By suspending the normal rules of earth-bound weight and motion, swimming pools bend certain rules of mental operation too, presenting possibilities for divine transformation and fatal transgression. Their creative potential often takes perverse and sometimes cruel forms. A Barbara Laing photograph from 1991 features a mule falling through the air towards a tank of water during ‘The World’s Only High-Diving Mules Show’ at the New Mexico State Fair in Albuquerque. Penned into a grandstand and shading their brows, fairgoers watch expectantly. One marvels at the bizarre freak-show machinations that brought this animal to its improbable plunge.

All swimming pools, however, deal in the unnatural. Southern California is the modern heartland of this glorious folly. Roman Polanski’s Chinatown (1974), in which the diversion of water away from Owens valley to Los Angeles is likened to an incestuous act of rape, still resonates. The city is now precariously fire-whipped, yet remains irrigated by dreams of oases in the desert as architectural firms woo their clients with rippling designer status symbols, above all the almost ubiquitous infinity pool that seeks to shimmer away the very boundary between earth and heaven.

Two new books invite us to reimagine the pool’s evolving cultural status. Splash is a clinically luxurious boutique of contemporary pool design, in which people are almost wholly absent and there are in fact no splashes. By contrast, The Swimming Pool in Photography is an astonishingly rich album of boisterous visual pageantry, documenting those who frolicked about the pools of the 20th century.

The function of swimming pools has never been limited to swimming. In the introduction to Splash, Annie Kelly traces their origins back to wonders such as the Great Bath of Mohenjo-daro, built in the third millennium BC in what is now Sindh in Pakistan, which may have been religious in purpose. The Greeks and Romans built pools for athletics, hygiene, keeping fish – hence piscina – and that ambiguous activity known as bathing (Christ’s College in Cambridge still refers to its own, dating from the 17th century, as a ‘bathing pool’). Swimming was shunned by most early modern Europeans, who regarded the talents of Asian, African and American divers as prodigiously alien; the titular character of Thomas Shadwell’s mocking 1676 play The Virtuoso thus taught the theory of swimming but not its practice. It was only in the early 20th century that swimming became common in the West through programmes of mass exercise in a eugenic age ultimately haunted by fascist visions of idealised neoclassical bodies. Photographs of divers taken at the 1936 Berlin Olympics by Leni Riefenstahl, who filmed Greek statues morphing into German athletes in Olympia (1938) and later shot underwater movies, document their disquieting mutation from human forms into clouds of bursting bubbles. Not for nothing did William Randolph Hearst invite Johnny Weissmuller, Olympic champion and star of Tarzan, to offer swimming lessons to guests in his Neptune pool at Hearst Castle.

While Splash’s empty pools yearn to be stared at more than swum in, The Swimming Pool in Photography glories in the giddy reveries of cavalcades of pool-goers. There are those who lie mesmerised by the sun, dying to cool off after burning up; those who perch on diving boards giggling and sipping drinks; and the many who stride the poolside like a catwalk. Pools bend the rules. Clothes slip off, skin glistens, consciousness heightens. A dreamlike scenario unfolds. Martine Franck’s photo of a boy in a hammock gazing at sunbathers round the elegant curves of Alain Capeillères’s pool in Le Brusc, near Marseilles, make those curves seem like the contours of his mind. A shot taken through the glass floor of a rooftop pool in Shanghai evokes the dream of swimming as flight by juxtaposing a swimmer with a jet tearing through the sky overhead. Yet other pools just seem extensions of everyday life. Guy Le Querrec’s portrait of Budapest’s Széchenyi Medicinal Bath features people chatting and playing chess in the water as though lounging at home on a sofa or in a social club.

Postwar American pools call up poignant visions of mass aquatic escape. These public pools were very often racially segregated, yet their promise was egalitarian. The technicolour paradise of the Tahiti Motel pool in Wildwood, New Jersey, is easily dismissed as boobish kitsch, with its palm trees drooping into a boxy, peach-tinted courtyard. But it was still an oasis. The dalliance between the pellucid and the lurid, the vulgar and the godlike, turned suburbanites into bronzed Poseidons, at least for a while. Filmmakers, however, could not resist casting swimming pools in parables not of baptismal rebirth but paradise lost. In The Swimmer, based on John Cheever’s story of the same name and released in 1968, Burt Lancaster’s fallen hero wants to swim home via a series of private suburban Connecticut pools – an unnatural ambition that symbolises his grand self-delusion. In La Piscine (1970), the pool itself turns from oasis into murderer, helping Alain Delon drown Maurice Ronet.

Despite their status as modernist exercise machines, swimming pools can still inspire baroque visions of puzzle and paradox. There are photos of cars submerged in suburban pools, ‘parked’ in the drink by drunks, and of swimmers studied by onlookers through portholes like fish in an aquarium. Leandro Erlich’s cunning 1999 installation Swimming Pool consists of a pool that contains no water except on what appears to be its surface, trapped in a thin sheet of glass, allowing fully clothed visitors to perceive water-blurred figures above and below. At the Hacienda Puerta Campeche hotel in Mexico, a ruined building has been flooded to create a fantasy where guests can walk through some rooms and swim through others. Such playful inversions of wet and dry evoke human ingenuity in mastering water yet also scriptural floods, divine punishment and ecological catastrophe. The sight of ocean waves crashing over the pool at Bondi Beach in Sydney vies with portraits of pools abandoned to weeds and cracks as images of the end of the world.

We now live in the age of the infinity pool. The bright curves, sugary tints and gay social melee of the 20th century have given way to darker, squarer tubs where the edge of the pool is designed (at least in theory) to vanish into the horizon. The jolly bourgeois riot of collective public bathing has yielded to an immersive solipsism at once outward and inward: the infinity pool bather often looks away from others to snap a selfie showcasing the view behind them. Kelly is one of the few humans to appear in Splash, photographed standing at the edge of a Balinese infinity pool, gazing out to sea, her back to the camera. Hers is a voyeuristic album of an invisible elite’s sparkling private paradises, utopias whose very form disavows social context.

If infinity pools represent one of the ways we swim now, our dreams of aquatic transformation are timeless. How we understand those dreams, however, varies. The paradoxical urge to discover something essential or transcendent about our natures through artificial waters is powerfully reasserted, for example, in Deanna Templeton’s recent portraits of individual friends swimming naked in Californian pools. These are serene, intimate and graceful. But Emma Hartvig’s group portraits of synchronised swimmers in gleaming white bathing-suits, performing their magnificent mechanical ballet, capture rather better the fact that the pool is always a work of art, not nature.