What about this:

Let us classify the information processing along two axis: a) low-level (evolutionarily ancient), direct stimuli-response, vs high-level (involving prefrontal cortex) b) processing stimuli from the outside world (sound, light) vs internal stimuli (tactile/pain ... all the way to internal stimuli originating in brain - 'thinking about thinking')

Note that both are continuous scale, not binary.

The consciousness would then be the high-level processing of internal signals. Obviously, consciousness also results being on continuous scale.

> Why some kinds of information processing and not others?

Using Rovelli's example: why some clouds create a thunderstorm and not others? It is just a complex phenomenon that happens only under right conditions.

Why is some software SuperMarioBros and other Microsoft Word? 'cause that's what the specific software is written to produce and the other is written to do produce else. Consciousness is not some magically thing on top of a information processing, it's what that specific bit of information processing produces. It's functional, it does stuff.

It should be kind of obvious due to the fact that we are conscious about our human self, not neurons, not brains, not microtubules or any other random implementation detail. We have zero clue what is going on in our brains, but we do have a high level description. Just as our brain can take some random electrical impulses from our eyes and decide that that's a "cat", it can take all the other input that goes around and conclude that that's a "self". It's perception, the brain trying to figure out what parts of the world it has direct control over.

> 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.

That would be part of the empirical facts we might hope to gather, if this is indeed the right direction for the explanation.

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