Hello. Good morning. (An information on fractals is at the bottom of the description for Chaos Theory.)
When my professor finishes marking my paper (A Recapitulation of Pannenberg’s “The Theology of Creation and the Natural Sciences” in: The Historicity of Nature, PA:Templeton, 2008, 25–39.) I will upload it here.
But first, as preliminaries, I want to share a few information that served as submitted-supplement to that paper and which I thought was necessary to have at least the minimum grip on in order to appreciate Pannenberg’s above-mentioned book-chapter.
That is, I did some readings on these in order to ready myself for the class report. Additionally, having a glimpse of the enormity of subject areas that Pannenberg has been trying to link [together] makes one appreciative of the breadth of Pannenberg’s outlook on the connectivity and source of everything: God. I wouldn’t have appreciated Pannenberg [that] much had I no inkling at all of concepts he had in his sights while doing his theological reflections in relation to the natural world.
I’m grateful to authors who make available on the web easily understood basic information on specialized areas of knowledge, like the ones here that I found, below.
Here is the Supplements now [very sligthly edited]:
SUPPLEMENT PAGE | PANNENBERG: The Theology of Creation and the Natural Sciences. [Oberseminar SS2014]
♦ natural science = any of the sciences (as physics, chemistry, or biology) that deal with matter, energy, and their interrelations and transformations or with objectively measurable phenomena (Merriam-Webster)
♦ quantum physics = the study or description of components and processes within the atom
♦ indeterminacy in quantum physics = Heisenberg’s term ‘inaccuracy relations’ (Ungenauigkeitsrelationen) or ‘indeterminacy relations’ (Unbestimmtheitsrelationen) was dealt with in his 1927 papers where he said of sub-atomic particles (paraphrased here ->) “You cannot know the position of a particle and how fast it’s moving with arbitrary precision at the same moment… The more accurately you know the position, more uncertain you are about the momentum and vice versa… So we have essentially given up on predicting the position of a particle accurately, because of the uncertainty principle. All we can do is predict the probabilities.” (http://www.buzzle.com/articles/basics-of-quantum-mechanics-for-dummies.html ; http://plato.stanford.edu/entries/qt-uncertainty/) both accessed 20June2014
♦ chaos theory = the study of how even simple systems can display complex behaviour. These systems can seem straightforward — but are very sensitive to initial starting conditions and this can cause seemingly ‘random’ effects. (homeschooling-ideas.com)
♦ field = in physics, region throughout which a force may be exerted; examples are the gravitational, electric, and magnetic fields that surround, respectively, masses, electric charges, and magnets. Fields are used to describe all cases where two bodies separated in space exert a force on each other. Each type of force has its own appropriate field. (The Columbia Electronic Encyclopedia)
♦ for descriptions on spacetime, etc, this webpage may be of help: http://www.ws5.com/spacetime/
What is Chaos Theory? http://fractalfoundation.org/resources/what-is-chaos-theory/ [accessed 20June2014]
Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. […] By understanding the complex, chaotic dynamics of the atmosphere, a balloon pilot can “steer” a balloon to a desired location. By understanding that our ecosystems, our social systems, and our economic systems are interconnected, we can hope to avoid actions which may end up being detrimental to our long-term well-being.
PRINCIPLES OF CHAOS:
• THE BUTTERFLY EFFECT: This effect grants the power to cause a hurricane in China to a butterfly flapping its wings in New Mexico. It may take a very long time, but the connection is real. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results.
• UNPREDICTABILITY: Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot hope to predict the ultimate fate of a complex system. Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless. Since it is impossible to measure the effects of all the butterflies (etc) in the World, accurate long-range weather prediction will always remain impossible.
• ORDER / DISORDER: Chaos is not simply disorder. Chaos explores the transitions between order and disorder, which often occur in surprising ways.
• MIXING: Turbulence ensures that two adjacent points in a complex system will eventually end up in very different positions after some time has elapsed. Examples: Two neighboring water molecules may end up in different parts of the ocean or even in different oceans. A group of helium balloons that launch together will eventually land in drastically different places. Mixing is thorough because turbulence occurs at all scales. It is also nonlinear: fluids cannot be unmixed.
• FEEDBACK: Systems often become chaotic when there is feedback present. A good example is the behavior of the stock market. As the value of a stock rises or falls, people are inclined to buy or sell that stock. This in turn further affects the price of the stock, causing it to rise or fall chaotically.
• FRACTALS: Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. […] Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. ⊗
That’s it. For a quick peek at fractals you may click on my Home tab, above, and the page opened will have a few illustrations of fractals beneath that themselves are links to explanatory pages on them.
Viel Spaß und alles Gute. Ciao.