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"Chaos" in terms of mathematics
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by
on 2008-05-03 23:03:23 (edited 2008-05-03 23:03:39)
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I was just introduced to this subject, skimming through the "dark areas" of the library and I was just wondering if anyone is up for it's discussion! So, how exactly does the input of a value, such as 1.734879, greatly effect the results if only the digits, 1.735, *were* to used?   "To bring you back into this world I’d break every rule Machines try to take me to hell I don’t really care I do it for love" dolly - HYDE <--- [ Naruto: Shippuden | NecroCircus ] ---> |
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Re: "Chaos" in terms of mathematics
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by SuicidopoliS
on 2008-05-04 04:33:24 (edited 2008-05-04 04:33:38)
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The number itself doesn't tell you much, everything depends on the function you feed it to. If you have a function that varies very fast, or in a rather unpredictable way (e.g.: non-linear systems), small changes in values of your argument can have a gigantic effect on the outcome. .oO° Life's THE CURE, the rest are details! °Oo. |
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Re: "Chaos" in terms of mathematics
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by
on 2008-05-04 13:46:02 |
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But how is this applied to an unpredictable system, ie. the weather. You can use chaos for predicting "unpredictable" patterns in weather, but what exactly is the extent of it? Like, when you predict, "It will be sunny on Thursday," and today is Monday, what is the likeliness of this? "To bring you back into this world I’d break every rule Machines try to take me to hell I don’t really care I do it for love" dolly - HYDE <--- [ Naruto: Shippuden | NecroCircus ] ---> |
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Re: "Chaos" in terms of mathematics
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by SuicidopoliS
on 2008-05-07 15:27:39
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Am i right when i read your question as: "How can something chaotic be predicted?"? Quite frankly, i don't know much about weather forecasting, nor how reliable those forecasts are. Matter of fact is, i never trusted them :) But i cannot give you an answer as to how likely such a forecast is. I also have no clue as to which extend weather is indeed "chaotic". I think it's not necessarily chaotic, but rather hugely complicated and hard to model. But for chaotic systems in general, they also are described by mathematics. The problem is that, again, a minuscule change in the value you feed to those mathematics can greatly change the outcome. So the thing is that you need to know with very high precision what you feed to those mathematics if you want your prediction to mean anything. Look at it as being a enormously sharply peaked mountain on top of which you're trying to balance a small object: unless you're putting that object EXACTLY in it's equilibrium position on top of that sharp peek, it will fall off the mountain. Unless your feeding your math with the exact numbers that describe your system, it'll return meaningless rubbish. So i'm guessing that, returning to the weather, the more precise your measured values are (pressure, temperature, humidity, blablabla... all those parameters they feed their models with), the more likely your prediction will be, with that extra little footnote that they need to be damn precise in order to mean something. But again, i am by far not an expert in weather forecasting. .oO° Life's THE CURE, the rest are details! °Oo. |