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Originally Posted by meglamaniac
Chaps theory hurts my head. I read a book about it once and went "muuuuuuuuuuhhhhh!" for days afterwards. Lots of stuff about ratios and "e" and how it crops up in nature a lot - i remember there being something about the factor a river bends being directly equal to it, or as near as makes no difference.
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The details of chaos theory can be difficult and mathematical, but the basic idea is simply - a system is chaotic iff tiny changes in the initial conditions can produce huge changes in the behavior of the system.
When I kick a football, the path it travels depends on a lot of factors, such as how hard I kick it, the wind speed, and so on. But a small change in one of these factors will not have much effect on the ball - if I kick it a bit harder, it will travel slightly further, but not much. If the wind is a bit stronger, it will curve a little extra, and so on. So this system isnt chaotic. But for something like the weather, even a tiny change in the starting conditions can produce huge changes to the weather. Therefore forecasting becomes difficult, because even if you correctly measure an initial condition to (say) 3 decimal places, the rounding errors you make in the lower decimal places can multiply rapidly and screw up your predictions.
edit: for instance, I'm currently trying to get a recurrence relation to work in C, but its messing up because precision is being lost in the calculation of floating point numbers. The values should be 0.333333 for every memebr of the sequence, but instead I'm getting
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x[1] = 0.333333
x[2] = 0.333333
x[3] = 0.333333
x[4] = 0.333333
x[5] = 0.333371
x[6] = 0.371457
x[7] = 38.494974
x[8] = 38200.135886
x[9] = 38238002.688755
x[10] = 38276240358.110352
x[11] = 38314516598135.125000
x[12] = 38352831114732920.000000
x[13] = 38391183945847652352.000000
x[14] = 38429575129793497661440.000000
x[15] = 38468004704923290697728000.000000
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ie, the tiny errors are producing huge divergence over successive iterations.