Systems modeled mathematically frequently end up in non-linear dynamic systems...frequently referred to as Chaos or Chaotic systems. For those who are less than perfectly math-geeky...the super-short version of chaos is: EVEN given starting conditions (to almost any level of precision), and exact rules...there are some cases where you cannot predict the future, even a little ways out.
One standard example is the butterfly and the hurricane, where a butterfly flapping it's wing in Egypt results in a Hurricane that hits North Carolina 8 weeks later. Basically...the math works out so that incredibly small changes in initial conditions result in massively different final outcomes.
Another standard example is the Mandlebrot set ... a (very pretty) fractal measuring how many iterations a function can be applied to itself, starting with an initial value in the complex plane before its absolute value exceeds some value.
An awful lot of the math in nonlinear dynamics consists of finding those boundaries at which the system has large (infinite?) sensitivity to initial conditions.
I fear that in my discussions of epistemology and statistical prediction, I've neglected to mention (a) my awareness of chaotic systems...and (b) it's obvious relevance to my radical uncertainty.
Consider it mentioned.
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