Consciousness is a very dynamic charachter, always changing like the quantum work or process. It has two facets, ignorance and knowledge, a bit like we see it is Shannon eq. where 1/2 means the maximal knowledge and ignorance. The mechanism of consciousness should be quantum, but the phenomena or outcome 'knowledge' is classical as ontologic state, like we can have 0/1 states. With many-body states it becomes more complex, and the knowledge-part can diminish as the sqrt part get higher.
The quantum 'jump' analogy therefore is actual. See plato.stanford.edu/entries/qt-consciousness/ About the Schrödinger cat analogy; does the cat know if it is dead or alive? It should? But we as observers outside does not know because the cat is in a closed system,so we need to open it up. Most quantum states are closed states theoretically.
Lorraine Ford This knowledge/ consciousness/ observer aspect of the world is entirely different to, and separate to, the law-of-nature relationships, categories and numbers aspect of the world.
I want to integrate consciousness as a 'feeling',' belief' or some 'possibilities' as an reading of a surface as instance in the 1/2 state (entangled superposition?). If we use open states we don't bother about the energy conservation
Lorraine Ford And being an entirely different aspect of the world, it is not surprising that the knowledge/ consciousness/ observer aspect of the world manifests itself differently, e.g. as “qualia”.
Qualia is the hard problem (that you rejected), but what aspect would it be then? It gives the experience of 'being' you like a transformational feedback to yourself, like a weighting. It could maybe give a Gödelian hierarchial state like an ultrametric state ex.? Mathematical facts are then not sufficient. It is more like 50 shades of grey. But the work part can be evaluated using XOR or other logic maybe? Consciousness as such is not computable, not axiomatic or 'functional' as you stated it. Hence it is also different from knowledge.
Do you have your thinking written somewhere?