This article discusses the interplay between mathematical models of physical entities and mathematical models of computing hardware, advocating its criticality concerning trustworthy virtual-twin technologies in near-future communication networks. The digital twinning of physical entities is widely recognized as a crucial factor in near-future information technology. Since the emerging applications increasingly affect sensitive aspects of human well-being, such as health and privacy, it is imperative to establish an unprecedented level of technological trustworthiness. This article aims to shed light on the intricate role of computing-hardware models in ensuring the trustworthiness of digital-twin technologies. Specifically, we examine Turing and Blum-Shub-Smale (BSS) machines, which represent digital and some forms of analog hardware, respectively. Despite the prominence of these hardware models in computer science, the implications of the resulting theory of algorithms for contemporary engineering remains poorly understood. We discuss two exemplary channel-classification problems from the field of networked control and network resilience, which are algorithmically solvable by BSS machines but remain beyond the reach of Turing machines. To highlight the capabilities that arise from transcending the realm of digital computing, we use the term 'virtual twin' in the appropriate context.