I will be the controversial one and say that I reject that "consciousness" even exists in the philosophical sense. Of course, things like intelligence, self-awareness, problem-solving capabilities, even emotions exist, but it's possible to describe all of these things in purely functional terms, which would in turn be computable. When people like about "consciousness not being computable" they are talking about the Chalmerite definition of "consciousness" popular in philosophical circles specifically.

This is really just a rehashing of Kant's noumena-phenomena distinction, but with different language. The rehashing goes back to the famous "What is it like to be a bat?" paper by Thomas Nagel. Nagel argues that physical reality must be independent of point of view (non-contextual, non-relative, absolute), whereas what we perceive clearly depends upon point of view (contextual). You and I are not seeing the same thing for example, even if we look at the same object we will see different things from our different standpoints.

Nagel thus concludes that what we perceive cannot be reality as it really is, but must be some sort of fabrication by the mammalian brain. It is not equivalent to reality as it is really is (which is said to be non-contextual) but must be something irreducible to the subject. What we perceive, therefore, he calls "subjective," and since observation, perception and experience are all synonyms, he calls this "subjective experience."

Chalmers later in his paper "Facing up to the Hard Problem of Consciousness" renames this "subjective experience" to "consciousness." He points out that if everything we perceive is "subjective" and created by the brain, then true reality must be independent of perception, i.e. no perception could ever reveal it, we can never observe it and it always lies beyond all possible observation. How does this entirely invisible reality which is completely disconnected from everything we experience, in certain arbitrary configurations, "give rise to" what we experience. This "explanatory gap" he calls the "hard problem of consciousness."

This is just a direct rehashing in different words Kant's phenomena-noumena distinction, where the "phenomena" is the "appearance of" reality as it exists from different points of view, and the "noumena" is that which exists beyond all possible appearances, the "thing-in-itself" which, as the term implies, suggests it has absolute (non-contextual) properties as it can be meaningfully considered in complete isolation. Velocity, for example, is contextual, so objects don't meaningfully have velocity in complete isolation; to say objects meaningfully exist in complete isolation is to thus make a claim that they have a non-contextual ontology. This leads to the same kind of "explanatory gap" between the two which was previously called the "mind-body problem."

The reason I reject Kantianism and its rehashing by the Chalmerites is because Nagel's premise is entirely wrong. Physical reality is not non-contextual. There is no "thing-in-itself." Physical reality is deeply contextual. The imagined non-contextual "godlike" perspective whereby everything can be conceived of as things-in-themselves in complete isolation is a fairy tale. In physical reality, the ontology of a thing can only be assigned to discrete events whereby its properties are always associated with a particular context, and, as shown in the famous Wigner's friend thought experiment, the ontology of a system can change depending upon one's point of view.

This non-contextual physical reality from Nagel is just a fairy tale, and so his argument in the rest of his paper does not follow that what we observe (synonym for: experience, perceive) is "subjective," and if Nagel fails to establish "subjective experience," then Chalmers fails to establish "consciousness" which is just a renaming of this term, and thus Chalmers fails to demonstrate an "explanatory gap" between consciousness and reality because he has failed to establish that "consciousness" is a thing at all.

What's worse is that if you buy Chalmers' and Nagel's bad arguments then you basically end up equating observation as a whole with "consciousness," and thus you run into the Penrose conclusion that it's "non-computable." Of course we cannot compute what we observe, because what we observe is not consciousness, it is just reality. And reality itself is not computable. The way in which reality evolves through time is computable, but reality as a whole just is. It's not even a meaningful statement to speak of "computing" it, as if existence itself is subject to computation, but Chalmerite delusion tricks people like Penrose to think this reveals something profound about the human mind, when it's not relevant to the human mind.

Here's the super luminescence research paper https://arxiv.org/abs/2302.01469

although, this PBS youtube video is the summary I actually understand