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Chaos


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#16    TheLight

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Posted 26 November 2003 - 09:45 PM

QUOTE (mowo @ Nov 26 2003, 02:03 PM)
disgust.gif didnt Mandelbrot say that equation and fractal are etymological opposites? chaos is exactly that- chaos, everything we dont understand. Its not "scientific" or "mathematical" as these words relate to mans understanding of things. Chaos has no rules, no formula so lets not complicate things by attempting to credit maths or science by including it. Thats my word.

The fact that you don't understand chaos doesn't mean it isn't very well understood from a mathematical standpoint (but you need a slightly above the average mathematical education for that). As I said, in mathematics chaos is when you cannot predict the convergence of a serie. So I leave the philosophical stuff about chaos to people that keep talking about what they don't know instead of actually studying what is already well known about it.


#17    mowo

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Posted 27 November 2003 - 09:31 AM

  rolleyes.gif OK here goes....

QUOTE
The fact that you don't understand chaos


tongue.gif Yes, I dont understand how to predict the future, or the meaning of life either

QUOTE
doesn't mean it isn't very well understood from a mathematical standpoint (but you need a slightly above the average mathematical education for that)


sad.gif But I dont understand exactly what is understood apart from the fact that it isnt understood. Do I need above average mathematical education to know this?

QUOTE
As I said, in mathematics chaos is when you cannot predict the convergence of a serie.


wacko.gif So, sorry, what is it again? I think I have an equation for this: serie convergence = ?

QUOTE
So I leave the philosophical stuff about chaos to people that keep talking about what they don't know instead of actually studying what is already well known about it.



huh.gif OK, just remind me again what is well known about it?

blink.gif Look, Im not saying people shouldnt waste their time, each to their own and all that. But just because we have a name for something doesnt necessarily mean we understand it. And if our only understanding of something is that we cannot predict or quantify it, no amount of analysis is going to make that fact more impressive.  wink2.gif






#18    Kryso

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Posted 28 November 2003 - 01:49 AM

So why’s it called the Chaos Theory, and not Chaos Fact? Because it is all theoretical. Everything balances on the fact that this could happen, or this might happen if this equation was thrown into the ball game (not a reference to Nameless bizarre example). So you can toss about theories of butterflies flapping their wings, or if a ball game goes on endlessly - and so on and so forth. As far as I’m concerned, so-called mathematicians should stick to what they know, rather than try and explain everything with their little number games! dontgetit.gif  


#19    TheLight

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Posted 28 November 2003 - 03:05 AM

Ok here we go (fractal set of Mandelbrot/Julia):

first you have to know what a complex number is, a complex number is composed of 2 numbers, the real and imaginery parts (this is used to described two dimensions, you can picture the real part as X and the imaginery part as Y). Such a number is written:
Z = X + iY (i is a special number such that i**2=-1 (**2 means squared).

A serie is defined as a recursive function: Z_n = f(Z_(n-1)), so in the case of the fractal set, it's the following equation:
Z_n = (Z_(n-1))**2 + C (where Z and C are complex numbers).
We start with Z_0 = C
Z_1 = Z_0**2 + C
and so on.

If the serie diverge (its modulus becomes superior to 2), we plot it in black. If after n iteration the serie hasn't diverged, we color it with a color representing its value.

So the fractal aspect here is that a finite equation cannot computes if the Z_infinite diverges or converges (and if so to what value).

You can see the display of computation I just described at:
http://mathforum.org/alejandre/applet.mandlebrot.html

But you see the problem is pretty simple, and the definition of chaos in this context is crystal clear. It's chaotic in the sense that it cannot be predicted by other means that actually computing it infinitely (which is not feasible apparently).

TheLight


#20    Phantom

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Posted 28 November 2003 - 08:02 PM

Wow, The_Light, if The Nameless One would only be here to be confronted with that.

Me, I'm no math genius.  original.gif  

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#21    gollum

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Posted 29 November 2003 - 09:50 PM

QUOTE
But you see the problem is pretty simple, and the definition of chaos in this context is crystal clear.


Who are you trying to kid????? huh.gif  wink2.gif  

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#22    mowo

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Posted 01 December 2003 - 01:08 PM

  dontgetit.gif OK, so we know that we can create apparent chaos within mathematics. Surely we need only investigate pi to know this? But I find it an obscure leap of faith to believe that because an equation can create chaos then it must work the other way. Dont get me wrong, Mandelbrot and Julia did make some pretty pictures, but I dont feel that they made any scientific advancements. wink2.gif  


#23    bathory

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Posted 01 December 2003 - 01:55 PM

QUOTE
So why’s it called the Chaos Theory, and not Chaos Fact?


tsk tsk, Theory is a set of statements or principles devised to explain a group of facts or phenomena, especially one that has been repeatedly tested or is widely accepted and can be used to make predictions about natural phenomena

Einstein made a few famous theories that seem to be considered fact..


#24    jimma

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Posted 01 December 2003 - 02:36 PM

it's chaos, this thread!


#25    Xenojjin

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Posted 01 December 2003 - 03:04 PM

Id say the light pretty much explained it . thumbsup.gif  

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#26    Melladior

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Posted 01 December 2003 - 07:26 PM

Math is hard.  I like lollipops.


#27    Kismit

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Posted 01 December 2003 - 09:44 PM

  The light,I actually managed to absorb some of that ...very interesting and well written so that the non-college graduates had a chance to understand it . thank you .


#28    TheLight

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Posted 02 December 2003 - 02:45 AM

Thanks Kismit and Xenojjin !!!

I tried to do my best at communicating the little bit I know because in the end that's the purpose of this forum in my opinion: to learn from each others rather than argue with each other wink2.gif I'm surprised that some other people seems to exhibit some kind of allergic reaction to mathematics since they represent a great tool (the best that we know of) for explaining things... such like Chaos wink2.gif But I guess the education system plays a great role at making people dislike maths, that's the way it goes I'm afraid...

By the way, I also wanted to mention that Chaos is also described in physics under the concept of entropy, which in other words is the degree of disorder in a system (in thermodynamics, it can also be the whole universe).

So the scientists believe that entropy is increasing in the universe, thus leading to more disorder/chaos. But I always find puzzling that the birth of life seems to contradict that: it is believed that it was self-organized molecules which formed the first primitive cellular organism... So in other words, order emerged from Chaos. Somehow on a philosophical level biology and physics disagree and it seems to be quite a challenging topic (I think physics doesn't get the full picture yet about entropy but that's just my gut feeling).

Anyway I'll leave it here if anyone wants to develop,

TheLight



#29    Kryso

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Posted 02 December 2003 - 04:32 AM

QUOTE (bathory @ Dec 1 2003, 06:55 AM)
QUOTE
So why’s it called the Chaos Theory, and not Chaos Fact?


tsk tsk, Theory is a set of statements or principles devised to explain a group of facts or phenomena, especially one that has been repeatedly tested or is widely accepted and can be used to make predictions about natural phenomena

Thanks for the - The American Heritage® Dictionary of the English Language, Fourth Edition, cut and paste job!

Down a little bit further – in the American Heritage® Dictionary- it also says: Abstract reasoning; speculation!



#30    bathory

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Posted 02 December 2003 - 08:07 AM

of course it was a cut and paste job:)
i got it from dictionary.com simply because its nicer package than having to write up a definition myself.
The thing though is that when regarding science, Theory is as i pasted, it isn't speculation. In science that would be the Hypothesis stage if i'm not mistaken:)





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