Space, Time and Number in the Brain (eBook)

Front Cover 1
Space, Time and Number in the Brain 4
Copyright Page 5
Contents 6
Contributors 8
Foreword 10
Quantity Codes 11
Developmental Origins 11
Cross-Dimensional Interactions and Metaphors 11
Quantitative Computations 12
Thought with or Without Symbols 12
Human Turing Machine 12
Impact of Culture and Education 12
Acknowledgments 13
Section I. Mental Magnitudes and their Transformations 14
Chapter 1. Mental Magnitudes 16
Computational Implications of Behavioral Results 18
Constraints on Mental Magnitudes 19
Conclusions 24
References 24
Chapter 2. Objects, Sets, and Ensembles 26
Representing Individual Items in Working Memory 28
Representing Sets of Items in Working Memory 29
Representing Ensembles in Working Memory 30
Conclusions 33
References 33
Chapter 3. Attention Mechanisms for Counting in Stabilized and in Dynamic Displays 36
Explicit Counting 36
Experiment 1: What is the Limit for Explicit Counting in Afterimages? 41
What is the Limit for Explicit Counting in Moving Displays? 44
Conclusions 45
Acknowledgments 47
References 47
Section II. Neural Codes for Space, Time and Number 50
Chapter 4. A Manifold of Spatial Maps in the Brain 54
Spatial Maps in the Brain 54
Hippocampal Maps 55
Entorhinal Maps 58
Relation Between Entorhinal and Hippocampal Maps 61
The Manifold of Entorhinal and Hippocampal Maps 61
Dynamic Maps 63
Can Several Maps Be Active Simultaneously? 65
Concluding Remarks 65
Acknowledgments 67
References 67
Chapter 5. Temporal Neuronal Oscillations can Produce Spatial Phase Codes 72
A Functional Role for Interference Between Neuronal Oscillations 73
An Oscillatory Interference Model of Grid Cell Firing 75
Oscillatory Interference and Representations of Sequential Order? 78
Summary and Conclusions 80
Acknowledgments 80
References 81
Chapter 6. Population Clocks: Motor Timing with Neural Dynamics 84
The Problem of Time 84
Motor Timing 86
Models of Timing 87
Dynamics in Recurrent Networks 90
Neural Correlates of Timing 92
Concluding Remarks 94
Acknowledgments 95
References 95
Chapter 7. Discrete Neuroanatomical Substrates for Generating and Updating Temporal Expectations 100
Temporal Orienting of Attention: Temporal Expectations Derived from Learned Cues 101
Rhythm and Speed: Temporal Expectations Derived from Regular Stimulus Dynamics 107
The Hazard Function: Temporal Expectations Derived from the Flow of Time Itself 107
Conclusions: Generating vs Updating Temporal Expectations 108
References 111
Chapter 8. The Neural Code for Number 116
Neurons Encoding Numerical Quantity 117
Coding of Continuous and Discrete Quantity 125
Coding of Proportions 127
Towards Symbolic Number Representations 128
References 130
Section III. Shared Mechanisms for Space, Time and Number? 132
Chapter 9. Synesthesia: Gluing Together Time, Number, and Space 136
Is it Really Synesthesia? 137
The Effect of TNS Synesthesia on Everyday Cognitive Processes 138
Neural Processes of TNS Synesthesia 140
TNS Synesthesia: Symbolic or Non-Symbolic? 142
Conclusions 142
Acknowledgments 142
References 143
Chapter 10. How is Number Associated with Space? The Role of Working Memory 146
Dissociating the Number Interval Bisection Bias from the Line Bisection Bias 149
Dissociating Snarc from the Number Line: Conceptual Vs Visuospatial Representations 151
The Snarc Effect: A Crucial Role for Working Memory 152
General Discussion 155
References 159
Chapter 11. Neglect “Around the Clock”: Dissociating Number and Spatial Neglect in Right Brain Damage 162
Number–Space Association in the Healthy Brain 163
Neglect in Visual and Number Space 170
A Further Twist to Number Space Neglect: Bisecting “Around the Clock” 174
Discussion and Conclusions 180
Acknowledgments 183
References 183
Chapter 12. Saccades Compress Space, Time, and Number 188
Space, Time, and Number as Visual Primitives 189
A Common Metric for Magnitude 189
A Visual Sense of Number 189
Interactions Between Space, Time, and Number 190
Effects of Saccades on Space, Time, and Number 193
Conclusions 196
Acknowledgments 197
References 197
Section IV. Origins of Proto-Mathematical Intuitions 200
Chapter 13. Origins of Spatial, Temporal, and Numerical Cognition: Insights from Comparative Psychology 204
Researching Human Cognition Through the Study of other Species 205
Are Some Cognitive Capacities in Place at Birth? 205
What is the Evolutionary Endowment of Human Cognition? 208
Closely Related Animal Models 208
Which Cognitive Abilities are Uniquely Human? 213
Distantly Related Animal Models 213
Concluding Remarks 215
References 217
Chapter 14. Evolutionary Foundations of the Approximate Number System 220
Shared Systems for Number Representation 222
The Relationship Between Time, Space, and Number 228
Arithmetic Reasoning 230
Conclusions 233
References 234
Chapter 15. Origins and Development of Generalized Magnitude Representation 238
The Big Three: Spatial Extent, Number, and Time 239
Beyond the Big Three Magnitudes and Cross-Modal Transfer 245
Particulars of the General Magnitude System 249
Conclusions 252
Acknowledgments 252
References 252
Section V. Representational Change and Education 258
Chapter 16. Foundational Numerical Capacities and the Origins of Dyscalculia 262
Why are People Bad at Learning Arithmetic? 262
Domain-Specific Foundational Capacities for Arithmetic 264
The Approximate Number System 266
The Small Numerosity System 267
Numerosity Coding 268
The Role of Language 270
The Neural Basis of Dyscalculia 271
Intervention 273
Concluding Remarks 273
Acknowledgments 275
References 275
Chapter 17. Neurocognitive Start-Up Tools for Symbolic Number Representations 280
The Approximate Number System 281
The Object Tracking System 283
The Role of the ANS and the OTS in the Acquisition of Symbolic Number Representations 285
Evidence for a Foundational Role of the ANS in Symbolic Number Processing 286
Evidence for a Foundational Role of the OTS in Symbolic Number Processing 291
Concluding Remarks 293
References 295
Chapter 18. Natural Number and Natural Geometry 300
A Core System of Number 302
A Core System of Geometry 307
More Core Systems 316
Constructing Natural Number 317
Constructing Natural Geometry 318
Conclusion and Prospects 326
References 327
Chapter 19. Geometry as a Universal Mental Construction 332
Universal Geometric Intuitions 334
Perception of Abstract Geometric Features 334
Normative Geometric Concepts 339
Conclusion 342
Acknowledgments 344
References 344
Chapter 20. How Languages Construct Time 346
The Axes of Time 347
Motion in Time 349
Reversing the Direction of Time 349
Duration 350
Representations of Time in Absolute Space 350
Summary 351
References 352
Chapter 21. Improving Low-Income Children’s Number Sense 356
Does Playing Numerical Board Games Improve Children’s Number Sense? 360
Generality of Learning Across Tasks and Time 361
Game Playing in the Everyday Environment 362
Which Features of Board Games Influence Learning? 363
Effects of other Preschool Mathematics Interventions 364
Conclusions 365
References 366
Index 368