Professor Barbara Grosz works in the School of Engineering and Applied Sciences at Harvard University, USA. In 1950, when Turing proposed to replace the question “Can machines think?” with the question “Are there imaginable digital computers which would do well in the imitation game?”, computer science was not yet a field of study, Shannon’s theory of information had just begun to change the way people thought about communication, and psychology was only starting to look beyond Behaviorism. It is stunning that so many predictions in Turing’s 1950 Mind paper were right. In the decades since that paper appeared, with its inspiring challenges, research in computer science, neuroscience and the behavioural sciences has radically changed thinking about mental processes and communication. Turing, were he writing now, might still replace “Can machines think?” with an operational challenge, but Grosz expects he would propose a very different game. This talk describes research on collaboration, collective intentionality and human-computer communication that suggests abilities to work together with others and to participate in purposeful dialogue are essential elements of human intelligence. It presents results in several areas of artificial intelligence that support the imagining of computer systems able to exhibit such abilities. The Turing Research Symposium was organised by the Royal Society of Edinburgh and the University of Edinburgh School of Informatics in partnership with SICSA and supported by Cambridge University Press.