Many of you probably have read my other threads about Chaos theory, So Ill try not to post too much on the subject, because I would have to either explain myself again, or do the copy paste method, and that would take to long.

So Picture this, their are two baseball teams, both start with Zero points, at the end of the 9th inning, Team one has 7 points, and Team two has 10 points. Neither team actually won the game, because who was to say that if they didn't keep playing that Team One would not have had 15 points, and Team two would have 12 points. Both teams could play forever and ever, until both scores looked like this. Team Ones score may be,
1000000022333400000000000000022000330000333335550000000000000.
And Team two's score may look like this. 244444444433099388111111188888888
888888880000000000000000000000000000000001019282827363
671818991093000000000000000000000000000000002299000.
Nobody can actually predict the outcome, because there is no outcome, by now some of you are thinking wow this sucks no it has no end. But yet is there an end?
By Chance (Randomness) certain events may unfold to cause an actual or possibly only postpone an outcome, under given conditions. These events could be Anything, the players may need a drink of water, disasters could happen, players may get bored of playing, but yet if they want under other given conditions they may begin to play again and start over thus Team two would win, or continue to play forever and ever again with the same scores they had, before Chance had occured.

No, the team that was ahead after nine innings wins the game. the rest is just nonsense.

go read your probability theory again.

I give up, you obviously have no idea what yourself or anyone else is talking about. Do you want me to hold your hand and walk you through this?

You stated, that given two baseball teams, playing 9 innings, team one scoring 7 points team two scoring 10 points, that neither team would actually win, because if they went on playing they would undeniably score more runs. Am I getting this right? And then you went into all this probability random conditions stuff, and that you can't actually predict the outcome of the game, because of all the independent variables going into it. Am I on the wrong track? I say after nine innings the point is moot, there is no reason to play more innings if one team is ahead after nine, and anything after that is pointless to discuss. You keep arguing a point that doesn't exist, baseball games only last nine innings, your analogy was bad, end of discussion. Or am I missing something here?

Snuffy scores and the crowd goes wild..... I'd like to thank Jesus and my mamma.

Chaos is a well defined concept in mathematics, it's the basis of fractals (discovered by the famous mathematician Benoit Mandelbrot, btw I attended to one of his conferences). Anyway, the chaos in mathematics as defined initially in the fractals is when you cannot predict if a serie is going to converge or not (see Mandelbrot's set for a nice picture of it).

The butterfly effect is something different in nature: due to the number of parameters influencing the weather, it's impossible to predict the weather for long periods of time, and the image of a the air moved by butterfly wing was used to explain to the non-scientist that such a small event could indirectly start a storm later somewhere else (but that's a rather exagerate image). This is not chaos in the mathematical sense, it's simply an error of prediction due to an approximation in our modeling of weather. And you cannot really escape this approximation due to the impossibility to measure and modelise all the parameters for weather prediction.

I think there's not much for fantasy in the notion of chaos, it's pretty simple (and well defined) to me as long as it remains in the mathematical context.

TheLight

Chaos theory = Sh#t happens. Sorry, but that's about as scientific as I can get.

I might fall down the steps and break my leg today, or I might not.

Just 1 thing : I did'nt understand a single world ! I try realy hard to understand but no way. Perhap's I'm to stupid ! By the way, be nice with each other ! You don't have to be rude to express yourself (that one is for THe Namelessone and Snuffy Puffer), Calm down, breath and just said I don't agree with you because.... That's very easy.

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.

OK here goes....

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!

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

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

Me, I'm no math genius.

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.

it's chaos, this thread!

Id say the light pretty much explained it .

Math is hard. I like lollipops.

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 .

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 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 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

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:)

No worries, I meant no offence. I only noticed it, because I use dictionary.com all the time for my work- writing, to check spelling, correct usage, etcetera… A handy site. Its saved my neck many times, when I was about to use a wrong word in a particular location!

The nameless one, I understood every word you typed and the corralations you are making, for the rest of you out there Chaos theory is a proven fact therfore it exists. Now my dear "nameless one" let them bang their heads against the monitor