The National Gallery exhibition doesn't encourage religiosity, however. It's too thorough. "Rembrandt By Himself" has 30 paintings, many etchings and a few drawings: a body of work. There are one or two major omissions, for instance the Frick Collection self-portrait. But almost everything that might qualify is present, including several doubtful cases. There are pictures perhaps not by Rembrandt. There are pictures, more tellingly, perhaps not of Rembrandt.
The usual story of Rembrandt's self-portraits is in two parts. Part one: in his youth, in his prime, he paints confident, sometimes openly boastful self-images - the successful artist shows off, acts up, dresses up, pulls faces, cuts a figure. Part two: from his mid-forties, as he gets older, goes broke, is bereaved, the artist subjects himself to intense self-scrutiny, drops the masks, pulls down vanity, looks deep, becomes one of the all-time role models of honesty. He died, aged 63, in 1669.
Yes: the late self-portraits are obviously the more intense. But it's not that he stops performing then, and tells it straight. What makes the Rembrandt of the self-portraits an exemplary Me is precisely that he sees the self as something plastic and changeable, sees so many potentialities in one face. His honesty is recognising multiple personality disorder as, within limits, the normal state of affairs. He etches himself in oriental dress and "orientalises" his physiognomy too. And in the late works, the performance does not let up.
In some ways, it gets more extreme. The distance between the Washington Self-Portrait with Beret and Turned up Collar (1659) and the Cologne Self- Portrait as Zeuxis (1662) is huge. They're hardly recognisable as the same man. In the one, a look of miserable shame or disappointment (modern dress, but it might be St Peter at cock-crow). In the other - supposedly laughing - an expression of almost Goyaesque vacuity. But it also gets more elusive. In each one, I've missed out a whole range of undertones.
Or is this self-searching our illusion? The Rembrandt scholar Ernst van Wetering argues in the exhibition catalogue that Rembrandt would not have seen the pictures assembled in this show as a contained or continuous body of work, let alone a project. He didn't have a conception of self- portraiture as self-exploration (a 19th-century development). He painted his own face for several different reasons - to study facial expression, as a model for paintings of "characters", self-advertisement, to supply a market for images of famous people (which included artists). The implied, tactfully unstated conclusion of this argument is that the present exhibition is arbitrary and misleading.
That might be true. But the practical and economic functions of a picture may not be the only reasons an artist finds for painting it. Other reasons may emerge in the act of painting. The fact that Rembrandt's self-portraits weren't - as once thought - painted just for himself, as a private kind of therapy, but rather for a public audience, doesn't necessarily mean that they weren't also intimately self-scrutinising.
Again, one can set out historical arguments - which usually rely on contemporary written evidence - about what could and couldn't have been on Rembrandt's mind. But pictures themselves are evidence. And it's clear at least that, whatever straightforward functions they may have had, the late self-portraits exceed those functions. Compare them with the selection of self-portraits by other Dutch artists, shown in the last room.
Imagine that these self-portraits were in fact all portraits - portraits, say, by different hands. What would we know about the sitter? Well, for one thing that he was a chief, a man of power. Nor do Rembrandt's self- portraits dispel that impression. It's not so much that, in earlier pictures, he dresses up as kings and potentates. It's more that, in the later ones - however honest - it's hard to imagine a more commanding pictorial presence. He yields to no one. The Kenwood House Self-Portrait with Two Circles is an image of colossal grandeur: the Kenwood Chef.
Does it matter that they are self-portraits, by the same person they're of? How much would be lost if we took them as a series of fictional "characters"? There'd remain a sense of exploration. In fact, without the nudging sense of Rembrandt's self behind it all, you'd see Rembrandt the more clearly as the virtuoso experimenter in facial expression. What a gallery of impersonations. He could be anyone. He could get any look.
What did Rembrandt look like anyway? It's hard to say. Is this because he kept doing himself different ways? Or because the face is so famous that - like the Queen's - we can't see it as a face of any particular type? Or is it because Rembrandt's features really aren't very strongly defined? But some pictures - such as the 1652 Vienna Self-Portrait - surprise because he definitely looks like something. He looks Dutch.
So what is Rembrandt's depth? An illusion? One essential component of this quality is clear enough. Rembrandt in the later self-portraits never looks on top of the world. This is essential. The feeling of depth requires "marks of weakness, marks of woe", to use Blake's words. Or, in our own words, signs of anxiety and insecurity. Or, to use a slightly different idiom, a troubled conscience, a sense of sin and its wages. And that sounds like a language Rembrandt might have been perfectly fluent in. In fact, it seems very odd to suggest that self-scrutiny would be an alien practice to someone living in a vigorously Christian Protestant culture.
Self-scrutiny - and then mercy. The achievement of the late self-portraits, their sublimity, is in the way they do both sides of the Christian deal. The mortal sinner is exposed, unsparingly revealed, and at the same moment pardoned, spared, forgiven. Rembrandt plays a double part: both sinner and Jesus. He paints the face he hopes Jesus will see - faces of hopeful penitence, with their frank, appealing, near-tearful eyes. Or call it simply cuddliness: you want to give the old boy a great big hug.
But the late faces have plenty of aspects that are neither sad nor sorry: humour, grumpiness, quizzicality, pride, doggedness. The stubborn, unregenerate self? Admirable, defiant humanity? Penitence and grandeur? Well, you can moralise Rembrandt until the cows come home according to preference. And this inconclusiveness is the real trick of depth. These faces deal in tensions and ambiguities whose very unresolvability is what encourages ideas of "the self as journey", a sense of mysteries never to be plumbed.
Perhaps that sense is anachronistic, Romantic. But for Rembrandt, a supreme dramatist of the face, such unresolvability would be the pitch of his art. It may be that Rembrandt's "deep self" was a kind of technical discovery, the unforeseen but extremely interesting result of playing about at the limits of the facial repertoire.
The exemplary Me? The merchandise for "Rembrandt by Himself" includes a Rembrandt artist's beret you can buy and wear. It doesn't include, unfortunately, a Rembrandt mask.
`Rembrandt by Himself': National Gallery, Trafalgar Square; from tomorrow to 5 September; open every day; admission pounds 7, concs pounds 4.50Reuse content