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Do numbers and the other objects of mathematics enjoy a timeless existence independent of human minds, or are they the products of cerebral invention? Do we discover them, as Plato supposed and many others have believed since, or do we construct them? Does mathematics constitute a universal language that in principle would permit human beings to communicate with extraterrestrial civilizations elsewhere in the universe, or is it merely an earthly language that owes its accidental existence to the peculiar evolution of neuronal networks in our brains? Does the physical world actually obey mathematical laws, or does it seem to conform to them simply because physicists have increasingly been able to make mathematical sense of it? Jean-Pierre Changeux, an internationally renowned neurobiologist, and Alain Connes, one of the most eminent living mathematicians, find themselves deeply divided by these questions.
The problematic status of mathematical objects leads Changeux and Connes to the organization and function of the brain, the ways in which its embryonic and post-natal development influences the unfolding of mathematical reasoning and other kinds of thinking, and whether human intelligence can be simulated, modeled,--or actually reproduced-- by mechanical means. The two men go on to pose ethical questions, inquiring into the natural foundations of morality and the possibility that it may have a neural basis underlying its social manifestations. This vivid record of profound disagreement and, at the same time, sincere search for mutual understanding, follows in the tradition of Poincar�, Hadamard, and von Neumann in probing the limits of human experience and intellectual possibility. Why order should exist in the world at all, and why it should be comprehensible to human beings, is the question that lies at the heart of these remarkable dialogues.
- Sales Rank: #1210964 in Books
- Brand: Brand: Princeton University Press
- Published on: 1995-05-07
- Original language: English
- Number of items: 1
- Dimensions: 8.75" h x 5.75" w x 1.00" l,
- Binding: Hardcover
- 280 pages
- Used Book in Good Condition
From Booklist
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
Review
One of Choice's Outstanding Academic Titles for 1995
"[The authors'] passion for discerning the truth about important issues and for formulating thoughts as precisely as possible shines through these conversations.... A stimulating and illuminating book."--Philip Kitcher, The New York Times Book Review
"A stimulating and illuminating book. . . . Mr. Changeux and Mr. Connes might best be characterized by reviving an old term. They are natural philosophers, concerned with large questions about the world and our place in it, who confront those questions with intelligence and lively imagination."--Philip Kitcher, New York Times Book Review
"The original Socratic dialogues were artificially constructed to present a coherent view. The dialogue between Connes and Changeux is quite different. It is the recording of real-life arguments where the speakers are frequently at cross-purposes and operate in different planes. For the reader this can be irritating but it also encourages him to become involved and frame his own answers. . . . "--Sir Michael Atiyah, The Times Higher Education Supplement
"A highly entertaining and erudite read, this conversation between two renowned scientists . . . is at all times informative, lively, and thought provoking. The reader is drawn into the argument and left pondering the issues well after the last page has been turned."--Choice
"A delight to read, and highly informative."--Keith Devlin, Nature
"The record of an intellectual encounter between two of Franco's leading scientific figures. . . . The result is a smooth, easy-to-read representation of a protracted, interesting . . . exchange between Alain Connes, an eminent mathematician, . . . and Jean-Pierre Changeux, a distinguished biologist."--Brian Rotman, Times Literary Supplement
Language Notes
Text: English (translation)
Original Language: French
Most helpful customer reviews
13 of 13 people found the following review helpful.
. . . another man's poison
By Christopher Grant
It's taken me about a decade to finish reading this relatively short book. I'm a mathematician with a modest interest in philosophy, so I thought I'd find something worthwhile in this dialogue between a prominent mathematician and a prominent neuroscientist, but it just didn't click for me.
I have learned some things through this prolonged reading experience, though:
(1) Being a fly on the wall during an unrehearsed conversation between two intellectual heavyweights is overrated. Connes' and Changeux's thoughts are often disorganized, and when they disagree they usually seem to end up speaking past each other.
(2) People with profound knowledge in one field don't necessarily have a lot of deep insights to share when speaking outside of that field.
(3) If the final chapter is representative of the views of elite scientists, then scientism has a stronger foothold than I'd thought. In particular, I found Changeux's vision of science's role in the future of human society to be rather disturbing. If nothing else, this book was a good wake-up call, I suppose.
15 of 19 people found the following review helpful.
a pleasant surprise
By A Customer
There are many "dialogue" books of this sort, but personally I haven't read anything matching the brilliance of this one. The two men featured in this book, both true masters in their fields, represent two very different philsophical views, which become quite obvious immediately, yet they manage to engage in an intellectual dialogue free of the venom characterizing so much academic polemics nowadays, true to the spirit of those "pre-modern" French intellectuals, even reminiscent of Socrates & company. This is a minor masterpiece.
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