Seattlegal said:
Alright, I'll throw out some descriptions of "non-linear reality" from various perspectives:
- effects not proportional to causes -->"he who causes to become"
- output not proportional to input -->metaphorical "transistor" effect
Feel free to add more.
Very misleading. There is a relationship between inputs and outputs in both linear and non-linear equations or systems. Y=aX is an example of linear. Y=aX^2 is an example of non-linear. For the non-linear example the output is '
proportional' to the input squared. It is deterministic and there is a determined relationship between inputs and outputs. In science there is a fixed and measurable relationship between cause and effect... even though not every input is measurable and known. That is to say for example science says the location that I place my fingers on this keyboard does factor into the resulting gravity for everyone else, whether anyone considers it significant or not.
Paladin said:
You bring up a good point here, aside from the antagonistic tone, about word usage. Had I realized your sensitivity on this point I would have avoided using the term nonlinear altogether, so for that I apologize. The term is used so much in mathematics and physics it is unusual to find it anywhere else, yet it does crop up in sociology as well, such as in this paper:
RFI - Symbolic Interactional Theory and Nonlinear Dynamics
Define antagonistic tone. If it bothers you that I ask for proof from an atheist, or clear definition of his terms I will stop. I am NOT bothered being asked for proof of God (swt) or definition of terms. So there is no need to apologize. There is no sensitivity to your words and I see it as a puzzle worth the applied thought.
The paper you provided is using the term nonlinear dynamics properly. In differential equations a linear example is Y = a * dX/dt A non-linear example is: Y = a * (dX/dT)^2. In words the equations mean Y is proportional to the speed of X or Y is proportional to the speed of X squared. Nothing magical. The second equation is a non-linear dynamic.
The paper you provided is using the term 'non-linear dynamic' from science correctly. Some non-linear systems get complex from seemingly simple equations. The study of that resulted into chaos theory. Complex systems but nevertheless deterministic systems where the outputs are proportional to some equation of inputs.
There are very real examples in the world but if you do not have the patience to learn the math then I can provide some intuitive examples to understand. Imagine placing a chair in an initial condition so that it rests balanced on one leg. The system is momentarily stable about a very complex set of outcomes. Then someone farts and an air molecule hits the chair and sets it on a path towards lower energy. To know the path the chair with any accuracy is going to take extreme knowledge of nearly every atom of it and its surroundings, especially at the pivot point and friction surfaces. Another example would be a boulder on a hill that is nudged to roll down and start an avalanche. Or a hurricane that was started by something very small. The path and state of that hurricane at any point in time depended on something very small. In most every case there is a potential energy that is being spent in an un-controlled fashion... with feedback. A little positive feedback makes it unstable. For example as the chair fell, the further it fell the harder it was driven away from its initial condition. That is positive feedback. A little force from an air molecule was amplified to a big force.
Amplification is critical to control systems. Another way to understand amplification is the accelerator in your car. Do you wish to drive your car with a hair trigger accelerator so that a remote cosmic ray influences your destination? Do you feel that is your best chance for success? If so then you will be a fan of the non-linear dynamics and chaos (complexity) described in that paper. Do you like to sit tilted on your chair so that it is balanced and might fall backwards? If so then you will be a fan of the non-linear dynamics and chaos (complexity) described in the paper.
Other good examples are pseudo-random number generators or the mandelbrot set. While they utilize recursion they can also be simplified and written out as a single equation. There is a one-to-one relationship between inputs and outputs, but the output is extremely sensitive to the input. Just as the example I provided. Seed the thing with an uncorrelated cosmic ray and you've got something complex driven by something unknown.
In fact stochastic dynamics is probably closer to what you are looking for. In the chair example it is equivalent to saying that nobody knows the trajectory of the air molecules that set the chair into motion, or the exact nature of the friction surfaces that effected its motion, so we call that noise and employ statistical methods to narrow down the trajectory. Or a hurricane where nobody knows the location of every particle, but we know with certainty that it is going to turn clockwise North of the equator as we look down on it from space.
Paladin said:
My original point was to share an insight into the difficulty a logical approach to the entire atheist/theist conflict could place us. This in no way was to disparage logic, or either side of the debate. Therefore there was no intent to prove rightness or wrongness in any direction. If you so desire, however to create these conditions, I will concede the point now and cut to the chase. It would be so much easier to just be wrong than to continue belaboring a tedious point.
I was answering to the question you posed in post #61 by providing an example. It is not only harder for the atheist using whatever logic, math, or terms he presents to explain his existance... it too is impossible. The paper you presented tries. It misleads people who are disarmed having not learned the math. When the terms are challenged and the unknown becomes known, that other option always remains.