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Overview
Humans' understanding of numbers is intuitive. Infants are able to estimate and calculate even before they learn the words for numbers. How have we come to possess this talent for numbers? In A Brain for Numbers, Andreas Nieder explains how our brains process numbers. He reports that numerical competency is deeply rooted in our biological ancestry; it can be traced through both the evolution of our species and the development of our individual minds. It is not, as it has been traditionally explained, based on our ability to use language. We owe our symbolic mathematical skills to the nonsymbolic numerical abilities that we inherited from our ancestors. The principles of mathematics, Nieder tells us, are reflections of the innate dispositions wired into the brain.
Nieder explores how the workings of the brain give rise to numerical competence, tracing flair for numbers to dedicated “number neurons” in the brain. Drawing on a range of methods including brain imaging techniques, behavioral experiments, and twin studies, he outlines a new, integrated understanding of the talent for numbers. Along the way, he compares the numerical capabilities of humans and animals, and discusses the benefits animals reap from such a capability. He shows how the neurobiological roots of the brain's nonverbal quantification capacity are the evolutionary foundation of more elaborate numerical skills. He discusses how number signs and symbols are represented in the brain; calculation capability and the “neuromythology” of mathematical genius; the “start-up tools” for counting and developmental of dyscalculia (a number disorder analogous to the reading disorder dyslexia); and how the brain processes the abstract concept of zero.
Product Details
| ISBN-13: | 9780262354325 |
|---|---|
| Publisher: | MIT Press |
| Publication date: | 11/19/2019 |
| Series: | The MIT Press |
| Sold by: | Penguin Random House Publisher Services |
| Format: | eBook |
| Pages: | 392 |
| File size: | 3 MB |
| Age Range: | 18 Years |
About the Author
Table of Contents
Preface xi
Introduction xiii
Part I Conceptual Foundations 1
1 Thinking about Numbers 3
1.1 Mathematical Reality 3
1.2 Cardinal Numbers as Objective Properties of a Set 5
1.3 Knowledge of Numbers 8
2 Numerical Concepts, Representations, and Systems 11
2.1 Numerical Concepts 11
2.2 Mental Numerical Representations and Mental Systems 12
Part II Numbers Deeply Rooted in Our Ancestry 19
3 Understanding Numbers across the Animal Tree of Life 21
3.1 The Diversification of Animal Life 21
3.2 The Theory of Evolution 25
3.3 Classic Studies on Animal "Counting" 28
3.4 How to Test Animals on Numerical Cognition 32
3.5 The Phylogeny of Numerical Competence 36
3.6 Signatures of Animal Number Discrimination 49
4 The Utility of Number for Animals 63
4.1 A Matter of Fitness 63
4.2 Staying Alive 64
4.3 Benefits for Reproduction 72
5 Biological Heritage in the Human Brain 77
5.1 Baby Steps 77
5.2 Approximate Number System versus Object Tracking System 81
5.3 Number Discrimination in Humans Lacking Number Words 82
5.4 The Ancient Logarithmic Number Line 85
Part III Numerical Quantity in the Brain 89
6 Localizing Numerical Quantity Representations in the Human Brain 91
6.1 The Building Plan of the Cerebral Cortex 91
6.2 At a Loss for Numerical Quantity after Brain Injury 101
6.3 Mapping Numerical Quantity on the Healthy Human Brain 104
7 Number Neurons 115
7.1 The Language of Neurons 115
7.2 The Discovery of Number Neurons in the Monkey Brain 119
7.3 The Neuronal Code for Number 127
7.4 Number Neurons Are Necessary for Number Judgments 129
7.5 Number Neurons Represent Different Presentation Types and Modalities 132
7.6 Convergent Evolution of Number Neurons: Lessons from Crows 137
7.7 Number Neurons in the Human Brain 140
7.8 An Innate Number Instinct 145
7.9 Number Models and Networks 148
7.10 Numerical Working Memory 151
Part IV Number Symbols 157
8 Signs for Numbers 159
8.1 Evolution Pushed Homo sapiens toward Symbolic Thinking 159
8.2 Number Signs: Icons, Indices, and Symbols 161
8.3 Invention of Number Symbols in Human History 163
8.4 How Children Learn to Deal with Number Signs 168
8.5 Teaching Number Signs to Animals 170
9 Neural Foundation of Counting and Number Symbols 177
9.1 The Patient Who Lost All Numbers beyond Four 177
9.2 Imaging in the Human Brain During Symbolic Numerical Tasks 180
9.3 Numerical Association Neurons in Monkeys 182
9.4 Symbolic Number Neurons in the Human Brain 186
9.5 A Brain Area Dedicated to Numerals 187
10 The Calculating Brain 193
10.1 Non-symbolic Calculation in Indigenous People, Infants, and Animals 193
10.2 Single-Neuron Arithmetic 200
10.3 Cortical Location of Calculation 206
10.4 Dissociation of Calculation Types: Procedure versus Facts 212
10.5 Left versus Right Brain 216
10.6 Dissociated Brain Networks for Calculation and Language 219
10.7 Professional Mathematicians and Mathematical Prodigies 224
11 Space and Number 233
11.1 Small Numbers on the Left, Large Numbers on the Right 233
11.2 Carried along the Number Line During Calculation 237
11.3 Space and Number in the Brain 240
Part V Development 245
12 The Developing Number Brain 247
12.1 Counting in Children 247
12.2 Startup Tools for a Symbolic Number System 249
12.3 Out of Approximate Quantity and into Symbolic Number 251
12.4 Brain Activity in the Developing Brains of Children 254
12.5 Abstractness of Number Representations in the Brain 259
13 Developmental Dyscalculia 265
13.1 Developmental Dyscalculia and How It Affects Life 265
13.2 Domain-General and Domain-Specific Impairment in Dyscalculia 267
13.3 Tracing Dyscalculia Back to Brain Anatomy 270
13.4 Functional Differences in Brain Activation of Dyscalculic Children 273
13.5 It's (Partly) in the Genes 274
Part VI The Brain Departing from Empirical Reality 281
14 The Magical Number Zero 283
14.1 A Special Number 283
14.2 Zero in Human History 285
14.3 Development of Zero-like Concepts in Children 292
14.4 Zero-like Concepts in Animals 295
14.5 Neuronal Representations of "Nothing" and Empty Sets 299
Epilogue 307
Notes 309
Index 365
What People are Saying About This
A compelling and up-to-date account of how the brain comes to grips with numbers—in humans and animals, many of which have their own number sense — and how these abilities evolved. Fascinating and surprising. Essential reading for anyone interested in numbers.
—Ian Stewart, author The Beauty of Numbers in Nature and Do Dice Play God?A Brain for Numbers teaches so much about the history and the study of number sense in all kinds of animal life from insects to birds to primates including humans. The various research approaches are fascinating, especially the use of statistical classifiers in analyzing the fMRI data. I loved this book from beginning to end.
—Maria M. Klawe, President, Harvey Mudd College