vol 3: Development
5 Cybernetics
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... to restore theology to the mainstream of science
Cybernetics: Table of contents
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Page 1: Spaces We may see the physical world as a lot of objects (particles) moving around space. All movement takes time, so the stage for physics is physcial spacetime. From as more abstract point of view, we can consider any sort of structure which can be used to assign addresses to particles to be a space. A movement in such an abstract space is simply modelled a change of address. The study of the dynamics of such abstract spaces is cybernetics: the science (and art) of communication and control in the animal and the machine.
Page 2: The Mathematical theory of communication One of the most important abstract spaces is probability space, defined axiomatically by Kolmogorov. Shannon went on to develop the mathematical theory of communication using ideas from the mathematics of probability. The chances of messages being confused with one another depend on how close together they are in the abstract space of messages. By encoding messages into long sequences of symbols, the size of this space may be increased without limit, so that the probability of confusion and error may be as much as we wish by suitable coding.
Page 3: The control system A system may be able to control itself if it has a defined ideal state, a means of measuring how near or far it is from that state, and a means of moving itself toward the ideal state. The archetypal control system is the oven thermostat, which turns up the heat when the oven becomes too cool and turns it down when the oven becomes too hot. Control will be maintained if the system is properly tuned and outside influences are not too strong. An important function of cybernetics is to determine when control is possible and what conditions are necessary to achieve it.
Page 4: The limits to control We find that there are limits to the control of complex dynamic systems. Under sufficient provocation, I will 'lose my temper'. It is probable that a certain level of atmospheric carbon dioxide will force the earth into a different climatic regime. Changes in the circulation of warm and cold waters in the oceans can have similar effects. Because they are of great political and economic importance, the study of such limits to control is a very active area of modern research.
Books
| Jammer, Max, Concepts of Space: The History of Theories of Space in Physics, Dover 1994 Jacket: 'Although the concept of space is of fundamental importance in both physics and philosophy, until the publication of this book, the idea of space had never been treated in terms of its historical development. ... Following an introductory chapter on the concept of space in antiguity, subsequent chapters consider Judeaeo-Christian ideas about space, the emancipation of the space concept from Aristotelianism, Newton's concept of absolute space and the concept of space from the 18th century to the present. ... It is essential reading for philosphers, physicists and mathematicians, but even the nonprofessional reader will find it accessible, for the author has kept the technical language and mathematical details to a minimum.' Amazon back |
| Kolmogorov, A N , and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. ... This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be incomplete analogy with the corresponding properties of orthogonal functions ... 'back |
| Pierce, John Robinson, An Introduction to Information Theory: Symbols Signals and Noise, Dover 1980 Jacket: 'Behind the familiar surfaces of thhe telephone, radio and television lies a sophisticated and intriguing body of knowledge known as information theory. This is the theory that has permitted the rapid development of all forms of communication ... Even more revolutionary progress is expected in the future.' Amazon back |
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