Chaos Theory: Chaotic Nonsense Or Possible?

[penguinraider]

How many of you think the chaos theory is possible?(Or vice versa?)
I believe it's foundations are correct, but the theory itself is ludicrous.
Correct me if I'm wrong.

 

[Jameson]

I know about the chaos theory, but I have heard many definions/interpretations of it. Would you please define exactly what you mean when you say "chaos theory"?

Jameson

For those who say that everything in the universe indirectly affects everything else, I would say "isn't that obvious?"

 

[Integral]

Would you please explain to us what you know of Chaos Theory and why you think it it ludicrous?

 

[SpaceTiger]

Your two options are a bit extreme, but I find it hard to see how chaos theory could be wrong in its basic assertions. They're very well tested.

 

[pervect]

IIRC chaos theory has been sucessfully used (possibly not under that exact name) to design some space missions, such as the Genesis proble.

See for instance
http://www.cds.caltech.edu/~shane/superhighway/description.html

(which talks about the link between chaos theory, invariant manifolds, and what has been called the "Interplantary Superhighway")

and

http://math.ucr.edu/home/baez/lagrange.html

which talks about some of the space missions designed with this concept.

 

[penguinraider]

when I say "chaos theory", I mean ' A butterfly flapping it's wings in the amazon will create tornadoes in America. Some-one walking in France will cause earthquakes in Japan' and the like. It's basically a particle moves another particle, which then moves another particle, ad nauseum.

I think that yes, particles do disturb others, but it is not all transferred to the other particles, some of it is absorbed by the other particles. Also, if a particle hit another two particles the energy would be divided between the two, therefore lowering the speed and power. It's quite similar to the way sound travels (just a bit slower). If the chaos theory is correct, we'd be able to hear people in Peru talking.

On a smaller scale, yes the butterfly would cause vibrations, but only for a maximum of a one to two metre radius

 

[SpaceTiger]

On a smaller scale, yes the butterfly would cause vibrations, but only for a maximum of a one to two metre radius

Are you just arbitrarily asserting this or do you have contradictory evidence? Like I said, chaos is well tested in many cases. I don't know how literally you should take the butterfly example (it's mostly a crude popularization), but weather is definitely chaotic on some scales.

 

[penguinraider]

Could you please give me an example?

 

[SpaceTiger]

Could you please give me an example?

http://www.dlk.com.au/beingmathematical/chaos/weather.htm

For future reference:

Google

 

[DaveC426913]

"A butterfly flapping it's wings in the amazon will create tornadoes in America."

An oversimplification. It is NOT suggesting the the air movement of the butterfy's wings is magnified NO! All it does is change one tiny mass of air. That tiny mass of air makes a dewdrop fall. The dewdrop wets the ground, the ground warms the air, the air rises a tiny bit, a wind is diverted, a cloud forms elsewhere, the ground warms more air, etc. etc.

All these things happen normally anyway, but if one doesn't happen, the others happen differently, and the cumulative effect is multiplied.

The upshot is that if you can't model every position and movement of every molecule of air over the last weeks and then extrapolate what the weather will be like; you're pretty much going to fail. Even the slightest initial conditions have a dramatic effect.



Here's a more intuitive example:

Try balancing a pencil on its tip. Try really hard. It will fall over. But it will not fall in the same direction each time, it will fall in all sorts of directions no matter how carefully you initially balance it. One time it will fall south, the next time, even though you spent five minutes trying to balance it exactly the same, it will fall north.

The final outcome of your pencil is extremely sensitive to the initial conditions, and the final result can be dramatically different. You simply cannot be so precise about the initial condiions so as to expect the same result to be generated each time.


(Caveat: This is not really an example of chaotic behaviour, it is merely a demonstration of one of the theory's core principles - an outcome that can be extremely sensitive on initial conditions.)

 

[DaveC426913]

Another way of looking at it:

Imagine you are away from school the day the Chem class was taught about Hydrogen> No worries, you will surely pick it up tomorrow while the teacher discusses Helium. That's a feedback loop that heals itself. The absence of one thing will not dramatically affect everything that follows, because the system works towards filling in that hole. This is actually a negative feedback loop - one that works to minimize variation from the norm.

But imagine if the rules of the school were such that you weren't allowed to learn about Helium until you knew all about Hydrogen. And you weren't allowed to learn about Lithium or any of the other elements until you learned about Helium. And you weren't allowed in the physics lab until you knew your chemistry. This feedback loop magnifies itself. It works towards accentuating small variations - making them into larger ones. It is a positive feedback loop, and it will very rapidly spin out of control. Missing one day of class means you fail the year.

Weather as a phenomenon does not work towards "healing" itself (as in: working to return to a normal state) Everything that happens after any given point will diverge very rapidly from what it would have done under very similar circumstances.

 

[motai]

I read a little about chaos theory once, and I am particularly interested in the chaos/order transfers between one and another. Take for instance a single pendulum, it can be calculated very easily because of the simple harmonic motion, in effect it is an ordered system. Now, if the pendulum has a joint halfway from the length of the pendulum bob and the attachment at the top (a double pendulum if you will), it gets more difficult (hence chaotic) to calculate where exactly the pendulum will be at a given time. Same goes with 3, 4, 5, etc. number of joints in between the pendulum bob and the top.

Here is the interesting thing though: Say we have a pendulum with a massive amount of joints, like say 300. The joints are nearly touching each other and now almost act as a massive chain instead of a rigid piece. Now, the pendulum swings almost as if it had no joints whatsoever, other than a slight sway or two at the ends.

Kinda cool, heh?

 

[rdt2]

'Chaotic' simply means that _some_ aspects of a system's response are very sensitive to the initial conditions - the 'butterfly effect' is a poetic illustration of this. There are many such systems in engineering and physics - including the weather. Try James Gleick's book 'Chaos' if you need convincing.

In chaos theory, the variables are functions of time. The corresponding theory with functions of position is fractal theory.

 

[HallsofIvy]

when I say "chaos theory", I mean ' A butterfly flapping it's wings in the amazon will create tornadoes in America.

Before you assert that any theory is "nonsense", you should get a clear concept of it, not just a newspaper popularisation. That is NOT what "chaos theory" is nor what it says.

 

[Chi Meson]

Dang. Everyone else got here before me.

It is not "THE" chaos theory. You are referring to "The Butterfy Effect" which is an example of a chaotic system (perfectly summarized by DaveC).

I have in my classroom a simple "chaos machine": A magnetic pendulum that is set to swing between three magnets on the support base. There is a "launch point" for the pendulum to make it seem that you release it from exactly the same point every time.

Since the pendulum interacts (repulsively) with the three magnets on the base, and since the magnitude and direction of the force from one magnet depends on how the pendulum reacted to the previous magnet, the slightest difference in initial position will make it impossible to predict the position fo the pendulum after a few seconds.

The unpredictablility is what makes it chaotic.

 

[LENIN]

I read a few books on choas theory and it sounded qouit normal to me. I do wonder howcome we never hear about it here at PF.