“Many workers in the biological sciences — physiologists, psychologists, sociologists — are interested in cybernetics and would like to apply its methods and techniques to their own specialty. Many have, however, been prevented from taking up the subject by an impression that its use must be preceded by a long study of electronics and advanced pure mathematics; for they have formed the impression that cybernetics and these subjects are inseparable.
The author is convinced, however, that this impression is false. The basic ideas of cybernetics can be treated without reference to electronics, and they are fundamentally simple; so although advanced techniques may be necessary for advanced applications, a great deal can be done, especially in the biological sciences, by the use of quite simple techniques, provided they are used with a clear and deep understanding of the principles involved. It is the author’s belief that if the subject is founded in the common-place and well understood, and is then built up carefully, step by step, there is no reason why the worker with only elementary mathematical knowledge should not achieve a complete understanding of its basic principles. With such an understanding he will then be able to see exactly what further techniques he will have to learn if he is to proceed further; and, what is particularly useful, he will be able to see what techniques he can safely ignore as being irrelevant to his purpose.”

—  W. Ross Ashby

Preface
An Introduction to Cybernetics (1956)

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W. Ross Ashby26
British psychiatrist 1903–1972

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“In the history of mathematics, the "how" always preceded the "why," the technique of the subject preceded its philosophy.”

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“Cybernetics was defined by Wiener as “the science of control and communication, in the animal and the machine” — in a word, as the art of steermanship, and it is to this aspect that the book will be addressed. Co-ordination, regulation and control will be its themes, for these are of the greatest biological and practical interest.
We must, therefore, make a study of mechanism; but some introduction is advisable, for cybernetics treats the subject from a new, and therefore unusual, angle… The new point of view should be clearly understood, for any unconscious vacillation between the old and the new is apt to lead to confusion.”

W. Ross Ashby (1903–1972) British psychiatrist

Source: An Introduction to Cybernetics (1956), Part I: Mechanism, p. 1: Lead paragraph

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“A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 286; Cited in: Moritz (1914, 106): Modern mathematics.

“Cybernetics is a young discipline which, like applied mathematics, cuts across the entrenched departments of natural science; the sky, the earth, the animals and the plants. Its interdisciplinary character emerges when it considers economy not as an economist, biology not as a biologist, engines not as an engineer. In each case its theme remains the same, namely, how systems regulate themselves, reproduce themselves, evolve and learn. Its high spot is the question of how they organize themselves.
A cybernetic laboratory has a varied worksheet - concept formation in organized groups, teaching machines, brain models, and chemical computers for use in a cybernetic factory. As pure scientists we are concerned with brain-like artifacts, with evolution, growth and development; with the process of thinking and getting to know about the world. Wearing the hat of applied science, we aim to create what Boulanger,' in his presidential address to the International Association of Cybernetics, called the instruments of a new industrial revolution - control mechanisms that lay their own plans.”

Gordon Pask (1928–1996) British psychologist

Source: An Approach to Cybernetics (1961), p. 11. Partly cited in: A.M.E. Salazar, A. Espinosa, J. Walker (2011) A Complexity Approach to Sustainability: Theory and Application. p. 11.

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“Many of the core ideas of cybernetics have been assimilated by other disciplines, where they continue to influence scientific developments. Other important cybernetic principles seem to have been forgotten, though, only to be periodically rediscovered or reinvented in different domains. Some examples are the rebirth of neural networks, first invented by cyberneticists in the 1940's, in the late 1960's and again in the late 1980's; the rediscovery of the importance of autonomous interaction by robotics and AI in the 1990's; and the significance of positive feedback effects in complex systems, rediscovered by economists in the 1990's. Perhaps the most significant recent development is the growth of the complex adaptive systems movement, which, in the work of authors such as John Holland, Stuart Kauffman and Brian Arthur and the subfield of artificial life, has used the power of modern computers to simulate and thus experiment with and develop many of the ideas of cybernetics. It thus seems to have taken over the cybernetics banner in its mathematical modelling of complex systems across disciplinary boundaries, however, while largely ignoring the issues of goal-directedness and control.”

Francis Heylighen (1960) Belgian cyberneticist

Source: Cybernetics and Second-Order Cybernetics (2001), p.5 : About the state of the art of contemporary cybenetics

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“Now "cybernetics" is the term coined by Wiener to denote "steersmanship" or the science of control. Although current engineering usage restricts it to the study of flows in closed systems, it can be taken in a wider context, as the study of processes interrelating systems with inputs and outputs, and their structural-dynamic structure. It is in this wider sense that "cybernetics" will be used here, to wit, as system-cybernetics, understanding by "system" an ordered whole in relation to its relevant environment”

Ervin László (1932) Hungarian musician and philosopher

hence one actually or potentially open
Source: Introduction to Systems Philosophy (1972), p. 38.

Mary Midgley photo

“Scientism exalts the idea of science on its own, causing people to become fixated on the assumptions that seemed scientific to them during their formative years. This prevents them from seeing contrary facts, however glaring they may be, that have been noticed more lately.”

Mary Midgley (1919–2018) British philosopher and ethicist

Are You an Illusion (2014). 5.

Stuart A. Umpleby photo

“During the 1950s and 1960s most of the work which was called cybernetics tended to focus on control systems in engineering or on applications of the concept of feedback in fields ranging from mathematics to sociology. At the 1970 meeting of the American Society for Cybernetics in Philadelphia Heinz von Foerster sought to redirect attention to the original interests which had led to the founding of the field of cybernetics. In a paper titled "Cybernetics of Cybernetics" he made a distinction between first order cybernetics, the cybernetics of observed systems, and second order cybernetics, the cybernetics of observing systems.”

Stuart A. Umpleby (1944) American scientist

Stuart A. Umpleby (1991) "Strategies for Winning Acceptance of Second Order Cybernetics." In George E. Lasker, et al. (eds.) Advances in Human Systems and Information Technologies. Windsor, Canada: International Institute for Advanced Studies in Systems Research and Cybernetics, 1992. pp. 97-196. (paper)

Thomas Little Heath photo

“Dr. James Gow did a great service by the publication in 1884 of his Short History of Greek Mathematics, a scholarly and useful work which has held its own and has been quoted with respect and appreciation by authorities on the history of mathematics in all parts of the world. At the date when he wrote, however, Dr. Gow had necessarily to rely upon the works of the pioneers Bretschneider, Hankel, Allman, and Moritz Cantor (first edition). Since then the subject has been very greatly advanced… scholars and mathematicians… have thrown light on many obscure points. It is therefore high time for the complete story to be rewritten.”

Thomas Little Heath (1861–1940) British civil servant and academic

A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

“The subject matter of mathematics has increased so rapidly and extensively that there is some element of truth in maintaining that mathematics is not so much a subject as a way of studying any subject, not so much a science as a way of life. We turn, then, from the attempt to characterize the material object of mathematics to an attempt to determine its formal object, i. e., its methodology.”

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

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