Question

Hello Rabbi,
I was having a synagogue conversation on the Sabbath with a PhD in mathematics, and I asked his opinion about the famous contradiction between foreknowledge and free choice, and in particular about Newcomb’s paradox. I was preaching to the choir, and he happily produced a whole collection of paradoxical equations and even paradoxical geometry, but to my surprise he still thought that the Holy One, blessed be He, knows, and we are permitted to choose. It turned out that he belongs to that strange school of mathematicians who think that mathematics is a narrow local language that describes a subjective reality, and that “there are things our minds are too limited to grasp” 🙄
In any case, he said something, and since I’m shy and not learned, I just nodded my head and thought I understood.
The claim was, in my words: ‘Since we can’t choose both options together and we must choose only one of them, there is no problem with the information existing about what we will choose.’
Maybe I don’t remember exactly what he said, but I have no way of asking him. Does the Rabbi make any sense of this claim? Or is it meaningless? (He said various other things around it too, but I don’t remember exactly, and it seems to me that was an explanation of the claim, not an elaboration.)
Thank you