In his Poetics, Aristotle argued that poetry was a more scientific and serious genre than history. This was because, he said, history is concerned only with individual and particular events. Poetry, on the other hand, is concerned with what might happen: that is, deep and general truths. In the newly revamped Museum of Modern Art in New York, which reopens on 21 October, the march of history, at least as it has been understood by MoMA in recent decades, is out and poetry is in.

Inside the refreshed museum – its gallery space enlarged by 30% thanks to architects Diller Scofidio + Renfro – a radical rehang reverses the museum’s old “Book of Genesis” approach, as MoMA director Glenn D Lowry characterised it. Recent decades have seen the museum organised by way of a stately procession, in which art movements and -isms were shown to have begotten other movements and -isms.

This lucid, but necessarily sealed-off, worldview has now been replaced with the kind of thematic approach familiar to British audiences from two decades of Tate Modern hangs. While still arranged according to a broad chronology, beginning with the 1880s on the fifth floor and descending to the present on the second, MoMA’s individual rooms are organised around ideas, with titles such as War Within, War Without, Inner and Outer Space, and True Stories.

The view of art history on show here is no longer one of straight lines and linear progressions, but one much more like the complex ripples set in motion by pebbles thrown into a pond. No longer will MoMA claim to tell a single story of modern and contemporary art. Every six months, the hang will substantially change.

Into orbit … The Moon, 1928, by pioneering female modernist Tarsila do Amaral. Photograph: Robert Gerhardt/MoMA

Some might say MoMA is letting itself off the hook: no definitive statements are made and everything is allowed to hover provisionally until the next remix. Lowry argues it is returning to the museum’s founding principles. The great first director, Alfred H Barr Jr, wrote: “Nothing that the visitors will see in the exhibition galleries, neither the works of art, nor the lighting fixtures, nor even the partitions, is at present permanent.”

Barr understood, said Lowry, “that the museum was to be a work in progress, changing and evolving as the world of contemporary art changed and evolved”. The museum’s glaciation of its displays came later, in the 1960s and 70s, he said. Nevertheless, even in the brave indeterminate future, there will remain a few constants. Some works – Monet’s Water Lilies, Picasso’s Les Demoiselles d’Avignon – will always be there. “We’d have a revolution if we took down the Water Lilies,” said Ann Temkin, chief curator of painting and sculpture, at a museum preview.

Underlying the new mix-it-up approach is the argument that teleological art history – seeing the present as the logical culmination of the past – lacks contingency, fails to take into account the idea that once upon a time Cézanne, say, was just a bloke making strange paintings in the south of France, not an art history colossus whose work had a mind-blowing market value. So the new hang is not a “bang, bang, bang” of famous masterpiece after famous masterpiece, as Temkin phrased it. While we spoke, we were sitting with our backs to Cézanne’s The Bather, newly cleaned, with zingy blue details revealed of its background of rocks and water. To our right were Van Gogh’s Starry Night and Henri Rousseau’s The Dream. So far, so “bang, bang, bang”.

Van Gogh, Cézanne and Rousseau now hang near ceramics by the ‘mad potter of Biloxi’ George Ohr. Photograph: Jonathan Muzikar

But in a case in front of us was a selection of exquisite, earth-toned ceramics by American George Ohr, the self-styled “mad potter of Biloxi”. You could argue that these modest pots made in obscurity in Mississippi are irrelevant to the masterpieces of French post-impressionism. The point, according to Temkin, is to try to bring us back to around 1890 – when Van Gogh was painting in an asylum, Rousseau was collecting taxes, and no one knew what would be inscribed into the canon and what wouldn’t. Above all, she explained, the connections are visual. Gesturing at the warm-brown ceramics, she said: “You could almost make a Cézanne out of those colours.”

Repudiating the Book of Genesis approach involves breaking up the patriarchal parade of white, male artists. So in a room titled Stamp, Scavenge, Crush – which centres on art using discarded or reused materials from the late 1940s to the early 60s, and features Jasper Johns, Robert Rauschenberg and Cy Twombly – are also a photographic work by the African American Romare Bearden and a bedsheet printed by Ruth Asawa in 1948 with a stamp to create a dense, graphic pattern.

She was using the Black Mountain College laundry stamp – she was running the art school’s laundry at the time, while learning about design and pattern from ex-Bauhaus masters such as Anni Albers.) Twenty-eight per cent of works now on view at MoMA are by women, a crushingly small proportion even taking into account the fact that 13% can’t neatly be assigned to a gender (because they are by collectives, for example). But 28% is still five times as high as the proportion in the galleries at the beginning of the century.

Fragile strength … Prison Notebook, 1976, by Ibrahim el-Salahi. Photograph: Robert Gerhardt/MoMA

This rebalancing has meant enlarging the collection – a process enabled by MoMA’s considerable resources and the tradition of American philanthropy along with its ability to sell off works in order to buy new ones. (British national museums’ constitutions prevent them from doing this.) Selling a Léger meant, Temkin explained, that the museum could purchase several works by “pioneering female modernists”. One, The Moon (1928), by Brazilian painter Tarsila do Amaral, acquired earlier this year, now holds court alongside Picasso, Brâncuși and Eileen Gray. Donations include the extraordinarily extensive and coherent Cisneros collection of Latin American art, which for the time being will be shown as a kind of museum-within-a-museum. A wall of shimmeringly delicate wire sculptures by the Venezuelan Gego are a particular joy.

