> Are there examples of failed reductions and where they fail?

A failed reduction would be a case where we try to say “x is really just y+z”, and in doing so we fail. “x” isn’t able to be accounted for wholly just in terms of “y+z”. That’s not a specific example, but we could make up some examples, some worse than others. An example: “chairs are just bits of wood stuck together”. Problems: there are plenty of things that are chairs that have no wood involved, and plenty of bits of wood stuck together that aren’t a chair. Or “money is nothing more than the physical notes and coins”, which is an attempt at reduction that misses out important things about the shared value we place on these notes and coins.

> And what’s the problem with non-reduction? Let me try it. Can you reduce plasma? It’s an emergent property of “atoms” and fields.

At some point, all our views will have irreducible components. For physicalists, our world of trees, oceans, stars, and so forth is made up of all and only physical stuff (I’m setting aside here questions about, for example, what mathematical things are). The physicalist says that they can explain things in terms of just physical stuff, but they won’t be able to answer the question of what physical stuff itself is made up of — at some point, there’s something that’s fundamental from which everything else is built. For the physicalist, the most fundamental physical objects exist but cannot be reduced to something else.

So there’s no problem with non-reduction per-se. There’s only a problem when your ontology says “everything is composed of just such and such”, and then someone points to a thing and says “this thing isn’t composed of just such and such”. For the physicalist, consciousness/the mental is that thing which isn’t amenable to explanation in terms of just physical stuff.

For a dualist, or an idealist of, say, Berkeley’s variety, there is no problem with consciousness being irreducible, because those ontologies take consciousness to be fundamental. Moreover, I'm not aware of any analogous problem for idealists -- no mirrored hard problem of non-consciousness (the dualist solves this problem by inflating their ontology with both physical and mental irreducible substances and/or properties).

Regarding your specific example, there are non-reductionists who think that there are layers within science, and certain higher layers (e.g., chemistry) can’t be explained purely in terms of lower layers (e.g., physics). That is, chemistry can’t simply be reduced to, say, really complicated purely physical interactions.

> Can I try to reduce hard consciousness? It’s an aggregate form of a complexity, which is complex enough to try to self-describe and probably fall into some misconceptions. QED?

Are you saying that consciousness is merely an aggregate form of a complexity? You’ve lost me here at ‘self-describe’. Without appealing to any non-physical terms/concepts, what does it mean for something complex to be self-describing? I genuinely don’t know what you mean, so you’d need to share more for me to understand your proposal, and how it tells us anything about how consciousness is really just such and such physical states (and nothing else).

> Edit: Also, it’s theoretically possible to build a human out of atoms, or take a human, and slowly and continuously transform it into a less conscious being, back and forth. Or into more or less believing into some sort of philosophy, back and forth again (which happened to many philosophers naturally). If you can volume-down the consciousness, doesn’t that mean that it’s not even “a thing”, only a property?

No-one has done what you propose (continuously transform a human into a less conscious being), so it’s just a view you hold, and it may or may not be possible. Also, you’re using the word ‘conscious’ here a little different. It’s a word with different meanings in different contexts. In some circumstances, we speak about degrees of consciousness — e.g., being asleep is a state of being unconscious. But for the mind-body problem, what philosophers have in mind (or at least, those philosophers who think there is a hard problem) is the fact that there is something having experiences. E.g., as Nagel puts it, there’s something that it’s like to be a bat. In the same sense, there’s something that it’s like to be asleep (whether or not you remember it). So whether you’re less or more conscious in the sense of sleep (or of continual transformation), it’s always conscious in the sense that there’s something that it’s like to be that.

If we suppose that the continual transformation you propose is indeed possible and the way the world works, then it shows what we already know — that there’s at least a one direction causal link from the physical to the mental. But we already know that’s the case. The hard problem is explaining how, using only physical terms and concepts, you get the mental from the physical. I don’t see how being able to scale up or down the intensity/volume/quality of the consciousness by tuning the physical entails that consciousness is nothing more than physical stuff appropriately arranged.