[Turing machines] don't figure out what they'd do and then do the opposite, unless you just invert the programming.
Again, there is nothing that the Turing machine would ever need to figure out... it simply needs to just blindly do the opposite of whatever some black box says is supposed to happen...
A Turing machine is a mathematical construction. You're trying to use the halting problem as a rationale for the universe being non-deterministic. However, the halting problem only applies to Turing machines. A Turing machine can't contain a black box, because that isn't part of the definition of a Turing machine.
It is a bit like proving that there are a countable number of integers and then trying to say that there must be a countable number of irrational numbers by just redefining the meaning of "integer." You're playing word games, but that doesn't prove anything.
To be honest, I'm not really sure how you could prove anything about the universe using an argument purely from discrete mathematics, unless it is a proof that there is no such thing as determinism at all (which certainly would be an interesting claim for a mathematician to make). Math is a world all its own, and while it can be used to describe the physical world, it has an existence apart from it in a sense.
It just means that you can't write down the state of the entire universe using only the matter present inside of it.
Except that's generally understood to be what materialistic determinism *IS*... so I'm not sure if you meant to or not, but you've really just sort of agreed with me there.
Again, you're playing word games. Determinism requires that the universe has some state, and some set of rules that determines what its next state will be (which is a really rough way of putting it when time isn't discrete and is relative, but I don't think we're arguing about that). If you're arguing that determinism means something else, then we're just talking past each other.
I have no idea whether the universe is deterministic.
For someone who is professing to have no idea, you seem to be abnormally determined to convince me that my conclusions are invalid... perhaps you should try to figure out why you believe what you do.... or if you don't know what you believe, I might suggest you should stop trying to point out what you think may be wrong with another person's ideas just because you don't happen to agree with their conclusions, because otherwise you just come across as somebody who wants to disagree for the sake of being disagreeable, and not somebody who has actually made any real attempt to rationally think through their beliefs.
Honestly, the only reason I'm continuing this discussion is because I thought you might have an interesting argument for determinism based on the halting problem, which was your original point. I wasn't sure if you were just having trouble communicating your ideas, or if they were not established in rigor.
I don't really care whether I convince you. I don't intend to be disagreeable for its own sake. I'm just skeptical. If you're going to assert that the universe is non-deterministic that is a really bold statement, and I'm not going to simply accept it at face value.
The only stand I'm taking is that I don't believe anybody has shown conclusively whether the universe is deterministic or not. I'm open to arguments one way or the other. I'm fine with thought experiments and hand-waving arguments, but I'm not going to accept them as some kind of conclusive proof.