Brains, Machines, and Mathematics

ISBN-13: 9781461291534 / Angielski / Miękka / 2011 / 202 str.

Michael A. Arbib

Opis

This is a book whose time has come-again. The first edition (published by McGraw-Hill in 1964) was written in 1962, and it celebrated a number of approaches to developing an automata theory that could provide insights into the processing of information in brainlike machines, making it accessible to readers with no more than a college freshman's knowledge of mathematics. The book introduced many readers to aspects of cybernetics-the study of computation and control in animal and machine. But by the mid-1960s, many workers abandoned the integrated study of brains and machines to pursue artificial intelligence (AI) as an end in itself-the programming of computers to exhibit some aspects of human intelligence, but with the emphasis on achieving some benchmark of performance rather than on capturing the mechanisms by which humans were themselves intelligent. Some workers tried to use concepts from AI to model human cognition using computer programs, but were so dominated by the metaphor "the mind is a computer" that many argued that the mind must share with the computers of the 1960s the property of being serial, of executing a series of operations one at a time. As the 1960s became the 1970s, this trend continued. Meanwhile, experi mental neuroscience saw an exploration of new data on the anatomy and physiology of neural circuitry, but little of this research placed these circuits in the context of overall behavior, and little was informed by theoretical con cepts beyond feedback mechanisms and feature detectors."

Spis treści

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.