OK, try this for size, bearing in mind that it is a heuristic argument.
No one can "know", with certainty, the location of any particle. Or, to be slightly more accurate, the more we know of its location, the less we know of its movement. This is essentially Heisenberg/QM 101.
But we see the results of "computation" all around us, all the time: Any time a chemical or physical reaction settles to an observable result, whether observed by one of us, that is, a human, or another physical entity, like a tree, a squirrel, a star, etc. This is essentially a combination of Rovelli's Relational QM and the viewing of QM through an information centric lens.
In other words, we can and do have solid reality at a macro level without ever having detailed knowledge (whatever that might mean) at a micro/nano/femto level.
Having said that, I read your comment as implying that "the human mind" (in quotes because that is not a well defined concept, at least not herein; if we can agree on an operational definition, we may be able to go quite far) is somehow disconnected from physical reality, that is, that you are suggesting a dualist position, in which we have physics and physical chemistry and everything we get from them, e.g., genetics, neurophysiology, etc., all based ultimately on QM, and we have "consciousness" or "the mind" as somehow being outside/above all of that.
I have no problem with that suggestion. I don't buy it, and am mostly a reductionist at heart, so to speak, but I have no problem with it.
What I'd like to see in support of that position would be repeatable, testable statements as to how this "outside/above" "thing" somehow interacts with the physical substrate of our biological lives.
Preferably without reference to the numinous, the ephemeral, or the magical.
Honestly, I really would like to see this. It would represent one of the greatest advances in knowledge in human history.
I'm only talking about the physical world - phenomena that don't correspond to something computable, which are very common, and include the next five seconds of the amplifier noise heard on your headphones, are dealt with by being ignored or averaged out. Collective motion is somewhat predictable and includes things like popular opinion or temperature, but individual deviations aren't covered.
The problem with translating that into proof of dualism is that everything outside the computable looks the same. A hypothesis is something you can assume to compute a prediction, so if any hypothesis is true, the phenomenon must be computable. If the phenomenon is not computable, no computable hypothesis will match. The second you ascribe properties to a soul that can distinguish it from randomness, or properties of randomness that distinguished it from free will you've made one or the other computable, and whichever is computable won't match reality, if we suppose we're looking for something outside of rational explanation and not a "second material."
Here's a concrete example. If you had access to a Halting oracle, it would only be checkable on Turing machines that you yourself could decide the halting problem for. Any answers beyond those programs wouldn't match any conceivable hypothesis.
