Integral Calculus isn't "tangible", but the human brain can store information about it in tangible constructs. Likewise, my bank balance. But the storage isn't the actuality, and the bank account information in my brain is no more the actual account than the bank account information on my hard drive is, even though that is likewise represented in tangible and measurable form.
I don't posit self-aware Quantum mechanics and I have no idea how you drew such a wild conclusion, You seem to take a delight with confusing the levers with the driver.
And how, pray tell can a neural network "see" what's at the controls of a bulldozer if the driver no more visible to man or computer than cosmic rays were to the Babylonians? On top of which you seem to be assuming that we have neural networks that can accurately conduct a Turing Test. As I recall, the original test specifically required a human as the test instrument/reference.