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Foreword; From Turing Machines to the Dynamical Explanation of Algorithmic Skills; Acknowledgements; Contents; Acronyms; Introduction; Outline of the Work; 1 Turing's Theory of Computation; 1.1 Turing Machine: Architecture and Functioning; 1.1.1 Architecture; 1.1.2 Some Examples of Turing Machines; 1.2 The Aim of Turing's 1936 Work; 1.3 The Classic-Computationalist Interpretation of the Turing Machine; 1.4 The Ecological Interpretation of the TM's Architecture (Andrew Wells); References; 2 Cognition as Organism-Environment Interaction; 2.1 Active Externalism.
2.2 Ontological Versus Functional-Explanatory Issues2.2.1 The Ontological Question; 2.2.2 The Functional-Explanatory Question; 2.3 The Cognitive Value of the TM; 2.3.1 Arguments Against the Computational Theory of Mind; 2.3.2 Neural Networks as Finite Automata; 2.3.3 Advantages and Disadvantages of the Turing Machine; 2.4 A Model for Gibson's Concept of Affordance; 2.4.1 Formal Models of Affordance; 2.4.2 Affordances and Effectivities as Quintuples of a TM; References; 3 Ecological Approach and Dynamical Approach; 3.1 Cognitive Systems as Dynamical Systems; 3.1.1 Lines of Investigation.
3.1.2 Philosophical Issues3.1.3 Dynamical Approach Versus Classic Computationalism; 3.2 Turing Machines as Dynamical Models; 3.2.1 Dynamical Systems; 3.2.2 Components and Basic Operations of the Turing Machine; References; 4 Modeling Algorithmic Skills: The Bidimensional Turing Machine; 4.1 A TM-Inspired Model of Computational Skills; 4.1.1 Definitions; 4.2 Two Examples of BTM; 4.2.1 BTM1 (Counting-All Strategy); 4.2.2 BTM2 (Counting Objects on a Grid); 4.3 Algorithms, Empirical Models, and Galilean Models; 4.3.1 Algorithmic Skills; 4.3.2 Empirical Interpretations.
4.3.3 A Possible Galilean Model of Algorithmic SkillsReferences; 5 BTM Models of Algorithmic Skills; 5.1 Core Systems Approach; 5.1.1 Nativism; 5.1.2 Constructivism; 5.2 Numerical Skills and Space Representation; 5.2.1 Ordering Numbers in Space; 5.2.2 Space and Algorithmic Execution; 5.2.3 Different Cognitive Contributions; 5.3 Algorithmic Performance and the Development of Numerical Abilities; 5.3.1 A Method of Investigation; 5.3.2 From Simple to Complex Strategies; 5.3.3 Single-Digit Addition: Two Algorithms of Decreasing Complexity; 5.3.4 Comparison Between Algorithms.
5.4 External and Internal Resources5.4.1 Working Memory and Algorithmic Skills; 5.4.2 BTM5: The Column Algorithm for Addition; 5.4.3 Model Analysis; 5.5 Mental Versus External Strategies; 5.5.1 BTM6: A Mental Algorithm for Multi-digit Additions; 5.5.2 BTM7: Mental Column-Based Addition; 5.5.3 BTM6 and BTM7: Comparison of Models; 5.6 From Cognitive to Subcognitive Skills: A Neural Net Simulation; 5.6.1 Finger Counting; 5.6.2 BTM8: Finger Counting Procedure; 5.6.3 A Neural Net for Performing SDAs; 5.6.4 Problem-Size Effect; References; Conclusion.
2.2 Ontological Versus Functional-Explanatory Issues2.2.1 The Ontological Question; 2.2.2 The Functional-Explanatory Question; 2.3 The Cognitive Value of the TM; 2.3.1 Arguments Against the Computational Theory of Mind; 2.3.2 Neural Networks as Finite Automata; 2.3.3 Advantages and Disadvantages of the Turing Machine; 2.4 A Model for Gibson's Concept of Affordance; 2.4.1 Formal Models of Affordance; 2.4.2 Affordances and Effectivities as Quintuples of a TM; References; 3 Ecological Approach and Dynamical Approach; 3.1 Cognitive Systems as Dynamical Systems; 3.1.1 Lines of Investigation.
3.1.2 Philosophical Issues3.1.3 Dynamical Approach Versus Classic Computationalism; 3.2 Turing Machines as Dynamical Models; 3.2.1 Dynamical Systems; 3.2.2 Components and Basic Operations of the Turing Machine; References; 4 Modeling Algorithmic Skills: The Bidimensional Turing Machine; 4.1 A TM-Inspired Model of Computational Skills; 4.1.1 Definitions; 4.2 Two Examples of BTM; 4.2.1 BTM1 (Counting-All Strategy); 4.2.2 BTM2 (Counting Objects on a Grid); 4.3 Algorithms, Empirical Models, and Galilean Models; 4.3.1 Algorithmic Skills; 4.3.2 Empirical Interpretations.
4.3.3 A Possible Galilean Model of Algorithmic SkillsReferences; 5 BTM Models of Algorithmic Skills; 5.1 Core Systems Approach; 5.1.1 Nativism; 5.1.2 Constructivism; 5.2 Numerical Skills and Space Representation; 5.2.1 Ordering Numbers in Space; 5.2.2 Space and Algorithmic Execution; 5.2.3 Different Cognitive Contributions; 5.3 Algorithmic Performance and the Development of Numerical Abilities; 5.3.1 A Method of Investigation; 5.3.2 From Simple to Complex Strategies; 5.3.3 Single-Digit Addition: Two Algorithms of Decreasing Complexity; 5.3.4 Comparison Between Algorithms.
5.4 External and Internal Resources5.4.1 Working Memory and Algorithmic Skills; 5.4.2 BTM5: The Column Algorithm for Addition; 5.4.3 Model Analysis; 5.5 Mental Versus External Strategies; 5.5.1 BTM6: A Mental Algorithm for Multi-digit Additions; 5.5.2 BTM7: Mental Column-Based Addition; 5.5.3 BTM6 and BTM7: Comparison of Models; 5.6 From Cognitive to Subcognitive Skills: A Neural Net Simulation; 5.6.1 Finger Counting; 5.6.2 BTM8: Finger Counting Procedure; 5.6.3 A Neural Net for Performing SDAs; 5.6.4 Problem-Size Effect; References; Conclusion.