This lecture will present an introduction to some of the big questions to be grappled with during our AHRC towards a National Collection-funded project entitled 'The Sloane Lab: Looking back to build future shared collections' (2021-24). Our project will aim to devise automated and augmented ways, of mending the broken links between the past and present of the UK's founding collection in the catalogues of the British Museum, Natural History Museum and the British Library. For this, we will use the collection of Hans Sloane (1660-1753) as a microcosm through which to explore the technical, infrastructural, conceptual, historical and social challenges faced in bringing together digital cultural heritage collections so as to help audiences use, learn and benefit from them. A key aim of the project is to facilitate richer, more critical understandings of the origins and development of museum collections by devising computational and conceptual approaches to the detection and exposition of often-hidden processes like colonialism, empire and slavery that have shaped collections and their classifications. Sloane's collection was created through the economic, political and culture processes of Britain's increasing global entanglements of the 17/18th century, to which the infrastructure for a 21st-century national collection must respond. The project will explore how we might develop new computational approaches to the detection and visualization of loss, absence and bias, so as to help publics, researchers and cultural heritage organisations to shape and engage with digital technologies in new ways.