AT THE END of a corridor upstairs at the Talbot Rice Gallery is a book of reproductions of digital images from Edinburgh University’s vast collection. It is ranked and archived in meticulous manner by a researcher who spent six months grappling with its parameters. But the result is not, perhaps, one that any archivist would recognise. Here, the mediaeval manuscripts, the Victorian photographs, the priceless early musical instruments, the jewels and ephemera of a few hundred years of collecting are reclassified into random groups according to shape or colour, action or state.

Here are the “Pointers”, a collection of images that depict people – or animals – with their arms in the air. Here are the “Red Dots”, images that contain dots of red, from royal seals to botanical illustrations. There are “Blobs”, “Blues”, “Marblings” and the marvellous “Zebras” which contains not simply zebras, but anything with zebra-ish stripes, from harpsichord keyboards to the skirts of a Newhaven fishwife. What Fabienne Hess, the artist who has compiled this book and who exhibited all the digital images in the collection in the Talbot Rice’s Round Room two years ago, shows is not the detail of history that traditional classification shows, but the extraordinary breadth of the university’s collections. How do we classify the “stuff” we value? And why?

It is a question of memory, when it comes down to it. A university collection, like any large institutional being, marking history, charting small points of interest from a certain moment in Time, giving a nod to what might be posterity.

We will keep this, acquire this. We will collect and remember. Blobs, Zebras, What You Will.

The more recent portion of the university’s collections is at the heart of Between Poles and Tides, a new exhibition which highlights the university’s art acquisitions in the six years since it merged with Edinburgh College of Art. The purchases, of some 50 artists in all, cover holes that, says Talbot Rice Assistant Curator Stuart Fallon, had emerged during the 1980s and 1990s when the university simply stopped collecting any contemporary art at all. To lose one decade might seem like misfortune. To lose two looks like carelessness.

And so what of this reckoning of the last six years catch-up? Fallon had his work cut out, whittling 50 artists down to twelve, the resolution involving a certain "archiving" that might not seem that dissimilar to Hess’s. And yet there is much sense here.

We wander around the partially-installed exhibition amidst the debris of installation – a tall scaffolding tower reaching the gallery’s not-inconsiderable ceiling, topped by a noisy projector casting the image of Isobel Turley’s Zane (2013) in super-massive size, high on the gallery wall. A repeating two second, close-up loop of an amur leopard, filmed at Edinburgh Zoo, the animal has a hungry look in its eye, uncertain, perpetually ready to pounce. It is unnerving and deeply claustrophobic, and provides a super-sized counter to the more intimate works elsewhere.

A textural David Batchelor painting hangs nearby, half-hidden by stepladders and gallery assistants. Upstairs, Daisy LaFarge represents the most recent batch of graduates with Not for Gain (2016), a gently disturbing botanical video from last year’s ECA degree show which pitched a post-apocalyptic poetic voiceover with shakey footage from the Royal Botanics. Nearby, works from Ian Hamilton Finlay, including Both the Garden Style (1987), a guillotine intertwined with honeysuckle and the shadow of Rousseau, range around a vitrine of Jessica Harrison’s Painted Ladies, a series of porcelain Doulton figures altered and displaced with tattoos.

Talbot Rice have commissioned two “poetic responses” to bring out the connections between the works, available from early March, although you may push all that aside and find yourself making your own classifications. You could blithely coral Jonathan Owens and Luc Tuymans into a group called “ghosts”, perhaps. Owen’s Eraser Drawings, created by meticulously rubbing out the protagonist in any particular image or photograph, suggest impermanence and the fallibility of memory in the images erased. This ephemerality is echoed in Luc Tuymans’ triptych of prints, The Arena (2016), depicting “the ghostly shadow of a crowd gathering in an unidentified city square.” There is an uncertainty and ambiguity in both works. An unease, too.

Down in the main hall, works by Katie Paterson and Ilana Halperin suggest a sense of geology, of Deep Time, from the miniature body stones – which Halperin calls “miniature planets” – of Physical Geology (new landmass) to Paterson’s Timepieces (2014), a series of nine clocks telling the time on all the planets in the solar system as well as our own moon.

Paterson, who has big, poetic ideas and makes them concrete, both in the mind and on the wall, is also represented by a certificate from her audacious project Future Library, which will create 100 new literary works over the next century.

Stored in a collection centre, unseen by anyone other than the authors themselves, the works will, in 97 years time, be printed on paper made from 1000 trees that Paterson has had planted just outside Oslo. The first author to put a new work in the collection was Margaret Atwood, the second David Mitchell, entrusting their work to the fragile notion of the collection itself. For what Edinburgh’s own collecting history tells us is that we can never predict the future. Posterity is a fickle thing.

Between Poles and Tides: New Acquisitions from the University of Edinburgh Art Collection, is at Talbot Rice Gallery, Old College, South Bridge, Edinburgh from February 11 to May 6

www.ed.ac.uk/talbot-rice