Not sure how, Chris, since I learned it from physicists. More a question of what kind of thing might conceivably exist to make chaotic events indeterminate (that is, to posit indeterminate forces is itself the faith-based statement unless one has evidence).
Take a simple limiting case: something balanced on the point of a pin. Extremely unstable: the most miniscule vibration or faint breeze would make it fall, but which way it will fall is unpredictable. It’s a chaotic systrem, but conceptually simpler than a hurricane or a three-body problem in gravity.
However, if we suppose it to be finely balanced but free of every specific force such as a puff of wind from the north, or a slight earth tremor from the southwest, would we expect it to sponteously fall in some random direction? Why? What force would make it do so, and why would it be indeterminate, unlike ever other force we know?
What I have gleaned from physicists is that a characteristic of chaotic systems is that tiny changes in initial conditions yield huge changes in outcomes. This characteristic does not necessarily imply that better knowledge of initial conditions could allow physicists to treat such systems in a conventional manner with highly predictable results, or even that better knowledge of initial conditions is theoretically attainable.
Sure. To posit determinate forces in chaotic systems is also a faith-based statement in the absence of evidence.
Please note I am not claiming that there is no such thing as a basically deterministic outcome: An apple that falls from a tree will strike Sir Newton on the head if he is sitting underneath. There is a deterministic regime in physics.
What I am suggesting is this: Just as many phenomena in the quantum regime can never be deterministically predicted by a human, it is possible that many phenomena in the chaos regime can never be deterministically predicted. How could this be? Here are 2 ideas that might apply to some chaotic systems:
Because it requires energy to gather information, it could be that not enough energy is available to gather the data required to make a deterministic prediction.
It could be that the infinitesimal changes that yield different outcomes can become so infinitesimal that Planck scale is reached, and all ability to predict deterministically is lost.
Since neither one of us is a physicist, I don’t want to make a big deal of our disagreement. And I would welcome the input of @physicists who can shed any more light on this discussion.
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.
Back from Warwickshire (Straford-on-Avon’s looking a pretty as ever), so a piece on chaos posted on the Hump. Hopefully it’s determined but not too predictable.