We live in the information age, and our lives are increasingly digitized. Our quotidian has been transformed over the last fifty years by the adoption of innovative networking and computing technology. The digital world presents opportunities for public archaeology to engage, inform and interact with people globally. Yet, as more personal data are published online, there are growing concerns over privacy, security, and the long-term implications of sharing digital information. These concerns extend beyond the living, to the dead, and are thus important considerations for archaeologists who share the stories of past people online. This analysis argues that the 'born-digital' records of humanity may be considered as public digital mortuary landscapes, representing death, memorialization and commemoration. The potential for the analysis of digital data from these spaces could result in a phenomenon approaching immortality, whereby artificial intelligence is applied to the data of the dead. This paper investigates the ethics of a digital public archaeology of the dead while considering the future of our digital lives as mnemonic spaces, and their implications for the living.