Interesting Proof of Limited Theorom
Nothing big enough going on here to merit an IW article as far as I can see. Using some very specific definitions of synergy, complexity, information etc. the authors show that on a certain model of mental processing, the information is too tightly integrated to be easily decoupled, and that a strictly computational model of consciousness would require that it could be decoupled in the way they say it can't be. A reasonable result that frankly depends much more on the definitions of concepts than on the mathematical "proof" they offer.
To put their point intuitively, conscious experience is not just more than the sum of the processing of sensory stimuli, it is the tight compression of that processing into a unified experience that cannot be de-unified by applying an algorithm. Thus the authors compare it, both metaphorically and mathematically, to data compression: you cannot, for example, change the word "too" to "also" in a compressed document simply by adding together information about the individual compressed bits and information about the compression algorithm. The reason is that the compression algorithm makes the meaning of each bit dependent on other bits. so that changing the compressed structure will not yield the result you want. I am not convinced beyond a doubt that this is true, but it does make sense when applied to consciousness: you cannot computationally back out the sensory stimuli from conscious experience itself. Part of this might have to do with the redundancy of brain structures, part with the ability of the brain to form new pathways on the fly, etc. In any case, when I look out of my window and experience the belief that I am seeing Brooklyn, I'm quite sure that this cannot be decomposed into the image of the white building, the sycamore tree and the slightly hazy air that I observe.
Like I said, nice result, but the inability to reduce consciousness to information processing has been demonstrated by numerous philosophical thought experiments before (Searle's Chinese Room, Frank Jackson's Mary, Ned Block's idea of connecting the entire Chinese population by telephone simultaneously, etc.) So I'm not sure that this "mathematical" result is big news. But it is always nice to have more evidence that Dan Dennett and his followers are wrong.