Conversations on Mind, Matter, and Mathematics

by Jean-Pierre Changeux, Alain Connes, M.B. DeBevoise (Translator)

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 Poincaré, 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.

Genres: Philosophy, Mathematics, Psychology, Science

280 pages, Hardcover

First published January 1, 1995

About the author

est un neurobiologiste français connu pour sa recherche dans plusieurs domaines de la biologie, de la structure et de la fonction des protéines (en particulier les protéines allostériques), au développement précoce du système nerveux jusqu’aux fonctions cognitives. Bien que célèbre dans les sciences biologiques pour le modèle Monod-Wyman-Changeux, il est aussi reconnu pour l’identification et la purification du récepteur nicotinique de l’acétylcholine et la théorie de l’épigénèse par stabilisation sélective des synapses. Changeux est connu du public non scientifique pour des idées concernant la relation entre l’esprit et le cerveau. Comme il l’écrit dans son livre Matière à pensée, Changeux défend la conception selon laquelle le système nerveux est actif plutôt que réactif et que l’interaction avec l’environnement, au lieu d’être instructive, résulte de la sélection de représentations internes préexistantes. Il est membre de l'Académie des sciences depuis 1986.

Reviews

[Two Readers in Love]

Recommended on page 105 of "A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age" by Alec Wilkinson: "a book I likes so much that I read it several times."

[Jeffrey Wack · Rating 2 out of 5]

Bleh. Did not finish. Should be interesting, but these guys cannot communicate and frankly Connes is out of his depth trying to talk philosophy, evidenced by him having to say “I can’t say it any more simply.”

Changeux is right on applying Darwinian thinking to math, but he does seem to undersell the power of the ‘formal content’ of a theory. Reminds me of the joke that all math is trivial since it follows from axioms.

Reading Connes talk just pisses me off, he clearly believes that mathematics has unique access to truth and it makes me mad because I kinda agree but don’t like the conclusion and he is no good a defending it.

[Bria · Rating 3 out of 5]

I think we can both agree that nobody's opinion is changed after having these conversations.