Chaos Theory

August 6, 2010 by Julio Fontán Jr.   Comments (5)

There has been always a question that burned in people's minds:

Is there something controlling the world?

The question could -should- be modified to 'Is there an all-mighty force that controls the world?'. The answer, of course, is YES.

The force that rules the world and mankind's lives is chaos. Chaos reigns in nature. Not just in trees, flowers and "animals", but in the very essence of men.

But, What is chaos? Why the hell does it control everything?

Chaos is not evil. Clear example: A room. Maybe your room. If your room is like a lion's den (something common), it's not because you took every book on your shelves and threw it down to the floor victim of an outrageous fury. The books are on the floor because you took one, read it, took another, read it, once and again, once and again... and every time you finish a book, you left it on the floor. It's not leaving the books on the floor because your an evil genius; it's leaving them on the floor because you were lazy at the moment, and being lazy is something natural. Natural, keep that word on your mind.

Another example: A tree. You throw a cigar to a dry, old tree. The tree won't burn for revenge, to get the bastard that burnt it's skin; the tree will burn because it's a natural thing.

Things go wrong, things get chaotic... because of the natural flows of life.

And it's something we can find everywhere on earth... Maybe it's part of the sourcecode.

yes - very nice post - trhis is what we are here for - discussion this kind of topics - perfect :)

KenoNitro 1542 days ago

i guess Einstein once said this "only the genuis rules the CHAOS" :)

KenoNitro 1542 days ago

HAHAHA

Maybe Einstein was right, but, if that phrase excludes any other possibility for being considered a genius, Einstein wasn't a genius. He didn't rule the chaos, but he did show us a part of the chaos. Chaos as the existence itself, I mean.

Thanks four your comments, BTW.

Julio Fontán Jr. 1542 days ago

Hehe,

so what i think describing chaos best in the sense of a sourcecode or kind of consciouss sourcecode is the random factor within and the part of trial and error. I believe in the existence of a sourcecode running behind and i think this code is transforming all the time - its learning like we humans do like every beeing is doing. It learns by random like us and by trial and error. So Darvinism would fit into the theory too. This might be the kind of chaos that is really behind. The learnig-part of a organism - you never know where it ends up :)

KenoNitro 1542 days ago

Thanks for your interesting post Julio!

I have to admit that I have difficulties to follow or understand your examples to the full extent. I think that has one reason and that is the differentiation between coincidence (or chance) and chaos. I would understand your examples to be more of coincidence-examples. But that might just be my own difficulty.

However Wikipedia give a small insight into the "Distinguishing random from chaotic data" problem:

It can be difficult to tell from data whether a physical or other observed process is random or chaotic, because in practice no time series consists of pure 'signal.' There will always be some form of corrupting noise, even if it is present as round-off or truncation error. Thus any real time series, even if mostly deterministic, will contain some randomness.[59][60]

All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[59][61] Thus, given a time series to test for determinism, one can:

  1. pick a test state;
  2. search the time series for a similar or 'nearby' state; and
  3. compare their respective time evolutions.

Define the error as the difference between the time evolution of the 'test' state and the time evolution of the nearby state. A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error.[62]

Essentially all measures of determinism taken from time series rely upon finding the closest states to a given 'test' state (e.g., correlation dimension, Lyapunov exponents, etc.). To define the state of a system one typically relies on phase space embedding methods.[63] Typically one chooses an embedding dimension, and investigates the propagation of the error between two nearby states. If the error looks random, one increases the dimension. If you can increase the dimension to obtain a deterministic looking error, then you are done. Though it may sound simple it is not really. One complication is that as the dimension increases the search for a nearby state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension) to find a suitably close candidate. If the embedding dimension (number of measures per state) is chosen too small (less than the 'true' value) deterministic data can appear to be random but in theory there is no problem choosing the dimension too large – the method will work.

When a non-linear deterministic system is attended by external fluctuations, its trajectories present serious and permanent distortions. Furthermore, the noise is amplified due to the inherent non-linearity and reveals totally new dynamical properties. Statistical tests attempting to separate noise from the deterministic skeleton or inversely isolate the deterministic part risk failure. Things become worse when the deterministic component is a non-linear feedback system.[64] In presence of interactions between nonlinear deterministic components and noise, the resulting nonlinear series can display dynamics that traditional tests for nonlinearity are sometimes not able to capture.[65]

 

Cheers so far!

Matthias

transiente-sichten 1542 days ago