Hi,
Well, we don't really need modeling for linear problems, Sturm–Liouville theory having pretty well gotten those under control. Also, not all non-linear problems are chaotic. It depends on the form of the non-linearity. Rankine–Hugoniot shocks in condensed matter are an example of non-linear, non-chaotic flow.
It's still just an educated guess. Ultimately, you have to take a bite to know what it tastes like. Make a prediction, figure out how to test it, run the test. That's science. Everything else is just label making and navel contemplating. At best, it might eventually lead to science.
--Pete
(06-22-2011, 04:07 AM)kandrathe Wrote: Enter Chaos Theory... Or, the non-linear equation.
Well, we don't really need modeling for linear problems, Sturm–Liouville theory having pretty well gotten those under control. Also, not all non-linear problems are chaotic. It depends on the form of the non-linearity. Rankine–Hugoniot shocks in condensed matter are an example of non-linear, non-chaotic flow.
(06-22-2011, 04:07 AM)kandrathe Wrote: I believe and tend to ... make a reasonable justifiable prediction.
It's still just an educated guess. Ultimately, you have to take a bite to know what it tastes like. Make a prediction, figure out how to test it, run the test. That's science. Everything else is just label making and navel contemplating. At best, it might eventually lead to science.
--Pete
How big was the aquarium in Noah's ark?