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.
Author: Jean-Pierre Changeux,Alain Connes
Publisher: Princeton University Press
Is contemporary continental philosophy making a break with Kant? The structures of knowledge, taken for granted since Kants Critique of Pure Reason, are now being called into question: the finitude of the subject, the phenomenal given, a priori synthesis. Relinquish the transcendental: such is the imperative of postcritical thinking in the 21st century. Questions that we no longer thought it possible to ask now reemerge with renewed vigor: can Kant really maintain the difference between a priori and innate? Can he deduce, rather than impose, the categories, or justify the necessity of nature? Recent research into brain development aggravates these suspicions, which measure transcendental idealism against the thesis of a biological origin for cognitive processes. In her important new book Catherine Malabou lays out Kants response to his posterity. True to its subject, the book evolves as an epigenesis – the differentiated growth of the embryo – for, as those who know how to read critical philosophy affirm, this is the very life of the transcendental and contains the promise of its transformation.
Epigenesis and Rationality
Author: Catherine Malabou
Publisher: John Wiley & Sons
Author: Jean-Pierre Changeux,Alain Connes
auf den Spuren des größten Rätsels der Mathematik
Author: Marcus Du Sautoy
This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.
New Approaches to an Ancient Affinity
Author: Nathalie Sinclair,William Higginson
Publisher: Springer Science & Business Media
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 an exchange between neuroscientist Jean-Pierre Changeux and philosopher Paul Ricoeur, this book explores the fraught 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, this book 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 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 best.--From publisher description.
A Neuroscientist and a Philosopher Argue about Ethics, Human Nature, and the Brain
Author: Jean-Pierre Changeux,Paul Ricoeur
Publisher: Princeton University Press
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. These are but a few of the wealth of fascinating observations contained here. We also discover, for example, that because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. The book also explores the unique abilities of idiot savants and mathematical geniuses, and we meet people whose minute brain lesions render their mathematical ability useless. This new and completely updated edition includes all of the most recent scientific data on how numbers are encoded by single neurons, and which brain areas activate when we perform calculations. Perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in learning, mathematics, or the mind. "A delight." --Ian Stewart, New Scientist "Read The Number Sense for its rich insights into matters as varying as the cuneiform depiction of numbers, why Jean Piaget's theory of stages in infant learning is wrong, and to discover the brain regions involved in the number sense." --The New York Times Book Review "Dehaene weaves the latest technical research into a remarkably lucid and engrossing investigation. Even readers normally indifferent to mathematics will find themselves marveling at the wonder of minds making numbers." --Booklist
How the Mind Creates Mathematics, Revised and Updated Edition
Author: Stanislas Dehaene
Publisher: Oxford University Press
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Author: Mario Livio
Publisher: Simon and Schuster
Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.
Die Schönheit der Mathematik
Author: Steven Strogatz
Publisher: Kein & Aber AG
Draft : Presented at the Show-Me Middle School Mathematics Teacher Preparation Conference, Branson, Missouri, May 19-21, 2000
A collection of 23 chapters devoted to understanding and promoting mathematical reasoning by teachers and students. After a section explaining four views of how reasoning works, sections are devoted to early, middle, and high school grades. The articles present empirical and theoretical evidence to explain how students think about measurement, statistics, algebra, and the connection of math to the real world. Finally a section devoted to the development of mathematical reasoning, the professional development of teachers, and possible curricular approaches is presented.
Author: Lee Stiff,Frances R. Curcio
Publisher: Natl Council of Teachers of
Provides an in-depth analysis of the cognitive science of mathematical ideas that argues that conceptual metaphor plays a definitive role in mathematical ideas, exploring such concepts as arithmetic, algebra, sets, logic, and infinity. 20,000 first printing.
How the Embodied Mind Brings Mathematics Into Being
Author: George Lakoff,Rafael E. Núñez
Publisher: Basic Books (AZ)
Mathematik versteht man oder eben nicht. Der eine ist dafür natürlich begabt, dem anderen bleibt dieses Fach für immer ein Rätsel. Stimmt nicht, sagt nun Barbara Oakley und zeigt mit ihrem Buch, dass wirklich jeder ein Gespür für Zahlen hat. Mathematik braucht nämlich nicht nur analytisches Denken, sondern auch den kreativen Geist. Denn noch mehr als um Formeln geht es um die Freiheit, einen der vielen möglichen Lösungsansätze zu finden. Der Weg ist das Ziel. Und wie man zum richtigen Ergebnis kommt, ist eine Kunst, die man entwickeln, entdecken und in sich wecken kann. Die Autorin vermittelt eine Vielfalt an Techniken und Werkzeugen, die das Verständnis von Mathematik und Naturwissenschaft grundlegend verbessern. (K)ein Gespür für Zahlen nimmt Ihnen — vor allem wenn Sie sich in Schule, Uni oder Beruf mathematisch oder naturwissenschaftlich beweisen müssen — nicht nur die Grundangst, sondern stärkt Ihren Mut, Ihren mathematischen Fähigkeiten zu vertrauen. So macht Mathe Spaß!
So bekommt man den Durchblick in Mathe
Author: Barbara Oakley
Publisher: MVG Verlag