This volume commemorates the work of Alan Turing, because it was Turing who not only introduced the most persuasive and influential concept of a machine model of effective computability but who also anticipated in his work the diversity of topics brought together here. As Newman put it in his memoir of Turing, "The central problem with which he started and to which he constantly returned is the extent and the limitations of mechanistic explanations of nature." Turing's paper "On computable numbers, with an application to the Entscheidungs problem" appeared in print in 1937. It contained Turing's thesis that every `effective' computation can be programmed on a Turing machine. Furthermore it contained the unsolvability of the halting problem and of the decision problem for first-order logic, and it presented the invention of the universal Turing machine. The publication of this idea is acknowledged as a landmark of the computer age. Part I of the volume explores the historical aspect with essays on the background, on Turing's work, and on subsequent developments. Part II contains an extensive series of essays on the influence and applications of these ideas in mathematics, mathematical logic, philosophy of mathematics, computer science, artificial intelligence, philosophy of language, philosophy of mind, and physics.

The mental ray series of handbooks is conceived to provide concise and up to date general and technical information about the commercially available rendering software mental ray. The series addresses the needs of professional and non-professional users of the software as well as of software developers who intend to integrate the stand-alone version of mental ray or the mental ray component software into applications that require interactive photorealistic and high image quality programmable rendering. In addition, the series provides comprehensive information to students and researchers in computer graphics. mental ray is a valuable tool for teaching and demonstrating the fundamental concepts of photorealistic and programmable rendering as well as a benchmark and catalyst for further research. The rendering software mental ray and many of its unique underlying concepts are the result of ongoing research and development at the company mental images since its incorporation in 1986. Leading vendors of 3D digital content creation and 3D CAD and product design software have made mental ray their rendering software of choice for all purposes of high end visualization and image synthesis ranging from digital special effects and 3D animation for motion picture, video ?lm, and games production to 3D mechanical and architectural CAD and to industrial product design and automotive styling.