THE ABILITY TO SAY two things simultaneously and be comprehended is unique to music and, therefore, to the human ear. That is a strict definition of counterpoint. To extend this principle to fiction, where a different sensory organ – the eye – is involved, is a radical act.

Take the 34th chapter of Julio Cortázar’s Hopscotch in which two narratives alternate, one in the odd-numbered lines, the other in the even. Or Vladimir Nabokov’s Pale Fire, in which the poem, commentary and index demand to be read together in a constant shuffling between pages, their interaction a gradual enlightening.

J. M. Coetzee’s new novel, Diary of a Bad Year, extends the discreet revolution that he has mounted in fiction since The Lives of Animals to the very form and shape that the novel takes. Each page is divided into three sections, containing different threads, or voices, running concurrently.

The topmost contains small essays, entitled Strong Opinions, in the first half of the book, on topics such as the origins of the state, music, democracy, terrorism, Tony Blair, al-Qaeda, Harold Pinter, paedophilia, Guantanamo Bay.

All purport to be contributions by the protagonist – like Coetzee himself, a South African novelist, with the initials J. C., now living in Australia – to a collection of opinions from renowned intellectuals to be published in German. The second set of essays, entitled Second Diary,are more personal, philosophical and meditative: on the writing life, on having thoughts, on birds, Bach and Dostoevsky.

The second third of each page is a first-person account by the 72-year-old J. C. of how he meets a beautiful woman, Anya, in the laundry room of their building, asks her to type out Strong Opinions for him and falls in love with her.

The last third is Anya’s first-person perspective of her involvement with J. C. and his project and of her relationship with her investment consultant partner, Alan.

Alan takes an excessive interest in the friendship between the old man and his girlfriend and the stage is all set for a collision, not just the age-old one between two men enamoured of the same woman but also between the old order and the new, socialist intellectual versus neo-liberal grabber, quietist thinker versus brutal man of action.

Coetzee is redrawing the contours of the novel and taking it places that it has rarely been before. Always a fluid, generous form that can smuggle in pretty much anything within its folds, in this master’s hands the novel receives a formal redefinition. How far can plot and narrative be dispensed with to accommodate the intellectual and political analyses that are commonly the preserve of other genres? How can the structure be bent and reshaped to tell a complex tale and simultaneously take the pulse of democracy in the age of late capitalism?

Never less than an uncompromisingly cerebral delight, this book offers manifold exaltations, one of which is the ways in which the three strands braid with each other, some of the linkages metaphorical, some gradually illustrative in oblique ways, others musical in how they pick up tones, variations and themes.

But this is no game: the quietly melancholic meditation on ageing and mortality and the way that it inflects the interaction between J. C. and Anya could break your heart.

Springing from “the disgrace of being alive in these times”, this book is, surprisingly, not as bleak as Coetzee’s earlier work – there is the whisper of redemption here, both creative and personal, and it achieves an unexpectedly lyrical timbre in the introspective essays of the Second Diary.To witness new possibilities flowering in this cross-pollination between fiction and nonfiction, to listen to its reframing of the question “How does one live?”, and to its answers, is to be exhilarated.

DIARY OF A BAD YEAR by J. M. Coetzee

Harvill Secker, £16.99; 304pp

Buy the book here for £15.29 (free p&p)

Times Recommends

• The Sunday Times 100 best holiday reads
• What will we be reading this summer: the booksellers predict
• Literary festivals: a survivor’s guide