Please, no more disdain for people's ideas and hypotheses about a fundamental topic that nobody has an answer for yet.
Conscious is a subjective experience. There's no clear definition of it in terms of measurable and repeating phenomena however much a given person feels sure they experience it (go head, give a definition that's subjectively satisfying for consciousness. Notice the whole "philosophical zombie" schema rests on nothing about consciousness being measurable or verifiable). Psychology, linguistics or neuroscience may indeed come up with one at some point.
But as far as I can tell, the argument of the article and of theories of this sort, is that since consciousness is "real", it should be taken as a building block of one's model of the universe. The problem here is that using an ill-defined thing as a building block makes exact science impossible - unless your basic model is itself predictable, you cannot actually say whether your experimental results follow the model or not.
It's not simply that an approach like this may be wrong - science is wrong all the time. It's that an approach like is injecting an atom of "anything-you-want-tium" into the mixture, a situation that let's you claim any result verifies your theory ("God does it all" would satisfying Occam's Razor for the simple "explanation of everything" if we let the inherently unexplainable into the competition).
So in this sense, scientists have every reason to keep approaches like this entirely outside the realm of "legitimate science".
This may sound positivist and one may say that a lot of science is looser than a pure positivism. Sort-of but every serious scientific discipline has to boil down to verification of predictive models by experiment specifically because it's easy for things to move "in the clouds" for periods of time and the verification is needed to weed-out models without predictiveness at all (string theorists have speculated a long and gotten kudos but the call for predictiveness is there is getting louder - but with string theory, things may be abstract however no "unexplainable" is taken as a given).
I was not discussing consciousness per-se, I was discussing the theory and the sort of theory discussed in the article - the claim that a subjective experience needs to be added to the scientific process to explain various supposed problems.
I have no objections to exploring subjective experience - believe it or not, I mediate, practice Qigong and Tai Chi and enjoy Eastern philosophies like Taoism.
A text like the Tao Te Ching is more applicable to the immediate problems of living than a text book on physics but that doesn't mean subjective intuitions can be uncritically applied to physics. Science is a particular discipline, applicable in a limited but important level of reality, specifically intended to benefit from limiting the use of the subjective messiness of most human reasoning - not that this subjective messiness isn't highly useful elsewhere.
What kind of tools would you suggest?
Anyway, there's certainly no evidence to suggest that consciousness requires anything more than our current understanding of physical laws. This article was pretty interesting with its topical exploration of self organization and a more math-based approach, but once it got into quantum physics it started to delve into the realm of pure conjecture and pseudo-science.
An experience people would label "conscious" exists in the sense that many people would label their state of mind with it. A scientific explanation would involve describing why people are attracted to this position and might or might-not involve describing actual brain states could be considered "consciousness states". There's no reason to think such an explanation would be "subjectively satisfying" - that it would make people lean back and say "oh, now I understand".
But the problem is the "theory of consciousness" folks want to create a theory that is both scientific and "subjectively satisfying" and indeed they sort of start their argument with a unit of that thing that's subjectively satisfying and try to go from there. That seems like recipe for non-science.
One fundamental reason why this is such a controversial and confusing topic with a wide range of opinions is that consciousness is meta-physical phenomenon. I.e. it's out of the scope of science in a way. But the concept that there's something beyond science is completely unintuitive to many people (by "beyond science" I obviously don't mean BS like spirituality etc., it's from a purely rational perspective). So trying to understand consciousness with science only will inevitably fail.
So, what would be a mirror for consciousness? Is there one?
I don't know if this is what the parent meant, but I interpreted that statement to mean that the concept and explanation of consciousness is beyond our current scientific frame of reference.
Think about past frames of reference which "science" attempted to utilize, to some effect and failure. I put quotes around science for a reason, because I have a specific example, to wit:
Think about alchemy. To a certain extent, a form of scientific process was used by these early - for lack of a better word - proto-chemists. They pondered, came up with ideas, experimented, took notes, compared results, etc. They discovered new substances and compounds we use to this day; they created the prototypes of some of the lab equipment still used. Their methods ultimately led to our current "scientific method" of inquiry.
But despite their successes and failures, despite their best attempts and experiments, in many ways they were hampered by the framework of "science" they were investigating. For instance, they knew little to nothing about atoms or elements - instead grouping things into the "classical" elements of earth, fire, water, and air (and in some cases "spirit"). They still had a mindset of "like for like", meaning that their experimentation led to them using substances or similar that had some nature which was like what they were attempting to perform or gain the result of.
I won't belabour this point - only to say that because their framework of reference limited them, they couldn't make the "giant leap" forward that was needed to really understand and do what it is they were trying to do (let's not dwell on the philosophical/spiritual aspects of the so-called Philosopher's Stone quest).
So perhaps that's where we are today, in regards to science and trying to explain and understand consciousness? That isn't to say we won't eventually be able to explain and explore the topic; our nature of asking questions, trying experiments, coming at the problem from a myriad of different angles, and the collaboration between these disparate fields will likely lead us to the knowledge (and also it will open up many more questions, as it always has and does). As noted in the article, we are taking more steps even today - and I am also pleased to see that there is a greater collaboration going on between the fields and people who deal with this at a basic level - the physicists, the neuroscientists, computer science, biologists, etc. This kind of cross-fertilization is absolutely needed in order to understand this problem.
There's a good word which describes that sentence: 'faith'
Leaving aside the specific ideas being outlined here, and the specific reasons for disdain some people have for it....
...while we may not know the truth regarding this topic, there may be demonstrable flaws in people's ideas and hypotheses! Flaws in there reasoning, or empirical flaws, or whatever.