C. R. Gallistel is Co-Director of the Rutgers Center for Cognitive Science. He is one of the foremost psychologists working on the foundations of cognitive neuroscience. His publications include The Symbolic Foundations of Conditional Behavior (2002), and The Organization of Learning (1990). Adam Philip King is Assistant Professor of Mathematics at Fairfield University.

• Preface viii1 Information 1Shannon’s Theory of Communication 2Measuring Information 7Efficient Coding 16Information and the Brain 20Digital and Analog Signals 24Appendix: The Information Content of Rare Versus Common 25Events and Signals2 Bayesian Updating 27Bayes’ Theorem and Our Intuitions about Evidence 30Using Bayes’ Rule 32Summary 413 Functions 43Functions of One Argument 43Composition and Decomposition of Functions 46Functions of More than One Argument 48The Limits to Functional Decomposition 49Functions Can Map to Multi-Part Outputs 49Mapping to Multiple-Element Outputs Does Not Increase Expressive Power 50Defining Particular Functions 51Summary: Physical/Neurobiological Implications of Facts about Functions 534 Representations 55Some Simple Examples 56Notation 59The Algebraic Representation of Geometry 645 Symbols 72Physical Properties of Good Symbols 72Symbol Taxonomy 79Summary 826 Procedures 85Algorithms 85Procedures, Computation, and Symbols 87Coding and Procedures 89Two Senses of Knowing 100A Geometric Example 1017 Computation 104Formalizing Procedures 105The Turing Machine 107Turing Machine for the Successor Function 110Turing Machines for fis even 111Turing Machines for f+ 115Minimal Memory Structure 121General Purpose Computer 122Summary 1248 Architectures 126One-Dimensional Look-Up Tables (If-Then Implementation) 128Adding State Memory: Finite-State Machines 131Adding Register Memory 137Summary 1449 Data Structures 149Finding Information in Memory 151An Illustrative Example 160Procedures and the Coding of Data Structures 165The Structure of the Read-Only Biological Memory 16710 Computing with Neurons 170Transducers and Conductors 171Synapses and the Logic Gates 172The Slowness of It All 173The Time-Scale Problem 174Synaptic Plasticity 175Recurrent Loops in Which Activity Reverberates 18311 The Nature of Learning 187Learning As Rewiring 187Synaptic Plasticity and the Associative Theory of Learning 189Why Associations Are Not Symbols 191Distributed Coding 192Learning As the Extraction and Preservation of Useful Information 196Updating an Estimate of One’s Location 19812 Learning Time and Space 207Computational Accessibility 207Learning the Time of Day 208Learning Durations 211Episodic Memory 21313 The Modularity of Learning 218Example 1: Path Integration 219Example 2: Learning the Solar Ephemeris 220Example 3: “Associative” Learning 226Summary 24114 Dead Reckoning in a Neural Network 242Reverberating Circuits as Read/Write Memory Mechanisms 245Implementing Combinatorial Operations by Table-Look-Up 250The Full Model 251The Ontogeny of the Connections? 252How Realistic Is the Model? 254Lessons to Be Drawn 258Summary 26515 Neural Models of Interval Timing 266Timing an Interval on First Encounter 266Dworkin’s Paradox 268Neurally Inspired Models 269The Deeper Problems 27616 The Molecular Basis of Memory 278The Need to Separate Theory of Memory from Theory of Learning 278The Coding Question 279A Cautionary Tale 281Why Not Synaptic Conductance? 282A Molecular or Sub-Molecular Mechanism? 283Bringing the Data to the Computational Machinery 283Is It Universal? 286References 288Glossary 299Index 312

"The book covers wide-ranging ground--indeed, it passes for a computer science or philosophy textbook in places--but it does so in a consistently lucid and engaging fashion." (CHOICE, December 2009) "The authors provide a cogent set of ideas regarding a kind of brain functional architecture that could serve as a thought-provoking alternative to that envisioned by current dogma. If one is seriously concerned with understanding and investigating the brain and how it operates, taking the time to absorb the ideas conveyed in this book is likely to be time well spent." (PsycCRITIQUES, November 2009) "Along with a light complement of fascinating psychological case studies of representations of space and time, and a heavy set of polemical sideswipes at neuroscientists and their hapless computational fellow travelers, this book has the simple goal of persuading us of the importance of a particular information processing mechanism that it claims does not currently occupy center stage." (Nature Neuroscience, October 2009)