Synopses & Reviews
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
Review
"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
"From the origin of Roman numerals to the latest MRI results, everything you might like to know about numbers and the brain, as filtered through the lively and engaging brain of Stanislas Dehaene."--Discover
"A delight."--Ian Stewart, New Scientist
"Whether he is explaining how this neural macherinery begins its numerical magic early in infancy, how it attains the sophistication required for complex calculations, or how it misfires when the brain suffers certain types of injuries, 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
"This interesting and informative book sets forth the latest findings by Dehaene and other psychologists trying to determine how the brain understands and manipulates numbers and other forms of mathematical information. Included are many startling results of experiments involving animals and infants that shed light on the extent and nature of our inborn number sense. These findings, if they receive the consideration they merit, should have a major impact on the way mathematics is taught at the elementary and secondary level. Highly recommended."--Library Journal (starred review)
"This may surprise those who have trouble carrying the remainder in division or figuring out a 15 percent tip on a $20 lunch bill, but according to mathematician and psychologist Stanislas Dehaene, mathematics is an inborn skill. In The Number Sense, Dehaene makes a compelling case for the human mind's innate grasp of mathematics. Dehaene's book is filled with examples to support his thesis, from young babies' ability to "count" (i.e., to react when single objects are replaced by two or more) to examples of how brain damage affects various individuals' number sense. Even more fascinating is his discussion of the relationship between language and numbers. Though Dehaene's book is about mathematics, even those readers with the worst math anxiety will find The Number Sense an intriguing exploration of the world of numbers--and the human mind." -Amazon.com Review
"In this lively and readable book, Dehaene integrates the latest scientific evidence on how numbers are represented in the brains of animals and humans, then relates this knowledge to the challenges of early mathematics education. Dehaene is masterful in his ability to explain complex scientific findings in a manner that will be accessible to any audience. His writing is clear, and his examples are fascinating, taking us through the worlds of animal mathematicians, idiot savants, newborn infants, and split-brain patients, all as a means of understanding our innate sense of number."--Jim Stigler, Professor of Psychology, University of California, Los Angeles
"It is now possible to see the human brain as it listens, reads, communicates and calculates. The Number Sense describes recent exciting findings on how the brain calculates. In a clear and exciting way it provides the needed background to understand both the innate endowment of numeracy and what may be necessary to acquire the skills of mathematics. For psychologists, neuroscientists, educators and all who work with number, this book is of basic importance."--Mike Posner, Professor of Psychology, Department of Cognitive and Decision Sciences, University of Oregon
"Dehaene's study of new brain imaging techniques, idiot savants, and mathematical prodigies illustrates humankind's innate ability to comprehend numberical data."--Science News
"Is number sense innate or learnt? A bit of both? How do our brains do math, anyway? And where did the ability come from? Stanislas Dehaene, a mathematician who became a neuroscientist, is uniquely qualified to answer such questions, and The Number Sense is a delight."--Ian Stewart, New Scientist
"In The Number Sense, Dehaene makes a convincing case, based on many experiments with rats, dolphins, chimpanzees and very young infants, that the ability to do what he calls "fuzzy counting" is hardwired into the brain. He even posits a very convincing neural machanism for this ability, an analog accumulator that keeps approximate track of objects, events, even sounds."--Lucy Horwitz, The Boston Book Review
"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."--Steven Rose, New York Times Book Review
"The first edition of The Number Sense was widely praised for its comprehensive
treatment of an important area of research and theory. No better book has emerged since
then... Dehaene provides readers who are new to the area with an excellent overview of the topic." -- Gordon Pitz, Adjunct Professor of Psychology at University of North Carolina, PsychCRITIQUES
Synopsis
Our understanding of how the human brain performs mathematical calculations is far from complete. There are still perplexing mysteries -- how, for instance, do idiot savants perform almost miraculous mathematical feats? -- but the picture has grown steadily clearer. In The Number Sense, Stanislas Dehaene offers readers a look into these stunning discoveries, in an enlightening exploration of the mathematical mind.
Using research showing that human infants have a rudimentary number sense, Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. But how then did we leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. Tracing the history of numbers, we learn that in early times, people indicated numbers by pointing to part of their bodies, and how Roman numerals were replaced by modern numbers. On the way, we also discover many fascinating facts: for example, because Chinese names for numbers are short, Chinese people can remember up to nine or ten digits at a time, while English-speaking people can only remember seven. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how math can open up a window on the human mind.
About the Author
Stanislas Dehaene teaches at the College de France and is Director of the Cognitive Neuroimaging Research Unit at INSERM.
Table of Contents
Preface to the Revised and Expanded Edition
Preface to the First Edition
Introduction
Part I: Our Numerical Heritage
Chapter 1: Talented and Gifted Animals
Chapter 2: Babies Who Count
Chapter 3: The Adult Number Line
Part II: Beyond Approximation
Chapter 4: The Language of Numbers
Chapter 5: Small Heads for Big Calculations
Chapter 6: Geniuses and Prodigies
Part III: Of Neurons and Numbers
Chapter 7: Losing Number Sense
Chapter 8: The Computing Brain
Chapter 9: What Is a Number?
Epilogue. The Contemporary Science of Number and Brain
Appendix
Notes and References
Bibliography
Main books consulted
Useful web resources
Detailed bibliography
Index