> Why some kinds of information processing and not others?

I have no idea. If that's what the hard problem of consciousness boils down to - we don't know why some complex math produces consciousness and other complex math doesn't - then it boils down to "we haven't found the means to sufficiently analyze the math that does produce it." Which would turn it into... a math problem?

My suspicion is that it has something to do with evolutionary pressure. Consciousness is something that evolves when systems that include their own existence within their data model become much more likely to continue existing versus those that don't. Statistics does the rest.

Mainly because of recursive processes that modulate attentional focus, but of a special sort that we are just beginning to understand.