A uniform hangs in the shadows inside the ruined temple, the name printed on it KURTZ. Water drips from somewhere, a voice recites TS Eliot, books lie in bronze light and you notice that this jungle library includes The Golden Bough. Of course it does. It's a book to read at the end of the river.

First published in 1890 by the Scottish anthropologist JG Frazer, The Golden Bough has had a more powerful influence on modern literature and cinema than Freud or Marx. A vast essay on comparative religion, it traced the roots of Christianity in folklore, of science in magic, and did so with the vulgarity of a bestseller. To know that Kurtz, in Francis Ford Coppola's Apocalypse Now, is a reader of The Golden Bough is to see him as a priest-king whom Martin Sheen's assassin must ritually slaughter, himself to become the new King of the Wood.

The chief literary source for Apocalypse Now is Eliot, whose 1925 poem "The Hollow Men" Marlon Brando recites for Dennis Hopper:

"We are the hollow men
We are the stuffed men
Leaning together
Headpiece stuffed with straw. Alas!"

Three years earlier, Eliot had acknowledged his debt to Frazer in "The Waste Land", writing of a "work of anthropology ... which has influenced our generation profoundly; I mean The Golden Bough". Eliot's generation - the modernists - were all victims, survivors or fortunately distant witnesses of the mass sacrificial slaughter of European youth of the first world war. And there is a startling image in The Golden Bough that casts new light on the war's resonance for this generation.

In his central discussion of the ancient near-eastern deity Tammuz, worshipped by the Greeks as Adonis, a corn god ritually mourned on his descent into death each year just as the corn "dies" and is reborn annually, and whose blood stains the ground, Frazer mentions the eerie appearance of the landscape after a terrible European conflict: "In the summer after the battle of Landen, the most sanguinary battle of the 17th century in Europe, the earth, saturated with the blood of 20,000 slain, broke forth into millions of poppies, and the traveller who passed that vast sheet of scarlet might well fancy that the earth had indeed given up her dead."

Frazer makes you see in the poppies of Remembrance Sunday an image of nature bleeding. Over his book hangs a deep pessimism about history. "If mankind had always been logical and wise," he comments, "history would not be a long chronicle of folly and crime." That sentence is key. Frazer sees human thought as capable of leading itself, through the false logic of magic and religion, to devastating cruelties.

Frazer begins his anthropological study looking at a single work of art. "Who does not know Turner's picture of the Golden Bough?" he asks in the first chapter. "The scene, suffused with the golden glow of imagination in which the divine mind of Turner steeped and transfigured even the fairest natural landscape, is a dream-like vision of the little woodland grove of Nemi - 'Diana's Mirror', as it was called by the ancients ... "

In fact, Turner's 1834 painting The Golden Bough, owned by Tate Britain, depicts Lake Avernus in Campania, with the Cumaean Sibyl, but no matter. Turner did also depict Lake Nemi, beside which in ancient times stood a sanctuary of the goddess Diana Nemorensis, Diana of the Wood; votive offerings left there can be seen today in the British Museum. The shrine, explains Frazer, was next to a sacred grove. And it's what took place inside the grove that concerns him.

Why does he invoke Turner? To answer this question is to discover the true nature of Frazer's book, The Golden Bough's golden bough.

Frazer started his book in the 1880s; Turner had died in 1851. Over the course of the book's successive editions (published in two volumes in 1890, it was expanded to 12 volumes by 1915, and condensed to a mere 714 pages in the author's own abridged version of 1922), the very identity of Turner as an artist changed. In his lifetime Turner had been controversial; people were constantly disparaging his "mustard" yellows and "harsh" light. He was famous as a painter of myth and history: a perspective on Turner of which we've almost lost sight. In 1905, the Tate Gallery exhibited a selection of some of the works left by Turner to the nation that had previously been considered unfinished; in the light of Monet it suddenly looked as if Turner had secretly invented impressionism, yet been unable to make this public in the culture of Victorian England.

Frazer was a Victorian and his view of Turner predates the modern preference for form over content. For him, Turner is a painter of stories set in landscapes: a grandiose mythologist. Visit the Clore galleries at Tate Britain and you see Frazer's Turner in paintings whose very titles, such as Apollo and Python, or The Goddess of Discord Choosing the Apple of Contention in the Garden of the Hesperides, are relics of a classical culture we've almost lost.

