Nonlinear Dynamics, and Theory of Error Correcting Code

[StatsManD]

Has anyone here taken courses on these two topics? If so how are they.




Also just wondering. Does mathematical dynamics have anything to do with dynamics physics and engineering?

 

[invidia]

I'm a physics major and never heard of those topics in my life, besides error correcting code. Those types of courses seem to be more geared towards engineering.

 

[StatsManD]

Nonlinear dynamics is also known as Chaos Theory.

 

[lightweight]

Sounds like the perfect icebreaker at a party. Hope you don't mind if I use it.

 

[StatsManD]

Nonlinear Dynamics is also sometimes refer to as the "Butterfly Effect". That a flap of a butterflies wing in South America could end up causing a tornado in Kansas.

 

[Motavian]

Originally posted by: StatsManD
Has anyone here taken courses on these two topics? If so how are they.

Also just wondering. Does mathematical dynamics have anything to do with dynamics physics and engineering?

It's interesting but not necessarly immediately useful in your daily life.

And yes those subjects are related somewhat. Physics and engineering use a lot of differential equations which lead to nonlinear behavior.


Edit: I meant Nonlinear Dynamics, I don't know anything about Error Correcting Code

 

[StatsManD]

So what kinds of systems in engineering behave chaoticaly? Where small changes in initial conditions produce large erratic changes in the system.

 

[TheoPetro]

im pretty sure the whole butterfly flying = tornado concept is bullsh!t. Unless there is some huge change in energy states (nuclear bomb) you wont have insane consequences. If there is one thing I learned from physics its that nothing is exact and there are some things that happen that just dont matter. I can drop a coin in my room right now and nothing will happen from it. I may be missing the point but from what youre saying it sounds more like utter BS to me.

 

[StatsManD]

The whole butterfly = tornado thing isn't bullshit. It has been proven using mathematics and physics.

 

[TheoPetro]

Originally posted by: StatsManD
The whole butterfly = tornado thing isn't bullshit. It has been proven using mathematics and physics.

I can understand and appreciate how something seemingly small can have huge implications but for 99% of events it doesnt work that way. Most stuff that happens has no real world effect on the next room let alone the other side of the world.

 

[Motavian]

Anything involving airflow can have it... like imagine holding a piece of paper at shoulder height, dropping it, and seeing how it lands. If you hold it at a slightly different angle before letting go it'll land somewhere else.

 

[StatsManD]

Originally posted by: TheoPetro

Originally posted by: StatsManD
The whole butterfly = tornado thing isn't bullshit. It has been proven using mathematics and physics.

I can understand and appreciate how something seemingly small can have huge implications but for 99% of events it doesnt work that way. Most stuff that happens has no real world effect on the next room let alone the other side of the world.

So you think Chaos Theory and NonLinear dynamics are utter pointless crap, and 99% of dynamic systems are linear.

 

[TheoPetro]

Originally posted by: Motavian
Anything involving airflow can have it... like imagine holding a piece of paper at shoulder height, dropping it, and seeing how it lands. If you hold it at a slightly different angle before letting go it'll land somewhere else.

Say I move the air in my room by waving my hand. The effect outside my room is very small. The effect of me waving my hand 10 miles away is insignificant. The effect in Africa of me waving my hand is so close to zero for any real world application it is zero.

 

[TheoPetro]

Originally posted by: StatsManD

Originally posted by: TheoPetro

Originally posted by: StatsManD
The whole butterfly = tornado thing isn't bullshit. It has been proven using mathematics and physics.

I can understand and appreciate how something seemingly small can have huge implications but for 99% of events it doesnt work that way. Most stuff that happens has no real world effect on the next room let alone the other side of the world.

So you think Chaos Theory and NonLinear dynamics are utter pointless crap, and 99% of dynamic systems are linear.

I think that at the quantum level chaos theory and probabilities have a real application but for anything on our order of magnitude it is utter bullshit people like to talk about to make themselves sound smarter.

 

[StatsManD]

So you must think Lorenz a Mathematician and Meteorologist from MIT was full of him self when he said "Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?" and concluded it does have a meaningful effect on the system.

 

[Motavian]

Well, it's true that not all systems are chaotic. Actually most systems aren't chaotic at all... you can study them using the normal stuff in a differential equations class. But there are some things that are chaotic.

 

[TheoPetro]

Originally posted by: StatsManD
So you must think Lorenz a Mathematician and Meteorologist from MIT was full of him self when he said "Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?" and concluded it does have a meaningful effect on the system.

For one Lorenz was an amazingly smart person and no I dont think he was full of him self.

Now for two,

There are many more factors to take into account. Your over simplification of the problem is whats wrong. If a butterfly flapped his wings inside of an air tight box then there would be no effect. It depends largely on where the butterfly is and the air currents around him. If the conditions were perfect to where the butterfly set off a chain reaction then yes it could possably cause a tornado. The chances of that actually happening are so slim its ludicris to talk about. The conditions have to be so perfect that it would never happen.

That is why I think that this type of theory being applied to every day life is bullshit. If you can show me an example with a decent probability of occuring (asside from nuclear chain reactions, which shouldnt count anyway because of the size) then I will believe ya. But for now its BS. Sorry.

 

[TheoPetro]

Originally posted by: Motavian
Well, it's true that not all systems are chaotic. Actually most systems aren't chaotic at all... you can study them using the normal stuff in a differential equations class. But there are some things that are chaotic.

Just from what I have pickedup (not much) there are very few systems that actually are chaotic. As in VERY few.

 

[StatsManD]

Well I don't know much about this topic, only what I have glanced over our book for next quarter.

I am not 100% sure I am taking this course though. Motavian have you taken a math course in "Numerical Analysis in Differential Equations", if so which do you think is more interesting.

 

[TheoPetro]

Differential Equations is a decently neat class. I dont know where youre at currently but you need multivariable calc (calc 3) to really appreciate ODE. Linear algebra (probably my favorite course so far asside from calc 3) is another course youre going to want to have too.

 

[StatsManD]

I have already taken Calc 3, lower division ODE, and lower division and advanced linear algebra. I enjoyed them all.

 

[StatsManD]

Nonlinear Dynamics course is a class in advanced ODE, but the focus and text book is on chaos theory and nonlinear dynamics.

 

[Motavian]

Originally posted by: StatsManDMotavian have you taken a math course in "Numerical Analysis in Differential Equations", if so which do you think is more interesting.

Any kind of Numerical Analysis is pretty boring, in my experience.