The Number Sense How the Mind Creates Mathematics

by Dehaene, Stanislas

• ISBN13: 9780195132403
• ISBN10: 0195132408
• Format: Paperback
• Copyright: 1999-12-09
• Publisher: Oxford University Press

Summary

The Number Sense is an enlightening exploration of the mathematical mind. Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. 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 our mathematics opens up a window on the human mind.

Author Biography

Stanislas Dehaene is Research Director at the Institut National de la Sante et de la Recherche Medicale, in Paris, France.

Table of Contents

Preface	ix
Introduction	3	(10)
Part I Our Numerical Heritage	13	(78)
Chapter 1 Talented and Gifted Animals	13	(28)
A Horse Named Hans	14	(3)
Rat Accountants	17	(6)
How Abstract Are Animal Calculations?	23	(5)
The Accumulator Metaphor	28	(3)
Number-Detecting Neurons?	31	(3)
Fuzzy Counting	34	(4)
The Limits of Animal Mathematics	38	(1)
From Animal to Human	39	(2)
Chapter 2 Babies Who Count	41	(23)
Baby Building: Piaget's Theory	41	(3)
Piaget's Errors	44	(3)
Younger and Younger	47	(3)
Babies' Power of Abstraction	50	(2)
How Much Is 1 plus 1?	52	(4)
The Limits of Infant Arithmetic	56	(5)
Nature, Nurture, and Number	61	(3)
Chapter 3 The Adult Number Line	64	(27)
1, 2, 3, and Beyond	66	(4)
Approximating Large Numbers	70	(3)
The Quantity Behind the Symbols	73	(3)
The Mental Compression of Large Numbers	76	(2)
Reflexive Access to Number Meaning	78	(2)
A Sense of Space	80	(3)
Do Numbers Have Colors?	83	(3)
Intuitions of Number	86	(5)
Part II Beyond Approximation	91	(84)
Chapter 4 The Language of Numbers	91	(27)
A Short History of Number	92	(3)
Keeping a Permanent Trace of Numerals	95	(3)
The Place-Value Principle	98	(2)
An Exuberant Diversity of Number Languages	100	(2)
The Cost of Speaking English	102	(4)
Learning to Label Quantities	106	(2)
Round Numbers, Sharp Numbers	108	(2)
Why Are Some Numerals More Frequent Than Others?	110	(5)
Cerebral Constraints on Cultural Evolution	115	(3)
Chapter 5 Small Heads for Big Calculations	118	(26)
Counting: The ABC of Calculation	119	(3)
Preschoolers as Algorithm Designers	122	(2)
Memory Appears on the Scene	124	(2)
The Multiplication Table: An Unnatural Practice?	126	(4)
Verbal Memory to the Rescue	130	(1)
Mental Bugs	131	(3)
Pros and Cons of the Electronic Calculator	134	(2)
Innumeracy: Clear and Present Danger?	136	(3)
Teaching Number Sense	139	(5)
Chapter 6 Geniuses and Prodigies	144	(31)
A Numerical Bestiary	147	(2)
The Landscape of Numbers	149	(3)
Phrenology and the Search for Biological Bases of Genius	152	(5)
Is Mathematical Talent a Biological Gift?	157	(5)
When Passion Produces Talent	162	(2)
Ordinary Parameters for Extraordinary Calculators	164	(3)
Recipes for Lightning Calculation	167	(3)
Talent and Mathematical Invention	170	(5)
Part III Of Neurons and Numbers	175	(78)
Chapter 7 Losing Number Sense	175	(32)
Mr. N, the Approximate Man	177	(4)
A Clear-Cut Deficit	181	(4)
A Champion in Numerical Non-sense	185	(4)
Inferior Parietal Cortex and the Number Sense	189	(2)
Seizures Induced by Mathematics	191	(1)
The Multiple Meanings of Numbers	192	(2)
The Brain's Numerical Information Highways	194	(5)
Who Orchestrates the Brain's Computations?	199	(3)
At the Origins of Cerebral Specialization	202	(5)
Chapter 8 The Computing Brain	207	(24)
Does Mental Calculation Increase Brain Metabolism?	208	(3)
The Principle of Positron Emission Tomography	211	(2)
Can One Localize Mathematical Thought?	213	(5)
When the Brain Multiplies or Compares	218	(2)
The Limits of Positron Emission Tomography	220	(1)
The Brain Electric	221	(2)
The Time Line of the Number Line	223	(4)
Understanding the Word "Eighteen"	227	(1)
Numerate Neurons	228	(3)
Chapter 9 What Is a Number?	231	(22)
Is the Brain a Logical Machine?	232	(3)
Analog Computations in the Brain	235	(3)
When Intuition Outruns Axioms	238	(4)
Platonists, Formalists, and Intuitionists	242	(3)
The Construction and Selection of Mathematics	245	(4)
The Unreasonable Effectiveness of Mathematics	249	(4)
Appendix	253	(2)
Notes and References	255	(12)
Index	267