New materialism considers that the world and its histories are produced by a range of material forces that extend from the physical and the biological to the psychological, social and cultural. In recognizing that heritage is not held in objects alone, new materialism discourses echo definitions of intangible cultural heritage (ICH) enshrined in the 2003 UNESCO Convention for the Safeguarding of the Intangible Cultural Heritage. While museums understand the weight of responsibility when engaging with communities of practice, many still restrict the representation of archived ICH material to oral histories, object biographies, video and audio recordings of songs and performing arts. The technical complexities of archiving the ‘live’ perpetuate nineteenth-century museum display conventions, such as fixed-point perspectives and linear approaches to representation. To address this gap, we introduce ‘computational museology’, which brings a systems thinking approach to 'whole of environment' encoding. Such a framework unites, for instance, artificial intelligence with data curation, and ontology with visualization, as well as embodied participation through immersive and interactive interfaces. The implications of such a framework has yet to be fully theorized but it is evident that a new paradigm of materiality comprising ‘radical intangibles’ is taking shape in museums, which signals a break with both Western historiographic orthodoxies and hypothetical paradigms of tangible and intangible heritage. This article foregrounds the emergence of radical intangibles as crucial new digital materialities that are transforming reenacted and embodied practices, which we demonstrate in the discussion of two longitudinal curatorial projects based in China and Hong Kong: the first, 'Hong Kong Martial Arts Living Archive' (HKMALA) in collaboration with the International Goushou Association in Hong Kong, and the second, ‘Remaking Confucian Rites’ (RCR), undertaken in conjunction with Tsinghua University in Beijing. Both of these projects are significant for having taken up ‘technologies of corporeality’ – digital paradigms at the forefront of computer graphics, spatial and temporal modelling, and virtual reality. The powerful tools being developed across the two instances have begun to revolutionize ICH as a practice, a mode of transmission, and an object of study.