Chaos Theory

[Isomotopes]

Is there any way the chaos theory can be proven or is it all just a large series of speculations and random coincedences that render the theory useless

[freeztar]

Originally Posted by Isomotopes

Is there any way the chaos theory can be proven or is it all just a large series of speculations and random coincedences that render the theory useless

Have a look at this:

In mathematics, chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

Chaos theory - Wikipedia, the free encyclopedia

and this:

Chaos theory is applied in many scientific disciplines: mathematics, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, and robotics.[35]

One of the most successful applications of chaos theory has been in ecology, where dynamical systems such as the Ricker model have been used to show how population growth under density dependence can lead to chaotic dynamics.

Chaos theory is also currently being applied to medical studies of epilepsy, specifically to the prediction of seemingly random seizures by observing initial conditions.[36]

Chaos theory - Wikipedia, the free encyclopedia

[Isomotopes]

Cool i thought it was only the butterfly effect but i was wrong thanks freeztar

[HydrogenBond]

I can see the practical usefulness of this theory. It can be used to simulate complex systems. But the determinism shows a goal in mind. I interpret this as meaning, since the beginning and end have a casual connection the middle part is also rational but may be too complex to explain. To keep progress moving forward, we will approximate the middle part with chaos since it does lead to good predictions. It allows us to extend the range of the human mind when the mind reaches limitations in its ability to explain things in a rational way. Where I get off the bus, is philosophy.

Let give an analogy of how the chaos philosophy can affects theory. Say we decide the composition of the moon's surface is random; we never know. We compare this to the assumption the composition of the moon's surface is not knowable at this time, but is knowable and rational. The random approach opens the door wider. The reason is, it allows us to start at the conclusion and then supply the casual logic later, since cause and affect are no longer in affect. Therefore, we can start in either direction. The other way around requires cause before affect, so the logic has to come first with the conclusions open until the end. There is a big difference.

I have no problem with the practical utility of chaos theory because when modeling complex systems this may be the best approach we have. I am more concerned about practical utility become the basis of a philosophy that allows conclusion to come before logic. Once this type of logic train is set up one will not be able to tell difference. This can create an illusion adding confusion that reinforces chaos. Chaos can sort of feed itself until theory is set up where chaos appears real and not just a good practical correlation that allows us to approximate complexity.

Lets go back to the moon example. I like cheese, so I will try to make the moon of cheese. This is my conclusion. Nobody knows for sure because we are leaving it open to chance. I show a picture of the moon next to some dusty looking swiss cheese. The correlation seems reasonable. It is not perfect, because I need to get the crater pattern to line up better. So I buy a lot a cheese and keep cutting until the hole pattern is perfect. I try to force fit my conclusion providing the logic and evidence after.

The other way around starts with no conclusions since we need to use affect first to develop reasoning, with the conclusion a mystery until the end. The moon appears to be a planetoid, connected to the earth. There is a good chance it may be similar in composition. This might eliminate cheese. There does not appear to be water visible since there is no blue or green. It looks more like maybe dirt, sand or soot? But we can't be sure. One can see the process is trying to narrow things down without jumping to a conclusion and trying to back prove. One is not given as much creative freedom. Chaos is better for science art.

Science has to keep in mind chaos used to rule philosophy before science and the age of reason. At one time life could spontaneously appear in a random way. Objects before Newton did not have to follow rational laws of gravity because it was assumed there was much more chaos even when determination made them all hit the ground. The alchemists were depending on chaos to allow gold from lead since the vat was ruled by whims of spirits that didn't obey the logic of humans. Why do back? Again there is practical usefulness with complex systems, but it is a retro philosophy.

[Nootropic]

Chaos theory is a clearly-defined mathematical concept. For a system to be chaotic, it must satisfy three conditions:

1. Sensitivity to initial conditions
2. It must be transitive
3. Its periodic orbits must be dense