'Hippie Modernism,' a major new exhibition at the Walker Art Center in Minneapolis, raises eyebrows as well as consciousness, yoking the tie-dye-clad, peace-and-love-preaching countercultural mascot with a movement high on more rational and precise versions of progress. This tension is at once heightened and explained by the show’s subtitle, 'The Struggle for Utopia' – a shared fight embodied by the catalogue cover image of Buckminster Fuller’s Expo 67 dome in flames.

'The Walker has always been interested in interdisciplinary things, but this show is really anti-disciplinary at its core,' says curator Andrew Blauvelt, who spent 17 years at the Center, most recently as senior curator of design, research, and publishing, before departing last month to become director of the Cranbrook Art Museum in Bloomfield Hills, Michigan. 'We wanted to look at the radical nature of these propositions, whether it’s social practice in art or speculative design out of the design sector.'

Determined to fill some historical blind spots in art, design and material culture, the show focuses on a decade that kicks off with the 1964 California-to-New York acid trip of Ken Kesey and his Merry Pranksters and concludes with the globe-spanning OPEC oil crisis. The countercultural journey unfolds according to a three-part thematic organisation borrowed from Timothy Leary – 'Turn In, Tune In, and Drop Out' – and is illuminated by Emmet Byrne’s pitch-perfect exhibition graphics and typography (this is Cooper Black’s moment to shine) that have long been a specialty of the Walker.

Spanning some 14,000 sq ft (1,300 sq m) of the Walker’s sublime Edward Larrabee Barnes-designed building, the exhibition opens in a psychedelic swirl of spheres, mandalas, mantras, and the altered states imagined by Ettore Sottsass in his out-of-this-world The Planet as Festival lithographs of 1971 before delving into the concepts of radical architectural groups such as Archigram and Ant Farm, who proposed better living through pods and inflatables such as Michael Webb’s 1966 'Cushicle,' which resembles the love child of a Poul Kjærholm chaise and a geodesic dome.

The 'Tune In' section is concerned with 'the interconnectedness of communities of interest', explains Blauvelt, who brought together original printed matter ('the Internet of its time') ranging from gig posters and protest flyers to countercultural periodicals such as Scanlan’s, a short-lived source of proto-gonzo journalism and a pioneer of infographics. An installation by Ken Isaacs immerses the viewer in images from Life and Look magazines that are projected onto six surfaces of The Knowledge Box (1962/2009), prefiguring today’s Instagram age.

The show’s final section turns its back on the mainstream, exploring the worlds of schemers and dreamers like The Cockettes, a post-Haight commune that gave birth to glitter rock. Another room is strung with the colourful hammocks of Neville d’Almeida and Helio Oiticica’s 1973 take on a Hendrix experience (lounging is encouraged), while the knitted dwelling of fibre artist Evelyn Roth is positioned not far from a copy of Computer Lib, the 1974 book in which Ted Nelson introduces the concept of hypertext and the 'deeply intertwingled' nature of personal computing.

The big finish is Newton and Helen Mayer Harrison’s Portable Orchard: 18 semi-dwarf citrus trees growing in hexagonal wooden boxes under artificial lights. The installation recreates a 1972 work undertaken by the Harrisons in California as a response to the rampant razing of orchards and farms to make way for suburban development. For Blauvelt, their 'cybernetic orange grove' is one more example of the transient reconciliation between the hippie and the modernist: a crossing of divergent paths, both bound for utopia. 'On the one hand it looks almost like a minimalist installation,' he says, walking amid the fragrant trees. 'But on the other hand it has everything to do with concerns about planetary survival.'