The deepest fundamental structures in the brain[0] are quantum fields, which are also the deepest fundamental structures in everything else.
There is no known quantum field of "soul" or "intelligence".
The right abstraction is higher, and could still be a whole lot of things; but as maths can be implemented in logic, which can be implemented in electronics or clockwork or hydraulics, it doesn't matter what analogy is used — and my mild disagreement here is that such inspiration has been useful and gotten us this far.
[0] that we know of