Saturday, December 8, 2012

Chaos theory; Toth Giza and Fibonacci connection

  • Toth Giza and Fibonacci connection -
     A dynamical system consists in two parts: the notions of a state (the essential information about a system) and a dynamic (a rule that describes how the state evolves with time). This evolution can be visualized in a phase space.
    Toth Giza and Fibonacci connection 
    you will see how Chaos theory fits/explains the pyramid configurations.!                                                                          

        Phase space is handy because it provides a way to represent all the possible states of a system with one picture. It is a graph of the variables, such as position and velocity, that determine the state of a system. We will talk about phase space in more depth in Unit 13. For our purposes here, it suffices to say that examining graphical representations of systems of differential equations can yield a wealth of qualitative information about the system, such as whether or not it will display cyclical or synchronous behavior.
    •  For example, think of a simple pendulum oscillating on a vertical plane. Assuming that there are no damping forces, there’s energy conservation. However, traditional numerical methods (such as Runge-Kutta methods) do not, in general, preserve energy. The numerical simulation of the pendulum may thus exhibit non-physical energy dissipation (or amplification). 
      In my early days as an undergraduate student, I had a lot of fun writing C code
      to integrate ODE’s numerically, so I could simulate physical systems in a computer (integrating the pendulum OD...
    •  I don't know much abt this stuff...but I love "Chaos - Making a New Science) by - James Gleick about Conrad Lorenz and his Lorenz Attractor, and Stephen Smale..Feigenbuam...Mandelbrot...most of the rest is commentary, albeit from some very brilliant people..but those guys are the berries....
      Strange attractor
      "Perhaps surprisingly, chaos may occur also in linear systems, provided they are infinite-dimensional.[20] A theory of linear chaos is being developed in a branch of mathematical analysis known as functional analysis."
      Chaos theory is a field of study in mathematics, with applications in several di
      sciplines including physics, engineering, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the butterfly effect..
      Mandelbrot set
      Chaos: Making A New Science is the best-selling book by James Gleick that first
      introduced the principles and early development of chaos theory to the public.[1] It was a finalist for the National Book Award[2] and the Pulitzer Prize[3] in 1987, and was shortlisted for the Science Book Prize in 1989...
        Stephen Smale is a mathematician.. He was awarded the Fields Medal in 1966, on the steps of Moscow University..First he pilloried the American war in vietnam, and the Russians loved him...then he shoved his foot up the russkies butt abt Afghanistan, and they took him away in black cars...true!!..Lorenz, smale, Feigenbaum..heroes..Mandlebrot...all genius...tremendous book..much of the scientists personal history has been whitwashed, but James Gleck tells all.. 
    •   Earlier in his career, Smale was involved in controversy over remarks he made regarding his work habits while proving the higher dimensional Poincaré conjecture. He said that his best work had been done "on the beaches of Rio".[2] This led to the withholding of his grant money from the NSF. He has been politically active in various movements in the past, such as the Free Speech movement. At one time he was subpoenaed by the House Un-American Activities Committee.
      Steven Smale a.k.a. Steve Smale, Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–61 and 1964–1995).

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