FTA:
> Then he declared that there is another distinct problem — why the brain’s behavior is accompanied by experience at all — which he christened the “hard” problem of consciousness.
The hard problem isn't about "why", it's about "what it's like".
Try to explain what it's like to hear a major and a chord to a deaf person, or what it's like to see magenta to someone who's blind.
None of the things you say, sign or write will make them experience these sensations.
Ultimately no one but you can know what it's like to be you.
This doesn't mean that subjective experience can't be modeled. but the caveats that apply to models in general are relevant here too: none are correct, some are useful.
Dualism doesn't necessarily means that subjectivity is ineffable. Mind and matter could work like mathematical duals: platonic solids (cube vs octahedron, dodecahedron vs icosahedron, tetrahedron vs itself), Voronoi diagrams and Delaunay triangulations, etc... These are intimately linked, and you can generate one from the other and inversely, yet they have their own distinct properties.
> Try to explain what it's like to hear a major and a chord to a deaf person, or what it's like to see magenta to someone who's blind.
I know this isn't what you wanted, but the dualism struck me:
A major chord is like a blend of two base colors that give rise to a pleasant composite color. Mix the wrong bases and the result is sensibly wrong.
Magenta is like when you play a D and an F# together. When you see it at sunset it's like a major D chord surrounded by the sound of babies laughing. When you see it on the battlefield it's like a minor D chord wrestling against the noise of wind and rain.
Qualia is the term people often use to mean "what it's like". The hard problem is "why is there qualia". This of course assumes that qualia exists as a coherent thing, which some philosophers dispute.