Some specific aspects of the process of discovery are explored as they are experienced in the visual arts and the physical sciences. Both fields use the same visual/brain processing system, and both disciplines share an imaginative and productive interest in the disciplined use of imagistic thinking. Many productive interactions between visual artists and scientists have been noted, including such fields as scientific illustration and the representation of research results or the illustration of science fiction. A factual basis for exploring the methods of visual discovery can be found in the literature on brain hemisphere function. Personal experiences of the author and examinations of one of Michelangelo's Sistine Chapel frescos and a Picasso painting illustrate a close connection between the domains of art and science. A scientific/artistic way of knowing, as distinct from analytical proof, logical understanding, or purely subjective reactions, is proposed. This synchronistic way of knowing concentrates on the visual and imagistic formation of ideas, informed by critical thinking, and leads to a type of purely visual logic. Seven figures and one table illustrate the discussion. (Contains 23 references.) (SLD)