The Chaos theory

[Schadenfroh]

My teacher was trying to explain this to me. It had something to do with the laws of thermodynamics? what exactly is it?

 

[sgtroyer]

Yikes, complicated question.

Chaos theory came about when someone was trying to come up with a set of differential equations to model weather patterns. He noticed that when he made very minor changes to the initial conditions, the end results changed radically. As in, if I start with a temperature of 86.53 today, it will be warm and sunny in a week, and if I start with a temp of 86.54, we'll get three feet of snow. This type of behavior can be observed for a large class of physical phenomena, those modelled by several variable nonlinear differential equations. The behavior of such systems isn't random: it's deterministic. You can't calculate it, though, because tiny initial errors completely change the outcome. In a classical linear system, if you're off by 1% at the beginning, you expect to get within a few percent in the answer. In a chaotic system, that 1% error could mean orders of magnitude in the answer.

 

[Shalmanese]

A simple chaotic formula is x = 3*sin(x). If you alter the starting paremeters by even a TINY bit, the forumla rapidly diverges after a few iterations.

 

[sao123]

The second law of thermodynamics sez...

The entropy of any closed system must never decrease.
When an object undergoes a irrevirsable change, the amount of entropy in the system must increase.
what does this mean in conjunction with your question?
entropy equates to disorder.

A piece of paper is an orderly peice of matter (relatively) Now Burn the piece of paper, which scatters and changes the molecules of the paper. the amount of disorder (entropy) in your system has increased. You cant reorder the molecules back into a sheet of paper. therefore the amount of entropy in your system cant be decreased again.

So now equate this to a macro scale.
If the entropy of the world/universe must always increase...eventually chaos will become dominant throughout the universe.

 

[Orsorum]

Originally posted by: sgtroyer
Yikes, complicated question.

Chaos theory came about when someone was trying to come up with a set of differential equations to model weather patterns. He noticed that when he made very minor changes to the initial conditions, the end results changed radically. As in, if I start with a temperature of 86.53 today, it will be warm and sunny in a week, and if I start with a temp of 86.54, we'll get three feet of snow. This type of behavior can be observed for a large class of physical phenomena, those modelled by several variable nonlinear differential equations. The behavior of such systems isn't random: it's deterministic. You can't calculate it, though, because tiny initial errors completely change the outcome. In a classical linear system, if you're off by 1% at the beginning, you expect to get within a few percent in the answer. In a chaotic system, that 1% error could mean orders of magnitude in the answer.

Essentially.

 

[LordSnailz]

Originally posted by: sgtroyer
Yikes, complicated question.

Chaos theory came about when someone was trying to come up with a set of differential equations to model weather patterns. He noticed that when he made very minor changes to the initial conditions, the end results changed radically. As in, if I start with a temperature of 86.53 today, it will be warm and sunny in a week, and if I start with a temp of 86.54, we'll get three feet of snow. This type of behavior can be observed for a large class of physical phenomena, those modelled by several variable nonlinear differential equations. The behavior of such systems isn't random: it's deterministic. You can't calculate it, though, because tiny initial errors completely change the outcome. In a classical linear system, if you're off by 1% at the beginning, you expect to get within a few percent in the answer. In a chaotic system, that 1% error could mean orders of magnitude in the answer.

thanks, good explanation.