The claim that "consciousness is what information processing feels like from the inside" strikes me as distinctly un-illuminating: why should information processing feel like anything from the inside?
Because it does. Why do charged particles attract or repel? Why do some particles experience mass? At some point the answer is simply "because that's how the universe works."
We know consciousness exists, as we each have first hand evidence. If we want to believe that we live in a reducible universe, then there must be some reduction bringing consciousness down to a most basic physical process. At some point that reductive explanation ends with a very unsatisfying "because that's just how the universe works."
But I would be very suspiciou...
Max Tegmark publishes a preprint of a paper arguing from physical principles that consciousness is “what information processing feels like from the inside,” a position I've previously articulated on lesswrong. It's a very physics-rich paper, but here's the most accessable description I was able to find within it:
The whole paper is very rich, and worth a read.