I've seen reference to the notions of "intelligence", "self-awareness" and "understanding" like they have concrete definitions. Is there a well defined definition I am ignorant of?

To clarify about the distinction between "computable" and deterministic - there are classes of problems such that there is no algorithm that can solve every problem in the class, but each problem in the class has a yes or no answer. The most famous example of this is probably the halting problem. It asks if there is an algorithm which, when given an arbitrary computer program, will figure out whether the program terminates or runs indefinitely.

Now, apparently, there are classes of problems in Quantum Mechanics which are undecidable. I do not know much Quantum Mechanics, but I at least know what "decidability" means. That's saying there are classes of problems in Quantum Mechanics for which there is literally no algorithm which can solve them. In fact,

__there will always be specific instances of the problem which resist a solution, regardless of your particular axiomatization of mathematics__ (all sensible modern mathematics is always done by making logical deductions from a consistent set of axioms. That's how we can come to absolute conclusions about truth and falsehood).

This is very different from simply saying "there are systems / models we use in Quantum Mechanics which involve probability and randomness". This is actually a far more damning issue than having a system that involves randomness. If an omnipotent being throws a "perfect die" which is "truly random", we cannot know for sure what number will come up. But I can perfectly model and understand its mathematical structure. It simply has a 1 in 6 probability of showing any particular side. For our purposes, this may be "random", but it is at least "decidable".

Undecidability would be more like if the mathematics involved in modelling what side comes up were so fucked up that I literally couldn't even calculate the probability. And the mathematics is so fucked up I can give a separate mathematical proof demonstrating that I literally cannot mathematically compute it.

p;edit this blog post gives an example of a class of problems in QM which are apparently undecidable. I can't vouch for its authenticity but.. erm... they seem like they know what they're talking about

https://www.i-programmer.info/news/1...decidable.html