A confession: I find few immersive theatre experiences as unpleasant as those in which performers take notice of me: I don’t like being talked to or touched or sequestered in solitude or asked to complete tasks. At least, that’s been my theatergoing mantra until now. But boy, did I ever long to be looked at or given some instructions – just once – in Mapped Productions’ Nova Insula, the “site-responsive deconstruction” of The Tempest currently reinventing the basement of the Putney Library as part of the Wandsworth Arts Fringe Festival.

Nova Insula spans a series of dimly lit, cramped rooms, mainly filled with the library’s overflow stacks, here reimagined as Prospero’s archive and laboratory. It’s a nifty repurposing of the space, and the shelf of props that greets visitors at the entrance features an intriguing array of editions of The Tempest, chess pieces, and Shakespeare busts all painted white and labeled with passages from the play. Deeper inside these rooms, there’s a similarly neat tiny model of a ransacked library (the sets are designed by Fabrizio Panella, Hyseung Baek, and Matilde Marangoni).

But we’ve been given no guidance, other than to look around until we run out of time or interest, so if these mysterious objects are clues to piece together, Nova Insula, directed by Marco Turcich, doesn’t provide any indication of what to focus on or what anything could possibly mean.

Presumably, that’s the point. One corridor includes the text of the play taped on to the walls; actors in white laboratory gowns and masks annotate the script by circling various lines and writing down who’s onstage in each scene. Elsewhere, these same ambiguous research figures review rocks and dirt, labeled Caliban and Ariel, under a microscope. In other words, Nova Insula’s unapologetically more interested in taking the Tempest apart and letting audiences deal with the shards than in creating clear new interpretations (the use of video screens is equally impenetrable). The actors who play Prospero and Miranda lurk between the bookshelves, respectively playing chess and writing speeches on a wall, adding some silent animation to the proceedings.

To be fair, it might have been a more successful evening with no choice but to linger in every corner. There was only one other audience member in the space when I attended so we were able to sail through the venue – perhaps I’d have noticed more if I’d had to wait my turn.

Nova Insula may rightly be categorized as an installation rather than a theatre piece, a display more aimed at modern art explorers than theatregoers. The researchers and the quasi-characters go about their business wordlessly, wholly ignoring the visitors. At one point, I turned a corner and jumped, startled to see a person standing there: she turned out to be a stage manager, waiting at the exit, but the sudden sense of momentary fright reminded me of what Nova Insula is missing. No one needs Caliban leaping out at unsuspecting guests from behind the books, but even the slightest step towards letting us know what to feel – let alone pointing us towards what this curious but static landscape can teach us about The Tempest – would be a welcome development.

Nova Insula is playing at the Putney Library as part of the Wandsworth Arts Fringe Festival until May 14.