There is no need to bring in "spirituality" (at least, as commonly and colloquially understood) or "souls" into the picture - see for instance qualia, whose existence is self-evident, and yet are also not amenable to examination by external observers. Irrespective of how much you can pick and probe at the brain and measure wavelengths of light, there is "something it is like" to actually experience the phenomenon of "red", and this experience itself is not readily accessible to objective/quantitative methods.
> It's a typical case of a chaotic system. Perhaps innovations in the modeling of such complex systems (not too different from the advancements we're seeing in ML) will be the key to better insights into the mind.
I could be convinced that minds are ultimately emergent phenomena of plain physical and mechanical processes which are too frighteningly complicated for us to analyze with contemporary methods.