conversations on mind matter and mathematics

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Conversations On Mind Matter And Mathematics

Author : Jean-Pierre Changeux
ISBN : 0691004056
Genre : Mathematics
File Size : 48. 66 MB
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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 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? 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? Jean-Pierre Changeux, an internationally renowned neurobiologist, and Alain Connes, one of the most eminent living mathematicians, find themselves deeply divided by these questions. 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.

What Makes Us Think

Author : Jean-Pierre Changeux
ISBN : 0691092850
Genre : Philosophy
File Size : 60. 15 MB
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Will understanding our brains help us to know our minds? Or is there an unbridgeable distance between the work of neuroscience and the workings of human consciousness? In a remarkable exchange between neuroscientist Jean-Pierre Changeux and philosopher Paul Ricoeur, this book explores the vexed territory between these divergent approaches--and comes to a deeper, more complex perspective on human nature. Ranging across diverse traditions, from phrenology to PET scans and from Spinoza to Charles Taylor, What Makes Us Think? revolves around a central issue: the relation between the facts (or "what is") of science and the prescriptions (or "what ought to be") of ethics. Changeux and Ricoeur ask: Will neuroscientific knowledge influence our moral conduct? Is a naturally based ethics possible? Pursuing these questions, they attack key topics at the intersection of philosophy and neuroscience: What are the relations between brain states and psychological experience? Between language and truth? Memory and culture? Behavior and action? What is a mental representation? How does a sign relate to what it signifies? How might subjective experience be constructed rather than discovered? And can biological or cultural evolution be considered progressive? Throughout, Changeux and Ricoeur provide unprecedented insight into what neuroscience can--and cannot--tell us about the nature of human experience. Changeux and Ricoeur bring an unusual depth of engagement and breadth of knowledge to each other's subject. In doing so, they make two often hostile disciplines speak to one another in surprising and instructive ways--and speak with all the subtlety and passion of conversation at its very best.

Triangle Of Thoughts

Author : Alain Connes
ISBN : 9780821826140
Genre : Mathematics
File Size : 69. 89 MB
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Our view of the world today is fundamentally influenced by twentieth century results in physics and mathematics. Here, three members of the French Academy of Sciences: Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger, discuss the relations among mathematics, physics and philosophy, and other sciences. Written in the form of conversations among three brilliant scientists and deep thinkers, the book touches on, among others, the following questions: Is there a ``primordial truth'' that exists beyond the realm of what is provable? More generally, is there a distinction between what is true in mathematics and what is provable? How is mathematics different from other sciences? How is it the same? Does mathematics have an ``object'' or an ``object of study'', the way physics, chemistry and biology do? Mathematics is a lens, through which we view the world. Connes, Lichnerowicz, and Schutzenberger examine that lens, to understand how it affects what we do see, but also to understand how it limits what we can see. How does a well-informed mathematician view fundamental topics of physics, such as: quantum mechanics, general relativity, quantum gravity, grand unification, and string theory? What are the relations between computational complexity and the laws of physics? Can pure thought alone lead physicists to the right theories, or must experimental data be the driving force? How should we compare Heisenberg's arrival at matrix mechanics from spectral data to Einstein's arrival at general relativity through his thought experiments? The conversations are sprinkled with stories and quotes from outstanding scientists, which enliven the discourse. The book will make you think again about things that you once thought were quite familiar. Alain Connes is one of the founders of non-commutative geometry. He holds the Chair of Analysis and Geometry at the College de France. He was awarded the Fields Medal in 1982. In 2001, he was awarded the Crafoord Prize by The Royal Swedish Academy of Sciences. Andre Lichnerowicz, mathematician, noted geometer, theoretical physicist, and specialist in general relativity, was a professor at the College de France. Marcel Paul Schutzenberger made brilliant contributions to combinatorics and graph theory. He was simultaneously a medical doctor, a biologist, a psychiatrist, a linguist, and an algebraist.

Loving And Hating Mathematics

Author : Reuben Hersh
ISBN : 1400836115
Genre : Mathematics
File Size : 79. 32 MB
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Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.