The labels beside works, specifically their date of acquisition, tell a story in themselves about recent innovations at MoMA. A wooden sculpture by Lebanon’s Saloua Raouda Choucair entered the collection last year. A set of works by Polish artist Edward Krasiński came in 2015. Ibrahim el-Salahi’s Prison Notebook, illustrated with ink drawings, made after he was wrongfully imprisoned in Sudan in 1975, was acquired in 2017. Despite its fragility and scale, it holds its own in a room themed around the conflicts of the 1970s opposite Philip Guston’s magisterial painting Deluge II, made at the same time. A dangling, curvaceous hemp sculpture by Indian artist Mrinalini Mukherjee was also acquired in 2017. Perhaps my eyes are drawn to familiar things, or perhaps it is just that curators in London and New York breathe the same air, but it strikes me that these last are all artists foregrounded by Tate Modern in current displays or recent exhibitions. At any rate, the message is loud and clear: the world is a big place, bigger than Manhattan and Paris – and great art is being made all around it.

‘We’d have a revolution if we took down Water Lilies’ … Monet at MoMA. Photograph: Kurt Heumiller/Museum of Modern Art, New York

These themed rooms frequently draw on items from several of the institution’s mighty departments, creating a mix of, for example, photography, film, publications and painting. So for example, in the room with Asawa’s bedsheet there is a film of Merce Cunningham’s dance work Antic Meet – like a lot of film in the galleries, simply projected on to a wall, offered as part of the mix. One of the most rewarding moments in the current hang is a modest, unobtrusive room devoted to Frank O’Hara – from his manuscripts and early editions of books to artworks made by a host of greats to illustrate his work, and Larry Rivers’s portrait of the poet.

All this has meant delving deep into the collection. Lowry said the museum had, to his eyes, become almost like two institutions in recent years – one that visitors had access to, and the other in store, where there was a much more varied and diverse set of art. A work by the Indian painter VS Gaitonde, for example, was purchased in 1963, and languished unseen for years – now, though, it’s sharing wall space with Rothko. There is an entire case of radical zines and leaflets mailed to the museum in the early 1980s from Brazil – these items, from the Movimento de Arte Pornò, were unsought by the institution but dutifully catalogued and preserved.

Some things, on the other hand, have been permanently banished from the galleries. Like Tate before it, MoMA will no longer bandy around terms such as cubism, post-impressionism, abstract expressionism, or conceptualism in its labels. “We were trying to imagine what we would say if we had a group of friends over to dinner who aren’t in the art world,” Lowry told me. “What would we want them to know? What would they need to know in order to have an interesting conversation?” It is certainly not, he argued, a “dumbing down”.

New look… a still from We Hold Where Study, 2017, by transgender artist Wu Tsang. Photograph: Roman Mensing Photograph: Photo: Roman Mensing

The results of this particular innovation are, at this point, mixed – after all, you can eradicate art-world lingo and still bypass lucidity. Sometimes, refusing the actual word seems like a round in the hat game – in which participants pull a name out of a hat and describe it, without using the name itself. The introductory text of one room, titled Readymade in Paris and New York, seems, for example, to be a more or less a hat-game description of the word dada. Indeed, hanging beside it is Richard Boix’s drawing of members of the New York dada group (Man Ray, Duchamp, Katherine Dreier and others), with the word DADA writ large on it. But since the room introduction doesn’t tell you what dada is, you’d be none the wiser if you didn’t already know.

All of these changes have been a long time coming. Back at the turn of the millennium, soon after Lowry was appointed, the museum experimented with a series of thematic displays called MoMA 2000. Some critics loved them; some utterly rejected them. Lowry denies the museum rowed back after the mixed reception, but, rather, the displays marked the beginning of a process that has culminated in this month’s reopening, one that involved great institutional change. “It required over time a new generation of curators who came with fresh and new ideas and for whom interdisciplinarity was something natural. And we had to expand on training our vision,” he said. Over the last decade, research groups on Asian, Latin American and African art have been formed at the museum. Curators have travelled more. The great MoMA tanker has gradually turned.

Unsealing the edges of modern and contemporary art in this way has, said Temkin, been “liberating, exhilarating. One thing I’ve been insisting on is changing the way people speak about gaps in the collection. It feels so wrong because it assumes there is a complete puzzle, and if we just find every single puzzle piece, one day it will be solved and complete. Right now, we are saying, ‘No, we don’t know – there is no way of knowing some complete art history.’”

Work by Duchamp, Man Ray, Richard Boix and others in the Readymade in Paris and New York room. Photograph: Denis Doorly/MoMA

The museum, once a place of such authority, is now letting that authority go, admitting the impossibility of a fully coherent narrative, embracing the fact that it cannot tell the viewer everything. Strangely, its sleek and efficient spaces, so four-square, pale and elegant, renewed and enlarged at a cost of $450m (£356m), seem slightly at odds with this new intellectual porousness, despite architect Elizabeth Diller’s efforts to make it more friendly and open. It remains an intensely decorous, formal, demure museum (and it is $25 for a ticket, though the ground-floor displays, which currently include a room of paintings by Kenya-born Michael Armitage, can be visited for free). Perhaps a longing for unruliness was why I was so happy to see the holes punched out of the walls, revealing the grubby plywood sheets and dust balls lurking behind them, in a display devoted to the multidisciplinary performance artist Pope.L.

The most striking example of MoMA’s new approach – as well as a relatively rare abjuration of broad chronology – is placing Picasso’s Demoiselles d’Avignon beside a visceral painting, by African American artist Faith Ringgold, documenting the 1965 Los Angeles race riots. (The 1967 work, American People Series #20: Die, was seen at Tate Modern in the 2017 exhibition Soul of a Nation.) The formal consonances between the works, made 60 years apart, are clear. MoMA’s contention is that the Picasso might illuminate the Ringgold – but also that the Ringgold might illuminate the Picasso. History, in other words, might not be working in only one direction. Which is where poetry comes in. Or, depending on your perspective and taste, the chaos.