I would say that consciousness is the "running narrative," the combined succession of whatever it is that has your "focus" at any given time. It may not always be a single object, multiple threads can weave in and out, or rise and fall from consciousness. This seems...hard to argue against.
For example, when trying to reason about a somewhat complex system, I am often trying to "multi-task" or "juggle" multiple things. Sometimes I will get caught on one thing, possibly draw some conclusion, and then remember, "oh yeah, that won't work because of X." I don't think it makes sense to discard the concept that X has entered, exited and re-entered my conscious thought process.
Another example - if I catch a whiff of an old girlfriend's perfume, or hear a song strongly connected to a time from my past, I am instantly thinking of those things in a way that I wasn't the moment before. But those memories have continuously existed in my head in some form, or I wouldn't be able to recall them. Over time they have mutated, morphed, and mixed with other experiences - I don't think it's like neatly organized and addressed computer memory - but there is some unbroken chain that lives "below the surface" most of the time. Again I don't see the value in discarding this concept.
But I think the more salient point of the article, and what I believe d-equivalence is referring to with the "interpretation of consciousness," is the concept of unreliability. Due to the ever-churning and "living" nature of our memories - combined with the fact that the brain is merely an evolved tool with certain properties useful for keeping humans alive (as opposed to an impartial processor/arbiter of "true experience") - our perspective on our own thought processes is unreliable. Most of the experiments described in the article seemed to me like standard "tricks of the mind." It edits, it rewrites history on the fly, it fills in the gaps, because it has learned to anticipate, to identify things it has seen before. The being that can create a mental model that correctly anticipates what happens next has the advantage. Our brains have been honed to do so as a matter of survival, going so far as to creatively make things up and eagerly overfit, and we've developed ways of catching it in the act.
I am a (lapsing) mindful meditator, and I'm still not sure this article contradicts any of that stuff (which is the distilled science from things like Buddhism.)
I understand, but forgive me, when I try to argue about consciousness using logic or read scientific studies about it, I always feel like being a 14 year old talking about sex, so I don't talk about it anymore. I prefer doing it.
Quite possibly its arrogance, or jadedness. But I've come to develop my own opinions about issues like that, through other means of acquiring knowledge than science, which I feel is grossly inadequate to address such issues. And no, I'm not talking about secular/clinic types of mindfulness.
Probably that makes me a weirdo in circles like HN, but oh well.