Matiere a Pensee

ISBN-10: 0691004056
ISBN-13: 9780691004051
Edition: 1995
List price: $45.00 Buy it from $8.96
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Description: 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  More...

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Book details

List price: $45.00
Copyright year: 1995
Publisher: Princeton University Press
Publication date: 12/27/1998
Binding: Paperback
Pages: 272
Size: 5.50" wide x 8.50" long x 0.75" tall
Weight: 0.682
Language: English

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 Poincareacute;, 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.

Caterina Consani is a professor in the Department of Mathematics at Johns Hopkins University. Alain Connes is a professor at the College de France, Institut des Hautes Etudes Scientifiques in Bures sur Yvette, and a distinguished professor in the Department of Mathematics at Vanderbilt University. He won the Fields Medal in 1982.

Translator's Note
Preface to the Original French Edition
Mathematics and the Brain
Plato as Materialist?
Nature Made to Order
The Neuronal Mathematician
Darwin among the Mathematicians
Thinking Machines
The Real and the Rational
Epilogue: Ethical Questions
Glossary of Mathematical Terms
Glossary of Neurobiological Terms
Index

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