Willard McCarty, King's College, London, gives the 2017 Besterman lecture. If the digital computer is to be a 'machine for doing thinking' in the arts and letters, rather than merely a way of automating tasks we already know how to perform, then its constraints and the powers these constraints define need to be understood. This lecture explores those constraints and powers across the three stages of modelling a research problem: its translation into discrete, binary form; manipulation by the machine; and re-translation into scholarly terms.