Memory and the Computational Brain offers a provocative argument that goes to the heart of neuroscience, proposing that the field can and should benefit from the recent advances of cognitive science and the development of information theory over the course of the last several decades.

Preface viii 1 Information 1 Shannon’s Theory of Communication 2 Measuring Information 7 Efficient Coding 16 Information and the Brain 20 Digital and Analog Signals 24 Appendix: The Information Content of Rare Versus Common 25 Events and Signals 2 Bayesian Updating 27 Bayes’ Theorem and Our Intuitions about Evidence 30 Using Bayes’ Rule 32 Summary 41 3 Functions 43 Functions of One Argument 43 Composition and Decomposition of Functions 46 Functions of More than One Argument 48 The Limits to Functional Decomposition 49 Functions Can Map to Multi-Part Outputs 49 Mapping to Multiple-Element Outputs Does Not Increase Expressive Power 50 Defining Particular Functions 51 Summary: Physical/Neurobiological Implications of Facts about Functions 53 4 Representations 55 Some Simple Examples 56 Notation 59 The Algebraic Representation of Geometry 64 5 Symbols 72 Physical Properties of Good Symbols 72 Symbol Taxonomy 79 Summary 82 6 Procedures 85 Algorithms 85 Procedures, Computation, and Symbols 87 Coding and Procedures 89 Two Senses of Knowing 100 A Geometric Example 101 7 Computation 104 Formalizing Procedures 105 The Turing Machine 107 Turing Machine for the Successor Function 110 Turing Machines for fis even 111 Turing Machines for f+ 115 Minimal Memory Structure 121 General Purpose Computer 122 Summary 124 8 Architectures 126 One-Dimensional Look-Up Tables (If-Then Implementation) 128 Adding State Memory: Finite-State Machines 131 Adding Register Memory 137 Summary 144 9 Data Structures 149 Finding Information in Memory 151 An Illustrative Example 160 Procedures and the Coding of Data Structures 165 The Structure of the Read-Only Biological Memory 167 10 Computing with Neurons 170 Transducers and Conductors 171 Synapses and the Logic Gates 172 The Slowness of It All 173 The Time-Scale Problem 174 Synaptic Plasticity 175 Recurrent Loops in Which Activity Reverberates 183 11 The Nature of Learning 187 Learning As Rewiring 187 Synaptic Plasticity and the Associative Theory of Learning 189 Why Associations Are Not Symbols 191 Distributed Coding 192 Learning As the Extraction and Preservation of Useful Information 196 Updating an Estimate of One’s Location 198 12 Learning Time and Space 207 Computational Accessibility 207 Learning the Time of Day 208 Learning Durations 211 Episodic Memory 213 13 The Modularity of Learning 218 Example 1: Path Integration 219 Example 2: Learning the Solar Ephemeris 220 Example 3: “Associative” Learning 226 Summary 241 14 Dead Reckoning in a Neural Network 242 Reverberating Circuits as Read/Write Memory Mechanisms 245 Implementing Combinatorial Operations by Table-Look-Up 250 The Full Model 251 The Ontogeny of the Connections? 252 How Realistic Is the Model? 254 Lessons to Be Drawn 258 Summary 265 15 Neural Models of Interval Timing 266 Timing an Interval on First Encounter 266 Dworkin’s Paradox 268 Neurally Inspired Models 269 The Deeper Problems 276 16 The Molecular Basis of Memory 278 The Need to Separate Theory of Memory from Theory of Learning 278 The Coding Question 279 A Cautionary Tale 281 Why Not Synaptic Conductance? 282 A Molecular or Sub-Molecular Mechanism? 283 Bringing the Data to the Computational Machinery 283 Is It Universal? 286 References 288 Glossary 299 Index 312

Memory and the Computational Brain spans the fields of cognitive science, linguistics, psychology, neuroscience, and education, to suggest new perspectives on the way we consider learning mechanisms in the brain. Gallistel and King propose that the architecture of the brain is structured precisely for learning and for memory, and that the concept of an addressable read/write memory mechanism should be integrated into the foundations of neuroscience. They argue that the field of neuroscience can and should benefit from the recent advances of cognitive science and the development of information theory over the recent decades. Based on three lectures given by Randy Gallistel in the prestigious Blackwell-Maryland Lectures in Language and Cognition, the text has been significantly revised and expanded with numerous interdisciplinary examples and models and reflects recent research to make it essential reading for both students and those working in the field.

"Any scientist seriously interested in how the brain does its work will find Gallistel and King's new book indispensable.  It challenges modern dogma and does so in a clear and compelling manner." –Michael Gazzaniga, University of California, Santa Barbara "Gallistel and King present a provocative challenge to our current "standard model" of information processing in the brain. This book's ideas should be read and digested by both cognitive scientists and neuroscientists - anyone seriously interested in the biological or computational underpinnings of learning." –Joshua B. Tenenbaum, Massachusetts Institute of Technology "A lucid and convincing argument for a particular architecture for encoding information in the brain, based on some key notions of computational cognitive science, a significant contribution to neuroscience." –Aravind K. Joshi, University of Pennsylvania