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Pondering the philosophy of understanding mathematics

  • Feb 25, 2000
When reading this account of a series of conversations between Jean-Pierre Changeux and Alain Connes, two main themes emerge. The first is how little progress there has been made in the philosophy of mathematics and knowledge since the time of Plato and the second is how much fun it is to discuss it. Changeux is Director of the Molecular Neurobiology Laboratory at the Institut Pasteur and Connes is a previous winner of the Fields Medal for mathematical excellence. His prime areas of work are in analysis and geometry. These two superb minds jointly explore the realm of consciousness, knowledge, and the inherent ambiguities in the search for truth and understanding.
As the conversations progress, many of the main themes of philosophy are covered, with an emphasis on mathematics and the abstract nature of the human mind. My favorite chapter was "The Neuronal Mathematician", where the neural basis of understanding theorems is discussed. If it were possible for Plato to eavesdrop on the conversation, he would be baffled by the references to computers, but the discussion on the "forms" of mathematics would seem like old news. One very profound question raised in this book bears repeating, "Is it necessary for a computer to experience pain and suffering to be considered conscious?"
A book that should be thought of as a primer only, this is one work that can keep you thinking and pondering for years.

Published in Journal of Recreational Mathematics, reprinted with permission.

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Charles Ashbacher ()
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Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more
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An intriguing argument by mathematician Connes in this spirited conversation with neurobiologist Changeux is that a mathematical reality exists independently of the human mind. For example, he considers it improbable that the cosmic harmony of the Jovian satellites orbiting in consonance with Kepler's laws is a product of the human brain. Thus, although an understanding of the brain as a tool may lead to expanded knowledge, Connes denies that such understanding will alter mathematical reality. However, Changeux believes that the concept of an immutable mathematical reality is merely "the fascination that the created object exerts upon its creator," and he rejects the idea that a "totally organized mathematical system exists in nature waiting to be gradually discovered." Among various other fascinating ideas discussed is the role of the brain's limbic system in cognition, such as how the emotions aroused by a pleasurable hypothesis may serve as a guide to a solution.Brenda Grazis--This text refers to an out of print or unavailable edition of this title.
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ISBN-10: 0691004056
ISBN-13: 978-0691004051
Author: Jean-Pierre Changeux
Publisher: Princeton University Press

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