Free Will: Masters of our destiny or puppets on a string? Do human beings have Free Will? Are we the masters of our destiny or are we puppets on a string? An examination of the laws of nature dealing with causality and randomness. Excerpt from Book: "How Life Really Works" Chapter 01.00: Objective Reality Sub-Chapter 01.07: Free Will vs. Determinism Due to space limitations, sections in Red are accessible only in the Book or CD "How Life Really Works". Causality Deviations from Causality Chaos and the Uncertainty Principle The Merger of Causality and Chaos Confirmation of Free Will Causality Free Will is the philosophical doctrine that human beings have the power to choose from alternatives, unrestrained by causality or by preordained mystical powers. Determinism is the philosophical doctrine that every event in the universe is the inevitable consequence of a preceding cause.
Similar but essentially unrelated concepts deal with Predestination and Predetermination. This generalization of cause/effect relationships leads to erroneous assumptions. Chaos. 1. Defining Chaos: Determinism, Nonlinearity and Sensitive Dependence The mathematical phenomenon of chaos is studied in sciences as diverse as astronomy, meteorology, population biology, economics and social psychology.
While there are few (if any) causal mechanisms such diverse disciplines have in common, the phenomenological behavior of chaos—e.g., sensitivity to the tiniest changes in initial conditions or seemingly random and unpredictable behavior that nevertheless follows precise rules—appears in many of the models in these disciplines. Observing similar chaotic behavior in such diverse fields certainly presents a challenge to our understanding of chaos as a phenomenon. 1.1 A Brief History of Chaos Arguably, one can say that Aristotle was already aware of something like what we now call sensitive dependence.
Writing about methodology and epistemology, he observed that “the least initial deviation from the truth is multiplied later a thousandfold” (Aristotle OTH, 271b8). PoincareTalk.pdf. The Butterfly Effect - Chaos & Fractals. Weather prediction is an extremely difficult problem. Meteorologists can predict the weather for short periods of time, a couple days at most, but beyond that predictions are generally poor. Edward Lorenz was a mathematician and meteorologist at the Massachusetts Institute of Technology who loved the study of weather.
With the advent of computers, Lorenz saw the chance to combine mathematics and meteorology. He set out to construct a mathematical model of the weather, namely a set of differential equations that represented changes in temperature, pressure, wind velocity, etc. In the end, Lorenz stripped the weather down to a crude model containing a set of 12 differential equations. On a particular day in the winter of 1961, Lorenz wanted to re-examine a sequence of data coming from his model. At first Lorenz thought that a vacuum tube had gone bad in his computer, a Royal McBee — an extremely slow and crude machine by today's standards. Chaos Theory. Chaos Chaos, in many traditional cosmogonies, is the earliest state of the universe. Perhaps surprisingly, this is also the view of modern cosmologists. They see the universe starting in a state of "thermodynamical equilibrium" or maximum entropy about 13.7 billion years ago.
Chaos is often defined as the complete absence of order, and consequently of information. For the Greeks, the opposite of chaos was cosmos, an ordered and beautiful universe. The Stoic Chrysippus (200 B.C.E.) said that a single uncaused cause could destroy the universe (cosmos), which would fall into chaos. Everything that happens is followed by something else which depends on it by causal necessity. Chaos and the Kinetic Theory of Gases The name "gas" was coined by a Dutch chemist as a variation on the word "chaos" The closest thing to perfect chaos in a physical theory is a gas in thermodynamical equilibrium, a state of maximum disorder or maximum entropy.
Deterministic Chaos (J. For Teachers For Scholars. Deterministic Chaos. Wjmsvol05no02paper09.pdf. PySpectrum Space. Spectral density, periodograms, Numeric « python-list « ActiveState List Archives. Qc.pdf. Pythonissue_3of4.pdf. CHAOS - CLASSICAL AND QUANTUM: extras. Iterated Function Systems - Chaos & Fractals. Fractals reproducing realistic shapes, such as mountains, clouds, or plants, can be generated by the iteration of one or more affine transformations.
An affine transformation is a recursive transformation of the type Each affine transformation will generally yield a new attractor in the final image. The form of the attractor is given through the choice of the coefficients a through f, which uniquely determine the affine transformation. To get a desire shape, the collage of several attractors may be used (i.e. several affine transformations). This method is referred to as an Iterated Function System (IFS). An example of an iterated function system is the black spleenwort fern. The resulting image is: This image is infinitely complex — it is a self-similar fractal on all scales. Iterated function system. In mathematics, iterated function systems or IFSs are a method of constructing fractals; the resulting constructions are always self-similar. IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system").
The canonical example is the Sierpinski gasket also called the Sierpinski triangle. The functions are normally contractive which means they bring points closer together and make shapes smaller. Definition[edit] Formally, an iterated function system is a finite set of contraction mappings on a complete metric space.[1] Symbolically, is an iterated function system if each is a contraction on the complete metric space Properties[edit] Hutchinson (1981) showed that, for the metric space has the property The set S is thus the fixed set of the Hutchinson operator for any nonempty compact set in . ). Notes[edit] Chaos.