Chris, I agree that many phenomena in the chotic realm cannot be humanly predicted, for the reasons you state below (though I may wish to examine the second more closely, wrt to infinitesimals and to quantum indeterminacy).
There is a need, though, to distinguish carefully (when speaking in a theological context) between unpredictability and non-reproducibility on the one hand, and indeterminacy on the other (and perhaps also between physical indeterminacy and divine indeterminacy, if that is a coherent distinction).
In this discussion I’m most interested in physical indeterminacy, and have a few thoughts on examining a chaotic system critically to do so. But it will take a blog-length discussion, so I aim to do it on the Hump, but will post a link here so the discussion can continue.
It’ll take a day or two, though, as I’m away into the weekend.