Gods and monsters populate Turner's art, and for his first audience, his great achievement was to visualise, in a modern, disturbing way, the ancient myths. In the greatest of all his mythological paintings, Ulysses deriding Polyphemus - Homer's Odyssey (1829) in the National Gallery, the ship representing intelligent, rational human aspiration sails away from the towering, formless mountains where the vague, shapeless giant Polyphemus rages in the clouds. Yet the sea is an unhealthy, fiery colour - the location of this adventure was said to be the Sicilian coast below volcanic Mount Etna - and the sea itself might be about to erupt in fire, anticipating the vicissitudes, the deaths, yet to come.

Turner is a doom-laden Romantic - he wrote an epic poem he called "The Fallacies of Hope" - and his vision of Greek myth is darkling. In his painting of Jason, the tiny hero faces a dragon too immense to be depicted, that lurks in a dreadful, ruinous mountain cleft. In his painting of Apollo and Python, the hideous broken body of the snake is more impressive than the god who is associated with reason and order.

In citing Turner at the very beginning of his book, Frazer might simply be announcing the kind of book it is. For Turner already had a history of inspiring baggy books. The biggest and most bonkers of all Victorian non-fiction tomes, John Ruskin's Modern Painters, takes Turner as a departing point for a rollicking journey through art history, aesthetics and even geology, much as The Golden Bough spins off a Turner painting into diffuse realms of folklore. Nor was Ruskin's the only big book inspired by Turner's big art. As if the sublime scale of his imagination were infectious, he fascinated Herman Melville. One of his paintings of whaling ships inspired the mysterious image that hangs on the wall at the Spouter Inn in Moby-Dick.

Just as Ruskin and Melville had found something they needed in Turner, so did Frazer. In late-Victorian Britain, the avant garde in art was "symbolism", the movement across Europe that looked beneath appearances, to the inward self. Classical mythology was seen in a new way by symbolist artists. In France, the painter Gustave Moreau imagined the world of Greek myth as a melting, pustulating psychic domain of febrile desire. If this shocking modernity is visible in Moreau it is still more explicit in Gustav Klimt's Pallas Athene (1898), a castrating goddess painted in Sigmund Freud's Vienna.

British artists not only participated in this movement - they got there first. As early as 1874, Dante Gabriel Rossetti painted Jane Morris, with those mythic lips, as Proserpine, the girl sentenced to spend part of the year in the Underworld and claimed by Frazer as yet another manifestation of the annually dying nature god. And just as Rossetti feasted on the twilight of myth, so does Frazer.

Frazer begins with art because he is an artist. The Golden Bough may be disguised as a sombre work of science but in reality it is a vast prose poem, whose images were to shape 20th-century culture. Frazer's images - of trees, fire, mannequins and slaughtered gods - hang above his pages. He begins with Turner in order to paint a landscape of his own: in deliberate contrast to the golden glowing Italian scene he remembers in Turner's painting The Golden Bough, he paints a grove of darkness:

"In antiquity this sylvan landscape was the scene of a strange and recurring tragedy ... In this sacred grove there grew a certain tree round which at any time of the day, and probably far into the night, a grim figure might be seen to prowl. In his hand he carried a drawn sword, and he kept peering warily about him as if at any instant expected to be set upon by an enemy. He was a priest and a murderer ... "

Frazer is an astonishing figure who connects our own culture with that of late-Victorian England. Transcribing his words I can hear the Doors' deceptively gentle guitar in the soundtrack to Apocalypse Now. The lesson of his debt to Turner is a fundamental one about the "soft" sciences, as physicists and biologists dismiss the human sciences - anthropology, sociology, psychoanalysis - invented in the late-19th century. The lesson, and this is what gives Frazer's book its enduring value, is that they really are soft. Frazer doesn't pretend to be a scientist delivering data; he makes it explicit from his first sentence that he is a human being who lives inside, not outside, culture. This is why, before leading us into the forest where culture begins, he reminds us that somehow humanity's path leads to the divine Turner.