It's easy to say X part of a system is "neither predetermined nor random" within a system defined as open (like a computer program or even a machine with a dial that can be set by an operator).

When a system is closed, things become harder.

Chaitin's number represents (very roughly) the structure of any complete mathematical system and it can be shown to be random in the sense of Kolmogorov.

but that just means there is more logical (predetermined) action 'out of our reality' The input of a program is predetermined by the physics that drive input to reach the program. (or it is from nowhere and is truly random, though I doubt this is the case)

This is a good explanation. We are saying we give the function x and y, but we can't guarantee that z comes out EVEN if we control for everything we are aware of. Thank you.

Still, I don't understand any of this even vaguely past the platitudes.