A PERSONIFICATION of Geometry, unable to conceptualise the metaphysical; or an angel who is too fat to fly? Who is the figure who dominates Albrecht Dürer's cryptic print Melencolia I? In a splendid half-hour of radio, the art historian Dr Janina Ramirez investigated this most enigmatic of Renaissance images in Melencolia (Radio 4, Monday of last week).

As well as the angel, the picture is full of bric-a-brac: compasses, books, a magic square, a lump of stone. The confusion of stuff brings on the instinctive melancholy of anybody who likes things tidy. It is, as one commentator here put it, "like a skip".

One question I had of the programme, and which I hardly dare ask, since it sounds so childishly simple, is this: Why is this number 1? Did the artist already know that there was going to be a sequel? But the programme dealt in high-concept theories, the most recent of which comes from the scholar Patrick Dooley. The key to Melencolia, apparently, lies in Plato's Hippias dialogue, which deals with the subject of The Beautiful.

In that text, we read of the despair that results from the realisation that we cannot define beauty per se, only identify examples of it. Our angel is experiencing that despair; her books and protractor are useless in the face of the immeasurable.

If, on the one hand, Dürer's work embodies an impotence in the face of beauty, it also displays humanity's ability to create it; and one of the fascinating elements of this programme was hearing about the techniques by which the artist created this print. Dürer's Nuremberg was a centre of Renaissance art and technology; and a small insight into the technical challenge of producing something like Melencolia is illuminated by way of a mistake in the magic-number square therein depicted.

In the first version of the print, the number "9" is rendered in reverse - a reminder that the entire plate from which prints were made would have had to be etched in reverse. If you are the type to get melancholic in the face of other people's brilliance, then Melencolia I may not be for you.

Reasons to be cheerful and sad, in almost equal measure, were provided by the World Service's Assignment programme last week. Educating Ulster (Thursday), presented by Andrea Catherwood, gave us an update on the trend towards non-segregated schools in Northern Ireland - something that the political parties in Stormont pay only lip-service towards, but which is driven on by determined parents.

These parents include people with more reason than most to shun the other community: people such as Jim McConville, whose mother, Jean, was the victim of a notorious shooting by the IRA in 1972. Mr McConville is a strong advocate of integrated schooling, even when, as we saw at Cliftonville Integrated Primary School, Belfast, the religious-education classes are still segregated.

"God doesn't make religion,men do," was nine-year-old Jordan Bell's response when asked what he thought of the arrangements. But, in a society where such schools as his are only seven per cent of the total, his opinion still finds little recognition at the institutional level.