The misuse of mathematics
The computer revolution has begotten new branches of mathematics: e.g., chaos theory and fractal geometry and their offspring, agent based modeling and complex dynamical systems. These new methods have extended and changed our understanding of the complex systems in which we live. But math models and computer simulations are frequently misunder-stood, or intentionally misrepresented, with disastrous results. In this essay, we recall the concept of structural stability from dynamical systems theory, and its role in the interpretation of modeling.
KeywordsDynamical System Theory Chaos Theory Structural Instability Complex Dynamical System Shoreline Erosion
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- 1.Abraham, R.: Dynamics. The Geometry of Behavior. Aerial Press, Santa Cruz, CA (1981)Google Scholar
- 2.Abraham, R.: Foundations of Mechanics, 2nd edn. AMS Chelsea, Providence, RI (2008)Google Scholar
- 3.Abraham, R.: Climate warming skeptics (2007) Available online. http://www.vismath.org/research/gaia/2007/climate-nay.htmlGoogle Scholar
- 4.Abraham, R.: Gaia theory (2000) Available online. http://www.vismath.org/research/gaia/Google Scholar
- 5.Hirst, H.: Using the historical development of predator-prey models to teach mathematical modeling. In: Shell-Gellasch, A., Jardine, D. (eds.) From Calculus to Computers: Using the Last 200 years of Mathematics History in the Classroom, pp. 45–54. Math. Assoc. of America, Washington, DC (2005)Google Scholar
- 6.Lovelock, J.: Gaia: A New Look at Life on Earth. Oxford, UK (1979)Google Scholar
- 7.Lovelock, J.: The Revenge of Gaia: Why the Earth is Fighting Back — and How We Can Still Save Humanity. Allen Lane, New York, London (2006)Google Scholar
- 8.Pilkey, O. H., Pilkey-Jarvis, L.: Useless Artithmetic: Why Environmental Sciencetists Can’t Predict the Future. Columbia University Press, New York (2007)Google Scholar