After seeing Ashton Kutcher's film 'The Butterfly Effect' all scientific credibility Chaos Theory had in my mind went out the window. After reading the first chapter of Gleick's book also titled 'The Butterfly Effect' my mind was completely changed.
Chapter 1: The Butterfly Effect
How does such a small error of 0.000127 change the weather forecast completely? What 12 mathematical equations can obscure results so much based on so little change? Since our initial conditions are measurements with error themselves is that way long rang forecasting is almost always wrong. What if our initial conditions had no error in them? What are the bounds of the Lorenz Attractor and why are they the bounds?
Chapter 2:Revolution
Hard to believe we are still learning new things from something as simple as a pendulum. I don't really understand what Smale is trying to show with his stretching/folding of shapes, i.e. Smale's Horseshoe. Quite interesting that one of the first big questions Chaos solved was over 400 years old and about another planet (Jupiter's Giant Red Spot).
Chapter 3: Life's Ups and Downs
I agree with Yorke's notion that we learned not to see chaos. Why does a growth rate of 3 send the population into a chaotic behavior. What happens when the growth rate is a special number such as Pi?
Chapter 4: A Geometry of Nature
I am very interested in learning more about fractals and their prediction of the economy. Fractals are so simple is very hard to believe humanity has overstepped them for this long. This chapter and the previously linked videos have left me with too many questions. The Mandelbrot set is unbelievable, literally. It seems like something out of a movie. I'm glad my area of research is focused around fractals for it's by far the most interesting topic in this book.
Chapter 5: Strange Attractors
This chapter was a little abstract so I tried to get a more solid definition first, http://en.wikipedia.org/wiki/Strange_attractor#Strange_attractor, I understand the idea of a strange attractor (the Lorenz example helps) but it is still foggy and I should read more about phase space. I feel the generally idea of the chapter was to show that dynamic systems follow some sort of "strange attractor" and when the phase space of this system is plotted it turns out to be some geometrical pattern (ex butterfly-ish wings for the lorenz attractor).
Chapter 6: Universality
Goethe thoughts on colour are very interesting. When Feigenbaum talks about the picnickers becoming incomprehensible as distance grew between them, does this have anything to do with why the Sierpinski Gasket can start with any image and produce the same result? That is the further you iterate the less comprehensible the original image. How does Feigenbaum's universality constant work? Why is the doubling period always 4.6692016090 for any bifurcating function? What are the implications of this?
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Looks really good!! Admittedly I don't really understand what Smale is trying to say either, nor do I know much about Feigenbaum's constant. Feel free to spend time looking into those things. And we can definitely try to find out more about fractals and the economy.
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