It has often been pointed out that twentieth-century painting and physics share a common tendency toward probing behind appearances into the underlying structure of things; that the 'retreat from likeness' in painting is akin to science's peering far within the surface of matter. The results of their probings are also significantly similar: extra-dimensionality connects Cubism and relativity; and random, indeterminate processes occur both in recent expressionist painting and in quantum physics. But although the common culture implicit in these parallels has often been remarked, not until now has it been studied in depth and in detail. The author provides a concise summary of those aspects of modern science that relate to his theme, including the development of a 'third science' that embraces information, communication, automation, and systems theory. He also provides in parallel a concise history of the modern movement in painting. Treating only those artists whose work clearly illustrates his viewpoint, he divides those active before the Second World War into two broad groups, the Geometricizers (members of such movements as Cubism, Constructivism, and the Bauhaus), who sought to make manifest the essential form of reality; and the Magicians (including Chirico, Kandinsky, the Dadaists, and the Surrealists), who transformed reality in accordance with their own internally developed laws. Postwar reactions, continuations, and new starts, including some very recent trends, are discussed....