I don't think you're right, I think that some things aren't tractable to this kind of analysis. Obv. Godel type things, but if you believe in freedom of will and an open universe then a lot of other things. For example, the path of true love, the next line of a poem, the summer after next's hot fashion trend.
More importantly (less) international events, earthquakes, solar flares.
Fractals, chaos and incompletness.
We're creatures of habit, and once you have enough information to identify those habits, you can do a pretty good job at predicting what we will do. Heck, with the little data I have access to, I can be pretty sure which articles I will see comments from big posters like jacquesm and tptacek, and what their comments will contain. I can't predict every story they will comment upon, nor the exact details of the comments, but at a higher level it is definitely predictable.
nice.
Given huge sets, much like reality, almost anything can be "proven" at some sort of local scale. It's not a religion or a cult or a new god. It's just observation.
Second, data is a recording of past events, and has surprisingly limited ability to predict future outcomes. There is a narrow window for the most instinctual tasks where it works well and there is a Tom of value there -- but it comes no where close enough to be meta-cognitions ability to give you free will.