Conventional computing, focussed upon algorithms or programs, requires processes of abstraction, decisions on function, and exclusion of the user from most of the computation. We shall describe a broader approach to computing we call Empirical Modelling (see www.dcs.warwick.ac.uk/modelling). Here the "user" constructs artefacts designed so as to resemble experientially a domain or task of interest. Initially the user is closely, and jointly, constructing with the computer their own idea – or construal – of the domain or problem. The approach has been influenced by the work of William James and offers deeper cognitive support from computing for both the humanities and sciences.