Anti-reductionists are always quick to point at "qualia", "subjective experience", "consciousness" (or the subjective experience of pain, in this case) as examples of Great Big Unexplained Mysteries which have not been/can not be solved by science, but they can never quite explain what exactly the problem is, or what a solution would look like.
A solution would help dissolve our confusion about how the territory of our consciousness can be produced by the map that is our brain's computation.
I feel I've made some small progress on elements of that front after connecting some seperate ideas from other fields, like Tegmark IV, fractals and great attractors, and calculus. I hope to most some of these ideas later this month, or on February.
I encounter many intelligent people (not usually LWers, though) who say that despite our recent scientific advances, human consciousness remains a mystery and currently intractable to science. This is wrong. Empirically distinguishable theories of consciousness have been around for at least 15 years, and the data are beginning to favor some theories over others. For a recent example, see this August 2011 article from Lau & Rosenthal in Trends in Cognitive Sciences, one of my favorite journals. (Review articles, yay!)
Abstract: