Adjustable pegs for all holes: The less qualified a minister appears, the more suitable he or she may be for the post, argues Mark Lawson

As a baritone who has given recitals on television, Peter Brooke is the first minister with responsibility for the arts who is qualified to sing in public on state occasions. Yet despite this distinction, he has been widely regarded as an unlikely replacement for David Mellor as Secretary of State for National Heritage. The loud, CD-collecting Mr Mellor was seen as 'arty', while the patrician history buff Mr Brooke is not. This perception leads those in the arts to fear the new minister will be less sympathetic and effective.

But the example also touches on the wider question of whether it is better for a new minister, in relation to his or her responsibilities, to be a well-thumbed book or a blank sheet. If we expect an arts minister to be arty, should a health minister be fit? (Kenneth Clarke wasn't) Must those running economies be numerate? (Alec Douglas-Home, when First Lord of the Treasury, reportedly found matchsticks a help in tricky fiscal calculations.) How dangerous a thing is a little knowledge?

On the side of ignorance - or, more politely, unfamiliarity - is the view that a ministerial career is a game of self-education, rather than a demonstration of stored knowledge. If a reshuffle occurs while Parliament is sitting, a new minister may be answering Commons questions on behalf of his or her new department within 24 hours. Spectators know that the politician is reading answers prepared for the previous incumbent, but the point of the exercise is to demonstrate the speaker's mock authority. It is the main reason why so many barristers prosper in British politics.

Supporters of the don't-know approach to legislation would argue that a minister needs only speed of learning and an alert mind capable of judging between the different lobbyists under his charge. In the present administration, Kenneth Clarke is a good example of such a ministerial all-rounder, plausible enough in charge of most departments, but never responsible for either of his pet subjects: Sport and Food.

Other politicians are pigeonholed by biography or image. The most comical example occurs when Michael Heseltine is mentioned as a potential Chancellor. 'Not good on money,' Tories mutter, despite his estimated personal net worth of pounds 40m. At a lower level of handicap, Glenda Jackson, the new Labour member for Hampstead, will struggle to avoid typecasting to Heritage in any future ministerial career.

The arts portfolio (now expanded as Heritage) provides an interesting test case, having in recent years alternated between the knows and the don't-knows. Two flamboyant first-nighters (Norman St John-Stevas and David Mellor) have been interleaved with three relatively anonymous non-specialists: Richard Luce, Tim Renton and Peter Brooke.

To identify with their subject as much as David Mellor did with the arts, a health minister would have to submit to major operations daily and spend evenings emptying bedpans. Yet it can be argued that Mr Mellor's deep love of classical music, his fanatical concert attendances, made him an imperfect person to adjudicate between the claims of rival orchestras. You might see him as The Man Who Knew Too Much.

Compare him with Richard Luce, a Foreign Office specialist reshuffled to the arts between 1985 and 1990. When I interviewed him early in his ministership, he spoke of the culture shock of his new job. At Foreign, he said, someone would wander in and murmur: 'War's broken out, old boy'. But in the arts world, people who came to see him about the most minor matter would stand on his desk and shout as if war had broken out. He never fully adjusted to the artistic temperament, but, in persuading the Treasury to schedule arts-funding three years ahead, achieved one of the more significant victories in the position.

So regret over Mr Mellor's departure should not obscure the case for the non-specialist. Peter Brooke's career already provides one example of how casting against type can work. I was one of those who thought his manner - heavy with English attitudes and history - made him an odd, even offensive, choice to serve in Northern Ireland. However, against the baseline of inevitable final failure, his record in Ulster looks impressive.

Perhaps the last word on the subject should be that when Mr Mellor resigned last week, a name began to circulate at Westminster of a possible successor, superficially ideally qualified to preside over arts, sport and television. He was a novelist and playwright, a prominent art collector. He had been a star athlete and had been frequently involved in broadcasting. And he took the Tory whip.

His name? Lord Archer of Weston-super-Mare. Those whose work falls within the Heritage department's remit might well settle for the non-specialist Mr Brooke.