Brains Machines and Mathematics

1 A Historical Perspective. - 1. 1 The Road to 1943. - 1. 2 Cybernetics Defined and Dissolved. - 1. 3 The New Rapprochement. - 2 Neural Nets and Finite Automata. - 2. 1 Logical Models of Neural Networks. - 2. 2 States Automata and Neural Nets. - 3 Feedback and Realization. - 3. 1 The Cybernetics of Feedback. - 3. 2 From External to Internal Descriptions. - 4 Pattern Recognition Networks. - 4. 1 Universals and Feature Detectors. - 4. 2 The Perceptron. - 4. 3 Learning without a Teacher. - 4. 4 Network Complexity. - 5 Learning Networks. - 5. 1 Connectionism. - 5. 2 Synaptic Matrices. - 5. 3 Hopfleld Nets and Boltzmann Machines. - 5. 4 Reinforcement Learning and Back-Propagation. - 6 Turing Machines and Effective Computations. - 6. 1 Manipulating Strings of Symbols. - 6. 2 Turing Machines Introduced. - 6. 3 Recursive and Recursively Enumerable Sets. - 7 Automata that Construct as well as Compute. - 7. 1 Self-Reproducing Automata. - 7. 2 Tesselations and the Garden of Eden. - 7. 3 Toward Biological Models. - 8 Gödel's Incompleteness Theorem. - 8. 1 The Foundations of Mathematics. - 8. 2 Incompleteness and Its Incremental Removal. - 8. 3 Predicate Logic and Godei's Completeness Theorem. - 8. 4 Speed-Up and Incompleteness. - 8. 5 The Brain - Machine Controversy. - Appendix Basic Notions of Set Theory. Language: English