A New Look at an Old Question Review of Andrei Khrennikov

Andrei Khrennikov's book returns us to the old question (going back to the pre-Socratics and Plato) of whether reality, either material or mental, may be fundamentally mathematical. This question, however, creates difficulties for those not suitably trained in mathematics. While this was already a problem for the Greeks, the exceedingly abstract and complex character of modern mathematics makes it especially acute now. Khrennikov's book confronts its readers with one of the more arcane areas of modern mathematics, namely p-adics and the p-adic version of the mathematics used in classical and quantum physics. At the same time, by dealing with Freudian and related theory, the book focuses primarily on the human mind rather than the material world or the brain as a physical object. Thus, while harking back to Greek thought on the possibly mathematical nature of mental reality, the project is unusual from a contemporary point of view. These days, the more usual role of mathematics lies in investigation of the biological, chemical, and physical bases of mental processes, including exploration of the possibility of their quantum origin (e.g. the Hameroff/Penrose Orch OR theory, or the work of Umezawa and, more recently, Vitiello). While using analogous (but, given its p-adic nature, not identical) mathematics, Khrennikov's project shifts the focus to the mathematical modeling of mental, rather than physical, processes. Andrei Khrennikov, Classical and Quantum Mental Models and Freud's Theory of Unconscious Mind, Vaxjo, Sweden: Vaxjo University Press, 2002, xix+207pp., ISBN 91-7636-315-5