So do I. Perhaps gallery directors were reluctant to lend because they didn't see the point of Miller's exercise. Basically, he's hoping to explore the use of mirrors in Western European art since the 15th century. On Reflection contains some curiosities and fascinating comments from Miller himself, but the show lacks direction, and makes no strong overall point. It's also short of truly first-class pictures. In many ways, the catalogue is better than the exhibition, for there we find many pictures that have interested Miller, yet are not displayed in Trafalgar Square.
First among the absentees must be Manet's Bar at the Folies Bergere, surely the grandest of modern pictures to use the mirror as a part of its overall theme. And then we miss many other works reproduced and discussed in the catalogue - Dutch still lifes, for instance - Seurat drawings, Millais's Bubbles, Velsquez's Las Meninas, which is one of the least borrowable paintings in the world, Magritte's portrait of Edward James, Picasso's Girl before a Mirror, as well as paintings by Pollaiuolo, Holman Hunt, Bonnard, Degas, Durer, Rembrandt, and many others.
These are disparate artists, and it's not surprising that Miller's comments on their pictures are partial, and take little account of art-historical knowledge. The paintings in the actual exhibition are also disparate. Many of them are of little consequence. There are some undisputed masterpieces, works of the highest order: Velsquez's Rokeby Venus, Van Eyck's Arnolfini Portrait, Rembrandt's Woman Bathing in a Stream and Ingres's Madame Matessier. But these paintings all belong to the National Gallery. They are familiar to every one of us and do not gain in beauty or significance by being hung in their present context. Other National Gallery pictures are Parmigianino's Mystic Marriage of St Catherine, Samuel van Hoogstraten's popular peep- show box, Velsquez's early Kitchen Scene and so on. In all, there are 17 National Gallery paintings in the exhibition. We normally see them for free, and visitors who pay the pounds 5.50 admission fee (concessions pounds 3.50) may feel overcharged, especially if they also buy the catalogue, which costs pounds 14.95.
Other well-known pictures from British public collections include Sir Joshua Reynolds's Self-Portrait (National Portrait Gallery), Whistler's The Little White Girl (Tate Gallery) and Matisse's The Painting Lesson (Scottish National Gallery of Modern Art). I looked for paintings unknown to me with this sort of quality. There are none. Canvases by Alfred Stevens and Gustave Caillebotte represent second-generation Impressionism at a low level. Late Pre-Raphaelite paintings by JW Waterhouse and Edward Burne- Jones add to the depression. Why did Miller not think of borrowing Millais's Ophelia from the Tate? This could be interpreted as a mirror painting, and even the curve of the upper part of its frame, common in mirrors of the day, suggests that its natural home should have been above a mantelpiece.
Millais's very clever picture, which has a bright sheen over it - for once, we can legitimately use the word "brilliant" - indicates that mirror paintings came to some sort of a crisis in the mid-19th century. Previously, they had been smart, lively, often paradoxical. With the approach of the symbolist period they were likely to be lugubrious, especially if their artist also decided to paint a landscape, as happened with Burne-Jones and others. Paintings that depict mirrors are by their nature interiors, and are most likely to succeed when they come from a bourgeois or courtly background and have a fine sense of fashion and style.
Jonathan Miller, who I think lacks such a sense, totally avoids the French (and Flemish) 18th century, the first area most of us would have explored when looking for a certain kind of mirror painting. One would leave the Sainsbury Wing basement with more of a spring in the step if Miller showed any liking for French frivolity. Alas, he is absorbed by the psychology of perception. Miller has not approached his exhibition as a lover of art. He regards painting as the subject of scientific curiosity.
Occasionally, though, he hits the mark. Art historians have always wondered about the inlaid scene in Velsquez's Kitchen Scene, in which we discern Christ blessing Martha and Mary. Is this vignette a painting within a painting, a view through a window, or a scene that is witnessed by us (as spectators) through Velsquez's depiction of a mirror? This last, says Miller. He knows it's a mirror because Christ blesses with his left hand rather than his right.
Christ and Christianity do not seem to go well with mirror art, yet another subject unexplored by Miller. Christ's luminous reality is not best portrayed by means of paradox. For paradox is central to art that makes use of mirrors, while Christianity is about certainty of vision. One of the least certain paintings in the show comes to London from St Petersburg. I reproduce it because it's so little known. What is going on? Who painted it, and in what circumstances? Miller answers the former question, not the latter. His catalogue ignores such matters, and this is the first time that the National Gallery has ever exhibited a picture without showing any interest in its date or author.
National Gallery, WC2 (0171 839 3321), to 13 December.