The author's 1999 doctoral submission, ‘Integrated Artworks: Theory and Practice in relation to Printmaking and Computers, and the influence of ‘non-Euclidean geometry’ and ‘the fourth dimension’ on developments in Twentieth-Century Pictorial Space’ examined relations between spatial art practice and theory, digital technology, print and photomechanical imaging methods, hyperspace philosophy and recent art-historical analyses of developments in pictorial space during the quarter-century preceding the First World War. This paper, presented at ‘The Enactment of Thinking’ conference at the University of Plymouth in July 2001, introduces aspects of this research and examines, specifically, ideas from geometry and hyperspace philosophy, and key terms including shadows, slices, projections and the dimensional analogy, to assist in understanding and visualizing historically significant but unconventional modes of spatial discourse. Examples of the author's work are included and help to relate theory to practice within the research.