Picador £14.99 (300pp) £13.49 (free p&p) from the Independent Bookshop: 08430 600 030

The Infinities, By John Banville

In this novel, his 15th, John Banville carries the concept of the omniscient narrator to a logical extreme. His principal narrative voice is Hermes, messenger of the gods - and a knowing and sardonic voice it is. You can't accuse Banville of shirking the large subject, the overwhelming question; but the literary impulse of this cosmic character is tempered by humour, urbanity and a spirited approach. Sometimes in The Infinities, the voice of Hermes is fused with that of Adam Godley, a renowned mathematician fading into eternity after suffering a stroke.

Adam lies in the Sky Room, a timber eyrie built onto the ancient house known as Arden (in Ireland). It is the home of Adam and his second wife Ursula, mother of his children young Adam and Petra - petrified Petra.

All these names, indeed, are slyly, wryly, significant, and here is another. Helen, young Adam's wife, is an object of desire on the part of Hermes' father Zeus, and of various individuals - deluded and denuded. Lord, we might find ourselves muttering, what fools these mortals be.

The scene is set and the action or reflection (not to say Shakespearean soliloquising) follows. The span is confined to a single midsummer's day. The cast is soon assembled: to the dying patriarch and his family are added Ivy Blount, one-time owner of Arden and now a kind of slovenly servant who goes about carrying a dead chicken on which she is about to inflict further violence; Duffy the tongue-tied, rustic cowman; an acolyte of old Adam named Roddy Wagstaff; and a pudgy Pan figure, Benny Grace, an unlikely mythological mischief-maker.

The Infinities is played out as a kind of celestial-cum-earthly comedy, with unsettling undertones. One character is permanently drunk; another ritually slits her arms. Misunderstandings, impersonations and manipulations occur. The infinities - time and eternity, essence and disintegration, "life, death etc" (as Virginia Woolf had it) - are balanced by wonderful particulars: "a fuchsia hedge hung with... intense red blossoms"; the "hush after thunder and before rain and the bird's sudden drench of song". Or Adam on his deathbed, revisiting his childhood, "trudging up a hill beside a high, grey-stone wall. He wears a tweed coat with a half-belt at the back, and a peaked cap, and thick woollen stockings the tops of which are turned down to hide homemade, soiled white elastic garters."

The rage for order is set against the triumph of dishevelment, and the sportive tone occasionally gives way to a bleak view of humanity ("their lies and subterfuges"). But the central drift of The Infinities is to celebrate the world and its infinity of riches. The interwoven texture of the novel, and its unimpeachable poise, are what gives point to its randomness of incident. "How all things hang together," thinks Banville's narrator at one point, "when one has the perspective from which to view them." Yes.

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