions?" And, from his perspective at least, the answer seems to be a decided "yes". The Minister without Portfolio has taken possession of the scheme. He reportedly refers to it casually as "my Dome" and far from maintaining a cautious distance between himself and a project which could easily bite the hand that feeds it, he has repeatedly jumped the safety moat. If it all does go wrong it will be virtually impossible for him to claim that he wasn't at the heart of the failure. And this needs explanation, surely. It may be that his admiration for his grandfather (who masterminded the Festival of Britain) has added an emotional allure to this task but there must be more to it than that.

We shouldn't rule out the possibility, first of all, that the possession has worked in the other direction entirely - that Mr Mandelson has succumbed to building fever, a delirium caused by the intoxicating fumes that rise from architectural models. It is an occupational hazard for architects, naturally, most of whom live their lives in a haze of never-to-be-realised magnificence. But architects are inured to the effects by repeated exposure, are far better able to maintain some notion of reality in order to survive the inevitable disappointments.

Outsiders often have weaker heads. When I worked at the BBC, for example, it was widely believed that the career advancement of Dick Francis, then head of radio, had been finally derailed after his seduction by a Norman Foster design for a new Broadcasting House. This was to occupy the site of the old Langham Hotel and it would have been a wonder - "responding to but not overwhelming" All Souls opposite, providing a "diagonal processional galleria" from Cavendish Square through to the flagship of public service broadcasting. Norman Foster came in to address staff about its potential glories, which included glass-walled recording studios to reveal broadcasters to their public and a U-shaped lift, which would carry workers between any floor of the old building and any level of the new. Such a lift had never been built before and seemed to some of us a slightly over-engineered substitute for the zebra crossing which had given years of maintenance- free service, but it was all part of the fantasy of advancement and achievement such endeavours generate, the bliss of tangible progress.

You can see that the Greenwich site is heady stuff in this respect. From toxic dereliction to wonder of the world in just a few short years; if it works it will be the make-over of the decade and it will reflect on its begetter a glow of mastery and control. Those who wonder why an able politician should pour all his energies into the erection of a glorified big top have to take account of the fact that the big top might be seen by Mr Mandelson to contain the one thing which he conspicuously lacks - public acclaim and even (let us dream a little along with him) public affection. (I don't want to be casually snotty about the Dome, incidentally: even in its skeletal state, a crown rack of lamb without the meat, it already inspires awe by its sheer scale. If Mr Mandelson has lost his heart, it is not to a mediocre edifice.) So we may have one speculative answer to the question we began with - in career terms the Dome may represent a zig which will only make obvious sense in the light of the succeeding zag, the route to high office often requiring some crab-like motions.

But it is worth remembering, too, that questions change their meaning depending on who is asking them. Imagine that same initial query put by Tony Blair, for example. It would, I think, sound a good deal more calculated and strategic and it is difficult to believe that Mr Mandelson has not taken that into account. In The Prince Machiavelli refers at one point to the admirable utility of the French parliament in insulating the king from public hatred. "From this," he writes, "we may draw an important conclusion: that princes should entrust unpopular measures to others, and reserve popular ones for themselves". On the face of it, though, Tony Blair seems to have done precisely the opposite - he has taken on the task of pushing through welfare reform, a potentially explosive task, while his trusted lieutenant is made Minister for Bread and Circuses. Never mind that the Dome is turning out to be a singularly unpopular project (a contempt reinforced almost daily by comedians, for whom its bulk and vacuity make it an unmissable target) that couldn't necessarily have been foreseen at the time when Mr Mandelson was given his job. But when you think about it the Dome took a sizeable stone out of Tony Blair's shoe. The Prime Minister's gifts of incredulity are considerable - as demonstrated by his ingenuous shock when anyone questions his good intentions - but even he must have recognised that the nation did not love Bobby as he did, never mind his colleagues in the Labour Party. And once the task of election was over it was difficult to see to what task Mr Mandelson could be applied without generating a persistent screech of internal friction. The job of supervising the Dome, safely beyond the pale of government policy, and ambiguously poised between reward and exile, could hardly be bettered as a solution. Mr Mandelson's friends can present it as a great opportunity, fraught with dangers that only amplify the eventual achievement, while his enemies can relish the diet of scepticism and contempt he will be obliged to consume for the next two years. It may well be staggeringly expensive, then, but in one respect at least, the Dome is already fulfilling its function.