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1987 | Buch

A Historical Perspective Kapitel lesen Erstes Kapitel lesen

Brains, Machines, and Mathematics

verfasst von: Michael A. Arbib

Verlag: Springer US

Enthalten in: Professional Book Archive

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. A Historical Perspective
Abstract
Many of the questions addressed in Artificial Intelligence (AI) and Brain Theory in fact have a long history. The aim of this chapter is to present briefly some of that history. Section 1, The Road to 1943, traces the story to 1943, which saw the publication of three remarkable papers: McCulloch and Pitts giving a logical theory of neural networks; Rosenbleuth, Wiener, and Bigelow asserting that a machine with feedback is imbued with purpose; while Craik saw the ability of the brain to simulate the world as providing the key to intelligence. Section 2, Cybernetics Defined and Dissolved, shows how Cybernetics emerged from these studies, only to give birth to a number of distinct new disciplines—such as AI, biological control theory, cognitive psychology, and neural modeling—which each went their separate ways, and shows how brain theory arose therefrom. Section 3 then charts the new rapprochement between AI and Brain Theory that gives new solutions to the cybernetic concerns of the 1940s and 1950s. We first note briefly the rap prochement among AI, cognitive psychology, and linguistics, which brought them together under the banner of cognitive science, and then see how the increasing concern of workers in AI and cognitive psychology with parallelism led to the development of the style known as “connectionism” or PDP (parallel distributed processing), which fosters the rapprochement with brain theory.
Michael A. Arbib
Chapter 2. Neural Nets and Finite Automata
Abstract
I want to start by giving a very sketchy account of neurophysiology—merely sufficient as a basis for our first mathematical model. We may regard the human nervous system as a three-stage system as shown in Figure 2.1.
Michael A. Arbib
Chapter 3. Feedback and Realization
Abstract
The word “cybernetics” was coined by Norbert Wiener, 1948, and his colleagues to denote “the (comparative) study of control and communication in the animal and the machine.” In a sense, then, all of the present book can be subsumed under the heading of “cybernetics.” However, in this section we will be primarily interested in feedback and related issues in control theory, which form one of the central themes discussed by Wiener in his book.
Michael A. Arbib
Chapter 4. Pattern Recognition Networks
Michael A. Arbib
Chapter 5. Learning Networks
Abstract
The cognitive science that emerged in the 1970s was based mainly on the serial information processing paradigm of artificial intelligence (AI) and the symbol-manipulation approach to linguistics, and had rather little contact with work in brain theory. However, there is now a growing interest in what is called the connectionist approach or Parallel Distributed Processing (PDP), the study of ways in which simple units may be interconnected to solve hard problems. This approach may to some extent be characterized as a reaction against the domination of AI by the paradigms of serial computation and, in some cases, explicit symbolic structures; but it can also be seen as the result of probing the microstructure of “symbols” and thus stressing the parallel processes underlying behavior. Of course, to the reader of this book, the approach is also a direct continuation of the work on adaptive pattern-recognition networks that we have sampled in Chapter 4.
Michael A. Arbib
Chapter 6. Turing Machines and Effective Computations
Abstract
In Chapter 2, we introduced the notion of a finite automaton by abstraction from the concept of a network of (McCulloch-Pitts) neurons. In this chapter, we wish to continue our study of automata in a more general setting. The Oxford English Dictionary defines an automaton (plural, automata) as “Something which has the power of spontaneous movement or self-motion; a piece of mechanism having its motive power so concealed that it appears to move spontaneously; now usually applied to figures which simulate the actions of living beings, as clockwork mice, etc.” Today the computer has replaced the clockwork mouse as the archetype of the automaton; and with it, our emphasis shifts from simulation of motion to simulation of information processing, although this will change again with the increasing importance of robotics. Automata theory, in its widest sense, might now embrace such diverse activities as the building of a space station’s control system or the programming of a computer to play chess. In the theory of abstract automata, we are less concerned with the design of automata to do specific tasks, and more concerned with understanding the capabilities and limitations of whole classes of automata. Our aim here is to develop enough abstract automata theory to allow us to answer interesting questions about the relationships among brains, machines, and mathematics.
Michael A. Arbib
Chapter 7. Automata that Construct as well as Compute
Abstract
In Section 7.1, we introduce the notion of a cellular (or tessellation) automaton, and show how to embed CT-machines within the cellular array. These have the computational power of Turing machines (thus the T) as well as the ability to Construct other CT-machines (thus the C). We then prove results about universal constructors and self-reproducing machines. In Section 7.2, we further formalize the notion of cellular automata, and prove that there exist Garden-of-Eden configurations that cannot arise in the cellular array without intervention of an external agency. Finally, Section 7.3 discusses differences between the type of self-reproduction formalized here and the growth processes of embryology.
Michael A. Arbib
Chapter 8. Gödel’s Incompleteness Theorem
Abstract
In this, our final chapter, we shift our center of interest first to the foundations of mathematics. In Section 8.1, we shall give a brief historical review of the formalist approach to the foundations of mathematics and see how Gödel’s incompleteness theorem invalidated much of the Formalist program. In Section 8.2, we shall discuss some general properties of recursive logics, yielding a proof of Gödel’s Incompleteness Theorem. We shall also follow Myhill’s surprising result that we can effectively remove this incompleteness, although never totally but only a part at a time. To deepen our understanding of Gödel’s work, we present a proof of his Completeness Theorem in Section 8.3, and show the way in which completeness and incompleteness coexist. Section 8.4 studies speed-up theorems: showing that adding an axiom to a logic may not only enable the proofs of new theorems, but also dramatic shortening of proofs that were already available. Finally, in Section 8.5, we return to the main theme of this book by discussing the philosophical controversy centering around the implications of Gödel’s theorem for the question: Are brains essentially superior to machines?
Michael A. Arbib
Backmatter
Metadaten
Titel
Brains, Machines, and Mathematics
verfasst von
Michael A. Arbib
Copyright-Jahr
1987
Verlag
Springer US
Electronic ISBN
978-1-4612-4782-1
Print ISBN
978-1-4612-9153-4
DOI
https://doi.org/10.1007/978-1-4612-4782-1