Social Networks in Nonlinear Dynamics, Chaos and Fractals
We show how the seeds of twentieth century mathematical Chaos Theory grew in the networks associated with the internal combustion engine and radio electronics. We trace the mathematical discoveries of Henri Poincare in France at the beginning of the twent
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Social Networks in Nonlinear Dynamics, Chaos and Fractals
Abstract We show how the seeds of twentieth century mathematical Chaos Theory grew in the networks associated with the internal combustion engine and radio electronics. We trace the mathematical discoveries of Henri Poincare in France at the beginning of the twentieth century to the fluid mechanics weather models of Edward Lorenz at MIT and electrical circuits of Yoshisuke Ueda in Kyoto a half-century later. This example was chosen because of the author’s close familiarity with chaotic and nonlinear dynamics. This example and the radio network show that the ideas of a network community for innovation go beyond the examples from mechanical science in Chaps. 1–4.
6.1 Introduction to Modern Chaos Theory In the late 1970’s, the concept of unpredictability in deterministic science, what we now call Chaos Theory, became a major research area in nonlinear science. By the late 1980’s thousands of research papers had been written, popular books such as James Gleick’s Chaos 1987 were published and the American public TV series NOVA (1989) screened a popular show on “The Strange New Science of Chaos” in which this author appeared. How did the mathematical field of ‘nonlinear science’ emerge from academic esoterica in the 1970’s to become a cocktail circuit topic of discussion by the early 1990’s? One of the phenomena that resulted from this popularization was the explosion of the use of the word chaos in the world’s major newspaper headlines beginning around 1984 (Fig. 6.1). In 1980 there were recorded approximately 50 headlines a year using the word ‘chaos’ in major newspapers, whereas in the year 2000 there were more than 3000 headlines using the term (Source; LEXIS NEXIS). In 1998, the New York Times proclaimed “Congress in Chaos” and the same year the Times of London posted a headline, “Currency Chaos Spills Over into Bond Market”. As we
F. C. Moon, Social Networks in the History of Innovation and Invention, History of Mechanism and Machine Science 22, DOI: 10.1007/978-94-007-7528-2_6, © Springer Science+Business Media Dordrecht 2014
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6 Social Networks in Nonlinear Dynamics, Chaos and Fractals
Fig. 6.1 Graph of the number of headlines per year using the word ‘chaos’ in the world’s newspapers (Source LEXIS NEXUS)
shall see below, the rise of the popular interest in chaos lagged more than a decade behind the rise of interest in the mathematics, science and engineering communities. This chapter may be difficult to follow for the layperson not familiar with applied mathematics. It’s not like IC engines where most people have some contact with automotive components. The field of nonlinear science also has a number of subnetworks of which we shall describe five. Most of the names in the nodes of these networks are only known to the aficionados of chaos theory. Although this field appears outside the realm of technology, it grew naturally out of the networks of two other technologies as well as abstract mathematical analysis. For the layperson, one way to
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