No, you believe [subjective experience is] there and it has a semi-obscure relationship to the physical facts
I think you understate the problem. The relationship is totally obscure.
On the one hand, there is the "it's all made of atoms" tradition that got started two centuries ago, which, together with the Baconian idea that you have to look at nature to discover anything about it, has proved enormously successful everywhere it has been applied, and continues to be so.
And on the other hand, there is subjective experience, the problem with which is that no-one has any idea at all of how such a thing could possibly exist in a world made of atoms. Not only do we not know how it arises, we cannot see any way it could possibly arise from atoms. The two things appear absolutely, utterly incompatible.
But hardly anyone looks squarely at that conflict and acknowledges it. Instead, they confabulate to fill the gap. Some invent ontologically fundamental mental entities, which amounts to no more than plastering labels like "soul" or "the divine" over their ignorance. Some deny the existence of subjective experience. Some give explanations only of how we come to talk about subjective experience, but leave the thing itself untouched -- p-zombie theories. Some come up with explanations that amount to finding a correlation with some observable physical phenomenon and identify it with that -- as if, in cruder terms, one were to explain the mind by saying it's the brain, or to take such fake explanation to the point of absurdity, one were to explain the mind by saying it's made of atoms.
This is more than just not knowing how it works: nobody knows how it could possibly work.
If one of the "confabulations" were true, how would you know?
Likewise for if no one knew how it worked, but thought they knew how it could possibly work; how would you know if they were right aside from having a full explanation?
Weisberg et al. (2008) presented subjects with two explanations for psychological phenomena (e.g. attentional blink). Some subjects got the regular explanation, and other subjects got the 'with neuroscience' explanation that included purposely irrelevant verbiage saying that "brain scans indicate" some part of the brain already known to be involved in that psychological process caused the process to occur.
And yet, Yale cognitive science students rated the 'with neuroscience' explanations as more satisfying than the regular explanations.
Why? The purposely irrelevant neuroscience verbiage could only be important to the explanation if somebody thought that perhaps it's not the brain that was producing certain psychological phenomena. But these are Yale cognitive science students. Somehow I suspect people who chose to study cognition as information processing are less likely than average to believe the mind runs on magic. But then, why would they be additionally persuaded by information suggesting only that the brain causes psychological phenomena?
In another study, McCabe & Castel (2008) showed subjects fictional articles summarizing scientific results and including either no image, a brain scan image, or a bar graph. Subjects were asked to rate the soundness of scientific reasoning in the article, and they gave the highest ratings when the article included a brain scan image. But why should this be?
I remember talking to a friend about free will. She was a long-time physicalist who liked reading about physics and neuroscience for fun, but she didn't read Less Wrong and she thought she had contra-causal (libertarian) free will.
"Okay," I said. "So the brain is made of atoms, and atoms move according to deterministic physical law, right?"
"Right," she said.
"Okay. Now, think about the physical state of the entire universe one moment before you decided to say "Right" instead of something else, or instead of just nodding your head. If all those atoms, including the atoms in your brain, have to move to their next spot according to physical law, then could you have said anything else than what you did say in the next moment?" (Neither of us understood many-worlds yet, so you can assume we're talking about a single Everett branch.)
She paused. "Huh. I'll have to think about that."
"Also, have you heard about those studies where brain scans told researchers what the subjects were going to do before the subjects consciously decided what they were going to do?"
"No! Are you serious?"
"Yup. Sometimes they could predict the subject's choice 10 seconds before the subject consciously 'made' the choice."
"10 seconds? Wow. I didn't know that."
I think that maybe the 'with neuroscience' explanations and brain scan images are more satisfying partly because they remind us we're physicalists. They remind us that reductionism marches on, that psychology is produced by physical neurons we can take pictures of.
Just like most people, physicalists walk around all day with the subjective experience of a 'unity of consciousness' and contra-causal free will and so on. If a physicalist isn't a researcher who studies all the latest successful reductions in neuroscience or biology or physics all week long, and doesn't read Less Wrong every day, then it's possible to get lost in the feel of everyday experience and thus be surprised by a headline like 'Brain Scanners Can See Your Decisions Before You Make Them.'
Sometimes even physicalists need to be reminded — with concrete reductionistic details — that they are physicalists. Otherwise their normal human anti-reductionistic intuitions may creep back in of their own accord. That's one reason it helps to study many sciences, so you have many successful reductions in your head, and see (at some resolution) the entire picture, from psychology to atoms. As Eliezer wrote:
To her credit, my friend no longer believes in contra-causal free will.