What is a mathematical structure of conscious experience?

All of which are things we can explain without any magic.

The literature on qualia pretty much has the same problem as the literature on consciousness.

* After spending time in research on parapsychology and the paranormal,[5] her attitude towards the field moved from belief to scepticism.[6][7] In 1987, Blackmore wrote that she had an out-of-body experience shortly after she began running the Oxford University Society for Psychical Research (OUSPR):[8][9]

"Within a few weeks I had not only learned a lot about the occult and the paranormal, but I had an experience that was to have a lasting effect on me—an out-of-body experience (OBE). It happened while I was wide awake, sitting talking to friends. It lasted about three hours and included everything from a typical "astral projection," complete with a silver cord and duplicate body, to free-floating flying, and finally to a mystical experience. It was clear to me that the doctrine of astral projection, with its astral bodies floating about on astral planes, was intellectually unsatisfactory. But to dismiss the experience as "just imagination" would be impossible without being dishonest about how it had felt at the time. It had felt quite real. Everything looked clear and vivid, and I was able to think and speak quite clearly."

In a New Scientist article in 2000, she again wrote of this:

"It was just over thirty years ago that I had the dramatic out-of-body experience that convinced me of the reality of psychic phenomena and launched me on a crusade to show those closed-minded scientists that consciousness could reach beyond the body and that death was not the end. Just a few years of careful experiments changed all that. I found no psychic phenomena—only wishful thinking, self-deception, experimental error and, occasionally, fraud. I became a sceptic.[10][11]"

* She is a Fellow of the Committee for Skeptical Inquiry (formerly CSICOP)[12] and in 1991, was awarded the CSICOP Distinguished Skeptic Award.[4]

* Susan Blackmore has made contributions to the field of memetics.[19] The term meme was coined by Richard Dawkins in his 1976 book The Selfish Gene. In his foreword to Blackmore's book The Meme Machine (1999), Dawkins said, "Any theory deserves to be given its best shot, and that is what Susan Blackmore has given the theory of the meme."[20] Other treatments of memes, that cite Blackmore, can be found in the works of Robert Aunger: The Electric Meme,[21] and Jonathan Whitty: A Memetic Paradigm of Project Management.[22]

This is all from her wikipedia, which is about a one minute read.

As I recall, her consciousness textbook is fairly opinionated but it still gives a fair tour of the mainstream theories. She happens to be an illusionist like Dan Dennett. There's no "woo" in her coverage of the topic.

So lets say in current models', or future, in very large neural nets, that there will not be some internal subjective awareness, just like we have. We've mapped the entire neural network/nervous system, of a nematode worm and translated it into software. The 'software worm' appears to behaves the same as the real worm, so what is that software experiencing?

I agree that "non-conscious qualia" is an incoherent notion, but I'm not convinced this rules out a "phenomenal unity" as you argue - they are positing the unity as "phenomenal" not as the substrate (or medium, as you put it) of qualia, so more than just the raw fact of consciousness is implied.

One point of comparison might be Wittgenstein's famous example of the duck-rabbit - a bistable ambiguous image that can be seen either as a picture of a duck or as a picture of a rabbit. One might assume the qualia associated with looking at the picture are the same whether one is seeing it as a duck or as a rabbit - the same shapes and colours - and yet there is a difference:

> The change of aspect. "But surely you would say the picture is altogether different now!" [...]

> If I saw the duck-rabbit as a rabbit, then I saw: these shapes and colours (I give them in detail) -- and I saw besides something like this: and here I point to a number of different pictures of rabbits [...]

> 'Seeing as ...' is not part of perception. And for that reason it is like seeing and again not like.

Perhaps this un-perceptual yet pervasive and arguably phenomenal unity subsuming the duck-rabbit qualia - that which flips from duck to rabbit and back - is analogous to what the authors intend with their "subsumptive unity thesis".

Congrats on commenting on TFA, btw :) I thought it was an interesting read, though I start to lose my grip on the math around the topology section.