Making Number Talks Matter

Author : Cathy Humphreys
ISBN : 9781571109989
Genre : Education
File Size : 20. 56 MB
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Making Number Talks Matter is about the myriad decisions facing teachers as they make this fifteen-minute daily routine a vibrant and vital part of their mathematics instruction. Throughout the book, Cathy Humphreys and Ruth Parker offer practical ideas for using Number Talks to help students learn to reason numerically and build a solid foundation for the study of mathematics. This book will be an invaluable resource whether you are already using Number Talks or not; whether you are an elementary, middle school, high school, or college teacher; or even if you are a parent wanting to support your child with mathematics. Using insight gained from many years of doing Number Talks with students of all ages, Cathy and Ruth address questions to ask during Number Talks, teacher moves that turn the thinking over to students, the mathematics behind the various strategies, and ways to overcome bumps in the road. If you've been looking for ways to transform your mathematics classroom--to bring sense-making and divergent thinking to the foreground, to bring the Standards for Mathematical Practice to life, and to bring joy back into your instruction--this book is for you.

Table Talk Math

Author : John Stevens
ISBN : 1946444022
Genre : Education
File Size : 25. 55 MB
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Making math part of everyday conversations is a powerful way to help children and teens learn to love math. In Table Talk Math, John Stevens offers parents (and teachers!) ideas for initiating authentic, math-based conversations that will get kids notice and be curious about all the numbers, patterns, and equations in the world around them.

Neuronal Man

Author : Jean-Pierre Changeux
ISBN : 0691026661
Genre : Medical
File Size : 25. 75 MB
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Over the past thirty-five years, there has been an explosive increase in scientists' ability to explain the structure and functioning of the human brain. While psychology has advanced our understanding of human behavior, various other sciences, such as anatomy, physiology, and biology, have determined the critical importance of synapses and, through the use of advanced technology, made it possible actually to see brain cells at work within the skull's walls. Here Jean-Pierre Changeux elucidates our current knowledge of the human brain, taking an interdisciplinary approach and explaining in layman's terms the complex theories and scientific breakthroughs that have significantly improved our understanding in the twentieth century. "Jean-Pierre Changeux ... explores the fascinating question of how the human brain, similar in so many ways to the brains of less developed species, is able to accomplish so much more.... [He] presents his ... view with verve, conviction, and an admirable lucidity".--Richard Restak, Washington Post Book World"An outstanding attempt to convey to the general public an interdisciplinary understanding of the human nervous system".-- Nature

The Physiology Of Truth

Author : Jean-Pierre Changeux
ISBN : 0674012836
Genre : Philosophy
File Size : 39. 59 MB
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In this wide-ranging book, one of the boldest thinkers in modern neuroscience confronts an ancient philosophical problem: can we know the world as it really is? Drawing on provocative new findings about the psychophysiology of perception and judgment in both human and nonhuman primates, and also on the cultural history of science, Jean-Pierre Changeux makes a powerful case for the reality of scientific progress and argues that it forms the basis for a coherent and universal theory of human rights. On this view, belief in objective knowledge is not a mere ideological slogan or a naïve confusion; it is a characteristic feature of human cognition throughout evolution, and the scientific method its most sophisticated embodiment. Seeking to reconcile science and humanism, Changeux holds that the capacity to recognize truths that are independent of subjective personal experience constitutes the foundation of a human civil society.

The Divine Challenge

Author : John Byl
ISBN : 0851518877
Genre : Religion
File Size : 88. 50 MB
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Since the Beginning of time man has challenged God's supremacy, striving to dethrone God and reinterpret the universe according to his own standards and purposes. In response God, who is determined to destroy the wisdom of the worldly wise and to unmask it for the foolishness that it really is, issues his own challenge to sinful man. Arrogantly, modern scientific man takes up that divine challenge, arming himself with scientific knowledge and technological power. Indeed, man has convinced himself that this rational wisdom has made foolish the wisdom of Scripture, with its tall tales of a personal God, of life after death, and of heaven and hell. 'Such notions', Einstein declared, 'are for the fears or absurd egoism of feeble souls.' John byl argues that the Christian worldview provides the only foundation for logic, mathematics, science and morality. The Divine Challenge aims to substantiate this bold claim. Byl shows the failure of today's predominant philosophies to provide a coherent worldview that can yield a plausible account of the various aspects of life as we experience it.

Birth Of A Theorem

Author : Cédric Villani
ISBN : 9780374710231
Genre : Biography & Autobiography
File Size : 90. 21 MB
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In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

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