Conversations on Mind, Matter, and Mathematics.

In 1985, a fascinating book titled, Neuronal Man, providing a new vista of understanding of the human nervous system, originally published in France, became available in this country. Its author, Professor Jean-Pierre Changeux, offered to the educated public a most descriptive and sophisticated interpretation of brain functioning. Now, he has collaborated with a distinguished mathematician, Alain Connes, to produce a new volume that presents a dialogue between the two of them concentrating on the relationship between the human mind and mathematical constructs.

The central question that is researched and emphasized within the framework of these discussions is whether mathematics exists in all of its forms from integers through its most advanced objects and theorems as something totally independent of the mind, which simply discovers these preexisting relationships, or whether the human brain, within its cellular organization, creates and devises them itself. In the exploration of these fascinating issues, the authors not only review, in a historical sense, human thought as it relates to mathematical concepts, but also the unique association of the human brain to the world of philosophy, sociology, and theology. As one reads their carefully crafted responses, one comes to wonder whether all we know and understand is reducible to nothing more than a series of intricate neuronal cellular pathways that have been developed through evolution and embryology to form the human brain an organ that is totally responsible for the development of all fields of human knowledge.

Admittedly, this is not an easy volume to read. It is one that may require, even with the use of the fine auxiliary vocabulary at the end of the volume, a reading pace of only a page or two per day unless one has had specialized training in both mathematics and neuroscience. Be that as it may, there are so many "points of intellectual light" Within the framework of this magnificent book that one should take the opportunity to study each page with as much care as one would exercise in viewing a beautiful piece of crystal or examining a fine painting. The authors truly probe the very limits of human understanding, particularly as it relates to the brain's participation in mathematical creation.

Theology and religion in general are not major themes in their journey through human cognition and mathematical formation; yet the authors emphasize repeatedly that the brain is totally responsible for all that we know and, in that sense, has constructed the complete intellectual universe in which we live and function. In the process they have reduced philosophy and theology to nothing more than the physics of neurocircuitry. Neither of the authors demonstrates much in the way of interest in the principles of established religion. In fact, Changeux advances the concept that human behavior in a moral sense must be based on a mathematical design. He is comfortable in offering a thesis that ethics, as we know it, is both universal and mathematical, but exclusively based on a neurocognitive design. In the process of providing this concept, he defines a belief (presumably in a religious sense) as follows: "A belief may be defined as a specific state of nerve cell activity characteristic of an individual's interaction with others of his kind, a sort of model constructed inside of the brain on a biological--that is to say, a physical, material--basis."

In spite of Changeux's "mathematicalization" of ethics, one could almost argue on the basis of his descriptions of the physical nature of the human brain that it could represent the anatomical substrate for the human soul! In the final analysis, these conversations offer an outstanding contribution to our understanding of the human mind's relationship to the cellular structure of the brain.

These issues are addressed in the final chapter of the book, which is written almost exclusively by Changeux and is certainly one of the most provocative essays written on the questions of belief, ethics, and morality in contemporary society. The thoughts and concepts expressed by both of the authors render this volume an intellectual treasure, and the translation and editing are also excellent.

Robert J. White, M.D., Ph.D., is professor of surgery and director of the Brain Research Laboratory at the School of Medicine, Case Western Reserve University, Cleveland.