Why is it beyond the scope of science? No experiments have shown that consciousness can violate the laws of physics and steady progress has been made in explaining consciousness from neuroscience.
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.